RECENT ADVANCES IN EARTHQUAKE GEOTECHNICAL
ENGINEERING AND MICROZONATION
GEOTECHNICAL, GEOLOGICAL AND EARTHQUAKE
ENGINEERING
Volume 1
Series Editor
Atilla Ansal, Kandilli Observatory and Earthquake Research Institute,
Boğaziçi University, Istanbul, Turkey
RECENT ADVANCES IN
EARTHQUAKE GEOTECHNICAL
ENGINEERING AND
MICROZONATION
edited by
ATILLA ANSAL
Kandilli Observatory and
Earthquake Research Institute,
Boğaziçi University,
Istanbul, Turkey
KLUWER ACADEMIC PUBLISHERS
NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
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This book is dedicated to our dear friend and colleague Prof. Dr. Aykut Barka.
He took part in the first phase of this initiative
but regrettably passed away much too early to see the end.
PREFACE
Outstanding advances have been achieved on Earthquake Geotechnical Engineering and
Microzonation in the last decade mostly due to the increase in the recorded instrumental
in-situ data and large number of case studies conducted in analyzing the observed
effects during the recent major earthquakes.
During the 15th International Conference on Soil Mechanics and Geotechnical
Engineering held in Istanbul in August 2001, the Technical Committee of Earthquake
Geotechnical Engineering, (TC4) of the International Society of Soil Mechanics and
Geotechnical Engineering organised a regional seminar on Geotechnical Earthquake
Engineering and Microzonation where an effort has been made to present the recent
advances in the field by eminent scientists and researchers. The book idea was first
suggested by the participants of this seminar.
The purpose of this book as well as of the seminar was to present the broad spectrum of
earthquake geotechnical engineering and seismic microzonation including strong
ground motion, site characterisation, site effects, liquefaction, seismic microzonation,
solid waste landfills and foundation engineering. The subject matter requires
multidisciplinary input from different fields of engineering seismology, soil dynamics,
geotechnical and structural engineering.
The chapters in this book are prepared by some of the distinguished lecturers who took
part in the seminar supplemented with contributions of few distinguished experts in the
field of earthquake geotechnical engineering. The editor would like to express his
gratitude to all authors for their interest and efforts in preparing their manuscripts.
Without their enthusiasm and support, it would not have been possible to complete this
book.
Atilla Ansal
vii
TABLE OF CONTENTS
Introduction: Role of Geotechnics in Earthquake Engineering, K. Ishihara.......................... 1
Chapter 1. Microzonation: Developments and Applications,
W. D. L. Finn, T. Onur and C. E. Ventura .............................................................. 3
1.1. Introduction ............................................................................................................ 3
1.2. The Structure of Probabilistic Seismic Hazard Analysis ....................................... 4
1.3. Developments in Seismic Hazard Analysis ........................................................... 5
1.3.1. Seismic sources ............................................................................................... 6
1.3.2. Recurrence relations ....................................................................................... 6
1.3.3. Attenuation relations....................................................................................... 8
1.3.4. Effects of local soil conditions ...................................................................... 10
1.3.5. NEHRP amplification factors ....................................................................... 13
1.3.6. Evaluating the hazard ................................................................................... 14
1.4. Microzonation for Risk ........................................................................................ 14
1.5. Case History ......................................................................................................... 17
1.5.1. Background ................................................................................................... 17
1.5.2. Victoria risk study ......................................................................................... 18
1.6. Final Remarks....................................................................................................... 25
Chapter 2. The Influence of Scale on Microzonation and Impact Studies, C. S. Oliveira... 27
2.1. Part I – Earthquakes and the Impact on Societies ................................................ 28
2.1.1. Earthquakes in the World and in Europe in the XXth century ...................... 28
2.1.2. The soil effect on the catastrophic events ..................................................... 31
2.1.3. Mitigation of earthquake risk and preparedness .......................................... 32
2.2. Part II – Definition of Problems and Techniques................................................. 33
2.2.1. Scenario Studies – geographic scale of intervention .................................... 33
2.2.2. Soil information............................................................................................. 36
2.2.3. Spectral shapes.............................................................................................. 39
2.3. Part III – Examples for Illustration ...................................................................... 41
2.3.1. Example 1. Studies at the country level: Portugal........................................ 41
2.3.2. Example 2. Studies at the regional level: The metropolitan area of Lisbon 49
2.3.3. Example 3. Studies at the county level: the case of Lisbon .......................... 56
2.3.4. Example 4. Studies at the building block level ............................................. 63
2.4. Final Considerations and Future Developments .................................................. 65
Chapter 3. Strong Ground Motion, M. Erdik and E. Durukal............................................... 67
3.1. Introduction .......................................................................................................... 67
3.2. Attenuation ........................................................................................................... 67
3.3. Factors Affecting Earthquake Strong Ground Motions ....................................... 73
3.3.1. Effects of the earthquake source ................................................................... 73
3.3.2. Subduction zone and shallow crustal earthquakes ....................................... 75
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Table of Contents
3.3.3. Effects of distance ......................................................................................... 75
3.3.4. Effects of near surface wave propogation (Site effects)................................ 76
3.3.5. Basin response effects ................................................................................... 77
3.4. Simple Earthquake Source Models ...................................................................... 77
3.5. Time Domain Characteristics of Strong Ground Motion..................................... 81
3.5.1. Modelling of RMS-acceleration .................................................................... 81
3.5.2. Duration of the strong ground motion .......................................................... 83
3.5.3. Time domain envelope of the strong ground motion .................................... 84
3.6. Frequency Domain Characteristics of Strong Ground Motion ............................ 84
3.6.1. Theoretical model of Fourier amplitude spectrum ....................................... 85
3.7. Radiation Pattern and Directivity ......................................................................... 88
3.8. Simulation of Strong Ground Motion .................................................................. 92
3.8.1. Stochastic simulations................................................................................... 93
3.8.2. Hybrid simulations ........................................................................................ 98
3.9. Conclusions ........................................................................................................ 100
Chapter 4. Geophysical and Geotechnical Investigations for Ground Response Analyses,
D. Lo Presti, C. Lai, and S. Foti ..........................................................................101
4.1. Introduction ........................................................................................................ 101
4.2. Mechanical Behaviour of Geomaterials............................................................. 102
4.3. Laboratory Tests................................................................................................. 106
4.3.1. Triaxial Tests............................................................................................... 106
4.3.2. Resonant Column and Torsional Shear Test .............................................. 108
4.4. Field Tests .......................................................................................................... 111
4.4.1. Geophysical Tests........................................................................................ 111
4.4.2. In situ large strain tests: Pressurimeter and Plate Load Tests................... 124
4.4.3. Empirical correlations from penetration tests ............................................ 127
4.5. Case History ....................................................................................................... 129
4.5.1. Field Tests ................................................................................................... 130
4.5.2. Laboratory Tests ......................................................................................... 131
4.5.3. Laboratory vs. Field tests............................................................................ 134
4.5.4. Definition Of Soil Parameters For Seismic Analysis.................................. 135
4.6. Conclusions ........................................................................................................ 137
Chapter 5. Site Effects, K. Pitilakis ......................................................................................139
5.1. Introduction ........................................................................................................ 139
5.2. Basic Physical Concepts and Definitions........................................................... 140
5.2.1. Site effects due to low stiffness surface soil layers ..................................... 142
5.3. Methods to Estimate Site Effects ....................................................................... 146
5.3.1. Experimental-Empirical.............................................................................. 146
5.3.2. Empirical Methods ...................................................................................... 150
5.3.3. Semi-empirical methods .............................................................................. 152
Table of Contents
xi
5.3.4. Theoretical (numerical and analytical) methods ........................................ 153
5.3.5. Concluding Remarks ................................................................................... 156
5.4. Site Effects in Horizontally Layered Soil Deposits ........................................... 157
5.4.1. 1D Site effect computations in the city of Thessaloniki .............................. 157
5.4.2. Conclusive remarks..................................................................................... 163
5.5. 2D Phenomena in Ground Response Modelling................................................ 164
5.5.1. 2D Experimental and Theoretical Studies in Euroseistest valley............... 164
5.5.2. 2D Experimental and Theoretical studies in Thessaloniki ......................... 169
5.5.3. Conclusive remarks..................................................................................... 174
5.6. Site Effects Due to Surface Topography............................................................ 176
5.6.1. Brief literature review ................................................................................. 176
5.6.2. Seismic Codes.............................................................................................. 178
5.6.3. Theoretical studies in an experimental site in Greece................................ 178
5.6.4. Conclusions ................................................................................................. 187
5.7. Site Effects and Seismic Codes .......................................................................... 188
5.7.1. The concept of Eurocodes ........................................................................... 189
5.7.2. International Building Code 2000 .............................................................. 189
5.7.3. Soil and Site Classification ......................................................................... 189
5.7.4. Compatibility of design forces .................................................................... 193
5.7.5. Spectral Amplification................................................................................. 193
Chapter 6. Evaluation of Liquefaction-Induced Deformation of Structures, S. Yasuda ....199
6.1. Introduction ........................................................................................................ 199
6.2. Design Procedures for Liquefaction................................................................... 199
6.2.1. Current design procedures.......................................................................... 199
6.2.2. Effect of the 1995 Kobe earthquake............................................................ 200
6.2.3. Liquefaction-induced settlement during the 1999 Kocaeli earthquake ...... 203
6.3. Studies on Liquefaction-induced Deformation of Structures in Dense Sand or
Silty Sand Grounds............................................................................................ 206
6.3.1. New methods for the prediction of the occurrence of liquefaction under
strong shaking ............................................................................................. 206
6.3.2. Soil density and SPT N-value which cause liquefaction under strong
shaking ........................................................................................................ 207
6.3.3. Behaviour of structures in liquefied dense sandy ground........................... 209
6.3.4. Behaviour of structures in liquefied silty ground ....................................... 216
6.4. Evaluation Methods for Liquefaction-induced Deformation of Structures ....... 218
6.4.1. Raft foundations .......................................................................................... 218
6.4.2. Pile foundations .......................................................................................... 220
6.4.3. Embankments .............................................................................................. 222
6.5. Countermeasures against Liquefaction-induced Damage of Structures ............ 224
6.5.1. Current countermeasures............................................................................ 224
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Table of Contents
6.5.2. Recent problems .......................................................................................... 224
6.6. Liquefaction-induced Flow of the Ground......................................................... 224
6.6.1. Concept of design method ........................................................................... 224
6.6.2. Countermeasures against the flow.............................................................. 229
6.7. Concluding Remarks .......................................................................................... 229
Chapter 7. Seismic Zonation Methodologies with Particular Reference to the Italian
Situation, A. Marcellini and M.Pagani................................................................231
7.1. Introduction ........................................................................................................ 231
7.2. Evaluation of the Expected Input Motion .......................................................... 234
7.2.1. Deterministic Approach .............................................................................. 236
7.2.2. Stochastic Approach.................................................................................... 238
7.2.3. Probabilistic Approach ............................................................................... 241
7.2.4. Discussion ................................................................................................... 243
7.3. Site Effects Evaluation ....................................................................................... 245
7.4. Final Remarks..................................................................................................... 250
Chapter 8. Seismic Microzonation: A Case Study,
A. Ansal, Y. Biro, A. Erken, and Ü .Gülerce .......................................................253
8.1. Introduction ........................................................................................................ 253
8.2. Regional Seismicity............................................................................................ 254
8.3. Geological and Geotechnical Site Conditions.................................................... 258
8.4. Earthquake Characteristics on the Ground Surface ........................................... 261
8.5. Seismic Microzonation with Respect to Ground Shaking ................................. 264
8.6. Conclusions ........................................................................................................ 265
Chapter 9. Dynamic Analysis of Solid Waste Landfills and Lining Systems
P. S. Sêco e Pinto..................................................................................................267
9.1. Introduction ........................................................................................................ 267
9.2. Performance of Solid Waste Landfills during Earthquakes............................... 267
9.3. Analysis of Solid Waste Landfills Stability during Earthquakes....................... 268
9.3.1. Introduction................................................................................................. 268
9.3.2. Experimental Methods ................................................................................ 268
9.3.3. Mathematical Methods................................................................................ 269
9.3.4. Selection of Design Earthquakes ................................................................ 270
9.3.5. Selection of Soil Properties for Dynamic Analysis ..................................... 272
9.3.6. Seismic response analysis ........................................................................... 277
9.3.7. Liquefaction assessment.............................................................................. 282
9.4. Monitoring and Safety Control of Landfills....................................................... 282
9.5. Safety and Risk Analyses ................................................................................... 283
9.6. Final Remarks..................................................................................................... 284
Table of Contents
xiii
Chapter 10. Earthquake Resistant Design of Shallow Foundations, A. Pecker..................285
10.1. Introduction ...................................................................................................... 285
10.2. Aseismic Foundation Design Process .............................................................. 285
10.3. Evaluation of Seismic Demand ........................................................................ 286
10.3.1.Fundamentals of Soil Structure Interaction................................................ 286
10.3.2.Code Approach to Soil Structure Interaction Analyses .............................. 288
10.3.3.Improved Evaluation of Seismic Demand................................................... 290
10.4. Bearing Capacity for Shallow Foundations ..................................................... 294
10.4.1.Fundamental Requirement of Code Approaches ........................................ 295
10.4.2.Theoretical Framework for the Pseudo-Static Bearing Capacity .............. 296
10.5. Evaluation of Permanent Displacements.......................................................... 298
10.5.1.Further Developments: Towards performance based design..................... 299
10.6. Construction Detailing ..................................................................................... 300
10.7. Conclusions ...................................................................................................... 301
Chapter 11. Behaviour and Design of Deep Foundation Subjected to Earthquakes,
K. Tokimatsu .........................................................................................................303
11.1. Introduction ...................................................................................................... 303
11.2. Performance of Near-Surface Soils and Pile Foundations during the 1995
Hyogoken-Nambu Earthquake .......................................................................... 304
11.2.1.Soil liquefaction and ground motion........................................................... 304
11.2.2.Characteristics of pile foundations of buildings ......................................... 305
11.2.3.Pile damage from detailed field investigation ............................................ 307
11.3. Cyclic and Permanent Ground Displacements during Earthquakes ................ 309
11.3.1.Cyclic and permanent shear strains in liquefied and laterally spreading
ground ......................................................................................................... 309
11.3.2.Permanent ground displacement near waterfront ...................................... 311
11.4. Pseudo-Static Analysis for Seismic Design of Pile Foundations..................... 312
11.4.1.Inertial and kinematic forces acting on foundation.................................... 312
11.4.2.Beam-on-Winkler-foundation method......................................................... 313
11.4.3.Non-linear p-y spring.................................................................................. 314
11.4.4.Earth pressure acting embedded foundation .............................................. 315
11.5. Effects of Cyclic Ground Displacements on Pile Performance ....................... 315
11.6. Effects of Permanent Ground Displacements on Pile Performance ................ 319
11.7. Conclusions ...................................................................................................... 324
References..............................................................................................................................325
Index.......................................................................................................................................353
INTRODUCTION
ROLE OF GEOTECHNICS IN EARTHQUAKE ENGINEERING
Kenji Ishihara
Science University of Tokyo, Japan
The large earthquakes over the years have left many lessons to be learned which are
essential in putting forward countermeasures or policy to mitigate similar calamities in
future. The degree and nature of damage incurred by earthquakes depends largely upon
states of social developments of the region in which an event occurs. The topography,
ground water conditions and subsurface soil conditions are also important factors
influencing features of the damage caused by great earthquakes. Needless to say, the
most important would be the intensity of shaking of the ground at the time of the
earthquake. There are so many factors as above to be considered that it is practically
difficult to forecast the intensity of shaking and the level of the damage resulting form
an earthquake at a given region.
Under the inherent circumstances as above, the earthquake engineering has been
developed by reflecting on bitter experiences of calamity that occurred during past
earthquakes. In this sense, the earthquake engineering could be cited as “experience
engineering”. It is thus mandatory for engineers to carefully investigate the damage
feature, exercise deep insight into causes of the incident, come up with good ideas for
mitigation and to implement them in the retrofit works that follows. The experiences
should be reflected as well on implementation of countermeasures for existing facilities
and structures and further on in renewing the design codes and regulations in future. It
is without saying that the geotechnical engineers specializing earthquake engineering
should recognize themselves to carry this responsibility and in this sense learning
lessons from past earthquakes are the most important things assigned to our profession.
Since individual earthquake has its own characteristics, it would be necessary to learn
new lessons as large earthquakes occur.
In the development of earthquake
geotechnology, for example, Niigata Earthquake in Japan 1964 could be cited as a
milestone event in that it has first demonstrated the importance of liquefaction in sand
deposits in bringing about various kinds of damage to the ground itself and structures
thereupon. The subsequent earthquake in 1978 in Japan off Izu peninsula triggered the
breach of a tailings dam located in the mountaintop, leading to widespread
contamination of river beds downhill. The liquefaction of sand containing silt with lowplasticity fines was first identified to be of importance as well in generating a state of
liquefaction in silty sand deposits. The Kobe Earthquake in Japan 1995 would be cited
as the first event where man-made islands suffered catastrophic damage along their
periphery where quay walls have grossly moved seaward involving large amount of soil
deposits behind them. The lateral spreading of once liquefied soils was found to exert
truly detrimental effects on the structures and facilities existing on such laterally
moving soil ground. Since then, problems related with lateral spreading have become a
subject of extensive studies and discussions in the international arena of the earthquake
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A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 1–2.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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Kenji Ishihara
geotechnics. Performance of structures resting upon, or foundations embedded in
liquefied deposit or those undergoing lateral spreading is now one of the major issues of
consideration for which some solutions and consensus are in urgent need.
The damage by the earthquakes may be divided into two groups, structural injury due
directly to inertia force during intense shaking and indirect damage due to liquefaction
or lateral spreading of the ground. The features of these two kinds of damage have been
found different between developing and developed countries. In the developed
countries, seismic code or regulations for earthquake-resistant design has been put
forward mainly for structures and implemented in the design of medium to large-scale
buildings or facilities. Thus, the structural damage has become less and less
pronounced and implementation of anti-seismic design is recognized to have
contributed greatly for reduction of distress during earthquakes. In contrast, in
developing countries codes or regulations have not yet been put into effect sufficiently
and death tolls or property damage result mostly from the collapse of poorly constructed
houses or buildings.
With respect to the geotechnics-associated damage, mitigation measures have not yet
been implemented both in developed and developing countries to an extent to reduce the
damage. Consequently, the damage due to geotechnical origin such as liquefaction and
landslides forms a major part of the distress by earthquakes. From considerations as
above, it may be mentioned that the ground damage due to liquefaction and landslides is
still the cause of major damage not only in developing countries but also in developed
region of the world, and there is a plenty of challenges emerging from one earthquake
after another that is worthy of notice and requires further studies before relevant
solutions become of use for mitigating the distress resulting from large earthquakes. In
this context, geotechnical engineers should be encouraged to seek the problem areas and
try to come up with some solutions in this unexplored area.
CHAPTER 1
MICROZONATION: DEVELOPMENTS AND APPLICATIONS
W. D. Liam Finn, Kagawa University, Takamatsu, Japan
Tuna Onur, Pacific Geoscience Centre, Sidney, BC, Canada
Carlos E. Ventura, University of British Columbia, Vancouver BC, Canada
1.1. Introduction
Building codes base seismic design forces on various seismic hazard parameters that
describe the intensity of ground shaking during an earthquake. The design parameter is
typically acceleration, velocity or spectral acceleration with a specified probability of
exceedance. These parameters are mapped on a national scale for a standard ground
condition, usually rock or stiff soil. Mapping to such a scale is called macrozonation.
Damage patterns in past earthquakes show that soil conditions at a site may have a
major effect on the level of ground shaking. Mapping of seismic hazard at local scales
to incorporate the effects of local soil conditions is called microzonation for seismic
hazard. The analysis for calculating the probability of exceeding different levels of the
mapped ground motion parameter is called seismic hazard analysis.
The basic structure of seismic hazard analysis is presented in this chapter and its
evolution to the present state of the art will be described. The presentation is geared to
the user, not the analyst. It attempts to give the user a useful level of understanding of
how the seismic hazard parameter of the microzonation is determined, what it means,
what uncertainties are associated with it and how they are handled in the analysis.
Microzonation for seismic hazard has many uses. It can provide input for seismic
design, land use management, and estimation of the potential for liquefaction and
landslides. It also provides the basis for estimating and mapping the potential damage
to buildings. Mapping the losses expected from a particular level of seismic shaking is
called microzonation for risk. The presentation of the procedures for microzonation for
risk is also geared to the user. The procedures for estimating losses for a selected
probability of exceedance of ground shaking level will be explained and the entire
process illustrated by means of a case history of loss estimation conducted for the
insurance industry in Canada.
Seismic hazard analysis, which is the major component of microzonation for seismic
hazard and seismic risk, can be a very expensive and time consuming activity.
Therefore the objectives of the microzonation and how the results are likely to be used
should be clearly understood by analyst and user before the levels of effort and
sophistication of the hazard analysis are decided. The potential range in useful effort is
exemplified by the following two examples.
Hensolt and Brabb (1990) published a microzonation map of San Mateo County,
California, showing the distribution of the site factors, S, in the Uniform Building Code.
These site factors define the amplification of ground motions by four different soil
profiles compared to the motions in rock or stiff soils. Therefore the map, in effect,
shows the relative seismic hazards at different locations in terms of S. In addition, if
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A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 3–26.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
4
W. D. L. Finn, T. Onur and C. E. Ventura
this map is overlaid on the basic hazard map for stiff ground, a revised map can be
drawn that reflects in a significant way the effects of local soil conditions. Such a map
is feasible in most metropolitan areas as the basic soil data is available from
construction records. This represents a very basic, elementary, and affordable way of
microzoning a metropolitan area for hazard, while taking into account local soil
conditions. The other extreme is represented by the probabilistic seismic hazard
analysis for ground motions at Yucca Flat, Nevada. This site is a potential geologic
repository for spent nuclear fuel. The seismic hazard study for this site has been
described as the largest and most comprehensive analysis ever conducted for assessing
the hazard from ground shaking (Stepp et al., 2001). The huge effort was driven by the
critical need to provide a stable basis for assessing the impact of ground motions on the
long term performance of the containment facility for the spent fuel.
1.2. The Structure of Probabilistic Seismic Hazard Analysis
The methodology for conducting probabilistic seismic hazard analysis was developed
by Cornell (1968) and an updated summary of the state of the art was prepared by the
EERI Committee on Seismic Risk (EERI, 1989). The method has 4 steps as shown in
Figure 1.1. The first step is to identify the active faults and areal seismic sources that
may affect the site (Figure 1.1a). The second step is to characterize the recurrence rates
of earthquakes of different magnitudes in each source. This involves specifying an
earthquake occurrence relation for each source and a maximum magnitude. The
distribution of occurrences is often given by the Gutenberg and Richter (1954) relation
in Equation (1.1),
Log10N(M) = a – bM
(1.1)
Here N(M) is the number of earthquakes per year with a magnitude equal to or greater
than M and a and b are constants for the seismic zone. N is associated with a given area
and time period. The constant ‘a’ is the logarithm of the number of earthquakes with
magnitudes equal to or greater than zero. The constant ‘b’ is the slope of the
distribution and controls the relative proportion of large to small earthquakes
(Figure 1.1b).
An alternative formulation for N(M) is given in Equation (1.2),
N(M) = eDEM = Noe-EM
(1.2)
The third step is to select an appropriate attenuation relationship that relates the median
value of the seismic motion parameter to be mapped to the magnitude of the earthquake
and distance from the source. An attenuation relationship for median acceleration is
shown in Figure 1.1c for magnitude M. Finally the fourth step is to compute the hazard
curve shown in Figure 1.1d taking into account all the data provided by the first three
steps.
The hazard curve gives the probability that a given level of acceleration will be
exceeded in a given time period.
Developments and Applications
5
Fig. 1.1. The four steps in seismic hazard analysis
1.3. Developments in Seismic Hazard Analysis
Two major factors have shaped developments in seismic hazard analysis, since Cornell
introduced the methodology in 1968. The first is the huge increase in the number of
strong motion records available, since the 1971 San Fernando earthquake in California.
This has led to improved forms of attenuation relations that take into account different
types of faulting, different tectonic environments and different soil conditions. The
second is the need of the nuclear power industry for stable estimates of ground motion
at low probabilities of exceedance. This need has shaped the standards for
implementing every element of the Cornell structure for seismic hazard analysis at the
highest level of practice.
The distinguishing characteristic of the best modern practice is the formal treatment of
the uncertainty associated with almost every aspect of seismic hazard analysis.
Uncertainty was not considered formally in the original Cornell paper. There are two
6
W. D. L. Finn, T. Onur and C. E. Ventura
kinds of uncertainty, aleatory and epistemic. Aleatory uncertainty is due to the random
nature of seismic events. No matter how much data are accumulated on ground motions
for example, the standard deviation about the median in attenuation relations remains
significant. Epistemic uncertainty is considered to be due to a lack of scientific
knowledge and is established by processing opinions from a number of experts. The
manner in which such opinions are elicited and interpreted is considered so crucial to
the final assessment of hazard that the nuclear industry has established standards for it
(SSHAC, 1997).
The process of getting the data for each step in the seismic hazard analysis, including
considerations of both aleatory and epistemic uncertainty is described in a general way
here. The objective is to show that though the analytical techniques for conducting
seismic hazard analysis are well established and accepted, getting the appropriate input
is often a process of chasing a very elusive target. This is something the user needs to
understand.
1.3.1. SEISMIC SOURCES
There are two kinds of seismic sources, areal sources and faults. Generally areal
sources are used to represent distributed seismicity that cannot be associated with
known faults. These sources are delineated by experts who take into account the
distribution of historical earthquakes and the seismotectonic regime and geology. There
can be wide differences in the expert definitions of the areal sources, reflecting the lack
of scientific information to constrain the delineation of sources. Source definition is
one major source of epistemic uncertainty. Expert opinions are used to deal with
epistemic uncertainty in each step of the hazard analysis. The differences in opinions at
each stage lead ultimately to wide differences in hazard estimation. To aggregate these
opinions to arrive at a stable hazard estimate, the different hazard estimates are
combined by a weighting process. In the Yucca Mountain study, for example, the
decision to give equal weight to all experts was taken at the beginning of the study.
All faults are potential sources. The challenge is to decide whether faults with no
history of earthquake occurrence should be considered active to meet the objectives of
the study. In this case it is necessary to rely on paleoseismicity. Trenching across a
fault will reveal the dislocation of strata by past earthquakes that can be dated. When
this information is considered in combination with geological or geodetic data on slip
rates, estimates of magnitude and frequency of past events outside the historical record
can be made.
Another area of uncertainty is how a fault will break; along the total length of the fault
or just along a segment. If potential breaking segments are identified, how many may
break at once. What about adjacent faults? As stresses readjust in the fault under
consideration as a result of an earthquake, will the changes in the stress regime of
nearby faults lead to sympathetic rupture? This again calls for the reconciliation of
different expert opinions.
1.3.2. RECURRENCE RELATIONS
Recurrence relations are a crucial component of seismic hazard analysis. They are the
means of defining the relative distribution of large and small earthquakes and
7
Developments and Applications
incorporating the seismic history into the hazard analysis. On the basis of worldwide
seismicity data, Gutenberg and Richter established the loglinear relation (G-R line)
given by Equation (1.1). This relation has been assumed to apply to individual areal
and fault sources also. One of the steps in characterizing seismic sources is the
assignment of a maximum magnitude to each source. This requires the G-R line to
taper into the maximum value as shown in Figure 1.2. This distribution is called the
truncated exponential and is given in exponential form in Equation (1.3),
N(M) = [ Eexp(-E(M-Mmin))]/[1- exp(-E(Mmax-Mmin))]
(1.3)
Here Mmax is the assigned maximum magnitude, Mmin is the smallest earthquake that
needs to be considered, E = b ln(10) and b is the slope of the G-R line in Figure 1.1b.
Source specific values of b are used in this equation. The divisor renormalizes the
distribution so that integration between Mmin and Mmax gives unity.
Fig. 1.2. Truncated exponential distribution of recurrence rates
An important problem in defining a recurrence relation is ensuring completeness. For
the time period under consideration, it is crucial to ensure that all earthquakes have been
recorded for each magnitude range of interest. For example, there is a threshold
magnitude below which earthquake occurrences have not been recorded completely in a
given time frame for a given layout of seismographs and a given distribution of
population. Fitting the Gutenberg –Richter relation to incomplete data at the lower end
will flatten the slope of the line which leads to an inflated estimate of the occurrence of
large earthquakes. Because of the long recurrence time, the historical record may be too
short to ensure completeness in the large earthquake range. It is imperative that any
data used to establish occurrence rates of earthquakes should be complete for the time
period under consideration for each magnitude range.
8
W. D. L. Finn, T. Onur and C. E. Ventura
The G-R line does not always apply. Some fault segments tend to have occurrences of
earthquakes of similar size or within a narrow range of magnitudes. These earthquakes
are called characteristic earthquakes. Typically smaller earthquakes on the fault follow
the G-R line and the characteristic earthquakes occur at higher rates. A typical
combined distribution is shown in Figure 1.3. A commonly used characteristic model is
that of Youngs and Coppersmith (1985) shown in Figure 1.4. Note the higher
occurrence rates of the characteristic earthquakes. More seismic energy is released by
the larger earthquakes according to this model than is released in the truncated
exponential model (Abrahamson, 2000). An alternative recurrence model can be
formulated by assuming that all the strain energy is released in characteristic
earthquakes (CDMG, 1996).
Fig. 1.3. Geological documentation of
characteristic earthquakes (after Schwartz
and Coppersmith, 1984; Courtesy of the
American Geophysical Union)
Fig. 1.4. Characteristic earthquake
occurrence model (after Youngs and
Coppersmith, 1985; Courtesy of the
Seismological Society of America)
1.3.3. ATTENUATION RELATIONS
A state-of-the-art assessment of the main attenuation relations in use in North America
may be found in a special issue of Seismological Research Letters (SSA, 1997).
Modern attenuation relations typically give the natural logarithm of a ground shaking
parameter such as acceleration or spectral acceleration as a function of magnitude and
distance. The dispersion about the median is characterized by a lognormal distribution
and the value of the standard deviation, as shown in Figure 1.1c. The lognormal
distribution is symmetrical. Therefore the distribution of the underlying ground motion
parameter itself is not symmetrical. Therefore the mean is greater than the median. As
pointed out by Abrahamson (2000),
Mean = Median * exp(- V2/2)
(1.4)
Here V is the standard deviation. The standard deviation is a measure of the aleatory
uncertainty associated with the ground motion parameter. In addition, there is also
epistemic uncertainty regarding the coefficients in the attenuation relation itself.
9
Developments and Applications
It is very important for the end user to understand what acceleration is being estimated
by the attenuation relation. In the United States, the attenuation relations give the
geometric mean of the two horizontal components of motion. Engineers are often under
the impression that it is the largest component. Practice varies in other countries where
the largest component is often used. According to Abrahamson (2000), the largest
component is on the average 15% greater than the mean. The difference becomes
greater at periods longer than 5s, especially for near fault ground motions.
Attenuation relations tend to be regionally specific. For example, in North America,
very different attenuation relations are used in the west and the east because of the
radically different geological and tectonic structures in these regions. Relations also
tend to be specific with respect to the type of faulting. Attenuation from subduction
sources is different than from strike-slip sources. There are also differences between
attenuation from strike-slip sources and reverse or thrust faults. Attenuation relations
may be site-specific in the sense that the relation may be established for a particular soil
condition such as rock, soft soil, deep stiff soil, shallow stiff soil, etc. Some attenuation
relations define these conditions by means of descriptive adjectives. Boore et al. (1993)
characterized the site conditions by means of the time averaged shear wave velocity, Vs,
in the top 30m of a site. The characteristics of attenuation relations will be illustrated
using the attenuation relation for crustal sources by Boore et al. (1997),
b1 b 2 M - 6 b 3 M - 6
Ln Y
2
b 5 Ln r b v Ln
VS
VA
(1.5)
Here:
r
b1
r
2
jb
h
2
b1SS for strike slip earthquakes
°
®b1RS for reverse slip earthquakes
°b
¯ 1ALL if mechanism is not specified
(1.6)
(1.7)
In this equation, Y is the ground-motion parameter (peak horizontal acceleration or
pseudo-spectral acceleration response at a particular period in g); the predictor variables
are moment magnitude (Mw), distance (rjb in km), and average shear-wave velocity to 30
m (Vs in m/s). Note that h is a regression parameter. Values of the coefficients in
Equation (1.5) are given in Table 1.1 for the attenuation of spectral accelerations at
periods from 0 to 2s to illustrate the structure of such tables. The entries for zero period
are the coefficients for peak horizontal acceleration. In Table 1.1, VInY, is the square
root of the overall variances of the regression. The complete table of coefficients is
given in Boore et al. (1997). Values of the parameter Vs will be presented later, when
the effects of local soil conditions on ground motions are considered.
The many different definitions of distance, r, from the earthquake source used in
attenuation relations are illustrated in Abrahamson and Shedlock (1997). The Boore et
al. (1997) distance, rjb, is the closest horizontal distance to the vertical projection of the
rupture surface. In the case of a vertical fault, this is the same as the distance to the
10
W. D. L. Finn, T. Onur and C. E. Ventura
fault break. For dipping faults, the distance can be as low as zero when the source is
within the vertical projection of the rupture surface. The attenuation relation (Equation
1.5) is valid for earthquake magnitudes ranging from M = 5.5 to M = 7.5 and for
distances D d 80 km.
Table 1.1. Smoothed values of the coefficients in the Boore et al. (1997) attenuation
relation
Period
b1SS
b1RV
b1ALL
b2
b3
b5
bV
VA
h
VLnY
0.000
-0.313
-0.117
-0.242
0.527
0.000
-0.778
-0.371
1396.
5.57
0.520
0.200
0.999
1.170
1.089
0.711
-0.207
-0.924
-0.292
2118.
7.02
0.502
1.000
-1.133
-1.009
-1.080
1.036
-0.032
-0.798
-0.698
1406.
2.90
0.613
Youngs et al. (1997) provide attenuation relations for horizontal response spectral
acceleration (5% damping) for subduction earthquakes applicable to rock and soil sites.
These attenuation relationships are considered appropriate for earthquakes with M = 5
and greater, and for distances to the rupture surface from 10km to 500km. Most
attenuation models for subduction zone events are based on recordings from Japan and
South America. Most of these events were recorded at large distances. However,
recordings were made during the 1985 Michoacan earthquake at distances as small as
13km, although recordings within 30km were sparse. Youngs et al. (1997) show that
peak ground motions from subduction zone earthquakes attenuate more slowly than
those from shallow crustal earthquakes and that intraslab earthquakes produce larger
peak ground motions than interface earthquakes for the same magnitude and distance.
However, the database contains a very limited number of intraslab recordings.
1.3.4. EFFECTS OF LOCAL SOIL CONDITIONS
Site conditions play a major role in establishing the damage potential of incoming
seismic waves from major earthquakes. Damage patterns in Mexico City after the 1985
Michoacan earthquake demonstrated conclusively the significant effects of local site
conditions on seismic response of the ground. Peak accelerations of incoming motions
in rock were generally less than 0.04g and had predominant periods of around 2s. Many
clay sites in the dried lakebed on which the original city was founded had site periods
also around 2s and were excited into resonant response by the incoming motions. As a
result the bedrock outcrop motions were amplified about 5 times. The amplified
motions had devastating effects on structures with periods close to site periods. In the
1989 Loma Prieta earthquake, major damage occurred on soft soil sites in the San
Francisco-Oakland region where the spectral accelerations were amplified 2 to 4 times
over adjacent rock sites (Housner, 1989). Clearly any assessment of seismic hazard or
seismic risk should incorporate the amplification effects of local soil conditions. The
crucial question is how this can be done effectively without unduly complicating the
hazard assessment process or increasing the cost significantly. There are three effective
ways to include the effects of local soil conditions in hazard and risk studies: use an
attenuation relationship that incorporates a variety of soil classes, use well-documented
Developments and Applications
11
empirical amplification factors or conduct site response analyses. The latter procedure
is time consuming and expensive and it is difficult to get reliable results for large areas.
Site response analysis is more appropriately used for estimating hazard to individual
structures.
Attenuation laws that incorporate site parameters for different types of soil conditions
offer a convenient way to include site effects. The BJF (1997) attenuation relation
described above includes a site parameter Vs that is related to site classes proposed by
NEHRP (BSSC, 1994). The site classes are given in Table 1.2. Values of Vs for the
NEHRP site classes of major interest, B, C and D and for rock and soil categories are
given in Table 1.3.
Table 1.2. NEHRP (BSSC, 1994) site classes
Soil Class
Description
Properties
A
Hard rock
Vs > 1500 m/sec
B
Rock
760 m/sec < Vs 1500 m/sec
C
Very dense soil
and soft rock
360 m/sec < Vs 760 m/sec
N > 50, su 100 kPa
D
Stiff soil
180 m/sec < Vs 360 m/sec
15 N 50, 50 kPa su 100kPa
E
Soil
Vs < 180 m/sec
>3m of soft clay (PI > 20, w 40% and su < 25 kPa)
Table 1.3. Values of average shear velocity, Vs, for use in the BJF attenuation relation
NEHRP site class B
1070 m/sec
NEHRP site class C
520
NEHRP site class D
250
Rock
620
Soil
310
The nonlinear behaviour of soils causes amplification factors to be dependent on the
intensity of shaking. This was demonstrated very clearly by Jarpe et al. (1989) by
comparing the amplification factors for a site on Treasure Island in San Francisco Bay
relative to the rock motions at adjacent Yerba Buena Island, using data from the main
shock of the 1989 Loma Prieta earthquake and 7 aftershocks. The amplification factors
for surface motions recorded at the Treasure Island site during the 1989 Loma Prieta
earthquake are shown in Figure 1.5. The solid line shows the variation in the NS
spectral ratio for the first 5 seconds of the shear wave in the main shock before any
liquefaction took place at the site.
12
Spectral Ratio - TRI / YBI
W. D. L. Finn, T. Onur and C. E. Ventura
12
8
4
0
2
4
6
8
10
12
14
16
Frequency - Hz
Fig. 1.5. Amplification of ground motions at Treasure Island site (after Jarpe et al., 1989;
Courtesy of the Seismological Society of America)
Acceleration on Soft Soil Sites (g)
The shaded area in Figure 1.5 shows the 95% confidence region for the spectral ratios
of 7 aftershocks. The amplification factors are drastically reduced in the strong motion
phase, although still 2 or greater over a wide frequency band of engineering interest.
The reduction in amplification with increased intensity of shaking is due to the
nonlinear stress-strain response of the soil, resulting from reduced effective shear
moduli and increased damping. The peak acceleration at the surface is only 0.16g, so
the amplification factors are associated with fairly low levels of earthquake shaking.
0.6
range of calculated
responses
0.5
1989 Loma Prieta
0.4
0.3
median relationship
0.2
0.1
1985 Mexico City
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Acceleration on Rock Sites (g)
Fig. 1.6. Accelerations on soft soil and associated rock sites (after Idriss, 1991;
Reproduced with permission from University of Missouri and Ed. S.Prakash)
13
Developments and Applications
Idriss (1990) has summarized the relationship between peak accelerations on soft soil
sites and on associated bedrock sites in Figure 1.6. The median curve is based on data
recorded in Mexico City during the 1985 Michoacan earthquake, strong motion data
from the 1989 Loma Prieta earthquake and data from equivalent linear site response
analyses. The curve suggests that, on the average, the bedrock accelerations are
amplified in soft soils until the peak rock accelerations reach about 0.4g. The higher
amplification ratios between rock and soil sites, in the range of 1.5 – 4, are associated
with levels of rock acceleration less than 0.10g, when the response is more nearly
elastic. The increased nonlinearity of soft soil response at the higher accelerations
reduces the amplification ratios.
1.3.5. NEHRP AMPLIFICATION FACTORS
After major studies of site amplification following the Loma Prieta earthquake, NEHRP
(BSSC, 1994) published the two sets of amplification factors given in
Tables 1.4 and 1.5 that are dependent on the NEHRP site classes (Table 1.2) and
shaking intensity. One set is for short period motions and one for long period motions,
centered on periods of 0.2s and 1.0s respectively.
Table 1.4. Short period amplification factors; T = 0.2s
Site Class
Shaking Intensity
Aa = 0.1
Aa = 0.2
Aa = 0.3
Aa = 0.4
Aa = 0.5
A
0.8
0.8
0.8
0.8
0.8
B
1.0
1.0
1.0
1.0
1.0
C
1.2
1.2
1.1
1.0
1.0
D
1.6
1.4
1.2
1.1
1.0
E
2.5
1.7
1.2
0.9
-
Table 1.5. Long period amplification factors; T = 1.0s
Site Class
Shaking Intensity
Av = 0.1
Av = 0.2
Av = 0.3
Av = 0.4
Av = 0.5
A
0.8
0.8
0.8
0.8
0.8
B
1.0
1.0
1.0
1.0
1.0
C
1.7
1.6
1.5
1.4
1.3
D
2.4
2.0
1.8
1.6
1.5
E
3.5
3.2
2.8
2.4
-
14
W. D. L. Finn, T. Onur and C. E. Ventura
1.3.6. EVALUATING THE HAZARD
Seismic hazard curves are first obtained for each seismic source and then combined to
obtain the total hazard. If the probability that a given level of seismic shaking k is
exceeded by a particular earthquake of magnitude m at distance r in source ‘i’ is given
by P(K!kµm,r), then the expected number of times K!k, termed Ok, is
mu r f
N
O ¦ O ³ ³ P( K !kµm, r ) f
k
i 1
i
me r 0
i
( m)
f
i
(r ) dmdr
(1.8)
Here Ok is the expected rate of exceedance of k in a given time, taking all sources into
account. For source i, Oi is the mean rate of occurrence of earthquakes between the
upper and lower bound magnitudes, ml and mu respectively and fi (m) and fi (r) are the
probability density functions for magnitude and distance. The summation is carried out
over all sources. The analysis is conducted using one of the commercial computer
programs such as EZ-FRISKTM (Risk Engineering, 1997) or SEISRISK III (Bender and
Perkins, 1987).
The occurrence of earthquakes is assumed to follow the Poisson probability density
function. Therefore the probability that the ground motion k will be exceeded at least
once (called the probability of exceedance) in a time period T, given the annual rate of
exceedance Ok , is
P(K!k) = 1 - e-OkT
(1.9)
-OkT
is the probability that the ground motion level will not be exceeded. If the
Here e
probability, P(K!k) is set for a time period, T, then the associated exceedance rate given
by Equation (1.8) is
Ok = ln(1 - P(K!k)/ T
(1.10)
If the desired probability of exceedance is a 10% chance in 50 years, then the annual
exceedance rate is Ok = 0.00211.
1.4. Microzonation for Risk
Microzonation for seismic risk is a mapping of the distribution of potential monetary
losses associated with the occurrence of a mapped distribution of seismic hazard. In
effect, microzonation for risk adds another layer of information to microzonation for
seismic hazard.
The crucial element in any loss estimation study is a correlation between an index of
seismic hazard and damage. This requires a definition of different damage states or
levels of damage. Experience in past earthquakes has demonstrated that different
classes of buildings sustain different levels of damage for the same intensity of shaking.
Therefore building class is also an independent variable.
Modified Mercalli Intensity (MMI) has been used most frequently as the index of
ground motion intensity in damage estimation methodologies (ATC-13, 1985; King and
Kiremidjian, 1994; Rojahn et al., 1997; Dowrick and Rhoades, 1997; Blanquera, 1999).
The MMI scale for intensities VI and up is presented in Table 1.6. MMI VI is the level
of shaking intensity at which structural damage begins to occur.
Developments and Applications
15
Table 1.6. Modified Mercalli Intensity Scale (MMI) from Level VI to XII
MMI
DESCRIPTION OF EFFECTS
VI
Felt by all, many frightened. Some heavy furniture moved. A few
instances of fallen plaster. Damage slight.
VII
Damage negligible in buildings of good design and construction; slight
to moderate in well-built ordinary structures; considerable in poorlybuilt structures. Some chimneys broken.
VIII
Damage slight in specially-designed structures; considerable in
ordinary substantial buildings with partial collapse; great in poorlybuilt structures. Fall of chimneys, factory stacks, columns, walls.
Heavy furniture overturned.
IX
Damage considerable in specially designed structures; well-designed
frame structures thrown out of plumb. Damage great in substantial
buildings, with partial collapse. Buildings shifted off foundations.
X
Some well-built wooden structures destroyed; most masonry and
frame structures with foundations destroyed. Rails bent.
XI
Few, if any masonry structures remain standing. Bridges destroyed.
Rails bent greatly.
XII
Damage total. Lines of sight and level are distorted. Objects thrown
into air.
The damage estimation methodology developed by the Applied Technology Council
(ATC-13, 1985) is widely used. In ATC-13, the intensity of ground shaking is specified
by MMI and the potential damage to different classes of buildings is described by
Damage Probability Matrices (DPMs). The DPMs describe for each building class, the
probability that a building is in a specified damage state given the level of ground
shaking intensity (MMI). The seven distinct damage states recognized in ATC-13 are
given in Table 1.7. Each of these damage states is associated with a range of damage
factors (DF), which are defined as the ratio of dollar loss to the replacement value.
These ranges and the corresponding central damage factors (CDF) are given in
Table 1.8.
16
W. D. L. Finn, T. Onur and C. E. Ventura
Table 1.7. Definition of damage states in ATC-13
DAMAGE STATE
DAMAGE DESCRIPTION
1. None
No damage.
2. Slight
Limited localized minor damage not requiring repair.
3. Light
Significant localized damage of some components
generally not requiring repair.
4. Moderate
Significant localized damage of many components
warranting repair.
5. Heavy
Extensive damage requiring major repairs.
6. Major
Major widespread damage that may result in facility
being demolished or repaired.
7. Destroyed
Total destruction of the majority of the facility.
Table 1.8. Damage factors for different damage states
DAMAGE STATE
DF RANGE (%)
CENTRAL DF (%)
1. None
0
0
2. Slight
0-1
0.5
3. Light
1 - 10
5
4. Moderate
10 - 30
20
5. Heavy
30 - 60
45
6. Major
60 - 100
80
100
100
7. Destroyed
The Damage Probability Matrix (DPM) for one of the building classes (WFLR = Wood
Frame - Low Rise) in ATC-13 (1985) is shown in Table 1.9 to illustrate the structure of
such matrices. The total level of damage in a building is described by mean damage
factors (MDF), in terms of the ratio of dollar loss to replacement cost. The MDFs for
each MMI level are the product of the CDFs and their corresponding probabilities of
occurrence for all distinct damage states. The total damage for a give prototype
building is given by the sum of the MDFs for all seven damage states,
17
Developments and Applications
MMI
MDF prototype
1
100
7
¦ CDF j P ds j
(1.11)
j 1
Here CDFj is the central damage factor for damage state j and P(dsj) is the probability of
the prototype being in damage state j.
As an example, for WLFR at an MMI level of VIII, the MDF is calculated as follows:
VIII
MDF URMLR
0.0 0.0 0.5 1.6 5.0 94.9 20.0 3.5 45.0 0.0 80.0 0.0 100 .0 0.0
100
(1.12)
5.35%
Here the first number of each pair in the numerator is the CDF (%) and the second
number is the probability (%) of occurrence of that CDF. The MDFs are calculated in a
similar way for all prototype building classes in the study area at the MMI levels of
interest.
The application of the ATC-13 methodology will be illustrated by an example from
engineering practice.
Table 1.9. Damage probability matrices for Wood Frame – Low Rise class
Central
DF
Modified Mercalli Intensity
VI
VII
VIII
IX
X
XI
XII
Wood Frame - Low Rise
0
3.7
0.5
68.5
26.8
1.6
5
27.8
73.2
94.9
62.4
11.5
1.8
3.5
37.6
76.0
75.1
24.8
12.5
23.1
73.5
20
45
80
1.7
100
1.5. Case History
1.5.1. BACKGROUND
After the 1989 Loma Prieta, 1994 Northridge and 1995 Kobe earthquakes, the insurance
industry in Canada became concerned about the potential for catastrophic loss due to
major earthquake impacting South-Western British Columbia where most of the
population is concentrated in the major cities. The industry began discussions with the
federal and provincial governments for cooperation in dealing with their concerns. To
assist in making their case, the insurance industry needed assessments of their potential
losses from insured buildings in key cities and commissioned a risk study at the
University of British Columbia which was funded by the federal government, the
18
W. D. L. Finn, T. Onur and C. E. Ventura
insurance industry and the City of New Westminster. The study covered three cities;
Vancouver, Victoria and New Westminister. The city of Victoria was selected as a case
history here because its compact size and variety of soil conditions make it a very clear
example of how the ATC-13 methodology is used in practice and how the results may
be presented. The insurance risk analysis for this study demonstrates the close
connection between the objectives of a risk study and the way the risk study is carried
out.
An essential requirement of the study was that neither the elements of the seismic
hazard study and nor the risk assessment methodology should give grounds for
controversy over the findings. It was essential that the predicted losses should be
acceptable to all parties in the discussions. The objectives of the insurance industry
were met in the following way. The seismic source zones and the associated recurrence
rates and maximum magnitudes adopted for the hazard study were those developed by
the federal government scientists for the National Building Code of Canada (NBCC,
1995; Adams et al., 1996). The attenuation relation for peak ground acceleration used
in the building code (Boore et al., 1993) was also used in the study. The aleatory
uncertainty given by the lognormal distribution about the expected value used in the
hazard calculations but no allowance was made for epistemic uncertainty. The widely
used ATC-13 loss estimation methodology was employed for the risk estimation. This
required a distribution of MMI in the study area, and a set of building classes and their
associated damage probability matrices. The task of classifying the buildings and
modifying the ATC-13 damage probability matrices was subcontracted to a local
consultant with wide experience in the seismic design and evaluation of structures.
Buildings in British Columbia were classified into 31 different types and associated
damage probability matrices were developed (Bell, 1998). Damage probabilities for
three prototype classes, unreinforced masonry-low rise (URMLR), wood light frameresidential (WLFR) and concrete frame-low rise (CFLR) are given in Table 1.10 as an
example. The risk study for Victoria was carried out by Onur and is described in detail
in her PhD dissertation (Onur, 2001).
Table 1.10. MMI based damage probabilities
Building
Prototype
MMI
URMLR
Discrete Probabilities (%) for Different Damage States
None
Slight
Light
Moderate
Heavy
Major
Destroyed
VIII
0.0
0.0
21.0
60.0
15.0
2.0
2.0
WLFR
VIII
1.0
6.0
86.0
5.0
2.0
0.0
0.0
CFHR
VIII
0.0
2.0
57.0
40.0
1.0
0.0
0.0
1.5.2. VICTORIA RISK STUDY
Risk analysis
The city of Victoria is located on the Southern tip of Vancouver Island on the West
Coast of Canada. It was incorporated as a City in 1862 and was proclaimed the capital
of British Columbia in 1871. It has a population of over 77,000 people as of 1999 and
has an area of roughly 23.5 square kilometres. The building inventory of the City has of
19
Developments and Applications
over 13,000 structures. The risk study area was confined to the downtown area and
adjacent districts and contains about 2,500 structures. A probabilistic seismic hazard
analysis for Victoria (48.5° N, 123.3° W), carried out for firm ground conditions and a
10 % chance of exceedance in 50 years, gave a PGA of 0.31g. This corresponds to
MMI VIII based on the Neumann (1954) correlation between PGA and MMI.
MMI = [log(PGA) + 0.041]/0.308
(1.13)
An alternative hazard analysis based on attenuation relations for MMI (Atkinson, 1997)
also gave an MMI VIII.
The Planning Department of the City of Victoria gave access to their building database,
which included location (street address), zoning and land use information on every
structure in the municipality. However, the database did not contain any information on
the structural properties of the buildings, such as building material, construction date,
load bearing system, height (or number of stories), and footprint area. These data were
collected by sidewalk surveys covering about 2,500 buildings in and around the
downtown core of the city. The most prevalent material type and building prototype
classes were determined for each block and mapped independently for the study area.
The distribution of prevalent building prototype classes is presented on a block-byblock basis in Figure 1.7.
About 65% of the buildings surveyed in Victoria are wood and it is the prevalent
material in about 51% of the blocks studied. In downtown Victoria, where most of the
historical buildings are located, the number of masonry buildings is quite high. About
28% of the buildings are masonry, and it is the prevalent material type in about 42% of
the blocks studied. Concrete buildings constitute about 7% of the buildings in the study
area. There are a few steel buildings in the study area but steel is not the prevalent
material type in any of the blocks.
The most common prototype is WLFR, which constitute about 45% of all the buildings
in the study area and about 67% of the wood buildings. The second most common
building prototype class is URMLR which represents about 20% of all buildings and
57% of the masonry buildings in the study area. Among concrete buildings, CFMR is
the most common prototype. It makes up about 3% of all buildings and 41% of
concrete buildings in the study area.
Damage estimation was carried out, using the MMI-based damage matrices developed
by Bell (1998). Total damage levels were estimated as a percentage of replacement cost
using mean damage factors, MDFs, for different MMI levels for each building
prototype. The mean MDF for each block was calculated by averaging the MDFs of the
buildings within that block, taking either the average or a weighted average obtained by
weighting the MDFs by the footprint areas of the buildings in the block.
The estimated structural damage distribution on a block-by-block basis, based on
weighted average MDFs, is shown in Figure 1.8. The majority the buildings in
downtown Victoria, about 35% of all the blocks in the study area, have MDFs between
10% and 30%. The surrounding neighbourhoods have lower MDFs, in the range of 5%
to 10%.
20
W. D. L. Finn, T. Onur and C. E. Ventura
Fig. 1.7. Prevalent buildings prototypes by block
Non-structural damage distribution was calculated in a similar manner using appropriate
MDFs for each of displacement-sensitive components, acceleration-sensitive
components and building contents (Cook, 1999). About half the blocks are expected to
have MDFs in the 20%-30% range and the other half in the 15%-20% range for
displacement-sensitive components. About half the blocks are estimated to have MDFs
between 5% and 10%, and the rest between 0% and 5% for acceleration-sensitive
components. Damage to building contents remain below 5% in all the blocks.
Developments and Applications
21
Fig. 1.8. Structural damage distribution by average MDF weighted by footprint area
Effects of soil conditions
In Victoria, the effect of geology was considered important because half the city rests
on softer material than the “firm soil” assumed in the hazard calculations. Therefore,
the effects of possible soil amplification were investigated. The geological units that
appear in the study area (Monahan et al., 2000) are presented in Table 1.11 and are
shown on a block by block basis in Figure 1.9.
The amplification depends on the geological unit, level of ground shaking and the
period of the ground motion. In Victoria, the expected PGA is equal to 0.31g. For this
22
W. D. L. Finn, T. Onur and C. E. Ventura
level of shaking, short-period ground motions are not amplified considerably, however
long-period ground motions are amplified roughly by 1.5 for C1 and F, 2.0 for C2 and
2.5 for O1 (Monahan et al., 2000). The geological unit R2 is not expected to amplify
the ground motion.
Table 1.11. 6 Main types of geological units in Victoria
Geologic
Unit
Description
NEHRP
Site
Class
Range
Fa
Fv
R2
Thin soil over bedrock with scattered
outcrops; generally <5m of Victoria
clay over < 10m of older Pleistocene
A to C
1.0
1.0
C2
>3m of the grey clay facies of the
Victoria clay, under the brown clay
facies and over thin (<10m) older
Pleistocene deposits
D to E
1.0
2.0
C1
Areas where units R2 & C2 cannot be
differentiated; also areas with >5m of
the Victoria clay but <3m of grey clay
facies
C to E
1.0
1.5
Anthropogenic
amplification
C to E
1.0
1.5
E to F
1.0
2.5
F
O1
fill
with
variable
Holocene peat over the grey clay
facies of the Victoria clay
The PGA’s were multiplied by the amplification factors corresponding to each
geological unit and the resulting PGA values were converted into MMI for use with the
damage probability matrices. The resulting damage distribution map was calculated
using these MMI levels. Total monetary losses resulting from the estimated structural
and non-structural damages were calculated for Victoria for MMI VIII, taking into
account the effects of soil amplification and summed over each block to display the
total loss in each block. The results are shown in Figure 1.10.
Developments and Applications
Fig. 1.9. Geological units in Victoria
23
24
W. D. L. Finn, T. Onur and C. E. Ventura
Fig. 1.10. Total monetary losses in Victoria, both structural and nonstructural, taking
soil amplification into account
Developments and Applications
25
1.6. Final Remarks
Seismic hazard analysis is the crucial element in a microzonation study. To plan and
use a microzonation study effectively requires an understanding of how the input to the
hazard analysis is developed, the ways in which the analysis may be carried out and the
uncertainties associated with almost every component of the analysis. The formal
treatment of uncertainty is one of the major conceptual changes since Cornell
introduced the method in 1968.
Today the aleatory uncertainty in attenuation relations is nearly always incorporated in
the analysis through the assumed lognormal distribution about the mean but the formal
inclusion of epistemic uncertainty is still rare except for the high level of practice
associated with critical structures. Epistemic uncertainty in seismic source definition is
a major source of uncertainty in final results. Here and in the other components of the
analysis, expert opinion is used to handle epistemic uncertainty. The different opinions
are weighted to arrive at a final judgment. Several opinions are required to make the
process viable, and it is a complex and expensive undertaking.
The elements of seismic risk have also been presented and illustrated with a case history
from practice. A key lesson from the case history is that the objectives of the
microzonation for risk and how the results are to be used should be clearly understood
before planning how the study will be conducted and at what level of sophistication.
Acknowledgement
The seismic risk study for South-Western British Columbia, referred to above, was
funded by grants to the first author from the National Science and Engineering Council,
the insurance industry and the City of New Westminster. The study was a joint
collaborative effort with Professor C. E. Ventura, Director of the Earthquake
Engineering Facility at the University of British Columbia and Professor Gail Atkinson,
Carleton University, Ottawa. A. Blanquera, S. Cook and T. Onur worked on different
aspects of the study for their theses. Their outstanding contributions were responsible
for the success of the project.
The assistance of Noboru Fujita, Kagawa University, in the preparation of this paper
was invaluable.
26
W. D. L. Finn, T. Onur and C. E. Ventura
Appendix 1
BC Building Classification
No.
Material
1
Wood
Building Type
Wood Light Frame Residential
Code
WLFR
2
Wood Light Frame Low Rise Commercial/Institutional
WLFCI
3
Wood Light Frame Low Rise Residential
WLFLR
4
5
Steel
Wood Post and Beam
WPB
Light Metal Frame
LMF
6
Steel Moment Frame Low Rise
SMFLR
7
Steel Moment Frame Medium Rise
SMFMR
8
Steel Moment Frame High Rise
SMFHR
9
Steel Braced Frame Low Rise
SBFLR
10
Steel Braced Frame Medium Rise
SBFMR
11
Steel Braced Frame High Rise
12
Steel Frame with Concrete Walls Low Rise
13
Steel Frame with Concrete Walls Medium Rise
14
Steel Frame with Concrete Walls High Rise
15
Steel Frame with Concrete Infill Walls
SFCI
16
Steel Frame with Masonry Infill Walls
SFMI
Concrete Frame with Concrete Walls Low Rise
CFLR
18
Concrete Frame with Concrete Walls Medium Rise
CFMR
19
Concrete Frame with Concrete Walls High Rise
CFHR
20
Reinforced Concrete Moment Frame Low Rise
21
Reinforced Concrete Moment Frame Medium Rise
22
Reinforced Concrete Moment Frame High Rise
RCMFLR
RCMFM
R
RCMFHR
23
Reinforced Concrete Frame with Infill Walls
17
Concrete
SBFHR
SFCWLR
SFCWM
R
SFCWHR
RCFIW
Reinforced Masonry Shear Wall Low Rise
RMLR
25
Reinforced Masonry Shear Wall Medium Rise
RMMR
26
Unreinforced Masonry Bearing Wall Low Rise
URMLR
27
Unreinforced Masonry Bearing Wall Medium Rise
URMMR
24
Masonry
28
Tilt Up
Tilt Up
29
Precast
Precast Concrete Low Rise
PCLR
Precast Concrete Medium Rise
PCMR
30
31
Mobile
Mobile Homes
TU
MH
CHAPTER 2
THE INFLUENCE OF SCALE ON MICROZONATION AND IMPACT
STUDIES
Carlos Sousa Oliveira
DECivil/ICIST, Instituto Superior Técnico, Lisbon, Portugal
Contents
A general overview of the methods for estimating earthquake impact in large urban
areas is presented. This overview includes the most important aspects, from geophysical
insight to engineering seismology, and the vulnerability of the existing stock of
buildings and other structures, as well as infrastructures. The role of each factor is
analysed, but emphasis is given to soil properties in the context of definition of strong
motion acting on the structure foundation and on possibilities for potential surface
rupture, liquefaction, land-sliding and subsidence.
As an introductory part, a brief analysis on the effects of earthquakes on the built
environment during the XXth century is presented and policies for mitigation of
earthquake risk are summarised, constituting Part I – “Earthquakes and the impact on
societies”. It calls the attention to the communities that seismic risk has been increasing
along the times, in spite of all the great advancements achieved in scientific and
technical grounds. Problems of bad use of “good engineering knowledge” and lack of
quality control are behind these observations.
Part II – “Definition of problems and techniques”, develops the main concepts of this
presentation. The first topic to be dealt with is the scale of analysis. Depending on the
level of detail (national, regional, local, site), hypotheses are different and so are data
quality, methods, uncertainties and conclusions. A second topic concerns seismic
scenarios which can be obtained through different processes, such as taking into
consideration historical seismicity, de-aggregation techniques, hazard analysis or having
in mind the minimization of any other objective function as total losses inflicted within
a given time period.
The way to incorporate soil influence into impact studies depends on the amount of
detailed work performed prior to the study. Sometimes only general geological
information exists; in other cases geological maps at a good scale or information on
borehole data are available. Methods for soil analysis are though very different and
require different analytical tools. A general analysis will act as a first filter to indicate
the areas that are more prone to amplification, attenuation of seismic waves, etc. On the
other hand, a more detailed method will clarify the zones of doubts. A large part of this
chapter is dedicated to the soil problem.
Building and infrastructure (lifeline) stocks are analyzed into their main topical issues
namely, classification of typologies, inventories and vulnerabilities.
Finally, in Part III – “Examples for illustration”, examples of impact studies illustrate
27
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 27–65.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
28
Carlos Sousa Oliveira
the effect of scale, scenario type, etc., as referred in Parts I and II. Applications to four
different cases emphasize each one with a different detail of analysis. Comparison and
discussion on the results and on the level of accuracy obtained are presented.
This chapter is essentially devoted to methods and does not develop the mathematical
algorithms to obtain the results presented. These can be found in the listed references.
2.1. Part I – Earthquakes and the Impact on Societies
2.1.1. EARTHQUAKES IN THE WORLD AND IN EUROPE IN THE XXTH
CENTURY
A simplified analysis of the evolution of human casualties and economic losses all
around the world caused by the seismic activity during the XXth century (Pinto, 1998,
Oliveira and Sánchez-Cabañero, 2002) (Figures 2.1 and 2.2), clearly indicates a steady
increase of economic losses (Figure 2.2), especially in the last decade, in contrast with a
slight decrease in human casualties (Yong et al., 1997, Figure 2.1). In fact, while
casualty figures oscillate around the 150 000 per decade (in a total of 1.5 million) and
are marked by the occurrence of very large events (Japan, Kwant, 1923, China, 1920,
etc., in the decade 1920-30 and Tangshan, China, 1976, decade 1970-80), the economic
losses, corrected to the year 1997, show an exponential increase. Such increase can be
attributed to earthquakes striking regions of high urban concentration, for which no
seismic protection has been implemented due to difficulty in transferring of technology
to the construction industry.
Human losses in the XXth century
(total of 1.5 millions - 15 000/year)
450000
400000
No. of deaths
350000
300000
250000
200000
150000
100000
50000
1990-00
1980-90
1970-80
1960-70
1950-60
1940-50
1930-40
1920-30
1910-20
1900-10
0
Per decade
Fig. 2.1. Human losses in the world during the XXth century
Even though great advances in seismology and earthquake engineering have been
acquired in the last 20 years, a great deal of implementation is still missing. Many
international organizations have spoken out for this problem, but results from these
campaigns are still difficult to judge. It is worth noting that the same pattern of damage
(human and economical) has been observed in the first years of the XXIth century.
29
Microzonation and Impact Studies
Million US Dollar/million
inhabitants
Economical Losses in the XXth century
(per million inhabitants - US$ normalized to
1997)
100
0.7045x
y = 0.0141e
2
R = 0.7099
10
1
0.1
1990-00
1980-90
1970-80
1960-70
1950-60
1940-50
1930-40
1920-30
1910-20
1900-10
0.01
Decades
Fig. 2.2. Economical losses in the world during the XXth century
In relation to earthquake risk, it is interesting to analyse the tendency to divide the
political world into two large geographic areas: the world of poor countries and the
world of rich countries. For the former ones, human casualties are increasing throughout
the century and are one order of magnitude above the rich countries, whereas, for these
ones, the opposite tendency is observed when dealing with economic losses. On the
other hand, it should be important to emphasize that in the last decade of the XXth
century very large events took place with catastrophic consequences, both in human and
in economic terms. Considering only the six earthquakes with magnitudes in the range
6.7 to 7.5, human casualties attained more than 70 000 and losses were above
150.000 x 106 Euros.
Looking in a more detailed way to the economic losses, the Kobe 1995 earthquake
alone was responsible for more than 100 x 109 Euros, which is equivalent to almost 2%
of the Japanese Gross National Product (GNP). This earthquake affected 3.6 million
inhabitants from a total of 4.5 million residents in the region, causing 5500 casualties
and 41 000 injures, important damage to 3500 buildings in reinforced concrete and steel,
and destroying around 80 000 dwellings. These incredible numbers when transferred to
other regions such as the metropolitan area of Lisbon, with a slight smaller population,
would cause losses of the order of the Portuguese GNP.
The Northridge 1994 earthquake caused about one third of the Kobe losses, but
economic loss estimation corresponding to the repetition of the Kwant (Tokyo) 1923
earthquake would surpass, in an order of magnitude, those numbers.
The XXth century has finished with two very large events with magnitude greater than
7.5, separated in time by just less than a month. The Kocaeli earthquake in Turkey
occurred in August 1999 and caused tremendous impact in the area east of Istanbul.
Over 15 000 people were killed, about 24 000 were injured and 600 000 people become
homeless. About 120 000 buildings and houses were considered beyond repair, among
which about 5000 were seriously damaged or completely collapsed. The total economic
30
Carlos Sousa Oliveira
impact of this earthquake is still difficult to establish. The second event, the Chi-Chi
earthquake of September 1999, affected a large area of Taiwan causing over 2000
deaths and an economical impact of the order of 3.2 x 109 Euros.
Whatever location around the world, the impact of earthquake activity is so large that,
in recent years, a great concern has led to the development of impact studies in large
metropolitan areas such as Mexico City, Tokyo, San Francisco, Istanbul, Bogotá, etc.
These studies, known as scenario evaluations for Megacities, are essential tools for
several different applications, which run from simple evaluations of earthquake risks, to
exercises for civil protection, indications for insurance companies, and re-evaluations of
mitigation measures.
Earthquake activity in time and space for a given region is not well known and cycles
with certain stability can be interrupted by other type of cycles. In recent times, large
earthquakes occurred in regions where no historical evidence was present. The cases of
Kobe and Athens earthquakes in 1995 and 1999, respectively, are among these events
occurring in regions of low seismicity. A great discussion was initiated on the
reliability of hazard methods, which cannot present good results if long period
observations are not taken into consideration. To avoid such difficulties, studies
including paleo-seismology and arqueo-seismology information should be made for
regions where long return period activity is suspected.
The lack of regularity in the pattern of earthquake activity has been a characteristic of
the seismic activity in continental Portugal (Oliveira and Sánchez-Cabañero, 2002). In
fact, periods of long quiescence alternate with periods of great activity. From the end of
the XIXth century to the second decade of the XXth century a high rate of activity was
observed throughout the country, with the occurrence the Benavento M=6.3 earthquake
in 1909, followed by an enormous number of aftershocks. Since then, approximately 80
years of very low seismic activity have passed, only interrupted by two isolated
episodes, one large M=8.0 event in 1941 with epicentre mid distance between the
Azores and the Continent, and a M=7.2 event in 1969, in the Gorringe Bank, near the
most seismic active interplate region SW of the Continent (see Example 1, Part III).
But a similar pattern can be visualized for the large area running from the Azores to the
Greek islands, in the neighbouring of the Euro-Asiatic and African plates. With the
exclusion of Greece, no event with magnitude larger than 5.8 was recorded in that area
from 1920 till 1980. In the year of 1980, three larger events occurred: in the Azores (Jan,
1st), in El Asnam Algeria (Oct 10th), and in Irpinia, south Italy (Nov 23th). Since then,
the most important events occurred in Algeria (1994) and in Italy (1997), the latter
causing great impact over the historical heritage in the centre of Italy
(http://emidius.itim.mi.cnr.it/, 1997, 1998)1. In summary, one can say that, in the period
1980 to 1995, about 5000 people lost their lives in the territory of the European Union
due to earthquake activity leading to a total economic loss above 430 x 106 Euros
(Ghazi and Yeroyanni, 1997).
In the topic of natural catastrophes, earthquakes play a very important role, world-wide.
As a matter of fact, statistics taken from the period 1973-1997 (http://www.cred.be),
1
This last period was interrupted by a Mw=6.7 earthquake in Algiers in 21 May, 2003
causing over 2200 deaths and more than 10 000 injures.
31
Microzonation and Impact Studies
organized by 5-year bins, show that earthquakes are among the disasters with larger
death impact (Figure 2.3), even though the total number of flood events is twice per
year.
This analysis on the effects of earthquakes on the built environment can be traced for
the entire XXth century. This calls the attention to the communities that seismic risk has
been increasing along the times in spite of all the great advancements achieved in
scientific and technical grounds. Problems of bad use of “good engineering knowledge”
and lack of quality control are behind these poor results.
Natural Disasters (Reported killed)
100.000
EARTHQUAKE
10.000
DROUGHT &
FAMINE
Annual average
FLOOD
1.000
HIGH WIND*
LAND- SLIDE
100
VOLCANO
10
1973 to
1977
1978 to
1982
1983 to
1987
1988 to
1992
1993 to
1997
Fig. 2.3. Comparison among different types of natural catastrophes
2.1.2. THE SOIL EFFECT ON THE CATASTROPHIC EVENTS
The effect of soil conditions on the general impact of large earthquakes has been
observed in several occasions in the XXth century, attributing to it the responsibility for
the great damage inflicted in several areas of the territory. Wide spread destruction,
such as in the Guerrero earthquake (1985) in Mexico City, the Spitak earthquake (1988)
in Leninakan, the Loma Prieta (1989) earthquake in the San Francisco Bay Area, the
Kobe earthquake (1995) in the coastal areas of the city, and the Kocaeli earthquake
(1999) in Adapazari are important examples of the influence of soil conditions on
ground motion acting in the foundations of structures located in areas away from the
epicentre.
But other cases not so well publicised in the literature are also good examples of this
important parameter. For example the Erzincan 1992 event, one of many in the
Anatolian fault, caused heavy damage, part of which was attributed to site conditions
and resonance; other reasons are poor workmanship quality of construction (Ansal et al.,
1993). Part of the large destruction caused by the Tangshan earthquake of July 28, 1976,
near Beijing, can be attributed to the existence of sedimentary deposits from the
Quaternary period (Chen, 1988). Not only the large magnitude (M=8.2) has contributed
32
Carlos Sousa Oliveira
to the wide spread damage (the 1 million industrial city was reduced to rubble), but the
soil influence was clearly marked in the geography of damage. Finally, the recent 2001
Gujarat-Bhuj earthquake (Narula et al., 2002) also caused great damage at a distance of
250 km from the epicentre, denoting a marked influence of soil conditions. This
circumstance, together with the resonance effects acting on several structures, caused
important damage.
The influence of soil conditions on the ground motion can be translated into the
modification of amplitude, of spectral content and of duration of incident motion due to
the presence of soft surface layers. But other problems related to the soil can also be
considered, such as potential surface rupture, liquefaction, lateral spreading, landsliding, etc. This is the reason all these features should always be considered in any
seismic study. They affect in a definite way the territory and contribute to the seismic
risk of the populations, of the building stock and of the lifelines. The incorporation of
soil influence in these studies can be seen directly in codes for new or existing
construction, in urban development layout and, in more generic sense, in scenario
studies. If they refer a particular area and invoke a great deal of specific studies, they
are usually referred in the literature as microzonation.
2.1.3. MITIGATION OF EARTHQUAKE RISK AND PREPAREDNESS
In order to mitigate the earthquake risk as seen in the previous chapters it is necessary to
act at several levels of the society, in a pure scientific/technical point of view, involving
the social, fiscal and political issues (SPES, 2001; “A Contribution to the reduction of
seismic vulnerability of the building stock”, http://www.spes-sismica.org/).
What can we do to reduce the impact of future earthquakes in the building stock and in
the monumental structures? The following general topics are of most importance:
(i) perception of the origin of earthquakes and of propagation of seismic waves;
(ii) understanding of the behaviour of all kind of structures under seismic action;
(iii) rehabilitation and retrofit of existing structures; (iv) development of appropriated
code of practice; and (v) development of quality control to insure a correct application
of all legislation.
In terms of earthquake preparedness, one can act at two different levels:
x Institutional
o
Different Ministries (risk mitigation)
o
Civil Protection:
Risk study;
Information and education;
Response preparedness (EMERGENCY PLANNING).
x Individual
o
Home preparation;
o
Family emergency planning;
o
Self-protection measures.
Because it is not possible to predict earthquakes, it is necessary to minimize the risk,
preparing a Preventive Planning and to minimize the effects of the event, developing an
Operational Planning.
Microzonation and Impact Studies
33
In order to minimize seismic risk, one should: (i) develop and enforce preventive
measures; (ii) improve building regulations for construction and reinforcement;
(iii) develop appropriate land use plans; and (iv) carry out civil protection awareness
and educational programs for the population, civil protection entities and decisionmakers.
The measures to minimize the effects after the occurrence of the event should be
prepared: (i) plan civil protection actions to activate when an earthquake occurs;
(ii) organise civil protection entities involved in aid operations, concerning its mission
and operational procedures; (iii) plan emergency means and resources and their
allocation, and plan management.
These last issues require Emergency Master Plans and Detailed Response Plans for
specific risks - i.e. the Seismic Risk Emergency Plan.
2.2. Part II – Definition of Problems and Techniques
2.2.1. SCENARIO STUDIES – GEOGRAPHIC SCALE OF INTERVENTION
Seismic scenarios for impact studies are essential exercises for a number of reasons:
(i) Help public authorities preparing emergency planning; (ii) define means and
resources to cope with potential earthquakes; (iii) accelerate “on-line” damage
assessment caused by an earthquake; and (iv) quantify the extent of any programme for
repair and retrofit of structures.
In the following, the several parts intervening in the process will be presented, with
greater emphasis on the soil component. Part III, by presenting several cases at
different scales, will develop in more detail the various subjects referred.
Elements of society in risk and overall impact estimation
1. Identification and characterization of elements of society in risk (vulnerability
identification)
The elements of society in risk considered for impact studies due to a serious seismic
action are the ones which can be seriously affected, causing human life loss and society
disruption, some times for a long period of time. The vulnerable elements to be
considered are:
- Building stock and industrial plants (dwelling with partial or total collapse);
- Lifelines: roadways; railways, including the subway; energy (electricity, gas, and
other combustibles); water; sewerage and telecommunications (disturbing seriously
the social tissue due to operation collapse, temporarily malfunction, etc.);
- Population (producing death, injures of various kinds, and homeless);
- Vital or important structures (those that are relevant for emergency management,
either due to its operational or political role).
2. Vulnerability evaluation
The vulnerability of each element in risk is analysed using functions that relate the
expected damages of each type of element with its characteristics and subjected to the
seismic action acting at the foundation level.
34
Carlos Sousa Oliveira
The building stock is statistically analysed having as reference the unit of the smallest
administrative territorial division, depending on the scale of work, and a diversity of
parameters of the buildings such as age, constructive typology, number of floors, etc.
Several techniques have been developed to derive these vulnerability functions, from
simple curves taken from observed behaviour during past earthquakes, to complex
engineered structured response analyses, or directly obtained from definitions of
intensity scales. Several typologies have been developed to consider the seismic
behaviour. Here, again, depending on the scale of work and on the knowledge on
individual units, building typologies range from 5 or 6 main categories (essentially by
epoch of construction and attending to the type of material) to a detailed analysis with a
few dozen cases (detailed construction types within, for instance, reinforced concrete),
as referred in the Hazus 99 methodology.
A similar methodology has been adopted when dealing with lifelines, by classifying
them according to types, materials, geometries, epoch of construction, etc., and defining
the corresponding vulnerability functions. For emergency planning purposes, the
results of each lifeline damage estimation, for each scenario, aims at a quick preliminary
restoration, in order to assure basic indispensable services.
To estimate the impact of earthquakes on the human life, it is indispensable to
characterise the demographic distribution for different periods of the day and around the
year. Not only the population living within the study area, but also the population
commuting to/from other adjacent areas, are of utmost importance to define their
geographical location at the time of the seismic event.
Vital or important structures have to be identified, and their vulnerability functions need
to be attributed. This is a very difficult task because only an individual detailed study
can more effectively produce reliable results, requiring the participation of the entities
responsible for them. The use of vulnerability functions adapted from the general above
mentioned ones has been commonly practised in impact studies, increasing the errors
associated with their evaluations.
3. Establishment of seismic occurrence scenarios
The establishment of feasible scenarios requires the study of past seismic occurrences,
the definition of different seismogenic zones affecting the area under study, and the
characterisation of their most important parameters (maximum expected magnitude and
frequency or probability). It may also involve the knowledge of attenuation functions,
if scenarios have to do anything with ground motion parameters, or the minimization of
any other objective function, as total losses inflicted within a given time period.
In many applications not only one single criterion prevails. Hypotheses to be analysed
are: the consideration of a largest historical event, as a measure of an extreme type
event; the 50, 100 or 1000-year mean return period event, requiring an hazard and deaggregation analysis; the most probable measure of impact over the entire stock in the
study area; or the eventual rupture of a possible fault structure.
4. Propagation of seismic energy
The release of seismic energy from their different possible sources (geotectonic
Microzonation and Impact Studies
35
structures) and its propagation through the crustal Earth layers to the bedrock
underneath the site under analysis is generally considered as the attenuation of seismic
waves. Local effects representing the transference of energy from bed-rock through the
upper soils, with the potential for ground motion amplification or reduction, liquefaction
and land-slide potential, are consequences of soil properties and characteristics of input
ground motion (level and energy content).
Several techniques can be used in the context of propagation of seismic waves, ranging
from peak ground values (acceleration - PGA, velocity - PGV or displacement - PGD),
spectral values, or seismic intensities (Mercalli Modified intensities - MMI, European
Macroseismic Scale - EMS-98, etc.). Primarily they relate these values with magnitude
and epicentral distance and, in the case of better tectonic definition, also with other
source parameters.
This task is of great importance to reduce uncertainties in the entire process of impact
estimation. Existing data from past earthquakes, even of small magnitude values,
should exercise the calibration of attenuation relationships.
5. Damage evaluation for the established scenarios
The evaluation of damages of the selected elements in risk, for each scenario, is
obtained using a simulation model that integrates all the above mentioned aspects, by
summing up all possible contributions. The damages of each element in risk are
classified in several different limit states, usually defined at five levels: no damage,
slight damage, moderate damage, heavy damage, and collapse. Depending on the
element under study, this damage classification may be lumped into coarser categories
or adapted to operational/non-operational terms, as in the case of sections of lifelines,
etc.
For a rapid visualisation and treatment of all information, Geographical Information
Systems (GIS) techniques are generally used. This requires a great deal of effort due to
the need of digital vectorization of many layers, but is of great benefit for future
applications, updating, corrections, alteration of algorithms, etc.
The GIS allows the visualisation of all types of variables organized by “layers”.
Examples of these are: intermediate results such as the geographical distribution of
characteristic motion parameters (maximum acceleration, response spectra, etc.), either
for bedrock and soils (local effects); the intensity distribution (Mercalli, EMS, etc.); any
damage category for any specific layer, etc. It can be made at the work-unit level or can
aggregate various units, depending on the objective pursued. Smoothing can also be
applied for geographical interpretation. At the same time statistical analyses, crossreferences, etc., are easily obtained with any standard statistical package.
Scenario studies are viewed in different perspectives according to the objectives to be
targeted. These define the scale of intervention which is very critical in the way to
obtain the elements necessary for the analysis. In this overview, special attention is
given to the problem of scale, with the presentation of impact studies at four different
scales: (i) scale of a country or large region, on the order 1:1 000 000; (ii) scale of a
region, 1:25 000; (iii) scale of a city or of a block, 1:5 000; and (iv) scale of a large
building, 1:1 000.
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Carlos Sousa Oliveira
GIS techniques can combine different scales, but the accuracy of final results is
determined by the one with poorer geographical detail.
2.2.2. SOIL INFORMATION
The soil information in each scale-case is analysed in a very different form: for the case
of a country scale the elements are only descriptions of the large geological units,
whereas for the regional scale a mixed large description with some more detailed
analysis is necessary; for the case of a city or block a more detailed description of
geotechnical units should be available, and for a building a detailed description
including borehole information might be important. The detail of this information
should be settled at a degree similar to the detail of the other types of information for
the impact studies, such as the building stock, the infrastructure network and the
population geographical location.
Geological published maps are used as fundamental tools for any of the analysis, but the
degree of detail has to be found in more specific studies. In this case information
obtained in construction sites where boreholes were made is of most interest, together
with data on the geological setting, and some other collateral information.
Regionalization is also made using other techniques for identification of soil properties,
among which are geophysical prospecting. Historical information on the zones of
systematic higher seismic intensities should be regarded as very important pieces of
evidence which deserve the most detailed analysis.
Several techniques for soil analyses, analytical as well as experimental, have been used
in connection with impact studies.
Among the analytical techniques, a first one considers soils as a one-dimensional (1-D)
representation defined by horizontal layers characterized by thickness and shear wave
velocity. It is only done for specific studies such as for important or critical structures
and includes in-situ and laboratory testing for determining the main geotechnical
properties and their associate mechanical properties such as the shear modulus of
elasticity G0 and density U, and a measure of their non-linear behaviour. This technique,
implying very good information, is only available for a reduced number of sites.
In most places where surface geology indicates stronger formations not deeper than
30m, knowledge of shear velocity down to 30m is considered to be sufficient.
An interpolation of the characteristics found in these sites to cover wider areas can only
be done by expert analysis based on lithographic description of the geological horizon
and on knowledge from other similar situations. If we are working in a more general
framework (e.g. in a larger scale), these descriptions are necessarily more vague,
smoothly considered and, consequently, reflecting average values.
The experimental technique which by far became very popular in the last 20 years,
considers the possibility of knowing the physical properties underlying the soil
substratum by obtaining, using ambient noise, the lower natural frequency of vibration
of the soil layer. This technique, known as Nakamura spectral ratio of horizontal to
vertical components (Nakamura, 1989 and 2000), can be used to identify frequencies
and possible amplification of ground motion in geotechnical zones of soft/hard
“impedance contrast” for moderate to large scale projects at low cost.
Microzonation and Impact Studies
37
In all cases, the motion at the surface requires the definition of ground motion at the
bed-rock which depends essentially on the magnitude, source properties and properties
of the path medium. The convolution of the input motion at the bed-rock with the
response of the upper soil layers will give the final surface result. More sophisticated
models, with 2-D and 3-D geometry, with linear and non-linear constitutive relations,
considering topographic implications, etc., are not used in studies of moderate to large
scale nature, even though great influence on the results may occur, such as in cases of
alluvial basins where gravity waves possibly dominate.
In impact studies several of the above mentioned techniques have been applied,
depending on the degree of knowledge and the scale of work. A convergence of results
from different techniques should be achieved when the information is of greater quality.
Naturally, working in wide regions, uncertainties may be quite large due not only to the
fact of the difficulty in generalising to the whole area the information from singular
points, but also due to the intrinsic uncertainty in the scrutiny methods used. This is the
main reason why results should always be used with caution and, if possible, margins of
uncertainty should be given.
Using the stratigraphy/lithology of the upper layers, Medvedev (1962) proposed a
simplified method that produces the macroseismic intensity at the soil surface by
increasing the intensity at the bed-rock horizon by an increment, function of the class of
soil. As an example, for a “rigid granite” there is no increase; “sandy soils” may
increase 1.2 to 1.8 (for MSK scale); “uncontrolled fill” 2.3 to 3. These numbers were
taken from empirical observations and reflect the propagation on a two-layer soil
system.
In all cases one has to deal with the process of knowing the seismic action that can be
acting at the bed-rock level, essentially as a function of magnitude and epicentral
distance. Of course other parameters may intervene in quite drastic way, such as the
source mechanism including the rupture process and the radiation pattern, but these
parameters are only considered at special situations when the geodynamic information
is good enough to be included. This issue involves the consideration of attenuation of
peak ground motion parameters, spectral ordinates or more simply intensities (MM,
MSK, EMS-98, etc.). Oliveira and Sanchez-Cabañero (2002) discuss these issues in
great detail.
An alternative way to this procedure is to use the concepts developed in the recent codes
for definition of seismic action, such as the approved version of Eurocode-8, where soils
are classified in great detail covering most common situations observed in many
different regions. Ground motion in terms of response spectra for each soil class at the
surface is also given, consequently avoiding the difficult part of analysing the wave
propagation within the soil layers. In this respect, the information leading to the
proposed spectra was supported in a large collection of strong motion data recorded at
the top of the various types of soil profiles. US policies through recent UBC97
legislation (FEMA, 1997, SEAOC, 1998) also consider a variety of soil classes, which
can be used in connection to the type of studies under analysis.
A classification of soil properties made within Eurocode-8 (2002) is as follows,
Table 2.1 (Sabetta and Bommer, 2002):
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Carlos Sousa Oliveira
Table 2.1. Classification of subsoil classes (EC8, 2002)
Subsoil
class
Description of stratigraphic profile
Parameters
VS,30
(m/s)
! 800
NSPT
(bl/30cm)
cu (kPa)
_
_
A
Rock or other rock-like geological
formation, including at most 5 m of weaker
material at the surface
! 50
! 250
B
Deposits of very dense sand, gravel, or very 360 – 800
stiff clay, at least several tens of m in
thickness, characterised by a gradual
increase of mechanical properties with depth
Deep deposits of dense or medium-dense
180 – 360
sand, gravel or stiff clay with thickness from
several tens to many hundreds of m
Deposits of loose-to-medium cohesionless
180
soil (with or without some soft cohesive
layers) or of predominantly soft-to-firm
cohesive soil
A soil profile consisting of a surface
_
alluvium layer with Vs values of class C or
D and thickness varying between about 5 m
and 20 m, underlain by stiffer material with
Vs > 800 m/s
Deposits consisting – or containing a layer at
100
least 10 m thick – of soft clays/silts with
high plasticity index (PI ! 40) and high
water content
Deposits of liquefiable soils, of sensitive
_
clays, or any other soil profile not included
in classes A–E or S1
15 - 50
70 - 250
15
70
_
_
_
10 - 20
_
_
C
D
E
S1
S2
Table 2.1, besides presenting a classification based on the lithology/stratigraphy
description of the layers and on the average shear wave velocity, also considers the NSPT
values (Standard Penetration Test) and the “undrained shear strength”, cu. Consistency
between the velocity bounds, NSPT and cu has been made for the different soil classes
(Ohta and Goto, 1976 and Clayton, 1995).
The consideration of five subsoil classes for the purpose of defining the elastic response
spectrum is the result of the latest developments in data collecting of recent events, the
Kobe, 1995, the Kocaeli, 1999, and the Chi-Chi, 1999. The classes are defined by the
average shear wave velocity of the upper 30 metres of soil (VS,30), by improved
descriptions of the stratigraphy, and by ranges of values of geotechnical parameters.
For special classes S1 and S2, which describe other geotechnical situations, special
studies for the definition of the seismic action, are required. For these classes, and
particularly for S2, the possibility of soil failure under the seismic action must be
considered.
39
Microzonation and Impact Studies
2.2.3. SPECTRAL SHAPES
Within the scope of Eurocode 8, the earthquake motion is represented by an elastic
ground acceleration response spectrum, dependent of sub-soil class defined in
Table 2.1 and on the magnitude value.
For application purposes only, two different response spectra, Type 1 and Type 2, have
been introduced, Figures 2.4 and 2.5, to be adopted respectively in high (Mw>5.5) and
low seismicity regions (Mw 5.5). The epicentral distance is not considered because it
controls the amplitude of the spectra but not their shape, and therefore has no effect on
normalized spectra. For other applications and tectonic environments, it may be
recommended the adoption of more spectral shapes, especially for the very large
magnitude values (M>7.5), for which Tc and Td may be higher.
Spectral Amplification
4
Tb
Type 1_soil A
Tc
Type 1_soil B
3
Type 1_soil C
Type 1_soil D
Type 1_soil E
2
Td
S
1
0
0
1
2
3
4
Period (sec)
EC8-00 TYPE 1
soil A Vs > 800 m/s
soil B 360<Vs<800 m/s
soil C 180<Vs<360 m/s
soil D Vs < 180 m/s
soil E (h < 20 m)
S
1,00
1,10
1,35
1,35
1,40
Tb
0,15
0,15
0,20
0,20
0,15
Tc
0,4
0,5
0,6
0,8
0,4
Td
2,0
2,0
2,0
2,0
2,0
Fig. 2.4. Type 1 elastic response spectra for the 5 subsoil classes and corresponding soil
parameter (S) and control periods (Tb, Tc, Td)2
2
S
- is the spectral value for period zero
Tb, Tc - are period limits (sec) for constant spectral acceleration branch,
Td
- is the period value defining the beginning of the constant displacement response range
of the spectrum.
40
Carlos Sousa Oliveira
Spectral Amplification
5
4
Type 2_soil A
Type 2_soil B
Type 2_soil C
3
Type 2_soil D
Type 2_soil E
2
1
0
0
1
2
3
4
Period (sec)
EC8-00 TYPE 2
soil A Vs > 800 m/s
soil B 360<Vs<800 m/s
soil C 180<Vs<360 m/s
soil D Vs < 180 m/s
soil E (h < 20 m)
S
1,0
1,2
1,5
1,8
1,6
Tb
0,05
0,05
0,10
0,10
0,05
Tc
0,25
0,25
0,25
0,30
0,25
Td
1,2
1,2
1,2
1,2
1,2
Fig. 2.5. Type 2 elastic response spectra for the 5 subsoil classes and corresponding soil
parameter (S) and control periods (Tb, Tc, Td)
It is important to point out that the value of S is larger for the Type 2 spectrum than for
the Type 1, for all classes other than A. This reflects the non-linear response of soil
layers and the fact that weak motion is amplified more than strong motion (Rey et al.,
2002).
In situations where the 30 m depth are not enough to reach a bed-rock type soil
formation, as it happens in certain geological environments in the centre of Europe such
as in deep sedimentary basins, it might be necessary to introduce more classes, which
are essentially the same as above but with specific deep ground geological constitution.
In conclusion, one can say that there are several possibilities to deal with the soil
problem in impact studies, depending on the working scale, the knowledge of the
geotechnical situation and the software availability. But it also depends on the detail of
knowledge of the other components of the entire process for estimating the seismic
impact. There is no point in studying the soil with great detail and treat the stock of
buildings by large geographical units.
Microzonation and Impact Studies
41
Liquefaction, land-slides and subsidence are other topics connected to soil performance
with great importance essentially for stabilisation of foundations and performance of
lifelines. The level of water content in the soil stratum is of major importance and,
consequently, the epoch of the year when the event takes place does have a great
influence on the potential for liquefaction, land-slides, etc. We will brief refer this topic
when analysing lifelines.
Tsunami and fires may aggravate the entire situation contributing to a chaotic
environment. They are not looked up in this review.
2.3. Part III – Examples for Illustration
Four examples will be analysed to illustrate the methodologies and problems
encountered in cases where scales of intervention are very different. The first case
shows an application to a large area which covers the entire Continental Portugal; the
second is the case of a regional-scale, the Metropolitan Area of Lisbon (AML); the third
case looks up to the Lisbon County, with the inclusion of a detailed geotechnical
description and the treatment of blocks of buildings; the last case discusses the situation
of blocks of buildings on the basis of individual structures.
In each example attention is given to a special topic, different from others to avoid
repetition of situations and to permit an analysis of broader subjects. Results obtained
using analyses at different scales are also discussed and compared.
2.3.1. EXAMPLE 1. STUDIES AT THE COUNTRY LEVEL: PORTUGAL
The first example is taken from a study done in late nineties for the entire Continental
Portugal (Campos-Costa et al., 1998). The seismicity of the country is moderate to
strong, alternating periods of large events with long periods of quiescence (Oliveira and
Sánchez-Cabañero, 2002). Figures 2.6a and 2.6b present a general view of the more
active zones of the surrounded area, showing the geodynamic and seismological
environments.
The attenuation models were evaluated at the country scale (Sousa and Olievira, 1997)
refined with the inclusion of three classes of subsoil conditions taken from Eurocode 8,
Part 1.1 (Eurocode 8, 1994). These subsoil classes are labelled A, B and C, and,
roughly speaking, corresponds to hard, intermediate and soft subsoil classes.
Portugal was divided into sub-regions corresponding to 275 administrative counties.
The class of soil assigned to each county was the most representative in terms of its
spatial distribution. Figure 2.7a presents the distribution of local ground conditions in
Portugal according to the three classes referred to above.
Figure 2.7b presents the hazard map for 1000 years return period. The seismic hazard
evaluation already comprehends the average ground condition of each county, as it is
included in the attenuation model.
Among the current distributions, it was verified that the one that globally fits the
evaluated seismic hazard annual distribution is the Beta distribution with, adjusted
parameters from county to county.
42
Carlos Sousa Oliveira
Lower
Lower
Tagus
Tagus
Valley
Valley
Gorringe
Bank
Gorrige Bank
Fig. 2.6a. Geodynamic environment for Continental Portugal (after Cabral, 1996;
Courtesy of “Colóquio/Ciências”, Lisbon)
Fig. 2.6b. Seismological environment for Continental Portugal (adapted from Sousa et
al., 1992)
43
Microzonation and Impact Studies
Bragança
MMI
Class A
VI - VII
VII - VIII
Class B
VIII - IX
IX - X
Class C
Lisbon
Lagos
Fig. 2.7 a. Average ground conditions in Portugal according to Eurocode 8 classes
(Eurocode 8, 1994); b. Hazard map for 1000 years return period; macroseismic intensity
in MM scale
10000
Return Period [year]
Bragança
Series6
1000
Lisboa
Series2
Lagos
100
Series1
10
4
5
6
7
8
9
10
11
MMI
Fig. 2.8. Hazard curves for Portugal: Lisbon County, higher (Lagos) and lower
(Bragança) seismic hazard conditions; best fit of Beta distributions (continuous lines)
44
Carlos Sousa Oliveira
Figure 2.8 exhibits the hazard curve for Lisbon County and for the counties with higher
and lower seismic hazard in Portugal for the return period of 1000 years, respectively
Lagos in the Southern cost and Bragança in the Northwest. Figure 2.8 also illustrates the
Beta distributions that best fit the hazard distributions. The ground conditions at Lisbon,
Lagos and Bragança are averaged as classes B, C and A, respectively. As it can been
seen the Beta distribution fits adequately the hazard evaluation. The mean, maximum
and minimum standard errors of the fitting, among the 275 Portuguese counties, are
0.021, 0.043 and 0.012, respectively.
Housing stock and probabilistic vulnerability analysis
The above-described methodology was preliminarily applied to the Lisbon County
(Sousa and Olievira, 1997). In that work a detailed analysis of the existing stock of
buildings was made, due to the fact that a considerable amount of information was
available for the Lisbon County. Unfortunately, the same can not be said on behalf of
the other 274 counties in the Continent due to: (i) lack of knowledge of the distribution
of the housing stock according to a set of typologies and (ii) problems in adapting the
world-wide damage earthquake statistics to the vulnerable typologies that were feasible
to identify. The consequence of the above encountered difficulties is the increase of the
dispersion of the vulnerability distribution, as it will be mentioned later on.
Housing Distribution
700 to 4000
4000 to 6000
6000 to 10000
10000 to 50000
50000 to 227611
Fig. 2.9. Distribution of number of housing units per county (data from Census 1991;
INE, 1994)
In the present study, the data available in the Portuguese 1991 Census (INE, 1994) were
adopted and the typological categories were grouped taking into account just one
vulnerability factor, the building age. The vulnerability curves were adapted from
world-wide earthquake statistics compiled by Tiedemann (1992), bearing in mind the
characteristics of the Portuguese housing stock.
45
Microzonation and Impact Studies
Figure 2.9 shows the distribution of total number of housing units per county (the total
number in the country is approximately 3 millions). Notice the high concentration of
housing units at Oporto and Lisbon metropolitan areas and in most littoral counties.
Beyond these elements, the Census also provides information at the county level to
classify the housing stock into five different typologies, according to the vulnerability
factor V1 = building age:
x
x
x
x
x
T1 - Buildings constructed prior to 1919.
T2 - Buildings constructed during the period 1919-1945.
T3 - Buildings constructed during the period 1946-1960.
T4 - Buildings constructed during the period 1961-1985.
T5 - Buildings constructed during the period 1985-1991.
Figure 2.10 illustrates the distribution of housing units per typology in the main five
Portuguese geographic regions.
700000
600000
500000
400000
300000
North region
North Region
Centre region
Lisbon and Tagus
Valley
Centre Region
Alentejo region
Algarve region
Lisbon and
Tagus Valley
200000
100000
Alentejo Region
0
Prior to 1919 to 1946 to 1961 to 1986 to
1919
1945
1960
1985
1991
Algarve Region
Fig. 2.10. Distribution of housing units per typology in the main five Portuguese
geographic regions (data from Census 1991; INE, 1994)
Another vulnerability factor, related to the main materials used in the building
construction, could be identified in the Census in order to reflect the main structural
properties of each typology (V2 = building materials). However, as building materials
can only be related to the number of buildings per county, and not with the housing
units, the vulnerability factor building materials was not considered in the present
analysis.
Figure 2.11 shows the vulnerability curves per typology. Notice that typology T4
corresponds to the first Portuguese seismic resistant code (RSCCS, 1958) and the
typology T5 corresponds to the actual code (RSA, 1983). The RSCCS code comprises
46
Carlos Sousa Oliveira
three different seismic regions and imposes an increase of the building resistance in
accordance with the region seismicity. The RSA code includes four different seismic
regions and three subsoil classes, compelling the building vulnerability to decrease with
the subsoil softness and/or with the increase of the region seismicity. For those reasons,
the actual ranges of the vulnerability curves for typologies T4 and T5 are grey
shadowed in Figure 2.11, as they correspond to different seismic designs from North to
South of the country, conjugated with different subsoil conditions, in case of typology
T5.
Mean Dam age Ratio [%]
100
10
T4 (1961-1985)
T5 (1986-1991)
T1 (prior 1919)
1
T2 (1919-1945)
T3 (1946-1960)
0.1
6
7
8
9
10
11
12
MMI
Fig. 2.11. Vulnerability curves per typology (Census 91)
0.995
100
0 .9 9 5
10
0 .5
Dam age Ratio
1
0 .1
0 .5
0 .0 1
0.001
99.0% Interval
50.0% fractile
0 .0 0 0 1
M DR
0 .0 0 0 0 1
0 .0 0 0 0 0 1
4
5
6
7
8
9
10
11
12
MMI
Fig. 2.12. Averaged Damage Ratio (DR) distribution for Lisbon County
47
Microzonation and Impact Studies
Figure 2.12 shows the Mean Damage Ratio (MDR) weighted average for Lisbon County.
It also shows the 99% variation domain and the median of the Damage Ratio
distribution (Lognormal distribution, V = 2.2%) as a function of macroseismic intensity.
For macroseismic intensities V and VIII the figure also presents the distribution
function of DR|MMI and the corresponding fractiles of 50% and 99.5% (For detailing
the computational algorithms, see Campos-Costa et al., 1998).
Probable Losses for various reference time intervals
Figure 2.13 shows the probability distribution of the Losses for the entire country for
the time reference intervals of 10 and 50 years. The shadowed grey areas, in the figure,
contain the domain of the distribution of Losses, county per county, denoting the
highest and lowest trend lines in the Losses distributions.
Losses [%]
0.001
0.01
0.1
1
10
100
1
0.9
0.8
0.6
Portugal
50 years
0.5
0.4
Cou ntie s var iation
10 ye ar s
Probability
0.7
Portugal
10 years
0.3
Co un tie s var iation
50 ye ar s
0.2
0.1
0
Fig. 2.13. Distribution of the overall Losses in Portugal and counties envelopes; 10 and
50 years reference time intervals
From this figure one can conclude that there is a ratio of 40 between the 50% fractile of
the 50 years distribution and the 10 years distribution for Portugal. Referring to the 10
years distribution, the median of the overall Losses in Portugal is 0.05% and there is a
90% probability that Losses are between 210-4% and 9%. If the 50 years distribution is
considered, those values are 2%, 0.08% and 41%, respectively.
These ranges reflect the high dispersion that one deals with in this work, and reveals the
importance of considering uncertainty in the vulnerability functions.
To visualise the relative importance of each county on the total value, Figure 2.14
shows the median Losses distribution for reference time intervals of 10 and 50 years,
and Figure 2.15 the geographic distribution of the Losses (median) normalized (Losses
incidence).
As expected, Figure 2.15, showing higher Losses incidence in the South and in zones
around Lisbon, reflects both the higher hazard region in the South and the higher
concentration of housing units in the metropolitan area of Lisbon. The highest value
was observed in the Lisbon County which is responsible for 11% of the total Losses of
the entire country.
48
Carlos Sousa Oliveira
10 Years
50 Years
% Losses
50% fractile
0.01 to 0.04
0.04 to 0.06
0.06 to 2.00
2.00 to 6.00
6.00 to 15.00
Fig. 2.14. Median of the Losses distribution per county for reference time intervals of
10 and 50 years
Distribution of
Total Losse
(50 Years, 50% fractile)
0.01 to 0.05 %
0.05 to 0.1 %
0.10 to 1.00 %
1.00 to 2.00 %
2.00 to 11.00 %
Fig. 2.15. Geographic distribution of incidence of the Losses; normalisation through the
median of total Losses in Portugal for the reference time interval of 50 years
Microzonation and Impact Studies
49
Comments
This methodology presents a wide range of possible applications and results. However,
caution should be exercised in relation to the results shown, because data used in the
application must be calibrated against local situations, e.g. historical seismic scenarios.
In fact, the confrontation of these results with the values that can be obtained directly
from the historical seismicity will be a further step to bring an additional degree of
validation.
From the application of this methodology to Portugal one can conclude that, for a time
reference interval of 50 years, the median of the total housing Loss in Portugal is 2%
and there is a 90% probability that housing Losses are between 0.08% and 41% for the
same time window. This high range of uncertainty is mostly attributed to the
uncertainties in vulnerability assessment of the building stock, emphasising the
importance of considering this randomness whenever seismic risk studies are carried out.
In order to obtain more precise estimates of losses, the present application requires
further refinements at the data level. A better knowledge of the building inventory in
Portugal, namely the distribution of buildings considering other vulnerability factors
beyond building age, such as building materials and number of storeys, is essential.
Data from 2001 Census is available at a more detailed geographical unit, allowing a
better accuracy in geographical terms. It also permits an updating of the presented
results, as significant changes in the stock of buildings have taken place during the
1990-2000 decade (M. L. Sousa, work in progress, 2003).
Sensitivity studies should be performed in order to identify the most important
parameters controlling losses, particularly: (i) in the hazard model the maximum
probable magnitudes and the dispersion of attenuation laws and (ii) in the vulnerability
analysis the adequate choice of the distribution of damage and its variance. In fact,
these last two parameters require a more profound study in order to reduce the high
dispersion of the results.
The present model can easily be extended to obtain the number of casualties and
injuries per county or for any other group of counties, the number of homeless, and the
number of destroyed or damaged housing, etc.
Other applications can be made in different fields such as insurance, urban planning,
disaster mitigation, earthquake preparedness, emergency planning, etc. The study of
extended structures such as lifelines is also of interest. To perform similar studies at a
more refined scale such as for a region around Lisbon, a better definition of the
parameters modelled at a more refined geographic scale are required, as will be shown
in Example 2.
2.3.2. EXAMPLE 2. STUDIES AT THE REGIONAL LEVEL: THE
METROPOLITAN AREA OF LISBON (AML)
This study, with phases similar to the ones of Example 1, developed recently,
culminated with the development of a simulator to be used for the elaboration of an
emergency plan to face the seismic risk in the region, Figure 2.16. The simulator allows
the damage evaluation (to humans, to the building stock, to various lifelines, to vital
structures, etc.) for given scenarios defined by a magnitude and an epicentral location.
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The geographical unit was of three types according to the layers under consideration:
(i) for soil characterization a detailed analysis of seismic profiles was made on the basis
of a 1:50 000 geological mapping and the information on boreholes was collected from
construction sites; (ii) the building stock was obtained from the 1991 Census at parish
level (INE, 1994), digitized from 1:25 000 scale, with a total of 277 units; the same can
be said about the areas that suffered land-slides in the past; (iii) the tracing of a few
lifelines, obtained by the entities in care, was based on a vectorization, sometimes at a
1:1000 scale.
The Metropolitan Area of Lisbon (AML) is a large area of approximately 100 km
diameter, with about 430 000 buildings, 1.1 Million dwellings and a resident population
of the order of 2.7 Million inhabitants (INE, 1994), representing 27% of the population
of the country.
Cartaxo
Torres Vedras
Alenquer
Azambuja
Portugal
S. de Magos
Mafra
S. M. Agraço
A. dos Vinhos
V. F. de Xira
i
Sintra
Cascais
Benavente
Loures
Amadora
Oeiras Lisboa
Alcochete
Montijo
Moita
Almada
Palmela
Barreiro
Seixal
AML
Montijo
Setúbal
Sesimbra
Fig. 2.16. Localization of the Metropolitan Area of Lisbon (AML)
All data, collected and produced, were implemented in a GIS environment. The detail
of the work was impressive in all respects (Rocha et al., 2002, and 2003 for a summary).
In this chapter, attention is essentially given to the soil analyses and briefly to the
vulnerability methodology. A few results are shown, together with discussion on
uncertainties and how to deal with them.
The soil classes were obtained by assigning a geotechnical profile to a geographical unit
of homogeneous characteristics (Campos-Costa et al., 2002), Figure 2.17, and treating
this area as a 1-D non-linear model subjected to a ground motion defined by a response
spectrum acting at the bed-rock level. Spectral attenuation relationships (Bommer et al.,
1998) were used to obtain the spectral contents at bed-rock as a function of magnitude
and epicentral distance.
Microzonation and Impact Studies
51
Soil profiles, in general with information down to the bed-rock, were identified, in a
total of 36 profiles, Figure 2.17 (A, AA, AB,…AK, B, C,…Z). These profiles, which
can be associated to the geomorphology of the area, as seen in the figure, vary from
“rigid” (A), to “sandy” (M) (Vs=250 m/s; h=15 m), to “very soft alluvial” (V) (Vs=150
m/s, h= 40 m). Figure 2.18 presents the profiles more common in the area, for which the
average geotechnical properties of the upper layer are given in Table 2.2.
Fig. 2.17. Soil profiles and topography for the “AML model” (adopted from CamposCosta et al., 2002; Reproduced with permission from Elsevier)
An example for illustration of the results obtained at the soil surface by means of the
simulator (called the “AML model”) is presented in Figure 2.19 (Rocha et al., 2003). It
corresponds to a seismic scenario of a strong historical event which took place in 1531
(magnitude 7.2 Richter). The seismic motion was transformed into MMI, for easier
comparison with the isosseismals of the historical event, Figure 2.20 (Justo and Salwa,
1998). Comparing the simulated with the historical, it is clear that the simulation
captures several patterns of the historical, even though the remarquable NNE-SSW
predominant propagation observed in the historical may suggest an important fault
rupture mechanism, not possible to simulate with a point source. On the other hand, the
softer soils to the East support the idea of higher intensities in these areas.
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Carlos Sousa Oliveira
Fig. 2.18. Detailed soil profiles for the AML (adopted from Campos-Costa et al., 2002;
Reproduced with permission from Elsevier)
Table 2.2. Characteristics of soil profiles presented in Figure 2.17 (approximate values
of upper layers - “AML model”)
Soil profile type(AML)
VS (km/s)
Depth, h (m)
EC-8 classif. (Table 2.1)
A
rock
A
AE
190
60
D
AF/E
220
26
C
AG
200
19
E
H
300
19
D/E
M
270
17
E
P
250
37
C
V
150
40
D
This simulation also permits to visualize the locations more prone to soil amplification,
by computing the ratio of top to bottom PGA and PGV at each location, Figure 2.21. In
this figure only the amplification/attenuation of PGA is presented, indicated the zones
with more influence on low rise buildings, which show high frequency content. The
pattern of Figure 2.21 follows closely the soil distribution of Figure 2.18.
Amplification/attenuation of PGV (not presented) will affect less rigid buildings.
Microzonation and Impact Studies
53
epicentre
Fig. 2.19. 1531 earthquake scenario – IMM (“AML model”)
Fig. 2.20. Isosseismals of the 1531 earthquake – IMM (Justo and Salwa, 1998; Courtesy
of the Seismological Society of America)
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Carlos Sousa Oliveira
Behind all the above referred topics and results there are several processes not discussed
here, which deal with earthquake source, spectral attenuation, non-linear soil modelling,
etc., and can be found in Campos-Costa et al. (2002), Carvalho et al. (2002) and M.L.
Sousa (work in progress, 2003).
Fig. 2.21. 1531 earthquake scenario – predominant amplifications (PGA´s) “AML
model”
Fig. 2.22. Damages in the roadway lifeline caused by slope sliding (on the left side) and
due to liquefaction (on the right side) (light gray: no problem; darker: higher potential
for sliding/liquefaction)
Microzonation and Impact Studies
55
Land-sliding and liquefaction were analysed under different perspectives. The first one
was based on the existence of past scars detected from aerial photography, together with
simple Hazus 99 techniques based on magnitude and distance. The second one was
based on the soil profiles defined earlier, for which the potential for liquefaction derives
directly. Water content in the soils determined by the epoch of the year is also
considered in the analysis. Figure 2.22 shows, in a zoom, a detail of damage inflicted to
a roadway due to land-side and liquefaction.
The classification of elements at risk was made according to their seismic vulnerability,
with building classes based on age, and structural type, as in Example 1, but also on the
number of storeys (Carvalho et al., 2002). The definition of fragility curves to adopt in
each class was based on Hazus 99 methodology, permitting the computation of
probabilities associated to each damage state, for a given seismic scenario. A
performance-based assessment for each building type was adapted from Hazus 99
proposals to define individual capacity curves. Calibration of these curves based on
more realistic models and on empirical observations is a matter of urgency.
Figure 2.23 illustrates the geographic distribution of total collapsed buildings for the
1531 scenario, and Figure 2.24 shows a comparison in numbers between the distribution
of damage among the different limit states for the entire AML and for the Lisbon
County. From Figure 2.23 one can observe the concentration of damage around the
epicentral region due to the proximity to the release of energy, and in the southern ring,
consequence of the soil profile type. (The characteristics of the building stock in these
two large areas are essentially of the same type).
epicentre
Fig. 2.23. 1531 earthquake scenario – total number of collapsed buildings, “AML
model”
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Carlos Sousa Oliveira
This simulator is now under probation in many of its functions in order to reproduce not
only historical earthquake experience, but also to be adjusted to data from recent small
magnitude events. In special for those events for which there exists strong motion
monitoring at free-field and in structural elements as well as direct field information.
Running several different seismic scenarios will help creating a body of knowledge
capable of providing the necessary confidence for pursuing with the setting of
Emergency Planning.
Fig. 2.24. 1531 Earthquake scenario – Comparison between AML and Lisbon County
The simulator has also helped defining the scenarios to be used in conjunction with the
pair (M-magnitude; E-epicentral location) which produces the most probable global
Losses in the entire or part of the region, considering given mean return periods
(Campos-Costa et al., 2002). To do so, deaggregation is applied having as object that
particular global characteristic. This scenario is one out of many others dealing with
what may happen in the region.
2.3.3. EXAMPLE 3. STUDIES AT THE COUNTY LEVEL: THE CASE OF LISBON
The topic of impact studies in the Lisbon County has been thoroughly analysed in the
past (Mendes-Victor et al., 1993, Oliveira and Pais, 1993, Pais et al., 1996). It gave rise
to the first GIS simulator in Portugal which, given a magnitude and an epicentral
distance, develops a set of damage scenarios in terms of victims, casualties, destroyed
facilities and any other structures. This simulator (called the “Lisbon Council model”)
has been widely used to produce the basis of the current Emergency Plan for the Lisbon
County.
Even though it was developed in the early nineties, Example 3 is referred in this chapter
because it deals with a more detailed scale, and still retains a lot of good and solid
scientific background. New updating of the model, now under study, will be discussed
at a later stage.
The model, as it is nowadays, considers: (i) an attenuation of MMI with one single
parameter (affecting the hypocentral distance) which can be changed according to the
earthquake source area; (ii) soil characterization considering several classes reflecting
the “impedance contrast” of the upper layers.
Microzonation and Impact Studies
57
Soil was analysed in great detail on the base of the information compiled from hundreds
of boreholes across the county. Figure 2.25a presents the geotechnical map of Lisbon
showing a great detail on the geological units. The influence of soil on ground motion
transmission from bed-rock to the surface was made taking into account the
amplification of energy in a 2-layer system defined by impedance [(VS1uU1)/(VS2uU2)]2,
(VSi and Ui are the S-wave velocity and density of layer i, respectively) as in Medvedev
(1962). The transformation into MMI was then made through a logarithm operation.
For the particular case of Lisbon County, 9 different situations with combination of the
2 layers were considered. A comparison with the classification made in Example 2 is
presented in Figure 2.25b. The main differences are: (i) in the tracing of zones, the first
linked to the geology and the second more related to the administrative units; and (ii)
the thickness of the upper layers, which the first does not consider and should be
introduced in updated versions of the model.
Figure 2.26a shows the distribution of MMI computed with the above mentioned
method (“impedance contrast”) for the earthquake similar to the 1531 already referred
in Example 2 (Figure 2.19). A zoom of Figure 2.19 for the Lisbon County is presented
in Figure 2.26b. It can be observed that the two methodologies lead to important
differences of MMI within the region, even though the overall values are similar. This
shows the significance of the scale as well as the method of analysis.
Buildings were classified in 5 categories, A to F (A being the oldest masonry
construction prior to the strong Lisbon earthquake of 1755, B the post-1755 to 1870
corresponding to the reconstruction, C the 1870-1930 with poor masonry and larger
number of storeys, D the 1930-1960, with introduction of reinforced concrete, E the
1960-1980, with the first codes applying lateral forces, and F the recent reinforced
concrete structures built in the last decade according to the updated seismic code of
actions, RSA, 1983), aggregated into a geographical area corresponding to the parish.
The Lisbon County is divided into 52 parishes, with a resident population of around 0.6
Million. Data on building and population were obtained from the Census 91 at the
parish level, together with other partial inventories to older buildings allowing
corrections of local indexes. It should be referred that when working at towns with a
particular important old stock of buildings, the existing published Building Census does
not cover well this portion of data because all buildings constructed before 1919 are all
in the same class. The building classification used in this Example reflects this
preoccupation and is much more detailed than the Census information.
Vulnerability and fragility functions used to compute damage inflicted were taken from
Coburn and Spence (1992), based on limit states D3 for severe damage and D5 for
collapse. The population present in 5 different periods of the day was obtained from a
study on its mobility. The simulator computes the percentage of damage per typology
in each parish, the number of buildings in class D3 and D5, and the costs of repair based
on average costs for reconstruction per m2, number of storeys and area in plant. It also
estimates the damage to population (deaths, injuries, homeless). Table 2.3 presents the
damage estimation to buildings (average with large dispersion) for four typical
earthquake scenarios affecting Lisbon (Oliveira et al., 2000).
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Carlos Sousa Oliveira
AML
Lisbon City Council
Fig. 2.25a. Detail surface geological units in Lisbon County: A1 – Alluvium, Reclaimed
Land, mainly mud and sand (90 Vs 150 m/s); A2 – Alluvium, Reclaimed Land, mainly
clay and sand (150 Vs 200 m/s); B – Non-cohesive sandy soils and weakly cemented
sandstones (400 Vs 600 m/s); C – Dense non-cohesive soils stiff clays and weak rock
(1000 Vs 1500 m/s); D – Cretaceous limestones and marnly limestones and volcanic
rocks (Vs>1500 m/s) - “Lisbon Council model”
Fig.2.25b. Detail surface geological units in Lisbon County taken from a zoom of
Figure 2.18 of Example 2, “AML model”
Microzonation and Impact Studies
59
Fig. 2.26a. 1531 earthquake scenario – MM Intensities: Detailed soil descriptionsimplified soil analysis (“impedance contrast”), “Lisbon Council model”
Fig. 2.26b. 1531 earthquake scenario – MM Intensities: Zoom of Figure 2.19 for Lisbon
Council; simplified soil description-detailed soil analysis (non-linear 1-D column),
“AML model”
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Carlos Sousa Oliveira
Table 2.3. Total number of damage occurrences in the area of the Lisbon County
Gorringe – 1969+
Epicentral
distance
(km)
150
Tagus Valley (1531)
30
6.5
346
11
Setúbal
20
6.5
808
27
Gorringe – 1755
150
8.5
10214
1236
Scenario
Magnitude
(local)
7.5
Buildings with
D3 (Coburn and
Spence)
1673
Buildings with
D5 (Coburn
and Spence)
61
Damage of type D5 suffered by the building stock in Lisbon for the 1531 scenario is
showed in Figure 2.27, with results similar to the ones referred in Example 2 (Figure
2.23). As referred in relation to MM Intensities, differences within the county are also
important here, due to scale and method.
Fig. 2.27. 1531 earthquake scenario – Total collapsed buildings per parish, “Lisbon
Council model”
Figures 2.28 presents the MM Intensities for the 1755 earthquake, observed (Figure
2.28a) and computed (Figure 2.28b) with the “impedance-contrast” method. The
comparison between the two Figures shows important differences, but the general
pattern can be attributed to the soil influence.
Microzonation and Impact Studies
61
Fig. 2.28a. Observed MM Intensities for the 1755 earthquake (from Pereira de Sousa,
1932)
Fig.2.28b. Computed MM Intensities for the 1755 earthquake (Impedance-contrast),
“Lisbon Council model”
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Let’s now compare the two large earthquakes of 1531 and 1755, as far as soil influence
can be considered. For 1531, the “impedance-contrast” model gives MMI variations
VII to IX, while the historical information indicates a general figure of IX, Figure 2.20,
dropping rapidly to VI westbound. In relation to 1755, Figure 2.28a presents the areas in
downtown Lisbon (Pereira de Sousa, 1932) with higher intensities attaining degree X.
The observed geographical variations, according to Pereira de Sousa (1932), are similar
to the “impedance contrast” model. The 1-D non-linear model for the 1531 is slightly
more discriminative, with values VI to VIII. If now one refers to the recent earthquake
of Jan 24, 1983, with a ML=5.8 at 380 km from Lisbon, the average MMI in Lisbon was
III, with variations from I-II to IV. So, in all cases, a difference of 3 degrees in the MMI
scale is observed.
Looking to the soil profiles in Lisbon, it is generally observed a 2-layer situation with
velocities on the order 250 to 300 m/s and the upper layer and 1000 m/s in the deeper
layer. There is one exception near downtown, where the upper layer is softer, reaching
values of 150 m/s. The thickness of the upper layers varies from 10-12 m in the thinner
cases to 50 m in the referred downtown case. There is also a large portion of the city
directly founded in “hard material”, to the west part of the town.
Fig. 2.29. Predominant frequencies (Hz) in the Lisbon County by Nakamura method
(Teves-Costa et al., 1995)
Frequencies of the first mode, apart the “hard” region, are essentially on the order of 4
to 5 Hz in the eastern part. On the soils bordering the river and along the main small
river outlets downtown, frequencies drop to around 3 Hz to the west of centre
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Microzonation and Impact Studies
downtown and to 1 Hz in the centre where soft material go to depths of 50 m. This
analysis is generally confirmed by field measurements using the Nakamura technique
(Teves-Costa et al., 1995), Figure 2.29. In fact, discounting the high values of 8 Hz in
three points to the northeast part, the general pattern of frequencies agree with the above
description, with the exception of the top centre north where Nakamura shows a lower
frequency. But on the other hand this area coincides with the zone which showed an
increase of intensities to a value of IX for the 1755 event.
Lifelines were studied in detail (Pais et al., 1999) in the context of this project. Ground
motion was transformed into PGV in order to apply the methodology of Isoyama et al.,
1998. Stratigraphy and morphology, to take into account soil and the presence of
valleys, hills, etc., were used to adapt ground motion for lifeline vulnerability analyses
(For more details, see Pais et al., 1999).
2.3.4. EXAMPLE 4. STUDIES AT THE BUILDING BLOCK LEVEL
The information available now at the Lisbon City Council (Câmara Municipal de
Lisboa) contains data from the Census 91 at the level of the statistic sub-section (block
of buildings), organized in a GIS, with digital cartography at 1:1 000 basis. Table 2.4
shows the main numbers related to buildings by statistical sub-sections. Census 91
contains information on the epoch of construction according to 6 typologies, on the
height according to 5 classes, and on the resident population.
Table 2.4. Data on statistical sub-sections, Lisbon County (Census 91)
Variables
Lisbon County
Number of Buildings
61575
Number of statistical sub-sections
3686
Average area of statistical sub-sections
22918 m2
Total area
84,5 km2
Average number of buildings per statistical sub-section
16,7 r 19,8
Using the methodology summarized earlier, the computation of damages to the building
stock from any single earthquake scenario is easily obtained. Figure 2.30 presents the
distribution of severe damage (D3) per sub-section (block) for one earthquake, 270 km
southwest of Lisbon, M=8.5, showing the detail of the obtained results. The system will
allow the estimation of human casualties and injuries, but this topic, exhibiting a great
deal of uncertainty, is not referred here. It also can be used to estimate other
consequential problems related to emergency, such as the volume of debris from
collapsed facades and buildings, or the determination of possible location of
obstructions.
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Carlos Sousa Oliveira
Fig. 2.30. Severe damage (D3 – in % of buildings block by block) inflicted by an event
similar to 1755 in Lisbon County, “Lisbon Council model”
It is interesting to notice that, in a recent work, Giovinazzi and Lagomarsino (2003),
developed a method for obtaining vulnerability functions based on the concepts
supporting the EMS-98 scale (Grunthal, 1998), by using fuzzy theory to interpret
incomplete information in the scale. An application of this method to the Lisbon
County led to approximately the same results as with the 1993 vulnerability curves,
slightly aggravating the older construction (in 10 to 20%, depending on the MMI) and
disaggravating the new construction (on approximately the same amount). This
indicates that both procedures lead to similar results.
In the following, several new refinements to be introduced in the model, at the level of
characterization of the building stock, are briefly referred.
x Using a digital model of the terrain and the level of the roof of each building, one can
estimate the height of the buildings and the corresponding number of storeys.
x The computation of individual areas and lateral discontinuities between adjacent
buildings is of great importance for a more detailed algorithm.
x The information at individual buildings has to be cross-correlated with information
already available at the sub-sections in order to validate the models.
An average vulnerability index can be assigned to a block of buildings, which would
make it possible to propose the definition of a typical block. This concept would be of
most importance for rapid assessment of damage after the occurrence of an event.
Monitoring the performance of various typical blocks could accelerate the process of
estimation of damage, by feeding back this information into the simulator, correcting
the overall picture of damage.
Microzonation and Impact Studies
65
2.4. Final Considerations and Future Developments
Further studies in progress are improving the concept of spectra at the source,
attenuation to the firm stratum beneath each site and propagating the waves to the
surface using more sophisticated models especially when the scale of interest is of great
detail. Calibration with simpler models as described in Example 3 should be done. The
selected pair earthquake source – magnitude is viewed as an event with a certain
probability of occurrence which is given to the operator (Sousa et al., 1997). Other
developments in progress refer to the calibration of capacity curves for the different
typologies. These curves, function of the initial frequency of vibration (given by the
height of the building) and of the non-linear behaviour of the structural system, can be
obtained in a first step by performing “pushover analysis”.
Also the collection of recent earthquakes that struck several areas around the world has
produced a large amount of data on vulnerability of different construction types as well
as of human casualties. This information will for sure increase quite significantly the
knowledge on damage, and will help to calibrate the entire damage estimation process.
The relation with the macroseismic scale should be pursued.
All these refinements are part of this new approach to the problem using the new tools
in the area of GIS and the new findings from recent earthquakes and research. Working
at several scales enriches the knowledge and should be well articulated at all levels.
This coordination of efforts is the only way to maximize the resources in case of
emergency.
A final word to call the attention to the importance of understanding the level of quality
control practiced in a region. This is an essential matter because, if quality control is
not considered in the analysis, the damage estimates may be completely erroneous. The
example of the Turkey earthquake of 17 August, 1999 is extremely clear, as in many
zones damage inflicted to the built stock was essentially attributed to poor quality
control in code enforcement. This is why a correction factor in vulnerability curves has
to be included in countries or regions where there is suspicion that codes are not fully
enforced.
Acknowledgement
This overview chapter corresponds to studies developed by the author for more than one
decade in the area of seismic scenarios in collaboration with two institutions, the
Serviço Nacional de Protecção Civil (SNPC) and Serviço Municipal de Protecção Civil
da Câmara Municipal de Lisboa. Many people have participated in the developments
summarized here, to whom I want to express my sincere acknowledgement:
Dr. A. Campos-Costa, M. L. Sousa and Anabela Martins from LNEC, Lisbon; Isabel
Pais from CNPCE, Lisbon; Fernanda Rocha, Sandra Serrano and Maria Anderson from
SNPC, Lisbon; F. Mota de Sá from “Fuzzy, Ltd”, Lisbon; Prof. Jorge Proença, from
IST, Lisbon; Prof. Paula Teves-Costa from FCUL, Lisbon; “Chiron, Ldt”, Lisbon,
collaborated in software development; and Gonçalo Caiado, Gonçalo Pais, Mónica
Ferreira, Mónica Oliveira and Paula Pestana, former students at IST, brought great
enthusiasm to these matters. This work was partially supported by Fundação para a
Ciência e a Tecnologia, Lisbon, “Programa Pluri-Anual”. Prof. Isabel Viseu helped
revising the final text.
CHAPTER 3
STRONG GROUND MOTION
Mustafa Erdik and Eser Durukal
Bo÷aziçi University, Kandilli Observatory and Earthquake Research Institute
Department of Earthquake Engineering, Istanbul, Turkey
3.1. Introduction
From engineering point of view strong ground motion study is concerned with the
understanding of the characteristics and effects of potentially damaging earthquake
ground motions. For earth sciences strong ground motion investigations provide
information on the source failure process and the near field wave propagation. Today
there exist about 20,000 strong motion instruments operating worldwide, 10% of which
are located in Europe.
With the introduction of performance based earthquake resistant design for buildings
and other civil engineering structures the capability of simulating realistic ground
motions has been indicated. Especially with the recent developments in software tools
and structural modelling techniques for time domain transient non-linear dynamic
analysis, the use of simulated time histories of ground motion gained utmost importance.
Although the use of recorded ground motion under similar conditions with the design
earthquake is appealing, there may never be an adequate suite of such data in terms of
tectonic structure, earthquake size, local geology and near-fault conditions.
This paper will first review the elements of the earthquake source physics important to
the characteristics and modelling of the strong ground motion. The time and frequency
domain characteristics and the attenuation of the strong ground motion will be covered.
An approach for the simulation of the strong ground motion is elaborated with an
example.
3.2. Attenuation
Attenuation relationships are empirical descriptions providing the median and standard
deviation of various intensity measures of the strong ground motion, assumed to be lognormally distributed, in terms of earthquake size, distance, source mechanism and site
conditions.
The moment magnitude is currently the preferred scale for the size of the earthquake.
For the distance parameter distance to fault has gained importance for correlation with
ground motion characteristics. The deviation of the observed from the predicted strong
ground motion (residual) generally fits to a lognormal distribution for up to two
standard deviations. The standard deviation of the predictions is in the order of 0.5
natural logarithm units, corresponding to a multiplicative factor of 1.6 (times the mean
value) to obtain the value, which exceeds 84 % of the data. Large degree of uncertainty
because of other source (near-fault rupture directivity), propagation path (crustal wave
guide), basin response and site effects are not treated as parameters.
67
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 67–100.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
68
M. Erdik and E. Durukal
Shallow earthquakes in active tectonic regions have provided the largest amount of
ground motion data and hence the largest number of ground motion attenuation
relationships. Most of the strong motion data used in attenuation relationships are
obtained from reverse and strike-slip earthquakes. However, due to regional differences
in some of the factors affecting earthquake ground motions, different ground motion
attenuation relationships have been developed for different regions, such as Europe,
Western United States (shallow crustal earthquakes), Eastern United States, and
subduction zones.
Most attenuation relationships are characterized by:
"Distance saturation" where the function slope decreases at close distances, reflecting
the fact that the earthquake is a distributed source, “magnitude saturation" where PGA
increase more gradually with magnitude for large magnitudes, reflecting the fact that
magnitude is not well correlated with PGA. Although the current attenuation
relationships use moment magnitude, various magnitude definitions used in earlier
attenuation relationships should be carefully studied (Figure 3.1). The distance
definitions used in the attenuation relationships also differ especially on near fault
conditions (Figure 3.2). It should also be noted that, ground motions in the near-source
region of earthquakes have certain characteristics not found in ground motions at more
distant sites, especially directivity, as evidenced by a high-energy intermediate-to-longperiod pulse that occurs when fault rupture propagates toward a site. Directivity effect
is currently only indirectly incorporated in the attenuation relationships.
The general for of the attenuation relationships used by the researchers has been of the
following form:
Y = b1 f1(m) f2(r) f3(M, r) f4(P) E
(3.1)
where: Y is the strong ground motion parameter to be predicted,
f1(m) is a function of the earthquake size M, usually given by the form
f1(m)=exp(b2 m),
f2(r) is a function of the distance r, the most common form being
b3
f2(r) = exp(b4 r) (r+b5) ,
where b3 and b4 represent respectively the geometric and anelastic attenuation rates,
f3(M,r) accounts for the possible variation of earthquake size measure with
distance,
f4(P) is the function accounting for the propagation path and site parameters,
E is a random variable representing the uncertainty in Y.
Following is short description of the currently used attenuation relationships.
Boore et al. (1997) PGA and Spectral Acceleration attenuation relationship is based on
the selected strong motion data from western North America. The equations predict the
random horizontal component peak acceleration and 5% damped pseudo acceleration
response spectra in terms of moment magnitude, distance and site conditions for strikeslip, reverse slip or unspecified faulting mechanism. Site conditions are represented by
the shear wave velocity averaged over 30 m. The smoothed coefficients in the
equations for predicting ground motion were determined using a weighted, two-stage
69
Strong Ground Motion
regression procedure. In the first stage, the distance and site condition dependence were
determined along with a set of amplitude factors, one for each earthquake. In the
second stage, the amplitude factors were regressed against magnitude to determine the
magnitude dependence. The general form of the ground motion estimation equation
used in the study is:
ln(Y) = b1 + b2 (M-6) + b3 (M-6)2 + b5 lnr + bV ln (VS / VA)
where:
r = (rjb2 + h2)1/2
(3.2)
(3.3)
In this equation:
Y = peak ground motion measure,
M = moment magnitude M t5.0,
r = closest distance from rupture to the station in km r t 20 km,
rjb = closest horizontal distance from the station to a point in km,
VS = average shear-wave velocity (m/s) to a depth of 30 m,
b1 = parameter related to fault mechanism,
b1SS, b1RS, b1ALL, b2, b3, b5, bV, VA and h are regression coefficients provided in
tabular form.
Campell (1997) study develops empirical attenuation relationships for horizontal and
vertical PGA, PGV, and SA using accelerograms generated by western USA and other
worldwide earthquakes of moment magnitude greater than 5 and sites with distances to
seismogenic rupture within 60 km.
Fig. 3.1. Relationship of the moment magnitude Mw with other well established
magnitude scales (Courtesy of the American Geophysical Union)
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M. Erdik and E. Durukal
Fig. 3.2. Definitions of distance used in the attenuation relationships
For the estimation of PGA values Campbell (1997) uses the following expression:
ln(AH) = -3.512 + 0.904M - 1.328 ln[RSEIS2 + (0 149e0.67M) 2]1/2
+ [1.125 - 0.112ln(RSEIS) - 0.0957M]F
+ [0.440 - 0.171 ln(RSEIS)] SSR + [0.405 - 0.222 ln(RSEIS)] SHR + H
(3.4)
where:
AH = median of the geometric mean of the two horizontal PGA (g)
M = moment magnitude,
RSEIS = the closest distance to seismogenic rupture on the fault (km),
F = 0 for strike-slip and normal faulting earthquakes and 1 for reverse, reverseoblique, and thrust faulting earthquakes,
SSR = 1 for soft-rock sites,
SHR = 1 for hard-rock sites,
SSR = SHR = 0 for alluvial sites,
H = random error term with mean of zero and a standard deviation equal to the
standard error of estimate of ln(AH).
Sadigh et al. (1997) present attenuation relationships for shallow crustal earthquakes
based on strong motion data primarily from California earthquakes. Relationships are
presented for the geometric mean of the two horizontal components, strike-slip and
reverse-faulting earthquakes, rock and deep firm soil deposits, earthquakes of moment
71
Strong Ground Motion
magnitude M between 4 and 8+ and distances up to 100 km. The site conditions
representative of rock attenuation models given here should be accepted as soft rock.
The deep soil data are from sites with greater than 20 m of soil over bedrock.
Attenuation relationships of horizontal Response Spectral Acceleration (5% damping)
are given in two separate equations according to the soil condition. Relationship for
reverse/thrust faulting are obtained by multiplying the given strike-slip amplitudes by
1.2. The general form of the equation for rock sites is as follows:
ln(y)=C1+C2M+C3(8,5-M)2.5+C4ln[rrup+exp(C5+C6M)]+C7ln(rrup+2)
(3.5)
y = PGA or SA (in g) represented by the geometric mean of the two horizontal
components,
C1 to C7 =amplitudes given in tabular form
M = moment magnitude,
rrup =Minimum distance to the fault rupture surface (km).
Ambraseys et al. (1996) attenuation relationship is based on 422 strong motion records
from 157 earthquakes in Europe and adjacent areas. The equations use the larger
horizontal acceleration response ordinate fort 5 per cent damping and give ground
motion in terms of surface wave magnitude, distance and site conditions. Site
conditions are represented by soil classes as rock, stiff soil and soft soil. The ground
motion estimation equation used is of the form:
log(Y) = C’1 + C2 M + C4 log (r) + CASA + CSSS
(3.6)
where:
r = (d 2 + h02)1/2
In this equation;
Y = peak horizontal accelerations in g,
M= surface wave magnitude 4 d M d 7.5,
d = shortest distance to the surface projection of the fault in km,
h0 = a constant determined with C1, C2, C3 and C4,
SA= 1 for stiff soils and 0 otherwise,
SS= 1 for soft soils and 0 otherwise.
The period dependent coefficients C’1, C2, C4, CA, CS and h0 and the error term V are
provided in tabular form.
Figure 3.3 and Figure 3.4 provide comparison of above attenuation relationships with
the strong motion data obtained from 1999 Kocaeli, Turkey Earthquake.
Spudich et al. (1997) collected ground motions from extensional regimes throughout the
world and derived attenuation relationship for PGA and SA in extensional tectonic
regimes using globally obtained data. In general, their values suggest that most other
attenuation models will significantly overestimate ground motions from normal faulting
earthquakes are smaller than for other tectonic regimes.
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M. Erdik and E. Durukal
Fig. 3.3. Comparison of 1999 Kocaeli earthquake data with attenuation relationships,
horizontal accelerations, rock sites (Durukal, 2002)
Fig. 3.4. Comparison of 1999 Kocaeli earthquake data with attenuation relationships,
horizontal accelerations, soil sites (Durukal, 2002)
Strong Ground Motion
73
The predictions in these attenuation relationships at large magnitudes and short
distances are based on rather limited data sets that do not incorporate the data from
Kocaeli, Turkey earthquake (August 17, 1999, Mw=7.6) and ChiChi, Taiwan,
earthquake (September 21, 1999, Mw=7.6). In both earthquakes, the peak ground
accelerations on rock at near-fault distances were below the existing ground motion
prediction equations. Among others, this discrepancy can be caused by low stress drop
and smooth fault rupture with limited asperities. Such variations on the dynamics of
fault rupture are currently treated as random uncertainties in the attenuation
relationships.
3.3. Factors Affecting Earthquake Strong Ground Motions
Findings (i.e. Somerville, 2000) indicate that while the average ground motions from
one large earthquake are similar to those of another, there are conditions that cause the
ground motions to vary significantly from one location to another at the same distance
from a given event. This variability is related to earthquake source process, propagation
and site response.
It has been well recognized that earthquake ground motions are affected by earthquake
source conditions, source- to-site transmission path properties, and site conditions. The
source conditions include the stress drop, source depth, size of the rupture area, slip
distribution, rise time, type of faulting, and rupture directivity. The transmission path
properties include the crustal structure and the shear-wave velocity and damping
characteristics of the crustal rock. The site conditions include the rock properties
beneath the site to depths of up to about few kilometers, the local soil conditions, and
the topography of the site.
3.3.1. EFFECTS OF THE EARTHQUAKE SOURCE
Recorded strong ground motion in the near field incorporates all the heterogeneities,
complex arrivals and the high frequency content of the source process. Patches on the
fault plane with higher slips are called asperities. Asperities are highly stressed regions
surrounded by weak or zero stress zones. The fault plane is then composed of patches
of high stress and low or zero stress, which leads no a non-uniform stress drop during an
earthquake event. Barriers are identified as those portions of the fault plane that do not
rupture. Simple source models assume that main fault rupture parameters (rupture
velocity, rise time and stress parameters) are homogenous and coherent over the plane
of the dislocation.
Seismic Moment, Stress Drop, Effective Stress and the Corner Frequency are the main
parameters of the earthquake source that influences the strong ground motion
characteristics. A short review of these parameters is provided below.
Seismic Moment, M0, is the most recognized measure of the earthquake size given by
the multiplication of the shear modulus (Lame’s constant) of the medium, the average
total dislocation (i.e. mean fault offset or slip) and the area of the dislocation surface (i.e.
fault rupture surface). The seismic moment, M0, is generally regarded as the best
available single number to describe the size of an earthquake and can be estimated from
the low frequency asymptote of the Fourier transform of the displacement seismogram.
The moment magnitude (Mw) is derived from the seismic moment on the basis of the
74
M. Erdik and E. Durukal
following equation (Kanamori, 1977)
Mw = (2/3) log Mo –10.73
(3.7)
Figures 3.5, 3.6 and 3.7 show the accelerograms, corresponding response spectra and
the Fourier amplitude spectra for six records provided by Anderson and Quaas (1988)
for a wide range of magnitudes (3.1 to 8.1). All records have epicentre distances of
about 25 km and are obtained on rock. As it can be seen in Figure 3.5 with increasing
magnitude the amplitudes of ground motion generally increase, and the duration of the
accelerogram rapidly increases. Figure 3.6 and 3.7 show that as the magnitude
increases, the amplitudes of the low frequency waves increase dramatically, while the
amplitudes of the high frequencies increase slowly. In other words, increasing
magnitude results in greatly enriched relative frequency content (higher spectral shapes)
at long periods with an approximately flat acceleration spectrum over a sizeable
frequency band. This flat spectral shape has contributed to the development of models
of strong motion as band-limited white noise.
Fig. 3.5. Accelerograms of six records for a magnitude range of 3.1 to 8.1 (after
Anderson and Quaas, 1988; Reproduced with permission from J.G. Anderson and the
Earthquake Engineering Research Institute)
Stress Drop is the difference between the initial state of the shear stress (before the
earthquake) and the final state of the shear stress (after the earthquake). Stress drop is
about 3 MPa for interplate earthquakes and about 10 MPa for intraplate earthquakes of
moderate and large magnitudes (Magnitude > 5).
Effective Stress is the difference between the initial static stress and frictional stress in
existence during the rupture process.
Corner Frequency is the frequency where the high and low frequency trends of the
Fourier Amplitude Spectrum. It is related to the inverse of the rise time (rate of growth
Strong Ground Motion
75
in dislocation or roughly, time duration of rupture). By measuring the corner frequency
from the Fourier Amplitude Spectrum the apparent duration of faulting at the source and
hence the fault dimension can be estimated. A large magnitude earthquake will
generally have a large fault dimension and hence a small corner frequency, implying a
longer rupture and also strong motion duration.
Fig. 3.6. PSRV of records shown in Figure
3.5 (Reproduced with permission from
J.G. Anderson and the Earthquake
Engineering Research Institute)
Fig. 3.7. Fourier spectra of records
shown in Figure 3.5 (Reproduced with
permission from J.G. Anderson and the
Earthquake Engineering Research
Institute)
3.3.2. SUBDUCTION ZONE AND SHALLOW CRUSTAL EARTHQUAKES
The collision of tectonic plates in subduction zones causes large and deep earthquakes.
Ground motion data from subduction zone earthquakes are associated with slower rate
of attenuation compared to those from shallow crustal earthquakes. Analysis of ground
motion data also indicates that the response spectral shapes obtained from subduction
zone earthquakes have smaller amplitudes in the long-period range than response
spectral shapes from shallow crustal earthquakes.
3.3.3. EFFECTS OF DISTANCE
Attenuation is strongly influenced by distance for both the geometric spreading and the
material damping. Excluding material damping and considering only geometric
attenuation it can be observed that the cylindrical body waves attenuated with inverse of
distance and spherical body waves attenuate with the inverse of the distance squared.
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M. Erdik and E. Durukal
The material attenuation is generally given by the following expression.
exp [-(Sf/Qc) x]
(3.8)
Where f is the frequency, Q is the quality factor that accounts for the material damping,
c is the shear wave propagation velocity and x is the distance to source. Assuming
almost constant Q, it can be seen that the rate of attenuation increases exponentially
with increasing frequency and distance.
The spectral shape of the strong ground motion on competent soil sites indicates
reduction in the high-frequency regions and increase in the low frequency regions with
increasing distance. However, within distances of about 50 km, the effect of distance
on spectral shape is much smaller than the effect of magnitude. The duration of the
accelerogram tends to increase with increasing distance (e.g., Dobry et al., 1978).
3.3.4. EFFECTS OF NEAR SURFACE WAVE PROPOGATION (SITE EFFECTS)
Variability that is introduced into the strong ground motions by effects of wave
propagation in the source to site propagation media are comparable to the complexities
introduced by the source dynamics. Site effects include modification of seismic waves
by the local soil layers, the effect of alluvial basins and effect of local topography. It is
well established that local soil conditions have a major effect on the amplitude and
response spectral characteristics of earthquake ground motions depending on the type
and depth of soil and on the level of ground motion. It was demonstrated by the
dramatic differences in ground motions in Mexico City in the 1985 Mexico earthquake,
in the San Francisco Bay Area in the 1989 Loma Prieta earthquake and in Adapazarı in
the 1999 Kocaeli earthquake.
The soft soils that form low velocity layers near the Earth’s surface trap energy, amplify
all frequencies due to the decrease in seismic impedance, and preferentially amplify
resonant frequencies. Several researchers have shown that for layers of given thickness,
the relative shaking response will be greatest where the surface geologic units have the
lowest impedance values and where the impedance contrast between the surface layer
and the underlying one is the greatest.
For peak ground acceleration, this dependence of amplification on ground motion level
is illustrated by the relationship for soft soil developed by Idriss (1991) shown in Figure
3.8. For peak rock accelerations less than about 0.4 g the ground motions are typically
amplified in soft soils. However, for higher levels of ground motion, higher soil
damping due to nonlinear soil behaviour tends to result in deamplification of peak
ground accelerations (or high-frequency response spectral components). Nonlinearity
in soil behaviour is generally recognizable in differences between site response (defined
by spectral ratios) when peak accelerations exceed about 0.4 g, peak velocity exceeds
30 cm/s, or peak strain exceeds 0.1%. The effects of nonlinearity generally reduce the
amplitudes by decreasing the effective shear stiffness of the sediments and increasing
the hysteretic damping.
Amplification due to topography has been identified in theoretical as well as empirical
studies. The top of isolated hills, elongated crests, edges of plateaus and cliffs are
usually zones of amplification due to diffraction and focusing. The main results are that
the topographic amplification is maximum at the top of the hill, and is maximum at the
77
Strong Ground Motion
frequency at which one shear wavelength equals the width of the hill base. Motions on
the hillsides are not amplified much, and motions around the base of the hill are usually
deamplified with respect to motions far from the hill.
Fig. 3.8. Dependence of amplification-deamplification on peak ground acceleration for
soft soil (After Idriss, 1991; Reproduced with permission from University of Missouri
and Ed. S.Prakash)
3.3.5. BASIN RESPONSE EFFECTS
Surface waves generated by conversion of body waves at the boundaries of sedimentary
basins dominate the ground motion amplitudes at long periods with much longer
durations of strong shaking. In the Kobe earthquake, the zone with the highest damage
is a linear band located at the zone of constructive interference of waves emanating
directly from the fault through the sedimentary basin structure and the other one
refracted into the basin. Other examples come from the Northridge earthquake, where
there was an isolated zone of high damage in Santa Monica basin and from Kocaeli
earthquake where a zone of heavy damage is located in the Adapazarı Basin (Beyen and
Erdik, 2002).
3.4. Simple Earthquake Source Models
To model near field ground motion (Brune, 1970) considered a tangential stress pulse
applied instantaneously to an interior of a dislocation surface (Figure 3.9). The fault
propagation effects are neglected. This stress pulse generates a shear wave along the
direction normal to the dislocation surface (i.e. fault surface). If x represents the
perpendicular distance from the fault surface and H(t) is the Heaviside unit-step
function and E is the shear-wave propagation velocity, the initial time function for shear
stress pulse can be written as:
V (x, t) = V H(t – x/E)
where Vis the effective shear stress (Figure 3.9).
(3.9)
78
M. Erdik and E. Durukal
Fig. 3.9. Brune (1970) dislocation model for s-waves (Courtesy of the American
Geophysical Union)
Ground displacement close to the fault centre in parallel direction to the fault surface, u,
can be obtained through integration:
V = P (Gu/Gx)
at x=0 u = (V/P) E t for 0 < t < T
(3.10)
(3.11)
where P is the Lame’s constant, T is the time required for the waves to propagate across
the fault surface. The initial particle velocity parallel to the fault is:
v = (V/P) E
(3.12)
For V=100 bars (1 x 108 dyn/cm2), P = 3 x 1011 dyn/cm2 and E= 3 km/s the initial
velocity takes a value of v=1m/s, in line with peak ground velocities experienced in
large earthquakes around the world.
Brune (1970) has estimated the maximum ground acceleration as 2g, by assuming a
stress drop of V=100 bars and by considering the contribution of the band of
frequencies between 0 and 10Hz. This value is also in line with the peak ground
accelerations measured in earthquakes. Brune (1970) indicates that the near-field
ground displacement parallel to the fault (Equation 3.11) increases linearly with time
until the effects of the boundaries of dislocation reach to the observation point and then
decrease gradually to zero. This effect is modelled by the following exponential factor:
v (x=0, t) = (V/P) Eexp (-t /W )
u (x=0, t) = (V/P) EW[ exp (-t /W )]
(3.13)
(3.14)
79
Strong Ground Motion
where W is the order of a/Ea being the appropriate fault dimension (dislocation surface)
and, in reality, governs the speed of rise in dislocation displacement to its final value.
For a large t, u(x=0,t) tends to a constant level (final dislocation) given by:
umax= (V/P) EW
(3.15)
The solutions of a static shear crack model with uniform stress drop on the fault plane
can generally be given as (Keilis-Borok, 1957):
D= [V a /P
(3.16)җ
Where D is the average final dislocation, a is the critical dimension of the fault (radius
for a circular fault) and[is a non-dimensional constant, equal to 1.37 for a circular fault.
Through the consideration of Equations (3.15) and (3.16):
Wav ҏ = [ (a/E ҏ
(3.17)
The Fourier amplitude spectrum of the near-field s-wave displacement, UNF (Z), and
acceleration, ANF (Z), can be computed from Equation (3.14).
UNF (Z) = (V/P) EZ Z W2)-1/2
ANF (Z) = (V/P) EZ Z W2)-1/2
(3.18)
(3.19)
The acceleration spectrum given by Equation (3.19) has a constant amplitude of
(VEP in high frequency regionsand and diminishes by (VPWE Zin low frequency
regions. The transition frequency (Zc, corner frequency) between these two regions is
given by 1/W
Zc = 2Sfc = 1/W
ANF (Z) = (V/P) EZ ZZc2)-1/2
(3.20)
(3.21
Figure 3.10 provides a plot of the Brune’s near-field spectrum in log-log coordinates.
As it can be seen the theoretical spectra has a flat high frequency amplitude that cannot
represent the high frequency decay observed in empirical spectra. The dashed line in
the high frequency region of Figure 3.10 illustrates the effect of high frequency
diminution. The important difference is that in Brune’s spectrum has only one corner
frequency whereas a high-frequency corner frequency (Zh=2Sfh) is generally evident
from the empirical spectra. The high frequency decay can be considered to be a
manifestation site effects, attenuation or source properties, such as, decay time of stress
drop or size of the asperities. This high frequency diminution of the spectral amplitudes
can be accounted for with the inclusion of a high frequency filter, with a high frequency
cut-off frequency given by Zh , in Equation (3.21) (Trifunac, 1976).
ANF (Z) = (V/P) EZ ZZc2)-1/2 [Z2h ZZ2h )-1/2]
(3.22
Far field shear wave displacement, u(r,t), from a point shear dislocation in a
homogenous elastic half space (with no energy loss and no surface effects) is given by
(Aki and Richards, 1980):
u (r, t) = [(RPA) / (4SUE3r)] dǯ(t-r/E)
(3.23)
where R is the scaling factor for the angular radiation pattern, Uisthe density of the
80
M. Erdik and E. Durukal
medium, r is the hypocentral distance, dǯ(t) is the time derivative of the average
dislocation on the rupture surface (source time function).
By defining the source time function, d(t), as:
d(t) = D [1- (1+ t/W) exp(t/W)]
(3.24)
and by using the definition of the Seismic Moment (Beresnev and Atkinson, 1997) has
shown that the Fourier Amplitude Spectrum (FAS) of the far field shear wave
displacement (Equation 3.23) becomes:
U(r,Z) = [(RM0) / (4SUE3r)] [1+(ZZc)2]-1
(3.25)
Where |U(r,Z)| is the FAS of the far-field shear wave displacement and Zc (or fc) is the
corner frequency equal to:
Zc = 2Sfc = 1/W
(3.26)
Using the definition of Seismic Moment, M0, it can be shown (Brune, 1970) that the
corner frequency becomes:
Zc = (7S/4)1/2 (Ea) = 2.34 (Ea)
(3.27)
Following (Brune, 1976) the following expression for the far-field shear wave RMS
acceleration spectrum, AFF (r, Z) can be given:
or as
A(r,Z)=R(VE/P)(a/r)[Z/(Z Ea)2)]=R(VE/P)(a/r)[Z/(ZZc2)]
(3.28)
A(r, Z) = RM0 (4SUrE)-1 Z [1+(ZZc)2]-1
(3.29)
where R is the scaling factor for the RMS radiation pattern.
Fig. 3.10. Brune (1970) near-fault s-wave acceleration Fourier amplitude spectrum
(Courtesy of the American Geophysical Union)
Strong Ground Motion
81
Figure 3.11 provides a plot of the Brune’s far-field spectrum in log-log coordinates. As
it can be seen for frequencies less then Zc the spectral amplitudes decay by Z The
spectral amplitudes reach asymptotically to a constant level equal to R(VE/P) (a/r). The
effects of high frequency diminution, not accounted by Equation (3.28), are indicated by
a dashed line in the high frequency regions.
Fig. 3.11. Brune (1970) far-field s-wave acceleration Fourier amplitude spectrum
(Courtesy of the American Geophysical Union)
3.5. Time Domain Characteristics of Strong Ground Motion
Peak ground acceleration (PGA), velocity (PGV) and displacement (PGD) are the most
common and easily recognizable time domain parameters of the strong ground motion.
PGA, PGV and PGD are related to respectively high-, mid- and low-frequency ground
motion components. Maximum recorded peak accelerations vary between 1g and 3g.
Peak ground velocities reaching 4 m/s have been measured in 1999 ChiChi, Taiwan
earthquake.
These parameters are indicated in Figure 3.12 where time history traces of acceleration,
velocity and displacement of the E-W component of the YPT record obtained in the
Aug. 17, 1999 Kocaeli (Mw=7.4) earthquake are illustrated (Erdik, 2001). This is a near
fault record from a major strike-slip earthquake as evidenced by the pulse-like velocity
and permanent displacement. This section will encompass the modelling of root-meansquare (RMS) acceleration, the duration of the strong ground motion and the time
domain envelope functions.
3.5.1. MODELLING OF RMS-ACCELERATION
McGuire and Hanks (1980) have obtained an estimate of the root-mean-square (RMS)
value of the ground acceleration associated with far-field shear waves through an
operation of Parseval’s theorem on the Brune (1970) source model. Hanks and
McGuire (1981) provides this estimate as follows:
82
M. Erdik and E. Durukal
acceleration (cm/s2)
Yarimca East-West
300
250
200
150
100
50
0
-50
-100
-150
-200
-250
-300
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
100
velocity (cm/s)
80
60
40
20
0
-20
-40
-60
-80
displacement (cm)
-100
250
225
200
175
150
125
100
75
50
25
0
-25
-50
0
2
4
6
8
time (s)
Fig. 3.12. Time history traces of acceleration, velocity and displacement of the E-W
component of the YPT record obtained in the Aug. 17th, 1999 Kocaeli (Mw=7.4)
(Durukal, 2002)
arms = 2 R [(2S)2/106] ['V Ur2/3)] [(QE Sfc)]1/2
(3.30)
for cases where the anelastic attenuation of Fourier amplitude spectrum is of the form
exp [(-Sf r) / (Q E)]
(3.31)
In these expressions R is the radiation pattern factor, 'Vis thestress drop, Uis density,
Eis shear wave propagation velocity, r is the hypocentral distance, Q is the so-called
quality factor and fc is the corner frequency.
Defining fmax=[(QE)/(Sr)] and assuming 2R=0.85, Equation (3.30) can be re-written as:
arms = 2 R [(2S)2/106] ['V Ur)] [fmaxfc)]1/2
(3.32)
Aki (1987) has developed a model for the estimation of the RMS value of the ground
acceleration. For a circular dislocation surface the level of the acceleration power
spectrum P0 observed at a distance (r) from the dislocation can be given as (Aki, 1987):
P0 = c W V vr4 ('VP)2 (Er)-2
(3.33)
Where W is the fault width, V is the velocity of the rupture front, and vr is the velocity
of rupture spreading within a circular crack. If the acceleration is band-limited within fc
and fmax, the root-mean-square acceleration arms becomes (Aki and Richards, 1980):
83
Strong Ground Motion
arms = [ P0 2 (fmax-fc)] ½
or approximately
arms = [ P0 2 fmax] ½
(3.34)
(3.35)
Since for California earthquakes of magnitude between 5.5 and 7.2, the cut-off
frequency fmax is nearly constant at about 4-5 Hz (Aki, 1987), the RMS acceleration
amplitudes are mainly controlled by the stress drop.
3.5.2. DURATION OF THE STRONG GROUND MOTION
Duration of a strong ground motion is a function of fault parameters (i.e. size of the
rupturing part of the fault, rupture velocity), path from source to station, local site
effects (soft soil, basin effects) and directivity. Duration of strong ground motion is
also an important parameter playing a direct role in the destructiveness of an earthquake.
A number of proposals exist in the literature for the identification of duration of the
strongest part of shaking (Bommer and Martinez-Pereira, 2000). Perhaps the most
widely used types of strong ground motion duration are the bracketed duration and the
significant duration. The Bracketed Duration is the interval between the two points in
time where the acceleration amplitude first and last exceeds a prescribed level such as
0.03 g (Ambraseys and Sarma, 1967) and 0.05g (Bolt, 1969). Significant Duration,
defined as the time required to build up from 5 to 95 percent of the integral of (³ a2 dt)
for the total duration of the record, where a is the acceleration (Trifunac and Brady,
1975). Arias (1970) showed that this integral is a measure of the energy in the ground
motion acceleration.
Fig. 3.13. Bracketed duration and significant duration using the August 17th 1999
Kocaeli, Turkey earthquake Sakarya accelerogram in the form of a Husid (1969) plot
(Erdik and Durukal, 2003; Reproduced with permission from CRC Press LLC)
84
M. Erdik and E. Durukal
Dobry et al. (1978) have provided an empirical correlation of the “Significant Duration”,
Ts, of strong ground motion with magnitude.
log (Ts)= 0.423 M – 1.83
(3.36)
The correlation is valid for rock sites in Western US and for magnitude ranges
4.5<M<7.6. Duration on soil sites may be up to twice the value for rock sites.
Bracketed duration and significant duration are shown in Figure 3.13 using the August
17 Kocaeli, Turkey earthquake Sakarya accelerogram in the form of a Husid (1969) plot.
The definition of significant duration is based on energy. For records at large distances
from an earthquake source the bracketed duration will have a smaller value than the
significant duration.
Boore (2000) defines the duration of the strong ground motion, Td, by:
Td = Ts + Tp
(3.37)
Where the first term (Ts) denotes the source duration and the second term (Tp) denotes
the path duration. The source duration is given as the inverse of the corner frequency.
3.5.3. TIME DOMAIN ENVELOPE OF THE STRONG GROUND MOTION
The Gaussian white time series of duration Tw is windowed using the shape (coda)
function, w(t), of Saragoni and Hart (1974) as described in Boore (1983).
w(t) = an tb exp(-ct) H(t)
(3.38)
where H(t) is the Heaviside (unit step) function, an is the normalizing factor, b and c are
the shape parameters. Saragoni and Hart (1974) showed that this window is a good
representation of the averaged envelope of squared ground motion acceleration.
3.6. Frequency Domain Characteristics of Strong Ground Motion
In the frequency domain: Fourier amplitude and phase spectrum, power spectrum and
several definitions of response spectra are used in the quantification of strong ground
motion. Response Spectra ordinates present the amplitude of the response of a SingleDegree-of-Freedom system at each frequency (or period). Five types of response
spectra are defined: relative displacement (Sd), relative velocity (Sv), absolute
acceleration (Sa), pseudo-relative velocity (PSV), and pseudo-relative acceleration
(PSA). Frequency content of the response spectrum has been described by Predominant
Period and Mean Period. The predominant period is generally linked to the peak
spectral acceleration at 5% damping. Rathje et al. (1998) defines mean period (Tm) of a
Fourier Amplitude Spectrum as
Tm = 6 Ci 2 / fi) / 6 Ci 2)
(3.39)
where Ci is the spectral amplitude at frequency fi.
The modelling of Fourier amplitude spectrum is of prime importance for simulation.
Both empirical and theoretical models of Fourier amplitude spectra exist. Spectra of
strong ground motion have been empirically estimated through. Trifunac and Lee (1989)
provide empirical models for scaling Fourier amplitude spectra in terms of earthquake
85
Strong Ground Motion
magnitude, source to site distance, site intensity and recording site conditions. These
models are based on the regression of the empirical amplitudes at specific frequencies.
Holistic theoretical models Fourier amplitude spectrum of the ground motion involves
the elements of source, propagation path attenuation, high frequency diminution and site
amplification is illustrated in Figure 3.14.
Fig. 3.14. Elements of the Fourier amplitude spectrum of the earthquake ground motion
modelling (Erdik and Durukal, 2003; Reproduced with permission from CRC Press
LLC)
3.6.1. THEORETICAL MODEL OF FOURIER AMPLITUDE SPECTRUM
Fourier amplitude spectrum of the free field acceleration of the horizontal ground
motion at an epicentral distance (r) caused by the propagation of shear waves from an
earthquake with a point source of slip model is given by (Boore 1983, Atkinson and
Boore, 1998 and Atkinson and Silva, 2000):
A(f,r) = C0 M0 S(f) Y(f,r) P(f) Z(f)
(3.40)
where C0 is the frequency independent scaling factor, M0 is the seismic moment, S(f) is
the source spectrum, Y(f,r) is the attenuation factor, P(f) is the high frequency decay
factor and Z(f) is the scaling factor that accounts for the site effects. For the ideal cases
where Y(f,r), P(f) and Z(f) are not considered A(f,r) will be given by:
A(f,r) = C0 M0 S(f)
(3.41)
Equation (3.41) has the same form and is essentially identical to the Fourier Amplitude
Spectrum of the far-field shear wave acceleration given in Equations (3.28) and (3.29).
S(f) is the “Source Spectrum” that accounts for the spectral model of the radiated waves
from the source. It consists of two parts: the spectral shape and the scaling law (the
relationship between the seismic moment and the corner frequency). One of the
simplest and most commonly used source spectrum with a single corner frequency, fc , is
called the “omega-squared” spectrum, similar to the Brune’s spectral shape
S(f) = (Sf)2 / ( 1 + (f / fc)2 )
(3.42)
The corner frequency and the seismic moment are related (Brune 1970) by the so-called
spectral scaling law:
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M. Erdik and E. Durukal
fc= 4.9 x 106 E( 'V0
(3.43)
where 'Vis in bars (1 bar = 105 Pa) and 0 is the seismic moment in (dyn-cm) and E is
in km/s. The variation of the corner frequency fc with respect to earthquake size can be
seen in Figure 3.15 using records of earthquakes with magnitudes changing between 3.1
and 8.1 and in Figure 3.16 using data from the 1999 Kocaeli, Turkey earthquake.
Fig. 3.15. Variation of the corner frequency fc with respect to earthquake size (after
Anderson and Quaas, 1988; Reproduced with permission from J.G. Anderson and the
Earthquake Engineering Research Institute)
Fig. 3.16. Variation of the corner frequency fc with respect to earthquake size, using
data from the August 17, 1999 Kocaeli earthquake sequence recorded at station Sakarya.
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Strong Ground Motion
Y (f, r) is called the attenuation factor.
Y(f, r) = YG (r) YA(f, r)
(3.44)
YG (r) is the geometric attenuation factor due to geometric spreading of the seismic
energy. At epicentral distances (r) less than about 100km, empirical evidence indicates
a geometric attenuation by (1/r). Atkinson and Silva (2000) states that the geometric
attenuation is proportional to (1/r) at epicentral distances less than 40km but to (1/r)1/2
at epicentral distances greater than 40km.
YA(f,r) is the anelastic attenuation (or whole-path attenuation) factor given by the
following expression:
(3.45)
YA(f, r) = exp [(-Sf r) / (Q E)]
Where Q is the so-called “quality factor” and, at its simplest definition, can be taken as
a constant (Q=Q0).
P(f) in Equation (3.40) serves as the high frequency diminution factor that accounts for
the decay of spectral amplitudes at high frequencies, believed to be caused by the
weathering in the upper layers of the medium. Boore (1983) assigns a fourth order
Butterworth filter for P(f).
P2(f) = [1 + (f/fm)8]-1/2
Anderson and Hough (1984) models P(f) by the spectral decay factor Nas
P1(f) = exp(-SNf)
(3.46)
(3.47)
Z(f) represents the scaling factor to account for the site effects. Boore and Joyner (1997)
provides amplification values as a function of frequency towards the assessment of Z(f)
in terms of typical soil profiles associated with NEHRP (1997) site classes.
Fig. 3.17. Estimation of corner frequency fc and near surface attenuation factor kappa, N
using data from the Nov. 12 Düzce, Turkey earthquake recorded at station Yarımca
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M. Erdik and E. Durukal
An estimation of kappa, Nand corner frequency fc, is presented in Figure 3.17 using
data from the November 12, 1999 Düzce, Turkey earthquake, as it is recorded at station
Yarımca.
3.7. Radiation Pattern and Directivity
Several phenomena observed in strong motion can only be understood in the context of
finite source models involving directivity and near-source pulse motions. The
amplitude and polarity of a seismic wave radiated from an earthquake source change
with the orientation of the source and the receiver. This dependence is called as the
radiation pattern. There is a difference in the radiation patterns of P and S waves for a
point source (Figure 3.18, from Das, 1997). The effect of an extended fault on the
radiation patterns of p- and s- waves can be seen in the same figure as well.
Directivity is the effect of rupture propagation along the fault on the ground motion. It
impacts both the high frequency and the low-frequency accelerograms. Let us imagine
a rupture propagating at a certain velocity along a fault plane. Stations located in the
direction of rupture propagation experience shorter duration ground motions than the
ones located in the direction opposite to the direction of rupture. This is called
directivity. Associated ground motion amplitudes are larger for stations in the forward
directivity region than the ones in backward directivity region due to conservation of
energy. At high frequencies, directivity shows up as a short, intense accelerogram at the
far end of the fault, in contrast with a lower-amplitude, long-duration accelerogram near
the origin of rupture. At high period ranges forward directivity effects at near-fault
locations result in high amplitude velocity pulses.
Fig. 3.18. Radiation patterns for p- and s-waves for a point source (from Das, 1997;
Reproduced with permission from Institute of Engineering Seismology and Earthquake
Engineering, ITSAK)
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Strong Ground Motion
The fault normal component of the ground velocity will generally consist of a full cycle
velocity pulse, which upon integration will not create a permanent displacement.
Whereas, the fault parallel components will generally have half-cycle velocity pulse,
which creates a permanent absolute displacement equal to the fault offset. These effects
can be clearly seen in the acceleration, velocity and displacement time history traces of
Sakarya record of 17.8.1999 Kocaeli earthquake given in Figure 3.19. The station is
located at about 3 km from the fault trace. The rise time of this displacement is about 3s.
1999 ChiChi, Taiwan, earthquake has confirmed that the hanging walls of thrust faults
move much more, and have greater high-frequency ground motions (peak accelerations)
than the footwalls during earthquakes.
Sakarya East-West
acceleration (cm/s2)
400
300
200
100
0
-100
-200
-300
-400
velocity (cm/s)
displacement (cm)
0
90
80
70
60
50
40
30
20
10
0
-10
-20
-30
240
220
200
180
160
140
120
100
80
60
40
20
0
4
8
12
16
20
24
28
32
36
0
4
8
12
16
20
24
28
32
36
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
40
44
48
52
56
60
64
68
72
76
80
40
44
48
52
56
60
64
68
72
76
80
time (s)
Fig. 3.19. Acceleration, velocity and displacement time history traces of the Sakarya
record of 17.8.1999 Kocaeli, Turkey earthquake (Durukal, 2002)
Luco and Anderson (1983) have studied the near-fault ground motions using a simple
theoretical model. The fault is modelled by a finite width, infinitely long vertical strike
slip dislocation. The fault, buried in a homogenous half space, extends from a depth of
zu=2km to zd=10km (as illustrated in the top of Figure 3.20). The p- and s-wave
propagation velocities of the medium are 6 km/s and 3.464 km/s. A step-type
dislocation of amplitude 100 cm propagates horizontally with a rupture velocity of
3.184 km/s along the fault. The rupture front is vertical. Fault-parallel, fault-normal
and vertical acceleration, velocity and displacement time histories at any observation
point along the fault for various distances to the surface projection of the fault are
shown in Figure 3.20 (Anderson and Luca, 1983).
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M. Erdik and E. Durukal
Fig. 3.20. Characterization of near-fault ground motion (after Anderson and Luca, 1983;
Courtesy of the Seismological Society of America)
Strong Ground Motion
91
Fig. 3.21. An empirical model of the ratio of the fault-normal spectral component
amplitudes to average spectral amplitudes (Somerville et al., 1997; Courtesy of the
Seismological Society of America)
As it can be seen the peak amplitudes occur at distances (about 2km) comparable to the
depth of the top of the fault. Figure 3.20 shows prominent velocity pulses in the faultnormal direction. The durations of the acceleration and velocity pulses increase,
especially for fault-normal components, with distance from fault. Fault-normal
displacement and velocities stay approximately constant for fault distances less than the
vertical distance to the top of the fault. The pulse amplitudes are sensitive to the
location of the top of the fault relative to the observation point and inclusion if softer
layers at the top of the half-space can lead to substantial amplifications ranging from 2
to 8 (Bouchon, 1987).
Quantification of rupture directivity effects is an emerging component of attenuation
studies. Somerville et al (1997) have used empirical recordings from shallow crustal
earthquakes in active tectonic regions to illustrate how directivity causes spatial
variation in ground motion amplitude and duration around faults, leading to different
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M. Erdik and E. Durukal
strike-normal and strike-parallel components of horizontal ground motion and to
develop modifications to ground motion attenuation relationships due to rupture
directivity. These variations appear to be significant at a period of 0.6 second, and
Figure 3.19 Acceleration, velocity and displacement time history traces of the Sakarya
record of 17.8.1999 Kocaeli, Turkey earthquake generally grow in size with increasing
period. The spectral acceleration is larger for periods longer than 0.6 second, and the
duration is smaller, when the rupture propagates toward a site. For sites located close to
faults, the strike-normal spectral acceleration is larger than the strike-parallel spectral
acceleration at periods longer than 0.6 second in a manner that depends on magnitude,
distance, and angle.
For design purposes, the variation of the average horizontal response spectra and the
difference between the fault-normal and fault-parallel components of the response
spectra in near-fault conditions becomes an important consideration. Somervillle et al.
(1997) has presented a procedure for the modification of response spectra of near-fault
strong ground motion to account for the rupture directivity. Figure 3.21 (Somerville et
al., 1997) provides an empirical model of the ratio of the fault-normal spectral
component amplitudes to average spectral amplitudes. Models of this ratio are given
for different magnitudes and epicentral distances against period, and for different
magnitudes and periods against distance. As it can be assessed, forward directivity
caused larger spectral amplitudes at periods larger than 0.6s and the ratio of the fault
spectral amplitudes to the average spectral amplitudes can be as high as 1.6 at periods in
the vicinity of 6 s under favourable forward directivity conditions.
3.8. Simulation of Strong Ground Motion
A major goal of strong motion studies is to be able to synthesize strong motion
seismograms suitable for use in engineering analyses. The simulation process is
generally expressed mathematically using a representation theorem. The ground motion
at the site is computed as the integral over space of the contributions (Green’s Function)
from each point on the fault surface. The integration over time incorporates the effect
of the rupture at each point taking a finite amount of time to reach its final value.
Green’s function characterizes the response of the earth to a point source earthquake. In
the summation process of the representation theorem it is used as a building block to
simulate ground motion from a more general source.
Forward modelling in strong ground motion seismology deals with the estimation of
ground motion at the ground surface by modelling the earthquake faulting process, the
earth medium between the earthquake source and the station, and local site effects near
the station, such as modelling of topography, basin structure and soft soil conditions.
There are two types of source models: kinematic and dynamic. In kinematic source
models the slip over the rupturing portion of a fault as a function of fault plane
coordinates and of time is known or given a-priori and it is not a function of stresses
causing it. In dynamic source models on the other hand, slip over the rupturing segment
of a fault is a function of tectonic stresses acting on the region.
Theoretical Green’s Function Models generate synthetic Green’s functions based on
Earth structure models of varying complexity, and combine these with a range of
models of the earthquake source. Empirical Green’s Function Models use records of
Strong Ground Motion
93
small earthquakes as empirical Green’s functions. Seismograms used as empirical
Green’s functions incorporate all the complexities of wave propagation. The limitation
is that the empirical Green’s functions may not have an adequate signal-to-noise ratio at
all the frequencies of interest, may not be available for the desired source-station pairs,
and may originate from sources with a focal mechanism different from the desired
mechanism. One relatively simple model that has been used increasingly to simulate
earthquake rupture and source-to-site wave propagation is the Band Limited White
Noise/Random Vibration Theory. The broad flat portion of the Fourier amplitude
spectrum provides support to model strong motion as band-limited white noise. The
process of constructing a seismogram with this model begins with generating a whitenoise time series, applying a shaping taper in the time domain to match the envelope of
the expected strong motion, and then applying a band-pass filter in the frequency
domain to mould the Fourier spectrum to the expected spectral shape.
For simulation of ground motion deterministic, empirical (e.g. Hartzell, 1978), semiempirical (e.g. Irikura, 1983; Somerville et al., 1991), stochastic (e.g Boore, 1983;
Silva et al., 1990) and hybrid methods have been proposed and are being widely utilized.
The recent trend and need in the earthquake engineering community is towards a
simulation technique that will incorporate broadband ground motions of longer period,
directivity effects and also higher frequencies.
3.8.1. STOCHASTIC SIMULATIONS
Stochastic approaches to the simulation of strong ground motion filter and window the
white-noise time series according to seismologically determined average spectra and
duration (Boore, 1983). Stochastic simulations for point source earthquakes are an
“Engineering” approach to the simulation of strong ground motion. Ground
acceleration modelled as a filtered Gaussian white noise modulated by a deterministic
envelope function (Safak, 1988). The filter parameters are determined by either
matching the empirical properties of the spectrum of the strong ground motion (e,g,
Trifunac and Lee, 1989), theoretical spectral shapes (i.e. Kanai-Tajimi Spectrum,
Housner and Jennings, 1964) or are determined on basis of reliable physical
characteristics of the earthquake source and propagation media (e,g. Hanks and
McGuire, 1981; Boore, 1983). The Fourier amplitude spectrum model used in the latter
stochastic simulations is essentially S-wave ground motion spectra based on the farfield model of Brune (1970). It has been found to satisfy main parameters of high
frequency ground motion for earthquakes within a wide magnitude range (McGuire and
Hanks, 1980).
The stochastic simulation of strong ground motions that relies on seismic source physics
has found substantial applications in Earthquake Engineering with successful
comparisons of predicted and recorded data. Boore (1983) developed a so-called Band
Limited White Noise model for stochastic simulation of strong ground motion with
seismological constraints. In the time-domain procedure, elaborated in Boore (1983), a
Gaussian white noise is windowed with a shaping function having a prescribed duration.
The window is chosen such that the mean level of the spectrum of the windowed white
noise is unity. The windowed time series is transformed into the frequency domain. Its
Fourier amplitude spectrum is scaled to the square root of the mean squared absolute
spectra and multiplied by the site-specific shape of the theoretical Fourier amplitude
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M. Erdik and E. Durukal
spectrum of the free field acceleration of the horizontal ground motion at the site, A(f,r),
given by Equation (3.40). Transformation back into time domain results in the
simulated (synthetic) time history of the horizontal component of the ground motion.
Software developed originally by Dr. Erdal Safak of USGS (Pasadena, California) with
modifications by the authors of this paper will be used to provide some examples for the
simulation of strong ground motion from point sources. The software is written in
MATLAB (http://www.mathworks.com) language and follows, almost exactly, the
time-domain procedure developed by Boore (1983) and coded in Boore (2000).
For the example simulations the spectral constants are taken as: Soil density = 2.8
g/cm3; Shear wave velocity = 3.6 km/s; Partition factor for energy = 0.707; Factor for
radiation pattern = 0.55; Factor for free surface amplification = 2
For geometric spreading a simple r -1 model is assumed. A single corner frequency Z2model is used for the spectral shape (Section 3.6.1, Equation 3.42). The frequencydependent Q model for the whole-path attenuation is taken identical to the model used
by Boore (2000) for Western US. Source duration is taken equal to the inverse of the
corner frequency and the path duration is modeled as 5% of the epicentral distance. An
exponential time windowing function is used. The high frequency diminution function
(Section 3.6.1) is modeled by a fourth order Butterworth filter with a cut-off frequency
of fm =50Hz and a spectral decay factor N=0.035 (Anderson and Hough, 1984).
One of the simulations of ground acceleration for a Mw=7.6 earthquake at 20km
epicentral distance is provided in Figure 3.22 together with the match of the averaged
Fourier amplitude spectra of 20 simulations with the target spectra. An example
simulation and the match of simulated and target spectra are provided in Figure 3.23 for
the same earthquake (Mw=7.6) but at an epicentral distance of 100km.
Fig. 3.22. A stochastic simulation of horizontal ground acceleration and the comparison
of average simulated and theoretical Fourier amplitude spectra (Mw=7.6 earthquake at
20km epicentral distance) (Erdik and Durukal, 2003; Reproduced with permission from
CRC Press LLC)
Beresnev and Atkinson (1997) have developed a procedure (FINSIM) for the stochastic
simulation of strong ground motion from finite-fault ruptures. The fault rupture plane is
modelled with an array of sub-faults. The radiation from each sub-fault is modelled as a
Strong Ground Motion
95
point source with a Z2-spectrum, similar to Boore (1983). Fault rupture initiates at the
hypocenter and spreads uniformly along the fault plane with a constant rupture velocity
triggering radiation from sub-faults in succession. Simulations from each sub-fault,
properly lagged and summed at the observation point, provide the simulation of ground
motion from the modelled finite fault rupture. The size of the sub-faults controls the
overall spectral shape at medium frequencies. The total number of sub-faults is
controlled by the constraint that the total seismic moment of the sub-faults must be
equal to the target seismic moment.
To provide an example for stochastic simulation of strong ground motion from finite
fault ruptures, the accelerations recorded by near-field stations during the Aug. 17, 1999
(Mw=7.4) Kocaeli (Turkey) earthquake will be simulated using the code FINSIM
developed by Beresnev and Atkinson (1997).
Fig. 3.23. A stochastic simulation of horizontal ground acceleration and the comparison
of average simulated and theoretical Fourier amplitude spectra (Mw=7.6 earthquake at
100km epicentral distance) (Erdik and Durukal, 2003; Reproduced with permission
from CRC Press LLC)
An isometric view of the fault rupture plane, location of the epicenter and the recording
stations Yarımca, øzmit and Adapazarı are indicated in Figure 3.24. The geometry of
the fault rupture plane and the relative distribution of slip have been adopted from the
slip model developed by Yagi and Kikuchi (2000) for the Kocaeli earthquake. The fault
dislocation is modelled as a 110 km long and 20 km deep vertical plane with sub-faults
of size 5km x 5km. Rupture velocity is 2.7 km/s.
For the whole-path attenuation a crustal Q model of Q(f) = 180 f 0.45 is adopted as
reported by Atkinson and Silva (2000) for Western US. For site amplification a
frequency-dependent amplification function values provided by Boore and Joyner (1997)
using the NEHRP site class for each station is used. As for the near surface attenuation
we used the kappa (N) values of 0.07, 0.05 and 0.03 respectively for the Yarımca, øzmit
and Sakarya stations. The factor that controls the strength of subfault radiation (sfact) is
1.5 for simulations in øzmit and Sakarya stations and 2.0 in Yarımca. A Saragoni and
Hart (1974) based envelope function is used for radiation from sub-faults similar to
Boore (1983).
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Fig. 3.24. Fault rupture geometry, hypocenter and the location of the recording stations
in 17.8.1999 Kocaeli (Mw=7.4) earthquake (Durukal, 2002)
Fig. 3.25. Simulated accelerations and velocities at stations Yarımca, øzmit and Sakarya
for Kocaeli earthquake using code FINSIM (Durukal, 2002)
Simulated accelerations for stations Yarımca, øzmit and Sakarya are presented in Figure
3.25. Spectral accelerations averaged over five simulations can be seen in Figure 3.26.
For comparison, we also show empirical spectral accelerations from (August 17, 1999
earthquake) in the same figure. With the model it was possible to get a very satisfactory
fit of spectral accelerations with the recorded data (Figure 3.26).
97
Strong Ground Motion
Yarimca
average response spectrum over 5 trials
1.000
spectral acceleration (cm/s**2)
500
100
50
Yarimca simulated
Yarimca EW, recorded
Yarimca NS, recorded
10
0.1
1
10
100
freq (Hz)
Izmit
average response spectrum over 5 trials
1.000
spectral acceleration (cm/s**2)
500
100
50
Izmit, simulated
Izmit EW, recorded
Izmit NS, recorded
10
0.1
1
10
100
freq (Hz)
Sakarya
average response spectrum over 5 trials
1.000
spectral acceleration (cm/s**2)
500
100
50
Sakarya, simulated
Sakarya EW, recorded
10
0.1
1
10
100
freq (Hz)
Fig. 3.26. Comparison of simulated and recorded acceleration response spectra (Durukal,
2002)
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M. Erdik and E. Durukal
Peak accelerations are somewhat lower than the recorded ones. Simulated peak
horizontal accelerations are 226 cm/s2, 186 cm/s2 and 334 cm/s2 for Yarımca, øzmit and
Sakarya stations respectively. The code FINSIM inherently cannot account for the
differences in the ground motion as a result of polarity. Calculated peak accelerations
are to be considered horizontal accelerations. Therefore it is believed that the calculated
accelerations are satisfactory. Respective velocities calculated from the accelerations
using a polynomial baseline correction are 28 cm/s, 21 cm/s and 25 cm/s for stations
Yarımca, øzmit and Sakarya.
3.8.2. HYBRID SIMULATIONS
3-D finite difference method, discrete wave-number method, indirect boundary element
method, modal summation method, ray theory, 2.5-D discrete wave number-boundary
integral equation method, 2.5-D pseudo spectral method and 2.5-D finite difference
method have been used for deterministic simulation of strong ground motion.
Essentially deterministic methods convolve the source function with synthetic Green’s
functions to produce the motion at ground surface.
Deterministic theoretical predictions of the ground motion can be achieved by
convolution of the Green’s Functions and the slip function. Green’s functions can be
calculated through empirical and synthetic means. Although certain predictions can be
made for the total slip and the mode of faulting no prediction can be made regarding the
rupture characteristics. This necessitates the consideration of different rupture models.
Such deterministic predictions cannot be extended into the frequency regions above
around 1Hz, since, high frequency ground motions are controlled by the heterogeneities
in the fault rupture, which cannot be a-priori accounted for in a deterministic manner.
This requires either the use of stochastic source models or the stochastic treatment of
the high frequency components in the ground motions. Thus hybrid procedures are
developed for simulation of strong ground motion, which address the low and high
frequency components of the ground motion separately and than combine the two
motions.
In the hybrid broadband simulation procedure adopted by Somerville et al. (2000) the
source is represented by an empirical source time function. For simulations of ground
motion for frequencies below 1Hz a theoretically rigorous representation of radiation
pattern, rupture directivity and wave propagation effects are incorporated in Green’s
function computations. At higher frequencies stochastic simulation techniques that
includes source radiation pattern and scattering in the path and site is utilized.
In a recent paper Erdik and Durukal (2001) applied a hybrid method to simulate strong
ground motion for a container port facility near the Sapanca segment of the North
Anatolian Fault. Low-frequency ground motion (DC-1Hz) calculated with the help of
the discrete wave number method is combined with the stochastically simulated high
frequency components using the methodology proposed by Boore (1983). The basic
tenets of the simulation procedure were chosen to: (1) Preserve the deterministic
displacement shape; (2) Satisfy the corresponding theoretical Fourier Amplitude
Spectrum and; (3) Yield a coda shape in conformance with applicable empirical
findings. Furthermore, the peak ground acceleration (PGA) and the pseudo spectral
relative velocity (PSRV) values should be favourably compared against those obtained
from empirical attenuation relationships for conformity. The essential elements of the
procedure were:
Strong Ground Motion
99
1. Assessment of the source parameters of the DBE motion associated with the
corresponding return period for specific conditions of site and seismicity.
2. Deterministic assessment of the low frequency (DC-1Hz) ground motion, at the
outcrop of a reference soil layer, due to rupture of seismic faults.
3. Use of a Boore (1983)-type stochastic simulation method to complement the
deterministic low frequency ground motion with high frequency (1Hz-50Hz)
components.
4. Combination of the two parts of ground motion to yield a site-specific
simulation for a frequency range of DC-50Hz.
5. Site response analysis, if required, to include the local wave propagation effects
in the soil media above the reference soil layer.
Time (s)
Fig. 3.27. Simulated low-frequency ground motion on competent soil (Bi-lateral rupture
on Sapanca segment) (Erdik and Durukal, 2001)
The design basis simulation is assumed to be controlled by the bi-lateral rupture of one
of the segments of the North Anatolian Fault (the 70km x 15km Sapanca Segment).
Haskell type ramp function is considered as the slip function with a rupture velocity of
2.8 km/s, 1s rise time, 1.5m final strike slip and 0.05m final dip slip. Figure 3.27
provides the simulated low frequency (less than 1Hz) fault-parallel, fault normal and
vertical velocity and displacements. The final broad-band hybrid simulations that
involve the combination of low and high frequency (stochastic) simulations at the
competent soil outcrop are given in Figure 3.28. These simulations were performed
prior to the 17.8.1999 Kocaeli earthquake that essentially hit the same region and site
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with same design earthquake level. Considering that the simulations also represent a
“blind-test”, comparison of simulated and recorded accelerations, velocities and
displacements, as well as of spectral accelerations, provide a remarkable fit to the
simulations (Erdik and Durukal, 2001).
Fig. 3.28. Hybrid simulation of broad-band strong ground motion on competent soil (Bilateral rupture on Sapanca segment) (Erdik and Durukal, 2001)
3.9. Conclusions
The availability of empirical strong ground motion data will always be less that what
would be needed to meet the needs of a variety of ever demanding engineering
problems. A set of strong ground motions, either recorded or theoretically simulated, is
the necessary database for the civil engineering design, regarding both new construction
and performance assessment of the existing built environment. The future of
performance based earthquake resistant design and sophisticated non-linear dynamic
analysis will rely on the development of analytical tools that can simulate realistic
ground motions in terms of tectonic structure, earthquake physics, local geological and
geotechnical conditions. This need is more acute for large magnitude earthquakes in
near-field conditions. The state-of-the art and success in strong ground motion
simulation is developing at a fast rate and we all hope that it meets the demand in
foreseeable future.
CHAPTER 4
GEOPHYSICAL AND GEOTECHNICAL INVESTIGATIONS FOR GROUND
RESPONSE ANALYSES
Diego Lo Presti, Carlo Lai, and Sebastiano Foti
Department of Structural and Geotechnical Engineering
Politecnico di Torino, Italy
4.1. Introduction
Seismic response analyses require thorough geophysical and geotechnical investigations
in order to assess the mechanical and geometrical parameters of the system. Planning
and selecting appropriate geophysical and geotechnical investigations are delicate tasks
that require a deep knowledge of available techniques. This chapter discusses in situ
and laboratory tests with particular focus on the following aspects:
- comparison of different laboratory tests (monotonic and cyclic triaxial tests, resonant
column tests, cyclic torsional shear tests);
- comparison of different geophysical testing methods (invasive and non-invasive
tests);
- interplay between geological, geophysical and geotechnical investigations.
Main objectives of the chapter are i) to point out the multi-disciplinary character of
seismic response studies and ii) to highlight capabilities and limitations of different in
situ and laboratory testing methods. The chapter ends with a brief description of the
lesson learnt from a case history.
Ground response analysis is a multi-disciplinary task involving various types of
professional competencies including engineering seismology, structural geology,
geophysics, geotechnical earthquake engineering. In fact, the whole process requires
the implementation of the following activities: i) definition of the expected ground
motion at the outcropping rock, ii) assessment of the geo-morphological features of the
area under study and iii) determination of the mechanical properties of the soil deposit
and of the underlying bedrock by means of geophysical and geotechnical investigation
campaigns. Ground response analysis is used to predict the design ground motion at a
site for seismic microzoning or alternatively to evaluate the seismic stability of slopes
and earth structures. The main purpose of microzonation is to provide the local
authorities with tools for assessing the seismic risk associated with the use of lands as
well as to estimate the seismic motion to be used in the design of new structures and/or
retrofitting existing ones.
The main focus of this chapter is on the geological, geophysical and geotechnical
investigations that need to be carried out when performing studies of microzonation.
Planning of such investigations depends primarily on the definition of following aspects
of the problem:
x Geology and geo-morphology of the area under study
101
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 101–137.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
102
D. Lo Presti, C. Lai, and S. Foti
x Kinematics of the wave-field and type of analysis concerning the geometry (1D, 2D,
3D)
x Constitutive modelling of the subsurface
Concerning the first aspect and the associated geometry of the problem, in the absence
of topographic irregularities and of deep geological structures, 1D-solutions yield
reasonable results and therefore are often used. In other cases 2D or 3D solutions are
required. The shape of the boundaries of non-consolidated sediment valleys as well as
of deeper geologic structures introduce additional wave field effects such as generation
of surface waves which tends to increase the amplitude as well as the duration of ground
motion (Dobry and Iai, 2000). These effects cannot be taken into account by simple 1D
or 2D modelling which considers only vertically incident plane wave (Riepl et al., 2000).
In these cases or when the kinematics of the problem cannot be represented by
vertically incident shear waves, a more complex wave field need to be considered which
includes both non-vertical impinging body waves rays and surface waves. As far as
constitutive modelling of geomaterials is concerned, current soil models can be divided
in three main families: equivalent linear models, simplified cyclic non-linear models,
advanced cyclic non-linear models. Of these families, equivalent linear and simplified
cyclic non-linear models are the most commonly used because of their simplicity of
implementation and ease of determination of the constitutive parameters. On the other
hand, advanced cyclic constitutive models use fundamental principles of continuum
mechanics to describe complex aspects of soil behaviour such as strain localization and
instability. Furthermore these models are applicable to a wide variety of initial stress
and drainage conditions, stress/strain paths, stress/strain magnitude etc. Unfortunately
the implementation of these models is generally complex and the calibration of their
constitutive parameters is not simple. For this reason, the use of advanced constitutive
models in geotechnical earthquake engineering practice is still limited. Some key
aspects of equivalent linear and simplified cyclic non-linear models will be illustrated in
the next section together with a brief illustration of the techniques used to solve the
dynamic equations of motion.
4.2. Mechanical Behaviour of Geomaterials
The mechanical response of geomaterials to earthquake loading can be modelled using a
large variety of constitutive models. A detailed description of the capabilities and
limitations of each of these models is beyond the scope of this work. Instead it will be
made reference for simplicity to the framework of soil behaviour proposed by Jardine
(1985, 1992, and 1995). Jardine's qualitative model considers in addition to the State
Boundary Surface (SBS, Y3), two other kinematic sub-yield surfaces (Y1 and Y2 ) which
are located inside the SBS and are always dragged with the current stress point. On the
contrary the SBS is relatively immobile so that any sharp change of the Effective Stress
Path (ESP) from the Y3 inwards leaves its position unchanged except in soils with
highly developed fabric in which the collapse of the structure can cause the SBS to
contract.
The essential features of this model are shown in the p'-q plane (Figure 4.1), that can be
divided into three distinct zones in order to match the behaviour of a large variety of
soils and soft rocks, which has mainly been observed in monotonic and cyclic triaxial
(TXT) and torsional shear (TST) tests.
Geophysical-Geotechnical Investigations
103
Fig. 4.1. Qualitative stress-strain behaviour of soils (Jardine 1985, 1992, 1995;
Reproduced with permission from Balkema)
Zone 1: within this zone, for all practical purposes, the soil exhibits a linear stress-strain
response. Soil deformability mainly depends on soil structure and state. The latter can
be conveniently expressed by the void ratio and effective geostatic stresses
(Jamiolkowski et al., 1995; Tatsuoka and Shibuya, 1992; Tatsuoka et al., 1995a).
Therefore, the Young's modulus E0 and shear modulus G0, within this zone, can be
regarded as the initial stiffness of the relevant stress-strain curves for a given soil. Both
these moduli, if properly normalised with respect to the void ratio and effective stresses,
are independent of the type of loading (monotonic or cyclic), applied shear strain level,
number of loading cycles N and exhibit a negligible dependence on the strain rate and
the stress/strain history. Energy dissipation, within this zone, is mainly due to frictional
losses between soil particles and fluid flow losses due to the relative movement between
the solid and fluid phases, and exhibits a strong dependence on the loading rate or
loading frequency (Tatsuoka et al., 1995b; 1997). The limits of the “linear” zone are
l
defined by the so-called linear threshold strain Ht (Vucetic, 1994; Jamiolkowski et al.,
1995). For young uncemented soils the linear threshold strain ranges in between
Htl 0.0007 ÷ 0.002% (Jamiolkowski et al., 1995). Aging, cementation and other
l
diagenetic processes increase Ht up to one order of magnitude (Tatsuoka and Kohata,
1995; Tatsuoka et al., 1997). The linear threshold strain also increases with strain rate
or frequency (Isenhower and Stokoe 1981, Tatsuoka and Shibuya, 1992; Lo Presti et al.,
1996; 1997). Such an increase is due to the fact that the size of the “linear domain” in
the q - p' space (see Figure 4.1) is to a certain extent rate dependent, especially in the
case of fine granular soils. With regard to constitutive modelling, it is reasonably to
assume that within Zone 1 soils behave like linear viscoelastic solids.
104
D. Lo Presti, C. Lai, and S. Foti
l
Zone 2: When soil is strained beyond Ht the ESP penetrates into Zone 2 (Figure 4.1).
In this zone the stress-strain response becomes non-linear. Consequently the secant
stiffness G and E depend not only on the current state of the soil but also on the
imposed shear stress or strain level. Moreover G and E are influenced by many other
factors such as strain rate, ageing, OCR, recent stress history, direction of the applied
ESP, etc. The decay of E and G for increasing strains generally does not exceed 2030% of their initial value. Moreover, in cyclic tests, the stiffness is only moderately
affected by the number of loading cycles and after few cycles the stress-strain response
becomes stable. This indicates that the plastic strains inside Zone 2 are negligible and
therefore the soil behaviour can be modelled as non-linear viscoelastic. The boundary
between Zones 2 and 3 can again be defined in terms of the strain level, which is called
the volumetric threshold strain Htv (Dobry et al., 1982). The volumetric threshold strain
p
coincides with the onset of important permanent volumetric strains (Hv ) and residual
excess pore pressure ('u) in drained and undrained tests respectively. The values of Htv
l
are at least one order of magnitude higher than those of Ht (Vucetic, 1994; Stokoe et al.,
1995; Dobry et al., 1982; Chung et al., 1984; Lo Presti, 1989). Moreover, the values of
Htv are influenced by the following factors and phenomena: creep, moderate cyclic
v
loading at strains larger than Ht , overconsolidation ratio or prestressing, direction of the
stress path and strain rate (Tatsuoka et al., 1997).
Zone 3: When the deformation process engages Y2, the soil starts to yield and the plastic
deformations become important. As the ESP proceeds towards the State Boundary
Surface (SBS) that coincides with Y3, the ratio of the plastic shear strain to the total
shear strain increases approaching values close to unity at Y3. In Zone 3 the stress-strain
response of soils becomes highly non-linear. G, E and D depend to a great extent on the
shear stress and strain level. Factors such as strain rate, creep and OCR greatly
influence the magnitudes of these parameters. Moreover, the stress-strain response to
cyclic loading is no longer stable and a continuous degradation of the mechanical
properties of soil is observed. In the case of undrained cyclic loading of granular soils,
this leads to a continuous accumulation of the pore pressure and eventually to
liquefaction. Within this zone appropriate soil modelling requires the adoption of
constitutive models based on viscoplasticity theories.
Figure 4.2 summarises some of the concepts that have been previously discussed,
showing, for different strain intervals, the essential features of the stress-strain
behaviour, the main influential factors, the constitutive model and the method of
analysis.
The soil parameters needed for the models considered in the present chapter are the
following:
x the small strain shear modulus G0. It can be obtained from i) the velocity of
propagation of shear waves VS according to the well-known formula G0 = U Vs2
with U= mass density; ii) the slope of unload-reload loops at very small strains
(less than 0.001%); iii) the initial slope of the stress-strain curve obtained for
monotonic loading at very small strains (less than 0.001%);
x the small strain Young modulus E0 or the small strain bulk modulus (K0) or the
small strain constrained modulus (M0) or the Poisson ratio (v0);
105
Geophysical-Geotechnical Investigations
10 -5
Shear Strains
10 -4
Small
Medium
10 -3
10 -2
10 -1
Large
Failure
J et
Linear elastic
J vt
Non-linear elastic
Elasto-plastic
Failure
Cyclic loads
Loading rate
Model
Linear
Viscoelastic
Non-linear
Visco-elastic
Elasto-plastic
with damage
Analysis
Method
Linear
Linear
equivalent
Time integration
Level of
deformation
Foundation of vibrating machines
Earthquakes
Nuclear explosions
Fig. 4.2. Soil behaviour - Constitutive models and methods of analysis - Strain levels
(modified after Ishihara, 1996; Reproduced with permission from Oxford University
Press)
x the small strain damping ratio D0. In principle, two values of the damping ratio,
from compression and shear tests, should be determined. Typically these two
values results experimentally almost coincident (Tatsuoka et al., 1995b);
x if adopting equivalent linear models the (G - J) and (DS - J and (E – H) and (DE – H)
curves should be determined to characterise the variation of stiffness and damping
ratio with strain level. If a constant Poisson ratio is assumed, only the (G - J) and
(DS - J) degradation curves are required.
x if adopting simplified cyclic non-linear models the following pieces of information
are required: i) the so-called “backbone” curve needed to describe the stress-strain
curve for monotonic loading; ii) a “rule” to simulate the unloading-reloading
behaviour and stiffness degradation as the seismic excitation progresses (Masing,
1926; Idriss et al., 1978; Tatsuoka et al., 1993). For 1D problems both in geometry
and kinematics, the definition of simplified cyclic non-linear models is
straightforward.
The parameters previously introduced can be determined from undrained tests and
typically they are used in total stress analyses. Effective stress analyses require the
106
D. Lo Presti, C. Lai, and S. Foti
experimental evaluation of pore pressure build-up with strain level and number of
loading cycles. Alternatively, it is possible to implicitly account for the effects of porepressure build-up by determining experimentally the corresponding degradation of soil
properties.
In order to complete the model for ground response analysis, it is finally necessary to
i) specify the spatial variation, within the domain considered in the analysis, of the soil
parameters previously defined, and ii) prescribe the location of the bedrock where the
ground motion is specified together with its mechanical properties.
4.3. Laboratory Tests
Assessment of soil non-linearity is mainly achieved with laboratory tests on undisturbed
or reconstituted samples. The influence of disturbance or destructuration on the
normalised G/G0 -J and D -J curves is not fully understood and contradictory results
have been published in the literature. The use of high quality samples and the
improvement of sample quality are therefore the only possibilities of obtaining more
reliable parameters.
4.3.1. TRIAXIAL TESTS
Triaxial tests are typically performed on cylindrical specimens with height to diameter
ratio H/D ranging between 2.0 and 2.5. The total stress-path during cyclic or monotonic
compression loading triaxial tests is shown in Figure 4.3 together with the scheme of the
apparatuses in use at the geotechnical laboratory of Politecnico di Torino.
The difference between the total stress-path of a triaxial test and that induced by an
earthquake is well recognised. Indeed, the loading history induced by an earthquake
can be decomposed into harmonic shear stresses. Hence the stress-path experienced by
the specimen during a resonant column or torsional shear test is more representative.
Indeed, due to the anisotropic behaviour of soils, it is expected a different stress-strain
response under different stress-paths. Nevertheless, the triaxial test offers some
advantages in comparison to other laboratory tests. In particular, triaxial tests can be
easily performed under stress or strain control and there is no limit in the maximum
achievable strain.
In the last 15 years the triaxial apparatus has been deeply innovated and enhanced.
Some of these innovations are fundamentals in order to obtain accurate stress-strain
measurements. In particular, the following requirements are extremely important:
- local strain measurements are always preferable and are strongly recommended for
any kind of soil. In particular, local strain measurements are imperative when testing
hard soils or soft rocks that usually exhibit very small strains during the
reconsolidation to the in situ geostatic stress;
- end capping is strongly recommended for hard soils and soft rocks;
- LDTs (Goto et al., 1991) have proved to be very effective in the measurement of
local axial strains of hard soils (gravels, sands) and soft rocks. In the case of clay
samples, the use of submersible LVDTs or proximity transducers seems to be
preferable. The ability to re-setting the sensor position from outside the cell
(Fioravante et al., 1994) can be very useful;
107
Geophysical-Geotechnical Investigations
Load
Piston
Air Cilinder
Piston
stop
Top
plate
Cap
external
LVDT
Counter-weight
Supports
Base
Base
plate
Supports
Load
cell
Local
LVDT
Local
proximity
transducers
(b)
Load
cell
t
D
Monotonic
digital device
Cyclic
a
(a)
KCV'VC
V'VC
s'
(c)
Fig. 4.3.Triaxial apparatus: (a) scheme; (b) cell structure; (c) stress path
- a cell structure with very low compliance and a loading ram virtually frictionless are
also critical (Tatsuoka, 1988);
- the actuator resolution and its ability to apply a given constant strain rate is another
essential feature of laboratory testing that should be carefully considered. The
actuator should also be able to apply small and large cyclic loading under
displacement control without backlash. Two examples of system having these
characteristics can be found in the literature. Tatsuoka et al. (1994) used an
analogous motor with Electro-magnetic clutches to change the direction of loading
ram motion without backlash. Shibuya and Mitachi (1997) used a digital servomotor
to control a minimum axial displacement of 0.00015 micrometer spanning over
several orders of the rate of axial straining.
108
D. Lo Presti, C. Lai, and S. Foti
4.3.2. RESONANT COLUMN AND TORSIONAL SHEAR TEST
The Resonant Column (RCT) gives a very accurate and repeatable estimate of the small
strain shear modulus. Recently, the measurement of shear wave velocity in the
laboratory by means of piezo-ceramics, called bender elements, has become popular.
This measurement is quite inexpensive and can be performed repeatedly during a
triaxial or torsional shear test; however, the results do not have the same repeatability
and accuracy of the RCT. The main drawbacks of RCT are the following:
- RCT uses very high frequencies and consequently the sample is subjected to very
high strain rates. Equivalent strain rates in cyclic tests can be computed as
J = 4 J SA f [%/s] where: J shear strain rate; J SA= single amplitude shear strain
[%]; f = frequency [Hz]. According to this equation the equivalent strain rates in a
RCT increase from several %/min to several thousands %/min as the strain increases
from 0.001 % to 0.1 % (Lo Presti et al., 1996). The influence of strain rate on the
small strain shear modulus is quite negligible for a great variety of geomaterials
(Tatsuoka et al., 1997) but it becomes increasingly important for higher strain level
(see as an example Figure 4.4). The influence of strain rate on G as a function of the
strain level can be evaluated by means of the following empirical parameter
(Tatsuoka et al., 1997; Lo Presti et al., 1996):
D (J )
'G (J )
' log J G J , J REF
(4.1)
Shear modulus, G [MPa]
i.e. the increase in shear modulus for one logarithmic cycle of strain rate normalised
with respect to the shear modulus correspondent to a reference strain rate.
G(J, J
80
REF
70
60
50
40
30
20
| 0.4%/min)
G( J , J )
1
G( J , J
A
B
Curve
Vcv
Kc
e
J
% min
Test N.
kPa
A
398
1
0.768
0.1
(CLTST )
B
398
1
0.768
0.4
(CLTST)
398
1
0.811 14.8 to 2262.0
10
C
0
0.0001
0.001
2
)
C
(RCT)
0.01
Shear strain, J [%]
0.1
1
Fig. 4.4. G-J curves from CLTST and RCT tests of Augusta clay (Lo Presti et al., 1996.
“Rate and creep effect on the stiffness of soils”, GSP No.61, ASCE; Reproduced with
permission from ASCE)
109
Geophysical-Geotechnical Investigations
Figure 4.5 shows, for a variety of geomaterials, that D( J ) increases with PI and, for a
given soil, increases with J. Consequently, the shear modulus decay curve G/G0 is rate
dependent and very different results can be obtained depending on the loading
frequency. Therefore, in the case of static problems or even for seismic problems it is
preferable to obtain the G/G0 curve from TST with constant J and frequencies not
larger than 10Hz;
Mukabi et al. (1991) - isotropic - PI = 41 %
Mukabi et al. (1991) - anisotropic - PI = 41 %
Berre and Bjerrum al. (1972) - PI = 10 %
Akai et al. (1975) - PI = 21- 27 %
J REF
0.01 % min
Pisa - PI = 54 %
Augusta - PI = 39 %
Pisa - PI = 20 %
Augusta - PI = 29 %
J REF
0.04 % min
Pisa - PI = 21 %
Augusta - PI = 38 %
J REF
0.4 % min
0.45
Coefficient of strain rate D J
0.4
0.35
0.3
DJ
'G J
' log J G J , J REF
0.25
0.2
0.15
0.1
0.05
0
0.0001
0.001
0.01
0.1
Shear strain, J [%]
1
10
Fig. 4.5. Coefficient of strain rate vs. shear strain (Lo Presti et al., 1996. “Rate and creep
effect on the stiffness of soils”, GSP No.61, ASCE; Reproduced with permission from
ASCE)
- damping ratio (D) is much more dependent on frequency or strain rate than G and
even at very small strains the frequency dependency of D has been observed (Papa et
al., 1988; Tatsuoka and Kohata, 1995; Stokoe et al., 1995; Lo Presti et al., 1997;
110
D. Lo Presti, C. Lai, and S. Foti
Cavallaro et al., 1998; d'Onofrio et al., 1999). In particular, the damping ratio values
obtained from RCT are markedly greater than those inferred from cyclic tests at
frequency from 0.1 to 1.0Hz as shown in Figure 4.6;
Fig. 4.6. Damping ratio vs. frequency (Lo Presti et al., 1997, Cavallaro et al., 1998,
D'Onofrio et al., 1999; Reproduced with permission from Balkema)
- according to Stokoe et al., (1995) the D values obtained with a RC apparatus should
be corrected by subtracting the equipment-generated damping (Dapp) which is a
frequency dependent parameter. The Dapp – f calibration curve is different for each
apparatus and it can be evaluated following an appropriate calibration procedure
(Stokoe et al., 1995).
The use of the Torsional Shear Tests (TST), instead of the Resonant Column, seems to
be preferable and many researchers have adapted the RC apparatus to perform TST
(Isenhower et al., 1987; Alarcon-Guzman et al., 1986; Lo Presti et al., 1993; Kim and
Stokoe, 1994; d'Onofrio et al., 1999). The advantage of this hybrid apparatus is that it is
possible to determine G0 from RCT and perform cyclic loading torsional shear tests at
various frequencies.
On the other hand, several hollow cylinder torsional shear apparatuses have been
developed in various research laboratories (Hight et al., 1983; Miura et al., 1986;
Pradhan et al., 1988; Teachavorasinskun, 1989; Alarcon-Guzman et al., 1986; Vaid et
al., 1990; Yasuda and Matsumoto, 1993; Ampadu and Tatsuoka, 1993; Cazacliu, 1996;
Di Benedetto et al., 1997; Ionescu, 1999; Yamashita and Suzuki, 1999). The main
advantage of these devices is that they can operate at constant strain rate and over a very
wide strain interval. Some of these devices have been developed to study the stressstrain relationship of geomaterials under a more general stress state and stress-path.
Other devices have been developed as an alternative to triaxial tests. An effort to
standardise this test has been undertaken in Japan (Toki et al., 1995).
Geophysical-Geotechnical Investigations
111
4.4. Field Tests
4.4.1. GEOPHYSICAL TESTS
Seismic tests are conventionally classified into borehole (invasive) and surface (noninvasive) methods. They are based on the propagation of body waves [compressional
(P) and/or shear (S)] and surface waves [Rayleigh (R)], which are associated to very
small strain levels (i.e. less than 0.001 %) (Woods, 1978). Assuming a linear elastic
response, the following relationships allow computing the small-strain deformation
characteristics of the soil from the measured body wave phase velocities:
Go
UV s2
(4.2)
Mo
UV p2
(4.3)
Q
(V p2 2Vs2 ) / 2(V p2 Vs2 )
(4.4)
where: G0, M0 = small strain shear and constrained modulus respectively; U = mass
density; VS, VP = velocity of shear and compressional waves respectively; Q = Poisson
ratio.
In saturated porous media the measured P wave velocity corresponds to the
compression wave of the first kind (Biot, 1956a, 1956b) that is strongly influenced by
the pore fluid. In this case the above equations are no longer valid and must be replaced
with the corresponding ones of poroelasticity theory.
Seismic tests may also be used to determine the material damping ratio by measuring
the spatial attenuation of body or surface waves:
Do
DV
( Do 10%)
2Sf
(4.5)
where D0 = small-strain material damping ratio; D, V = attenuation coefficient and
velocity, respectively, of P, S or R waves and f = frequency.
Material damping measurements are difficult because they require accurate
measurements of seismic wave amplitude and accurate accounting of the effects of
geometric (radiation) attenuation (Rix et al., 2000).
Even at strains less than the linear threshold strain, soils have the capability not only of
storing strain energy (elastic behaviour) but also of dissipating it over a finite period of
time (viscous behaviour) (Ishihara, 1996). This type of behaviour can accurately be
modelled by the theory of linear viscoelasticity. An important result predicted by this
theory is that soil stiffness and material damping are not two independent parameters,
but they are coupled due to the phenomenon of material dispersion (Aki and Richard,
1980). Assuming that material-damping ratio at small strains is rate-independent over
the frequency range of interest (i.e. the viscoelastic response is assumed hysteretic), the
following dispersion relation describes the coupling between the material damping ratio
and the velocity of propagation of seismic waves:
112
D. Lo Presti, C. Lai, and S. Foti
V( f )
V ( f ref )
ª 2 Do § f ref ·º
¸»
ln¨¨
«1
¸
S
f
«¬
¹»¼
©
(4.6)
where: fref = reference frequency (usually 1Hz).
This implies that a vigorous procedure to estimate the small-strain dynamic properties
of geomaterials should determine velocity of propagation of seismic waves and material
damping ratio simultaneously rather than separately as it is done in the current practice
(Lai and Rix, 1998; Lai et al., 2001; Rix et al., 2001; Lai et al., 2002).
Borehole methods
The most widely used borehole methods in geotechnical engineering are Cross Hole
(CH), Down Hole (DH), Suspension PS logging (PS) (Nigbor and Imai, 1994) tests.
Strictly speaking, the Seismic Cone (SCPT) test is not a borehole method, but it is based
on the same principle. Their popularity is due to the conceptual simplicity. The
measurement of the travel time of P and/or S waves, travelling between a source and
one or more receivers is determined from the first arrival of each type of wave. Current
practice and recent innovations of borehole methods are covered by many
comprehensive works (Auld, 1977; Stokoe and Hoar, 1978; Woods, 1978; Woods and
Stokoe, 1985; Woods, 1991, 1994). In the following, only some aspects of the borehole
methods are briefly summarized. In particular, the focus is placed on emphasising the
importance of respecting these testing procedures:
- good mechanical coupling between receiver, borehole casing (if used) and
surrounding soil must be guaranteed. A distinct advantage of the SCPT is that good
coupling is virtually assured. With conventional cased and grouted boreholes, good
coupling is less certain and, more importantly, is difficult to verify. The need for
good coupling is particularly important for attenuation measurements, which require
accurate amplitude data;
- a check of the borehole verticality with an inclinometer is also highly recommended
in order to determine accurately the length of wave travel path in CH tests;
- it is important to generate repeatable waveforms with the desired polarity and
directivity. This allows receivers to be oriented in such a way to optimise the
measurement of a particular wave type, the use of reversal polarity to make the
identification of wave arrivals easier, and measurements along different directions to
infer structural and stress-induced anisotropy as explained below;
- in down-hole measurement, the use of two of receivers located at a fixed distance
apart (Patel, 1981) can increase the accuracy and the resolution because the true
interval method for data interpretation can be implemented;
- dedicated portable dynamic signal analysers and computer-based data acquisition
systems allow more sophisticated data processing methods. Thanks to these
enhancements, it is now possible to routinely use cross correlation (time domain) or
cross power spectrum (frequency domain) techniques to estimate travel times instead
of subjective identification of the first arrivals in the time histories. In addition, as
multi-channel data acquisition systems become more common, the logical extension
will be to use arrays of receivers and array-based signal processing (seismic
tomography).
Geophysical-Geotechnical Investigations
113
Generally, the shear wave velocity profiles inferred from various borehole tests are in
good agreement (see the example in Figure 4.7). However, SCPTs generally provide
values of the shear wave velocity slightly higher than those inferred from down-hole or
cross-hole tests.
Fig. 4.7. Shear wave velocity in Po river sand (Jamiolkowski et al., 1998; Reproduced
with permission from Balkema)
In the past, differences between CH and DH velocities have been attributed to soil
heterogeneity and anisotropy. The following considerations explain why anisotropy is
not responsible for these differences. In CH tests, S waves propagate in the horizontal
direction with vertical particle motion (S hv ). In DH tests, propagation of the S wave is
vh
sub vertical with horizontal particle motion (S vh ). In a continuous medium, the Vs
hv
and Vs shear wave velocities are the same and a unique value of the shear modulus
vh
hv
(Gvh Ł Ghv) is expected. Figure 4.8 illustrates that Vs = Vs or Gvh Ł Ghv using BE
measurements of S vh and S hv waves on a reconstituted sample of Fujinomori clay (Lo
Presti et al., 1999). Similar results have been obtained in the case of reconstituted sands
by Stokoe et al. (1991), Lo Presti and O'Neill (1991) and Bellotti et al. (1996). Hence,
different values of shear wave velocity from CH and DH tests are most likely due to soil
heterogeneity (Stokoe and Hoar, 1978).
114
200
120
150
90
100
60
50
30
[m/s]
150
hv
250
0
vh
Vs , Vs
Stresses [kPa]
D. Lo Presti, C. Lai, and S. Foti
0
0
2
4
6
8 10 12 14
Axial strain H a [%]
16
18
20
22
Fig. 4.8. V svh and V shv measured with BE during drained CLTX test on Fujinomori clay
(Lo Presti et al., 1999; Reproduced with permission from Balkema)
The assessment in situ of inherent and stress induced elastic anisotropy is possible by
measuring the velocity of propagation of both S hv and S hh waves in CH tests
(Jamiolkowski and Lo Presti, 1991; Mitchell et al., 1994; Fioravante et al., 1998). S hh
waves propagate in the horizontal direction with particle motion polarized in the
complementary horizontal direction. This additional information enables the evaluation
of the G hh /G vh ratio, which is a function of inherent and stress-induced anisotropy.
Figure 4.9 summarises some field and calibration chamber data. Figure 4.9 indicates
that, for the considered granular soils, the inherent anisotropy (inferred at K C =1) causes
a 20% to 25% increase in G hh over G vh . The influence of stress induced anisotropy is
apparent for other values of K C .
Recently researchers devoted more attention to inferring the small-strain damping ratio,
D0 from borehole tests. The current methods are based on measures of the spatial
attenuation between two or more receivers. The most widely used methods include:
a)
The spectral ratio method (Mok, 1987; Fuhriman, 1993) is based on the following
assumptions which hold only in the far field: i) the amplitude of the body waves
decreases in proportion to r -1, where r is the distance from the source, due to
geometric attenuation and ii) the soil-receiver transfer function can be considered
identical for both receivers. Based on the above assumptions, the damping ratio
can be computed by means of the following equation:
D( f )
ln>A1 ( f ) r1 / A2 ( f ) r 2@
)( f )
(4.7)
where: r1 and r2 are the distances from the source of a pair of receivers, A 1 ( f ) and
A 2 ( f ) are the amplitude spectra at the two receivers and ) ( f ) is the phase
difference between the two receivers.
Geophysical-Geotechnical Investigations
115
Fig. 4.9. Small strain stiffness anisotropy: field versus laboratory data (modified after
Bellotti et al., 1996; Reproduced with permission from the Institute of Civil Engineers)
b) The spectral slope method, originally developed for downhole measurements
(Redpath et al., 1982; Redpath and Lee, 1986), differs from the spectral ratio
method because it assumes that material damping is frequency independent and
that it is not necessary to define the law for geometric attenuation. The
attenuation constant, defined as the ratio of attenuation coefficient to frequency
k = D /f, represents the spectral slope, i.e. the slope of the spectral ratio vs.
frequency curve:
k
'^ln>A1 ( f ) / A2 ( f )@`
'f (r 2 r1)
(4.8)
therefore the material damping can be computed using the following expression:
'^ln>A1 ( f ) / A2 ( f )@`
D( f )
(4.9)
'f 2S 't ( f )
Both methods require signal processing prior to interpretation to isolate direct arrivals
and frequency ranges. They provide damping values in the bandpass range of the filter.
Khawaja (1993) and Fuhriman (1993) recommend performing crosshole tests with four
boreholes, in order to obtain stable values of damping with the spectral ratio method.
116
D. Lo Presti, C. Lai, and S. Foti
They suggested placing the source in the outer boreholes, in order to propagate waves in
both forward and reverse directions, and the receivers in the two central boreholes. The
spectral ratio method with combined directions provides stable values of damping and
avoids the extreme case of negative damping values (Campanella and Stewart, 1990).
Campanella and Stewart (1990) studied the applicability of the above methods to the
downhole SCPT's. They found that the spectral slope method provides more realistic
values of material damping. However, in downhole tests, wave amplitudes are also
affected by reflection/transmission phenomena at the interfaces between layers and by
ray path divergence: these phenomena make more complicate the interpretation of the
particle motion amplitude.
0
(a) Spectral slope method
LN (Spectral Ratio) [-]
-0.2
-0.4
D=1.59 %
-0.6
-0.8
Linear trend:
(100÷1500Hz)
Y=m×freq+q
m = -0.000321
q = -0.473902
-1
-1.2
-1.4
Seismic Tests no.: 1
Material type: Ticino Sand
Wave type: Svh
No. geophones: 2 - 5 - 8
Vv = 20.8 kPa
-1.6
-1.8
Vh = 9.3 kPa
-2
0
200
400
600
800 1000 1200 1400 1600 1800 2000
Frequency [Hz]
1
(b) Spectral ratio method
0.9
Seismic Tests no.: 330
Material type: Ticino Sand
Wave type: Szx
No. geophones: 28 - 19 - 8
Vnom= 300 kPa
Damping ratio, D [%]
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
500
1000
1500
Frequency [Hz]
2000
2500
3000
Fig. 4.10. Damping ratio from geophysical tests in calibration chamber (Puci and Lo
Presti, 1998; Reproduced with permission from Balkema)
117
Geophysical-Geotechnical Investigations
Examples of damping measurements with the spectral ratio and spectral slope methods
are given in Figures 4.10a and 4.10b for reconstituted Ticino sand (Puci and Lo Presti,
1998). The results are from seismic tests, performed with miniature geophones
embedded in large-size calibration chamber specimens. Figure 4.11 (Puci and Lo Presti,
1998) compares the damping ratio values obtained in the case of reconstituted Ticino
sand from laboratory tests (RCT) and those inferred from the spectral ratio and spectral
slope methods applied to calibration chamber seismic tests. In this very controlled
experiment, the seismic methods yield values of the material damping ratio that
generally agree with laboratory values. Measured damping ratios are plotted vs. the
corresponding consolidation stresses which have a great influence on the results.
Other approaches to measure the material damping ratio include the rise time method,
based on the experimental evidence that a seismic wave signal broaden with distance
because of material damping, and the waveform matching method. However, at the
present time, none of the available borehole methods to measure material damping ratio
appears to be robust enough for routine use in geotechnical engineering practice.
10
Ticino Sand
Damping ratio: D [%].
J#10-4%
f #1000÷3000Hz
-3
J#10 %
f #80÷140Hz
1
Seismic Tests (Spectral Ratio Method: Dr=45%)
Seismic Tests (Spectral Slope Method:Dr=45%)
Resonant Column (Dr=45%)
Resonant Column (Dr=85%)
0.1
100
1000
10000
100000
Consolidation Stress: V'v · V'h [kPa]·[kPa]
Fig. 4.11. Damping ratio from laboratory and geophysical seismic tests on reconstituted
sands (Puci and Lo Presti, 1998; Reproduced with permission from Balkema)
Surface methods
Surface methods are non-invasive field techniques that are executed from the ground
surface of a soil deposit; hence they do not require drilling of boreholes or insertion of
probes. They include seismic refraction, high-resolution reflection and surface wave
methods. Seismic refraction and reflection methods are based on the analysis of body
wave propagation and can be performed considering either compressional (P) or shear
waves (S) waves. P-wave refraction is often used to locate underlying bedrock
formations, while S-wave refraction can be used to obtain the small strain stiffness
118
D. Lo Presti, C. Lai, and S. Foti
profile. However particular care must be taken in planning such investigations because
there are situations (stiffer-over-softer layers; hidden layers) where the seismic
refraction method is not reliable (Reynolds, 1997). High-resolution reflection, on the
other hand, does not suffer such limitations; however it requires very intensive data
processing.
Advantages of surface methods are mainly related to their non-invasive nature. They
are more economical and can be performed more rapidly than borehole methods.
Furthermore, in sites like solid waste disposals and landfills, due to environmental
concerns, surface methods can be the only choice for geotechnical investigations.
Another peculiar aspect of surface methods is related to the volume of soil involved in
the test, which is much larger than in borehole methods. As a result, surface methods
are particularly useful if the average properties of a soil deposit are to be assessed as in
the case of ground response analyses.
In the following, the discussion on surface methods will focus exclusively on surface
wave methods mainly because of their relevance in near-surface site characterization.
Early surface wave methods employed laborious field procedures to measure the
dispersion curve (i.e. a plot of Rayleigh phase velocity vs. frequency) and crude
inversion techniques to obtain the S-wave profile from the experimental dispersion
curve (Jones, 1958). Stokoe and his co-workers (i.e. Nazarian, 1984; Stokoe et al., 1989)
re-invented engineering surface wave testing by taking advantage of portable dynamic
signal analysers, to efficiently measure the dispersion curve, and of the widespread
availability of high-speed computers, to implement theoretically-based robust inversion
algorithms. In recent years, the Spectral Analysis of Surface Waves (SASW) method
has been further improved by incorporating i) the results of a better understanding of
surface wave propagation in stratified media, ii) robust and efficient procedures for
phase velocity measurements including those associated with passive methods, iii)
techniques to determine the shear damping ratio profile from attenuation measurements,
and iv) efficient algorithms capable of performing the coupled and uncoupled inversion
of surface wave data. Later in this section some of these recent innovations will be
briefly described.
The traditional SASW method uses either impulsive sources such as hammers or
steady-state sources like vertically oscillating hydraulic or electro-mechanical vibrators
that sweep through a pre-selected range of frequencies, typically between 5 and 200Hz
(Rix, 1988). R-waves are detected by a pair of transducers located at distances D and
D+X from the source (Figure 4.12). The signals at the receivers are digitised and
recorded by a dynamic signal analyser. The Fast Fourier Transform is computed for
each signal and the cross power spectrum between the two receivers is calculated.
Multiple signals are averaged to improve the estimate of the cross power spectrum. The
phase angle of the cross power spectrum is used to determine the travel time between
the two receivers:
t ( f ) I ( f ) / 2Sf
(4.10)
where I ( f ) is the phase difference in radians and f is the frequency in Hz. The
Rayleigh phase velocity is then computed as:
Geophysical-Geotechnical Investigations
VR
X
t( f )
119
(4.11)
The wavelengths corresponding to the frequency dependent Rayleigh phase velocities
are computed as O R =VR (f ) /f. The result is the experimental dispersion curve for the
considered receiver spacing. The calculations are then repeated reversing the source
position and with different receiver spacing (Figure 4.13): the results are combined to
form the composite dispersion curve of the site (Figure 4.14a).
Signal Analyzer
Impulsive
Source
Near Receiver
D
Far Receiver
X
Fig. 4.12. Typical configuration for SASW test
Fig. 4.13. Common receiver midpoint geometry used for SASW test
120
D. Lo Presti, C. Lai, and S. Foti
Fig. 4.14. Example of SASW test: a) experimental dispersion curve from multiple
receiver spacings, b) Comparison between experimental and theoretical dispersion
curves, c) Shear wave velocity profile obtained with the inversion process compared to
cross-hole test results (Foti, 2000)
121
Geophysical-Geotechnical Investigations
The use of a multi-station testing setup (Figure 4.15) can introduce several advantages
in surface wave testing. In this case, the motion generated by an impact source is
detected simultaneously at several receiver locations and the corresponding signals are
analysed as a whole (i.e. in both the time and space domains) using a double Fourier
Transform. It can be shown (Tselentis and Delis, 1998) that the dispersion curve can be
easily extracted from the location of the spectral maxima in the frequency-wavenumber
domain in which the original data are transformed. Using this technique, the evaluation
of the experimental dispersion curve becomes straightforward; furthermore, the
procedure can be easily automated (Foti, 2000). With the adoption in SASW testing of
the multi-station method, the need of several testing configurations required by the
conventional two-station procedure is avoided with the result that testing and
interpretation times are considerably reduced.
Seismograph
Impulsive
Source
2
1
D
X
3
n
X
Fig. 4.15. Multistation configuration for SASW test
The experimental dispersion curve is used to obtain the shear wave velocity profile via a
process called inversion. A theoretical dispersion curve is calculated for an assumed
vertically heterogeneous layered soil profile using one of several available algorithms
(Haskell, 1953; Thomson, 1950; Kausel and Roësset, 1981; Chen, 1993; Hisada, 1994,
1995). The theoretical dispersion curve is then compared with the corresponding
experimental curve and the “distance” between the two curves is used as a basis of an
iterative process consisting of updating the current soil profile until the match between
the two curves is considered satisfactory. The soil profile may be updated manually by
trial and error or using an automated minimisation scheme based on an unconstrained
or constrained inversion algorithm (Lai and Rix, 1998). When a satisfactory agreement
between theoretical and experimental dispersion curves is attained (Figure 4.14b), the
final shear wave velocity profile (Figure 4.14c) is taken as representative of the site
conditions.
For a successful application of SASW testing, it is recommended to observe the
following guidelines:
x in choosing the relative spacing between source and receivers, attention should be
placed to minimize near-field effects and spatial aliasing. In this context, the nearfield is defined as a region close to the source where the magnitudes of the body wave
components of the wave field are of comparable magnitude to the surface wave
122
D. Lo Presti, C. Lai, and S. Foti
components. Efforts should be made to eliminate or minimize near-field effects
unless they are explicitly accounted for during the inversion process (Roësset et al.,
1991; Ganji et al., 1998). In normally dispersive media, the body wave field is
significant until D/O exceeds about 0.5, hence the nearest receiver should be located at
least one-half wavelength from the source:
DtO/2
(4.12)
This recommendation is consistent with other studies of the influence of near-field
effects, but more strict requirements are necessary for inversely dispersive
stratigraphies (Sanchez-Salinero, 1987; Tokimatsu, 1995). It is also important to
limit the distance between receivers to avoid spatial aliasing; a simple criterion is
given by:
X dO/2
(4.13)
x the length of the receiver array must be sufficiently large, if the stiffness profile at
great depth has to be estimated. A rule of thumb is that the survey length must be as
long as about 3 times the maximum depth of interest. This requirement may not be
compatible with the space available at the site. Moreover, massive sources are needed
to get good quality signals with long testing arrays, causing an increase of testing time
and cost;
x it is important to account for multiple modes of surface wave propagation, especially
in irregular, inversely dispersive soil profiles (Gucunski and Woods, 1991; Tokimatsu,
1995). Currently several approaches are used to account for multiple modes.
Individual, modal dispersion curves can be calculated and compared with the
experimental dispersion curve during the inversion process. Unfortunately, the use of
only two receivers in the traditional SASW method prohibits resolving individual
modes in the experimental dispersion curve; only the effective velocity representing
the combination of several modes can be determined. Also using a multi-station
approach the individual modes cannot be separated if a relatively short receiver array
is used, as required by engineering practice (Foti et al., 2000). Thus, it must be
assumed that the experimental curve represents an individual mode, usually the
fundamental mode. This approach is satisfactory only in normally dispersive profiles.
Another approach is to calculate the effective velocity directly and use it as the basis
of the inversion. Lai and Rix (1998) have developed an efficient procedure based on
the normal mode solution to calculate the effective velocity as well as closed-form
partial derivatives required for inversion. Finally, it is possible to numerically
simulate the SASW test using Green’s functions that calculate the complete wave
field (Roësset et al., 1991). This approach is computationally expensive, in part
because the partial derivatives must be calculated numerically, but it accurately
models the actual field procedure used in SASW tests;
x for the inversion of the experimental dispersion curve, it is essential to use
theoretically-based inversion algorithms. Prior to the widespread availability of highspeed computers, simple empirical inversion techniques were used. Furthermore, in
recent years, there have been attempts to develop simple methods based on parametric
studies and regression equations. These methods have limited usefulness and are
Geophysical-Geotechnical Investigations
123
likely to yield erroneous results. It is remarked that the rapidly increasing power of
personal computers makes it possible to use theoretically-based inversion methods
routinely;
x the non-linear inversion of the experimental dispersion curve is inherently ill-posed
with the consequence that the solution (i.e. the S-wave profile) is not unique. This
problem can be overcome with the recourse of two strategies (Lai and Rix, 1998).
First, a priori information about the soil profile can be used to limit the range of
possible solutions. Second, additional constraints such as smoothness and regularity
(e.g., Constable et al., 1987) may be imposed on the solution.
Among the most recent advances in surface wave testing, there are the determinations
of shear damping ratio profile from attenuation measurements and the combined use of
active and passive sources to determine the experimental dispersion curve. In the
following, some aspects of these two topics will be briefly discussed.
Damping ratio profile. As a surface wave travels away from the source, its amplitude
decreases. This decay is due in part to the geometrical spreading of energy over wider
wavefronts (geometrical attenuation) and to the energy dissipation (material attenuation).
If the material attenuation is estimated experimentally from field measurements, it is
possible to evaluate the damping parameters of the soil deposit by using an inversion
process similar to that used to infer the stiffness profile. The difference is that, in the
case of the damping ratio profile, the experimental curve to be inverted is the
attenuation rather than the dispersion curve.
Rix et al. (2000) proposed a method to determine the shear damping ratio profile based
on the following assumptions: a) the soil can be modelled as a layered weakly
dissipative medium, and b) the propagation of Rayleigh waves is governed by the
fundamental mode. The experimental attenuation curve can be estimated using the
multi-station method based on measuring the amplitude of the particle motion at several
receiver offsets placed on the ground surface at increasing distance from a frequencycontrolled source (Rix et al., 2000). One of the most delicate aspects of this procedure
is related to a correct estimation of the geometrical attenuation, which is needed to
separate the material attenuation. For a homogenous medium, the geometrical
attenuation is inversely proportional to the square root of the distance from the source,
but in a layered medium it becomes a non-trivial function of the stiffness profile.
Lai and Rix (1998) have proposed a technique where the shear damping ratio profile is
determined simultaneously with the shear wave velocity profile in a joint inversion of
experimental dispersion and attenuation curves. The method is based on combining
results from linear viscoelasticity with some theorems of complex analysis. A coupled
simultaneous inversion of both dispersion and attenuation curves is a mathematically
better-posed problem, if compared with the corresponding uncoupled inversion. In this
view a new multi-station scheme for the simultaneous measurement of dispersion and
attenuation curves has also been proposed, based on the transfer function concept
(Rix et al., 2001). The experimental transfer function is obtained measuring the
acceleration of a controlled harmonic source and the induced motion at several receivers
placed along the ground surface. Once the experimental transfer functions have been
determined, they are used to compute, in a complex-valued non-linear regression, the
frequency dependent complex wavenumbers, which contain information about both the
124
D. Lo Presti, C. Lai, and S. Foti
phase velocity and the attenuation. After the experimental dispersion and attenuation
curves have been simultaneously measured, the process is completed by using the
simultaneous inversion algorithm described above to yield the stiffness and damping
ratio profiles (Lai et al., 2002).
Passive measurements. A limitation of surface wave methods based on the use of active
sources is related to the depth of investigation. Stiffness characteristics of deep strata
can be obtained only using very massive sources and very long receiver arrays. A
possible alternative is the measurement of short-period microtremors (T<1s), which are
caused by natural events or by human activities in the nearby of the site. Because of the
absence of a specific source, such methods are often called passive methods.
Microtremors can be associated to Rayleigh waves if the measurements are conducted
in favourable weather condition, i.e. in absence of strong winds (Horike, 1985) and if
the presumable sources of noise (e.g. heavy traffic on a highway) are far enough from
the testing site.
A satisfactory characterisation of a site can be obtained with a hybrid method using
short period microtremors for the investigation of deeper layers jointly with an active
method to cover the need of high resolution at shallow depth, because in the high
frequency range microtremors are strongly affected by noise.
The basic steps of soil characterization using microtremors (Horike, 1985; Tokimatsu,
1995; Zwycki and Rix, 1999) are essentially the same of the SASW test: i) field
measurements, ii) determination of the experimental dispersion curve, and
iii) inversion process. Several sensors are required because there is no restriction to a
single mode or a single direction of propagation, since the actual position and geometry
of the source are unknown. Usually the receivers are deployed in a circular array either
with or without a receiver in the centre of the array. Using three-dimensional receivers,
it is possible to analyse both vertical and horizontal particle motions related to
microtremors (Tokimatsu, 1995). As for active surface wave measurements, more than
one receiver configuration is needed because spatial aliasing, wavenumber resolution
and leakage in the wavenumber domain limit the spectrum of frequency that can be
obtained from a single receiver lay-out (Zywicki and Rix, 1999).
Data analysis is performed using high-resolution frequency-wave number spectral
estimation techniques, steering the data array with a trial wavenumber array in many
directions. The resulting spectrum can be represented as a 2D wavenumber (kx-ky)
contour plot for each analysed frequency. The peak of this spatial plot is used to
evaluate the wavenumber that is associated to the dominant surface wave and its
direction of propagation. The experimental dispersion curve is determined by repeating
the above procedure for different frequencies. Finally the dispersion curve is inverted
using the same algorithms used in active surface wave testing.
4.4.2. IN SITU LARGE STRAIN TESTS: PRESSURIMETER AND PLATE LOAD
TESTS
Pressuremeter and Plate Load Tests (PLT) are used to determine the large strain
stiffness of soils in situ.
Several different pressuremeter devices are currently used. The differences mainly
concern the way in which the probe is inserted into the soil. In the following, only the
Geophysical-Geotechnical Investigations
125
Self Boring Pressurimeter (SBPT) is considered because it causes a limited soil
disturbance. On the contrary, the insertion of kinds of probes causes an unavoidable
destructuration of the soil fabric and a consequent underestimation of the stiffness
especially in the case of aged deposits. The SBPT has been developed in France and
UK at the beginning of the 1970s (Baguelin and Jezequel, 1973; Wroth and Hughes,
1973).
A pressuremeter test consists of the expansion of a cylindrical cavity which has a finite
length L and diameter D. During the test, the applied cavity pressure (p) and the
corresponding circumferential strain at the cavity wall H are measured. The test yields
an expansion curve of the type shown in Figure 4.16 which allows, at least in principle,
the direct determination of the following shear moduli:
Effective cavity stress p’
x G0 from the initial slope of the expansion curve;
x Gur from small unload-reload cycles which can be performed during the expansion
curve or even during the contraction phase of the test.
Cavity strain H =
a
'R
R
o
Fig. 4.16. Shear moduli from SBP tests
These moduli can be directly determined from the expansion curve because in both
cases it is possible to neglect soil non-linearity as a first approximation. However, the
initial shape of the expansion curve is sensitive to soil disturbance and to the
compliance of the measuring system even in the case of SBP tests. Consequently, the
direct assessment of G0 from the expansion curve is not possible in practice, while the
determination of a pseudo-elastic stiffness from small unload-reload cycles seems quite
suitable and reliable if appropriate assumptions are made (Bellotti et al., 1986; 1989;
Byrne et al., 1990; Fahey, 1991; Fahey and Carter, 1993; Ghionna et al., 1994).
126
D. Lo Presti, C. Lai, and S. Foti
The interpretations of small unload reload loops (u-r loops) in sand have been
accomplished by several researchers. By referring to the SBP expansion curve obtained
at the Viadana site (Bruzzi et al., 1986; Bellotti et al., 1989) in Holocene Po river sand
(Figure 4.17), the Gurvalue of the loop can be computed using the following expression:
Gur
1 ( p B uo ) ( p A uo )
2
HB HA
(4.18)
where: pA, pB = total cavity stress applied at points A and B respectively; HA ,HB =
corresponding circumferential strains at the cavity wall; uo= hydrostatic pore pressure.
2G
i
1
Fig. 4.17. Example of SBPT in Po river sand (Bellotti et al., 1989; Reproduced with
permission from the Institute of Civil Engineers)
Considering the pressure-dependency and non-linearity of soil stiffness, it is evident
that any rational interpretation of the ur-loop should attempt to link the Gur value to the
following factors:
1 '
1 '
(V r V T' ) existing at
(V 1 V 3' )
2
2
the start of the loop which is a function of p´C (V´r= radial effective stress; V´T =
circumferential effective stress, p´C = effective cavity stress at the start of unloading);
- the average plane strain effective stress s '
Geophysical-Geotechnical Investigations
- the relative depth of the loop R
pC' p 'A
'
'
2 sin M PS
pC' /(1 sin M PS
)
127
(Fahey, 1991) (M PS=
plane strain angle of shear resistance which can be inferred from the expansion
curve).
The R relates the current depth of the unload loop (p´C - p´A ) to the amount of stress
unload at which the reverse plasticity can occur. In practice, R plays the same role of
the shear stress ratio WWmax that describes the non-linearity of soil stiffness measured in
laboratory tests (WWmax = mobilisation factor, i.e. the ratio of the current shear stress to
the failure value).
Plate load tests (PLT) can provide an average (operational) stiffness linked to the load
vs. displacement characteristics of the considered boundary value problem. Usually the
values of E from these tests are evaluated using the formulae of the theory of elasticity
of an isotropic medium. In this case, the soil elements beneath the test foundation not
only experience very different strain levels, as in the SBPT, but also follow different
stress-paths. To extend such investigations at depth it is necessary to run the test inside
a pit excavation.
4.4.3. EMPIRICAL CORRELATIONS FROM PENETRATION TESTS
In spite of the fact that the penetration resistance represents the soil response to very
large deformations, it is possible to establish reliable correlations between small strain
moduli and penetration parameters. Indeed, both of them are mainly dependent on the
soil state, although to a different degree.
Many empirical correlations between the penetration resistance from Standard
Penetration Test (SPT) (Ohta and Goto, 1978; Imai and Tonouchi, 1982) or Cone
Penetration Test (CPT) (Sykora and Stokoe, 1983; Robertson and Campanella, 1983;
Rix, 1984; Baldi et al., 1986; 1989a; 1989b; Bellotti et al., 1986; Lo Presti and Lai,
1989; Rix and Stokoe, 1991; Mayne and Rix, 1993) and the small strain shear modulus
G0 have been established using different databases. Among the many available
correlations, it is worthwhile to mention the following:
a)
Ohta and Goto (1978), adapted by Seed et al. (1986)
Vs
0.17
69 N 60
Z 0.2 FA FG
(4.19)
where: Vs = shear wave velocity (m/s), N60 = number of blow/feet from SPT with
an Energy Ratio of 60%, Z=depth (m), FG =geological factor (clays=1.000,
sands=1.086), FA = age factor (Holocene=1.000, Pleistocene=1.303)
b) Jamiolkowski et al. (1988) have shown that the ratio G0/qc mainly depends on
relative density and is only moderately influenced by overburden stress.
Figure 4.18, which is based on field and CC data, can be used to infer the small
strain shear modulus from CPT for sands.
128
D. Lo Presti, C. Lai, and S. Foti
Fig. 4.18. qc vs. G0 correlation for uncemented predominantly quartz sand
(Jamiolkowski et al., 1988; Reproduced with permission from Balkema)
Mayne and Rix (1993) have proposed the following empirical correlation between the
shear wave velocity and the cone penetration resistance:
Go
99.5( p a ) 0.305 (q c ) 0.695 / eo1.130
(4.20)
This correlation is based on database from 31 clay sites and takes into account the in
situ void ratio which significantly influences G0, whilst it has much smaller impact on qc.
Site specific empirical correlations can be profitably used to assess the spatial
variability of soil properties in a very cost effective way. However, due to their purely
empirical nature, these correlations, when applied to sites which are different from those
considered in the original database, can provide just an approximate estimate of G0
which, in many cases, can be quite far from the actual value.
Empirical correlations between G0 and the Flat Dilatometer Test results (DMT)
(Marchetti, 1980; 1997) have also been established. A review of the many existing
Geophysical-Geotechnical Investigations
129
correlations has been provided by Mayne and Martin (1998). For a given soil, relatively
good correlations have been found between G0 and the following DMT measurements:
the conventional lift-off pressure (p0), the pressure corresponding to a displacement of
1.1 mm of the central part of the steel membrane (p1), the wedge resistance (qD) and the
horizontal stress index (KD= (po- uo)/V´vo). On the other hand, poor correlations have
been found between G0 and the conventional dilatometer modulus [ED=34.7 (p1-p0)].
4.5. Case History
This case history is related to a extensive project for the evaluation of site effects in
about 60 municipalities, located in the territories of Garfagnana and Lunigiana (Ferrini
et al., 2000). Castelnuovo Garfagnana is the first site in which the comprehensive
program of field and laboratory investigations has been completed (Calosi et al., 2001).
The preliminary step for field investigation is the reconstruction of the geology of the
whole representative area. This delicate task has to be accomplished accurately because
it leads to the choice of significant sections, which will be investigated with
geotechnical tests. The location of boreholes and sections for detailed investigations
must be chosen carefully, so that the main geological formations are adequately
characterised.
The geology of Castelnuovo has been investigated by classification of existing
information, field inspection and some seismic refraction tests, aimed at locating the
main discontinuities in the formations. According to the simplified geological cross
sections reported in Figure 4.19, the main geological formations are (Ferrini et al.,
2000):
Fig. 4.19. Geological cross-sections of Castelnuovo Garfagnana
x Quaternary deposits that mainly consist of: i) Holocene alluvial deposits of wellgraded gravels, sands and silts of variable thickness (ALL), ii) Holocene alluvial
terrace of well graded gravels sands and silts (CT), iii) Pleistocene alluvial terrace of
130
D. Lo Presti, C. Lai, and S. Foti
uniform pebbles of sandstone in a sand matrix (CT/MG) and iv) Other Holocene
deposits (CD, DT);
x fluvial-lacustrine formations from Plio-Pleistocene epoch (i.e. 1.5 to 3 million year
old) that mainly consists of i) clay and grey sand, sandy clay and clayey sand of
thickness up to 90m (ARG) and ii) gravel and conglomerate in a clayey sandy matrix
and pebbles of sandstone (CG, C/MG) of thickness even greater than 50m;
x Macigno sandstone (MG) from Oligocene epoch (i.e. 20 to 30 million year old) of
thickness up to 2000m. This formation is strongly weathered at the top and becomes
intact after a transition zone. The thickness of the weathered zone ranges from 10 to
20m while that of the transition zone is much more variable.
4.5.1. FIELD TESTS
Once the main geological formations were recognised, a series of geophysical seismic
tests have been planned to assess their shear wave velocity and hence their small strain
shear modulus. Three down-hole (DH) tests have been executed using a pair of
receivers and interpreting the data both with the direct travel time and the visual true
interval methods, without significant differences. During the drilling of the boreholes,
SPT data have been collected.
Seismic refraction tests using horizontally polarised shear waves (SH) and multistation
SASW tests have been performed at the same locations of the DHTs. An array of 24
geophones has been used for multistation SASW measurements that have been
interpreted in the frequency-wave number domain (fk).
VS (m/s)
0
200
400
600
800
1000
0
Depth (m)
3
6
9
SASW
down-hole
SH
12
Fig. 4.20. VS – profiles from different geophysical methods at Castelnuovo
Figure 4.20 shows a comparison between the shear wave velocities obtained with the
different methods at the S3 borehole location. A very high initial shear modulus has
been found for the ARG formation, leading to the idea that this formation could be
131
Geophysical-Geotechnical Investigations
locally considered as bed-rock. This initial statement was later modified on the basis of
laboratory test results.
Table 4.1 reports the average values of the shear wave velocity for each formation,
which have been estimated on the basis of the field test results.
Table 4.1. Average Vs values at Castelnuovo Garfagnana
Geological Formation
Shear wave velocity Vs [m/s]
Holocene Alluvial Deposits (ALL)
250
Holocene Alluvial Deposits (CT, DT, CD)
200
Pleistocene Alluvial Terrace (CT/MG)
380
Fluvial-Lacustrine Deposit (ARG)
800
Fluvial-Lacustrine Deposit (CG)
500
Weathered Sandstone (MG1)
600
Sandstone - transition zone (MG2)
950
Intact Sandstone (MG3)
1200 – 1500
4.5.2. LABORATORY TESTS
Laboratory tests have been performed on samples retrieved using a Shelby tube sampler
for the ARG formation and a double core sampler for the MG (Ferrini et al., 2000). On
the basis of classification test results the ARG samples are mainly classified as CL-ML
and rarely as SM-SC. ARG can be defined well-graded and very dense soils of low
plasticity. On the undisturbed ARG samples several Resonant Column (RC) and Cyclic
Loading Torsional Shear tests (CLTS) have been performed. Moreover one specimen
was tested in the triaxial apparatus in Cyclic Loading Triaxial conditions (CLTX), at
constant strain rate and, after a rest period of 24 hrs with open drainage, in Monotonic
Loading Triaxial conditions (MLTX). During both CLTX and MLTX tests, the shear
wave velocity was measured using bender elements (BE), in order to assess the "elastic"
damage due to the progressive straining imposed to the specimen. The details of the
testing operations can be found in Calosi et al. (2001).
Normalised shear modulus G/G0 and damping ratio (D) obtained with CLTX, RC and
CLTS tests are compared in Figure 4.21. Because of the high non-linearity exhibited by
the ARG specimens in the laboratory tests, it was decided that it would have been better
to consider the Macigno formation as bedrock.
Another important aspect to be assessed was the effect of loading cycles. Figure 4.22
shows the degradation parameter (t = – log G / log N ) (Idriss et al., 1978) and Figure 4.23
reports a comparison of CLTX and MLTX results. At large strains the stiffness from
CLTX becomes even smaller than that from MLTX, because of cyclic degradation. The
influence of the number of cycles on the stiffness and damping ratio of ARG specimen
is quite negligible, as confirmed by the shear wave velocity (Vs) measurements before
and after each loading cycle of the CLTX test, which gave almost the same results.
132
D. Lo Presti, C. Lai, and S. Foti
Fig. 4.21. Normalised shear modulus and damping ratio from RC, CLTS and CLTX
tests
Geophysical-Geotechnical Investigations
133
Fig. 4.22. Degradation parameter from CLTX tests
Fig. 4.23. Young modulus from MLTX and CLTX
One specimen of weathered MG (MG1) and another of intact MG (MG3) have been
firstly subjected to unconfined cyclic compression loading test UCCL and after to
unconfined monotonic compression loading test UMCL (Calosi et al., 2001). The
normalised stiffness decay and damping ratio are shown in Figure 4.24.
134
D. Lo Presti, C. Lai, and S. Foti
Fig. 4.24. Stiffness and damping ratio from UCCL and UMCL
4.5.3. LABORATORY VS. FIELD TESTS
The small strain shear modulus of ARG inferred from RC and CLTX tests is plotted vs.
depth in Figure 4.25. The G0 values inferred from CLTS and MLTX tests are almost the
same. Figure 4.25 also shows the small strain shear modulus inferred from DH tests at
S3 location. Laboratory tests largely underestimate the initial stiffness probably
because of sampling disturbance, which can be very important if Shelby samplers are
used in very dense low plasticity soils. The poor sample quality should not influence
the shear modulus decay curves if the sampling disturbance influences the soil stiffness
Geophysical-Geotechnical Investigations
135
at small and at large strains. Yet, high quality samples, retrieved with in-situ freezing
should be taken in order to clarify this aspect. Laboratory tests on high quality samples
could definitely confirm the non-linearity of ARG specimens.
As the MG formation is concerned, the values of shear wave velocity inferred from in
situ and laboratory tests are shown in Table 4.2.
The shear wave velocities inferred from in situ and laboratory tests show very similar
values. In the case of intact sandstone, those measured in the laboratory are even
greater than those determined in situ. It is possible to assume that the effect of sampling
disturbance is not very important in the case of rock specimens. On the other hand,
possible scale effects could explain why the shear wave velocity of intact sandstone
determined from laboratory tests is larger than that obtained from in situ tests.
DH
RC
Depth, z [m]
CLTX
Fig. 4.25. Comparison between G0 from in situ and laboratory tests
Table 4.2. MG Shear wave velocity from in situ and laboratory tests
Type of soil
Vs m / s
Vs m / s
Weathered sandstone (MG1)
Transition zone (MG2)
Intact sandstone (MG3)
Situ
600
900
1200-1500
Laboratory
530 - 550
1700-1800
4.5.4. DEFINITION OF SOIL PARAMETERS FOR SEISMIC ANALYSIS
Two different sets of parameters had to be selected in the reported case history, indeed
the site response was analysed by mean of two different approaches: linear equivalent
analysis and non-linear analysis.
136
D. Lo Presti, C. Lai, and S. Foti
1D and 2D linear equivalent analyses
Laboratory test results on ARG specimens have been used to analytically describe the
G-J and D-J curves, adopting the following equations, proposed by Yokota et al. (1981):
1
G
Go
1D J E
D
Dmax exp(O
(4.21)
G
)
Go
(4.22)
where the shear strain J is expressed in percent [%]. Note that the knowledge of the
shear strength is not required for the evaluation of the curves using the above
formulation.
The shear modulus decay was defined by a single set of parameters inferred from CLTS
and RC tests (D = 65 E = 1.15). The triaxial test results were disregarded for this
purpose, because the effect on the seismic response of the higher non-linearity exhibited
in triaxial tests was considered negligible. On the contrary, two sets of parameters were
defined to describe the damping ratio decay (Dmax= 34.8 O= –1.9) from RC tests and
(Dmax= 23.3 O= –2.2) from cyclic quasi-static tests, CLTS and CLTX). Distinct
analyses have been performed with the two sets of parameters.
The G-J and D-J curves, obtained according to the method described above, have been
used to characterise the stiffness and damping non-linearity of both ARG, CG and
CT/MG formations in the framework of linear equivalent analyses.
For the MG formation, shear modulus and damping ratio decay curves have been
defined numerically on the basis of experimental results. Finally, for quaternary
deposits (ALL, CT, CD and DT), for which no undisturbed sampling was possible, the
decay curves proposed by Rollins et al. (1998) with their range of variation have been
adopted.
1D Non-linear analysis
The Ramberg-Osgood (1943) equation was used for the stress-strain backbone curve:
E
Eo
where: H rif
1
E Ha
1D
E o H rif
q max / E o ;
(4.23)
R
E
G
{
;J
E o Go
(1 Q ) H a
In the case of ARG, CG and CT/MG formations the Ramberg-Osgood (RO) parameters
were obtained from the MLTX test. The RO parameters were obtained from UMCL
tests, in the case of MG formation. For the alluvial deposits, the RO parameters were
obtained fitting a numerical curve derived from the Rollins et al. (1998) equation.
Geophysical-Geotechnical Investigations
137
The unload-reload branches were simulated by means of the second Masing (1926) rule
as modified by Tatsuoka et al. (1993). In particular they proposed to assume a scale
amplification factor “n” not necessarily equal to 2 as postulated by the second Masing
rule. For the case under consideration, the only available experimental data concerning
the n parameter where deducted by the comparison of CLTX and MLTX results on
ARG specimen. It was decided to assume n=2.6 for ARG, CG, CT/MG and ALL and
n=2 for MG.
4.6. Conclusions
A seismic ground response analysis must always be preceded by an accurate dynamic
characterization of the site whose main objective is the identification of:
x
x
x
x
x
shallow subsurface geology;
lithostratigraphic-geotechnical units;
hydrogeological regime;
physical properties and state parameters of the formations;
parameters of mechanical and hydraulic behavior of the formations under earthquake
loading.
Typically, the dynamic characterization of the site is carried out implementing an
adequate program of geophysical and geotechnical field-lab investigation testing
campaign. This Chapter presented an overview of the capabilities and limitations of
some of the most common geophysical and geotechnical investigation techniques as
well as a detailed case history.
The starting point for planning the investigation is an accurate geological and geomorphological model constructed on the basis of geological maps and cross-sections at
an adequate scale (at least 1:5000).
Near-surface geophysical investigations are especially important for the definition of
the dynamic soil properties at the site (i.e. shear wave velocity and damping ratio fields)
and of the shallow subsurface geological structure. Often, the results of the geophysical
investigations are used to re-define the original geological model. On the other hand,
laboratory testing methods are important to determine the soil non-linear stress-strain
relationships and their damping ratio degradation curves. A still open question, only
partially discussed in the Chapter, concerns with undisturbed sampling, sample quality
and the effect of sample disturbance on the normalized shear modulus and damping
ratio degradation curves. In-situ large strain techniques should be used for those soils
that cannot be successfully retrieved and tested in the laboratory. However the costs of
these methods can be very high and not affordable in many cases.
CHAPTER 5
SITE EFFECTS
Kyriazis Pitilakis
Aristotle University, Thessaloniki, Greece
5.1. Introduction
Surface geology and geotechnical characteristics of soil deposits have a paramount
importance on seismic ground shaking. The variations of ground shaking in space,
amplitude, frequency content and duration are called “site effects”. Site effects include
primarily the effects of impedance contrast of surface soil deposits to the underlined
bedrock, or firm soil considered as rock, which is rather well modelled using 1D ground
models (i.e. linear elastic, equivalent linear or non-linear). They also include deep basin
effects, and basin edge effects, produced from strong lateral geological discontinuities
(i.e. geological anomalies, faults etc). These effects which are dominated by the
presence of surface waves additionally to body waves can only be studied using 2D and
3D models. Finally, site effects are also dealing with spatial variation of ground
shaking characteristics due to surface topography.
The physics and the importance of site effects is more and more understood and
quantified with the increasing number of strong motion measurements in dense
accelerometric arrays all over the world. Advanced numerical models using powerful
computer facilities have also contributed significantly to the progress during the last two
decades. Mexico City (1985) and Loma Prieta (1989) earthquakes, recorded in many
stations located in different and well constrained ground conditions, relieved for the first
time in a very precise experimentally documented way, the importance of the
impedance contrast. Additional evidence of the significance of the more complex site
effects on seismic ground motions have been brought from recent destructive
earthquakes (Armenia 1988, Philippines 1990, Northridge 1994, Kobe 1995, Kozani
1995, Aegion 1995, Kocaeli and Duzce, Turkey 1999, Athens 1999, Ji-Ji Taiwan 1999
etc).
Specific experimental sites, operating the last ten years, such as Euroseistest
(http://euroseis.civil.auth.gr) and Ashigara valley as well as other accelerometric arrays,
mainly in Japan (i.e. K-net) and in California, are continuously producing high quality
experimental data in densely instrumented sites, often sedimentary valleys, which
allowed very detailed experimental and theoretical analyses of complex site effects, and
revealing their complexity due to deep basin and basin edge effects, additionally to the
pronounced role of the impedance contrast and the role of soil non-linear behaviour.
However, there is not yet a wide-spread agreement as regards to what could be the best
way to estimate the amplification or de-amplification or the spatial variability caused by
site effects. There are also different approaches to model and account for site effects in
seismic risk studies. A typical example is the very different approach to model site
effects, which range from 1D to 3D models, using linear or non-linear material
behaviour. Probably this may be attributed to the fact that, still, very few site effect
studies have been performed both involving a detailed study of subsurface structure and
139
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 139–197.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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Kyriazis Pitilakis
numerous high-quality recordings and/or observations of earthquake ground motion.
In general, site effects may be defined as the modification of the characteristics
(amplitude, frequency content and duration) of the incoming wave field, due to the
specific characteristics and geometrical features of the soil deposits and the surface
topography. The modification is manifested as an amplification or de-amplification of
ground motion amplitudes at all frequencies, which is dependent on many parameters.
Some of them are inherent of the dynamic soil behaviour and its physical properties (i.e.
Dr, PI, Vs, Vp, Go, shear modulus degradation with shear strain increase, soil internal
damping, soil non-linearity, etc), others are related to the characteristics and the
intensity of the incoming wave-field and others are related to purely geometrical
features like surface/bedrock topography, lateral geological discontinuities etc.
In order to understand the physics and the spatial variation of ground motion in each
particular case and particularly to be able to quantify the phenomenon, it is necessary to
have an accurate description of the above characteristics for the specific site. As a
result, site and soil characterization is an important and indispensable parameter for site
effect analyses.
In the present chapter we are discussing few basic topics outlined previously, using
mainly experimental data and results from studies performed during the last few years
in Greece. More precisely, after a brief overview of the physical concepts and the
definitions of site effects, we first present a critical evaluation of the most usual
methods to assess site effects both experimentally and theoretically and then we present
and discuss site effects in case of (a) horizontally layered soil deposits, (b) basin edge
effects and (c) topographical relief. Finally, the last part of this chapter is devoted to (a)
discuss the way that modern seismic codes, like NEHRP, IBC 2000 and EC8, take in to
account site effects, and (b) propose a new site categorization and a new set of
amplification factors and normalized response spectra to specify input design
earthquake motion for engineering purposes.
5.2. Basic Physical Concepts and Definitions
Earthquake recordings at soil surface include “information” that is related to three
stages of the earthquake phenomenon evolution: a) the source activation (fault rupture),
b) the propagation path of seismic energy and c) the effect of local geology on the
wave-field at the recording site (Figure 5.1). The physical amplitude r(t), potentially
representing acceleration, velocity or displacement, which is recorded at a site, can be
written in the time domain in the form of the convolution of three factors:
rt
et * pt *st
(5.1)
where e(t) is the source signal, p(t) is the function that characterize the propagation
from the source to the site and s(t) expresses the effect of local soil conditions on
ground motion (which from now on will be denoted as site effects). In the frequency
domain, Equation (5.1) is written with the form of a product
R f
E f P f S f
(5.2)
Site Effects
141
where R(f), E(f), P(f), and S(f) are the Fourier transform of the time depended functions
r(t), e(t), p(t), and s(t) respectively. All of the above mentioned factors contribute to
overall site response, either independently or in combination with the others. However,
in the framework of this chapter, only the “site effects” factor is discussed. The other
two factors are simply considered in the presentation of different models that are used to
estimate ground response.
The term “site effects” introduces the effect of local geology in the modulation of
seismic wavefield at a recording site; where local geology consists of surface
sedimentary sites and surface topography. The main parameters that characterize a site
are the geometry of the soil stratigraphy (thickness and lateral discontinuities), the shape
of the topographic relief and the dynamic, physical and mechanical properties of soil
and rock materials.
Fig. 5.1. Schematic illustration of the wave propagation from fault to ground surface
(Yoshida and Iai, 1998; Reproduced with permission from the Swets & Zeitlinger Publ.)
Surface soil formations are the product of the long-lasting process of erosion,
weathering and deposition; they are responsible for significant amplification and spatial
variation of surface ground motion. Surface topography, in its simplest form, consists
of convex (ridges, mountains, hills …) or concave surfaces (valleys, basins, canyons …)
with different behaviour during an earthquake. In case of convex topographies,
significant amplification is observed at the crest compared to that at the foot, while in
the concave ones, the amplification varies at the lateral parts than at the base.
The effect of local geology on ground motion also depends on other parameters such as
the intensity, the frequency and the incidence angle of the incoming wavefield (for
strong or weak earthquakes) which in combination with the local site conditions might
introduce non-linear phenomena. Generally, it could be stated that there is a large
variety of parameters according to which, someone could categorize site effects, a fact
that confirm the complexity and the need to understand the physical background of this
phenomenon.
A general description of “site effects” could be defined as follows: “Surface soil
formations and surface topography modify the characteristics (amplitude, frequency
content and duration) of the incoming wavefield resulting to the amplification or
deamplification of ground motion”. A simple qualitative and quantitative estimation of
site effects is often expressed by the amplification factor Amax and resonant –
fundamental and higher ones - frequencies fres.
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Kyriazis Pitilakis
5.2.1. SITE EFFECTS DUE TO LOW STIFFNESS SURFACE SOIL LAYERS
It has been long recognized that the amplitude of earthquake ground motion is affected
by both the properties and configuration of the near surface material through which
seismic waves propagate. These properties are impedance - resistance to particle
motion - (Aki and Richards, 1980) and damping (attenuation).
Influence of Impedance and Damping in frequency and time domain
For horizontally polarized shear waves (SH), impedance can be defined (Equation 5.3)
as the product of the density ( ȡ), the shear wave velocity (Vs) and the cosine of the
angle of incidence (Figure 5.2).
I
U Vs cosT , cosT # 1 thus I
U Vs
(5.3)
Incidence angle, T, is usually small near the surface of the earth and its cosine can be
assumed to be equal to unity. As a seismic wave passes through a region of decreasing
impedance, the resistance to motion decreases and, to preserve energy, the amplitude of
the seismic wave increases. When there are sharp changes (decrease) in impedance
below the earth’s surface (such as sediments/rock interfaces), an increase in amplitude
of the upwardly seismic wave is observed due to resonance, as some of the seismic
waves transmitted into the upper layer get trapped in this layer and begin to reverberate.
Damping or inelastic attenuation is substantially greater in soft soils than in hard rocks
and mitigates the increase in amplitude of seismic motion due to resonance. The
fundamental phenomenon responsible for the amplification of motion in soil sediments
is the trapping of seismic waves due to the impedance contrast between sediments and
the underlying bedrock. For the simplest case of a soil layer with density U1 and shear
wave velocity Vs1 overlying a stiffer layer with density U2 and shear wave velocity Vs2
(Figure 5.2a), the impedance contrast is expressed by the formula:
C
U 2 Vs2
U1 Vs1
(5.4)
To understand the basic concept of site effects, the simplification of the physical
complex phenomena is instructive. Thus, when the structure is horizontally layered (1dimensional structures), this trapping affects only body waves travelling up and down in
the surface layers (Figure 5.2). When the sediments form a 2- or 3- dimensional
structure due to soil thickness variations, this trapping also affects surface waves which
develop on the sediments/bedrock interfaces and thus reverberate back and forth. In all
cases, this effect is maximum when the reverberating waves are in phase with each
other. The interference between these trapped waves leads to resonance.
Resonance therefore, is a frequency-dependent phenomenon related to the geometrical
and mechanical (density, P-wave and S-wave velocities, damping) characteristics of the
soil structure. While these resonance patterns are very simple in the case of a 1D
structure (vertical resonance of body waves), they become more complex in 2D and 3D
structures. The fundamental resonant frequency may vary between 0.2 Hz (for very
Site Effects
143
thick deposits or for extremely soft materials) and 10 Hz or more (for very thin layers of
deposits or weathered rocks).
The amplitude of fundamental resonant peaks is mainly related to the impedance
contrast between surface soil layers and underlying bedrock, to the material damping of
sediments and to a lesser degree with the characteristics of incident wavefield (type of
waves, incidence angle, near or far field …). For the simplest case discussed above, the
amplification at the fundamental resonant frequency is given by the formula:
A0
2
1
0.5 S ] 1
C
(5.5)
where C is the impedance contrast and ]l the material damping of the sediments. For
the case of very small damping (]l =0), the maximum amplification is simply double the
impedance contrast. Another interesting observation is that when the wavelength, Ȝ,
O Vs1 T
(5.6)
is much longer than the thickness of the layer (meaning that ȦH/Vs1 # 0), the amplitude
of surface displacements is doubled. This is called the free surface effect and is caused
by upgoing seismic waves being reflected off the free surface of the earth. At the
surface, both upgoing and downgoing reflected waves are exactly in phase and the
resultant amplitude at that location is doubled.
Figure 5.2 provides an illustration of the effect of resonance in the frequency domain,
particularly a low resistance sedimentary layer overlying hard rock (impedance contrast
c=5). Without taking into account the free surface effect (where the amplification
would be doubled as mentioned previously), a 100 m thick layer produces peaks of
amplification at about 0.5, 1.5, 2.5 Hz and higher. On the other hand, a 50 m thick layer
produces peaks at 1.0, 3.0 Hz and higher. It can be stated therefore that, the
amplification of higher peaks decreases with increasing frequency, due to the
consideration of inelastic attenuation or damping, which in this specific case takes a
relatively large value. It has been shown, both experimentally and theoretically that this
amplitude very often reaches values between 6 and 10, while in the extreme case,
exceeds 20 (high impedance contrast and small damping).
In case of 2D and 3D structures, fundamental frequency depends also on the geometry
of the soil structures. The lateral geometry of these structures is affecting the
amplification level at resonant frequencies especially when the material damping is
small. Complex effects that are introduced due to the consideration of the finite lateral
extent are due to the locally generated at the discontinuities (edges, faults, etc) and
laterally propagated surface waves. The effect of these surface waves is manifested in
two ways:
144
Kyriazis Pitilakis
Sediments
H
Vs1=200m/sec
ȗ1=5%
Rock
ȡ2Vs2
=5
ȡ1Vs1
H=100m
4
SH wave
H=50m
Amplification
3
șȠ : angle of incidence
for vertical propagation
of SH waves ș=0Ƞ
2
1
0
0
1
2
3
Frequency (Hz)
4
5
Fig. 5.2. Example of a simple model of 1D site amplification
When the semi-length of the soil structure is much larger than its maximum thickness
(shallow basins), the waves have the same frequency characteristics as 1D resonance,
thus increasing the 1D amplification level. When the semi-length of the soil structure is
comparable to its thickness (deep basins), and the rebervarating back and forth surface
waves are in phase, the waves interfere with each other leading to 2D resonance patterns.
The same resonance effects are involved in the seismic wave modulation due to 3D soil
structures. The consideration of the second and third lateral dimension in the wave
propagation phenomena, in case of 2D and 3D resonance, leads to an increase in ground
motion amplification and a shift towards higher values of the peak frequencies. An
interesting comparison between 1D, 2D and 3D resonance, spectral peaks of
amplification is presented in Figure 5.3. The differences between 1D and 2D resonance
are much more pronounced than between 2D and 3D cases. This means that the
consideration of the third dimension in the simulation of ground motion leads to
quantitative differences relative to 2D analysis (much larger amplification and a small
shift in resonant frequencies).
Site Effects
145
Fig. 5.3. Spectral responses computed at the basin center for 1D, 2D and 3D models of
semi-shaped basin (Bard and Riepl 1999; Reproduced with permission of the publisher
WIT Press)
In the time domain, these resonance patterns affect the peak amplitudes of ground
motion (mainly peak ground acceleration, PGA and peak ground velocity, PGV), the
waveforms and the motion duration, especially in 2D soil structures. Experimental
evidence (records) from recent earthquakes (Mexico, Loma Prieta, Northridge etc)
showed that PGA were up to 4 times larger at soil than at rock sites. Statistical analyses
of records have shown that PGA is most likely to be amplified when the fundamental
resonant frequency of a site exceeds 2-3Hz. On the other hand, it was also observed
that liquefied sandy deposits induce important reduction of peak acceleration (i.e. Kobe
case). Therefore, PGA values on sediments cannot be predicted straightforwardly from
PGA values on rock and this issue is strongly related to the non-linear phenomena in
soil behaviour. A general trend however do exists, for moderate accelerations levels
(<0.2-0.3g), in the sense that amplification of PGA is expected at soil sites compared to
rock sites.
This behaviour of PGA amplification may be attributed to a) the fact that in soils with
low S wave velocity, the accumulated energy results in amplification and therefore, as
the ground becomes “softer”, amplification becomes larger (elastic range) and b) the
fact that under strong dynamic loading the ground becomes “softer”, (shear strength
decreases) and hence, the peak acceleration becomes smaller and the predominant
period of soil profiles is shifted to higher value (non-linear behaviour of soil materials).
Consequently, amplification occurs under small ground shaking with decreasing
absolute value as the ground shaking level is increased.
This observation has been already included in UBC97, UBC 2000, NEHRP and EC8draft code previsions with the introduction of an amplification coefficient depending
146
Kyriazis Pitilakis
both on soil classification and input motion amplitude. Further discussion on these
issues is given in subsequent part of this chapter.
Regarding the duration of ground motion, all recent studies report a significant increase
of duration in sediments especially at longer periods when soil stratigraphy is complex.
This fact is closely related to the geometry of the structure (2D or 3D) and the existence
of strong lateral discontinuities; that will be discussed in the following sections.
5.3. Methods to Estimate Site Effects
There are various methods that may be used for site effect evaluation. The choice of the
method usually related to the significance of the engineering project for which it is
applied. Generally, the methods are classified in five main categories:
- Experimental-empirical techniques that utilise recordings of ground motion or
ambient noise to estimate the basic characteristics of the expected ground motion usually in the frequency domain.
- Empirical methods that evaluate parameters of earthquake motions such as
acceleration, velocity and response spectra based on site classification, average Swave velocity, topography, earthquake magnitude and existing amplification
relationships; usually these methods are incorporated in seismic code provisions.
- Semi-empirical methods that compute time histories of earthquake motion by
combining recorded earthquake motion of smaller earthquakes as element motions
(i.e. Green’s functions); these methods may account for the detailed fault rupture
process and the effects of asperities.
- Theoretical methods where site effects are computed through an analytical and more
often numerical 1D, 2D or 3D wave propagation model; different wave types with
different incident angles may be used; the main advantage of these methods is the
possibility to use complex constitutive relationships for describing soil behaviour
under dynamic loading conditions and the ability to model accurately site
stratigraphy inclusive of basin topography.
- Hybrid methods that compute time histories of earthquake motions by coupling a
longer period component determined by a theoretical seismic fault model with a
computational seismic wave propagation model having a shorter period component
determined by a semi-empirical method.
The use of each method depends on many parameters and, in any case, requires an
increased level of expertise. In the following paragraphs some aspects of the first four
methods will be briefly discussed.
5.3.1. EXPERIMENTAL-EMPIRICAL
The majority of the experimental techniques that have been developed during the last
decades analyze site effects in the frequency domain because this is a relatively easier
way to handle earthquake recordings. It is reminded that earthquake recordings may be
represented in the frequency domain as the product of Fourier spectra of the source
effect, the path effect and the site effects. In order to estimate the influence of local
geology (site effects), the removal of the influence of the first two terms (source and
path effects) is necessary. For this purpose, several methods have been proposed which
Site Effects
147
are classified in two major categories based on the criterion of the use of a “reference
site”; the reference site can be generally defined as this particular control location that is
free of all kinds of site effects and it is usually the nearby rock site. The most
commonly applied experimental techniques are shortly presented in the following
paragraphs.
Standard Spectral Ratio Technique (SSR)
The most popular and widely used technique to characterize site amplification has been
the Standard Spectral Ratio, SSR, (Borcherdt, 1970), which is defined as the ratio of the
Fourier amplitude spectra of a soil-site record to that of a nearby rock-site record from
the same earthquake and component of motion (Figure 5.4). Source information is the
same for this pair of records and when the two sites are closely located, the path effect
is also considered the same. Hence, the ratio of the Fourier amplitude spectra expresses
only the effect of the local soil conditions at the specific site. Theoretically speaking
though, this technique is applicable only to cases that the data are derived from dense
local arrays with at least one station on outcropping conditions defined as reference
station.
A usual option for the selection of the reference station is a site of outcropping rock,
while less frequently, a bedrock site having a downhole accelerometer installed in a
borehole is the used for this purpose. The basic conditions for the application of this
particular technique in the case of a surface reference station are: a) the existence of
simultaneous recordings at a soil site and at the reference site, b) the reference site has
to be free of any kind of site effects (sediments and topography) and c) the distance
between the soil site and the reference one ought to be small (i.e. smaller than the
epicentral distance), in order to consider that the effect of the propagating path of the
seismic energy is the same for the two sites.
However, the condition that an outcrop rock reference site should be free of any kind of
site effects often it is not valid. For this reason, a careful examination of the reference
site is obligatory in order to correctly estimate amplification in sedimentary sites (Stiedl
et al., 1996).
Generalized Inversion Scheme Technique (GIS)
Andrews (1986), having in mind that The Standard Spectral Ratio technique is reliably
applicable only to data from dense, local arrays, proposed a generalized technique to
look for all source, path and site effects in large data sets recorded in local or regional
networks, by applying the solution of a large inverse problem. In this generalized
inversion scheme, the path term is generally assumed to follow an a-priori known law.
Thus, for a given data set, the unknown source and site effects Fourier amplitude
spectra are simultaneously estimated from the whole data set generally through least
square weighted inversion. The main advantage of this technique is the reliable
estimation of the source and site effects terms from the whole data set especially in
cases where there are not simultaneous records of all earthquakes at all sites of the
network (Field and Jacob, 1995).
Coda wave technique
Phillips and Aki (1986) on the other hand, proposed an alternative method based on the
148
Kyriazis Pitilakis
use of coda waves. The estimation of the site effects term is exclusively based on the
latest part of the recordings (coda waves), starting from that point, where time is double
of that of the first S arrival. The spectral shape of these coda waves is independent of
the source and of the recorded site because this part of the recordings is dominated by
multi-scattered waves at the heterogeneities of the Earth’s crust. More details could be
found in Phillips and Aki (1986).
Fig. 5.4. General description of the Standard Spectral Ratio Technique (SSR)
Horizontal to Vertical Spectral Ratio Technique (HVSR)
All techniques mentioned above are using a reference site but in practice, appropriate
reference sites are not always available. For this reason different methods that are not
depending on reference sites have been developed. One of them is the Horizontal to
Vertical Spectral Ratio. This extremely simple technique consists of using the spectral
ratio of the horizontal to the vertical component of ground motion and estimates the
Fourier amplitudes in different frequencies accordingly. The basic assumption of the
method is that the vertical component of the ground motion in cases where the soil
stratigraphy is flat and horizontal is supposed free of any kind of influence related to the
soil conditions at the recording site. Figure 5.5 shows the general layout of the method
which was first applied to the S wave portion of the earthquake recordings obtained at
three sites in Mexico City by Lermo and Chavez-Garcia (1993). Generally, the Fourier
spectra ratio exhibit similarities between SSR and HVSR technique, with a better fit in
frequencies rather than amplitudes of the resonant peaks.
Site Effects
149
Fig. 5.5. Description of the Horizontal to Vertical Spectral Ratio Technique (HVSR)
Comments on SSR and HVSR
SSR and HVSR are the most commonly used experimental techniques for the
estimation of site amplification due to local soil conditions; there are plenty of literature
references on comparative results on their applicability and reliability. Herein, some of
these works are briefly summarized and their main conclusions are highlighted.
Detailed comparisons between SSR technique and other reference station techniques
(Field et al., 1992; Stiedl, 1993; Field and Jacob, 1995) led to few basic qualitative
conclusions such as: a) the estimation of site effects with the use of SSR technique is
relatively stable even if records are quite noisy, b) the process should be based on a
significant number of earthquake recordings (the use of a limited number of records
should be avoided) and c) the amplification level determined with SSR technique is
quite similar with that determined from other techniques and especially with the GIS.
Other comparisons between results of SSR and HVSR techniques led to controversial
conclusions. As it is already stated above, Lermo and Chavez-Garcia (1993) applied
HVSR to the S wave portion of the earthquake recordings and found similarities
between standard spectral ratios and these HVSR with a good fit in both frequencies
and amplitudes of the resonant peaks. Some other researchers used HVSR technique on
150
Kyriazis Pitilakis
data sets from weak and strong motion records and concluded that the shape of the
spectral ratios presents very good statistical stability with minor dependency on source
and path effects and that it is quite well correlated with surface geology, while their
amplification level seems to depend on the type of incident wave, a fact that does not
affect the fundamental resonant frequency. Field and Jacob (1995) after systematic
comparisons with other techniques concluded that the shape of the transfer function is
satisfactorily reproduced by HVSR technique, although there is an underestimation of
the amplification factor compared to SSR. On the same issue Raptakis et al. (1998,
2000), using a large and high quality date set from EUROSEISTEST experimental site,
proved that the significant differences between SSR and HVSR amplitudes at the
fundamental frequency are attributed to the considerable amplification of the vertical
component due to diffracted Rayleigh waves at the lateral discontinuities of the basin
(Figure 5.6).
TST
AMPLIFICATION
10
1
HVSR
SSR VERT.
SSR HORIZ.
1
FREQUENCY (Hz)
10
Fig. 5.6. Mean spectral ratios of HVSR technique compared to SSR horizontal and
vertical components (after Raptakis et al., 1998; Reproduced with permission from
D.Raptakis and the Earthquake Engineering Research Institute)
In conclusion, both SSR and HVSR techniques are reliable in estimating the
fundamental frequency of the soil profile. However the amplification amplitude is
comparable only when the soil layering is horizontal and there aren’t lateral geometrical
variations. In those cases, due the presence of in-ward propagating surface waves, it is
expected that part of them will affect the vertical component and hence the amplitude of
the HVSR method. For this reason, in cases where the stratigraphy is not flat and
horizontal, which is pertinent in many real site conditions, the use of HVSR technique
should be applied with caution at least for the derivation of the amplification factor at
the fundamental frequency.
5.3.2. EMPIRICAL METHODS
Empirical methods are practically used either for preliminary analyses or in the frame of
seismic code prescriptions with well specified amplification factors defined according
to the soil classification and the earthquake intensity. Simple relationships giving the
amplification factors for the peak acceleration or/and velocity with the average shear
151
Site Effects
wave velocity of the soil profile are proposed in the literature (Joyner and Fumal 1984,
Midorikwa 1987, Borcherdt et al., 1991). All these relationships should be used only
for preliminary studies and with extreme caution.
The last part of the present chapter will be devoted to the discussion of code provisions
regarding site effect estimates. In this paragraph a senior problem is discussed
concerning the site characterization using exclusively the average S-wave velocity over
the 30m from the surface, which was first introduced by Borcherdt (1994) and then
adopted in most modern codes.
The major question is how accurate is the use of Vs30 for soil and site characterization.
Certainly, the main advantage is the simplicity in evaluating the site conditions by
conventional geotechnical surveys which rarely exceed 30-40m. On the other hand, the
question remains whether the simple knowledge of the s-wave velocity over the limited
depth of 30m is an accurate parameter to estimate site amplification characteristics. It is
interesting to notice two examples from recent down-hole recordings that prove the
opposite (Figure 5.7).
RESPONSE SPECTRA (g)
6.0
TST-0.0m
(a)
0.09
TST-17.0m
0.08
TST-72.0m
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
TST-0.0m/TST-17.0m
5.0
4.0
3.0
2.0
1.0
0.0
1.0
1.0
2.0
0.0
PI-16.0m
0.8
PI-32.0m
0.7
PI-83.0m
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.0
6.0
PI-0.0m
(c)
0.9
3.0
(d)
RESPONSE SPECTRA RATIOS
0.0
RESPONSE SPECTRA (g)
TST-0.0m/TST-72.0m
(b)
RESPONSE SPECTRA RATIOS
0.10
2.0
3.0
PI-0.0m/PI-83.0m
PI-0.0m/PI-32.0m
5.0
4.0
3.0
2.0
1.0
0.0
0.0
1.0
2.0
PERIOD (SEC)
3.0
0.0
1.0
2.0
PERIOD (SEC)
3.0
Fig. 5.7. Response spectra (left) and response spectra ratios (right) at the Euroseistest
(up) and Port Island (down) vertical arrays. (Pitilakis et al.,1999; Reproduced with
permission from the Swets & Zeitlinger Publ.)
152
Kyriazis Pitilakis
In both sites the spectral ratios between the surface and down-hole records at various
depths are considerably different at long periods (T>1sec). Large amplifications of the
deep incident wave field are practically absent when we are computing the transfer ratio
for shallower depths. Long period waves, mainly surface waves, generated at the lateral
discontinuities disappear when only the uppermost layers are taken into account
together with a 1D SH wave pattern (the case of Euroseistest valley). In the Port Island
array in the U.S., due to liquefaction and strong inelastic behaviour of surface soils, the
ground motion is de-amplified and the most severe response is observed at the
fundamental period of the deposit (T=1sec). The recorded response spectral ratio
between surface and -32m presents practically no amplification for T>0.5sec, while the
amplification between surface and -83m is quite important.
In conclusion the use of Vs,30 as a basis for soil and site characterization is misleading in
many cases. It should be used only when the actual site conditions are appropriate to
that i.e. relatively shallow “seismic bedrock” or very firm soil conditions, flat
stratigraphy.
In conclusion, empirical methods are mainly used for a quick simplified evaluation of
the basic parameters of ground amplification: fundamental frequency of the soil profile
and amplification ratio. They are useful (a) for microzonation studies and (b) with their
special form of spectral amplification factors for different soil categories in seismic
code prescriptions for the design of structures. In all cases they should be applied and
used very carefully because their statistical background and the a-priori limited
information required regarding site characterization may lead to serious errors.
5.3.3. SEMI-EMPIRICAL METHODS
The semi-empirical methods compute time histories of earthquake motions caused by
large scenario earthquake by combining recorded earthquake motions by smaller
seismic events. The Green’s function technique is based on the idea that the total
motion at a particular site is equal to the sum of the motions produced by a series of
independent ruptures of many small parts on a causative fault. The method requires an
approximate definition or estimation of certain parameters such as the geometry of the
source, the slip functions describing the slip displacement vector with time for each
elementary source, the velocity structure of the crustal materials between the source and
the site and the Green’s functions that describe the motion at the site due to an
instantaneous unit slip at each elementary source. Normally the Green’s function at
each site, account implicitly the particular site specific ground behaviour in the linear
elastic range.
The empirical Green’s functions technique (EGF) (Hartzell 1978) bypasses these
complicate computations by using the weak motions of small earthquakes as empirical
Green’s functions to simulate strong motion. Figure 5.8 illustrates the principles of the
method. The method is essentially a deterministic one as it computes time histories for
a defined earthquake scenario and other parametres. However it is possible to use
statistical Green’s functions which are computed as the statistical average of the
recorded earthquake motions for different small seismic events. The EGF technique is
particularly useful for generating near-field motions and when it is important to account
the detailed fault rupture process and the effects of asperities. It is less accurate when
strong non-linear behaviour is expected for local soils.
153
Site Effects
Site
Recordings of
small earthquake
motions
Local soil deposit
Seismic
wave
propagation
Initiation of
fault rupture
Fault rupture process
Assuming a small
earthquake motion is
generated from each
fault element
Superposition of
small earthquake
motions taking into
account rupture
process and distance
time
small
earthquake
Fault plane for large
earthquake
Scaling relation between
the large and small
earthquakes is used
for determining size
and number of fault
elements
Large earthquake motion
Fig. 5.8. Procedure for generating earthquake strong ground motions with the empirical
Green’s function technique (reproduced from ISO/WD 23469-draft).
5.3.4. THEORETICAL (NUMERICAL AND ANALYTICAL) METHODS
When the geological structure of an area and the geotechnical characteristics of the site
are known, site effects can be estimated through theoretical analysis. The prerequisite
of sufficient geotechnical knowledge of the soil structure including surface and deep
topography is therefore obvious. Such an approach requires an in-depth understanding
of the constitutive models describing the soil behaviour under dynamic solicitations and
methods used to solve the wave propagation problem in 1, 2 or 3 dimensions. There are
many models and methods which make the simple reference a rather difficult task and
anyway beyond the task of the present chapter and book. Thus, in the present section
the basis of the most conventionally used methods to account for site effects in ground
response studies for microzonation purposes will be discussed.
Simple analytical models
As already mentioned, site amplification in soil sediments is related to resonance effects
which are presented in the frequency domain in the form of spectral peaks in the Fourier
transfer functions. A simple analytical approach which does not require any numerical
computations, aims to estimate the fundamental period of the soil, W0, and the
corresponding amplification factor A0. A simple simultaneous estimation of these two
parameters is possible only for sites that can be approximated as one layer over bedrock
structure. This is a relatively easy way since only soil density, S-wave velocity,
thickness, and damping of sediments as well as S-wave velocity of bedrock are required.
For multi layered sites, only the fundamental period could be satisfactorily estimated;
Dobry et al. (1976) summarized the most significant methods. On the contrary there is
154
Kyriazis Pitilakis
no approximate and reliable formulae for the estimation of fundamental amplification
factor A0 in horizontally multi layered sites. Such formulae would imply many
parameters, including damping, S-wave velocities and thickness of each layer.
However, an upper bound of A0 may be estimated using the impedance contrast between
the lower stiffness surface layers and most rigid deep formations, together with the
material damping of the surface soil deposits. The approximation is very crude and may
lead to large overestimations and potential errors.
One dimensional response of “soil columns”
A number of analytical methods exist that allow numerical computations of the seismic
response of a given site. The most widely used computations are based on the multiple
reflection theory of S-waves in horizontally layered deposits (1D analysis of soil
columns). According to this theory, “soil columns” are excited by incoming vertically
incident plane S-waves that correspond to a surface bedrock motion representative of
what is expected to occur in the area for a specific earthquake scenario. The parameters
required for the analysis are the shear wave velocity, density, the material damping
factor and the thickness of each layer. The above parameters may be obtained through
in-situ geophysical and geotechnical surveys and appropriated dynamic laboratory tests.
Alternatively, but with less accuracy, approximate correlations may be applied using
conventional geotechnical parameters such as SPT, CPT, PI, Dr among others. These
analyses may be performed considering either linear or non-linear behaviour for the soil.
In the latter case, the non-linearity is usually approximated with an equivalent linear
method that uses an iterative procedure to adapt soil parameters (i.e. stiffness and
damping) to the strain level that each particular soil layer experiences during a specific
earthquake motion. Specific curves expressing the degradation of shear modulus G and
the respective increase of material damping, with the increasing shear strain level have
been proposed by numerous researchers according. Figure 5.9 presents a typical set of
G/Go-Ȗ-D% curves. They have been estimated from resonant column tests on
undisturbed specimens and they describe the dynamic behaviour of soil in the
Euroseistest experimental site.
Average curves have been also proposed for different soil materials (clay with varying
PI, sands, soil mixtures, etc). They must be used with caution because the actual
behaviour for a given soil at a specific site may strongly vary from these average curves.
This was the case in Mexico City where the lacustrine clayey deposits of extremely
high plasticity index were found, through appropriate dynamic test (RC, CTX), to
behave almost linearly despite the large strains experienced during the strong 1985
event and contrary to the previous belief that they should exhibit highly nonlinear
behaviour because of their very low rigidity.
The last twenty years many interesting numerical codes have been developed with
advanced non-linear and elastoplastic constitutive models that may also account for
liquefaction phenomena. They certainly require additional parameters describing soil
behaviour under complicated loading and drainage conditions which are not easily
acquired even with sophisticated laboratory tests. Moreover the validation of these
models with experimental results, mainly from actual seismic recording, is still a major
unsolved problem. This fact combined with the need of complicate soil parameters is
affecting seriously their wide use in practice.
155
1
20
0.9
18
0.8
16
0.7
14
0.6
12
0.5
10
0.4
8
0.3
6
0.2
4
0.1
2
0
1.0E-004
1.0E-003
1.0E-002
Ȗ%
1.0E-001
DT %
G/Gmax
Site Effects
0
1.0E+000
SM : silty sand -sandy silt
CL-ML : silty clay (5<IP<10, e=0.4-0.6)
CL : clay (IP=10-20, e=0.5-0.7)
CH : clay (IP=40, e=0.7-1.0)
CL-ML: stiff silty clay with gravels (deep layers D>100)
Weathered rock (G*)
Rock (G)
Fig. 5.9. Shear modulus and material damping dependency on shear strain for the soil
formations at EUROSEISTEST site (after Pitilakis et al., 1999; Courtesy of the Journal
of Earthquake Engineering)
Advanced 2D/3D models and methods
All numerical and analytical methods have the same theoretical basis (i.e. wave motion
equations). However, many different models have been proposed to investigate several
aspects of site effects which involve complex phenomena. For example, one has to
consider for the various types of incident wave-field (near or far field, body and/or
surface waves), the geometry of the structure (1D, 2D and 3D), the behaviour and the
dynamic properties of soil materials (visco-elasticity, nonlinear behaviour, saturated
media, etc). Typically, these advanced methods may be classified into four groups:
156
Kyriazis Pitilakis
- Analytical methods which may be used for a limited number of simple geometries.
- Ray methods which are difficult to use when the wavelengths are comparable to the
size of heterogeneities (usually the most interesting case).
- Boundary based techniques which are the most efficient when the site under
consideration consists of a limited number of homogeneous geological units.
- Domain based models (finite difference and finite element methods) which allow
accounting for very complex soil structures and constitutive models for the dynamic
behaviour of soils but they are expensive from a computational point of view.
The development of these methods contributed significantly to the breakthrough in the
understanding of site effects during the last three decades. They allow for parametric
studies and more important the study of uncertainties of the seismic ground response at
a site, considering the incomplete knowledge regarding the mechanical and geometrical
characteristics of the site under consideration. However, there is still an important lack
of reliable and detail validations.
5.3.5. CONCLUDING REMARKS
Theoretical models and computation tools have been developed during the last years.
They allow detailed and advanced studies of wave propagation under complicated
geometrical and material conditions. A complete comparative presentation and
discussion on the advantages and the shortcomings of each model is beyond the scope
of this chapter. Few examples of successful applications are therefore simply presented
to highlight their capabilities.
More precisely the subsequent parts of this chapter are as follows: (a) 1D equivalent
linear SH wave propagation computations performed in the frame of the detailed
microzonation of Thessaloniki (Section 5.4), (b) 2D finite difference modelling of
complex site effects in valleys (EUROSEISTEST and Thessaloniki, Section 5.5) and
strong topographic irregularities (CORSEIS-Aegion Section 5.6), and 2D finite element
equivalent linear computations in Thessaloniki (Section 5.5).
Future advances in these methods could be expected for the proper consideration of
diffraction effects in complex surface or subsurface topography and realistic modelling
of strong non-linear behaviour of soft soils, especially of sands (liquefaction
phenomena). Nonetheless, the routinely use of these methods raises the following main
concerns:
Theoretical models have been very rarely validated towards their ability to predict
ground motion. Most of the comparisons between observations and theoretical results
were made a-posteriori.
Numerical models are not panacea, but can be used only to some limited cases. The
knowledge of their validity domain is a prerequisite in order to avoid erroneous
estimations of site response attributes.
Their cost may sometimes be really high due to the detailed geotechnical and
geophysical investigations required to provide a good knowledge of the constitutive soil
properties needed as input parameters.
The deployment of instrumented experimental test sites in seismic regions with various
local soil and site conditions that are deeply known in terms of their geological,
Site Effects
157
geotechnical and seismological features, is a powerful tool to understand the nature of
the complicate wave propagation phenomena, to study different aspects of the problem
while it is a prerequisite condition for further development, validation and extension of
all theoretical models and tools. Finally, experimental test sites and local arrays may be
of great important to improve existing code prescriptions.
To this extent,
EUROSEISTEST (http://euroseis.civil.auth.gr) and CORSSA experimental sites
(http://www.corinth-rift-lab-org) contribute significantly.
5.4. Site Effects in Horizontally Layered Soil Deposits
It has been shown previously that the dominant phenomenon governing the
amplification of motion in sedimentary deposits overlying the rigid bedrock formations
is the trapping of seismic waves due to the impedance contrast between sediments and
rock. When the subsoil stratigraphy is almost horizontally layered, then the medium is
practically 1-dimensional and the trapping phenomenon affects only body waves
travelling up and down in the layered medium. For this reason, seismic ground
response is very often calculated using only horizontally polarized shear waves (SH).
When the soil stratigraphy is more complex forming a 2D or even 3D medium, then the
trapping also affects surface waves, which are generated on the interface of sediments
and bedrock exhibiting various inclinations. The trapping wave effect is maximized
when the reverberating waves are in phase with each other. The interference between
these trapped waves leads to resonance and hence to maximum ground motion
amplitudes. The resonance which is a frequency depended phenomenon is quite simple
in case of 1D medium (vertical resonance of body waves), and it becomes more
complex for 2D/3D structures.
Material damping and generally, the non-linear soil behaviour particularly for seismic
events of moderate and strong intensities, affect this trapping wave phenomenon by
modifying amplitudes of ground motion in different frequencies and duration.
Nevertheless, the fundamental phenomenon is still governed by the impedance contrast
between sediments and bedrock. In turn, the impedance contrast, as expressed by the
ratio of the product of shear wave velocities and densities between two layers, is the
final and crucial result of the site characterization procedure in each particular site.
Some of the representative results are presented herein, involving a conventional 1D SH
analysis, and implementing the well-known equivalent linear model for the soil
behaviour, specifically for the city of Thessaloniki. The work is part of the
microzonation study of the city (Pitilakis et al., 2003). In the following chapter the
results of 1D analysis will be discussed in the light of 2D computations (finite
difference and finite element method) as well as analyses of experimental data
(recordings).
5.4.1. 1D SITE EFFECT COMPUTATIONS IN THE CITY OF THESSALONIKI
Thessaloniki, having almost one million inhabitants, is the second largest city of Greece
(Figure 5.10). It has a long seismic history as it has been founded in the 4th century BC
and it remained always through the centuries an important and big city. The more
recent event was the large M=6.4, R=25 km event of June 20th 1978 that caused severe
damage in the city buildings. Since then, considerable research has been undertaken
leading to the microzonation study of the city, which has been concluded recently.
158
Kyriazis Pitilakis
Fig. 5.10. Thessaloniki. Location and topographic relief
In the framework of this research project an extensive program of geotechnical and
geophysical surveys and tests have been performed in order to construct an accurate
geotechnical map appropriate for seismic response analysis of ground motion
(Anastasiadis et al., 2002 and Pitilakis et al., 2003). Dynamic soil tests both laboratory
and in situ were the most important part of all surveys. The detailed statistical analysis
of all these data resulted in 9 main soil categories with full description of the dynamic
soil properties (Vs, density, G/Go-Ȗ-D) (Figure 5.11).
Various thematic maps have been also constructed; an example is illustrated in
Figure 5.12 where four maps of the thickness corresponding to different soil categories
are presented. These maps have been constructed based on a large number of cross
sections for the whole area. Geological information and tectonics also played an
important role. Based on these maps and cross-sections it can be concluded that the
subsoil stratigraphy in Thessaloniki is not really flat and horizontally layered.
Nevertheless, as the 1D analysis is always the basic reference study it was decided to
perform a detailed “equivalent linear” analysis first in more than 300 representative
“soil columns” estimated through the detailed geotechnical mapping of the city and then
to examine the possible implications of 2D effects.
According to the seismic hazard analysis the design outcrop acceleration is
PHGA=0.25g (i.e. 10% probability of exceedance in 50 years for design earthquake in
many codes like NEHRP, EC8, EAK2000 for ordinary constructions). Five different
input motions selected for outcrop conditions were applied, all scaled to 0.23g-026g to
159
Site Effects
account for different epicentre distance from the focus. Figure 5.13 shows a typical
example of the analysis in a specific location along the coastal area of the historical
center of the city. Figures 5.14 and 5.15 illustrate in the form of GIS maps some of the
most representative results of the detailed ground response analyses for the city of
Thessaloniki.
Microzonation of
Thessaloniki
1.0
Microzonation of
Thessaloniki
Based on Resonant Column Tests & Literature
A
B1
B2
B3
C
Based on Resonant Column Tests & Literature
A
B1
B2
B3
C
D
E
F
G
0.8
D
E
F
G
20.0
G/G
DS (%)
max
0.6
0.4
10.0
0.2
0.0
0.0001
0.001
0.01
0.1
1
10
0.0
0.0001
Shear Strain, ã(%)
Forma
tion
Description
A
B2
B3
Surficial
B1
Artificial Fills, demolition materials and debris
parts
Very Stiff sandy-silty clays to clayey sands,
low plasticity
Soft sandy-silty clays to clayey sands, low to
medium plasticity
Stiff to hard high plasticity clays
0.001
0.01
0.1
1
10
Shear Strain, ã(%)
VS (m/s)
200-350
(250)
300-400
(350)
200-300
(250)
300-400
(350)
120-220
(180)
VP (m/s)
QS
400-1700 8-20 (15)
1900
15-20 (20)
1800
20-25 (20)
1800
20-40 (30)
1800
20-25 (25)
Very soft buy mud and silty sands
D
Alluvium deposits, sandy-silty clays to clayey
sands-silts, low strength and high
compressibility
150-250
(200)
1800
15-25 (20)
E
Stiff to hard sandy-silty clays to clayey sands
350-700
(600)
2000
6-30 (30)
Very stiff to hard low to medium plasticity
clays to sandy clays
Overconsolidated with rubbles and thin layers
of gravels
700-850
(750)
3200
50-60 (60)
1750-2200
(2000)
4500
180-200
(200)
F
G
Subbase
C
GreenSchists and Gneiss
Fig. 5.11. Dynamic properties, (mean “design” values), of the basic soil formations in
Thessaloniki
160
Kyriazis Pitilakis
(a)
(b)
(c)
(d)
Fig. 5.12. Maps of different geotechnical formations, a) thickness of the historical
center’s debris and fills, b) thickness of the coastal loose silty sand and silty clay, c)
depth of the upper surface of the basic stiff clay formation, and c) iso-depth of the
“seismic” bedrock (Anastasiadis et al., 2001; Courtesy of the Birkhaeuser Publishing)
Site Effects
161
Fig. 5.13. Typical example of 1D analysis using 5 input motions, all scaled to the design outcrop acceleration (PHGA=0.25g)
162
Kyriazis Pitilakis
Fig. 5.14. Maps of the mean peak horizontal ground accelerations (m/s2) for different
spectral periods (T=0.0 sec, 0.3 sec, 0.6 sec and 1.0 sec)
The computed ground motion amplifications vary considerably in different parts of the
city. This can be attributed to the local impedance contrast and the non-linear behaviour
that exhibit some loose-soft soil materials, which are found especially along the shore
line. The detailed site and soil characterization played a paramount role on the spatial
variability and the amplitudes of the computed ground motion. An important practical
Site Effects
163
conclusion drawn from the above observations is that the “effective values”, (65% of
the peak values), differ considerably from the “design value” proposed by the Greek
Seismic Code (bearing in mind that according to EAK2000 Thessaloniki belongs in
category II with a value of 0.16 g that is independent of the soil category). The question
is therefore, whether this 1D body wave SH computations accurately describe the
complex nature of wave propagation in case of non-horizontally layered media. In the
following chapter an effort will be made to discuss this important issue.
Fig. 5.15. Maps of the mean peak horizontal ground a) velocity PHGV (m/s) and b)
displacement PHGD (m)
5.4.2. CONCLUSIVE REMARKS
One dimensional body wave propagation models are the basic tool for ground response
analyses. In their simplest form (i.e. linear elastic or equivalent linear elastic soil
behaviour) they are rather simple while they need for few parameters which are easily
estimated even without performing specific dynamic field and laboratory tests, as there
are many correlations with conventional geotechnical parameters (i.e. Vs-SPT, Vs-CPT,
G/Go-Ȗ-DT% with PI and DR% for clays and sands etc). For fully non-linear and
elastoplastic soil behaviour the evaluation of appropriate soil parameters and models is
still a difficult task. Successful predictions of all parameters of ground response under
strong seismic excitation (peak amplitudes, frequency content, spectral values and
duration) for cases that soils exhibit highly non-linear behaviour (sometimes in the
presence of liquefaction) are rare and often they are made a-posteriori.
Generally 1D models are reliable for nearly horizontally layered deposits and in cases
when the impedance contrast between soil deposits and underlying rock is the
controlling parameter of ground motion. The velocity of the bedrock and the incident
164
Kyriazis Pitilakis
wave field characteristics are playing an equally important role. With the 1D modelling
the higher frequency parts of the expected ground motion can be captured quite
accurately. Low frequency parts are less reliable and this is an important shortcoming
for the case of deep basins (>300m).
In the case of Thessaloniki the 1D modelling of ground response was proven quite
successful from an engineering point of view, both qualitatively and quantitatively. As
it will be shown later on, the 2D ground response, in this particular case, is simply
improving the general picture. The main features are already well described with a
detailed 1D SH waves equivalent linear model.
5.5. 2D Phenomena in Ground Response Modelling
Site effects due to complex surface geology are examined through experimental and
theoretical analyses in two cases. First the high quality set of data of EUROSEISTEST
experimental site (http://euroseis.civil.auth.gr) are used in order to study, both
experimentally and numerically, the potential appearance and relevant effects of surface
waves that are generated, additionally to the 1D body waves, which propagate up-words.
In the second case similar experimental and numerical analyses are performed on a
specific cross-section of Thessaloniki, where seismic recordings and an accurate 2D
ground model are disposed. In both cases it is proven that locally generated surface
waves, propagating horizontally, contribute considerably in all basic parameters of
ground motion (amplitude, frequency content and duration).
5.5.1. 2D EXPERIMENTAL AND THEORETICAL STUDIES IN EUROSEISTEST
VALLEY
EUROSEISTEST experimental site is deployed in a valley near Thessaloniki in the
epicentral area of the strong 1978 Ms=6.4 earthquake. The cross-section of the valley
(Figure 5.16) is very well constrained through numerous geotechnical, geophysical and
geological surveys (Pitilakis et al., 1999).
The database of ground motions recorded in surface and down-hole accelerographs
comprises of many records from small and moderate earthquakes (Mw<5.8,
5<R<120km). An example of a far field event (Kozani Mw=6.5, R=100km earthquake)
is given in Figure 5.17 together with the computed 1D SH wave synthetics that are
derived using as input motion the record of the same transversal component at the
reference site PRO. It is clear that 1D model is inadequate to simulate accurately the
recorded motion, especially in the central part of the valley.
The reasons of the observed discrepancies have been discussed in detail in many studies
(Raptakis et al., 2000; Chavez-Garcia et al., 2000; Makra, 2000; Makra et al., 2001;
Pitilakis et al., 2001). In the frequency domain we observe through the transfer
functions of P, S and SW waves composing the recorded signal (Figure 5.18.), large
amplitudes of SW waves for frequencies up to 2Hz while the S window part has much
lower amplitudes. This general trend is also observed in the downhole records, (TST17m, TST-72m), which shows that surface waves affect the whole volume of the subsoil,
at least in the central part of the valley and all three components. As surface waves are
not observed at the reference site (PRO) or at the edges of the valley, it is concluded
that the observed strong surface waves traces are locally generated on the lateral
165
Site Effects
geological discontinuities of the valley, which is actually a graben (see Figure 5.16).
Moreover the fact that observed maxima in both S and SW parts appear at the same
frequency (0.7Hz), implies that both body S waves propagating upwards and locally
generated surface SW waves contribute to the spectral amplification of the fundamental
peak.
250
NNW
STE
ST22
200
150
STC
PRO
C
FRM
100
ALTITUDE (m)
SSE
0
TST
TST17
TST72
F
-50
A
B
D
E
G
D
C
E
D
F
G*
F1
G
E
F4
G
C
GRA GRB
B
C
C
E
F
G*
50
G*
B
G*
G
-100
F
F3
F2
G*
-150
G
-200
-0.5
0.0
Layer
Description
0.5
1.0
1.5
2.0
2.5
3.0
DISTANCE (Km)
3.5
4.0
4.5
5.0
5.5
6.0
Swave
Density
QS
A
Silty, clayey sand
130
2.05
15
B
Silty sand and sandy clay
200
2.15
25
C
Marly silt and silty sand
300
2.075
30
D
Marly, sandy clay and clay silt
450
2.100
40
E
Alternating sublayers of clayey, silty sand and
sandy clay with stones and gravels
650
2.155
60
F
Alternating sublayers of clayey, silty sand and
sandy clay with stones and gravels
800
2.20
80
G*
Weathered schist bedrock
1250
2.50
100
G
Gneiss basement
2600
2.60
200
Fig. 5.16. EUROSEISTEST valley cross-section and strong ground motion instrumentation array layout amplification (Chavez-Garcia et al., 2000; Reproduced with
permission from Elsevier)
166
Kyriazis Pitilakis
TIME(sec)
10
TIME(sec)
10
300
200
100
0
-100
-200
C
BHU
E
D
FF
A
IE
R
B
U
T
O
N
I
K
O
YR
E
L
T
E
S
D
E
P
M
A
I
T
O
B
R
O
TC
S
R
G
C
E
RU
E
0
5
15
20 0
5
TRANS. COMPUTED
TRANS. RECORDS
ALTITUDE(m)
15
20
P
R
O
B
A
N
M
U
R
TRANSVERSAL COMPONENT
0
500
1000
1500
2000
2500 3000 3500
DISTANCE (m)
4000
4500
5000
5500
6000
Amplification
Amplification
Amplification
Fig. 5.17. Transversal seismograms from a far field event and 1D synthetics (Raptakis
et al., 2000 Reproduced with permission from Elsevier)
10
STE
STC
10
1
10
1
FRM
GRB
10
1
10
TST0
TST17
1
GRA
1
10
Frequency (Hz)
10
TST72
Transversal Component
P-waves
1
1
S-waves
1
10
Frequency (Hz)
SW-waves
1
10
Frequency (Hz)
Fig. 5.18. Transfer functions for P, S and SW windows of surface (STE, STC, FRM,
GRB, GRA, TST0) and downhole (TST-17, TST-72) transversal accelerograms
(Raptakis et al., 2000 Reproduced with permission from Elsevier)
167
Site Effects
2D numerical analysis on the other hand, clearly indicates that the largest amplitudes of
motion are not related to the vertically propagating SH waves, since the synthetic
seismograms (Figure 5.19) are dominated by locally generated Love waves that
converge to the center of the valley and thus, result to large amplitudes and a
consequent increase of the duration; phenomena which are not seen outside the central
part of valley. As a result, the synthetic ground motions verified the experimentally
observed phenomenon of the existence and the importance of surface waves, which are
locally generated at the edges of the valley and propagate to the center of the valley. A
comparison between recorded and computed ground motion (Figure 5.20) proves that
while the 2D model is reproducing successfully the recorded time histories, 1D
modelling significantly fails to reproduce the observed long period surface waves.
GRA GRB
TST
FRM
STC
STE
15.0
10.0
Time (sec)
5.0
0.0
PRO
0.0
1.0
2.0
3.0
4.0
5.0
Distance (km)
Fig. 5.19. 2D synthetics (f < 10 Hz) (Anastasiadis et al., 2001; Courtesy of the
Birkhaeuser Publishing)
The important 2D effects described above, are further examined by introducing the
notion of “aggravation factor” which is the ratio of the acceleration response between
2D and 1D ground response analyses (Makra 2000, Makra et al., 2001). After proper
experimental verification this ratio along the whole cross-section of the valley
(Figure 5.21) was calculated. 2D response spectra are significantly larger than 1D in a
large band of frequencies and almost along the whole valley. This effect may have
serious implications on design seismic motions since the vast majority of codes are
based on the simple concept of 1D SH upward propagation. The case of Euroseistest
valley is certainly a good and representative example; but in order to quantify the 2D
and possibly the 3D effects for design input motion purposes, a number of additional
cases should be examined. Thessaloniki is probably a second interesting case.
168
Kyriazis Pitilakis
Fig. 5.20. Comparison between recordings (REC) of the transversal component and 1D,
2D synthetics at TST (centre), FRM and STC (south) stations all filtered at fc=3.5Hz.
REC
2D
TST
1D
0.0
2.0
4.0
6.0
8.0
10.0
Time (sec)
12.0
14.0
16.0
18.0
20.0
REC
2D
FRM
1D
0.0
2.0
4.0
6.0
8.0
10.0
Time (sec)
12.0
14.0
16.0
18.0
20.0
REC
2D
STC
1D
0.0
2.0
4.0
6.0
8.0
10.0
Time (sec)
12.0
14.0
16.0
18.0
20.0
Fig. 5.21. Variation of the 2D/1D aggravation factor (ratio of acceleration response
spectra) along the EUROSEISTEST cross-section for different periods
Site Effects
169
5.5.2. 2D EXPERIMENTAL AND THEORETICAL STUDIES IN THESSALONIKI
The complex site effects in Thessaloniki are examined in a characteristic cross-section
(Figure 5.22) where there are three simultaneous recordings in broadband seismometers
of a Mw=4.8 event occurred on 16.12.1993 (Figure 5.23). One of the stations (OBS) is
on the outcrop and can be considered as a reference site. From the experimental
transfer functions computed for stations LEP and ROT, it is shown that the transversal
component, in both stations, correspond to higher amplifications and fundamental peaks
at lower frequencies than the radial one (Figure 5.24).
Fig. 5.22. Typical geotechnical cross-section in the historical centre of Thessaloniki
(Anastasiadis et al., 2001; Courtesy of the Birkhaeuser Publishing)
The fact that the fundamental peak amplification of the transversal component is larger
than the radial one and moreover shifted at lower frequencies is a strong indication of
the appearance of diffracted Love waves and of their pronounced role in the recorded
ground motions. Furthermore, the higher amplification of the vertical component at the
most distant station (LEP) compared to ROT which is closer to the edges, is an
indication that Rayleigh waves are also generated at the edges affecting the vertical
component. Examining separately the S and SW parts of the recorded motions at the
most distant station LEP (Figure 5.25), it was observed that S and SW waves appear
having the same frequencies along the entire time history, and the major portion of the
amplitude amplification is due to the SW part. The same phenomenon has been
observed at Euroseistest; locally generated surface waves at the edges of the valley
induce additional amplification to the 1D body wave propagation particularly at the
fundamental 1D frequency. All three components were amplified (the vertical due to
the Rayleigh waves), while a clear increase of the duration of the shaking was also
observed
170
Kyriazis Pitilakis
Fig. 5.23. Radial (left) and transversal (right) component of an Mw=4.8, R>100km event
(16.12.93) recorded at 3 stations (seismometers) along the cross-section (Raptakis et al.,
2003a)
Fig. 5.24. Experimental transfer functions (reference station at OBS), and time windows
of S and SW parts of signal recorded at station LEP (on the shore line) (Raptakis et al.,
2003a)
Site Effects
171
Fig. 5.25. Experimental transfer functions of S, SW and S+SW parts of the complete
signal (Raptakis et al., 2003a)
The experimental observations of the complex site effects, mainly in the frequency
domain, are followed by a numerical study of a 2D model of the cross-section
(Figure 5.26) The synthetic ground motion is clearly dominated by two locally
generated Love wave trains; the first appearing at the fundamental mode (latest part of
the seismograms), while the second one represents a higher mode of Love waves. It is
shown that the topmost layers with small Vs values dominate the fundamental mode,
while higher modes are guided by the deeper soil layers with higher Vs propagation
velocities.
The presence of the surface waves modifies considerably the ground motion
characteristics and as it is illustrated in Figure 5.27, the 2D simulations, using either a
finite difference or a finite element model, are much better simulating the actual
recordings. 1D model is proven rather inadequate to accurately describe the
complicated site effect pattern at the most distant station (LEP), which is dominated by
the presence of surface waves.
172
Kyriazis Pitilakis
Distance (m)
0
100
200
300
400
500
600
700
800
900 1000 1100 1200 1300 1400
0.0
1.0
Time(sec)
2.0
3.0
4.0
5.0
6.0
50
LEP
ROT
Altitude(m)
0
-50
-100
-150
-200
Fig. 5.26. a)2D model. Synthetic seismograms, b)2D Finite difference method (Raptakis
et al., 2003b)
Site Effects
173
Fig. 5.27. Comparison between 1D, 2D synthetics (Finite Difference and Finite Element
models) and recorded acceleration time histories at station LEP for the same event as in
Figures 5.23 and 5.24 (Raptakis et al., 2003b)
To further examine the importance of the 2D effects compared to conventional 1D
analyses the PGA values were computed at T=0.0sec along the cross-section for two
potential strong seismic events. The input motion records correspond to outcrop ground
accelerations from the Thessaloniki 1978 major aftershock and have been recorded on
outcrop conditions (station OBS); they are scaled at 0.1g and 0.3g. The 1D analysis has
been performed on vertical 1D profiles extracted from the 2D model using an equivalent
linear model. The 2D computations are using a finite element model, which allows for
equivalent linear simulation of the soil behaviour as well. The amplification ratio is
higher for the 2D model almost all along the sedimentary part of the cross-section. The
differences between 2D and 1D modelling are increased for the stronger excitation
while the 1D model in certain areas presents no amplification at all.
As PGA (T=0.0sec) is not always the best indicator of the site amplification severity,
especially for engineering applications, the amplification ratio was computed for the
whole range of periods (Figure 5.29). It is shown that the 1D spectral amplification at
the fundamental frequency (around 1Hz) is about 6.25 for a region between 100m and
500m from the coastal section for two events (input motion 0.1g and 0.3g) (Raptakis et
al., 2003b) area. On the contrary, the highest 2D spectral amplification factor, reaching
the value of 10, is found practically close to the shoreline of the cross-section. This is
due to the predominant effect of surface waves, as discussed earlier, which is certainly
more pronounced at longer distances from the edges where the surface waves are
generated. No important differences have been observed for 0.1g and 0.3g input motion
with respect to the above remarks.
174
Kyriazis Pitilakis
AP G A
4
Input maximum acceleratio n: 0.3g
2D
3
1D
2
1
AP G A
4
Input maximum acceleration : 0.1g
2D
3
1D
2
Kasandrou Str.
Ag.Dimitriou Str.
Rotonda
Egnatia Str.
50
Nikos
Ag.Konstantinos & Eleni
Lefkos Pirgos
100
Tsimiski Str.
1
0
-50
-100
-150
-200
0
500
1000
1500
Fig. 5.28. Computed peak ground acceleration amplification factor along the crosssection at T=0.0sec (PHGA-soil/PHGA-rock) (Raptakis et al., 2003b)
5.5.3. CONCLUSIVE REMARKS
It is readily shown both experimentally and theoretically that in case of rather shallow
sedimentary valleys, such as in EUROSEISTEST, that the wave field and the ground
response is strongly dominated by surface waves locally generated at the lateral
geological discontinuities. These waves contribute significantly to the 1D fundamental
amplification and to the elongation of the strong motion duration. 1D models cannot
capture all these characteristics of the complex wave-filed in geologically complex sites
contrary to the 2D modelling.
Similar phenomena are observed in the case of Thessaloniki which is presenting similar
geological and topographical features. Again surface waves were generated at the
northern lateral geological discontinuities and propagating horizontally “in-wards”
modify the spectral amplification pattern all along the city. The phenomenon is more
pronounced at longer distances from the “generating” discontinuities, i.e. along the
shore-line of the city. The 2D ground response is certainly better portraying the
Site Effects
175
“reality”. However for practical engineering applications the computed 1D SH-wave
“averaged and smoothed” spectral amplitudes, especially at the fundamental mode, are
not very much different. When there is an accurate knowledge of site conditions and
soil characteristics, 1D modelling is still offering a good description of the average
ground response. It is perfectly adequate for microzonation studies where a large
number of computations is needed using many different input motions (at least five for
each seismic scenario) to get average and smoothed design motion response spectra.
Fig. 5.29. Spectral Amplification factor SA(T) soil / SA(T) rock along the cross
There is no doubt that 2D analyses offer a much more detailed description of the
complicated ground response phenomena in geologically complex sites. For the
moment most of 2D or even 3D models are linear elastic with constant damping and
moreover their applications and results are “site and case depended”. Numerical 2D/3D
models with more advanced soil models are very “heavy” from computational point of
view and they cannot be applied easily, especially for parametric studies. For this
reason, so far, 2D models are mainly used to understand the physics of complex wave
propagation phenomena, less for design purposes and even less for detailing code
prescriptions. Moreover a full and reliable validation of each model, including the
simplest 1D ones, is always a major requirement. To this respect EUROSEISTEST 3D
accelerometric array and all other combined surveys and studies programmed in the
frame of this experiment , together with other similar experiments in Japan and USA
and the analyses of data coming from many accelerometric arrays installed all over the
world, are expecting to contribute seriously in better understanding and modelling of
complex site effects.
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Kyriazis Pitilakis
5.6. Site Effects Due to Surface Topography
5.6.1. BRIEF LITERATURE REVIEW
It has been reported after destructive earthquakes (Friuli, Italy 1976, Irpinia, Italy 1980,
Chile 1985, Whittier Narrows 1987, Kozani, Greece 1995, Aegion, Greece, 1995 and
Athens, Greece 1999) that buildings located at hill tops suffer more intensive damage
than those located at the base (Brambati et al., 1980; Siro, 1982; Celebi, 1987; Kawase
and Aki, 1990).
Fig. 5.30. Normalized peak accelerations recorded on mountain ridge at Matsuzaki,
Japan (after Jibson, 1987)
There are few but strong instrumental evidence that surface topography affects the
amplitude and frequency content of ground motion (Geli et al., 1988; Faccioli, 1991;
Finn, 1991; Chavez-Garcia et al., 1996; 1997, LeBrun et al., 1999; Jibson, 1987). Two
well known examples of apparent topographic effects are observed on the abutment of
Pacoima Dam in San Fernando 1971 Earthquake (Boore, 1972), where an impressively
high acceleration of 1.25g was recorded at the crest of a narrow ridge adjacent to the
dam in Tarzana station during the Northridge 1994 earthquake for which the
amplification was of the order of 5 in the vicinity of 3Hz reaching comparable peak
acceleration values. In Europe weak motion measurements (Bard and Meneroud 1987
and Nechtschein et al., 1995; Chavez-Garcia et al., 1996; LeBrun et al., 1999) reported
similar observations of large amplifications, almost with a ratio of ten, in a narrow
frequency band around 5Hz.
Theoretical models predict a systematic amplification of seismic motion at convex
topographies while de-amplification phenomena are observed over concave geometries
such as valleys. According to Bard (1999) these effects are related mainly to three
physical phenomena: (a) the sensitivity of surface motion to the incidence angle around
the critical especially for SV waves, (b) the focusing and d-focusing of seismic waves
along the topographic relief and (c) the diffraction of body and surface waves which
propagate downwards and outwards from the topographic features and lead to
interference patterns between direct and diffracted waves. Different researchers have
contributed to define the importance of various parameters.
Site Effects
177
Fig. 5.31. SH Fourier transfer functions to homogeneous half-space outcrop motions
(after Geli et al., 1988; Courtesy of the Seismological Society of America)
- The nature of the incident waves is studied by Ashford and Sitar (1997) who reported
that the amplification of incident SV is higher because reflection and diffraction of
SH waves does not generate other wave types.
- The incident angle has been studied also by Ashford and Sitar (1997) who found that
in generally the greatest absolute acceleration at the crest is observed for the case of
vertically propagating waves.
- Boore et al. (1981) and Ashford and Sitar (1997) studied the effect of slope
inclination and observed that the amplification becomes higher when the slope
becomes steeper.
- The spatial variation of ground motion along the bank of canyons with different
geometry (triangular, semi-cylindrical, semi-elliptical etc) have been studied by
Sanchez-Sesma et al. (1982), Trifunac (1973) and Wong and Trifunac (1974). Both
outlined the importance of the ratio of the canyon width to the wavelength of the
incident SH waves and of the incident angle.
- The frequency content of the input motion is also a key parameter. It is observed that
for long wavelengths, i.e. very low frequencies, topographic effects are negligible,
while the effects become significant for wavelengths comparable to the geometric
characteristics of the relief. (Ashford and Sitar, 1997, Ohtsuki and Harumi, 1983).
- Other parameters like soil stratigraphy and dynamic soil properties (Go, material
damping etc) have also an important effect on the qualitative and quantitative
modulation of the ground motion in topographic irregularities.
The main conclusions of the instrumental and theoretical results can be summarized in
the following:
178
Kyriazis Pitilakis
- Amplification is generally larger for the horizontal components that for the vertical.
- The steeper the slope, the higher the crest amplification
- Qualitatively the maximum effects correspond to wave lengths comparable to the
horizontal dimension of the topographic feature.
- The absolute value of the amplification ratio cannot be estimated or computed among
other reasons because the amplification of the displacement at the crest is generally
combined with a de-amplification at the base of the topographic irregularity and their
respective absolute values are not easily estimated a-priori.
5.6.2. SEISMIC CODES
It may be seen from the preceding paragraph that quantification of topographic effects
on seismic ground motion is a very difficult task where many parameters of different
nature are involved. The lack of high quality experimental data to better understand the
physics of topographic effects and to validate the numerous theoretical and numerical
analyses and results makes ambiguous the incorporation of the acquired experience in
seismic codes.
However the ongoing version of the European Seismic Code EC8 is an exception.
Based on earlier French Code AFPS-1990 it is proposing a correction factor, called
aggravation factor F, for both ridge and cliff type topographies as a function of the
height H and the slope angle i (Figure 5.32). The aggravation factor is defined as
(a) 2D = Ftopo (b)1D and takes values according to Figure 5.32; an extra 20% increase is
anticipated when a surface “soft” layer with thickness more than 5m is present.
Fig. 5.32. European Seismic Code provisions (EC8-2000) for topographic effects
5.6.3. THEORETICAL STUDIES IN AN EXPERIMENTAL SITE IN GREECE
The array
The Gulf of Corinth is one of the most seismically active regions in Greece. The most
recent destructive earthquake occurred in 1995 (Ms=6.5) and caused serious damages in
the city of Aegion (Figure 5.33) which is built in a sort of terrace right on the foot wall
of the Aegion fault. Part of the city, mainly harbour facilities and small old masonry
factory buildings are on the hanging wall part of the fault along the coastal area. The
fault of Aegion itself has not been activated during the recent Aegion earthquake
Site Effects
179
sequence. Most of the damages are reported up-hill. The earthquake has been recorded
in one station also up-hill (see Figure 5.33 site: OTE).
Important spectral accelerations are recorded (Figure 5.34) especially in the transversal
component which are not fully justified by the magnitude and the epicentral distance of
this particular event. The simplified cross section of the area is given in Figure 5.35. It
is based on an extensive geotechnical and geophysical survey contacted in the
framework of European research program (CORSEIS http://www.corinth-rift-lab.org
and Pitilakis et al 2003). The main part of the city terrace is dominated by hard-stiff
soils (CL-GC with Nspt>40 and average Vs=400m/s); the “seismic” bedrock may be
considered at the level of conglomerates found at -20m to -25m. On the contrary at the
coastal area the surface soils are mainly very loose saturated silty- sands (ML-SM with
Nspt<8 and Vs<200 m/s) presenting high liquefaction susceptibility and exhibiting clear
non linear behaviour. The equivalent to seismic bedrock conglomerate layer is found at
-180m from the level of the sea (approximately 250m from the terrace).
a) Investigated area
180
Kyriazis Pitilakis
b) Geological N-S cross section
Fig. 5.33. (a) Location and (b) Geological cross section of the investigated area
181
Site Effects
0.015
PSA (m/s2)
0.012
recording
0.009
analysis
0.006
a
0.003
0
0
0.5
1
1.5
2
2.5
3
Period (s)
0.015
PSA (m/s2)
0.012
recording
0.009
analysis
0.006
b
0.003
0
0
0.5
1
1.5
2
2.5
3
Period (s)
Fig. 5.34. Computed (1D SH waves) acceleration response spectra at the free surface
resulting from the recording at depth z=-178m; a) x-direction, b) y-direction,
Comparison with recordings
Fig. 5.35. Simplified cross section of the area
182
Kyriazis Pitilakis
In the frame of CORSEIS project a vertical down hole array has been installed at the
coastal area of Aegion consisting of five 3D broad band accelerometrers and two
dynamic pore pressure transducers. The deepest station is installed in the conglomerate
layer at -178m and the other four stations at -60m -30m -14m and at the free surface.
The pore pressure transducers are installed in the saturated loose marine deposits at -6m
and -14m depth where liquefaction phenomena are very prominent. The vertical array
(CORSSA, after CORinth Soft Soil Array) combined with two more surface
accelerometric stations operating on the terrace, form a unique array to study site effects
in the presence of soil liquefaction, soil nonlinearities, near or far field conditions and
topographic irregularity.
Y-direction
0.005
0.004
0.003
0.004
0.003
Ac c e le r a tion (m /s 2 )
A c c e le r a tio n (m /s 2 )
X –direction
0.005
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
0
5
10
15
20
25
30
35
40
0
5
10
15
0.005
0.005
0.004
0.003
0.004
0.003
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
30
35
40
25
30
35
40
25
30
35
40
25
30
35
40
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
5
10
15
20
25
30
35
40
0
5
10
15
Time (s)
20
Time (s)
0.005
0.005
0.004
0.003
Ac c e le r a tion (m /s 2 )
A c c e le r a tio n (m /s 2 )
25
-0.005
0
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
0
5
10
15
20
25
30
35
0.004
0.003
0.002
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
40
0
Time (s)
5
10
15
20
Time (s)
0.005
0.005
0.004
0.004
0.003
0.002
0.003
0.002
Ac c e le ra tion (m /s 2 )
A c c e le r a tio n (m /s 2 )
20
Time (s)
Ac c e le r a tion (m /s 2 )
A c c e le r a tio n (m /s 2 )
Time (s)
0.001
0
-0.001
-0.002
-0.003
-0.004
0.001
0
-0.001
-0.002
-0.003
-0.004
-0.005
-0.005
0
5
10
15
20
Time (s)
25
30
35
40
0
5
10
15
20
Time (s)
Fig. 5.36. Recorded and computed (1D-SHwaves) time histories for a small event
Site Effects
183
Preliminary 1D linear elastic computations of small event recorded during the validation
period of the instrumentation, (Pitilakis, D., 2002), proved that 1D modelling is enable
to simulate successfully the wave propagation pattern in the foot-hill of Aegion, most
probably due to strong 2D effects which could not be captured by the SH waves
propagating up-wards with input motion the recorded signal at -178 m
(Figure 5.36). Hence the 2D wave propagation is necessary even for weak motions.
Two-Dimensional modelling
A two dimensional wave propagation analysis is then performed using the finite
difference code FLAC (Ktenidou, 2003). The motivation of the present analysis is to apriori study the effects of topography using simple input motions of Ricker type with
different frequencies in the spatial variation and the intensity of ground shaking along
the irregularity. Apart from the understanding of the physics of wave propagation in the
presence of Aegion irregularity, we are expecting to check the theoretical results with
actual small-moderate and maybe strong ground motion recordings when available in
the whole surface and downhole array.
The finite difference discretization of the two dimensional model is shown in
Figure 5.37 together with the studied cases for the case of SV waves. The frequency
fo=0.88 Hz of the selected Ricker wavelet is comparable to the fundamental frequency
of the foot-hill side of the mesh; fo= 1.43 Hz is the fundamental 1D frequency of the left
up-hill side of the mesh and the highest (fo=3 Hz) is selected for a more realistic
incident motion. All analyses are linear elastic.
Fig. 5.37. Finite difference discretization of the analysed configuration
The vectorial representation of the computed velocities, having arbitrarily selected
scales, for the three incident wavelets is very interesting (Figure 5.38). After 1-2 sec the
ground motion is dominated by surface waves with relative high amplitudes. The
absolute amplitudes are decreased considerably after the first 2 sec but the motion
continues. The frequency of the incident monochromatic motion modifies considerably
the wave pattern. The upper part of the mesh seems to be less sensible comparatively to
the hanging wall part when higher frequencies than its fundamental one are present in
the signal.
184
Kyriazis Pitilakis
f = 0.88Hz
f = 1.43Hz
t=1s
t=1s
t=2s
t=2s
t=3s
t=3s
t=4s
t=4s
t=5s
f = 3Hz
t=1s
t=2s
t=3s
Fig. 5.38. Velocity vectors for three Ricker wavelets (fo=0.88Hz, 1.43Hz and 3Hz);
linear elastic analysis with constant damping ȟ=2%. Scale is magnified for late spots
The spatial distribution of the computed horizontal and vertical accelerations along the
surface is shown in Figures 5.39 and 5.40.
185
Site Effects
X
X
(a) ABSOLUTE MAXIMUM HORIZONTAL ACCELERATION: aHmax(x)
140
aH(max) [m/s2]x10
120
100
f=0.88Hz
f=1.43Hz
f=3Hz
80
60
40
20
0
500
400
300
200
100
0
0
100
200
x [m]
300
400
500
x [m]
(b) NORMALIZED MAXIMUM HORIZONTAL ACCELERATION:
aHmax(x)/aHmax(500)
aHmax(x) / aHmax(500)
2
1.5
f=0.88Hz
1
f=1.43Hz
f=3Hz
0.5
0
500
400
300
200
100
0
0
100
200
x [m]
x [m]
300
400
500
c) RATIO: a2DHmax(x) / a1DHmax(x)
a2DHmax(x) / a1DHmax(x)
2
1.5
f=0.88Hz
f=1.43Hz
1
f=3Hz
0.5
0
500
400
300
200
x [m]
100
0
0
100
200
x [m]
300
400
500
Fig. 5.39. Computed horizontal accelerations at the free surface (a) maximum
accelerations for the 2D model and different frequencies of input motion; (b) effect of
the frequency content of the input motion on the normalized peak horizontal
accelerations; (c) 2D peak ground accelerations normalized to 1D peak accelerations for
Ricker fo=3Hz
186
Kyriazis Pitilakis
X
X
(a) ABSOLUTE MAXIMUM VETRICAL ACCELERATION ĮVmax(x)
100
90
aV(max) [m/s2]x10
80
70
f=0.88Hz
f=1.43Hz
f=3Hz
60
50
40
30
20
10
0
500
400
300
200
100
0
0
100
200
300
400
500
x [m]
x [m]
(b) NORMALIZED MAXIMUM VETRICAL ACCELERATION
ĮVmax(x) / ĮVmax(500)
18
aVmax(x) / aVmax(500)
16
14
12
f=0.88Hz
f=1.43Hz
f=3Hz
10
8
6
4
2
0
500
400
300
x [m]
200
100
0
0
100
200
300
400
500
x [m]
Fig. 5.40. Computed vertical accelerations at the free surface (a) maximum
accelerations for the 2D model at different frequencies of input motion; (b) effect of the
frequency content of the input motion on the normalized peak vertical accelerations
From the velocity vectors it is evident the generation of surface waves, mainly Rayleigh
which propagate inwards modifying the motion. The cales have been magnified after 2
sec because the motion has decreased considerably. These surface waves produces
complicated wave patterns which involves, among other issues, the development of
strong vertical acceleration components at the ground surface on both sides of the
topographic irregularity. The amplitudes of these vertical accelerations, which are not
related to the incident wave field, are not negligible compared to the peak horizontal
acceleration (Figures 5.39a and 5.40a). Bearing in mind that real excitations are
containing vertical acceleration components as well, and based on these result, it should
be expected that in reality the vertical acceleration will be very strong in the vicinity of
topographic irregularities.
Another important observation is that the peak horizontal accelerations are increased
(about 30%) near the crest; on the contrary they are considerably decreased near the
foot of the cliff (almost 60%in average). Comparing the 2D horizontal accelerations
with the “free topography field” (i.e. at least 500m far from the crest) accelerations
(Figure 5.39b), it is observed that the influence of the topography is concentrated at a
short distance from the crest (about 200m) and the important variations in amplitudes
Site Effects
187
even more close to that. The influence of the frequency content of the incident SV
wave is affecting seriously the response, especially the vertical component. Higher
frequencies amplify more the “parasitic” vertical acceleration of the computed ground
motion in both sides of the irregularity.
In Figure 5.41 the so called “Topographic Aggravation Factor” (denoted as TAF) is
plotted. It is defined as the ratio of the Fourier amplitude spectra at certain location (i.e.
at the crest) and at long distance from it (x=500m) which may be considered as “freefield”. It can be readily seen that the topographic effect is more important at high
frequencies. In the range of frequencies of interest for ordinary buildings (1-4 Hz), the
Fourier amplification factor due to the topography (TAF) is varying between 1.2 and 1.5
which may have an important effect. This amplification is well compared with the
amplification factor proposed in EC8-Draft (Figure 5.32).
Fig. 5.41. Spectrum of Topographic Aggravation Factor at the crest for a Ricker wavelet
fo=3 Hz excitation and different values of material damping.
5.6.4. CONCLUSIONS
The analyses performed have proven that there is a strong diffracted wave field at the
topographic irregularity which generates important modifications on the ground motion
at both sides of the cliff. Additional amplifications in the horizontal and vertical
component of the motion are observed near the crest. At the foot side we noted the
existence of very strong “parasitic” vertical accelerations while the horizontal
component is seriously decreased.
The frequency content of the incident wave field has a serious influence at the
amplitudes of the motion. The Topographic Aggravation Factor computed at the crest
has been proven practically invariant for different frequencies of the incident wave. It
has been found in particular that a 25%-50% of extra amplification due to topographic
effects should be expected at least for the case considered herein. In general it is
concluded that site topographic effects maybe quite important. There are very few
188
Kyriazis Pitilakis
experimental observations and records to better understand the complex phenomena
related to the topography and more important to quantify them. It is expected that the
CORSSA array will play a very positive role to this issue.
5.7. Site Effects and Seismic Codes
Seismic ground response characteristics, defined generally as “site effects”, are
inevitably reflected in seismic code provisions. The selection of appropriate elastic
response spectra according to soil categories and seismic intensity is the simplest way to
account for site effects both for engineering projects and for a general purposes
microzonation study.
Modern seismic codes (IBC2000, UBC97, NEHRP, EC8) all introduced in the last few
years, after the recent strong earthquakes in America, Europe, Japan and worldwide,
which produced numerous valuable data, have incorporated the most important
experimental and theoretical results with the necessary adjustments and simplifications
for purely practical reasons.
The main improvement is that amplification factors of spectral values are varying with
the seismic intensity; lower shaking intensity earthquakes introduce higher
amplification factors due to the more linear elastic soil behaviour, contrary to higher
intensities where soils are exhibiting non-linear behaviour resulting to a decrease of
peak spectral values. Additionally, a more accurate soil categorization is introduced
based on a better description of soil profiles using standard geotechnical parameters (i.e.
plasticity index PI, undrained shear strength Su) and average Vs values. In IBC2000
and other codes of the same family, a special attention is given to near field conditions
introducing higher amplification factors for the same earthquake magnitude. Also for
soil layers of small thickness presenting high impedance contrast, the new version of
codes attribute higher amplification factors which is compatible with observations and
theory.
In general the parameters describing site effects in seismic codes are expressed through
(a) soil categorization and (b) spectral amplification factors and shapes. The pioneering
work of Seed et al. (1976) is still the basic reference. Since then all improvements are
basically resulting from a more detailed soil categorization and a large number of
numerical analyses from numerous researchers all over the world. 1D site effect
computations using the equivalent linear model is the main and almost universal tool for
all improvement and modifications introduced so far (i.e. Dickenson and Seed 1996,
Pitilakis et al., 2003). The increasing number of records during the last two decades
gave the minimum necessary validation background to these theoretical efforts and
simulations. Full non-linear and elasto-plastic models are not really used mainly
because of the difficulty in defining soil parameters for all soil categories, while it is
known that probably for strong earthquakes, the use of elastoplastic models shall lead to
an even more important decrease of ground amplification, especially in low resistance
soil layers (Pitilakis et al., 1999).
Modern codes are certainly a serious step forward for a better evaluation of design input
motions at least for ordinary buildings. Future improvements should be addressed to
the following issues: Azimouthal effects (i.e. different spectral values for the two
horizontal components), basin edge and deep basin effects, evaluation of ground motion
Site Effects
189
for large and very large shear strains, vertical component, topographic effects, velocity
and displacement spectra, spatial variability of ground motion etc.
The complete description of the real ground motion at a specific site under a hazardous
in time and space seismic event is still a utopia. Seismic codes should always reflect the
basic knowledge and technology of the present time, keeping in mind that they must be
simple and realistic, having an acceptable level of accuracy, compatible among others,
with the tools used for the seismic design of the structures.
In the following paragraphs the two more recent seismic codes (IBC2000 and EC8Draft) are presenred, together with an improved site categorization proposal and the
corresponding spectral amplification values and shapes which is the result of a long
research effort in Aristotle University in Greece.
5.7.1. THE CONCEPT OF EUROCODES
The purpose of the Eurocodes is to achieve harmonization between structural and
geotechnical design in Europe. The Commission of the European Communities (CEC)
initiated a work in 1975 of establishing a set of harmonised technical rules for the
structural and geotechnical design of buildings and civil engineers works based on
article 95 of the Treaty. In a first stage it was planned to serve as alternative to the
national rules applied in the various Member States and finally when reaching an
acceptable level of harmonization to replace them and serve as a unique document.
Since 1989, ‘EN 1990: Basis of Structural Design’ is considered the primary document
in the Eurocode suite and establishes the principles and requirements for safety and
serviceability of structures. EN 1990 must be applied whenever the Eurocodes 1 to 9
are used. The Eurocode 8 (EC8) “Design of Structures for Earthquake Resistant” deals
with the design and construction of buildings and civil engineering works in seismic
regions.
5.7.2. INTERNATIONAL BUILDING CODE 2000
The need and motivation for a ‘uniform’ design code has always been very strong in the
Unites States. Due the different geographic regions of the U.S., and the corresponding
significantly different level of probabilistic seismic risk, seismic codes have been issued
primarily for the Western coast by the Californian authirities. At the end of 1994, the
three existing model code groups together formed the InternationalCodeCouncil (ICC)
with express purpose of developing a single set of construction codes for the entire
United States, leading to the combination of UBC (Uniform Building Code) and
NEHRP (National Seismic Hazard Reduction Program) into the IBC2000 (International
Building Code). Although IBC2000 is not a ‘real’ international code, but rather, a
common code for all States of America, it is indeed a significant step forward towards
harmozation and a major scientific breakthrough.
5.7.3. SOIL AND SITE CLASSIFICATION
Soil and site characterization is provided in Eurocode 8 and not in Eurocode 7 on
account of being directly related to the design spectra proposed for considering the
seismic force that is statistically expected to act on a structure. In its latest revision, the
soil is classified in five major categories (Table 5.1) and two spesific sub-categories that
190
Kyriazis Pitilakis
correspond to very loose or liquefiable material respectively. The advantage of such a
classification is that the three parameters that are used for soil identification (shear wave
velocity, Nspt values and undrained strength) is relatively easy to me measured, but on
the other hand the soil stiffness is determined by the Vs values of the 30 uppermost
layers only. The average shear wave velocity Vs,30 is computed according to the
following expression:
Vs ,30
30
(5.7)
h
¦ i
i 1,N Vi
where hi and Vi denote the thickness and shear wave velocity of the N formations of
layers existing in the top 30 meters. In case that the value of Vs,30 is unknown, the value
of NSPT will be used. Nevertheless, its has been shown and discussed in previous
paragraphs that the above approach may be a particular simplification which can
potentially lead to eroneous results especially in cases of deep soil formations or abrupt
stiffness change between the soil layer at -30m and the bedrock laying deeper.
Table 5.1. Soil classification according to Eurocode 8 (prEN1998-1, Draft 4, 2001)
Description
NSPT
su
(kPa)
Vs,30
(m/sec)
A
Rock or other rock-like geological formation,
including at most 5m of weaker material at the surface
-
-
> 800
B
Deposits of very dense sand, gravel or very stiff clay
at least several tens of m in thickness characterized by
a gradual increase of mechanical properties with
depth.
>50
>250
360-800
C
Deep deposits of dense or medium-dense sand, gravel
or stiff clay with thickness from several tens to many
hundreds of m
15-50
70-250
180-360
D
Deposits of loose-to-medium cohesionless soil (with
or without some soft cohesive layers) or of
predominantly soft-to-firm cohesive soil
<15
<70
<180
E
A soil profile consisting of a surface alluvium layer
with Vs,30 values of class C or D and thickness varying
between about 5 and 20 m, underlain by stiffer
materials with Vs,30 >800 m/sec
S1
Deposits consisting – or containing a layer at least
10m thick – of soft clays/silts with high plasticity
index (PI>40) and high water content
-
10-20
<100
(indicative)
S2
Deposits of liquefiable soils, of sensitive clays, or any
other soil profile not included in classes A-E or S1
191
Site Effects
For sites with ground conditions matching the two special subsoil classes S1 and S2
special studies for the definition of the seismic action are required. For these classes
and particularly for S2 the possibility of soil failure under the seismic action must be
considered. Further sub-division of this classification is permitted to better conform to
special soil conditions. The seismic action defined for any sub-class shall not be less
than those corresponding to the main class specified in Table 5.3, unless this is
supported by special site-classification studies foreseen in the National Annex.
The classification according to IBC2000 as seen in Table 5.2 is identical to the
provisions of Uniform Building Code 1997, and practically distinguishes soil profiles in
five main categories while a special condition F case is also prescribed. Conceptually,
the soil categorization is similar to that of EC8, both in terms of the Vs,30 assumption and
the Vs threashold values that separate the subsoil classes. The latter is illustrated in the
comparative Table 5.3 where most of the present seismic code soil classifications are
compared.
Table 5.2. Site Classes – Specifications according to Uniform Building Code 1997 and
International Building Code 2000.
Description
Vs,30
(m/sec)
1500
A
HARD ROCK-Eastern United States sites only
B
ROCK
760-1500
C
VERY DENSE SOIL AND SOFT ROCK
Undrained shear strength su > 100 kPa or NSPT > 50
360-760
D
STIFF SOILS
Stiff soil with undrained shear strength 50 kPa < su < 100 kPa or 15 <
NSPT < 50
180-360
E
SOFT SOILS
Profile with more than 3 m of soft clay defined as soil with PI > 20,
moisture content w>40%, undrained shear strength su < 50 kPa and
NSPT < 15
180
F
SOILS REQUIRING SITE SPECIFIC EVALUATIONS
1. Soils vulnerable to potential failure or collapse under seismic
loading:
e.g. liquefiable soils, quick and highly sensitive clays, collapsible
weakly cemented soils.
2. Peats and/or highly organic clays: 3 m or thicker layer
3. Very high plasticity clays: 8 m or thicker layer with PI>75
4. Very thick soft/medium stiff clays: 36 m or thicker layer
192
Kyriazis Pitilakis
Table 5.3. Comparison of soil classification in modern seismic codes worldwide
Vs,30 (m/sec)
180
360
760
1500
UBC/97
IBC/2000
SE
SD
GREEK
SEISMIC CODE
EAK2000
D–C
C
Ǻ
ǹ
ǹ
EC8 (ENV1998)
C
C
Ǻ
ǹ
A
EC8 (prEN1998)
(Draft4, 2001)
D
C
B
A
D
(ȉ>0.6s
=>Vs,30<200)
III
(ȉ>0.6s
=>Vs,30<200)
C
(ȉ<0.6s
=>Vs,30>200)
B
A
New Zealand,
2000 (Draft)
Japan, 1998
(Highway Bridges)
SC
SB
II
(I)
(ȉ=0.2-0.6 s => Vs,30=200-600)
I
(ȉ<0.2s
=>Vs,30>600)
Turkey/98
Z4 – Z3
Z3 – Z2
Z3 – Z2 – Z1
Z1
AFPS/90
S3 – S2
S3 – S2 – S1
S1 – S0
S0
SA
Table 5.4. Soil amplification parameter and corner periods as a function of subsoil class
for earthquake Type 1 (Eurocode 8).
Ground Type
A
B
C
D
E
S
TB
Tc
TD
1.0
1.20
1.15
1.35
1.40
0.15
0.15
0.20
0.20
0.15
0.40
0.50
0.60
0.80
0.50
2.00
2.00
2.00
2.00
2.00
Table 5.5. Soil amplification parameter and corner periods as a function of subsoil class
for earthquake Type 2 (Eurocode 8)
Ground Type
A
B
C
D
E
S
TB
Tc
TD
1.0
1.35
1.50
1.80
1.60
0.05
0.05
0.10
0.10
0.05
0.25
0.25
0.25
0.30
0.25
1.20
1.20
1.20
1.20
1.20
A more refined soil and site characterization (Table 5.6) has been performed by the Lab.
of Soil Mechanics and Foundation Engineering of the Aristotle University Thessaloniki,
based on a more comprehensive approach using a large date base of high quality records
in perfectly known soil conditions and over 800 1D computations of ground response
with different soil profiles in terms of impedance contrast, soil type and relative
thickness, depth of the rigid or non-rigid bed-rock etc and of course input motion
characteristics (Pitilakis et al., 2003).
Site Effects
193
5.7.4. COMPATIBILITY OF DESIGN FORCES
Although technically feasible, designing a structure to respond elastically the design
earthquake input leads to disproportionally increased construction cost. Moreover, the
actual demand is related to the seismic energy dissipation ability and not a particular
performance under given seismic forces. For these reasons, seismic design codes
prescribe and allow inelastic response under certain hierarchy, while ensuring collapse
prevention and structural integrity. The correlation of the elastic with the design spectra
therefore, is inevitably related to the level of energy absorption which is anticipated to
take place through cycles of inelastic behaviour and damage of the structural members.
The latter is usually described as the behaviour factor q (in Eurocodes, the Greek
Seismic Code and a number of other codes) and the response modification factor R in
the U.S. codes. It is therefore necessary, before proceeding to the critical and
comparable evaluation of the code-defined spectra to account for the different
assumptions on the reduction of forces prescribed in different codes and proceed to the
appropriate calibrating calculations.
5.7.5. SPECTRAL AMPLIFICATION
Typically, the shape of the spectrum is a function of the soil category that the
foundation soil can be classified into, according to the soil and site characterization
procedure described previously: for softer materials, the spectrum is generally shifting
rightwards representing a higher level of bedrock ground motion amplification that is
expected to occur when higher period pulses propagate through the (relatively) loose
soil profile. Moreover though, it has been widely recognized in recent versions of
seismic codes (i.e. UBC since 1997) that the epicentral distance also has a crucial role
on the spectral amplification at particular period ranges, i.e. a near field earthquake is
expected to be rich in high frequencies with respect to a distant event for which the
amplification at long periods is expected to be relatively lower. Additionally, both
IBC2000 and the latest version of Eurocode 8 (prEN1998-1, Draft 4, 2001) account for
the effect of earthquake magnitude; in Eurocode 8 by distinguishing to Type 1 (Ms>5.5)
and Type 2 (Ms<5.5) spectra as seen in Figure 5.42. Figure 5.43 and the accompanying
Tables 5.8 and 5.9 are illustrating the proposed acceleration response spectra in
IBC2000.
Fig. 5.42. Recommended Type 1 (left) and Type 2 (right) elastic response spectrum for
soils A to E according to Eurocode 8 (prEN1998-1, Draft 4, 2001).
194
Kyriazis Pitilakis
Fig. 5.43. Design spectra according to IBC2000.
The new normalized acceleration response spectra suggested by Aristotle University for
the soil classification presented in Table 5.6 are given in Figure 5.44. The parameter S
is expressing, as in EC8, the spectral amplification at T=0.0sec while the parameter ȕ is
the maximum spectral acceleration coefficient describing with the three corner periods
TB, TC and TD, the shape of the acceleration response spectrum for each soil category.
Table 5.6. Soil and Site Classification (Pitilakis et al., 2003)
CATEGORY
A1
A
A2
Ǻ1
Ǻ
Ǻ2
C1
C
C2
C3
DESCRIPTION
ȉȠ
(sec)
Vs 1500 m/sec
Surface weathered
Healthy rock formations
Slightly weathered / segmented rock formations,
provided that the weak, highly weathered surficial
layer has a thickness of less than 5.0m
Geologic formations which resemble rock formations
in their mechanical properties and their composition
(e.g. conglomerates)
Highly weathered rock formations whose weathered
layer has a considerable thickness of 5.0 - 30.0m
Soft rock formations of great thickness or formations
which resemble these in their mechanical properties
(e.g. stiff marls)
Soil formations of very dense sand – sand gravel
and/or very stiff clay, of homogenous nature and small
thickness (up to 30.0m)
Soil formations of very dense sand – sand gravel
and/or very stiff clay, of homogenous nature and
medium thickness (30.0 - 60.0m), whose mechanical
properties increase with depth
Soil formations of dense to very dense sand – sand
gravel and/or stiff to very stiff clay, of great thickness
(> 60.0m), whose mechanical properties and strength
are constant and/or increase with depth
Soil formations of medium dense sand – sand gravel
and/or medium stiffness clay (PI > 15, fines
percentage > 30%) of medium thickness (20.0–60.0m)
Category C2 soil formations of great thickness (>60.0
m), homogenous or stratified that are not interrupted
by any other soil formation with a thickness of more
than 5.0m and of lowerr strength and Vs velocity
REMARKS
0.2
layer: V s 300 /sec
Rock formations: Vs
800 m/sec
Vs 800 m/sec
Weathered layer:
V s (2) 300 m/sec
0.4
V s =400-800 m/sec
NSPT (3)>50 Su(4)>200
kPa
V s = 400 - 800 m/sec
NSPT > 50 Su > 200
kPa
0.8
V s = 400 - 800 m/sec
NSPT > 50 Su > 200
kPa
1.2
V s = 400 - 800 m/sec
NSPT > 50 Su > 200
kPa
1.2
V s = 200 - 400 m/sec
NSPT > 20 Su > 70kPa
1.4
V s = 200-400 m/sec
NSPT > 20 Su > 70 kPa
195
Site Effects
D1
D
D2
D3
Ǽ
ȋ
Recent soil deposits of substantial thickness (up to
60m), with the prevailing formations being soft clays
of a high plasticity index (PI>40), with a high water
content and low values of strength parameters
Recent soil deposits of substantial thickness (up to
60m), with prevailing fairly loose sandy to sandy-silty
formations with a substantial fines percentage (so as
not to be considered susceptible to liquefaction)
Soil formations of great overall thickness (> 60.0m),
interrupted by layers of category D1 or D2 soils of a
small thickness (5 – 15m), up to the depth of ~40m,
within soils (sandy and/or clayey, category C) of
evidently greater strength, with
Surface soil formations of small thickness (5 - 20m),
small strength and stiffness, likely to be classified as
category C and D according to geotechnical
properties, which overlie category ǹ formations (Vs
800 m/sec)
Loose fine sandy-silty soils beneath the water table,
susceptible to liquefaction (unless a special study
proves no such danger, or if the soil’s mechanical
properties are improved)
Soils near obvious tectonic faults
Steep slopes covered with loose lateral deposits
Loose granular or soft silty-clayey soils, provided they
have been proven to be hazardeous in terms of
dynamic compaction or loss of strength
Recent loose landfills
Soils with a very high percentage in organic material
2.0
V s 200 m/sec
NSPT < 20 Su <
70KPa
2.0
V s 200 m/sec
NSPT < 20
1.2
V s 300 m/sec
0.5
Surface soil layers:
V s = 150 - 300
m/sec
Table 5.7. Values of Fa as a function of site class and shaking intensity (IBC2000).
Table 5.8. Values of Fa as a function of site class and shaking intensity (IBC2000)
196
Kyriazis Pitilakis
Fig. 5.44. Suggested acceleration response spectra for each soil category normalized to the maximum acceleration value
(PGArock*S)
Site Effects
197
In conclusion, it can be stated that, the spectral values are a function of local soil
properties, distance from the source (only for IBC2000) and intensity of the seismic
event. On the other hand, there is a number of inherent uncertainties in the definition of
the appropriate local soil profile determination due to the inadequate process to evaluate
the overall dynamic response of the soil formations from the Vs profile of the uppermost
30 meters. This is the reason that in the new soil categories suggested by Aristotle
University instead of Vs,30 we are using the average Vs over the whole soil column under
consideration. Moreover, it has been extensively shown that the geometrical
characteristics of soil profiles (considered as 1-Dimensional soil columns) are rather
inadequate to describe the complex nature and physics of the multilayered, non-linear,
3-Dimentional and possibly inclined soil layers that lay over a non-rigid bedrock and for
which the actual amplification of the amplitude of incoming waves in particular
frequencies is a function of the overall soil complexity, topography and geology, hence
a very complex and multi-parametric phenomenon codified as ‘site effects’. It is clear
therefore, that, although considerable steps have been taken with respect to the
consideration of the role played by soil on the seismic input, there are a number of
issues that are either scientifically unresolved or the progress made has not yet been
reflected to modern seismic codes.
Acknowledgements
The work presented herein is reflecting the scientific research work performed the last
10 years in Aristotle University by many graduate and post graduate students and
mainly by my students and presently collaborators Dr. D. Raptakis, Dr. K. Makra and
Dr. A. Anastasiadis. Text notes prepared by Dr. D. Raptakis and Dr. K. Makra as well
as by Dr. A. Sextos were most valuable. Dr A. Sextos and Ms. V. Terzi, MSc-AUTH,
kindly took care of the final version of the text and Figures. I would like to express my
acknowledgements to all of them.
CHAPTER 6
EVALUATION OF LIQUEFACTION-INDUCED DEFORMATION OF
STRUCTURES
Susumu Yasuda
Department of Civil and Environmental Engineering, Tokyo Denki University, Japan
6.1. Introduction
In the current design of countermeasures against liquefaction, about 200 gals or less of
the maximum surface acceleration has been applied to estimate cyclic shear stress.
However, far greater shaking such as 400 to 600 gals of the maximum surface
acceleration caused severe liquefaction-induced damages during the 1995 HyogokenNambu (Kobe) and 1999 Kocaeli earthquakes. Liquefaction-induced flow also occurred
in Kobe. After these earthquakes, new design concepts and methods for evaluating
liquefaction, which can be applied for strong ground shaking, have been studied by
conducting model tests, laboratory tests and analyses. This chapter focuses on these
recent studies and introduces the new design methods. The liquefaction-induced
damage due to the strong ground shaking by the two earthquakes is introduced at first.
Then, the behaviour of structures in liquefied dense or silty grounds is discussed.
Design methods for liquefaction-induced deformation of structures and
countermeasures are introduced. Finally design methods and countermeasures for
liquefaction-induced flow are shown.
6.2. Design Procedures for Liquefaction
6.2.1. CURRENT DESIGN PROCEDURES
In 1964 the Niigata and Alaska earthquakes inflicted huge damage to buildings, bridges
and other structures by liquefying loose-sandy soils. After these earthquakes many
studies on the liquefaction of sandy soils have been conducted by laboratory cyclic
shear tests, shaking table tests, site investigations and analyses. Then many kinds of
methods for the prediction of the occurrence of liquefaction have been developed.
Countermeasure methods against liquefaction have proposed and applied also. These
prediction methods were introduced by TC4 (1999), JGS (1998), Yasuda (1999), etc.
Current countermeasures were summarized by JGS (1998). Based on these methods,
the conventional approach shown in Figure 6.1 has been used for the design of
liquefaction. In this approach, the assessment of liquefaction potential is done first.
Then the acceptability of the likely degree of damage is roughly judged and, if
necessary, appropriate countermeasures are selected. However, in general, the degree
of damage expected from liquefaction is not evaluated because it is difficult to evaluate.
In the current design, around 200 gals or less of the maximum surface acceleration has
been used as design input motion. It is not always necessary to judge the degree of
damage because it is easy to improve the ground not to liquefy under this level of
shaking. However, liquefaction cannot be prevented by current countermeasures under
strong ground shaking, such as 600 gals, which was observed during the 1995
199
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 199–230.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
200
Susumu Yasuda
Hyogoken-Nambu (Kobe) and Kocaeli earthquakes. Therefore, it is necessary to
introduce a new design concept based not on the occurrence of liquefaction but on the
likely degree of damage to structures. This new design concept is rational and will be
used for not only for strong ground shaking but also normal ground shaking.
Start
: not evaluated in usual
current design
Assessment of liquefaction
No
Possibility of
liquefaction
Yes
Identification of failure modes and
evaluation of degree of damage
Acceptability of
degree of damage
No
Selection of
appropriate
countermeasure
Yes
End
Fig. 6.1. Current design procedure
6.2.2. EFFECT OF THE 1995 KOBE EARTHQUAKE
The 1995 Hyogoken-Nambu (Kobe) earthquake, with a magnitude of 7.2, caused
liquefaction of many artificially reclaimed land areas and alluvial plain deposits along
Osaka Bay, as shown in Figure 6.2. In Kobe City, several waterfront areas and two
large islands had been constructed by reclamation along Osaka Bay. Liquefaction
occurred in almost all of the artificially reclaimed lands and islands because the
reclaimed soil was loose and the ground shaking was very strong, i.e., more than 600
gals of maximum surface acceleration.
A large number of structures, such as bridges, tanks, quay walls, buildings, houses,
earth dams, river dikes and buried pipes, were seriously damaged by liquefaction, as
shown in Photo 6.1. Moreover, many quay walls and revetments moved toward the sea
and brought about extensive flow of the ground behind them as shown in Photo 6.2.
201
Liquefaction Induced Deformations
Ro
kko
M
Higashinada-ku
t ai n
oun
C
B
D
E
C'
Chuo-ku
Nada-ku
A
F
B'
J'
H
I
Osaka Bay
Kobe Port
I'
A'
K
D'
G'
G
Hyogo-ku
J
E'
Port Island
F'
Rokko Island
N
zones where sand and water were ejected
H'
Kobe Port
K'
Fig. 6.2. Sites on Kobe and surrounding cities liquefied during the 1995 HyogokenNambu earthquake
Photo 6.1. Settled school houses in
Kobe
Photo 6.2. Liquefaction-induce flow
behind a quay wall in Kobe
For example, the average horizontal and vertical displacements of quay walls on Port
Island were 2.7m and 1.3m, respectively. The ground behind quay walls liquefied and
flowed toward the sea due to the movement of the quay walls, as shown schematically
in Figure 6.3. The ground flow brought severe damage to many structures, such as
bridges, buildings, houses and pipelines. Piles of bridges and buildings were deformed,
continuous footings of wooden houses were ruptured, and buried pipes were bent. The
displacement of the ground was measured by surveying the opening of the ground
cracks (Ishihara et al., 1996; Ishihara, 1997) and by aerial photogrammetry. Figure 6.4
shows the distribution of ground surface displacement behind quay walls, measured by
Ishihara et al. (1996). Displacements just behind quay walls reached about 2 to 3.5m
and decreased with distance from the wall. Flow extended back almost 100 to 150m
behind the quay walls.
202
Susumu Yasuda
Flow
Liquefied Layer
Fig. 6.3. Outline of the ground flow behind quay wall
Laterral displacement (cm)
400
350
:P-1
:P-2
:P-3
:P-4
:P-5
:P-6
:NB-2
P-6
300
NB-2
250
P-5
200
P-3
150
P-2
100
Port
Island
Nishinomiya
P-1
50
P-4
0
0
50
100
150
Distance from waterfront line (m)
Fig. 6.4. Distribution of horizontal displacement behind quay wall (Ishihara et al., 1996;
Courtesy of the JSSMFE)
This earthquake pointed out the following two problems in the current design procedure
for liquefaction:
1. In the current design procedure, as shown in Figure 6.1, the design acceleration
on the surface is about 200 gal or less in general. However, very intense
seismic motion, such as 600 to 800 gals of the maximum surface acceleration,
hit Kobe and surrounding cities and caused severe liquefaction-induced damage.
Liquefaction Induced Deformations
203
If the input acceleration is very strong, even medium dense and dense sand
would liquefy. However, it is not clear that severe damage would occur or not
in the medium dense or dense sandy ground.
2. The damage of structures due to liquefaction-induced flow must be considered
in the design.
6.2.3. LIQUEFACTION-INDUCED SETTLEMENT DURING THE 1999 KOCAELI
EARTHQUAKE
During the 1999 Kocaeli, Turkey earthquake, many RC buildings of 4 to 6 stories
settled and tilted in the zones shown in Figure 6.5, which were recognized by the
reconnaissance team of the Japanese Geotechnical Society (2000). Typical damage to
buildings is shown in Photos 6.3 and 6.4. The building in Photo 6.3 tilted about 30° just
after the earthquake without damage to glass windows then gradually tilted to 60°.
Cracks in the ground occurred due to a slide at the site shown in Photo 6.4. The
building on the crack was torn, as shown in the photo. Boiled sands were observed at
several sites. However, the number of sites where boiled sands were observed and the
volume of the boiled sands were not much, compared with the liquefied sites during
past earthquakes, such as Niigata and Dagupan cities during the 1964 Niigata and the
1990 Luzon Philippines earthquakes, respectively.
Photo 6.3. A settled building at Site 16 and Photo 6.4. A settled building at Site SK4 in
S4 in Adapazarı
Adapazarı
The reconnaissance team of the Japanese Geotechnical Society tried to measure the
settlement and angle of inclination for about 200 buildings (JGS, 2000). Among them
the data for settled buildings only were selected and the relationship between average
settlement and angle of inclination was drawn as shown in Figure 6.6 (Yasuda et al.,
2001a). The average settlement of each building was calculated from the maximum
settlement, inclination and the width of the building. The largest settlement was about
50cm. Typical settlements of the buildings and inclination were 20cm to 40cm and 1
degree to 3 degrees, respectively. These values were smaller than those induced in
Niigata and Dagupan cities.
After the earthquake, Swedish weight sounding tests, borings and undisturbed soil
samplings were carried out by a research team (Yasuda et al., 2001b, Kiku et al., 2001,
Tsukamoto et al., 2001). Figure 6.7 shows the data investigated at site SK4 shown in
Figure 6.5. Buildings around site SK4 were severely damaged, as shown on Photo 6.4.
Weak soil layers which are silt layers and a sandy silt layer lay to a depth of about 6m.
204
Susumu Yasuda
The upper two silt layers were especially quite soft. Underlying sandy silt layer is
relatively weak. According to the Swedish weight sounding tests, the Nsw values of the
weak soft silt layers were mostly below zero. Undisturbed samples were taken at
several depths. Undrained cyclic triaxial tests and sieve analyses were carried out on
samples from depths of 2.40 to 4.75m. The fines contents, Fc of the samples from GL.2.5m and GL.-4.5m were 97.5% and 65.2 to 99.7%, respectively. The Plasticity Index,
Ip was 38.4 and NP to 25.1, respectively.
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Borehole site
Sounding site
0
500m
Liquefied area
Location of site (Swedish Sounding)
Fig. 6.5. Liquefied zone and investigated sites in Adapazarı City (Yasuda et al., 2001b)
The liquefied soils at Niigata and Dagupan were clean sands. Therefore the reason why
there were fewer sand boils and settlement of buildings were few at Adapazarı than at
Niigata or Dagupan must be the differences between liquefied soils. The liquefied soil
in Adapazarı was silt and had some cohesion, which decreased the settlement.
205
Liquefaction Induced Deformations
Angle of inclination (°)
10
8
6
4
2
Adapazari
0
0
100
200
300
Settlement of buildings (cm)
Fig. 6.6. Relationship between settlement of building and angle of inclination (Yasuda
et al., 2001a)
(a)
Soil type
(b)
Swe dish
sounding
WSW
0
NSW
0 0.5 1.0 50 100
(g)
(e )
(d)
(c)
(f)
Lique faction Safe ty factor Young's
Estimate d Fine s
modulus at
conte nt, stre ngth ratio, against
SPT NRl 20(DA=5%) lique faction, 5% strain,
Fc(%)
v alue
Et(M Pa)
FL
0
10
0 50 100 0 0.3 0.6 0 1 2
0 1 2 3 4
(h)
Estimate d
se ttle me nt,
S(cm)
0
25
50
T. S.
Silt
Depth (m)
Silt
-5
Sandy
silt
Silt
Fine
sand
-10
Gravel
and
Fine
sand
Fig. 6.7. Results of in-situ and laboratory tests at Site SK4 (Yasuda et al., 2001b)
206
Susumu Yasuda
6.3. Studies on Liquefaction-induced Deformation of Structures in Dense Sand or
Silty Sand Grounds
6.3.1. NEW METHODS FOR THE PREDICTION OF THE OCCURRENCE OF
LIQUEFACTION UNDER STRONG SHAKING
The shaking in Kobe during the 1995 Hyogoken-Nambu (Kobe) earthquake was very
strong, as the maximum acceleration was 600 to 800 gals on the ground surface. In
Japan, about 200 gals of the maximum surface acceleration had been considered in the
estimation of the liquefaction potential before the Kobe earthquake. After that
earthquake, it became necessary to develop a new design concept to consider the strong
shaking which is called as “Level 2 shaking”.
Some studies have been conducted to develop a new method for the estimation of
liquefaction potential under strong shaking. In the new specification for highway
bridges (The Japanese Road Association, 1997), the formula for evaluating undrained
cyclic strength was revised because the previous formula could not be applied to “Level
2 shaking”. Several cyclic triaxial tests were carried on frozen samples and case studies,
and a new formula, shown in Table 6.1 was proposed. Figure 6.8 shows the relationship
between N1 and RL for clean sand. The big difference compared with the relationship
introduced in the previous specification is that RL increases rapidly with N1 in the range
of N1>20.
Table 6.1. (a) Method to evaluate liquefaction potential (JRA, 1997)
R
cw RL
N a᧸14
RL
0.0882 N a 1.7
RL
0.0882 N a 1.7 1.6 u 10 6 N a 14
4.5
N a ฺ 14
<Sandy soil case>
N a c1 N 1 c2
N 1 1.7 N V vc 0.7
c1 1
c1 FC 40 50
c1 FC 20 1
c2
c2
0
FC 10 18
0% ู FC᧸10%
10% ู FC᧸60%
60% ู FC
0% ู FC᧸10%
10% ู FC
<Gravelly soil case>
Na
^1 0.36 log10
D50 2 `N 1
R : Dynamic shear strength ratio
R L : Cyclic triaxial strength ratio
cw : Modification factor based on earthquake motion properties
N a : Corrected N-value accounting for the effects of grain size
N 1 : N-value convertd to correspond to effective overburden pressure of 1kgf/cm2
N : N-value obtained from standard penetration testing
V vc : Effective overburden pressure (kgf/cm2)
c1 ,c2 : Modification factor of the N-value based on the fine-grained fraction
FC : Fine-grained fraction (%)
D 50 : Mean grain diameter (mm)
Liquefaction Induced Deformations
207
One more important revision is the correction factor Cw. Two types of ground motion:
generated by interplate fault in the ocean (named Type 1), and generated by inland
fault (named Type 2) are introduced in the specification. The maximum surface
acceleration for the two types of ground motions are 0.3g to 0.4g and 0.6g to 0.8g in
high seismic zones, respectively. The factor to correct the irregularity of seismic shear
stress, Cw is defined as follows:
[Type 1] Cw=1.0
[Type 2]Cw=1.0 (0᧸RL0.1), Cw=3.3 RL+0.67 (0.1᧸RL0.4)
(6.1)
Cw=2.0 (0.4᧸RL)
(6.2)
1.0
Sandy soil
Undrained cyclic strength ratio , RL
DA=5%, Nc=20, FC=<5%
0.8
0.6
0.4
0.2
0
0
30
20
50
10
40
Corrected N-value accounting for
the effects of grain size , Na
Fig. 6.8. Na vs. RL in the new design code
6.3.2. SOIL DENSITY AND SPT N-VALUE WHICH CAUSE LIQUEFACTION
UNDER STRONG SHAKING
As the maximum surface acceleration in the “Level 2 shaking” is very high, even dense
sand ground is judged to induce liquefaction. This means that a low degree of
compaction cannot prevent liquefaction under a strong earthquake. If a clean sand
ground such as that shown in Figure 6.9 is assumed, the maximum SPT N-value which
causes liquefaction under different maximum surface accelerations can be calculated
based on Table 6.1. Figure 6.10 shows the relationship between the maximum surface
acceleration and the calculated critical SPT N-value at the depth of GL-8.1m, where
effective overburden pressure V’v=98kPa. As shown in the figure, the critical SPT Nvalue increases with the maximum surface acceleration.
208
Susumu Yasuda
GL
]᧤
P᧥
Jt
18 kN/m
3
WL=GL-2m
J sat
20 kN/m
3
V vc
98 kPa
Fig. 6.9. Model ground to estimate critical condition of liquefaction
Critical SPT N-value to cause
liquefaction (FL = 1), N1c
50
40
30
20
Type1
10
Type2
0
0.00
0.20
0.40
0.60
0.80
1.00
Maximum surface acceleration, Amax (g)
Fig. 6.10. Critical SPT N-value to cause liquefaction under different maximum surface
acceleration
Critical relative density to cause
liquefaction (FL=1), Drc
120
100
80
60
40
Type2
Type1
20
0
0.00
Type2
0.20
0.40
0.60
0.80
1.00
Maximum surface acceleration, Amax(g)
Fig. 6.11. Critical relative density to cause liquefaction under different maximum
surface acceleration
Liquefaction Induced Deformations
209
The author proposed the following relationship between SPT N-value, Dr and mean
confining pressure, p’ for Toyoura Sand, which is a clean sand in Japan.
N=(-2.25×10-6p’+3.37×10-6)×(Dr+60)(0.477p’+2.95)
(6.3)
By using this relationship, critical SPT N-value, shown in Figure 6.10 can be converted
into relative density, as shown in Figure 6.11. If the maximum surface acceleration is
0.15g to 0.20g (“Level 1 shaking”) the critical SPT N-value is about 10 to 15 and the
critical relative density is 50% to 70%. On the contrary, under the strong shaking of
0.35g to 0.60g (“Level 2 shaking”) the critical SPT N-value is about 25 to 30 and the
critical relative density is about 90% to 100%. Therefore, it can be said that medium
dense and dense sand with relative density of about 50% to 90% is the soil that liquefies
under Level 2 shaking but not liquefies under the Level 1 shaking. However, it may be
that structures are not severely damaged by the liquefaction of medium dense or dense
ground. This basis for this conclusion is discussed in the following paragraph based on
an experience during the 1995 Hyogoken-Nambu earthquake and several test results.
6.3.3. BEHAVIOUR OF STRUCTURES IN LIQUEFIED DENSE SANDY GROUND
Subsidence of Compacted Dense Ground during the 1995 Hyogoken-Nambu
Earthquake
Kobe City is built on a narrow alluvial plain facing Osaka Bay. Coastal areas have been
reclaimed for many years to enlarge the flat land areas. Liquefaction occurred in these
reclaimed lands and two large man-made islands, Port and Rokko islands. In Port
Island, some zones were improved by installing sand drains and preloading. In addition,
some zones were compacted with sand compaction piles or rod (vibro) compaction.
The purpose of the soil improvement was not the mitigation of liquefaction of reclaimed
sand but the consolidation of the underlying soft clay layer. Figure 6.12 shows the
zones of soil improvement on Port Island (Watanabe, 1981). The central areas, which
are residential, were improved by installing sand drains, preloading and a combination
of the two methods. High-rise apartments and office buildings are constructed in these
areas. The ground for amusement park, tanks, some structures and tram depot was
improved using sand compaction piles or rod (vibro) compaction. Most of this soil
improvement work was applied to the bottom of the alluvial soft clay.
SPT N-values of uncompacted soils below the ground water table were mostly 10 or less.
Figure 6.13 compares SPT N-values in untreated zones with those in zones treated with
sand drains and sand compaction piles derived from other published data (Yasuda et al.,
1996). The SPT N-value in zones compacted by sand compaction piles and rod
compaction were 18 to 31. The SPT N-values in the zones treated by sand drains were
14 to 25. The sand drain method does not normally densify the subsoil. However,
densification of the reclaimed soils must have been induced by the special construction
condition in Port and Rokko islands. Since the reclaimed sandy soil is 15m to 20m
thick and contains much gravel, strong vibration forces and a long time were necessary
to advance the casing down to the alluvial clay layer.
210
Susumu Yasuda
Unimproved
Preloading
Sand drains
L1
C6
C1
Sand drains plus preloading
L2
C9
L3
C8
Rod(vibro) compaction or
gravel compaction
C7
C2
L4
C3
L5
L6
L14
L13
L7
L8
L9
L15
C4
L12
L11
L10
C5
C10
C11
C12
Fig. 6.12. Improvement zones in Port Island (quoted and modified from Watanabe,
1981)
50
SPT N -value
40
ż Port Island
Ⴠ Rokko Island
rod(vibro) compaction
sand drains
ǻ
30
Ǵ
20
ǻ
10
sand compaction piles
sand drains plus preloading
0
Unimproved
Sand drains
Compaction
Fig. 6.13. Comparison of SPT N-value before and after improvement (Yasuda el at.,
1996; Courtesy of the JGS)
Liquefaction Induced Deformations
211
Number of sites measured
0 5 10 15
Ground subsidence(cm)
100
90
Port Island(P.I.)
80
Rokko Island(R.I.)
70
Average in R.I.
Average in P.I.
60
50
40
30
20
10
0
Unimproved Preloading Sand drains Sand drains
Rod(vibro) Sand compaction
plus preloading compaction piles
Fig. 6.14. Comparison of ground subsidence in zones treated with different methods
(Yasuda el at., 1996; Courtesy of the JGS)
By comparing Figure 6.12 with Figure 6.2, it was determined that no sand and water
were ejected in zones treated with sand compaction piles, rod (vibro) compaction, sand
drains plus preloading and sand drains. Sand and water were ejected in un-treated zones
and in a few locations in zones treated by preloading. Large ground subsidence, of up
to several tens of centimetres, was observed in the zones where sand and water were
ejected. Many buildings settled and tilted in these zones. On the contrary, no
subsidence and no damage to structures were observed in the zones densified with sand
compaction piles and rod (vibro) compaction, and only slight subsidence was observed
in the zones treated by other methods. The average subsidence in the untreated zones
was about 40cm to 45cm as shown in Figure 6.14. Subsidence decreased with the
degree of compaction. The average subsidence in the zones treated by preloading, sand
drains, sand drains plus preloading, rod (vibro) compaction piles was about 30cm, 15cm,
12cm and 0cm, respectively. The order of decrease of subsidence is the same as the
order of increase in N-values in SPT, mentioned before.
Stress-strain Curves of Dense Sand obtained by Laboratory Tests
The author has studied post-liquefaction behaviour by conducting torsional shear tests.
Toyoura sand, which is a clean sand, was used at first to study the effects of density,
confining pressure and severity of liquefaction. Then several sands were tested to study
the effect of fines content (Yasuda et al., 1998). Specimens were saturated by applying
back pressure and were consolidated. Then a prescribed number or prescribed
amplitude of cyclic loadings was applied in undrained condition. The safety factor
against liquefaction, FL, which implies the severity of liquefaction, was controlled by
the number of cycles or amplitude of the cyclic loadings. After that a monotonic
loading was applied under undrained condition with a relatively high speed of J =10%
per minute, as shown in Figure 6.15.
212
ic
on
ot g
n
o
M adin
lo
Consolidation
time
Cyclic loading
Excess
porewater
pressure
Shear stress
Susumu Yasuda
Liquefaction
time
Fig. 6.15. Procedure of cyclic and monotonic loading (Yasuda el at., 1998)
Shear stress (kPa)
200
Porewater
Pressure (kPa)
Relationships among shear stress, W, excess pore pressure, 'u, and shear strain, Jin the
monotonic loading were measured. Figure 6.16 shows stress-strain curves and excess
pore water pressure-strain curves in the case of Toyoura sand with different relative
densities, Dr. Scales of axes in Figure 6.16(c) are enlarged scales of Figure 6.16(a).
Shear strain increased with very low shear stress up to very large strain. Then, after a
resistance transformation point, the shear stress increased comparatively rapidly with
shear strain, following the decrease of pore water pressure.
100
150
100
50
0
0
Toyoura Sand V'0=49 kPa
FL=1.0
Dr=65.9% Dr=53.9%
'u/V'0=1.0
Dr=32.6%
Dr=-5.2% C
10
20
30
40
50
60
Dr=-5.2%
0
D r=
65.9%
-100
-200
-300
Dr=32.6%
Dr=53.9%
D
0
10
20
30
40
50
60
Shear stress (kPa)
Shear strain (%)
1.0
E
D r=53.9%
D r=
65.9%
Dr=32.6%
0.5
D r=-5.2%
0
0
10
20
30
40
Shear strain (%)
Fig. 6.16. Stress-strain and strain-pore water pressure curves for Toyoura sand (Yasuda
el at., 1999b; Courtesy of the JSCE)
213
Liquefaction Induced Deformations
The amount of strain up to the resistance transformation point is called the “reference
strain at resistance transformation, JL” as shown in Figure 6.17. The reference strain at
resistance transformation increased with the decrease of r as shown in Figure 7.16 (c).
Stress-strain curves before and after the reference transformation point can be presented
approximately by a bilinear model with G1, G2 , and JL :
W= G1Jfor J JL
(6.4)
W= G1JL + G2(J-JL) for J JL
(6.5)
where G1 and G2 are the shear moduli before and after the reference transformation
point, respectively. The G1 decreased with the decrease of Dr as shown in Figure 7.16(c).
To estimate the reduction rate of shear modulus due to liquefaction, the rate of shear
modulus G1/G0, which is the ratio of shear modulus after and before liquefaction, was
calculated. Two types of G0 were selected: G0,I : secant modulus of stress-strain
curves atJ=0.1% in the case of no cyclic loading ('u/V’v=0) and GN : estimated from
SPT N-value by the formula of GN(kPa)=2800N. In the first shear modulus, 0.1% of
shear strain was selected because the strain of soils which occurs in the ground due to
overburden pressure is estimated as aroundJ =0.1% in the usual case. The second one
is widely used for the design of foundations in Japan. Figure 6.18 shows relationships
among the reduction rate of shear modulus, relative density and FL. The reduction rate
of shear modulus of Dr=90% is about 10 times the rate of Dr=50%. This means that if
liquefaction occurs in dense ground, shear modulus does not decrease so much.
W
Static
G2
Turning
point
1
G0,i
1 0.1%
G1
1
JL
J
Small resistant region
Fig. 6.17. Definition of G0,i, G1, G2 and JL (Yasuda el at., 1998)
Behaviour of Structures in Liquefied Dense Ground obtained by Model Tests
The author has conducted several shaking table tests to demonstrate liquefactioninduced deformation of structures in grounds with different density. Figure 6.19 shows
a schematic diagram of equipment for plate loading tests. In these tests, the soil
container was shaken for 10 cycles with 3Hz to cause liquefaction. The severity of
liquefaction FL was controlled by the amplitude of shaking. Then a plate was pushed
into the ground quickly. Figures 6.20 and 6.21 show relationships among load and
settlement of the plate and FL. As shown in these figures, the plate settled up to several
centimetres with very low resistance. Then resistance recovered. Settlements up to the
recover of the load for the grounds of Dr =50% and Dr =90% were 5 to 8cm and 1 to
2cm, respectively.
214
Susumu Yasuda
Reduction rate of shear modulus
due to liqufaction,G 1/G0,i
0.01
FL=1.0
FL=0.9
FL=0.8
FL=0.7
0.001
0.0001
50
60
70
80
90
Relative density, Dr(%)
Fig. 6.18. Relationship among relative density, FL and reduction rate of shear modulus
Plate loading equipment
Pore pressure meter
Soil container
Accelerometer
5cm
5cm
5cm
CL
No.1
No.6
No.3
No.5
15cm
No.2
No.4
50cm
120cm
Fig. 6.19. Schematic diagram of equipment for plate loading test
Using the same shaking table, the floatation of a buried common utility duct was tested.
Figure 6.22 shows schematic diagram of the test equipment. Shaking was applied for
215
Liquefaction Induced Deformations
10 cycles to cause liquefaction with different amplitude of acceleration. Figure 6.23
compares the floatation of the model duct for the ground with different relative densities.
As shown in this figure, the floatation of the model duct in the ground of Dr =50% was
about several times that in the ground of Dr =90%.
Load(kN)
Static
Static
75gal(FL=1.0)
100gal(FL=0.7)
190gal(FL=0.4)
370gal(FL=0.2)
Boiling
1
0
0
1
2
3
4
5
6
7
FL=0.2
FL=1.0
Toyoura sand, Dr=50%
FL=0.7
2
FL=0.4
As shown in the two series of tests, the settlement or floatation of structures due to
liquefaction is strongly affected by the density of the ground.
8
Boiling
9
10
Settlement(cm)
Fig. 6.20. Load-settlement curves in plate loading tests for liquefied loose sand
2
Toyoura sand, Dr=90%
FL=0.6
Load(kN)
FL=1.0
Static
200gal(FL=1.0)
250gal(FL=0.8)
360gal(FL=0.6)
590gal(FL=0.3)
Boiling
FL=0.3
1
Static
FL=0.8
Boiling
0
0
1
2
3
4
5
6
7
8
9
Settlement(cm)
Fig. 6.21. Load-settlement curves in plate loading tests for liquefied dense sand
10
216
Susumu Yasuda
Wire displacement transducer
Piezometer
Accelerometer
Table accelerometer
Soil container
6cm
5cm
5cm
10cm
Model of common utility duct
50cm
12cm
12cm
Fig. 6.22. Schematic diagram of model test for floatation of common utility duct
Floatation of model
common utility duct (mm)
30
FL=0.0~0.1
FL=0.1~0.2
FL=0.2~0.3
FL=0.3~0.4
FL=0.4~0.5
FL=0.5~0.6
FL=0.6~0.7
FL=0.7~0.8
FL=0.8~0.9
FL=0.9~1.0
25
20
15
10
5
0
50
55
60
65
70
75
80
85
90
Relative density, D r (%)
Fig. 6.23. Relationship among relative density, FL and floatation of model common
utility duct in shaking table tests
6.3.4. BEHAVIOUR OF STRUCTURES IN LIQUEFIED SILTY GROUND
Comparison of the Settlement of Buildings in Different Grain Size of Grounds
As mentioned in 6.2.3, many buildings settled and tilted due to soil liquefaction in
Adapazarı during the 1999 Kocaeli, Turkey earthquake. The settlement of buildings
was induced in Niigata, Dagupan, Kobe, and Yuanlin cities during the 1964 Niigata,
Japan earthquake, the 1990 Luzon, Philippines earthquake, the 1995 Hyogoken-Nambu
(Kobe), Japan earthquake and the 1999 Chichi, Taiwan earthquake. However the
217
Liquefaction Induced Deformations
Percent finer by weight (%)
settlement of buildings differed by city. Many buildings settled more than 1m in
Niigata and Dagupan. On the contrary, the settlement of buildings in Adapazarı, Kobe
and Yuanlin was less than 0.5m. The author compared grain size distribution curves of
liquefied sands in these cities as shown in Figure 6.24 (Yasuda et al., 2001a). The sand
in Niigata has no fines. On the contrary, the sands in Adapazarı and Yuanlin have about
20% and 100% of fines (less than 0.075mm). Figure 6.25 compares the relationship
between fines content of the liquefied soils and the maximum settlement of buildings in
five cities. The settlement of buildings decreased with the fines content. It seemed that
the grain size, especially fines content, of liquefied soil strongly affected the settlement
of buildings.
100
Adapazari
(Turkey)
50
Kobe
(Japan)
Yuanlin,
Minsheng
(Taiwan)
Dagupan
(Philipines)
Yuanlin,
Lunya
(Taiwan)
Niigata
(Japan)
0
0.001
0.01
0.1
1
10
Particle diameter (mm)
Fig. 6.24. Grain size distribution curves of liquefied sand in five cities (Yasuda el at.,
2001a)
Maximum settlement in
each city (m)
4
3
Niigata
Dagupan
2
1
Kobe
Yuanlin
0
0
20
40
60
Adapazari
80
100
Fines content, FC(%)
Fig. 6.25. Relationship between fines content and actual maximum settlement (Yasuda
el at., 2001a)
218
Susumu Yasuda
Stress-Strain Curves of Silty Sand obtained by Laboratory Tests
Yasuda et al. (1998, 1999a) conducted many cyclic torsional shear tests to study the
stress-stain relationship of liquefied sands as mentioned in 6.3.2. Figure 6.26 shows a
summary of these tests with the relationships among the reduction rate of shear modulus,
fines content and FL. As shown in this figure, the reduction rate of shear modulus ratio
is strongly influenced by the fines content. This implies that settlement or floatation of
structures in silty ground is smaller than that in clean sandy ground.
Reduction of shear modulus,G1/G0,i,G1/GN
1
FL=1.0
0.1
FL=0.9
0.01
FL=0.8
0.001
0.0001
FL=0.7
0
10
G1/G0,i
G1/GN
20
30
40
Fines content,FC(%)
50
Fig. 6.26. Relationship between shear modulus ratio and fines content (Yasuda el at.,
1999b; Courtesy of the JSCE)
6.4. Evaluation Methods for Liquefaction-induced Deformation of Structures
6.4.1. RAFT FOUNDATIONS
Empirical Method
Yoshimi and Tokimatsu (1977) collected data on the settlement of buildings during the
1964 Niigata earthquake, and found the relationship shown in Figure 6.27 between the
width ratio and settlement ratio. Settlements of oil tanks during the 1983 Nihonkaichubu earthquake in Japan were compared with the depth of liquefaction and diameter
of the tanks by Yasuda and plotted in Figure 6.27. Settlement of buildings and tanks
can be estimated roughly by these relationships.
Liquefaction Induced Deformations
219
Fig. 6.27. Relationship between width ratio and settlement ratio (Yasuda and Berrill,
2000; Reproduced with permission from Technomic Publishing Co.)
Analytical Methods
The settlement of raft foundations can be evaluated by a seismic response analysis in
which liquefaction is considered. In 1992, joint analyses of a building that settled
during the Niigata earthquake were carried out by eight program codes (JGS, 1991).
Estimated settlements were smaller than the actual settlement at that time.
Subsequently, those computer codes have been modified to include large strains.
However, further joint analyses have not been conducted, and it is not clear yet whether
these codes can evaluate large settlements of the order of 2 to 3 meters accurately.
Alternatively, the residual deformation method can be applied to the settlement of raft
foundations. For example, the residual deformation method “ALID” was used to
estimate the settlement of a footing of a power transmission tower (Yasuda et al.,
2001c). Figure 6.28 shows the results of the analysis. In this method, it is assumed that
residual deformation occurs in liquefied ground due to a reduction of shear modulus.
Relationships among the shear modulus ratio, G1 /G0,i the factor of safety against
liquefaction, FL , and fines content FC (percentage of particles smaller than 75µm)
shown in Figure 6.26 were used. In the analysis, the finite element method is used
twice as follows: (1) In the first step, the deformation of the ground is calculated by the
finite element method using the shear modulus before the earthquake. (2) The finite
element method is applied again using a reduced shear modulus, due to liquefaction., (3)
The difference in the deformation measured by the two analyses is assumed to equal the
residual ground deformation.
220
Susumu Yasuda
Liquefied layer
17.5 m
Settlement: 1.46m
20m
G1/GN=1/475, F L=0.95, SPT-N=6.4, B=3.2m, FC=0%
Fig. 6.28. Settlement of a footing of a transmission tower, analysed by residual
deformation method “ALID” (Yasuda el at., 2001b)
6.4.2. PILE FOUNDATIONS
Concept of Design
Figure 6.29 demonstrates the concepts of pile behaviour, with time histories of ground
displacement, pile head displacement, pile bending moment, pore pressure and soil
spring stiffness during the process of liquefaction and associated ground flow (Yasuda
and Berrill, 2000). Amplitude of the displacement and the bending moment in the pile
increase rapidly just or slightly before the occurrence of liquefaction. Then these
amplitudes decrease after the initiation of liquefaction. The soil spring stiffness
decreases with liquefaction. Liquefaction-induced ground flow or settlement of
structures with raft foundations begins just after the occurrence of liquefaction. Ground
displacement due to the flow increases gradually. Then the flow stops after a short time
due to dissipation of the excess pore water pressure and/or topographical balance of the
soil mass. The displacement and bending moment of the pile also increase gradually
and reach maximum values.
As shown in this conceptual diagram, the bending moment of the pile suffers large
values at two distinct times: during the initial occurrence of liquefaction (Time “A”) and
during the subsequent flow (Time “B”). Detailed dynamic response analyses may be
used to estimate these values. However, the displacement and bending moment at these
stages are evaluated independently in recent design methods, because the behaviour of
the pile and the ground are grossly different at the two points in time.
221
Liquefaction Induced Deformations
(a) Shear stress
Time
L
(b) Excess pore water pressure
(c) Displacement of the surroundig ground
(d) Soil spring stiffness
A
B
(e) Bending moment on a pile
Fig. 6.29. Concept of time histories of shear stress, bending moment and other items
(Yasuda and Berrill, 2000; Reproduced with permission from Technomic Publ. Co.)
Recent Design Methods
In recent practice for the design of pile foundation in liquefied ground, two grades of
method are used: i) Dynamic response analysis, and ii) The static evaluation method.
Several methods of dynamic response analysis considering liquefaction have been
developed in recent years. However, the dynamic response analysis of pile foundations
considering liquefaction is still complex and not easy to use for design. Therefore,
static evaluation methods are used in recent design.
As shown in Figure 6.30, there are two approaches in the static method: the seismic
coefficient method and the seismic deformation method. In the seismic coefficient
method, reduction factors for bearing capacity and for soil spring stiffness coefficients
are different among current design codes in Japan, as shown in Figure 6.31. The
reduction rate is affected by several factors, such as density and grain size of the soil,
severity of liquefaction, differential displacement between the pile and surrounding soil
etc. Further studies of the effect of liquefaction on soil spring stiffness are necessary.
222
Susumu Yasuda
Fig. 6.30. Two types of design method for static analyses
Reduction rate of bearing
capacity, D E
1.2
1
0㧨Z҇10m
Highway Bridges
0.8 R㧪0.3
R҇0.3
0.6
Railways
B1
0.4
0.2
0
B2
B3
B4
0
0.2 0.4 0.6 0.8
1
Safety factor against liquefaction, F L
Buildings
B2: 14㧨Na҇20
B1: Na㧪20
B3: 8㧨Na҇14 B4: Na҇8
Fig. 6.31. Comparison of reduction rate for bearing capacity among three design codes
in Japan
6.4.3. EMBANKMENTS
Design Methods
Two grades of design methods have been used for embankments: i) detailed seismic
response analyses considering the effect of liquefaction, and ii) simple analyses. The
detailed seismic response analyses have been carried out for special embankments, such
Liquefaction Induced Deformations
223
as high filled dams. However, like raft and pile foundation analyses, seismic response
analyses are still complex. On the contrary, some simple analytical methods have been
proposed recently and applied to normal embankments, such as river, road and railway
embankments. One simple method proposed by the author and his colleague is
introduced below.
An Example analyzed by a Simplified Method
The simplified method “ALID” mentioned before was applied to estimate the settlement
of river levees damaged or non-damaged during the 1993 Hokkaido-nansei-oki and the
1995 Hyogoken-Nambu (Kobe) earthquakes, and tested by centrifuge equipment.
Figure 6.32 shows the analyzed results for the levee at Site No.9 of Shiribeshitoshibetsu River. The levee body settled and the liquefied soil under the levee body was
pushed out, as shown by the heave of the ground at the toe of the dike in Figure 6.32.
Figure 6.33 compares the analyzed settlements and actual settlements. Though the data
are scattered, the analyzed settlements agreed fairly well with the actual settlements
during the past two earthquakes.
Analysed settement of embankment(m)
Fig. 6.32. Deformation of the river levee at Site No.9 analysed by “ALID” (Yasuda el
at., 2001c)
3
Centrifuge loading tests
Measurement
2
1
0
0
1
2
3
Actual settlement of embankment(m)
Fig. 6.33. Relationship between actual and analysed settlements
224
Susumu Yasuda
6.5. Countermeasures against Liquefaction-induced Damage of Structures
6.5.1. CURRENT COUNTERMEASURES
Current countermeasures against liquefaction are shown in Table 6.2. These methods
are classified into two categories (JGS, 1998): i) improve the liquefiable soil to prevent
liquefaction, ii) strengthen structures to prevent their collapse if the ground should be
liquefied. In the first category, ground is improved to increase liquefaction strength by
the following factors: high density, not-liquefiable grain size, stable skeleton or
low saturation. Other methods to prevent liquefaction are: immediate dissipation
of increased excess pore pressure, reduction of shear stress by increasing confining
pressure, reduction of shear stress by building an underground wall. Appropriate
countermeasures in the second category differ by the type of structure. In the
countermeasures shown in Tables 6.2 to 6.4, the additional pile method has been
applied for bridge foundations, but other methods have been applied for few structures
only.
6.5.2. RECENT PROBLEMS
After the Kobe earthquake two problems in the current countermeasures were pointed
out:
1. Effectiveness of countermeasures under strong shaking must evaluate not only
the occurrence of liquefaction but also the deformation of structures.
2. The gravel drain method is not effective under the strong shaking evaluated by
the current design method. However, it is necessary to discuss whether the
gravel drain method is in reality useless under strong shaking, and if not,
appropriate design method must be developed.
6.6. Liquefaction-induced Flow of the Ground
6.6.1. CONCEPT OF DESIGN METHOD
Concept of Design Methods
Liquefaction-induced ground flow can be divided into two classes, as illustrated in
Figure 6.34: ground flow on gentle slopes, and ground flow behind quay walls.
There are four approaches to allowing for the effect of ground flow in the design of
piled foundations:
a) Evaluating the deformation of both piles and ground simultaneously,
b) Evaluating the pressure acting on piles due to the ground flow first, then
evaluating the resulting deformation of the piles,
c) Estimating ground displacement first, and then evaluating the deformation of
piles (seismic deformation method)
d) Estimating deformation, assuming that the liquefied ground behaves as a viscous
fluid.
225
Liquefaction Induced Deformations
Table 6.2. Current countermeasures against liquefaction (modified from JGS, 1998)
Principle of
improvement
Description
Sand compaction pile
Vibro rod method
Vibro flotation
Dynamic consolidation
Vibro tamper
Compaction by roller
Hammer
Liq
Liq
Increase of
density
Non-liq
Sand pile
Compaction by explosion
Group pile method
Liq
Liq
Upper structure
Pile
Non-liq
Non-liq
Deep mixing method
Quick lime pile method
Injection method
Liq
Liq
Grout
Non-liq
Soildification
Cement or lime column
Non-liq
Pre-mixing method
Cement-mixed sand
Quay
wall
Liq
Non-liq
Deep well
Dewatering by trenches
pump
Reduction of
degree of
saturation
and increase
of effective
stress
Liq
Liq
Drainage canal
Non-liq
Non-liq
Liq : Liquefiable layer
Non-liq : Non liquefiable layer
226
Susumu Yasuda
Table 6.3. Current countermeasures against liquefaction (modified from JGS, 1998)
Principle of
improvement
Description
Drain pile
Drain installation for surrounding area
Liq
Liq
Drain
Underground
structure
Dissipation
and control of
pore water
pressure
Non-liq
Non-liq
Drain pile
Steel pile with drainage function
Drainage function
Liq
Sheet pile
Non-liq
Underground diaphragm wall
Control of
shear deformation and
interception
of excess
pore water
pressure
Upper structure
Liq
Diaphragm wall
Non-liq
Pile foundation
Strengthen of pile and spread foundation
Upper foundation
Additional pile
Liq
Liq
Pile
Existing pile
Countermeasure from
structual
aspect
Non-liq
Non-liq
Strengthen of quay wall
New
quay
wall
Existing sheet pile
Liq
Non-liq
Liq : Liquefiable layer
Non-liq : Non liquefiable layer
227
Liquefaction Induced Deformations
Table 6.4. Current countermeasures against liquefaction (modified from JGS)
Principle of
improvement
Description
Lift prevention pile or sheet pile
Constraint of surroundings
Buried pipe
Liq
Liq
Weight
Sheet pile
Underground
structure
Non-liq
Non-liq
Absorption of ground deformation by flexible joint
Provision of supplemental foundation for mat foundation
Upper structure
Structural
countermeasure
Liq
Liq
Upper structure
Frexible joint
Top-sharped concrete block
Non-liq
Non-liq
Reinforcement of mat foundation by geogrid
Sheet piling for embankment
Upper structure
Liq
Tie rod
Geogrid
Liq
Sheet pile
Non-liq
Non-liq
Liq : Liquefiable layer
Non-liq : Non liquefiable layer
Fig. 6.34. Patterns of liquefaction-induced flow
The first approach is logically correct, but it is not an easy one, even by the latest
effective-stress response methods of analysis, because of the difficulty of incorporating
large ground displacements and interaction between the ground and structure. The
second approach is simple and was introduced immediately after the Hyogoken-Nambu
earthquake in the new specification for highway bridges in Japan (The Japanese Road
Association, 1996). The third approach is also simple and can be applied to complex
228
Susumu Yasuda
topographical conditions of the ground and quay walls. This approach was also
developed after the Hyogoken-Nambu earthquake, and has been adopted recently in the
design codes for Railways and High Pressure Tanks in Japan. Application of the fourth
approach is still experimental, and it has not yet been introduced into design codes.
Earth Pressure Method
In the new design code for highway bridges in Japan (The Japanese Road Association,
1996), the forces, shown in Figure 6.35, are applied to the foundation:
qNL=CsCNLKp JNLX (0 X HNL)
qL=CsCL{JNLHNL+ JL(X-HNL)} (HNL< X HNL+HL)
(6.6)
(6.7)
where, Cs: correction factor for the distance, S, from quay wall, 1.0 for S 50 m, 0.5 for
50 < S 100 m, CNL: correction factor in non-liquefiable layer, 0 for PL 5,
(0.2PL-1)/3 for 5 < PL 20, 1 for PL > 20, CL: correction factor in liquefiable layer, =0.3,
Kp: coefficient for passive pressure, X: depth (m)
non-liquefiable
layer
HNL
liquefiable layer H L
q NL
qL
non-liquefiable layer
Fig. 6.35. Earth pressure considered in the specification for highway bridges (JRA,
1997)
It must be noted that these methods were derived from inverse analyses of the piles
damaged during the Hyogoken-Nambu earthquake only, and the coefficients CS and CN
have not been derived from analyses or tests. Therefore further study is necessary to
fully establish and validate this method.
Seismic Deformation Method
In the seismic design method, the displacement of the ground during flow must be
estimated first. Then, horizontal forces are applied to the pile through soil springs.
Therefore, both ground displacement due to flow and the value of soil-spring stiffness
for the liquefied ground must be evaluated in some way. There are three classes of
method to estimate the flow-associated displacement: i) by use of an empirical formula,
ii) by a residual deformation analysis, and iii) by an effective stress response analysis.
Iai et al. (1998) succeeded in analyzing the deformation of quay walls and the ground
229
Liquefaction Induced Deformations
Thickness of the liquefied layer, H2
Relative displacement, UG- UP
by use of the detailed seismic response analysis code “FLIP.” Yasuda et al. (1999) tried
to analyze the ground deformation by a simple residual deformation method, “ALID”
same procedure as 6.4.1.
0.15
,
,
Pile Diameter, 30-40cm
FCH Building (Niigata)
HN Building (Kobe)
Spherical tank (Kobe)
UG
UP
H1
0.1
H2
0.05
0
Passive earth pressure
Zero lateral force the
unliquefied surface layer
10-4
10 -3
10-2
10-1
100
Stiffness degradation parameter, ˟
Fig. 6.36. Relationship between stiffness degradation parameter and the ratio of relative
displacement to thickness of liquefied layer (Ishihara and Cubrinovski, 1998;
Reproduced with permission from Balkema)
The properties of equivalent soil springs to represent liquefied ground during flow have
been studied by conducting inverse analyses on damaged piles and by shaking table
tests. Ishihara et al. (1998) made inverse analyses of damaged piles during the 1964
Niigata and 1995 Hyogoken-Nambu earthquakes. Figure 6.36 summarizes the
relationship between the stiffness degradation parameter, E and the ratio of relative
displacement and thickness of the liquefied layer. Estimated E, which is same as the
reduction rate of soil-spring stiffness shown in Figure 6.26, was found to be about 1/100
to 1/10000, and decreased with the ratio of relative displacement and thickness of the
liquefied layer.
6.6.2. COUNTERMEASURES AGAINST THE FLOW
Countermeasures against liquefaction-induced flow have been studied since the 1995
Kobe earthquake. Some methods have been applied to quay walls and express
highways in Tokyo, Kobe and Osaka.
Table 6.5 summarise the applied
countermeasures together with some ideas which have not been applied yet (Kanatani et
al., 2000).
6.7. Concluding Remarks
New design methods for liquefaction which have been developed recently were
introduced in this chapter. The evaluation of liquefaction-induced deformation of
structures seems very important for rational design. So, studies on the methods to
evaluate deformation must be studied more, together with discussions on the allowable
value of deformation of each structure.
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Susumu Yasuda
Table 6.5. Countermeasures against liquefaction-induced flow behind the quay wall
(Kanatani el at., 2000)
Concept of
countermeasure
Existing structure
New structure
<New quay wall>
<Existing quay wall>
New quay wall
Existing quay wall
Prevent the
occurrence of
liquefaction
Improve by compaction or
cementation
<New quay wall>
<Existing quay wall>
(1)Construct of stable quay wall
(1)Strengthen quay wall
Anchor
Stiff sheet pile
Prevent the
occurrence of
flow though
liquefaction
occurs
Improve by compaction or cementation
Existing sheet pile
New cell type wall
Decrease of earth pressure
by light material
Decrease of earth
pressure by light
material
Mound by stones
Improve by compaction or
cementation
Pile foundation
Partial improvement by
compaction or cementation
Strengthen by pile foundation
(2)Decrease of displacement of the ground behind quay wall
Steel piles or diaphragm wall
<New pile foundation>
Increase of number or
diameter of piles
Keep
serviceability
though
liquefactioninduced flow
occurs
Caisson type
foundation
Improve by compaction or
cementation
Improve by compaction or
cementation
<Existing pile foundation>
Additional piles
Surrounding by diaphragm or
cement mixing wall
CHAPTER 7
SEISMIC ZONATION METHODOLOGIES WITH PARTICULAR
REFERENCE TO THE ITALIAN SITUATION
Albero Marcellini and Marco Pagani
Istituto per la Dinamica dei Processi Ambientali, CNR, Milano and
Dipartimento di Scienze della Terra, Università degli Studi di Milano
7.1. Introduction
Experimental evidences of both large and moderate earthquakes show a high degree of
variability of damage distribution. Since the mid of the fifties of past century, scientists
realised the existence of a strong influence of soil characteristics and of near field
source effects on the recorded values of strong motion. These observations constitute
the premises of microzonation studies; the intention is to provide a tool to prevent
damages by means of detailed assessing of design forces and land use planning in
seismic areas.
After the adoption of some over-simplified approaches in the fifties using microtremor
analysis (Kanai, 1957), in the sixties Medvedev (1977), proposed a zonation method
based on an empirical correlation between the seismic impedance ratio and the variation
of macro seismic intensity. In the early eighties, the microzonation approaches became
more sophisticated partly owing to the boost of nuclear power plants installations and
the deployment of dense accelerometric arrays. Since then, the methods were
implemented and nowadays Figure 7.1 well represents a scheme of microzonation
methodology commonly adopted. As it is possible to see it encompasses the whole
topics necessary to perform a microzonation that basically can be subdivided into three
major items:
(1) Evaluation of the expected input motion
(2) Site effects analysis
(3) Preparation of microzonation maps and recommendations for practical
application
Now, whenever the scheme of Figure 7.1 is worldwide applied, the relative importance
one component has with respect to the others is subjected to large variability (Marcellini
et al., 2001a) due both to the physics of the phenomenon and to goal of the study.
Actually the following factors play the key role: a) the administrative situation of the
zone (regulations and seismic codes are significantly different country to country and in
some cases even region by region) b) the size of the expected earthquake (generally the
stronger the earthquake the larger becomes the importance of the source with respect to
the amplification factors), c) the nature of soils (for instance, the presence of potentially
liquefying soils urges detailed and expensive geotechnical investigations).
This article focus on the experiences gained in Italy during the last ten years. In other
words, the microzonation suggestions of this paper should be considered particularly
relevant for seismic areas subjected to moderate earthquakes, that is, earthquakes with
magnitude lower than 7.
231
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 231–252.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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A. Marcellini and M. Pagani
Fig. 7.1. Microzonation scheme (after Marcellini et al., 2001a; Reproduced by
permission of Italian Geotechnical Journal - Patrone Editore)
Before tackling the strictly scientific aspects we want stress the fact that microzonation
falls into the category of “applied research”, that is, to perform a microzonation that will
not (or cannot) applied is waste of time. It means that the typologies of expected results
must be defined with local administrators (or in some cases central government). As an
example we report three typologies of results.
Figure 7.2 shows the microzonation outcomes of three municipalities situated along the
Adriatic Sea coast in the Emilia-Romagna region (Daminelli et al., 2000). These
municipalities are located within a zone subjected to moderate earthquakes (maximum
expected magnitude around 6.5). Soils data available for microzoning consisted on a
detailed geological survey and a number of CPT tests (around 100). Given the lack of
geophysical investigations, shear wave velocities have been estimated using statistical
correlations with lithology and CPT data: as a result the obtained amplification values
are affected by a consistent degree of uncertainty. The microzonation representative
parameter was the ratio of Housner Intensity (with integration limits between 0.1 and
0.5 s) between the site and the outcropping bedrock. Housner intensity has been
selected to address ground shaking because of its greater stability with respect to other
parameters like PGA, strongly unstable in particular in the high frequency range.
Figure 7.2 shows an example of the computed maps.
Seismic Zonation Methodologies
233
Fig. 7.2. Microzonation of Rimini, Santarcangelo di Romagna and Bellaria:
amplification map in terms of Housner intensity ratio (0.1-0.5s). Higher seismic
amplifications decrease moving toward the mountainous area (in the figure from NE to
SW)
In other cases microzonation maps in terms of response spectra, as we did for the
municipalities of Gatteo, Savignano and S. Mauro Pascoli (see Figure 7.3) are more
suitable for local administrators (Marcellini et al., 1999). To note that these cited
microzonations were performed not after an earthquake.
The microzonation of Fabriano, situated in the Marche Region at the foothills of the
Apennine chain, has been performed just after the 1997 Umbria-Marche earthquake.
Boosted by the necessity to start the reconstruction as soon as possible, the request was
a clear and compulsory zonation of the area of the town. Fortunately supported by a lot
of data and experimental evidences (pattern of damage), it was possible to provide the
planners the map reported in Figure 7.4. The ground motion parameter (F.A.) was not
selected by experts and scientists involved in the project, but were obliged by the
administrators in order to translate it immediately into a seismic coefficient
multiplicative of the standard design forces provided by the national seismic code.
Henceforth through the Fabriano case history, we will deal with the different aspects of
microzonation.
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A. Marcellini and M. Pagani
Fig. 7.3. Microzonation of Gatteo, Savignano and S. Mauro Pascoli: Amplification
maps. Top left PGA/PGAH, top right Sa/SaH (T=0.2s), bottom left Sa/SaH (T=0.5s) and
bottom right Sa/ SaH (T=1.0s). PGAH and SaH are Peak ground acceleration and spectral
acceleration ([=5%) computed by hazard analysis (RP=474 yr) whereas PGA and Sa
were obtained after the evaluation of site effects. It is possible to observe that the
amplification pattern changes dramatically as a function of T.
7.2. Evaluation of the Expected Input Motion
We define the reference motion at a site as the ground motion evaluated without taking
into account site effects (as an example reference motion could be represented by
accelerograms derived by the response spectrum computed via standard probabilistic
hazard assessment, where soil conditions are only roughly accounted for by specific
attenuation relationships). The reference motion (usually in terms of accelerograms) to
use in microzonation studies for site effects evaluation is one of the most crucial
problems and constitutes the link between regional and local hazard.
Seismic Zonation Methodologies
235
Fig. 7.4. Fabriano zonation map; FA represent an amplification coefficient, eventually
used by the designer as multiplicative factor of design forces (after Marcellini et al.,
2001a, Reproduced by permission of Italian Geotechnical Journal - Patrone Editore).
There are at least three major approaches that can be adopted for the evaluation of
reference motion: the probabilistic approach, the stochastic and the deterministic one.
We usually rely on a two-step procedure to evaluate the reference motion. The first step
consists on the evaluation of expected acceleration response spectrum (5% damping)
using standard probabilistic seismic hazard assessment with response spectra
attenuation laws, horizontal component. The second step lies on the determination of
accelerograms from the above obtained response spectrum. There are different
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A. Marcellini and M. Pagani
procedures to generate artificially accelerograms whose response spectra match a target
response spectrum. As a personal opinion, we prefer to use accelerograms actually
recorded, selected by means of a simple procedure here synthesised: (1) to browse into
the accelerograms database (2) to choose the accelerograms recorded at or nearby the
site (if available; in case not, to choose the accelerograms produced by earthquakes
originated in a similar seismogenic situation), (3) to compute the response spectra of the
sorted accelerograms, (4) to adopt as reference motion the accelerograms whose spectra
best fit the target spectrum (hazard spectrum).
The deterministic approach computes the expected motion at the given site by means of
a kinematic or sometimes dynamic description of the earthquake source whereas
“intermediate” methods generally require stochastic approaches to compute reference
motion.
Through the case history of Fabriano microzonation, we will present three different
procedures to compute reference motion: a) deterministic, b) stochastic, c) probabilistic
and we will discuss advantages and disadvantages of each method.
7.2.1. DETERMINISTIC APPROACH
It is the well-known approach adopted to compute synthetic seismograms. Basically it
requires: 1) the definition of seismic source parameters (in general kinematics models
are adopted); 2) the application of Green’s function of elastodynamic; 3) the use of the
wave equation in elastic media, or pure viscoelastic media (attenuation taken into
account using the quality factor Q); 4) the application of the representation theorem.
Different authors applied deterministic approaches in seismic microzonation (Panza et
al., 1996).
The deterministic approach has been applied to Fabriano microzonation by Priolo
(2001). The first step consisted on the determination of the “scenario” earthquake; in
the present case it has been decided to consider the strongest earthquake that hit
Fabriano in the past. Castelli and Monachesi (2001) on the basis of historical
investigations defined the event of April 24, 1741 (IMCS=9) as the “scenario” earthquake;
through empirical correlation the estimated magnitude for this event was 6.2. The
epicentre was placed at some 8km North -East of the town.
Priolo (2001) used the wave number integration method, a 3-D method that solves the
full equation of seismic wave propagation through a layered medium, to compute
seismic signal in Fabriano under the assumption of the repetition of the 1741 event.
Source parameters adopted were 13 MPa stress-drop and a seismic moment (Mo) of
3.11018 Nm together with the assumption of a normal fault mechanism (I 150°,
G 40°O=-90°) such as the earthquake recently occurred in 1997 in Central Italy. The
crustal model consisted of 14 layers (in the uppermost 300m the average values of VP
and VS are 2500 and 1400 m/s, respectively).
The signals at Fabriano have been computed using both point source and extended
source. Figure 7.5 shows some of the results obtained by Priolo considering a point
source: to note the significant difference between horizontal and vertical components
and the relevant influence of the depth. Considering a realistic hypocentral depth (6 km)
the computed horizontal PGA in Fabriano (8.24km from the source) has been estimated
to be 0.21g.
Seismic Zonation Methodologies
237
Fig. 7.5. Deterministic simulation using point source model: computed PGA values
against epicentral distances and source depths (zS): h - horizontal component; v vertical component (after Marcellini et al., 2001b; Reproduced with permission from
Elsevier).
Fig. 7.6. Acceleration response spectra (5% damping) computed at Fabriano, using an
extended source model (after Marcellini et al., 2001b; Reproduced with permission
from Elsevier).
Using the same normal fault mechanism Priolo tackled the extended source simulation
by decomposing the entire fault area (20 x 12 km2) into 15 elementary sub sources of
4 x 4 km2 and Mo=2.1x1017 Nm, regularly distributed on the fault. The simulation has
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A. Marcellini and M. Pagani
been performed considering several hypothesis of rupture nucleation point, with a
velocity rupture of 2.8 km/s. Results obtained using an extended source, as it is
expected, show lower acceleration values, but the differences decrease in terms of
velocity and displacement (Priolo, 2001). Figure 7.6 shows the computed response
spectra, 5% damping, considering a bilateral source that nucleates at the epicentre of the
1741 earthquake.
7.2.2. STOCHASTIC APPROACH
The stochastic nature of high-frequency ground motion is clearly visible on the
acceleration time-histories commonly recorded during an earthquake (Hanks and
McGuire, 1981), and different empirical approaches can be used to tackle this aspect.
They basically consist in simulating time sequences that match existing data with
respect to amplitude, frequency content and signal duration. However, in many cases
simple propagation and source mechanism deterministic models, can successfully
predict the acceleration amplitude Fourier spectrum. Therefore, in order to simulate the
acceleration time histories to use as “reference motion” in seismic microzonation
analysis, it seems reasonable to take into account of:
1. stochastic properties of the recorded ground motion;
2. simplified description of the physical properties of source and path to evaluate
a reliable far field acceleration spectrum.
An approach of this kind, has been introduced by Boore (1983), where point 1) is
achieved by using a time sequence of band-limited random white Gaussian noise and
point 2) by considering the far field Brune spectrum (1970, 1971) multiplied by three
attenuation terms representing the geometrical spreading, the whole attenuation path
and the high frequency decay of the acceleration spectrum (due to same kind of source
effect or site effect according to Papageorgiou and Aki (1983) and Hanks (1982)
interpretations, respectively). A modified version of this procedure has been used in
this work and it is here briefly summarised (see Tento (1999) for further details).
The stochastic properties of the acceleration time history are simulated by means of a
time sequence of band-limited random white Gaussian noise windowed by (Saragoni
and Hart, 1974):
w(t )
at b e ct H (t )
(7.1)
where H(t) is the Heaviside function and coefficients a, b, and c are chosen to normalise
the resulting time sequence and to match the Saragoni and Hart window. The above
coefficients are related to strong-motion duration Td that is established by Td=1/fc (fc is
the earthquake corner frequency).
The Fourier spectrum of the resulting signal is then multiplied by the model spectrum:
SR
EQE
e
(7.2)
R
where S(f) is the acceleration far field source spectrum, k and QE represent the anelastic
attenuation and the scattering mechanism respectively (see Rovelli et al. (1988) among
A( f , R )
S( f )
e
kS f
Seismic Zonation Methodologies
239
the others), R is the hypocentre distance and the 1/R factor models the geometrical
spreading, E represents the S wave velocity. The source spectrum predicted by the
Brune model (1970, 1971) is taken as average far field spectrum, thus:
S( f )
FS RT ,I P
4SUE 3
M0
( 2S f ) 2
§ f ·
1 ¨¨ ¸¸
© fc ¹
2
(7.3)
where FS, ¢Rș,I ², P, M0 and U represent the free surface amplification factor, the average
radiation pattern, the partition energy factor into two horizontal components, the seismic
moment and the medium density. The Brune stress drop is related to M0 and fc by
'V B v M 0 f c3 .
Fig. 7.7. Predicted PGA by means of stochastic simulation: mean value and mean plus
and minus one standard deviation are compared with Priolo point source simulation
(Priolo, 2001). Ambraseys 50 and 84 percentile attenuation laws (shaded area) are also
shown for comparison (Ambraseys, 1995) (after Marcellini et al., 2001b; Reproduced
with permission from Elsevier).
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A. Marcellini and M. Pagani
The above procedure has been applied to Fabriano microzonation by using a point
source model of the April 24, 1741 M=6.2 earthquake, in order to compare the results
obtained by this method with Priolo point source simulation (Priolo, 2001) assuming,
the same value of the seismic moment and two stress-drop values (13 and 7 MPa). The
attenuation terms QE and k were fixed, on the basis of the simplified crustal model of
Priolo, to 100 and 0.01s whereas E and U values adopted were 3.5 km/s and 2.8 gr/cm3.
The simulation was performed for two values of hypocentre depth (6 and 10 km) and
epicentral distances ranging between 2 and 12km. The results are shown on Figure 7.7,
where the Priolo (2001) simulation and the 50 and 84 percentile values of the
Ambraseys (1995) attenuation law are also plotted for comparison.
Contrary to the deterministic point-source simulation, the stochastic procedure shows a
monotonic decay of the PGA with distance. For 6km hypocentre depth, in the
examined range of distances, the stochastic simulation shows a less rapid decay with
respect to the deterministic one. For 10km hypocentre depth, this discrepancy becomes
noticeable only for distances greater than about 10km. In Fabriano, by considering the
hypocentre depth of 6 km, the stochastic model predicts a 2.4 times greater PGA value
than Priolo result.
The comparison with Ambraseys (1995) attenuation law is really impressive. At all
distances, the mean value of the predicted PGA is very close to the 84 percentile value
of the attenuation law for 'V B 13 MPa and to the 50 percentile value for 'V B 7
MPa. Figures 7.9 and 7.8 show some examples of the obtained time histories and of the
corresponding spectra.
Fig. 7.8. Acceleration Fourier spectra (thin lines) of the time histories showed in
Figure 7.9 and Fourier spectrum of the adopted model (thick line) (after Marcellini et al.,
2001b; Reproduced with permission from Elsevier).
Seismic Zonation Methodologies
241
Fig. 7.9. Acceleration time histories obtained by stochastic simulation with
3.11018 Nm seismic moment, 13 MPa stress drop and 6 km source depth; QEand k have
been fixed to 100 and 0.01s, respectively (after Franceschina et al., 2001; Reproduced
by permission of Italian Geotechnical Journal - Patrone Editore).
7.2.3. PROBABILISTIC APPROACH
One of the main advantages of this approach is to assess a reference motion compatible
with the hazard at regional level; basically the procedure is a two-step approach:
1) evaluation of seismic hazard at the reference site; 2) assessment of the reference
motion.
Seismic hazard evaluation
The approach here adopted is the classical one (the so called “Cornell approach”;
Cornell, 1968) that consists on seismic source identification, temporal behaviour
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A. Marcellini and M. Pagani
described by a Poisson model and a negative exponential distribution for the magnitude.
Seismic hazard is computed at the site in terms of probability of non exceedance of the
strong motion parameter used in the adopted attenuation law.
A 474 years return period is considered as a standard for seismic classification and
building code purposes, generally PGA is assumed as the strong motion parameter. As
far as Fabriano is concerned seismic hazard has been computed by Peruzza (2000) using
SEISRISK III computer code (Bender and Perkins, 1987). Seismic source zones have
been drawn following Scandone et al. (1990) and historical seismic catalogue
Fig. 7.10. Hazard response spectra computed via probabilistic approach (RP=474 yr, 5%
damping) using different attenuation laws (after Marcellini et al., 2001b; Reproduced
with permission from Elsevier)
Reference motion
As noted previously, different approaches can be used to obtain accelerograms from
uniform hazard response spectra but because there is not a biunique correspondence
between response spectrum and accelerogram, some statistical procedure must be
applied.
An appealing procedure is the generation of artificial accelerograms that match the
target response spectrum. One of these methods is the Auto Regressive Moving
Average (ARMA) technique, which is illustrated for example in Ciampoli (1997).
As discussed above we prefer to adopt real accelerograms; the procedure followed to
match the accelerograms with response spectra is very simple (a description can be
found in Tento, 1999). It is important to note that this type of procedure suggests the
adoption of several accelerograms as a reference motion. In the case of Fabriano ten
accelerograms have been considered (Figure 7.11); they were taken from the Italian
accelerograms database.
Seismic Zonation Methodologies
243
Fig. 7.11. Selected accelerograms obtained from the uniform probability response
spectrum.
7.2.4. DISCUSSION
We presented three different approaches to evaluate the reference motion: the choice of
one method instead of another is not a simple matter. On the other hand what seems a
good solution, that is, the use of all the three approaches brings to a non-uniqueness of
results. The three types of reference motion, when used to estimate site effects can
produce contradictory results. As shown in Figure 7.12, the results obtained using a
simple 1-D model in a site at Fabriano (where the reference motion has been computed
with the three mentioned approaches) with lithology and VS profile shown in Figure
7.13, are strongly dependent on the type of reference motion. Generally seismologists
do like the deterministic approach because the physical background sounds better; the
objection raised by risk experts is that the motion obtained is subjected to strong
variations depending on source or path parameters.
Therefore the deterministic approach is not recommended, unless the source and path
parameters can be adequately modelled by suitable probabilistic distributions, and it is
well known that right now probability functions of stress drop, seismic moment or Q
value in a given area are not available: it is enough difficult to estimate with sufficient
accuracy average values.
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A. Marcellini and M. Pagani
Fig. 7.12. Computed response spectra for the site shown in Figure 7.13 under different
input motions (continuous line: input motion obtained following a probabilistic
approach; dashed line: input motion obtained by deterministic computation; dark
continuous line: input motion computed using a stochastic approach). The input motion
is the ground shaking at bedrock as obtained after a deconvolution of reference motion
(after Franceschina et al., 2001; Reproduced by permission of Italian Geotechnical
Journal - Patrone Editore).
Fig. 7.13. Site MS2 in Fabriano: stratigraphic profile and measured shear waves
velocity (m/s) obtained by down-hole measurements.
Seismic Zonation Methodologies
245
Probabilistic approach fulfils the requirements of compatibility with regional hazard
(that means compatibility with seismic codes). The computed response spectrum is
uniform probability ensuring equal risk to building of different characteristic (mass,
stiffness and damping). However there are two weak points in this approach, the first is
the arbitrariness when choosing the procedure to derive the signal from the spectrum
(real or artificially generated accelerograms?) and about the number of accelerograms to
use (1, 10 or more?). The second is due to the probabilistic approach itself. The
uniform hazard response spectrum obtained for a given return period overestimates
short periods and underestimates long periods (of the spectrum) compared to the
spectrum expected from an earthquake with the same return period (Marcellini et al.,
1994). This fact is unavoidable and is dependent on the E of Gutenberg-Richter relation,
actually only if E is equal to 0 this mismatch will disappear, but in practice it never
happens.
The stochastic approach here presented could be thought of as a compromise: it is more
“physical” than the probabilistic approach, it does not require input parameters highly
unpredictable as the deterministic approach, but, once again it does not fully satisfy
requirements of risk experts, that is to say what is the probability of the evaluated
ground motion for a given return period.
How to deal with this puzzle? There is not a full agreement among the experts. The
choice depends on the goal of the study, the maximum expected magnitude and the soil
type. As an example, for microzonation of a municipality in an area subjected to
moderate seismicity, we found the probabilistic approach more suitable, but using the
deterministic one for specific conditions such as in the presence of loose soils
susceptible to liquefaction or ground failures. Deterministic approach can also be used
to estimate the “upper boundary” of the expected motion. In case of strong earthquake
deterministic approach becomes more important, due also to the importance of the
directivity effects. To design a special industrial plant, the deterministic approach
assumes also a crucial role; in particular it helps to estimate the motion in the long
period range, where the probabilistic approach is not too much reliable. As a matter of
fact the experience plays a significant role in the choice of the approach to adopt.
7.3. Site Effects Evaluation
The importance of site effects is very well known. Due to the fact that this argument is
tackled in a number of papers of the present book we limit this paragraph to the
presentation of some results of site effects analysis obtained in the framework of
Fabriano microzonation (Tento et al., 2001)
In particular we focus on the results obtained with a dense seismic temporary network
installed just after the quake (Figure 7.14). Both aftershocks and noise were recorded in
order to assess the different soil amplification factors. Figure 7.15 shows that receiver
function and Nakamura methods exhibit a good agreement and they agree also with
spectral ratios as far as the fundamental period of soils is concerned (to note that, in the
light of preparation of the microzonation map, we attribute greater importance to the
spectral ratios).
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A. Marcellini and M. Pagani
Fig. 7.14. Fabriano: geological map, locations of seismological stations and of
microtremor measurements
Fig. 7.15. Fabriano: Receiver Function (dark grey) and spectral ratios (light grey)
evaluated using weak motion recordings and H/V ratios as obtained by noise (black
line). The line thickness (dark and light grey lines) represents the 95% confidence
interval.
Seismic Zonation Methodologies
247
Concerning aftershocks we remind that Fabriano is situated some 30km North with
respect to epicentre area. A great concern was (before analysing the data) about the
influence of the back-azimuth. Figure 7.16 presents spectral ratios computed by rotating
the horizontal components in the longitudinal and transverse directions of the valley
(longitudinal means approx at N45°E as represented in Figure 7.14).
Fig. 7.16. Fabriano: Spectral ratios. Horizontal components of the recorded signals are
rotated parallel (dark grey) and perpendicularly to the valley (light grey). The line
thickness (dark and light grey lines) represents the 95% confidence interval.
Sometimes the crude observation of data bring to interesting results: it is the case shown
in Figure 7.18 where it is represented the incidence angle at the station simply computed
using the horizontal-vertical ratio of the first pulse: the comparison with figures 7.14
and 7.16 evidences a significant correlation between low incidence angle and softer
materials, also characterized by higher spectral ratios.
A very crucial aspect of site effects in microzonation is the density of points to consider
in the analysed area because to translate point information into areal information it is
necessary to adopt some interpolation procedure. Figures 7.17 represent a map of
predominant periods obtained by integrating weak motion data and microtremors
measurements.
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A. Marcellini and M. Pagani
Fig. 7.17. Fabriano: soils natural period map obtained by microtremors (Nakamura
method) and weak motion data
Fig. 7.18. Fabriano incidence angle map as evaluated by the analysis of the P-wave first
arrival of the recorded earthquakes. Symbols represent recording stations sites as in
Figures 7.14 and 7.17
Seismic Zonation Methodologies
249
Fig. 7.19. Forlì-Cesena area: seismic hazard assessment. Each box contains PGA (gal)
values computed considering and without considering local amplifications (top and
bottom values in each box, respectively). The geology of the area is shown in the
background.
Fig. 7.20. Forlì-Cesena area: ratios of Housner intensity (SI) between values computed
at each down-hole site and SI at the outcropping bedrock (top values in each box),
bottom values in each box represent ratios of average spectral acceleration
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A. Marcellini and M. Pagani
7.4. Final Remarks
We want to stress again about the choice of the parameter to represent the expected
ground motion. Figures 7.19 and 7.20 refer to the microzonation of the area of ForlìCesena (Emilia-Romagna Region). Figure 7.19 shows computed PGA values at the
surface and at the bedrock for few sites (where down-hole measures were available)
whereas Figure 7.20 represents ratios of Housner Intensity (SI) and ratios of average
spectral acceleration (evaluated within the interval 0.1-2.5s), between values computed
at the surface and at the outcropping bedrock.
In general, we recommend to adopt Housner Intensity ratios for two reasons: the first is
that, an integral parameter is more likely to express the strength of the ground motion
(is a common observation that several times very high acceleration are recorded after
moderate earthquakes), the second is that the range of values are comparable with the
range of soil coefficients prescribed by several seismic codes including the Italian one.
Non-linearity is another crucial and sometimes ambiguous problem in microzonation
(generally overemphasized by geotechnical engineers - the opposite by seismologists).
Without entering in the technical nature of non-linear soil behaviour already described
in other papers, we would like to stress the close relation between input motion and
non-linearity. Being strain dependent, non-linearity is function of the magnitude of
input motion. As shown in Figure 7.21 it means that it depends from hazard analysis.
In turn, hazard values depend on the choice of return periods, or in other words from the
probability of non-exceedance of a given ground motion value. In conclusion the
choice of a level of risk could determine if the behaviour of a given soil must be
considered linear or non- linear.
Fig. 7.21. Non-linear soil effects at MS2 site in Fabriano. Upper panel: the amplification
ratio (PGAMS2/PGAZone 0) decreases as the PGAZone 0 increases (in other words, as the
PGA of the input motion increases). The lower panel shows the PGA computed
adopting linear and non-linear models: it is evident that the behaviour of the upper panel
curve depends on non-linearity. This graph well explains that the decreasing of
amplification factor in terms of PGA does not imply a diminution of risk (after Tento et
al., 2001; Reproduced by permission of Italian Geotechnical Journal - Patrone Editore).
Seismic Zonation Methodologies
251
Fig. 7.22. Epicentre locations of the September 26th 1997 00.33 GMT and 09:40 GMT
shocks (Amato et al., 1998). Small boxes report values of recorded PGA (g)
(after Franceschina et al, 2001; Reproduced by permission of Italian Geotechnical
Journal - Patrone Editore).
Fig. 7.23. Accelerometric recordings of the September 26th 1997, ML=5.8 earthquake,
09:40 GMT (after Franceschina et al, 2001; Reproduced by permission of Italian
Geotechnical Journal - Patrone Editore).
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A. Marcellini and M. Pagani
A final remark is devoted to the nature of ground motion. Figure 7.22 shows the
accelerometric network that recorded the M=5.8 earthquake of Central Italy. It is
possible to note the high spatial variability of recorded ground motion (Figure 7.23):
compare Nocera and Matelica records, situated at some 20km apart. This fact
underlines once again that source and directivity factors require more attention by
investigators (at least the same devoted to soils).
Acknowledgements
The authors are indebted with R. Daminelli for preparation and correction of this
manuscript. We would like to thank all the participants of the GNDT-Umbria-Marche
microzonation project and in particular: G.L. Franceschina, E. Priolo, A. Tento
CHAPTER 8
SEISMIC MICROZONATION: A CASE STUDY
Atilla Ansa1, Yeúim Biro
Bo÷aziçi University, Kandilli Observatory and Earthquake Research Institute
Ayfer Erken, Ümit Gülerce
Istanbul Technical University, Civil Engineering Faculty
8.1. Introduction
The earthquake damages are controlled basically by three interacting factor groups;
earthquake source and path characteristics, local geological and geotechnical site
conditions, structural design and construction features. Seismic microzonation can be
considered as the assessment of the first two groups of factors. In general terms, it is
the process for estimating the response of soil layers under earthquake excitations and
thus the variation of earthquake characteristics on the ground surface. Seismic
microzonation is the initial phase of earthquake risk mitigation and requires multidisciplinary approach with major contributions from geology, seismology, geotechnical
and structural engineering. The final output should contain recommendations suitable
for application by local administrators, urban planners and engineers.
The key issue affecting the applicability and the feasibility of any microzonation study
is the usability and reliability of the parameters selected for microzonation. These
parameters need to be meaningful for city planners as well as for public officials and
should not lead to controversial arguments among the property owners and city
administrators.
It was shown over and over again (Gazetas et al., 1990; Faccioli, 1991; Ansal, 1994;
Bard, 1994; Chavez-Garcia et al., 1996; Chin-Hsiung et al., 1998; Gueguen et al., 1998;
Kawase, 1998; Ansal, 1999; Athanasopoulus et al., 1999; Hartzell et al., 2001) based on
the encountered earthquake damage and strong ground motion records that there are
numerous source and site factors (i.e. near field effects, directivity, duration, focusing,
topographical and basin effects, soil nonlinearity, etc.) that are important in assessing
ground motion characteristics. The national seismic zoning maps are generally
prepared in small scales such as 1:1,000,000 or less neglecting all these factors and
independent of geological and geotechnical site conditions. However, seismic
microzonation requires 1:5,000 or even 1:1,000 scale studies taking into consideration
both earthquake source and regional geological and geotechnical site conditions in order
to be used for urban and landuse planning. Thus, detailed seismological, geological and
geotechnical studies are necessary to establish seismic microzonation maps.
A Seismic microzonation study consists of three stages: (1) estimation of the regional
seismic hazard, (2) determination of the local geological and local geotechnical site
conditions (3) assessment of the probable ground response and ground motion
parameters on the ground surface.
There may be differences among the adopted procedures with respect to these three
stages (Marcellini et al., 1995a, 1995b; Lachet et al., 1996; Fäh et al., 1997; Ansal, et al.,
253
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 253–266.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
254
A.Ansal, Y.Biro, A.Erken, and Ü.Gülerce
2003; Ansal, 2002). These differences mostly arise from different intentions that
produced microzonation maps and different levels of accuracy achieved based on the
available input data in terms of local geological and geotechnical site conditions. One
preference may be to produce microzonation maps to be used mainly for city and
landuse planning. A second preference is to use the microzonation maps to estimate the
possible earthquake characteristics for the assessment of structural vulnerability in an
earthquake scenario study. A third preference may be to provide input for the
earthquake design codes. The methodology presented in this chapter is more directed
towards the first preference considering a microzonation case study performed in Silivri
Municipality in Istanbul, Turkey, particularly relevant for regions characterized by high
level of seismicity.
8.2. Regional Seismicity
The first phase of any seismic zonation study is the estimation of the regional seismic
hazard based on probabilistic analyses using the available seismic and geological
database (Mcguire, 1995; Frankel et al., 2000). Ground motion characteristics can be
determined for a specific return period or exceedance probability depending on the
purpose of the study. The sophistication of the adopted approach can vary between a
single areal source models to very detailed multi-source models (e.g. Erdik, et al., 2003).
In areas with active seismicity and complex tectonic formations, it may be realistic to
assume a single tectonic areal source with a fixed radius around the investigated area to
determine the earthquake recurrence relationship for calculating exceedance
probabilities with respect to earthquake magnitudes for the purpose of defining a
probable earthquake magnitude. A simple single areal source model was adopted to
estimate the regional earthquake hazard for Silivri.
The proposed seismic hazard analysis may be considered as composed of four
consecutive stages that can be assumed independent and thus can be evaluated
separately (Ansal and Iyisan, 1998). The first stage is the estimation of the probable
earthquake magnitude based on seismological and geological data for the region. The
second stage is the estimation of the source distance of the probable earthquake. The
third stage is the estimation of the earthquake characteristics at the competent soil or
rock outcrop based on appropriate attenuation relationships. The fourth stage is the
estimation of earthquake characteristics on the ground surface based on the local
geotechnical site conditions. Each of these stages involves various degrees of
uncertainties; therefore probabilistic approaches were adopted at each stage to account
for the variability by selecting identical exceedance probabilities at all stages to keep the
overall risk level constant.
In the first stage of seismic microzonation studies for Silivri, Gutenberg-Richter
recurrence relationship with a Poisson model was adopted using the available
instrumental and historical seismic databases for evaluating the seismic hazard as shown
in Figure 8.1(a) for a source radius of 100 km.
Earthquake records for the historical era (approximately between 496 B.C. and 1916)
with intensity Io >V, for Silivri region were compiled based on available earthquake
catalogues (Ergin et al., 1967; Sipahio÷lu, 1984; Ambraseys and Finkel, 1995;
Papazachos et al., 1997). Since the records for this period are in terms of intensities, the
Seismic Microzonation
255
relation developed for Turkey by Ansal (1997);
M = 0.594 Io + 1.36
(8.1)
was used to convert the intensities (Io) to magnitudes (Ms). The seismic hazard analyses
were performed in terms of these calculated magnitudes. Due to the nature of the
historical earthquake records, it would be more reliable to base the seismic hazard
analyses on medium strong and strong earthquakes. Thus, only earthquakes with
intensity Io tVI have been used in the analyses.
The earthquake records for the instrumental era (approximately between 1904 and 2002)
were compiled based on available earthquake catalogues (BUKOERI, 2002; Ergin et al.,
1967, 1971; Genço÷lu et al., 1990; Güçlü et al., 1986).
One shortcoming with the use of instrumental records is the limited time interval for the
compiled data that would not represent the tectonic regime going on for millions of
years. The other weakness is the non-uniform statistical distribution of earthquakes
with respect to their magnitudes and the presence of relatively large number of small
events that affects the selected probability distribution function. On the other hand,
historical data compiled for a longer time interval may not be very accurate with respect
to epicentre locations, dates, and intensities.
It would be more reliable to utilise the earthquake records from historical and
instrumental era together to perform seismic hazard analyses. A weighted averaging
procedure was adopted by assigning weights of 40% and 60% for historical and
instrumental records, respectively. Thus, the magnitude of a probable earthquake
corresponding to the average exceedance probability of 10% for a period of 50 years
was estimated as M=6.7, as shown in Figure 8.1b.
Fig. 8.1. Seismic activity within 100 km of Silivri and evaluation of seismic hazard for
based on single areal source model
The next stage is the estimation of the possible epicentre locations for this probable
earthquake. A statistical analysis was conducted for this purpose by assuming that all
epicentres of past earthquakes are possible epicentres for future earthquakes
(Ambraseys et al., 1996; Kafka and Walcott, 1998). The statistical distribution of
epicentre distances of instrumentally recorded earthquakes with magnitude M>2 around
Silivri was determined as shown in Figure 8.2(a).
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A.Ansal, Y.Biro, A.Erken, and Ü.Gülerce
One way to obtain the statistical distributions for probability analysis is to use the
probability density functions. The Beta probability density function was observed to
give the best fit for the distribution of epicentre distances. Another way is to define the
observed distribution of data as a discrete statistical density distribution for evaluating
the probabilities. Figure 8.2(b) shows both methods and demonstrates the similarity in
both procedures. By this approach, the epicentre distance for M=6.7 earthquake
corresponding to 10% exceedance probability around Silivri is determined as 24 km,
with a 10% probability of being less.
Fig. 8.2. Estimation of the probable epicentre distance
The third step is the estimation of the earthquake characteristics at the bedrock or
competent soil outcrop using a suitable attenuation relationship in accordance with the
geological and tectonic features of the region. One option that may be suitable for
microzonation studies is to use a contemporary attenuation relationship to estimate the
spectral accelerations at the competent soil outcrop. Once the probable acceleration
spectrum is obtained then spectrum compatible outcrop acceleration time histories can
be calculated to be used for the site response analyses.
In the case of Silivri study, the acceleration response spectrum was determined using
the spectral attenuation relationship proposed by Abrahamson and Silva (1997). The
simulated acceleration time histories were calculated based on the method suggested by
Deodatis (1996) using the computer code developed by Papageorgiou et al. (2000). The
target acceleration spectra compatible time history (TARSCTHS -Papageorgiou et. al,
2000) is a ground motion simulation program generating a synthetic time history of
ground accelerations. The time domain simulations are non-stationary with random
phases. Six spectrum compatible acceleration time histories were calculated as shown
in Figure 8.3. The simulations were performed taking into account the possible
earthquake magnitude and (a) using the estimated epicentre distance as a parameter for
duration control for the first three and (b) by specifying the duration as 30 seconds for
the remaining three records.
The acceleration response spectra of the simulated acceleration time histories are in
very good agreement with the target spectra for the high period range but with some
discrepancies in the low period range as shown in Figure 8.4. However, since this low
period or high frequency range of the acceleration time histories would not produce
significant effects on the site response analyses, the calculated acceleration time
histories were considered suitable.
Seismic Microzonation
257
Fig. 8.3. Six simulated acceleration records calculated for site response analyses
Fig. 8.4. Comparisons of the acceleration response spectra of the six simulated spectrum
compatible acceleration time histories with the acceleration spectra calculated by
Abrahamson and Silva (1997) spectral attenuation relationship
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A.Ansal, Y.Biro, A.Erken, and Ü.Gülerce
8.3. Geological and Geotechnical Site Conditions
The second stage in seismic microzonation would start with the assessment of the local
geological formations and with the mapping of the surface geology based on available
information, site surveys, site investigations, and soil explorations. The purpose is to
determine the boundaries and the characteristics of the geological formation and to
prepare a geology map at a scale of 1:5000 or larger as shown for Silivri in Figure 8.5.
Fig. 8.5. Geological formations in Silivri
This map clearly indicates the geological formations and their variation in Silivri.
However, it is important, as pointed out by Willis et al., (2000), to base the site
classification on measured characteristics of geologic units taking into consideration the
possible variations in each unit. The deviations from the mean values obtained for each
geological unit may exceed the permissible limits to justify its use for assessing the
effects of local soil conditions. It should be noted that the studies in Silivri also
demonstrated that the existing geological units are not homogenous and significant
changes in their properties could be observed from one point to another, even in the
same formation. Therefore, considering the geological units as the only criteria in
seismic microzonation is not appropriate. The major purpose of the geology map may
be regarded as the basic information to plan the detailed site investigations and to
control the reliability of the results obtained by site characterisations and site response
analyses.
Wills and Silva (1998) suggested using average shear wave velocity in the upper 30 m
as one parameter to characterise the geological units while also admitting the
importance of other factors such as impedance contrast, 3-dimensional basin and
topographical effects, and source effects such as rupture directivity on ground motion
characteristics. In their compiled database, they have encountered significant variations
in the equivalent shear wave velocities especially in the case of alluvium deposits.
Wills and Silva (1998) suggested using shear wave velocity for classifying site
conditions rather than geological units, even though the determination of shear wave
velocities requires extensive field investigations.
During site characterisation it is necessary to determine the variations in soil
stratification and engineering properties of soil and rock layers encountered at the site
preferably based on in-situ tests and laboratory tests conducted on the samples obtained
during the soil exploration. The purpose is to determine the site conditions as accurate
as possible in order to realistically assess the site response characteristics.
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259
The site characterisation in Silivri was conducted by adopting a grid system. The
investigated area was divided into cells of 500×500 meters. A representative
hypotetical soil profile was determined for each cell based on all available borehole data,
in-situ and laboratory test results. The purpose is to estimate the effects of site
conditions at a scale of 1:5000 by assigning these representative boreholes at the centre
of each cell, as shown for Silivri in Figure 8.6.
Fig. 8.6. Site characterisation by a grid system for Silivri
There are basically two reasons behind this approach (1) to utilise all the available data
in each cell in order to have more comprehensive and reliable information about the soil
profile; (2) to eliminate the effects of different distances among boreholes or site
investigation points during GIS mapping.
The results obtained were mapped using GIS techniques by applying linear interpolation
among the grid points, thus enabling a smooth transition of the selected parameters.
Soft transition boundaries were preferred to show the variation of the mapped
parameters. Better defined clear boundaries were not used and are not recommended
due to the accuracy of the study and in addition to allow some flexibility to the urban
planners and to avoid misinterpretation by the end users that may consider the clear
boundaries as accurate estimations of the different zones.
Fig. 8.7. Zonation with respect to site classification defined in Turkish Earthquake Code
(1997) in comparison to the surface geology for Silivri
The objective of site characterisation is the determination of each representative soil
profile estimated for each cell with respect to a site classification criterion. Borehole
samples and geological studies were used to classify the site conditions in Silivri
260
A.Ansal, Y.Biro, A.Erken, and Ü.Gülerce
according to the Turkish Earthquake Code (1997). The zonation map with respect to
the site classes specified in the Turkish Earthquake Code (1997) is shown in Figure 8.7.
There appears to be a reasonable agreement with respect to surface geology. Softer
sites Z4 and Z3 were mostly in the areas that were classified as Quaternary sand dunes
and Quaternary alluvium deposits while Z1 and Z2 are in areas that were classified as
claystone and sandstone formations.
It is important to note that these results are based on representative site profiles that
were estimated based on the available data and the accuracy of this site classification
map may not be suitable for assessing the local site conditions to be used for structural
design purposes. Site specific soil investigations are required to determine local site
conditions for each building area to be used in the structural design.
The approach adopted in the assessment of the calculated zonation maps involves
division of the area into three zones as (A, B, and C). Since the site characterisations, as
well as all the analyses performed, require various approximations and some important
assumptions, it was preferred not to present the numerical values for any parameter. In
all cases, the variations of each calculated parameter are considered separately and their
frequency distributions were determined for the whole microzonation study region.
Thus the zone A shows the most favourable (in terms of earthquake hazard) 33%
percentile (e.g. higher equivalent shear wave velocities, lower spectral amplifications
and lower spectral accelerations), zone B the medium 34% percentile and zone C shows
the most unsuitable 33% percentile (e.g. lower equivalent shear wave velocities, higher
spectral amplifications and higher spectral accelerations). In this way it was possible to
define three zones with different earthquake hazard levels in a relative way enabling the
urban planners and municipal officials to have the flexibility in deciding the appropriate
planning alternatives taking into consideration all other relevant factors besides
earthquake hazard.
One popular criterion for site characterisation is to use equivalent (average) shear wave
velocity defined as the weighted average of shear wave velocities of soil and rock layers
in the top 30 meters. Equivalent shear wave velocities are being used in earthquake
codes for the purpose of evaluating the design earthquake characteristics on the ground
surface (Borchert, 1994). In addition, it is also possible to use empirical relationships to
estimate spectral amplifications based on equivalent shear wave velocity.
Equivalent shear wave velocity can be calculated by conducting in situ seismic wave
velocity measurements or by using correlations developed in terms of SPT-standard
penetration or CPT-cone penetration tests. In Silivri, shear wave velocities for the soil
layers were determined from seismic refraction tests and by using the relationship
proposed by Iyisan (1996);
VS = 51.5 N 0.516
(8.2)
where N is the SPT blow counts for 30 cm and VS is the shear wave velocity in m/sec.
This relationship is valid for all soil types for estimating shear wave velocities from
SPT tests. There are large numbers of similar correlations in the literature. The Iyisan
relationship was used because it was developed based on local data sets under similar
site conditions.
The zonation with respect to the equivalent shear wave velocity in Silivri is shown in
Seismic Microzonation
261
Figure 8.8 in terms of three percentile groups in comparison with the surface geology.
Zones determined as A are the areas with the higher 33% percentile of equivalent shear
wave velocity and zones determined as C are the areas with the lower 33% percentile of
equivalent shear wave velocity. The zonation with respect to equivalent shear wave
velocity is in agreement with the geology where zone C, representing relatively higher
earthquake hazard zones coincides mostly with the Quaternary alluvium deposits while
zone A representing the upper 33% percentile of the equivalent shear wave velocity
concides with the Danismen (sandstone & claystone) formations.
Fig. 8.8. Zonation with respect to equivalent shear wave velocity in comparison to
surface geology for Silivri
8.4. Earthquake Characteristics on the Ground Surface
One option to estimate the earthquake characteristics on the ground surface is to use an
empirical relationship in terms of equivalent shear wave velocities. In the case of Silivri
microzonation study, the peak spectral amplifications based on equivalent shear wave
velocity were calculated using the relationship given by Midorikawa (1987);
Ak = 68 VS-0.6
(8.3)
where Ak is the spectral amplification and VS is the equivalent shear wave velocity in
m/sec.
Fig. 8.9. Zonation with respect spectral amplifications calculated from equivalent shear
wave velocities in comparison with the surface gology for Silivri
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A.Ansal, Y.Biro, A.Erken, and Ü.Gülerce
The peak spectral amplifications calculated based on Equation (8.3) were evaluated and
the zonation with respect to peak spectral amplifications were also mapped based on
three percentile groups, as shown in Figure 8.9 where C shows the areas with relatively
higher spectral amplification and thus higher level of earthquake hazard.
The second and more comprehensive assessment of earthquake characteristics on the
ground surface can be achieved by conducting site response analyses for all
representative soil profiles. In the case of the Silivri study, site response analyses were
conducted for the spectra compatible six simulated acceleration time histories
determined based on the regional earthquake hazard study using the site response
analysis code proposed by Schnabel et al. (1972) and later modified by Idriss and Sun
(1992).
The variation of spectral accelerations calculated for six input motion as well as the
average of all 6 response spectra are shown in Figure 8.10. As can be observed from
Figure 8.10, there are significant differences among different soil profiles both in terms
of the ordinates of the spectral accelerations as well as the predominant periods
indicating the variability of the site conditions.
Fig. 8.10. Some typical elastic acceleration response spectra for 6 input motions and the
calculated average that are plotted in terms of spectral acceleration versus period
Representative parameters reflecting the calculated site amplification characteristics
could be peak spectral accelerations or average spectral accelerations calculated
between the periods of 0.1-1.0 second. It was assumed that peak spectral accelerations
could be used as a zonation criterion since a linear correlation was observed between
these two parameters with relatively high regression coefficient as shown in Figure 8.11.
Seismic Microzonation
263
Fig. 8.11. Correlation between the calculated peak spectral accelerations and average
spectral accelerations between 0.1-1.0 sec. periods
The average of the six peak spectral accelerations was used as the representative
parameter for microzonation that was performed with respect to three percentile groups
where A shows the lower 33% percentile and C shows the higher 33% percentile in
terms of calculated spectral accelerations in comparison with the surface geology as
shown in Figure 8.12. The zonation with respect to spectral accelerations is in general
agreement with the surface geology where C shows the areas with relatively higher
earthquake hazard. These areas mostly coincide with the Quaternary deposits however,
as can be observed from Figure 8.12, there are also zones classified as C in regions that
were defined as claystone formations in the surface geology map. These were the areas
where the claystone formation shows different characteristic mostly due to weathering.
Fig. 8.12. Zonation with respect to peak spectral accelerations calculated by site
response analyses in comparison with the geology in Silivri
Microtremor records are being widely used in the recent seismic microzonation studies.
Microtremors are very low amplitude vibrations, which may only be measured by very
sensitive seismometers. The methodology is relatively easy and economically feasible
that enables quick assessment of predominant soil periods and approximate estimates of
spectral amplifications (Nakamura, 1989).
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A.Ansal, Y.Biro, A.Erken, and Ü.Gülerce
Even though it is generally accepted that H/V ratios obtained from microtremor records
would not lead to very reliable spectral amplification values (Bard, 1999, Lachet and
Bard, 1994) they can still be taken into consideration when finalising the microzonation
with respect to site amplification. Therefore, the results obtained from the microtremor
study were utilised to map the variation of spectral amplifications for Silivri as shown in
Figure 8.13.
Fig. 8.13. Variation of spectral amplifications obtained from microtremor records in
comparison with surface geology in Silivri
8.5. Seismic Microzonation with Respect to Ground Shaking
The basic intention of the site response analysis is to estimate the effect of local site
conditions in assessing the site amplification with respect to ground shaking. It would
be logical to base this decision on all the available results obtained from site
characterisation based on equivalent shear wave velocity, site response analysis as well
as from microtremor measurements conducted in the region.
As briefly described in the preceding sections, many parameters such as geological
formations, local soil conditions, equivalent shear wave velocity, spectral amplification
and their variations are among the controlling factors in seismic microzonation studies.
A consistent approach has to be implemented to assess each parameter with respect to
all other parameters. However, the main objective of seismic zonation is to establish a
seismic hazard map in a large scale taking into account, earthquake source and local site
conditions. Thus, estimation of the earthquake induced forces and their variation in the
investigated area must be the main target in seismic microzonation.
Even though seismic microzonation contains important information for city and
regional planning, considering different structures with different functions, site specific
studies need to be performed at each site during the design stage to evaluate the local
site conditions. A classification in terms of priority levels can be used to resolve this
restriction and site characteristics determined from seismic microzonation studies may
be used in the design process of the selected structures, e.g. one or two storey residential
buildings. On the other hand, site specific studies, including in-situ and laboratory tests,
must be obligatory in the assessment of the required parameters for the structures with
higher importance levels.
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265
The final seismic microzonation map with respect to ground shaking was obtained by
evaluating all the available data based on the grid system given in Figure 8.6 where
spectral amplification is estimated for each grid point based on the results obtained from
equivalent shear wave velocity, site response analysis and microtremor H/V ratio taking
into consideration the representative soil profiles for each cell. The final seismic
microzonation map with respect to ground shaking is shown in Figure 8.13 in
comparison with the surface geology. In general there is good correlation with respect
to alluvial deposits but there are also significant differences for the sandstone and
claystone formations as expected. The advantage of this assessment is the capability to
consider the variations of the calculated spectral accelerations with respect to three
different methodologies: equivalent shear wave velocity, site response analysis, and
microtremor H/V ratio. Thus, it can be considered partly independent of the approach
adopted to determine the site amplification characteristics.
Fig. 8.14. Proposed seismic microzonation with respect to ground shaking in
comparison to surface geology for Silivri
The interpretation of the seismic microzonation map with respect to ground shaking
involves three zones that are classified relatively according to the expected ground
motion characteristics taking into consideration source and site factors. For the purpose
of urban planning areas classified as zone A are the areas that will be less affected with
lower earthquake hazard. These are the areas that are most suitable for the critical
structures and higher population densities. On the contrary areas classified as zone C
are the areas that will be most adversely affected during possible earthquakes in the
future. However, it is important to point out that this classification was conducted for
the three zones that were defined relatively with respect to each other. Thus considering
only the Silivri municipality, zones classified as C are the areas that would experience
more severe ground shaking in comparison to the other parts of Silivri. The relative
level of ground shaking should not be interpreted as absolute level and areas that are
classified as C should not be regarded as areas that are unsuitable for urban settlements.
8.6. Conclusions
The major purpose of seismic microzonation is to offer urban planners and city officials
some guidelines to mitigate earthquake risk. For this purpose, a seismic microzonation
study was conducted for the Silivri Municipality in Istanbul. Assuming that the main
factors affecting the earthquake characteristics on the ground surface are source and site
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A.Ansal, Y.Biro, A.Erken, and Ü.Gülerce
factors, regional seismic hazard study was conducted at a regional scale adopting a
single areal source model. The earthquake characteristics on the ground surface was
determined based on the evaluation of site conditions with respect to equivalent shear
wave velocity and with respect to site response analyses conducted for each
representative soil profile. In determining the seismic microzonation for ground
shaking, all available results were utilised by adopting a grid system to estimate the
variation of spectral amplification in the investigated region, namely in the town of
Silivri.
Acknowledgements
The authors would like to express their gratitude to Prof. Haluk Eyido÷an and Arif
Cemal Seçkin, who made significant contributions to this study. It would not have been
possible to conduct such comprehensive assessment without their input and support.
The authors would also like to express their thanks and gratitude to the mayor of Silivri
who has supported and financed the whole project.
CHAPTER 9
DYNAMIC ANALYSIS OF SOLID WASTE LANDFILLS AND LINING
SYSTEMS
Pedro Simão Sêco e Pinto
National Laboratory of Civil Engineering (LNEC), University of Coimbra and New
University of Lisbon, Portugal
9.1. Introduction
The need of construction of high solid waste landfill in order to protect human health
and the environment has created new engineering challenges. In this framework the
seismic behaviour of solid waste landfills has deserved considerable attention. This
behaviour has been analysed by experimental methods or mathematical methods. The
characterization of material properties for seismic design is a difficult task as due the
heterogeneity of the material large samples are needed.
The seismic design of solid waste landfill follows the same procedures for the design of
embankment dams and so both pseudo-static and deformational analysis methods are
used. However it is important to assess the behaviour of the geosynthetic elements used
in the cover systems and bottom lining systems to the seismic induced permanent
displacements. The monitoring tasks and the safety control of landfills are analysed.
Risk analysis and safety are addressed.
9.2. Performance of Solid Waste Landfills during Earthquakes
From the lessons learned from past earthquakes, such as Loma Prieta earthquake
(Johnson et al., 1991; Buranek and Prasad, 1991; Sharma and Goyal, 1991) and
Northridge earthquake (Matasovic et al., 1995; Stewart et al., 1994; Augello et al., 1995)
it is important to stress that modern solid waste landfills withstand the design
earthquake without damages to human health and environment.
From well documented case histories the following failure mechanisms can be selected:
x
x
x
x
x
x
x
x
x
x
Sliding or shear distortion of landfill or foundation or both;
Landfill settlement;
Transverse and longitudinal cracks of cover soils;
Cracking of the landfill slopes;
Damage to the gas system header pipes;
Tears in the geomembrane liners;
Disruption of the landfill by major fault movement in foundation;
Differential tectonic ground movements;
Cracks about the contact between refuse landfill and canyon;
Liquefaction of landfill or foundation.
The damage modes listed are not necessarily independent of each other.
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© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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Pedro Simão Sêco e Pinto
Experience has shown that well built waste landfills can withstand moderate shaking
peak accelerations up to at least 0.2g with no harmful effects. Nevertheless this
scenario, the integrity of solid waste landfills during strong earthquakes to achieve
environmental and a public health objective deserves more consideration.
Fig. 9.1. Flowchart for solid waste landfills
9.3. Analysis of Solid Waste Landfills Stability during Earthquakes
9.3.1. INTRODUCTION
The stability analysis of solid waste landfills can be established by the flow chart
presented in Figure 9.1.
The behaviour of solid waste landfills during the occurrence of earthquakes can be
analysed by experimental methods or mathematical methods. Seismic design of solid
waste landfills uses the same principles of seismic design of embankment dams (Sêco e
Pinto, 1993). The capabilities and limitations of these methods are briefly summarised.
9.3.2. EXPERIMENTAL METHODS
Experimental methods are used to test predictive theories and to verify mathematical
models. The most popular techniques for solid waste landfills are shaking table and
centrifuge models.
Solid Waste Landfills and Lining Systems
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Yegian et al. (1995) by conducting shaking table tests have concluded that: (i) the
geosynthetic interface reduces the level of the acceleration pulses of the ground motion;
and (ii) the geosynthetic interface acts as base isolator absorbing the wave energy
through interface slip.
Centrifuge model tests have been carried out to understand the principle of wastestructure interaction and to investigate deformation induced stress redistribution within
the waste body near a structure (Kockel et al., 1997)
9.3.3. MATHEMATICAL METHODS
The following dynamic analysis of embankment dams is used (Sêco e Pinto et al., 1995):
1. pseudo-static analyses;
2. simplified procedures to assess deformations;
3. dynamic analysis.
The slope stability of waste landfills is generally evaluated by limit equilibrium slope
stability analyses. For the pseudostatic analyses a seismic coefficient value equivalent
to the peak ground acceleration divided by 1.5 can be considered (Sêco e Pinto et al.,
1998). For solid waste landfills an acceptable seismic behaviour is anticipated if the
calculated pseudo-static factor of safety ranges from 1.3 to 1.5.
Simplified procedures to assess landfills deformations were proposed by Newmark
(1965), Sarma (1975) and Makdisi and Seed (1977) and have given reasonable answers
in areas of low to medium seismicity.
Newmark´s original sliding block model considering only the longitudinal component
was extended to include the lateral and vertical components of earthquake motion by
Elms (2000).
The use of dynamic pore pressure coefficients along with limit equilibrium and sliding
block approaches for assessment of stability of earth structures during earthquakes was
demonstrated by Sarma and Chowdhury (1996).
Several finite element computer programs assuming an equivalent linear model in total
stress have been developed for 1D (Schnabel et al., 1972; Idriss and Sun, 1992), 2D
(Lysmer et al., 1974) and pseudo 3D (Lysmer et al., 1975). Since these models are
essentially elastic the permanent deformations cannot be computed by this type of
analysis and are estimated from static and seismic stresses with the aid of strain data
from laboratory tests (cyclic triaxial tests or cyclic simple shear tests).
To overcome these limitations, nonlinear hysteretic models with pore water pressure
generation and dissipation have been developed using incremental elastic or plasticity
theory. The incremental elastic models have assumed a nonlinear and hysteretic
behaviour for soil and the unloading-reloading has been modelled using the Masing
criterion and incorporate the effect of both transient and residual pore-water pressures
generated by seismic loading (Finn, 1987).
Sargent (1990) has introduced the concepts of verification and validation and the
relations established between the three entities: the physical problem; the conceptual
model; and the computer model and its numerical implementation are illustrated in
Figure 9.2.
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Pedro Simão Sêco e Pinto
Fig. 9.2. Relations between physical problem, conceptual model and computer model
(after Sargent, 1990)
Verification intends to ensure that the computer program is correct and its represents
faithfully the conceptual model and validation applies essentially to the conceptual
model, and its ability to reproduce satisfactorily the physical phenomena.
A slightly different terminology is adopted by ICOLD (1993) that considers that the
numerical modelling process for dams should be checked in order to avoid unreliable
results considering the following aspects:
1. justification of the whole modelling method (the relevance to physical reality);
2. validation of the computer code;
3. quality assurance of the whole computation process.
9.3.4. SELECTION OF DESIGN EARTHQUAKES
The Code of Federal Regulations (US-CFR, 1991) requires for the new municipal solid
waste landfills to be designed for a maximum horizontal acceleration with a 10 percent
probability of exceedance (90 percent probability of non exceedance) in 50 year and
250 year of exposure periods. The related return periods are 475 years and 2375 years,
respectively.
It is important to refer that EC8 (1995) recommends for the seismic design of buildings
and bridges a return period of 475 years.
The selection of seismic design parameters for municipal solid waste landfill following
the dam projects depends on the geologic and tectonic conditions at and in the vicinity
of the site. The regional geologic study area should cover a 100km radius around the
site to include any major fault or specific attenuation laws.
The probabilistic approach quantifies numerically the contributions to seismic motion,
at the landfill site, of all sources and magnitudes larger than 4 or 5 Richter scale and
includes the maximum magnitude on each source.
Solid Waste Landfills and Lining Systems
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The landfill should be designed for Operating Basis Earthquake (OBE) and Maximum
Design Earthquake (MDE). Both depend on the level of seismic activity, which is
displayed at each fault or tectonic province. For the OBE only minor damage is
acceptable and is determined by using probabilistic procedures.
For the MDE only deterministic approach was used (ICOLD, 1983) but presently it is
possible to use a deterministic and probabilistic approach. If the deterministic
procedure is used, the return period of such an event is ignored, if the probabilistic
approach is used a very long period is taken (ICOLD, 1989).
Neotectonics
The tectonic conditions should include tectonic mechanisms, location and description of
faults (normal, strike and reverse), and estimation of fault activity (average slip rate, slip
per event, time interval between large earthquake, length, directivity effects, etc), these
factors are important to assess the involved risk.
Determination of neotectonic activity implies first the qualitative geomorphologic
analysis of air photos and topographic maps. The GPS system is another powerful
means of monitoring the crustal mobility. Cluff et al. (1982) have proposed the
following classification for slip rates: extremely low to low for 0.001 mm/year to 0.01
mm/year, medium to high 0.1 mm/year to 1 mm/year and very high to extremely high
10 mm/year to 100 mm/year.
The most dangerous manifestation concerning the landfill stability and integrity is the
surface fault breaking, intersecting the landfill site. The current practice is the
deterministic approach in which the seismic evaluation parameters were ascertained by
identifying the critical active faults, which show evidence of movements in Quaternary
time.
Following (ICOLD, 1989) an active fault is a fault, reasonably identified and located,
known to have produced historical fault movements or showing geologic evidence of
Holocene (11000 years) displacements and which, because of its present tectonic sitting,
can undergo movements during the anticipated life of man-made structures.
To assess if there is the potential for a significant amount of surface displacement
beneath the dam several backhoe trenches are excavated with 3 to 4 meters deep and 30
to 50 meters long and should be inspected and log the exposures geologic features.
Recently a fault investigation method other than trenching has been developed, called
the long Geo-slicer method in which long iron sheet piles with a flat U-shaped cross
section are driven into an unconsolidated bed, iron plate shutters are inserted to face
these iron sheet piles and the piles and shutters are pulled out to take undisturbed
samples of strata of a certain width. This method is advantageous in regard to the ease
of securing land for conducting investigations compared with trenching and the ease of
bringing the strata samples back to the laboratory for detailed observations (Tamura et
al., 2000).
When active faults are covered with alluvium geophysical explorations such as seismic
reflection method, sonic prospecting, electric prospecting, electromagnetic prospecting,
gravity prospecting and radioactive prospecting can be used (Takahashi et al., 1997).
Of these the seismic reflection method can locate faults if geological conditions are
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Pedro Simão Sêco e Pinto
favourable, and confirm the accumulation of fault displacements based on the amount of
displacements in strata that increases with strata age.
Attenuation relations
Attenuation relations can be divided into 3 main tectonics classification shallow crustal
earthquakes in active tectonics regions, regions subduction earthquakes and shallow
crustal earthquakes in stable continental regions.
The following attenuation relations were proposed: Idriss model (1995) and Sadigh et al.
(1997) model have only horizontal component and Abrahamson and Silva (1977)
relation have been used for vertical component.
Sommerville et al. (1977) have shown that directivity has a significant effect on longperiod ground motions for sites in the near-fault region.
9.3.5. SELECTION OF SOIL PROPERTIES FOR DYNAMIC ANALYSIS
The shear strength properties of waste landfills are not easily determined since the
physical composition of the mixture makes it unsuitable for the conventional laboratory
strength testing. The size of testing equipment is too small relative to the normal size of
the refuse. Also the shear parameters of municipal solid waste show a broad variety and
a differentiation between fresh and old wastes. To overcome this situation the waste
properties are established based on the type of waste, the waste processing and the
placement procedures.
Fig. 9.3. Unit weight of MSW (after Kavazanjian, 1995; Reproduced with permission
from Balkema)
Some properties are measured directly, such as dry density and water contents and other
properties due the difficulties related with sampling are obtained from indirect methods
Solid Waste Landfills and Lining Systems
273
combining with the existent knowledge of waste properties (Sêco e Pinto, 1997).
Total unit weights of the material are determined from in-place testing or laboratory
compaction tests. Kavazanjian (1995) has proposed a unit weight profile with depth
(Figure 9.3).
From literature survey the particle size distribution of municipal solid waste is shown in
Figure 9.4 (Jessberg, 1994).
Fig. 9.4. Particle size distribution of waste for laboratory tests (after Jessberg, 1994;
Reproduced with permission from Balkema)
Fig. 9.5. Shear parameters of municipal solid waste (after Jessberg, 1996; Reproduced
with permission from Balkema)
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Pedro Simão Sêco e Pinto
From results of laboratory and field tests the shear parameters of municipal waste
exhibits a differentiation between fresh and old waste (Jessberg, 1996) (Figure 9.5).
Also direct simple shear test laboratory tests on reconstituted large samples are used to
determine large strain properties.
A wide range of reported Vs values for MSW compiled by Kavazanjian et al. (1996) is
shown in Figure 9.6.
Fig. 9.6. Shear wave velocity of MSW (after Kavanzanjian et al., 1996; Reproduced
with permission from Balkema)
To characterise the strength of solid waste Grândola landfill dynamic penetrometer tests
were performed and the obtained results are shown in Figure 9.7.
Fig. 9.7. Dynamic penetrometer tests (after Sêco e Pinto et al., 1999; Reproduced with
permission from Balkema)
Solid Waste Landfills and Lining Systems
275
The measurement of the shear waves velocity by crosshole and downhole techniques
need drilling boreholes in landfills. Spectral analysis of surface waves (SAWS) provide
relatively accurate Vs profiles without the need for drilling and sampling the landfill
material. Taking this into consideration geophysical measurements to estimate dynamic
strain-dependent materials of solid wastes of Grandola landfill were implemented and a
value of shear waves velocities between 330 - 350 m/s was obtained (Figure 9.8) (Sêco
e Pinto et al., 1999).
Fig. 9.8. Shear wave velocities of Grândola solid wastes (after Sêco e Pinto et al., 1999;
Reproduced with permission from Balkema)
The obtained results have not shown a variation of shear wave velocities with depth,
probably due the height of landfill being only 12m, and are in reasonable agreement
with the results reported by Kavazanjian et al. (1995).
The variation of shear modulus G and damping ratio O with shear strain can be derived
by laboratory tests (Sêco e Pinto, 1990).
Limitations include health and safety constraints on sampling and testing of solid waste
and the small size of test specimens relative to the size of the waste constituents.
For the variation of shear modulus and damping characteristics of waste materials,
sandy silt material and silty material, with shear strain, the curves proposed by Singh
and Murphy (1990) are presented in Figure 9.9.
The variation of shear modulus and damping ratio with shear strain for peat and clay
material and the curves proposed by Kavazanjian and Matasovic (1995) for waste
materials are presented in Figure 9.10.
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Pedro Simão Sêco e Pinto
Fig. 9.9. Waste modulus degradation and damping curves used in study (after Singh and
Murphy, 1990; Reproduced with permission from ASTM)
Fig. 9.10. Modulus and damping of MSW (after Kavazanjian and Matasovic, 1995,
“Seismic analysis of solid waste landfills”, Proc. of Geoenvironment 2000, ASCE
Specialty Conference, New Orleans, Louisiana; Reproduced with permission from
ASCE)
Solid Waste Landfills and Lining Systems
277
When solid waste landfills incorporate construction demolition debris the curves
proposed for rockfill and gravel materials can be used. The shear interface resistance of
liner and cover systems landfills has deserved increasing attention.
The dynamic properties of the geosynthetic liner can be replaced by the dynamic
properties of the equivalent soil layer measured by shaking table tests.
9.3.6. SEISMIC RESPONSE ANALYSIS
The seismic responses obtained by computer finite element 1D programs are considered
reasonable. These analyses are based on the solution of the equation of motion
considering a homogenous and continuous soil deposit composed by horizontal soil
layers and assuming a vertical propagation of shear waves.
Due the situation that slopes of landfills are flatter than slopes of earth dams and
landfills decks are larger than dam crests, two dimensional response effects in landfills
should be less significant than in earth dams. For the soil behaviour the equivalent
linear methods is used and the shear modulus and damping ratio are adjusted in each
iteration until convergence has occurred.
Fig. 9.11. Shear stresses distribution (after Sêco e Pinto et al., 1999; Reproduced with
permission from Balkema)
Due to the uncertainties related with the materials properties, foundations geometry and
also to check the influence of the seismic actions parametric and sensitivity studies are
in general performed.
The shear stresses distribution and the acceleration distribution for solid waste Grandola
landfill for three foundation geometries (30m, 40m and 50m depths) are presented in
Figures 9.11 and 9.12 (Sêco e Pinto et al., 1999).
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Pedro Simão Sêco e Pinto
Fig. 9.12. Acceleration distribution (after Sêco e Pinto et al., 1999; Reproduced with
permission from Balkema)
The seismic actions near source and far source were analysed. Due the geometry of the
landfill (height and slopes) the effect of the HDPE geomembrane/geotextile liner was
ignored, i.e. the dynamic properties of the geosynthetic liner was not replaced by the
dynamic properties of the equivalent soil layer.
The Table 9.1 summarises for near source and far source the transference functions of
acceleration (TFRA) between the bedrock and the ground level, the fundamental period
of the layer (TF), the maximum ground acceleration (Max A) and the amplification ratio
(AR).
Table 9.1. Summary of the seismic analyses results
Profile
TRFA
TF (s)
MaxA
(m/s2)
A (m/s2)
AR
Near
Source
P1
4.572
0.409
2.533
Near
Source
P2
4.524
0.489
2. 321
Far
Source
P1
4.475
0.414
1.656
Far
Source
P2
4.447
0.499
1.607
0.945
2.68
0. 941
2.467
0.617
2.683
0.620
2.592
It can be noticed that the amplification effects for the near source and for the far source
are of the same order.
The values of TFRA decrease with the increasing of the thickness of foundation layer.
The fundamental period values increase with the increasing of the thickness of
foundation layer. The obtained results are in good agreement with the seismic
performance of solid waste landfills.
Comparison the results of the analyses performed by SHAKE 91 and QUAD 4M codes
Solid Waste Landfills and Lining Systems
279
Rathje and Bray (1999) have concluded that: (i) the maximum seismic loading for base
sliding within a landfill can be estimated conservatively with 1D analysis; (ii) the 1D
analysis underpredicts the surface maximum horizontal acceleration (MHA) along the
slope of a landfill by 10% on average, and by as much as 40 %; (iii) at the crest 1D
analysis consistently underpredicts the MHA about 25%; (iv) along the deck the
analysis is only moderately unconservative and the effect of base rock topography is not
captured with 1D analysis.
It is important to stress that the dynamic characteristics of solid waste materials play an
important role on the seismic response of landfill and this area deserves more
consideration (Sêco e Pinto et al., 1998).
It is important to assess the dynamic shear strengths of liner materials due the effect of
inertial forces in the refuse mass. Horizontal geosynthetic interfaces have a potential
effect to modify the seismic response of overlying material.
Smooth HDPE geomembrane/geotextile liners reduce significantly the accelerations and
shear stresses transmitted through the landfill profile, especially when the base
acceleration exceeds 0.2g, as pointed by Yegian and Kadakal (1998). These effects
should be taken into account to avoid unrealistic estimates of seismic acceleration, shear
stresses and permanent deformations in a landfill.
Fig. 9.13. Amplification of peak acceleration by landfills (after Kavazanjian and
Matasovic, 1995, “Seismic analysis of solid waste landfills”, Proc. of Geoenvironment
2000, ASCE Specialty Conference, New Orleans, Louisiana; Reproduced with
permission from ASCE)
The effect of the wave propagation through the waste was analysed by Anderson and
Kavazanjian (1995) and the results are presented in Figures 9.13 and 9.14.
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Pedro Simão Sêco e Pinto
Deformations ranging from 150 to 300mm are accepted in practice for design of
geosynthetic liner systems. For cover systems large deformations can be accepted
taking into consideration that most cover failures can be detected and repaired at
reasonable costs.
During earthquakes inertial forces in the refuse mass may result in the mobilization of
shear stress in excess of the dynamic shear strengths of liner materials.
Fig. 9.14. Amplification of acceleration by earth dams and waste landfills (after Singh
and Sun, 1995 “Seismic evaluation of municipal solid waste landfills”, Proc. of
Geoenvironment 2000, ASCE Specialty Conference, New Orleans, Louisiana, 22-24
February; Reproduced with permission from ASCE)
Fig. 9.15. Design charts for evaluating yield acceleration for lined landfills of
(a) 2h:1v and (b) 4h:1v (after Shewbridge, 1996,“Yield acceleration of lined landfills”,
J. of Geotechnical Eng., 122(2): 156-158; Reproduced with permission from ASCE)
Solid Waste Landfills and Lining Systems
281
Based on a simplified block analysis, Shewbridge (1996) presents in Figure 9.15 a chart
to evaluate a yield acceleration of lined landfills.
The permanent displacement induced in the cover soil using four different earthquake
records: Imperial Valley record of the 1940 El Centro Earthquake, Kern County record
of the 1952 Taft earthquake, Capitola record of 1989 Loma Prieta earthquake and
Newhall record of the 1994 Northridge earthquake computed by Ling and Leshchinsky
(1997) is shown in Figure 9.16.
Fig. 9.16. Permanent displacements of finite and infinite slopes (after Ling and
Leshchinsky, 1997. “Seismic stability and permanent displacement of landfill cover
systems”, Journal of Geotechnical and Geoenvironmental Engineering, 123(2): 113122; Reproduced with permission from ASCE)
The allowable value for the calculated permanent seismic displacement of geosynthetic
liner systems is 150 to 300mm. The upper value of 300mm is appropriate for simplified
analyses which use upper bound displacement curves for generic Newmark
displacement charts, residual shear strength and/or simplified seismic analyses
(Kavazanjian, 1998). The lower value 150mm is more appropriate for more
sophisticated analyses and formal Newmark displacement analyses.
The knowledge of interaction between waste and structures is still poor and mainly
limited to field observations.
Centrifuge model tests have been carried out to understand the principle of wastestructure interaction and to investigate deformation induced stress redistributions within
the waste body near a structure (Kockel et al., 1997).
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Pedro Simão Sêco e Pinto
Yegian and Kadakal (1998) have shown that smooth HDPE geomembrane/geotextile
liners significantly reduce the accelerations and shear stresses transmitted through the
landfill profile, especially when the base acceleration exceeds 0.2g. Ignoring these
effects can result in unrealistic estimates of seismic acceleration, shear stresses and
permanent deformations in a landfill. The dynamic properties of the geosynthetic liner
were replaced by the dynamic properties of the equivalent soil layer measured by
shaking table tests.
9.3.7. LIQUEFACTION ASSESSMENT
The methods available for evaluating the cyclic liquefaction potential of landfills or
foundation are based on laboratory tests and field tests.
In general the following laboratory tests are used: (i) cyclic triaxial test, (ii) cyclic
simple shear tests, (iii) torsional cyclic shear tests. Due the difficulties in obtaining high
quality undisturbed samples field test such as SPT tests, CPT tests, seismic cone, flat
dilatometer and methods based on electrical properties of soil are used.
To estimate liquefaction resistance from shear wave velocity there are two procedures:
(i) methods based on a combination in situ shear wave velocity measurements and
laboratory tests on undisturbed tube and in situ freezing samples from Tokimatsu et al.
(1991); (ii) methods based on in situ shear wave velocity measurement and a correlation
between liquefaction resistance and shear wave velocity deduced from liquefaction
degree in the field from Stokoe et al. (1999). The assessment of liquefaction resistance
from shear wave crosshole tomography was proposed by Furuta and Yamamoto (2000).
Liquefaction resistance of silty sands during seismic liquefaction conditions for various
silt contents and confining pressures was investigated by Amini and Qi (2000).
The post-liquefaction strength of loose silty sediments is commonly less than that of
sands, but moderately dense silts at shallow depths are generally dilative, making them
more resistant to ground deformation than cleaner sands (Youd and Gilstrap, 1999).
A probabilistic method considering the uncertainty in the liquefaction criterion was
proposed by Todorovska and Trifunac (1999).
9.4. Monitoring and Safety Control of Landfills
Landfill behaviour during construction and operation is monitored to check methods,
results of analyses and model tests and to analyse it safety against deterioration of
failure.
Seismic downhole-array data provide a unique source of information on actual soil
behaviour over a wide range of loading conditions. Correlation and spectral analyses
are performed to evaluate shear wave propagation characteristics, variation of shear
wave velocity with depth, and site resonant frequencies and modal configurations
(Elgamal et al., 1995).
In regard of seismic instrumentation of the response of the landfill to such seismic
activity the type of instruments currently designated by accelerographs are strong motion accelerographs, peak recording accelerographs and seismoscopes.
Solid Waste Landfills and Lining Systems
283
In comparison with manual readings the automatic system allows a rapid data
processing of results a great number of instruments. Once in operation an automatic
system allows a reduction of personal, both in the field and office. The automatic
system and the central data processing allow a quicker updating of the information. An
automatic system implies an increase of complexity, with the electronic equipment to be
installed in unfavourable environment of temperature and humidity.
For data validation a preliminary check on the raw values (following the execution of
function tests on measurement equipment) by comparing the actual values from the
sensor readings with the established limits and data reduction (computation of
engineering quantities) is performed For the interpretation of the measurements it is
necessary to establish a procedure, a mathematic model that can be a statistical model a
deterministic model or a hybrid model.
Safety control is the group of measures taken in order to have an up-to-date knowledge
of the condition of the landfill and to detect in due time the occurrence of any anomalies
to define actions to correct the situation or, at least, to avoid serious consequences.
9.5. Safety and Risk Analyses
Safety analysis for geotechnical structures, such as slopes, retaining walls, piles and
shallow foundations implies the verification of limit states: ultimate limit states and
serviceability limit states. For dams also two levels of safety are considered, depending
of whether they correspond to normal conditions for use of the structures (current
scenario) or are associated with an exceptional occurrence (failure scenarios).
From the above considerations it seems that for solid waste landfill a level of damage
can be accepted provided there is no harmful discharge of contaminants to the
environment.
For cover systems large displacements can be accepted taking into consideration that
most cover failures can be detected and repaired at reasonable costs.
The allowable values of deformation of landfill systems, depends of several factors,
namely of geosynthetic liner systems and gas recovery system.
Municipality waste landfills owners, regulatory authorities and consultants are
interested in carrying out a risk analysis. Its purpose is to identify the main real risks
associated with each type and height of landfill for all circumstances and can be
conducted: (i) in extensive risk analysis of very large landfills, to substantiate reliably
the probabilities chosen in event trees; (ii) in simplified risk analysis of smaller landfills,
to focus low-cost risk analysis on a few main risks; (iii) and in identifying possibilities
for reducing these risks through low-cost structural or non-structural measures.
Although the annual failure probability of landfills is lower than 10-6 in most cases, it
may be higher for landfills in seismic areas.
Consideration of human behaviour is essential when assessing the consequence of
failures: well organised emergency planning and early warning systems could decrease
the number of victims and so the study of human behaviour plays an important role in
assessment of risk analysis.
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The results of a risk analysis can be used to guide future investigations and studies, and
to supplement conventional analyses in making decisions on waste landfills safety
improvements. With increasing confidence in the results of risk analyses, the level of
risk could become the basis of safety decisions.
9.6. Final Remarks
In the precedent sections the different methods to analyse solid waste landfills and
lining systems stability during earthquakes were presented. These tools are very
important to assist the design engineer in incorporating the adequate design measures to
prevent deleterious effects of earthquake shaking.
All the essential steps of good analyses, whatever the type of material are involved shall
be performed with a sufficient degree of accuracy that the overall results can be
extremely useful in guiding the engineer in the final assessment of seismic stability.
This final assessment is not made by numerical results but shall be made by experienced
engineers who are familiar with the difficulties in defining the design earthquake and
the material characteristics, who are familiar with the strengths and limitations of
analytical procedures, and who have the necessary experience gained from studies of
past performance.
CHAPTER 10
EARTHQUAKE RESISTANT DESIGN OF SHALLOW FOUNDATIONS
Alain Pecker
Géodynamique & Structure, Bagneux, France
10.1. Introduction
Aseismic design of foundations still remains a challenging task for the earthquake
geotechnical engineer. Leaving aside the seismic retrofit of existing foundations, which
is a more difficult issue, even the design of new foundations raises issues which are far
from being totally resolved. One of the main reasons stems from the complexity of the
problem which requires skills in soil mechanics, foundation engineering, soil-structure
interaction along with, at least some knowledge of structural dynamics.
A parallel between static design and seismic design reveals some similarity but also
very marked differences. In the early days, static design of foundations put much
emphasis on the so-called bearing capacity problem (failure behaviour); with the
introduction of an appropriate safety factor, close to 3, the short term settlements were
deemed to be acceptable for the structure. It is only with the increase in the
understanding of soil behaviour and the development of reliable constitutive models that
sound predictions of settlements could be achieved. Not surprisingly, earthquake
geotechnical engineers have focused their attention on the non linear behaviour of soils
and on the evaluation of the cyclic deformations of foundations. This was clearly
dictated by the need for an accurate evaluation of the soil-structure interaction forces
which govern the structural response. It is only during the last decade that seismic
bearing capacity problems have been tackled. These studies have clearly been
motivated by the foundation failures observed in the Mexico City (1985) and Kobe
(1995) earthquakes.
These two aspects of foundation design have reached a state of development where they
can be incorporated in seismic building codes; Eurocode 8 - Part 5 is certainly a
pioneering code in that respect.
In this paper, which is an abridged version of the lecture presented at the GeoEng2000
Conference (Pecker and Pender, 2000) the fundamental aspects underlying the
earthquake resistant design of shallow foundations will be reviewed and their
implementation in seismic building codes will be discussed.
10.2. Aseismic Foundation Design Process
The aseismic design process for foundations is a "very broad activity requiring the
synthesis of insight, creativity, technical knowledge and experience" (Pender, 1995).
Information is required and decisions have to be made at various stages including:
1. the geological environment and geotechnical characterization of the soil profile;
2. the definition of the loads that will be applied to the foundation soil by the
facility to be constructed;
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© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
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Alain Pecker
3. information about the required performance of the structure;
4. investigation of possible solutions with evaluation of load capacity, assessment
of safety factors and estimates of deformations;
5. consideration of construction methods and constraints that need to be satisfied
(finance and time);
6. exercise of judgment to assess potential risks.
Obviously the process described above is not a linear progression. Several iterations
may be required, at least from step 1 to step 6, before arriving at a feasible, reliable and
economic design. In the following we will focus on steps 2 and 4. We will assume that
all the required information related to the soil characterization and structural
performance is available. This in no way means that these two items are of secondary
importance; the data listed under these items are probably the most difficult to assess
and considerable experience is required as well as the exercise of judgment.
10.3. Evaluation of Seismic Demand
10.3.1.FUNDAMENTALS OF SOIL STRUCTURE INTERACTION
The earthquake design loads applied to the foundation arise from the inertia forces
developed in the superstructure and from the soil deformations, caused by the passage
of seismic waves, imposed on the foundations. These two phenomena are referred in
the technical literature as inertial and kinematic loading. The relative importance of
each factor depends on the foundation characteristics and nature of the incoming wave
field.
The generic term encompassing both phenomena is Soil-Structure Interaction (SSI).
However, more often, design engineers refer to inertial loading as SSI, ignoring the
kinematic component. This situation stems from the fact that:
x kinematic interaction may in some situations be neglected;
x aseismic building codes, except for very few exceptions like Eurocode 8, do not
even mention it;
x kinematic interaction effects are far more difficult to evaluate rigorously than
inertial interaction effects.
Figure 10.1 illustrates the key features of the problem under study (adapted from
Gazetas and Mylonakis, 1998). It is presented in the general situation of an embedded
foundation.
The soil layers away from the structure are subjected to seismic excitation consisting of
numerous incident waves: shear waves (S waves), dilatational waves (P wave), surface
waves (R or L waves). The nature of the incoming waves is dictated by seismological
conditions but the geometry, stiffness and damping characteristics of the soil deposit
modify this motion; this modified motion is the free field motion at the site of the
foundation. Determination of the free field motion is in itself a challenging task
because, as pointed out by Lysmer (1978), the design motion is usually specified at only
one location, the ground surface, and the complete wave field cannot be back-calculated
from this incomplete information; that is the problem is mathematically ill posed.
Assumptions have to be made regarding the exact composition of the free field motion
and it can be stated that no satisfactory solution is available to date.
287
Shallow Foundations
a st
Soil-Pile-Structure
System
mass
Free-Field
a ff
Seismic waves R, L
Soil layer
ar
ar
Seismic
waves
S, P
Fig. 10.1. Sketch of the soil-structure interaction problem
Let us now consider the motion around the structure and its foundation: the seismically
deforming soil will force the embedded foundation to move, and subsequently the
supported structure. Even without the superstructure, the motion of the foundation will
be different from the free field motion because of the difference in rigidity between the
soil on one hand, and the foundation on the other hand; the incident waves are reflected
and scattered by the foundation. This is the phenomenon of kinematic interaction.
The motion induced at the foundation level generates oscillations in the superstructure
which develop inertia forces and overturning moments at its base. Thus the foundation,
the piles, and eventually the surrounding soil experience additional dynamic forces and
displacements. This is the phenomenon of inertial interaction.
Obviously the foundation, in a broad sense, must be checked for the combined inertial
and kinematic loading.
The above decomposition of the problem into three tasks (site response analysis,
kinematic interaction, inertial interaction) is convenient for highlighting the various
contributions of each to the final result. It does not necessarily imply that the steps must
be performed separately as a complete interaction analysis (usually with the finite
element method) is conceptually possible. However from a design and practical
standpoint the computation of the foundation seismic loads usually follows the three
step approach.
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Alain Pecker
A direct (or complete) interaction analysis is very time demanding and not well suited
for design, especially in 3D, which requires that the steps described above under item 2
to 6 be repeated several times. The multistep approach reduces the problem to more
amenable stages and does not necessarily require that the whole solution be repeated
again if changes occur, let's say, in the superstructure. In addition, it has the advantage
that some of the intermediate steps can be neglected, as shown later.
The multistep approach is not only attractive for illustrating the fundamental aspects of
soil structure interaction, it is also of great mathematical convenience. This
convenience stems, in linear systems, from the superposition theorem (Kausel and
Roesset, 1974). This theorem states that the seismic response of the complete system of
Figure 10.2 can be computed in two steps:
x the kinematic interaction involving the response to base acceleration of a system
which differs from the actual system in that the mass of the superstructure is equal
to zero;
x the inertial interaction referring to the response of the complete soil-structure system
to forces associated with accelerations equal to the sum of the base acceleration plus
those accelerations arising from the kinematic interaction.
The later system is further divided into two consecutive steps:
x computation of the dynamic impedances at the foundation level;
x analysis of the dynamic response of the superstructure supported on the dynamic
impedances and subjected to the kinematic motion, also called effective foundation
input motion.
Provided each step described above is performed rigorously and under the restriction
that the system remains linear, i.e. superposition is valid, the breakdown of the complete
interaction analysis into consecutive steps is rigorous. For a mathematical description
of the superposition theorem, the reader is referred to Kausel and Roesset (1974) or
Gazetas and Mylonakis (1998).
With this, now classical, theoretical background on soil-structure interaction, in mind,
one can proceed to examine the practical implementation of SSI in the state of practice.
The extent to which this state of practice could be improved at a minimal cost will also
be examined.
10.3.2.CODE APPROACH TO SOIL STRUCTURE INTERACTION ANALYSES
In almost every seismic building code, the structure response and foundation loads are
computed neglecting the soil-structure interaction that is a fixed base analysis of the
structure is performed. The belief is that SSI always plays a favorable role in
decreasing the inertia forces; this is clearly related to the standard shape of code spectra
which almost invariably possess a gently descending branch beyond a constant spectral
acceleration plateau. Lengthening of the period, due to SSI, moves the response to a
region of smaller spectral accelerations. However there is evidence that some structures
founded on unusual soils are vulnerable to SSI. Examples are given by Gazetas and
Mylonakis (1998) and Resendiz and Roesset (1985) for instance.
289
Shallow Foundations
ast
Soil-Pile-Structure
System
mass
Free-Field
aff
Seismic waves R, L
Soil layer
ar
ar
Seismic
waves
S, P
massless
superstructure
m akin
Seismic waves R, L
Soil layer
ar
Seismic
waves
S, P
(a)
Kinematic
Interaction
(b)
Inertial Interaction
m a kin
(b1)
Foundation
Dynamic Impedances
(b2)
Superstructure
Inertial Response
Fig. 10.2. Superposition theorem for soil-structure interaction problems
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Alain Pecker
This has been recognized in some codes. Eurocode 8 states that "The effects of
dynamic soil-structure interaction shall be taken into account in the case of:
x
x
x
x
structures where P-G effects play a significant role;
structures with massive or deep seated foundations;
slender tall structures;
structures supported on very soft soils, with average shear wave velocity less than 100
m/s."
In addition, an annex to the code describes the general effect of SSI. To the best of our
knowledge, Eurocode 8 is the only code which recognizes the importance of kinematic
interaction; however, this is restricted to piled foundations and not mandatory for
shallow or embedded foundations.
10.3.3.IMPROVED EVALUATION OF SEISMIC DEMAND
Linear Systems
With the tremendous development of computer facilities, there does not seem to be any
rational reason for neglecting soil-structure interaction. Most building codes now
require that the structural response be evaluated using a multimodal analysis, as
opposed to a former monomodal analysis and this can be performed with most computer
codes available on the market.
Referring to the multistep approach described previously, the last step of an SSI
analysis (response of the structure connected to the impedances) can be performed on a
routine basis provided that:
x the system remains linear;
x the kinematic interaction can be neglected;
x dynamic impedance functions are readily available.
Although the superposition theorem is exact for linear soil and structure, it can
nevertheless be applied to moderately non linear systems. This can be achieved by
choosing reduced soil characteristics which are compatible with the free field strains
induced by the propagating seismic waves: this is the basis of the equivalent linear
method, pioneered by Idriss and Seed (1968). This engineering approximation implies
that all the soil non linearities arise from the passage of the seismic waves and that
additional non linearities developed around the edges of a mat foundation, are negligible.
Experience shows that it is a valid approximation in many situations where large soil
instabilities do not occur.
For some situations, kinematic interaction can be neglected and the second step of the
multistep approach can be bypassed. It must be realized however that, if kinematic
interaction is thought to be significant, there is no simple means for evaluating it; as a
matter of fact, evaluation of kinematic interaction is almost as difficult as solving the
complete SSI problem. Obviously kinematic interaction is exactly zero for shallow
foundations in a seismic environment consisting exclusively of vertically propagating
shear waves or dilatational waves.
During the last decade, numerous solutions for the dynamic impedances of any shape
291
Shallow Foundations
foundations have been published (Gazetas, 1990). They are available for homogeneous
soil deposits but also for moderately heterogeneous ones
Therefore provided all the aspects listed above are properly covered, seismic soil
structure interaction can be covered at a minimal cost and reduces to the last step of the
multistep approach: dynamic response of the structure connected to the impedance
functions and subjected to the free field motion (equal to the kinematic interaction
motion). However to be fully efficient, and to allow for the use of conventional
dynamic computer codes, the impedance functions which are frequency dependent
(Figure 10.4) must be represented by frequency independent values. The simplest
versions of these frequency independent parameters are the so-called springs and
dashpots. From the published results, it appears that only under very restrictive soil
conditions (homogeneous halfspace, regular foundations) can these dynamic
impedances be represented by constant springs and dashpots. Nevertheless, structural
engineers still proceed using these values which, more than often, are evaluated as the
static component (zero frequency) of the impedance functions.
However, fairly simple rheological models can be used to properly account for the
frequency dependence of the impedance functions. These models can be developed
using curve fitting techniques, or with physical insight, such as the series of cone
models developed by Wolf (1994). Figure 10.3 shows examples of such models: Figure
10.3a is the model proposed by De Barros and Luco (1990) based on a curve fitting
technique; Figure 10.3b is a class of cone models proposed by Wolf. With such models,
which are most conveniently used in time history analyses, the actual dynamic action of
the soil can be properly accounted for; even "negative stiffness", which are frequently
encountered in layered soil profiles, can be apprehended with those models. As an
illustrative example, Figure 10.4 presents the application of model 3a to an actual bridge
pier foundation; the foundation is a large circular caisson, 90 m in diameter, resting on a
highly heterogeneous soft soil profile. The "exact" impedances were computed using a
frequency domain finite element analysis. Note the very good fit achieved by the model
(square symbols) even for the negative stiffness of the rocking component. Clearly,
implementation of such simple rheological models does not impose a heavy burden to
the analyst and represents a significant improvement upon the lengthy and tedious
iteration process in which springs and dashpots are updated to become compatible with
the SSI frequencies.
(b)
(a)
Fig. 10.3. Examples of cone models
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Alain Pecker
However, care must be exercised when implementing the models sketched in
Figure 10.3; due to the presence of the additional mass which induces inertia forces, the
input motion, called the effective input motion, is different from the free field input
motion. Although determination of the effective input motion is not difficult by itself, it
might be more advantageous to make use of rheological models without masses; such
models, made of an assembly of springs and dashpots, have recently been proposed and
seem efficient for surficial foundations (Wu and Lee, 2002).
1.E+07
1.E+08
Model
Finiteelement analysis
Model
Finite element analysis
8.E+06
Dashpot (MN-s/m)
Stiffness (MN/m)
5.E+07
6.E+06
0.E+00
4.E+06
-5.E+07
2.E+06
0.E+00
-1.E+08
0
0
1
2
3
4
5
1
2
3
4
5
Frequency (Hz)
Frequency (Hz)
Fig. 10.4. Rocking dynamic impedances - example
Before moving onto consideration of nonlinear SSI, there in one section of Eurocode 8
which provides for a transition between the linear elastic approach discussed above and
non linear methods discussed below. Table 10.1 (taken from Eurocode8) acknowledges
that with increasing ground acceleration the soil adjacent to a shallow foundation will
experience increasing shear strains and consequently the stiffness will decrease and the
material damping increase. Table 10.1 suggests how the apparent average shear
modulus and material damping of the soil adjacent will change with increasing peak
ground acceleration and envisages that an elastic SSI calculation would be done with
the modified values for the soil stiffness and damping. (Following this simplification
there is, of course, no frequency dependence on the stiffness and damping parameters
for the foundation).
Table 10.1. Average soil damping factors and average reduction factors (± one standard
deviation) for shear wave velocity vs and shear modulus G within 20m depth.(vs max =
average vs value at small strain (< 10-5), not exceeding 300m/s. Gmax = average shear
modulus at small strain.)
Ground
acceleration
ratio, D
Damping factor
0,10
0,20
0,30
0,03
0,06
0,10
vs
vs , max
G
Gmax
0,9(±0,07)
0,7(± 0,15)
0,6(#0,15)
0,80(± 0,10)
0,50(+ 0,20)
0,35(± 0,20)
Shallow Foundations
293
Non Linear Systems
One of the main limitations of the multistep approach is the assumption of linearity of
the system for the superposition theorem to be valid. As noted previously, some non
linearities, such as those related to the propagation of the seismic waves, can be
introduced but the non linearities specifically arising from soil-structure interaction are
ignored. The generic term "non linearities" covers geometrical non linearities, such as
foundation uplift, and material non linearities, such as soil yielding around the edges of
shallow foundations, along the shafts of piles, and the formation of gaps adjacent to pile
shafts. Those non linearities may be beneficial and tend to reduce the forces transmitted
by the foundation to the soil and therefore decrease the seismic demand. This has long
been recognized for foundation uplift for instance (see ATC 40).
Giving up the mathematical rigor of the superposition theorem, an engineering
approximation to these aspects can be reached by substructuring the supporting medium
into two sub-domains (Figure 10.5):
x a far field domain, which extends a sufficient distance from the foundation for the
soil structure interaction non linearities to be negligible, non linearities in that
domain are only governed by the propagation of the seismic waves,
x a near field domain, in the vicinity of the foundation where all the geometrical and
material non linearities due to soil structure interaction are concentrated
Fig. 10.5. Conceptual subdomains for dynamic soil structure analyses
The exact boundary between both domains is not precisely known but its location is
irrelevant for practical purposes. This concept of far field and near field domains can be
easily implemented if one assumes that the degrees of freedom of the foundation are
uncoupled: the far field domain is modelled with the linear (or equivalent linear)
impedance function whereas the near field domain is lumped into a non-linear macroelement. A simplified rheological representation of this sub-structuring is shown in
Figure 10.6 (Pecker, 1998): the macro-element is composed of a finite number of
springs and Coulomb sliders which are determined from curve fitting to the non-linear
force-displacement (or moment-rotation) backbone curve, computed for instance with a
static finite element analysis.
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Alain Pecker
NEAR FIELD
FAR FIELD
O
C
O
O
O
FOUNDATION
.
.
.
.
Fig. 10.6. Non linear rheological model for SSI
Damping in the near field domain arises only from material damping and obeys
Masing's law; damping in the far field domain is of the viscous type. Calibration of this
simplified rheological model against a rigorous 2D dynamic finite element analysis,
including all the non linearities mentioned previously, shows very promising results.
Figure 10.7 compares the overturning moments at the foundation level of a bridge pier
foundation computed with both approaches: not only the amplitudes are correctly
matched but also the phases are preserved.
This model has been extended in a more rigorous way to account for the coupling
between the various degrees of freedom of the foundation, especially between the
vertical and rotational one when uplift occurs (Cremer et al., 2001).
25000
Overturning moment (MN-m)
20000
Simplified model
Finite element model
15000
10000
5000
0
-5000
-10000
-15000
-20000
-25000
0
5
10
15
20
25
30
35
40
45
50
Time (s)
Fig. 10.7. Comparison between finite element analysis and the non linear rheological
model for the foundation
10.4. Bearing Capacity for Shallow Foundations
Once the forces transmitted to the soil by the foundation are determined, the design
engineer must check that these forces can be safely supported: the foundation must not
experience a bearing capacity failure nor excessive permanent displacements. At this
point a major difference appears between static, permanently acting loads, and seismic
loads. In the first instance excessive loads generate a general foundation failure
whereas seismic loads, which by nature vary in time, may induce only permanent
Shallow Foundations
295
irrecoverable displacements. Failure can therefore no longer be defined as a situation in
which the safety factor becomes less than unity; it must rather be defined with reference
to excessive permanent displacements which impede the proper functioning of the
structure. Although this definition seems rather simple and the methodology has been
successfully applied to dam engineering (Newmark, 1965), its implementation in a code
format is far from an easy task. One of the difficulties is to define what are acceptable
displacements of the structure in relation to the required performance. Another
difficulty obviously lies in the uncertainty linked to the estimation of permanent
displacements.
10.4.1.FUNDAMENTAL REQUIREMENT OF CODE APPROACHES
As an example of code documentation Eurocode 8 states that "The bearing capacity of
the foundation shall be checked under the combination of the design action effects. To
check the seismic bearing capacity of the foundation, the general expression and criteria
provided in informative annex F may be used, which allow to take into account the load
inclination and eccentricity arising from the inertia forces in the structure as well as the
possible effects of the inertia forces in the supporting soil itself. The rise of pore water
pressure under cyclic loading should be considered either in the form of undrained
strength or as pore pressure in effective stress analysis. For important structures, non
linear soil behaviour should be considered in determining possible permanent
deformation during earthquakes."
More specifically, in most seismic codes the design engineer is required to check the
following general inequality:
Sd d Rd
(10.1)
where Sd is the seismic design action (demand) and Rd the system design resistance
(capacity). These two terms are explained below.
The design action represents the set of forces acting on the foundations. For the bearing
capacity problem, they are composed of the normal force Nsd, shear force Vsd,
overturning moment Msd and soil inertia forces F developed in the soil. The actions Nsd,
Vsd, and Msd arise from the inertial soil-structure interaction. The inertia force, F = Ua
(U soil mass density, a acceleration), arises from the site response analysis and
kinematic interaction. The term design action is used to reflect that these forces must
take into account the actual forces transmitted to the foundation i.e. including any
behaviour and over-strength factors used in inelastic design.
The design resistance represents the bearing capacity of the foundation; it is a function
of the soil strength, soil-foundation interface strength and system geometry (for instance
foundation width and length).
Obviously, inequality (10.1) must include some safety factors. One way is to introduce
partial safety factors, as in Eurocode 8. This is not the only possibility and some other
codes, like the New Zealand one, choose the Load and Resistance Factored Method
(LRFD) and factor the loads and resistance (Pender, 1999). The Eurocode approach is
preferred because it gives more insight in the philosophy of safety; on the other hand it
requires more experimental data and numerical analyses to calibrate the partial safety
factors.
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Alain Pecker
With the introduction of partial safety factors inequality (10.1) is modified as follows:
Sd (JF. actions) d
1
J Rd
§ strength parameters
·
Rd ¨
, geometry ¸
Jm
©
¹
(10.2)
where "actions" represent the design action and "strength" the material strength
(soil cohesion and /or friction angle, soil-foundation friction coefficient).
JF is the load factor applied to the design action: JF is larger than one for
unfavorable actions and smaller than 1.0 for favorable ones.
Jm is the material safety factor used to reflect the variability and uncertainty in the
determination of the soil strength. In Eurocode 8, the following values are
used: 1.4 on the undrained shear strength and cohesion and 1.25 on the tangent
of the soil friction angle or interface friction coefficient.
JRd is a model factor. It acts like the inverse of a strength reduction factor applied
to the resistance in an LRFD code. This factor reflects the fact, that to
evaluate the system resistance some approximations must be made: a
theoretical framework must be developed to compute the resistance and like
any model it involves simplifications, and assumptions which deviate from
reality. It will be seen later on that the model factor is essential and can be
used with benefit to differentiate a static problem from a seismic one.
10.4.2.THEORETICAL FRAMEWORK FOR THE PSEUDO-STATIC BEARING
CAPACITY
Since the devastating foundation failures reported after the Mexico earthquake (Auvinet
and Mendoza, 1986) a wealth of theoretical and experimental studies have been carried
out to develop bearing capacity formulae which include the effect of the soil inertia
forces (Sarma and Iossifelis 1990; Budhu and Al Karni, 1993; Richards et al., 1993;
Zeng and Steedman, 1998).
The theoretical studies mentioned above are based on limit equilibrium methods (Chen
1975; Salençon, 1983); although they represent a significant improvement over the
previous analyses which neglected the soil inertia forces, they suffer from limitations
which restrict their use (Pecker, 1994):
x the horizontal accelerations of the soil and of the structure are assumed to have the
same magnitude;
x the results are derived from an assumed unique failure mechanism which does not
allow for foundation uplift;
x the methods only consider upper bound solutions without any indication on how close
they are from the exact solution.
At the same time numerous studies have been initiated in France and Europe with the
objective of providing more general solutions (Pecker and Salençon 1991, Dormieux
and Pecker 1995, Salençon and Pecker 1994a, 1994b, Paolucci and Pecker 1997,
PREC8, 1996). The solutions were developed within the framework of the yield design
297
Shallow Foundations
theory (Salençon 1983, 1990): the loading parameters N, V, M and F are considered as
independent loading parameters thereby allowing for any combination of actions to be
analyzed; many different kinematic mechanisms are investigated and lower bound
solutions are also derived to (i) obtain the best possible approximation to the bearing
capacity, (ii) bracket the true value to obtain a quantitative measure of the goodness of
the solution. It is interesting to note that the results have been later completed by
additional lower bound solutions which confirm the merit of the upper bound solutions
and help to narrow the gap between upper and lower bound solutions (Ukritchon et al,
1998 ). Finally the results, mainly based on the upper bound solutions are cast in the
general format (Pecker, 1997):
I (N, V, M, F) d 0
(10.3)
where I ( ) = 0 (Figure 10.8) defines in the loading parameter space the equation of a
bounding surface.
Inequality (10.3) expresses the fact that any combination of the loading parameters
lying outside the surface corresponds to an unstable situation; any combination lying
inside the bounding surface corresponds to a potentially stable situation. The word
potentially is used to point out that no assurance can be given since the solutions were
derived from upper bound solutions. Indications on the merit of the solutions are
obtained by comparison with the lower bound solutions and the model safety factor of
Equation (10.2) is introduced to account for that uncertainty. The uncertainty is twofold:
the solution is obtained from an upper bound approach and, although various kinematic
mechanisms were investigated, their number remains necessarily limited when a
comprehensive implementation of the upper bound theorem would require that all the
conceivable mechanisms be investigated.
These results are put in a simple mathematical expression and implemented in the
current version of Eurocode 8 (Annex F) and are applicable to cohesive and purely
frictional materials. The equation, (Pecker, 1997), is:
1 eF
N
a
where : N
cT
EV
cT
k'
ª§
º
k·
« ¨ 1 mF ¸ N »
¹
¬« ©
¼»
J RD Nsd
,
N max
V
b
1 f F
N
J RDVsd
,
N max
c
c 'M
JM
cM
k'
ª§
º
k·
« ¨ 1 mF ¸ N »
¹
¬« ©
¼»
M
d
1 d 0
(10.4)
J RD Msd
.
B N max
Nmax is the ultimate bearing capacity of the foundation under a vertical centered load,
Nsd, Vsd, and Msd are the design action effects at the foundation level, B the foundation
width, and JRd the material safety factor. The soil inertia forces are accounted for by the
normalized parameter F equal to UaB/cu for cohesive soils and to a/g tanI for frictional
298
Alain Pecker
soils. The other parameters entering Equation (10.4) are numerical parameters derived
by curve fitting to the "exact" bearing capacity, the values of which can be found in
Pecker (1997).
Fig. 10.8. Bounding surface for cohesive soils
10.5. Evaluation of Permanent Displacements
As noted previously and as recommended in Eurocode 8, in seismic situations, the
permanent displacements should be evaluated. However such an evaluation is anything
but an easy task. Probably the most rigorous approach would be to use a global model
(finite element model) including both the soil and the structure. Obviously, the results
depend on the non linear constitutive relationship used to model the soil behaviour and
are only meaningful if a realistic model is used. Owing to this constraint, to computer
limitations, and to the required skill from the analyst in geotechnical engineering,
structural engineering, soil-structure interaction and numerical analysis, such an
approach is seldom used in everyday practice.
The alternative approach, once the seismic forces are known, is to rely on a Newmark
type of approach (Newmark, 1965). The bounding surface defined by Equation (10.3)
is used as the surface defining the onset of permanent displacements. Sarma and
Iossifelis (1990), Richards et al. (1993) used the Newmark's approach assuming that the
soil moves together with the foundation in a rigid body motion. The method has been
further extended by Pecker and Salençon (1991) considering a deformable soil body
corresponding to the assumed kinematic failure mechanism. Using the kinetic energy
theorem, these authors computed the foundation angular velocity, and by integration
over time, the foundation permanent rotation. When applied to actual case histories the
method proved to be reliable (Pecker et al., 1995).
A potential use of the method can be found for the development of a code like approach.
Computed permanent displacements develop when the resultant of the design action
lies outside the bounding surface: the larger the distance to the bounding surface, the
greater the displacements.
Shallow Foundations
299
This can be expressed mathematically by writing that for such situations:
Sd = O.Rd
(10.5)
with O > 1 ; O = 1 corresponds to the onset of permanent displacements.
Comparing Equation (10.5) to Equation (10.2), it is readily apparent that allowing Sd to
reach regions outside the bounding surface is equivalent to specifying a model safety
factor JRd smaller than 1.0. Therefore, JRd can be used, in addition to reflecting the
uncertainties in the model, to relax the constraint that at any time the capacity shall be
larger than the demand, recognizing the fundamental difference between a static
problem and a seismic one in which forces vary in time.
This approach has been implemented in Eurocode 8 and the tentative values proposed in
its Annex F are intended to allow for the development of small permanent
displacements in potentially non dangerous materials (medium to dense sand, non
sensitive clay). These values range from 1.0 (medium dense to dense sands, non
sensitive clays) to 1.5 (loose saturated sands) with intermediate values of 1.15 for loose
dry sands. If this phenomenon were disregarded, JRd values would always be larger than
1.0 (in the range 1.2 to 1.5).
In the case of non sensitive clays further justification for setting JRd equal to 1.0 is the
observation that shallow foundations in clay have generally been observed to perform
well under seismic loading. As mentioned above, a reason for this may be the enhanced
undrained shear strength available under rapid loading (Romo 1995, and Ahmed-Zeki et
al 1999).
10.5.1.FURTHER DEVELOPMENTS: TOWARDS PERFORMANCE BASED
DESIGN
One of the strong assumptions underlying the seismic bearing capacity checks is the
independence between the computed design actions and soil yielding. Except for the
sophisticated approaches involving the partition in near and far fields, the design actions
are computed assuming quasi-linear foundation behaviour. However it is recognized
that partial yielding of the foundation may affect the forces.
Attempts have been made by Nova and Montrasio (1991) for monotonic static loading
based on the concept of a macro-element modelling the soil and foundation; the
constitutive law for the macro-element is rigid plastic strain hardening with non
associated flow rule. That concept of macro-element expressed in global variables at
the foundation level has been extensively used in mechanics but seldom applied to soilstructure interaction. Paolucci (1997) and Pedretti (1998) have extended the method to
seismic loading. These last two studies definitively prove that yielding of the
foundation cannot be ignored in the evaluation of the design action.
A more general formulation has been proposed recently by Cremer et al. (2002). The
developed macro-element taking advantage of the partition between near field and far
field describes the cyclic behaviour of the foundation, reproduces the material nonlinearities under the foundation (yielding) as well as the geometrical non-linearities
(uplift), and accounts for the wave propagation in the soil. The strength criterion for the
macro-element is represented by the bounding surface defined by the bearing capacity
300
Alain Pecker
formula and a non associated flow rule with kinematic and isotropic hardening is used
to compute the pre-failure displacements; the plastic model is coupled with an uplift
model to integrate the influence of soil yielding on the uplift. Although presently
restricted to strip shallow foundations the model shows some promising capabilities and
should represent a step forward in the evaluation of permanent seismic displacements of
shallow foundations.
10.6. Construction Detailing
Although the safety of a constructed facility does not rely only upon a blind application
of seismic codes and standards which are used for its design and construction, those
documents help significantly to minimize the most commonly encountered causes of
deficiencies and failures.
Because all phenomena described previously cannot be analyzed with the necessary
mathematical rigor and are not often relevant to even sophisticated calculations,
construction detailing must always be enforced in seismic design of foundations. This
is one of the major merits of seismic codes.
Many of these detailing practices, which are found in the most recent codes, are little
more than common sense and by no means, the points raised herein, constitute an
exhaustive list. However based on the author's experience, they represent the most
common mistakes made in design by non-experienced designers:
x Foundations must not be located close to (or across) major active faults. Ground
motions in the near field are far from being predictable and attempts to design
buildings to accommodate such movements, especially the static co-seismic
displacements associated with fault rupture, are almost hopeless.
x Liquefiable deposits and unstable slopes must always be treated before construction.
x The foundation system under a building must be as homogenous as possible unless
construction joints are provided in the structure. In particular, for individual footings,
the situation where some of them rest on a man-made fill and some on in-situ soils
must always be avoided. It is also highly desirable that the foundations respect the
symmetries of the building.
x The choice of the foundation system must always account for possible secondary
effects such as settlements in medium-dense or loose dry sands, the post-earthquake
consolidation settlements of clay layers, the settlements induced by the postearthquake dissipation of pore pressures in a non liquefiable sand deposit. Raft
foundations or end bearing piles are to be preferred whenever the anticipated
magnitude of the settlements is high or when they can be highly variable across the
building.
x Individual footings must always be linked with tie beams at the foundation level.
These longitudinal beams must be designed to withstand the differential settlements
between the footings.
Shallow Foundations
301
10.7. Conclusions
The state of the art in the seismic design of shallow foundations is developing towards a
rational, although still simplified, analysis. Sound, easy to use representations of the
stiffness and damping of the soil foundation system can be provided to the structural
engineer to perform the dynamic analysis of the structure when the system remains
linear. The geotechnical engineer has at hand a theoretical framework to compute the
seismic bearing capacity of foundations for which much progress has been achieved in
the last decade leading to a rational, rigorous, approach. This bearing capacity is
expressed in terms of a bounding surface defined by simple analytical formulae
expressed in terms of dimensionless variables related to the inertial or kinematic loading
parameters.
Recent developments in modeling the soil structure interface allow the designer to
compute the earthquake induced permanent displacements of his foundation and
therefore to rely on a, more rational, performance based approach for foundation design.
It has been shown that performance based design can also be included in building codes
as it has been tentatively done in the recent Eurocode 8 – Part 5 design code.
CHAPTER 11
BEHAVIOUR AND DESIGN OF DEEP FOUNDATION SUBJECTED TO
EARTHQUAKES
Kohji Tokimatsu
Tokyo Institute of Technology, Tokyo, Japan
11.1. Introduction
Extensive soil liquefaction that occurred in the Hyogoken-Nambu earthquake (M=7.2)
of January 17, 1995, damaged various structures and infrastructures in the reclaimed
land areas along the coastline of Kobe. In particular, many of the quay walls in these
areas moved up to several meters towards the sea due to liquefaction of their foundation
soils and/or back-fills. This induced large horizontal ground movements as well as
differential ground settlements near the waterfront. As a result, not only buildings with
spread foundations but also those supported on piles settled and/or tilted without
significant damage to their superstructures (Photo 11.1). Similar damage patterns were
also observed at many buildings on liquefied level ground far away from the waterfront
(Photo 11.2).
There was a serious concern that the piles of those buildings might have been damaged.
Excavation surveys after the quake showed that pile heads in some tilted buildings
actually failed (Photo 11.3) while others did not. This suggests that the piles might have
failed at depths other than pile head (Photo 11.4) due to liquefaction-induced ground
movement. However, little is known concerning the actual failure and deformation
patterns of those piles, and their relation to ground displacements.
Photo 11.1. Tilted building in lateral
spreading area
Photo 11.2. Tilted building in liquefied
level ground
The object of this chapter is to summarize the failure and deformation modes of piles
that experienced soil liquefaction and/or lateral spreading in the 1995 Kobe earthquake,
together with cyclic and permanent ground displacements that might have developed
during past earthquakes. Pseudo-static analyses using p-y curves are then presented and
conducted for well-documented case histories of pile foundations from the Kobe
earthquake.
303
A. Ansal (ed.), Recent Advances in Earthquake Geotechnical Engineering and Microzonation, 303–324.
© 2004 Kluwer Academic Publishers. Printed in the Netherlands.
304
Kohji Tokimatsu
Photo 11.3. Damage to pile head
Photo 11.4. Damage to pile
near ground water table
11.2. Performance of Near-Surface Soils and Pile Foundations during the 1995
Hyogoken-Nambu Earthquake
11.2.1.SOIL LIQUEFACTION AND GROUND MOTION
Figure 11.1 is a map showing the area of heavy damage to buildings (Chuo-Kaihatsu,
1995) and the area where field manifestation of soil liquefaction was evident after the
1995 earthquake. Most of the buildings discussed in this paper were located in
reclaimed land areas including Port and Rokko Islands, Fukaehama, and Mikagehama
where soil liquefaction extensively occurred. Liquefaction developed to a lesser extent
in central Port Island and southern Rokko Island where the fills had been treated or
consisted of soils containing significant amounts of clay.
Also shown in Figure 11.1 are the particle orbits of ground displacements that have
been double-integrated from the strong motion accelerograms obtained in those areas
during the earthquake (CEORKA, 1995; Sekisui House, 1996). The peak cyclic ground
displacements were 35cm at a non-liquefied site on Rokko Island, and 46cm and 55cm
near liquefied areas on Port Island and in Fukaehama. It is estimated that about two
thirds of these displacements resulted from shear strains induced in the reclaimed fills.
Figure 11.2 shows the acceleration response spectra with damping ratios of 10% for the
ground motions at the same stations. The response acceleration in the period range less
than 0.5s, which is equal to the natural period of buildings investigated in the study, is
approximately equal to 0.3-0.5g.
Behaviour and Design of Deep Foundations
305
Fig. 11.1. Map showing zones of extensive building damage and liquefaction with
displacement orbits of strong ground motions recorded in reclaimed lands
Fig. 11.2. Response acceleration spectra at three stations in reclaimed lands
11.2.2.CHARACTERISTICS OF PILE FOUNDATIONS OF BUILDINGS
The piles used in the Kobe area for building foundations are classified into precast
concrete or steel pipe (S) piles and cast-in-place concrete piles. Most precast piles are
hollow with outer diameters typically ranging from 35 to 60cm, which contrasts with
solid cast-in-place concrete piles with diameters typically over 100cm. The precast
concrete piles encountered in the Kobe area include prestressed concrete (PC) piles used
before the 1980s and prestressed high strength concrete (PHC) piles used after the
1980s. To strengthen their capacity and ductility, steel pipe reinforced concrete (SC)
piles and reinforced prestressed concrete (PRC) piles have been also used.
Table 11.1 summarizes the case histories to be analyzed in this study, with
characteristics of piles. Figure 11.3 shows the relations of bending moment with
curvature for those piles. Both PC and PHC piles have three different capacities for a
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Kohji Tokimatsu
given diameter, i.e., Types A, B, and C in ascending order of capacity. In the following,
Mu is the bending moment at concrete crashing at extreme compression fibber of PC,
PHC, and SC piles or at which compression fibber strain of S piles reaches a limiting
value; My is the bending moment at yielding of tension bars of PC and PHC piles or at
yielding of steel at extreme tension fibber of SC and S piles; and Mc is the bending
moment at concrete cracking at extreme tension fibber of PC and PHC piles.
RC
5
1.7
C
RC
4
1.732.13
SC+PHCA
SC+PHCB
D
RC
6
1.78
E
NA
NA
F
RC
G
H
Thickness of
Reclaimed
Fill (m)
B
Ground water
Table (m)
1.2
Axial Force
(MN)
Depth of Pile
head (m)
4
Pile Length
(m)
No.of Story
RC
Pile Diameter
(mm)
Building Type
A
Pile Type
Building
or Site
Table 11.1. Case histories analyzed in this study
PHC-A
350
22
0.3
3
13
600
31
0.9
2.2
11.5
500
35-42
0.63
3
17
S
500
30
0.66
3
13
1
SC+PHCA
500
33
0
2
14
3
1.65
PC-A
400
20
0.39
2
8
RC+S
2
2.5
S
406.4
27.55
0.63
3.5
15.4
SRC
NA
2.102.30
CC
1500
47-48
0.14
1.65
15
Fig. 11.3. Relation between bending moment and curvature of various piles
Behaviour and Design of Deep Foundations
307
11.2.3.PILE DAMAGE FROM DETAILED FIELD INVESTIGATION
A large number of performances of pile foundations during the Kobe earthquake have
been revealed based on field investigation including excavation of pile heads
(Photo 11.5, e.g., Kansai Branch of Architectural Institute Japan (AIJ), 1996; AIJ et al.,
1998). In addition to integrity tests for piles, several methods were used to detect pile
damage below the ground surface. Borehole cameras (Photo 11.5, Oh-oka et al., 1996)
have identified damage portions and severity of hollow or cored solid piles, and
inclinometers (Photo 11.6, Shamoto et al., 1996) have provided data to estimate
deformed shapes with depth of hollow piles.
Photo 11.5. Borehole camera survey followed by
excavation
Photo 11.6. Inclinometer
The main findings from the field investigation are summarized below and illustrated in
Figures 11.4 and 11.5 in the level ground without occurrence of lateral spread
(Tokimatsu and Asaka, 1998, and Tokimatsu, 1999):
1. Damage concentrated near pile heads, and the top and the bottom of the
liquefied layer (Figures 11.4(a)-(e)).
2. In some PC and PHC piles, damage occurred only near the top and/or bottom of
liquefied layers, with no damage near pile heads (Figures 11.4(b)- (d));
3. Damage near pile heads often resulted in significant tilts of buildings with high
aspect ratios (Figures 11.4(a), (b)).
4. Damage to piles through a thick non-liquefied crust did not necessarily lead to
large tilts (Fig. 11.4(c); BTL Committee, 1998).
5. The failure and deformation modes of piles within a building were very similar
to each other (Figures 11.4(a)-(e)).
6. Damage concentrated on PC and PHC piles, but no extensive damage to S and
CC piles was reported.
7. PHC piles without any vertical load also suffered extensive damage near the
bottom of the liquefied layer (Fig. 11.4(e); Horikoshi and Ohtsu, 1996).
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Kohji Tokimatsu
8. In the treated level ground, buildings supported on piles bearing on firm soils
beneath the fills often had no apparent settlement while the surrounding ground
settled to some extent, creating vertical gaps around the bases of many
buildings (Figure 11.4(f)).
Fig. 11.4. Typical damage pattern of piles subjected in level ground
In the area where liquefaction-induced lateral spreading occurred, particularly along the
waterfront of artificial islands (Tokimatsu and Asaka, 1998, and Tokimatsu, 1999):
1. Damage also concentrated near the pile head, or the top and/or the bottom of
the liquefied layer.
2. Damage was not limited to PC and PHC piles but extended to cast-in-place
concrete piles (Tokimatsu et al., 1996) and some ductile S piles (JASPP, 1996).
3. The damage to PC and PHC piles often resulted in a large tilt of the
superstructure, whereas the damage to S and CC piles rarely led to similar
consequences.
4. A cast-in-place concrete pile foundation that carried only a small load was also
damaged and displaced horizontally by as much as 1 m (Kuwabara and Yoneda,
1998).
5. Damage to pile caps and foundation beams often preceded or accompanied the
damage to S and CC piles.
6. The piles within a building near the waterfront showed different failure and
deformation modes in the direction perpendicular to the shoreline as shown in
Figs. 11.5(a) and 11.5(d) (Tokimatsu et al., 1997). In such a case, when facing
the span side of the building with the sea on the left, the seaside pile cap rotated
clockwise around its longitudinal axis, whereas the land-side pile cap rotated
counter clockwise (Oh-oka et al., 1997a, 1997b).
7. Cast-in-place concrete piles surrounded by deep mixing walls as well as steel
pipe piles driven in the ground treated by sand compaction piles did not suffer
any serious damage (BTL Committee, 1998). Moderate to severe damage to
their superstructures was, however, observed in these cases.
8. Cast-in-place concrete piles surrounded by cement column walls or continuous
diaphragm walls did not suffer any serious damage (BTL Committee, 1998).
The permanent horizontal displacements of bridge piers founded on diaphragm
walls were negligibly small, while those of bridge piers founded on piles or
Behaviour and Design of Deep Foundations
309
caissons were as large as a half of the permanent ground displacements nearby
(Yokoyama et al., 1997).
The above findings confirm that, in addition to horizontal forces and overturning
moments imposed on pile heads from superstructures, kinematic forces induced by
dynamic and permanent ground displacements of liquefied and laterally spreading soils
had significant impact on pile damage. In particular, the damage to piles without
vertical loads confirms significant effects of ground movements.
The difference in failure and deformation modes of piles within a building near the
waterfront as shown in Figures 11.5(a) and (d) probably reflects rapid changes in
horizontal ground displacement. In addition, Figure 11.5 suggests that the lateral
ground movement leads to more serious tilt in the span direction than that in the
longitudinal direction. This indicates that to place the longitudinal direction of the
building parallel to the direction of ground movement is effective for mitigating damage
due to lateral ground movement.
Fig. 11.5. Typical failure and deformation modes of pile foundations subjected to lateral
spreading
The difference in damage of different pile type indicates that to use ductile piles or rigid
foundations is also effective for mitigating damage resulting from lateral ground
movement. Conversely, however, the inertial forces acting on their superstructures
during shaking would increase with increasing rigidity of foundation. The earth
pressure acting on the upstream side the building from laterally spreading soils would
also increase with increasing rigidity of foundation.
11.3. Cyclic and Permanent Ground Displacements during Earthquakes
11.3.1.CYCLIC AND PERMANENT SHEAR STRAINS IN LIQUEFIED AND
LATERALLY SPREADING GROUND
The field investigation described in the previous chapter has shown that the cyclic and
permanent ground displacement to be developed in the liquefiable deposit had
significant effects on pile performance, and thus these displacement patterns should be
310
Kohji Tokimatsu
identified. Figure 11.6 summarizes the relation of cyclic and permanent shear strains
with adjusted SPT N-values from the results of recent studies. In the figure, the cyclic
shear strains in the level ground are plotted in Figure 11.7(a), while permanent shear
strain near the waterfront are plotted in Figure 11.8(b). Also shown in Figure 11.8 in
the solid curves are the limiting shear strains. Note that the maximum permanent shear
strain is much larger than the cyclic shear strain for the same N-value.
Based on Figure 11.6, Tokimatsu and Asaka (1998) proposed preliminary charts for
estimating maximum cyclic shear strain to be developed during and after earthquakes,
as shown in Figure 11.7(a).
Fig. 11.6. Field correlation of cyclic and permanent shear strains with adjusted SPT Nvalue: (a) cyclic shear strain, (b) permanent shear strain
Fig. 11.7. Maximum cyclic and permanent shear strains due to soil liquefaction and
lateral spreading
Behaviour and Design of Deep Foundations
311
Figure 11.7(a) enables one to estimate cyclic ground displacement profile of a liquefied
deposit in a simplified manner described below, as is the case in the liquefaction
evaluations using SPT N-values (e.g., Tokimatsu and Yoshimi, 1983; Seed et al., 1985):
1. Determine adjusted SPT N-values, Na, and equivalent cyclic stress ratios during
earthquake, Wav/Vvo’, with depth.
2. Estimate Jcy from Figure 11.7(a), with depth.
3. Estimate a cyclic ground displacement profile, fcy(z), by integrating Jcy upwards
from the bottom of the liquefied layer, assuming Jcy develops in the same
horizontal direction.
For example, when an 8-m thick sand layer with Na=10 liquefies extensively (Jcy=4%),
the resulting ground surface displacement, D cy=fcy(0), is estimated to be 32cm.
Fig. 11.8. Relation between horizontal
displacement of waterfront and length of
laterally spreading area
Fig. 11.9. Relation of horizontal
ground displacement with distance
from waterfront
11.3.2.PERMANENT GROUND DISPLACEMENT NEAR WATERFRONT
The permanent horizontal displacement induced by lateral spreading near the waterfront
takes a maximum value at the waterfront and decreases with distance from the
waterfront. Thus, the maximum value together with its attenuation characteristics
should be identified. Figure 11.8 summarizes, based on recent studies, the relations
between the horizontal ground surface displacement at the waterfront, Do, and the length
of the laterally spreading area, L, both normalized in terms of the thickness of the
liquefied layer, H. The relation between the two may be expressed as:
L/H = (25-100)Do/H
(11.1)
This indicates that lateral spreading may extend horizontally inland about 50 times the
horizontal ground surface displacement at the waterfront.
Figure 11.9 shows a typical relation of horizontal ground displacement, D, with distance
from the waterfront, x, from the studies by Shamoto and Hotta (1996), and Ishihara et al.
(1997) in which D and x are normalized in terms of Do and L. The relation may be
expressed as:
D(x)/Do = (1/2)5x/L
(11.2)
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Kohji Tokimatsu
Assuming that L=50Do, the equation leads to
D(x) = (1/2)x/10Do Do
(11.3)
Figure 11.9 and Equations (11.2) and (11.3) show that the horizontal ground surface
displacement in laterally spreading areas decreases to a half at x=L/5 and less than 1/5
at x=L/2.
The permanent ground displacement profile with depth z at distance x of a laterally
spreading deposit, fls(z,x), may be then approximated as:
for z < zw
fls(z,x) = D(x)
(11.4)
for z > zw
fls(z,x) = D(x)cos(S(z- zw )/2H)
(11.5)
= D(x)(1-(z- zw )/H)
(11.6)
in which z is depth below the ground surface, and zw is depth of the groundwater table or
the top of the liquefied layer.
Do in Equation (11.2) depends significantly on the type and seismic design of quay
walls as well as the strong motion characteristics and soil conditions behind and below
the quay wall, and may be expressed as:
Do = min (Dmax,Dw)
(11.7)
in which Dw is the displacement of the quay wall and Dmax is the maximum possible
ground surface displacement of the liquefied soil determined by integrating Jmax with
depth. In this estimation, Jcy , fcy(z), D cy, and Figure 11.7(a) in the procedure described
in Section 11.3.1 should be replaced by Jmax, fmax(z), D max, and Figure 11.7(b). If the
quay wall moves seaward by 3 m with a 10-m thick liquefied sand layer having Na=10
(Jmax= 40%), the permanent ground displacement near the waterfront is expected to be
3m. In contrast, it is only 1 m for a layer with Na =20 (Jmax= 10%).
11.4. Pseudo-Static Analysis for Seismic Design of Pile Foundations
Seismic design of foundations may be made based on either dynamic response or
pseudo-static analyses. In this section, a pseudo-static analysis based on Beam-onWinkler-springs method is described, with emphasis placed on how the ground
displacement determined in the previous section is incorporated into the design.
11.4.1.INERTIAL AND KINEMATIC FORCES ACTING ON FOUNDATION
Figure 11.10 schematically illustrates the soil-pile-structure interaction in liquefiable
soils during and after an earthquake. Before liquefaction, the inertia force from the
superstructure may dominate (Case I). After liquefaction during shaking, not only the
inertial force but also the kinematic force induced by the cyclic ground displacement
comes to play an important role (Cases II). Towards the end of shaking, residual shear
strain may accumulate, resulting in permanent horizontal ground displacement. At this
stage, the kinematic force due to permanent ground displacement may have a dominant
313
Behaviour and Design of Deep Foundations
effect on pile performance (Case III), particularly near quay walls which failed or
moved seaward (Case III-b). Such permanent ground displacement may also occur
even in a horizontally stratified soil deposit with level ground (Case III-a); however, it
is generally less than and hardly ever exceeds the maximum cyclic ground displacement
unless it is extremely loose.
Fig. 11.10. Schematic figure showing soil-pile-structure interaction in liquefied and
laterally spreading soil
The above discussions indicate that piles in the level ground could suffer the most
severe loading conditions in either Case I or II, whereas piles in laterally-spreading soils
also experience severe loading condition in Case III. These loading conditions should
be properly considered in stress and deformation analysis of piles in liquefiable soils.
11.4.2.BEAM-ON-WINKLER-FOUNDATION METHOD
Simplified pseudo-static design methods using p-y curves for pile foundations (AIJ,
1988, 2001; JRA, 1997), i.e., a single pile supported on nonlinear Winkler springs as
shown in Figure 11.11(a), are based on the following equation:
EI(d4y/dz4)=-kBy
(11.8)
in which E and I are Young’s modulus and moment of inertia of pile, y is horizontal
displacement of pile, z is depth, k is coefficient of horizontal subgrade reaction, and B is
pile diameter.
Fig. 11.11. Schematic figure showing simplified pseudo-static analysis using p-y
springs for pile foundations
If liquefaction and/or lateral spreading occur during and after shaking as shown in Cases
II and III in Figure 11.10, the equation may be defined as:
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Kohji Tokimatsu
EI(d4y/dz4)=kB{f(z)-y}
(11.9)
in which f(z) is either cyclic or permanent ground displacement profile described in
Section 11.3, which is applied to the pile through the p-y springs as shown in Figures
11.11 (b) or (c).
11.4.3.NON-LINEAR P-Y SPRING
The value of k in Equation (11.8) is defined as:
k=2ko/(1+|y/ y1 |)
(11.10)
k=ko(y/ y1)-0.5
(11.11)
in which y1 is reference displacement equal to either 1cm or 0.01B depending on the
codes, and ko may be defined as (JRA, 1980):
ko = 56NB-3/4 (MN/m3)
(11.12)
in which B is pile diameter in cm, N is SPT N-value. The ultimate lateral resistance or
pressure, py, may be defined as:
py=3KpVvo’
(11.13)
in which Vvo’ is the initial effective confining pressure, and Kp is the Rankine passive
earth pressure coefficient.
When the ground displacement induced by soil liquefaction cannot be neglected in
Equation (11.9), y in Equations (11.10) and (11.11) has to be replaced by yr =y-f(z).
Both Py and ko of liquefied soils should be reduced, for example, according to the
following equations, as illustrated in Figure 11.12 (AIJ, 2001).
kol = El ko
pyl = Dl py
(11.14)
(11.15)
in which Dl and El are scaling factors in terms of SPT N-value as show in Figure 11.13
where Dl is tentatively equal to El (AIJ, 2001).
Fig. 11.12. Analytical model for
p-y spring
Fig. 11.13. Scaling factor for p-y spring
Behaviour and Design of Deep Foundations
315
11.4.4.EARTH PRESSURE ACTING EMBEDDED FOUNDATION
The earth pressure acting on the embedded porting of foundation also depends on the
relative displacement between soil and foundation. When the ground displacement is
negligibly small, the soil always resists the foundation to deform, as shown in
Figure 11.14(a). In contrast, when the ground displacement gets large, the soil tends to
push the foundation, the extent of which depends on the rigidity of foundation, as show
in Figures 11.14(b), (c). Such effects should be properly taken into account in the
analysis.
Fig. 11.14. Schematic figure showing earth pressure acting on foundations due to
inertial force and ground displacement
11.5. Effects of Cyclic Ground Displacements on Pile Performance
While many PC and PHC piles in an extensively liquefied area suffered severe damage,
most piles of the same types in the non-liquefied area in reclaimed lands survived
without visible damage (Tokimatsu et al., 1996). This suggests that Case II shown in
Figure 11.10 provides more severe loading conditions than Case I for pile foundations
supporting buildings. In order to clarify this point, a case history of 35cm diam PHC
piles supporting a 4-story building in Mikagehama (Shamoto et al., 1997; Building A in
Table 11.1) is examined. Figure 11.15(c) shows a boring log of the site. A field survey
showed that the piles cracked near the pile head as well as near the bottom of the fill as
shown in Figure 11.15(d), causing a large tilt of the building.
Both Cases I and II are considered in the analysis. It is assumed that the piles are
subjected to an inertial force with a base shear coefficient of 0.4 for both cases. In Case
II, the cyclic ground displacement profile computed from the proposed method as
shown in Figure 11.15(b) is also considered. The computed displacement on the ground
surface is about 36cm, which appears consistent with the observed values described
previously. A scaling factor for the horizontal subgrade reaction of 1/10 is used from
Figure 11.13 for liquefied soils throughout the study, since a preliminary analysis
indicates that the difference in scaling factor does not have a significant effect on
estimated failure patterns of piles.
Figures 11.15(a) and (e) show the distribution of computed bending moments with
depth and the relations between bending moment and curvature at critical depths for the
two cases. The computed bending moments in Case II are close to Mu near the pile
head and the bottom of the liquefied fill, while those in Case I are considerably smaller
at all depths. The computed result of Case II is consistent with the pile damage in
Figure 11.15(d), while that of Case I appears to reproduce the better performance of pile
foundations in non-liquefied deposits. These results confirm that Case II creates more
316
Kohji Tokimatsu
severe loading conditions than Case I and that the ground displacement in liquefied
deposits has significant effects on pile performance during earthquakes. Thus, the
analyses for Case I will be omitted hereafter.
Fig. 11.15. Computed bending moment of PHC pile at Building A for Cases I and II,
with ground displacement, boring log and pile damage
Fig. 11.16. Computed bending moment of PHC pile at Building A for Case II, with
ground displacement, boring log and pile damage
In order to examine the effects of pile type and ground displacement on pile damage,
similar computations are made for four buildings including the one described above and
three supported on either SC+PHC-A piles, SC+PHC-B piles, or S piles (Buildings A-D
in Table 11.1). The different field performance of two follower piles of different
capacities and the critical behaviour of S piles may provide a good basis to identify the
major factor influencing pile damage.
Behaviour and Design of Deep Foundations
317
Fig. 11.17. Computed bending moment of pile at Building B for Case II, with ground
displacement, boring log and pile damage
A five-story building supported on the SC+PHC-A piles in the center of Fukaehama
(Building B) tilted by 1/29 to the northeast after the quake without any damage to
superstructure (Nagai, 1997). 50-60cm diameter SC piles 6m long, and PHC-A piles 13
and 12m long were used as the upper, and middle and lower piles. The piles penetrated
to a depth of about 33m through a reclaimed fill with a thickness of about 10 m (Figure
11.17(c)). An excavation survey suggested that the pile heads inclined to the southwest,
the opposite direction of the tilting of the building, by 1/30-1/23. In addition, boring
and inspection into a hollow space of a pile through the pile cap suggested that the pile
was damaged and bent largely near the bottom of the liquefied layer (depths between
9.6 and 11.3m (Figure 11.17(d)).
Fig. 11.18. Computed bending moment of pile at Building C for Case II, with ground
displacement, boring log and pile damage
A four-story building supported on the SC+PHC-B piles in an untreated area on Port
Island (Building C) suffered neither differential settlement nor structural damage (Fujii
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Kohji Tokimatsu
et al., 1996). 50 cm diameter SC piles 8m long, and PHC-B piles 13 and 14 m long
were used as the upper, and middle and lower piles. The piles penetrated to a depth of
about 37 m through a thick reclaimed fill (Figure 11.18(c)). An excavation survey with
pile integrity tests on some exposed pile heads suggested that the piles had no damage.
Five-story school buildings supported on the 50 cm diameter S piles 30 m long in
Fukaehama (Building D) experienced insignificant damage, though the ground surface
around the building settled by 10 to 50 cm (JASPP, 1996). Figure 11.19(c) shows the
boring log of the site. An excavation survey, however, showed that large residual
deformation occurred at the horizontal steel plate connecting the pile head and the pile
cap.
It is assumed in the analysis that the piles are subjected to inertial force with a base
shear coefficient of 0.4 as well as kinematic forces resulting from the cyclic ground
displacement profile shown in Figures 11.16(b)- 11.19(b). In addition, computations
are also made, using the same base shear coefficient, for several ground displacement
profiles scaled from the computed ones.
Fig. 11.19. Computed bending moment of pile at Building D for Case II, with ground
displacement, boring log and pile damage
Figures 11.16(a)- 11.19(a) compare the distributions of the computed bending moment
with depth for several ground surface displacements, and Figures 11.16(e)- 11.19(e) the
relations between bending moment and curvature at critical depths, i.e., the pile head
and/or the bottom of the liquefied layer. The computed results in Figures 11.16 to 11.19
show that the piles themselves may not suffer severe damage for a ground surface
displacement less than 15 cm as the bending moment at any depth is below the critical
value. In contrast, for ground surface displacements greater than 20-45 cm, pile
foundations may suffer significant distress depending on their capacity and ductility,
since the bending moments near the pile head and the bottom of the liquefied layer
reach the critical value. For example, the bending moments at the critical depths of
S+PHC-A pile in Figure 11.17 exceed Mu for a ground surface displacement of about 25
cm, while those of S+PHC-B pile in Figure 11.18 and of S pile in Figure 11.19 are still
below My or Mu for the same displacement. In addition, most of the piles are estimated
to experience severe stress conditions near the bottom of the liquefied layer as well as
Behaviour and Design of Deep Foundations
319
near the pile head. The above results appear consistent with the field performance and
damage features of the various pile foundations in reclaimed lands summarized
previously, suggesting the significance of ground displacement in pile damage.
A case history of a group of piles (Horikoshi and Ohtsu, 1996; Site E in Table 11.1) also
provides a good basis to evaluate the effects of ground displacement, since neither
inertia force nor vertical load from the superstructure was imposed on the piles during
the earthquake. The piles 33 m long (SC pile 5 m long + PHC piles 13m and 15 m long)
with diameters of either 40 or 50 cm had been driven through a reclaimed fill in the
centre of Fukaehama about 350 m away from the shoreline. The pile heads were
located at a depth in between 0.5 and 1.5 m with a groundwater table of 2 m. The piles
experienced the earthquake before placement of any pile caps or foundation beams and
failed at a depth of about 8 m, i.e., the interface between gravelly medium sand with
SPT N-values of 5 and gravelly coarse sand with SPT N-values of 12 (Figure 11.20(c)
and (d)).
Fig. 11.20. Computed bending moment of pile at Site E for Case II, with ground
displacement, boring log and pile damage
Figure 11.20 (b) shows the estimated cyclic displacement profiles for two cases where
soil liquefaction is assumed to have developed only in a loose fill above 8 m depth or
throughout the fill. The pseudo-static analysis has been conducted without any inertial
forces using the estimated cyclic displacement profiles and their scaling values. Figures
11.20(a) and (e) summarize the computed results only for the former case since it has
yielded more severe stress conditions in the pile. The computed moments near the
interface between liquefied and non-liquefied layers reach the ultimate bending moment,
Mu, for a ground surface displacement of about 25 cm. The computed result appears
consistent with the observed damage pattern of the pile, confirming the significant
effects of cyclic ground displacement in pile damage.
11.6. Effects of Permanent Ground Displacements on Pile Performance
It is conceivable that the difference in the failure mode near the waterfront such as
shown in Figures 11.5(a), (d) might have been induced by the variation of horizontal
ground displacements in the direction perpendicular to the shoreline such as shown in
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Kohji Tokimatsu
Figure 11.9. The p-y analysis for a single pile cannot simulate such deformation
patterns. Thus, an analytical model shown in Figure 11.21 is developed for Case III in
which a group of piles connected with a foundation beam are subjected to permanent
displacement profiles varying with distance from the waterfront.
First, case histories of two pile foundations in and around Fukaehama (Buildings F and
G) are examined. Building F of three stories, supported on 40 cm diameter PC piles
20m long, was situated 6 m from a quay wall that displaced by about 2m towards the
sea (Tokimatsu et al., 1997). Its span direction was perpendicular to the shoreline.
Figure 11.22(d) shows a boring log of the site, which indicates that a loose fill 8m thick
might have liquefied during the earthquake.
Fig. 11.21. Analytical model of pile foundation subjected to lateral spread
Fig. 11.22. Computed bending moment of pile at Building F for Cases II and III, with
ground displacement, boring log and pile damage
A field survey conducted after the quake showed that the building had moved by about
80 cm and inclined by three degrees towards the sea, without any damage to its
superstructure. An inclinometer survey also showed that the piles in the building failed
Behaviour and Design of Deep Foundations
321
in a different mode depending on their location. Namely, the piles on the sea side were
bent towards the sea with failures at three depths, while the piles on the land side
inclined simply towards the sea with failures at two depths, as shown in Figure 11.5(a).
Building G of two stories, supported on 40.6 cm diameter S piles, was situated about
100m away from a quay wall on the north side that displaced by about 4 m. Its span
direction was perpendicular to the northern shoreline. Figure 11.23(d) shows a boring
log of the site. Despite minor damage to the superstructure, an inclinometer survey
showed that the pile heads displaced northern seawards by 20 to 60 cm and western
seawards by 20 to 80 cm. The deformation modes of the piles within the building are
very similar, in contrast to those near the waterfront.
Fig. 11.23. Computed bending moment of pile at Building G for Cases II and III, with
ground displacement, and boring log
The analysis is performed in the span directions of both buildings for both Cases II and
III. In Case II, a base shear coefficient of 0.4 is assumed with a cyclic ground
displacement profile as shown in Figure 11.22(c) or 11.23(c). In Case III, the assumed
permanent ground surface displacements are 100cm and 60cm at both ends of the
building near the waterfront, and 40 cm and 30cm at both ends of the building away
from the waterfront. Figures 11.22(a), (b) and 11.23(a), (b) show the distributions of
computed bending moments with depth for the two cases. In Figure 11.22, the
computed bending moments in Case II are close to Mu near the pile heads and exceed
Mc near the bottom of the liquefied fill, being consistent with the observed damage
shown in Figure 11.22(e); however, the failure at the middle of the liquefied layer on
the sea side pile can only be simulated in Case III. In addition, Case III appears to
create more severe loading conditions than Case II for both cases, i.e., the bending
moments at the bottom of the liquefied layers reach the ultimate values, which might
have produced the observed large displacements of piles. Thus, the results from Case
III are discussed hereafter.
322
Kohji Tokimatsu
Fig. 11.24. Computed displacement and
curvature of piles at building F, compared
with the observed values
Fig. 11.25. Computed displacement
and curvature of piles at Building G,
compared with the observed values
The computed displacements of two pile foundations for Case III are shown in Figures
11.24 and 11.25 in broken lines. Also shown in the Figures in solid lines are observed
displacement and curvature patterns from inclinometer surveys. It is found that in both
cases the deformation and curvature patterns of the piles are in reasonably good
agreement with the observed ones. The comparison of the assumed ground surface
displacements with the computed displacements of the pile heads near the waterfront
indicates that the soil pushes the pile on the sea side, while the pile pushes the soil on
the land side. This difference could have induced the difference in failure patterns
between the piles as shown in Figure 11.24, as well as the difference in the pile cap
rotations observed on both sides of the buildings. A similar soil-pile interaction also
occurred but to a lesser extent in the piles away from the waterfront, as shown in Figure
11.25. These findings indicate that the amount and the distribution of permanent
ground displacements could have significant influence on the final deformation and
failure patterns of pile foundation near the waterfront, although some of the damage
might have occurred during shaking.
The failure of piles of a building under construction in a lateral spreading zone
(Kuwabara and Yoneda, 1998; Building H in Table 11.1) also provides a good basis for
analysis. Since these piles carried only 2% of the long-term design load, the kinematic
force is considered to have dominated during and after shaking. The building 16.1 m
wide in NS direction by 41.8 m long in EW direction was located about 25 m and 90 m
inland from the east and south shorelines that displaced seawards by about 2.5 m and 3
Behaviour and Design of Deep Foundations
323
m, respectively. Its span direction was perpendicular to the southern shoreline. This
building was supported on 1.2-1.7 m diameter cast-in-place concrete piles that
penetrated through a reclaimed fill about 15-m thick (Figure 11.26(c)) and down to a
depth of about 48 m.
Fig. 11.26. Computed bending moment and displacement of piles at Building H, with
ground displacement, boring log and pile damage
After the earthquake, the ground surface around the building settled by 30-50 cm.
Vertical cracks were observed in almost all foundation beams, and the south side of the
building settled by 2.8cm with respect to the north side. In addition to an excavation
survey to examine damage to pile heads, a television camera was inserted into boreholes
cored vertically through two east side piles with diameters of either 140 or 150cm.
These surveys showed that horizontal and/or diagonal cracks occurred from the pile
head to a depth of 5 m as well as at depths between 11 and 15.2m (Figure 11.26 (d)) and
that the piles on the east end tilted towards southwest to south-southwest by 1/17-1/20
at least above a depth of 15.2m. Thus, the building might have been displaced towards
that direction by at least 88cm, i.e., about 62-85cm southwards and 23-62cm westwards.
The deformation of the foundation beams and the direction of the pile displacement
suggest that the kinematic force might have been more crucial in the span direction than
those in the longitudinal direction.
Since inertial forces during shaking were negligibly small, only Case III was considered
with the maximum ground displacements of 75cm on the seaside and 50cm on the
landside. Figures 11.26(a), (b) and (e) show the distribution of computed bending
moments and displacements with depth. The computed bending moments indicate that
failures might have occurred near the bottom of the liquefied layer as well as near the
pile head, which shows fairly good agreement with the field observation shown in
Figure 11.26(d). In addition, the computed displacement of 62cm of the pile head is
consistent with the observed displacement. These findings confirm that the amount and
the distribution of permanent ground displacements could have significant influence on
the final deformation and failure patterns of pile foundations subjected to lateral
spreading near the waterfront. Such effects therefore should be taken into account in
the foundation design where lateral ground spreading is expected to occur.
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Kohji Tokimatsu
11.7. Conclusions
Field performance of various pile foundations that experienced soil liquefaction and
lateral spreading in the 1995 Hyogoken-Nambu earthquake have been compiled and
summarized, together with their failure and deformation modes identified by surveys
using borehole cameras and/or slope-indicators. Cyclic and residual shear strains in soil
deposits during and after earthquakes have been estimated from field and aerial
photographic surveys as well as analysis of strong motion records, and a simplified
method for evaluating ground displacements has been developed. A simple p-y analysis
using the ground displacement profile from the proposed method has been conducted to
evaluate pile performance during the earthquake. The field observation together with
the analytical results leads to the following conclusions:
1. The field investigation using a borehole camera and a slope-indicator has
confirmed that failures of piles concentrated at the interface between liquefied
and non-liquefied layers, as well as near the pile heads, indicating significant
effects of ground displacements on pile damage.
2. The failure and deformation patterns of piles in the lateral spread zone vary
with distance from the waterfront, probably due to the variation of lateral
ground movements in the direction perpendicular to the waterfront.
3. Cyclic and permanent shear strains to de developed in sands during earthquakes
are expressed in terms of normalized SPT N-values.
4. The simple p-y method combined with the proposed estimates for ground
displacements can differentiate the damage from undamaged pile foundations
subjected to cyclic and/or permanent ground displacements in the Kobe
earthquake and can simulate reasonably well the failure and deformation modes
of damaged piles. This indicates that the ground deformation could have
played an important role on pile performance. Although preliminary and
required further refinement and verification, the proposed model appears
promising for evaluating the effects of ground displacements on piles.
Acknowledgements
The study described herein was made possible through the post-earthquake field
investigation and their compilation conducted by various organizations including but
not limited to the Committee on Building Foundation Technology against Liquefaction
and Lateral Spreading, Japan Association for Building Research Promotion; the
Committees on Damage to Building Foundations in Hyogoken-Nambu Earthquake,
both Architectural Institute of Japan and Kansai Branch of AIJ; and Japanese
Association for Steel Pile Piles. The strong motion accelerograms at the Higashi-Kobe
Bridge station was provided by the Public Works Research Institute, Ministry of
Construction. The authors express their sincere thanks to the above organizations and
persons.
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INDEX
geometric spreading, 91, 99
Green’s function, 97, 103, 159, 248
grid system, 273
ground shaking, 280
ground subsidence, 220
Gutenberg and Richter, 4, 257
G-J curves, 114, 143
Heaviside function, 81, 250
horizontal ground displacement, 329
horizontal to vertical spectral ratio, 154
Housner intensity, 244, 245, 262
Human losses, 30
Husid plot, 88
ICOLD, 286
inertial interaction, 306
Isosseismals, 57
Kanai-Tajimi spectrum, 98
kinematic interaction, 304, 308
kinematic source models, 97
lateral spreading, 326, 327, 338
liquefaction potential, 215, 299
liquefied zone, 212
microtremor, 258
Microtremor, 278
microtremors, 261
Modified Mercalli Intensity, 16, 63, 65
modulus degradation, 293
moment magnitude, 9, 73, 77
municipal waste, 290
NEHRP, 11, 13
partial safety factors, 314
Particle size distribution, 289
peak spectral accelerations, 278
pile damage, 334, 335, 336, 337, 339,
341
Poisson model, 254
acceleration power spectrum, 86
aleatory uncertainty, 6, 19
amplification coefficient, 247
amplification factor, 181
attenuation relation, 9, 10, 72, 74, 75,
76, 254, 288
average shear wave velocity, 9, 11, 138,
157, 198, 274, 275
bracketed duration, 87, 88
Butterworth filter, 92, 99
characteristic earthquakes, 8
coda waves, 154
coefficient of strain rate, 115
corner frequency, 78, 83, 84, 90, 91, 92
countermeasures against liquefaction,
235, 237, 239
cross power spectrum, 125
damage factors, 17
damage probabilities, 20
damage probability matrix, 16, 18
damage ratio, 49
deamplification, 80
directivity, 93
dislocation, 82, 83
dispersion curve, 127
displacement orbits, 323
earthquake scenario, 56, 58, 59, 64
economical losses, 31
epistemic uncertainty, 6
Eurocode 8, 40, 198, 200, 308, 313
fines content, 226, 227
Fourier amplitude spectrum, 84, 89,
100
fragility curves, 59
fundamental resonant frequency, 149
geological units, 24, 25, 62, 272
353
354
predominant frequencies, 66
probability of exceedance, 15
probable epicentre distance, 270
pseudo-static analyses, 285
pseudo-static analysis, 331
p-y curves, 331
qc vs. G0 correlation, 135
radiation patterns, 93
Ramberg-Osgood, 143
Rayleigh phase velocity, 125
receiver function, 259
recurrence model, 8
residual deformation method, 228
resonant column, 161
root-mean-square acceleration, 87
seismic coefficient method, 230
seismic moment, 77, 90
significant duration, 87, 88
simulated accelerations, 101, 271
Index
single areal source model, 269
site amplification, 279
soil amplification, 55
soil-pile-structure interaction, 331
source spectrum, 90, 251
source time function, 84
spectral amplification, 275
spectral analysis of surface waves, 125,
291
spectral decay factor, 92
spectral ratio method, 120
spectral slope method, 121
stress drop, 78, 251
threshold strain, 109
topographic aggravation factor, 195
truncated exponential distribution, 7
ultimate bearing capacity, 315
vulnerability curves, 47, 49
yield acceleration, 297
Atilla Ansal