Support Theory and Technology of Geotechnical Engineering

Topic Information

Dear Colleagues,

Support theory and technology of geotechnical engineering involve a wide range of fields, including transportation, roads and highways, railways and public transport systems, underground stations, water and wastewater transmission, power and energy, and underground storage facilities. They have the characteristics of difficult construction, long cycle, high cost and far-reaching social impact. At present, they have become an important research discipline. This topic focuses on the support theory and technology of underground space and covers a very wide scope of underground space and geotechnical engineering, including geo-investigation, geomechanics analysis, support design and modelling, construction, and monitoring; tunnels and large underground and earth-sheltered structure maintenance and rehabilitation; and underground space and underground space environment planning and development.

We invite papers on innovative technical developments, reviews, case studies, as well as analytical and assessment papers from different disciplines that are relevant to the topic of support theory and technology of geotechnical engineering.

Prof. Dr. Qi Wang
Dr. Bei Jiang
Dr. Xuezhen Wu
Dr. Hongke Gao
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Remote Sensing remotesensing	4.2	8.3	2009	24.7 Days	CHF 2700
Energies energies	3.0	6.2	2008	17.5 Days	CHF 2600
Minerals minerals	2.2	4.1	2011	18 Days	CHF 2400
Geosciences geosciences	2.4	5.3	2011	26.2 Days	CHF 1800
Geotechnics geotechnics	-	-	2021	16.9 Days	CHF 1000

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20 pages, 5070 KiB  

Open AccessArticle

Calculation Method for Traffic Load-Induced Permanent Deformation in Soils under Flexible Pavements

by Mate Janos Vamos and Janos Szendefy

Geotechnics 2023, 3(3), 955-974; https://doi.org/10.3390/geotechnics3030051 - 21 Sep 2023

Cited by 3 | Viewed by 1183

Abstract

Rutting is one of the most common types of distress in flexible pavement structures. There are two fundamental methods of designing pavement structures: conventional empirical methods and analytical approaches. Many analytical and empirical design procedures assume that rutting is mostly of asphalt origin [...] Read more.

Rutting is one of the most common types of distress in flexible pavement structures. There are two fundamental methods of designing pavement structures: conventional empirical methods and analytical approaches. Many analytical and empirical design procedures assume that rutting is mostly of asphalt origin and can be reduced by limiting the vertical deformation or stress at the top of the subgrade, but they do not quantify the rutting depth itself. Mechanistic–empirical models to predict the permanent deformations of unbound pavement layers have been well investigated and are rather common in North America; however, they are not widely utilized in the rest of the world. To date, there is no generally accepted, widely recognized, and documented procedure for calculating permanent deformations and thus for determining the rutting depth in flexible pavement courses originating from the unbound granular layers. This paper presents a layered calculation method with which the deformation of soil layers (base, subbase, and subgrade courses) under flexible pavements due to repeated traffic load can be determined. In the first step, the cyclic strain amplitude is calculated using a nonlinear material model that is based on particle size distribution parameters (d₅₀ and C_U) and dependent on the mean normal stress, relative density, and actual strain level. In the second step, the HCA (High Cycle Accumulation) model is used to calculate the residual settlement of each sublayer as a function of the number of cycles. It is shown that the developed model is suitable for describing different types of subgrades and pavement cross-sections. It is also demonstrated with finite element calculations that the developed model describes both the elastic and plastic strains sufficiently accurately. The developed model can predict the settlement and rutting of pavement structures with sufficient accuracy based on easily available particle size distribution parameters without the need for complex laboratory and finite element tests. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>The main calculation steps of the developed layered model.</p> Full article ">Figure 2
<p>Particle size distribution of the pavement layers [<a href="#B30-geotechnics-03-00051" class="html-bibr">30</a>].</p> Full article ">Figure 3
<p>Distribution of the additional vertical stress for traffic load classes A-C-E-R.</p> Full article ">Figure 4
<p>The calculated relative error as the function of the number of load steps (<b>a</b>) at the depth of 0.5 m and (<b>b</b>) at the depth of 2.5 m.</p> Full article ">Figure 5
<p>(<b>a</b>) The cumulative settlements and (<b>b</b>) the settlements of each individual sublayer with depth using the uniform and optimized arrangement of sublayers.</p> Full article ">Figure 6
<p>The calculated settlements as the function of number of sublayers. (<b>a</b>) For the subgrade and (<b>b</b>) for subbase and base courses.</p> Full article ">Figure 7
<p>Elastic strains (2<math display="inline"><semantics> <mrow> <msubsup> <mi>ε</mi> <mn>1</mn> <mrow> <mi>a</mi> <mi>m</mi> <mi>p</mi> <mi>l</mi> </mrow> </msubsup> </mrow> </semantics></math> and 2<math display="inline"><semantics> <mrow> <msubsup> <mi>ε</mi> <mn>3</mn> <mrow> <mi>a</mi> <mi>m</mi> <mi>p</mi> <mi>l</mi> </mrow> </msubsup> </mrow> </semantics></math>) calculated via the simplified layered procedure and with finite element modelling (Plaxis) (<b>a</b>) ε₁-z for the base and subbase courses; (<b>b</b>) ε₃-z for the base and subbase courses; (<b>c</b>) ε₁-z for the subgrade; and (<b>d</b>) ε₃-z for the subgrade.</p> Full article ">Figure 8
<p>The calculated ε^ampl-z function with the simplified layered model for five different subgrades and with finite element model (<b>a</b>) Traffic load class “A”; (<b>b</b>) Traffic load class “C”; (<b>c</b>) Traffic load class “E”; (<b>d</b>) Traffic load class “R”.</p> Full article ">Figure 9
<p>Calculated rutting depths for traffic load class “C” obtained by the simplified procedure and the finite element model for three different subgrades.</p> Full article ">Figure 10
<p>The relationship between rutting depth and number of cycles for subgrade “Soil 1” for traffic load classes “A”-“C”-“E”-“R” with the simplified procedure and with finite element modelling.</p> Full article ">

25 pages, 7340 KiB  

Open AccessArticle

Conceptual Model of Expansive Rock or Soil Swelling

by Boris Kavur, Nataša Štambuk Cvitanović, Jasmin Jug and Ivan Vrkljan

Geosciences 2023, 13(5), 141; https://doi.org/10.3390/geosciences13050141 - 11 May 2023

Viewed by 1681

Abstract

The paper presents a simple yet efficient way to track the void ratio, the water content, and the degree of saturation of a swelling material during saturation. The research aimed to quantitatively describe the drying and wetting processes of the swelling material, which [...] Read more.

The paper presents a simple yet efficient way to track the void ratio, the water content, and the degree of saturation of a swelling material during saturation. The research aimed to quantitatively describe the drying and wetting processes of the swelling material, which should enable their better understanding and easier modelling. Two identical tall samples, named “twins”, were formed by consolidating the paste prepared from the swelling material in which montmorillonite is the dominant mineral. The twins were together exposed to one-dimensional drying. After drying, lasting for 40 days, one twin was dissected to determine its water content profile. The other twin was subjected to 1D wetting (ponded infiltration experiment) with a constant water column for a period of 21 days and then dissected to determine the moisture profile. The sample preparation reduces uncertainties about the initial state. The results show that during wetting, the material follows a path in the e-w plot which is parallel to the full saturation curve. After reaching some degree of saturation, the path becomes parallel to the residual (shrinking) line. The proposed model predicts the primary and secondary phases of swelling, and under appropriate conditions, it assumes the tertiary phase. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Shrinkage curves determined for reconstituted samples that were consolidated at different vertical loads: 1, 800 kPa; 2, 1600 kPa; 3, 3200 kPa [<a href="#B28-geosciences-13-00141" class="html-bibr">28</a>].</p> Full article ">Figure 2
<p>Swelling phases of the representative elementary volume (REV).</p> Full article ">Figure 3
<p>Reinterpretation of the results of the wetting test of a Vertisol sample with an initial height of 6.2 cm, performed by Garnier et al. [<a href="#B23-geosciences-13-00141" class="html-bibr">23</a>] (swelling curves interpreted at different levels of the test sample during the wetting test).</p> Full article ">Figure 4
<p>Stages of preparation (<b>a</b>–<b>c</b>); relaxation in water (<b>d</b>), and 1D drying (<b>e</b>,<b>f</b>) of the twins.</p> Full article ">Figure 5
<p>Mass loss of samples (twins) during drying in the laboratory.</p> Full article ">Figure 6
<p>Preparation of VU-3 for the 1D wetting phase: (<b>a</b>) the VU-3 on the stand with the cylinder on the top; (<b>b</b>) the VU-3 without the rubber membrane with the engraved marks; (<b>c</b>) the cylinder on the top filled with water at the start of the wetting phase.</p> Full article ">Figure 7
<p>VU-3 at different times after the start of the wetting phase: (<b>a</b>) 10 min; (<b>b</b>) 1 h; (<b>c</b>) 24 h; (<b>d</b>) 72 h; (<b>e</b>) 240 h; (<b>f</b>) 500 h.</p> Full article ">Figure 8
<p>Changes in the mass of infiltrated water and changes in the sample volume during the wetting experiment.</p> Full article ">Figure 9
<p>Changes in the height of the VU-3 during the wetting experiment.</p> Full article ">Figure 10
<p>Profiles of the void ratio in the wetting experiment of VU-3.</p> Full article ">Figure 11
<p>Moisture content profiles in the wetting experiment of VU-3.</p> Full article ">Figure 12
<p>Degree of saturation profiles in the wetting experiment of VU-3.</p> Full article ">Figure 13
<p>Assumed swelling curves in the wetting experiment of VU-3.</p> Full article ">Figure 14
<p>Top surface of VU-3 at different times after the start of the wetting phase: (<b>a</b>) 1 min; (<b>b</b>) 3 min; (<b>c</b>) 60 min; (<b>d</b>) 21 days.</p> Full article ">Figure 15
<p>Measured and calculated curves of infiltrated water mass in the wetting of VU-3.</p> Full article ">

14 pages, 2961 KiB  

Open AccessArticle

A New Approach for Analyzing Circular Tunnels in Nonlinear Strain-Softening Rock Masses Considering Seepage Force

by Hao Fan, Lei Wang and Shaobo Li

Minerals 2023, 13(2), 138; https://doi.org/10.3390/min13020138 - 17 Jan 2023

Viewed by 1422

Abstract

Accurate calculation of the stresses and deformations of tunnels is of great importance for practical engineering applications. In this study, a three-region model for tunnels considering seepage force was established. A new nonlinear strain-softening model is proposed. Then, a unified solution for the [...] Read more.

Accurate calculation of the stresses and deformations of tunnels is of great importance for practical engineering applications. In this study, a three-region model for tunnels considering seepage force was established. A new nonlinear strain-softening model is proposed. Then, a unified solution for the stresses and deformations of tunnels is deduced. Through a series of discussions, the effects of seepage force, softening modulus coefficient of cohesion, and initial support resistance on the stress distribution, radii of the post-peak zone, and surface displacement around the tunnel are discussed. Results show that the tangential stresses are always larger than the radial stresses. As the distance from the tunnel center increases, the radial stress continues to increase, while the tangential stress first increases and then decreases. With the increases in seepage force, the radii of the post-peak zone and surface displacement all increase. With the increases in softening modulus coefficient of cohesion, the radii of the post-peak zone increase while the surface displacement decreases. Tunnels with a higher initial support resistance experience lower radii of the post-peak zone and surface displacement. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Different constitutive models. (<b>a</b>) elastic–perfectly plastic; (<b>b</b>) elastic–brittle-plastic; (<b>c</b>) linear strain-softening; (<b>d</b>) nonlinear strain-softening.</p> Full article ">Figure 2
<p>Mechanical models. (<b>a</b>) Three-region model of a tunnel cylindrical considering seepage force. (<b>b</b>) Nonlinear strain-softening model of surrounding rock.</p> Full article ">Figure 3
<p>Nonlinear strain-softening model of cohesion.</p> Full article ">Figure 4
<p>Dilation model of rock mass.</p> Full article ">Figure 5
<p>Flowchart of the calculation.</p> Full article ">Figure 6
<p>Location of the main return laneway.</p> Full article ">Figure 7
<p>Effect of seepage force on the radii of strain-softening and crushed regions and surface displacement. (<b>a</b>) <span class="html-italic">R_s</span> and <span class="html-italic">R_c</span>; (<b>b</b>) <span class="html-italic">u</span>₀.</p> Full article ">Figure 8
<p>Effect of seepage force on the stress distribution in the tunnel surrounding rock. (<b>a</b>) <span class="html-italic">σ_r</span>; (<b>b</b>) <span class="html-italic">σ_θ</span>.</p> Full article ">Figure 9
<p>Effect of softening modulus coefficient of cohesion on the radii of strain-softening and crushed regions and surface displacement. (<b>a</b>) <span class="html-italic">R_s</span> and <span class="html-italic">R_c</span>; (<b>b</b>) <span class="html-italic">u</span>₀.</p> Full article ">Figure 10
<p>Effect of softening modulus coefficient of cohesion on the stress distribution in the tunnel surrounding rock. (<b>a</b>) <span class="html-italic">σ_r</span>; (<b>b</b>) <span class="html-italic">σ_θ</span>.</p> Full article ">Figure 11
<p>Effect of initial support resistance on the radii of strain-softening and crushed regions and surface displacement. (<b>a</b>) <span class="html-italic">R_s</span> and <span class="html-italic">R_c</span>; (<b>b</b>) <span class="html-italic">u</span>₀.</p> Full article ">Figure 12
<p>Effect of initial support resistance on the stress distribution in the tunnel surrounding rock. (<b>a</b>) <span class="html-italic">σ_r</span>; (<b>b</b>) <span class="html-italic">σ_θ</span>.</p> Full article ">

16 pages, 3495 KiB  

Open AccessArticle

Mechanical Behavior Analysis of Fully Grouted Ground Anchor in Soft-Hard Alternating Stratum

by Xiujun Liu and Zhanguo Ma

Minerals 2023, 13(1), 59; https://doi.org/10.3390/min13010059 - 29 Dec 2022

Viewed by 1468

Abstract

Assuming that the ground anchor is connected with the rock–soil of the sidewall by a tangential linear spring, the load transfer model of the fully grouted ground anchor is established by using the spring element method, and the analytical solutions of the displacement, [...] Read more.

Assuming that the ground anchor is connected with the rock–soil of the sidewall by a tangential linear spring, the load transfer model of the fully grouted ground anchor is established by using the spring element method, and the analytical solutions of the displacement, axial force, and shear stress distribution of the ground anchor in the upper and lower parallel strata foundation and sandwich foundation are given, respectively. Corresponding to the above two kinds of alternating strata, the mechanical behavior of the vertical fully grouted ground anchor in the soft–hard alternating stratum is analyzed using the four conditions in Case 1 and the six conditions in Case 2, respectively. Through the case analysis, it can be concluded that the mechanical behavior of the round anchor is greatly affected by the shear modulus of the shallow stratum, and is less affected by the shear modulus of the deep stratum. The depth of the stratum interface and the thickness of the interlayer have some influence on the mechanical behavior of the whole ground anchor but have little influence on the displacement and axial force distribution of the ground anchor. This paper has certain guidance and reference significance for the design of vertical fully grouted ground anchors in the alternating strata. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Schematic diagram of discretization of free rod.</p> Full article ">Figure 2
<p>Schematic diagram of discretization of anchor.</p> Full article ">Figure 3
<p>Force analysis diagram of the <span class="html-italic">i</span>th spring element.</p> Full article ">Figure 4
<p>Ground anchors buried in upper and lower parallel strata foundation.</p> Full article ">Figure 5
<p>Ground anchors buried in sandwich foundation.</p> Full article ">Figure 6
<p>Effect of shear modulus change of Stratum-1 on mechanical behavior of ground anchor. (Case 1: condition 1) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 7
<p>Effect of the depth of stratum interface on mechanical behavior of ground anchor. (Case 1: condition 2) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 8
<p>Effect of shear modulus change of Stratum-2 on mechanical behavior of ground anchor. (Case 1: condition 3) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 9
<p>Effect of the depth of stratum interface on mechanical behavior of ground anchor. (Case 1: condition 4) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 10
<p>Effect of shear modulus change of Stratum-1 on mechanical behavior of ground anchor. (Case 2: condition 1) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 11
<p>Effect of interlayer thickness change on mechanical behavior of ground anchor. (Case 2: condition 2) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 12
<p>Effect of the depth of stratum interface on mechanical behavior of ground anchor. (Case 2: condition 3) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 13
<p>Effect of shear modulus change of Stratum-2 on mechanical behavior of ground anchor. (Case 2: condition 4) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 14
<p>Effect of interlayer thickness change on mechanical behavior of ground anchor. (Case 2: condition 5) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">Figure 15
<p>Effect of the depth of stratum interface on mechanical behavior of ground anchor. (Case 2: condition 6) (<b>a</b>) displacement distribution curve; (<b>b</b>) axial force distribution curve; (<b>c</b>) shear stress distribution curve.</p> Full article ">

15 pages, 2852 KiB  

Open AccessArticle

Mechanical Behavior Analysis of Fully Grouted Bolts under Axial Cyclic Load

by Xiujun Liu and Zhanguo Ma

Minerals 2022, 12(12), 1566; https://doi.org/10.3390/min12121566 - 5 Dec 2022

Cited by 2 | Viewed by 1319

Abstract

Fully grouted bolts are widely used in engineering. In order to deeply understand the load-transfer mechanism of a fully grouted bolt, it is necessary to analyze and study its mechanical behavior under axial cyclic load. First of all, based on the idea of [...] Read more.

Fully grouted bolts are widely used in engineering. In order to deeply understand the load-transfer mechanism of a fully grouted bolt, it is necessary to analyze and study its mechanical behavior under axial cyclic load. First of all, based on the idea of discretization and the force balance analysis of each mass spring element, this study proposes a method for analyzing the force of the bolt—the spring element method. Second, the load-transfer model of the fully grouted bolt is established by using the spring element method, assuming that the bolt and the sidewall rock and soil are connected by tangential linear springs. The analytical solutions for the displacement, axial force, and shear-stress distribution of the bolt before and after the damage of the sidewall spring are given. It is found that the analysis results of the analytical model proposed in this paper have a great relationship with λ, which is the square root of the ratio of sidewall spring stiffness k′_u to bolt stiffness k_u. Further analysis found that this model is more suitable for the two working conditions of λ ≈ 0 and λ ≈ 1, and the relationship between sidewall spring stiffness k′_u and pull-out stiffness K of the bolt was established under these two working conditions. Finally, the rationality and accuracy of the analytical model proposed in this study are verified by an analysis of two typical test cases under the two working conditions of λ ≈ 0 and λ ≈ 1. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Schematic diagram of discretization of free rod.</p> Full article ">Figure 2
<p>Schematic diagram of discretization of bolt.</p> Full article ">Figure 3
<p>Force analysis diagram of the <span class="html-italic">i</span>th spring element.</p> Full article ">Figure 4
<p>Load-transfer model.</p> Full article ">Figure 5
<p>Variation of <span class="html-italic">K</span> and Δ<span class="html-italic">P</span>/Δ<span class="html-italic">s</span> with test load and number of cycles during the test (working condition of <span class="html-italic">λ</span> ≈ 0). (<b>a</b>) Variation of pull-out stiffness <span class="html-italic">K</span>; (<b>b</b>) variation of pull-out stiffness change rate Δ<span class="html-italic">P</span>/Δ<span class="html-italic">s</span>.</p> Full article ">Figure 6
<p>Comparison of measured axial force distribution curve and simulated curve: (<b>a</b>) 9 m-long bolt; (<b>b</b>) 12 m-long bolt; (<b>c</b>) 15 m-long bolt.</p> Full article ">Figure 6 Cont.
<p>Comparison of measured axial force distribution curve and simulated curve: (<b>a</b>) 9 m-long bolt; (<b>b</b>) 12 m-long bolt; (<b>c</b>) 15 m-long bolt.</p> Full article ">Figure 7
<p>Comparison of measured shear stress distribution curve and simulated curve: (<b>a</b>) 9 m-long bolt; (<b>b</b>) 12 m-long bolt; (<b>c</b>) 15 m-long bolt.</p> Full article ">Figure 7 Cont.
<p>Comparison of measured shear stress distribution curve and simulated curve: (<b>a</b>) 9 m-long bolt; (<b>b</b>) 12 m-long bolt; (<b>c</b>) 15 m-long bolt.</p> Full article ">Figure 8
<p>Variation of <span class="html-italic">K</span> and Δ<span class="html-italic">P</span>/Δ<span class="html-italic">s</span> with test load and number of cycles during the test (working condition of <span class="html-italic">λ</span> ≈ 1): (<b>a</b>) pull-out stiffness <span class="html-italic">K</span>; (<b>b</b>) pull-out stiffness change rate Δ<span class="html-italic">P</span>/Δ<span class="html-italic">s</span>.</p> Full article ">Figure 9
<p>Comparison of model analysis and test results: (<b>a</b>) axial force distribution; (<b>b</b>) shear stress distribution.</p> Full article ">

25 pages, 75898 KiB  

Open AccessArticle

Geological Exploration, Landslide Characterization and Susceptibility Mapping at the Boundary between Two Crystalline Bodies in Jajarkot, Nepal

by Yubraj Bikram Shahi, Sushma Kadel, Harish Dangi, Ganesh Adhikari, Diwakar KC and Kabi Raj Paudyal

Geotechnics 2022, 2(4), 1059-1083; https://doi.org/10.3390/geotechnics2040050 - 1 Dec 2022

Cited by 4 | Viewed by 4555

Abstract

The geology of the Himalayas is intricated and intriguing. It features numerous tectonic bodies and structures too complex to interpret. Along with such mysteries it has too many common geohazards, such as landslides. In this study, a detailed geological investigation is carried out [...] Read more.

The geology of the Himalayas is intricated and intriguing. It features numerous tectonic bodies and structures too complex to interpret. Along with such mysteries it has too many common geohazards, such as landslides. In this study, a detailed geological investigation is carried out to overcome the discrepancies in structural interpretation, the nature of two crystalline bodies, and non-uniformity in geological mapping in the central Himalayan arc, in the Jajarkot district of Nepal. Along with the geological exploration and landslide characterization of the area, consequent landslide susceptibility mapping is performed considering 13 causative factors related to geology, topography, land use, hydrology, and the anthropogenic factor, using two bivariate statistical models. This study concludes that the two metamorphic crystalline bodies in the study area are most probably the klippen, due to the absence or erosion of the root zone. The field study revealed that haphazard road excavation without the consideration of geological and geotechnical features has caused shallow landslides. The results obtained from the susceptibility maps, with a varying range of susceptibility zones, are in good agreement with the spatial distribution of pre-historic landslides. The results of the susceptibility modeling are validated by calculating landslide density and plotting area under curves (AUC). The AUC value for the WOE, and the FR method, revealed an overall success rate of 79.42% and 77.62%, respectively. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Location map of the study area: (<bold>a</bold>) Jajarkot district in Nepal around neighboring countries; (<bold>b</bold>) location of the study area within Jajarkot district and bordering districts of Nepal; (<bold>c</bold>) the study area with major streams.</p> Full article ">Figure 2
<p>Geological map of the study area representing the region between Chhedachaur to Saureni.</p> Full article ">Figure 3
<p>Meso-scale geological structures showing top-to-the-south movement: (<bold>a</bold>) S-type folded vein exposed in Dasera section; (<bold>b</bold>) Z-type drag fold exposed in Karkigaun section.</p> Full article ">Figure 4
<p>Some photographic references of the landslides reported within the study area: (<bold>a</bold>) excavation-induced landslides with multiple scarps, (<bold>b</bold>–<bold>d</bold>) are landslides that are converted into debris flows; (<bold>e</bold>,<bold>f</bold>) are Google Earth images of the Bhoor Landslide and Kaptola landslide, which are deep-seated complex paleo-landslides.</p> Full article ">Figure 4 Cont.
<p>Some photographic references of the landslides reported within the study area: (<bold>a</bold>) excavation-induced landslides with multiple scarps, (<bold>b</bold>–<bold>d</bold>) are landslides that are converted into debris flows; (<bold>e</bold>,<bold>f</bold>) are Google Earth images of the Bhoor Landslide and Kaptola landslide, which are deep-seated complex paleo-landslides.</p> Full article ">Figure 5
<p>Landslide inventory map of the study area showing elevation ranges.</p> Full article ">Figure 6
<p>Landslide conditioning factor maps of the study area: (<bold>a</bold>) slope angle; (<bold>b</bold>) slope aspect; (<bold>c</bold>) slope shape, (<bold>d</bold>) TWI; (<bold>e</bold>) SPI; (<bold>f</bold>) stream proximity; (<bold>g</bold>) lithology (<bold>h</bold>) distance from thrust; (<bold>i</bold>) distance from major anticline; (<bold>j</bold>) distance from major syncline; (<bold>k</bold>) distance from the road; (<bold>l</bold>) land use; and (<bold>m</bold>) precipitation.</p> Full article ">Figure 6 Cont.
<p>Landslide conditioning factor maps of the study area: (<bold>a</bold>) slope angle; (<bold>b</bold>) slope aspect; (<bold>c</bold>) slope shape, (<bold>d</bold>) TWI; (<bold>e</bold>) SPI; (<bold>f</bold>) stream proximity; (<bold>g</bold>) lithology (<bold>h</bold>) distance from thrust; (<bold>i</bold>) distance from major anticline; (<bold>j</bold>) distance from major syncline; (<bold>k</bold>) distance from the road; (<bold>l</bold>) land use; and (<bold>m</bold>) precipitation.</p> Full article ">Figure 6 Cont.
<p>Landslide conditioning factor maps of the study area: (<bold>a</bold>) slope angle; (<bold>b</bold>) slope aspect; (<bold>c</bold>) slope shape, (<bold>d</bold>) TWI; (<bold>e</bold>) SPI; (<bold>f</bold>) stream proximity; (<bold>g</bold>) lithology (<bold>h</bold>) distance from thrust; (<bold>i</bold>) distance from major anticline; (<bold>j</bold>) distance from major syncline; (<bold>k</bold>) distance from the road; (<bold>l</bold>) land use; and (<bold>m</bold>) precipitation.</p> Full article ">Figure 6 Cont.
<p>Landslide conditioning factor maps of the study area: (<bold>a</bold>) slope angle; (<bold>b</bold>) slope aspect; (<bold>c</bold>) slope shape, (<bold>d</bold>) TWI; (<bold>e</bold>) SPI; (<bold>f</bold>) stream proximity; (<bold>g</bold>) lithology (<bold>h</bold>) distance from thrust; (<bold>i</bold>) distance from major anticline; (<bold>j</bold>) distance from major syncline; (<bold>k</bold>) distance from the road; (<bold>l</bold>) land use; and (<bold>m</bold>) precipitation.</p> Full article ">Figure 7
<p>Photomicrographic reference of representative rock samples from the study area: (<bold>a</bold>) schist; (<bold>b</bold>) meta-diamictite; (<bold>c</bold>) garnetiferous schist; (<bold>d</bold>) micaceous quartzite; (<bold>e</bold>) amphibolite (meta-basic rocks); and (<bold>f</bold>) siliceous marble. plg = plagioclase feldspar.</p> Full article ">Figure 8
<p>Landslide susceptibility models prepared using: (<bold>a</bold>) WOE method, (<bold>b</bold>) FR method.</p> Full article ">Figure 9
<p>Success rate curve showing cumulative percentage of observed landslide occurrences versus cumulative percentage of decreasing landslide susceptibility index value.</p> Full article ">

37 pages, 47005 KiB  

Open AccessArticle

Stress–Strain–Time Description and Analysis of Frozen–Thawed Silty Clay under Low Stress Level

by Haigang Qu, Dianrui Mu, Zhenlu Ren, Ziyuan Huang, Yang Huang and Aiping Tang

Geotechnics 2022, 2(4), 871-907; https://doi.org/10.3390/geotechnics2040042 - 24 Oct 2022

Viewed by 1646

Abstract

The construction of high-speed railways in cold regions needs to consider the effects of freeze–thaw cycles (FTHs) on the long-term deformation of subgrades. However, at present, research on the creep characteristics of frozen–thawed rocks and soils is not extensive. In the limited studies [...] Read more.

The construction of high-speed railways in cold regions needs to consider the effects of freeze–thaw cycles (FTHs) on the long-term deformation of subgrades. However, at present, research on the creep characteristics of frozen–thawed rocks and soils is not extensive. In the limited studies on frozen–thawed soil creep properties, current research focuses more on high stress–strain–time responses, but for the subgrades, the inner stress is usually low. This paper presents the results of triaxial compression creep tests on remolded, frozen–thawed silty clay sampled in the Yichun-Tieli area and describes its stress–strain–time relationship in an arctan function-based mathematical model. Each creep test condition is studied using three specimens. Frozen–thawed silty clay exhibits attenuation creep under low-level stress. In general, from 4 FTHs to 11 FTHs, the mean elasticity modulus decreases first, and then, increases. The exerted stress is higher than the yield stress; the more FTHs the specimens experience, the more time they need to be deformed stably under the same axial deviatoric stress (ADS). Under the same mean ADS, the mean stable strain of 7 FTHs exceeds the other two FTH conditions and, in general, the mean stable strain of 4 FTHs exceeds 11 FTHs. By dissecting the phenomena, it can be concluded that with FTHs increasing, moisture and voids reconstitute in the process; the elastic strain accounts for most of the total strain and significantly decides the extent of creep deformation; the arctan function-based model is basically able to describe, but not perfectly predict, the stress–strain–time relationship of frozen–thawed silty clay. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Photos of (<bold>a</bold>) the external surface section of undisturbed silty clay island permafrost; (<bold>b</bold>,<bold>c</bold>) the internal cross-section of undisturbed silty clay island permafrost; and (<bold>d</bold>,<bold>e</bold>) the external surface of remolded frozen soil.</p> Full article ">Figure 2
<p>Grain distribution curve of the silty clay.</p> Full article ">Figure 3
<p>The <inline-formula><mml:math id="mm101"><mml:semantics><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mi>d</mml:mi></mml:msub></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm102"><mml:semantics><mml:mi>W</mml:mi></mml:semantics></mml:math></inline-formula> curve of compaction test.</p> Full article ">Figure 4
<p>External axial stress load levels of stepwise loading in the triaxial creep tests. This figure is mainly to display the stress levels. The time duration of each stress level is generally not equal, but decided based on the deformation to be stable.</p> Full article ">Figure 5
<p>Axial strain <inline-formula><mml:math id="mm103"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 11, 4 FTHs.</p> Full article ">Figure 6
<p>Axial strain <inline-formula><mml:math id="mm104"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 12, 4 FTHs.</p> Full article ">Figure 7
<p>Axial strain <inline-formula><mml:math id="mm105"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 23, 4 FTHs.</p> Full article ">Figure 8
<p>Axial strain <inline-formula><mml:math id="mm106"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 15, 7 FTHs.</p> Full article ">Figure 9
<p>Axial strain <inline-formula><mml:math id="mm107"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 16, 7 FTHs.</p> Full article ">Figure 10
<p>Axial strain <inline-formula><mml:math id="mm108"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 24, 7 FTHs.</p> Full article ">Figure 11
<p>Axial strain <inline-formula><mml:math id="mm109"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 25, 11 FTHs.</p> Full article ">Figure 12
<p>Axial strain <inline-formula><mml:math id="mm110"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 26, 11 FTHs.</p> Full article ">Figure 13
<p>Axial strain <inline-formula><mml:math id="mm111"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>–time curve of No. 28, 11 FTHs.</p> Full article ">Figure 14
<p>Appearances of tested specimens going through 4 FTHs.</p> Full article ">Figure 15
<p>Appearances of tested specimens going through 7 FTHs.</p> Full article ">Figure 16
<p>Appearances of tested specimens going through 11 FTHs.</p> Full article ">Figure 17
<p>Isochronous <inline-formula><mml:math id="mm112"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm113"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 11, 4 FTHs.</p> Full article ">Figure 18
<p>Isochronous <inline-formula><mml:math id="mm114"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm115"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 12, 4 FTHs.</p> Full article ">Figure 19
<p>Isochronous<inline-formula><mml:math id="mm116"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm117"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 23, 4 FTHs.</p> Full article ">Figure 20
<p>Isochronous<inline-formula><mml:math id="mm118"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm119"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 15, 7 FTHs.</p> Full article ">Figure 21
<p>Isochronous<inline-formula><mml:math id="mm120"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm121"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 16, 7 FTHs.</p> Full article ">Figure 22
<p>Isochronous<inline-formula><mml:math id="mm122"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm123"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 24, 7 FTHs.</p> Full article ">Figure 23
<p>Isochronous<inline-formula><mml:math id="mm124"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm125"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 25, 11 FTHs.</p> Full article ">Figure 24
<p>Isochronous<inline-formula><mml:math id="mm126"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm127"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 26, 11 FTHs.</p> Full article ">Figure 25
<p>Isochronous<inline-formula><mml:math id="mm128"><mml:semantics><mml:mrow><mml:mtext> </mml:mtext><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula>-<inline-formula><mml:math id="mm129"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>ε</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> curves of Specimen No. 28, 11 FTHs.</p> Full article ">Figure 26
<p>Accumulative time–axial deviatoric stress curves when FTH = 4.</p> Full article ">Figure 27
<p>Accumulative time–axial deviatoric stress curves when FTH = 7.</p> Full article ">Figure 28
<p>Accumulative time–axial deviatoric stress curves when FTH = 11.</p> Full article ">Figure 29
<p>Comparison of mean accumulative time–mean axial deviatoric stress under different FTHs.</p> Full article ">Figure 30
<p>Mean axial deviatoric stress–mean stable strain under different FTHs.</p> Full article ">Figure 31
<p>Mean stable strain–FTH under confining pressure = 150 kPa and the preset ADS.</p> Full article ">Figure 32
<p>The fitting image of strain(%)–time(min) of Specimen 23.</p> Full article ">Figure 33
<p>The correlations between <italic>A</italic> and <inline-formula><mml:math id="mm130"><mml:semantics><mml:mrow><mml:mfenced><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:semantics></mml:math></inline-formula> of all the specimens.</p> Full article ">Figure 34
<p>The correlations between <italic>A</italic> and low-level <inline-formula><mml:math id="mm131"><mml:semantics><mml:mrow><mml:mi>ADS</mml:mi><mml:mo>≤</mml:mo><mml:mn>0.14268</mml:mn><mml:mrow><mml:mtext> </mml:mtext><mml:mi>MPa</mml:mi></mml:mrow></mml:mrow></mml:semantics></mml:math></inline-formula> under different FTHs.</p> Full article ">Figure 35
<p>The correlations between <italic>A</italic> and high-level <inline-formula><mml:math id="mm132"><mml:semantics><mml:mrow><mml:mi>ADS</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0.14268</mml:mn><mml:mrow><mml:mtext> </mml:mtext><mml:mi>MPa</mml:mi></mml:mrow></mml:mrow></mml:semantics></mml:math></inline-formula> under different FTHs.</p> Full article ">Figure 36
<p>The correlation among <italic>k</italic>, <italic>b</italic> and FTH.</p> Full article ">Figure 37
<p>Comparison of theoretical and practical strain rate–time of ADS = 37.98 kPa of Specimen 23.</p> Full article ">Figure 38
<p>Comparison of theoretical and practical strain rate–time of ADS = 168.00 kPa of Specimen 23.</p> Full article ">Figure 39
<p>Comparison of theoretical and practical strain rate–time of ADS = 192.97 kPa of Specimen 23.</p> Full article ">Figure 40
<p>The time needed until stable creep under the preset axial deviatoric stresses withstanding different confining pressures.</p> Full article ">Figure 41
<p>The mean stable strain under the preset axial deviatoric stresses withstanding different confining pressures.</p> Full article ">

13 pages, 2416 KiB  

Open AccessArticle

An Analytical Model for the Excavation Damage Zone in Tunnel Surrounding Rock

by Xiaoding Xu, Yuejin Zhou, Chun Zhu, Chunlin Zeng and Chong Guo

Minerals 2022, 12(10), 1321; https://doi.org/10.3390/min12101321 - 19 Oct 2022

Cited by 1 | Viewed by 1796

Abstract

An accurate theoretical model to predict the extent and mechanical behavior of the excavation damage zone (EDZ) in the surrounding rock of deep-buried tunnel is of great importance for the practical engineering applications. Using the elastic-plastic theory and combined with the analysis on [...] Read more.

An accurate theoretical model to predict the extent and mechanical behavior of the excavation damage zone (EDZ) in the surrounding rock of deep-buried tunnel is of great importance for the practical engineering applications. Using the elastic-plastic theory and combined with the analysis on the stress characteristics of the tunnel surrounding rock, this paper present a predict model for the EDZ formation and evolution. A three-zone composite mechanical model was established for the tunnel surround rock and the corresponding stress state and displacement field of three zones were derived. The effects of the strain softening and dilatancy during rock deformation was taken into account. The correctness of the proposed model was validated by the existing theoretical models. A sensitivity analysis for different influencing factors in this model was also performed. The results can benefit for the future numerical and experimental studies. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Mechanical model of tunnel surrounding rock.</p> Full article ">Figure 2
<p>Equivalent model of elastic zone for tunnel surrounding rock.</p> Full article ">Figure 3
<p>Strain-softening model of tunnel surrounding rock. (<b>a</b>) Cohesion strain-softening model; (<b>b</b>) Internal friction angle strain-softening model.</p> Full article ">Figure 4
<p>Dilatation effect model of tunnel surrounding rock.</p> Full article ">Figure 5
<p>Plastic range under different lateral pressure coefficient.</p> Full article ">Figure 6
<p>Plastic range under different original rock stress.</p> Full article ">Figure 7
<p>Plastic range under different cohesions.</p> Full article ">Figure 8
<p>Plastic range under different support resistances.</p> Full article ">

16 pages, 2533 KiB  

Open AccessArticle

Conversion of Triaxial Compression Strain–Time Curves from Stepwise Loading to Respective Loading

by Haigang Qu, Dianrui Mu, Zhong Nie and Aiping Tang

Geotechnics 2022, 2(4), 855-870; https://doi.org/10.3390/geotechnics2040041 - 30 Sep 2022

Viewed by 1579

Abstract

Numerous researchers of soil creep behavior adopt stepwise loading (SL) rather than respective loading (RL) to perform the triaxial creep tests. However, a complete continuous strain–time curve of SL needs to be converted into assumed curve clusters supposing obtained under RL before the [...] Read more.

Numerous researchers of soil creep behavior adopt stepwise loading (SL) rather than respective loading (RL) to perform the triaxial creep tests. However, a complete continuous strain–time curve of SL needs to be converted into assumed curve clusters supposing obtained under RL before the deformation data are used to develop creep constitutive models. Classical methods realize the conversion mainly by focusing on the creep deformation parts and classifying them into linear and nonlinear compositions. Mostly, the linear parts are simply superposed while the nonlinear parts are complex to consider and so are neglected. Moreover, classical methods are not sufficiently valid to eliminate the stress history effect on the conversion. Here, a new method is proposed to achieve the conversion without neglecting the stress history effect. The method rebuilds the triaxial creep test mathematically and physically, adhering to the revising of energy. The method treats the tested deformation in its entirety, instead of distinguishing it into elastic, visco-elastic, plastic and creep (linear and nonlinear) deformation to convert respectively. The comparison among actual measured SL and RL strain–time curves and the curves converted by the new method proves the stress history effect should not be neglected. The higher the vertical load level, the larger the discrepancy between the RL and SL strain–time curve, and the disparity becomes larger with time. The new method highlights the necessity of considering the stress history effect in analysis and design for higher accuracy. The comparisons illustrate the conversion method at least produces more satisfactory results for clayey soil. Primarily examined, at the later stages of loading, the disparity in strain between the converted RL and measured RL decreases by 52.5%~53.5% compared with strain between the measured SL and measured RL. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>(<bold>a</bold>): RL mode and corresponding creep strain–time curves. (<bold>b</bold>): SL mode and corresponding creep strain–time curves [<xref ref-type="bibr" rid="B2-geotechnics-02-00041">2</xref>].</p> Full article ">Figure 2
<p>SL creep curve for sandstone and its conversion to RL creep curve [<xref ref-type="bibr" rid="B20-geotechnics-02-00041">20</xref>]. The colors of angle of twist per cm–time lines represent the following: gray line, under 612.50 KG-CM torque; red lines, under 921.25 KG-CM torque; blue lines, under 1254.90 KG-CM torque; yellow line, under other later torque levels.</p> Full article ">Figure 3
<p>Illustration of SL process on specimen A and RL process on specimen B and C. (<bold>a</bold>) Specimen A is deformed under <italic>F</italic>₁ load. (<bold>b</bold>) Specimen A is continually deformed under another <italic>F</italic>₂ load after it reached a stable deformation state under <italic>F</italic>₁ load. (<bold>c</bold>) Specimen B is deformed under <italic>F</italic>₁ load. (<bold>d</bold>) Specimen C is deformed under (<italic>F</italic>₁ + <italic>F</italic>₂) load.</p> Full article ">Figure 4
<p>Soil specimen instances after creep tests. Specimen (<bold>a</bold>), under presupposed confining pressure <italic>σ</italic>₃ = 200 kPa. Specimen (<bold>b</bold>), under presupposed confining pressure <italic>σ</italic>₃ = 150 kPa. Specimen (<bold>c</bold>), under presupposed confining pressure <italic>σ</italic>₃ = 100 kPa. <inline-formula><mml:math id="mm164"><mml:semantics><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:semantics></mml:math></inline-formula> exerted to the three specimens ranges from 37.98 kPa~360.23 kPa. The original sizes of all the three specimens are <italic>d</italic>₀ = 61.8 mm and <italic>h</italic>₀ = 125 mm.</p> Full article ">Figure 5
<p>Comparison of converted RL axial deformation and tested RL and SL axial deformation when <inline-formula><mml:math id="mm165"><mml:semantics><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>120</mml:mn><mml:mo> </mml:mo><mml:mi>kPa</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> (Test 4, 2).</p> Full article ">Figure 6
<p>Comparison of converted RL axial deformation and tested RL and SL axial deformation when <inline-formula><mml:math id="mm166"><mml:semantics><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>240</mml:mn><mml:mo> </mml:mo><mml:mi>kPa</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> (Test 4, 3).</p> Full article ">Figure 7
<p>Comparison of converted RL axial deformation and tested RL and SL axial deformation when <inline-formula><mml:math id="mm167"><mml:semantics><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>240</mml:mn><mml:mo> </mml:mo><mml:mi>kPa</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> (Test 5, 3).</p> Full article ">Figure 8
<p>Comparison of axial strain tested in different loading modes when <inline-formula><mml:math id="mm168"><mml:semantics><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="sans-serif">σ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mn>240</mml:mn><mml:mo> </mml:mo><mml:mi>kPa</mml:mi></mml:mrow></mml:semantics></mml:math></inline-formula> (Test 3, 4, 5).</p> Full article ">

17 pages, 5965 KiB  

Open AccessArticle

Macro-Microscopic Deterioration Behavior of Gypsum Rock after Wetting and Its Constitutive Model Based on Acoustic Emission

by Xiaoding Xu, Yuejin Zhou, Weiqiang Chen, Yubing Gao, Qiang Fu, Xue Liu and Chundi Feng

Minerals 2022, 12(9), 1168; https://doi.org/10.3390/min12091168 - 15 Sep 2022

Cited by 8 | Viewed by 2042

Abstract

Gypsum rock is highly sensitive to a water environment due to its unique physical and chemical properties, such as high solubility. After wetting, the internal microstructure of gypsum rock is damaged, and the mechanical properties deteriorate accordingly, leading to serious engineering problems for [...] Read more.

Gypsum rock is highly sensitive to a water environment due to its unique physical and chemical properties, such as high solubility. After wetting, the internal microstructure of gypsum rock is damaged, and the mechanical properties deteriorate accordingly, leading to serious engineering problems for gypsum-bearing geotechnical structures. Therefore, it is particularly necessary to investigate the mechanical deterioration behavior of gypsum rock after wetting. In this paper, the mechanical behavior of gypsum rocks with different water contents were studied. The relationship between the rock water content and the water immersion time was established through the water content test. The scanning electron microscope (SEM) images of the gypsum rock after the water immersion showed that the internal microstructure of the gypsum rock became looser and more complex as the immersion time increased. The fractal dimensions of the SEM images were calculated to quantify the degree of damage to the gypsum rocks after wetting. These images showed that the degree of damage increased with the increasing immersion time, but the increase rate tended to be slow. The relationship between the rock water content and the mechanical responses of gypsum rock were established by triaxial compression tests, and the concomitant acoustic emission (AE) characteristics in the loading processes showed that the immersion time had a positive correlation with the AE frequency and a negative correlation with the AE cumulative count. Based on the AE characteristics, a damage constitutive model of gypsum rock as a function of immersion time was developed and this can reproduce the mechanical responses of gypsum rock after wetting. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>A standard sample of gypsum rock.</p> Full article ">Figure 2
<p>The rock sample under triaxial compression and the microscopic element, where <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>1</mn> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>2</mn> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mn>3</mn> </msub> </mrow> </semantics></math> are the three principal stresses, and <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>c</mi> </msub> </mrow> </semantics></math> is the applied circumferential confining pressure.</p> Full article ">Figure 3
<p>The relationship between the rock water content and the immersion time.</p> Full article ">Figure 4
<p>SEM images of the rock samples with different water immersion times: (<b>a</b>) Natural, (<b>b</b>) 7 days, (<b>c</b>) 15 days, and (<b>d</b>) 30 days.</p> Full article ">Figure 5
<p>The analysis procedure of the fractal dimension of the SEM image.</p> Full article ">Figure 6
<p>The calculation of the fractal dimension for the gypsum rock with different soak times: (<b>a</b>) Natural, (<b>b</b>) 7 days, (<b>c</b>) 15 days, and (<b>d</b>) 30 days.</p> Full article ">Figure 7
<p>(<b>a</b>) The relationship between the fractal dimension/degree of damage and the water immersion time. (<b>b</b>) The relationship between the fractal dimension/degree of damage and the water content.</p> Full article ">Figure 8
<p>The stress-strain curves of the gypsum rocks after immersion in water for different durations.</p> Full article ">Figure 9
<p>The relationship between the triaxial compressive strength and the rock water content.</p> Full article ">Figure 10
<p>The relationship between the elastic modulus and the rock water content.</p> Full article ">Figure 11
<p>The relationship between the Poisson’s ratio and the rock water content.</p> Full article ">Figure 12
<p>The stress-time-AE count curves of the gypsum rocks with the different immersion times: (<b>a</b>) Natural, (<b>b</b>) 1 day, (<b>c</b>) 7 days, (<b>d</b>) 15 days, and (<b>e</b>) 30 days.</p> Full article ">Figure 13
<p>The stress-time-AE cumulative count curves of the gypsum rocks with the different water immersion durations, where <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>ci</mi> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>ci</mi> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mrow> <mi>cd</mi> </mrow> </msub> </mrow> </semantics></math> indicate the crack initiation stress, the secondary crack stress, and the crack damage stress: (<b>a</b>) Natural, (<b>b</b>) 1 day, (<b>c</b>) 7 days, (<b>d</b>) 15 days, and (<b>e</b>) 30 days.</p> Full article ">Figure 14
<p>The experimental and simulated curves of the gypsum rocks under triaxial compressions after immersion in water for different durations: (<b>a</b>) 1 day, (<b>b</b>) 7 days, (<b>c</b>) 15 days, and (<b>d</b>) 30 days.</p> Full article ">

21 pages, 5205 KiB  

Open AccessArticle

Energy-Based Approach: Analysis of a Vertically Loaded Pile in Multi-Layered Non-Linear Soil Strata

by Prakash Ankitha Arvan and Madasamy Arockiasamy

Geotechnics 2022, 2(3), 549-569; https://doi.org/10.3390/geotechnics2030027 - 6 Jul 2022

Cited by 2 | Viewed by 2594

Abstract

Numerous studies have been reported in the published literature on analytical solutions for a vertically loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. This study presents an analytical model based [...] Read more.

Numerous studies have been reported in the published literature on analytical solutions for a vertically loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. This study presents an analytical model based on the energy-based approach to obtain displacements in an axially loaded pile embedded in multi-layered soil considering soil non-linearity. The developed analytical model incorporating Euler-Bernoulli beam theory proved to be an effective way in estimating the load-displacement responses of piles embedded in multi-layered non-linear elastic soil strata. The differential equations are solved analytically and numerically using the variational principle of mechanics. A parametric study investigated the effect of explicit incorporation of soil properties and layering in order to understand the importance of predicting appropriate pile displacement responses in linear elastic soil system. It is clear from the results that the analyses which consider the soil as a single homogeneous layer will not be able to produce an accurate estimation of the pile stiffnesses. Therefore, it is highly important to account for the effect of soil layering and the non-linear response. The pile displacement response is obtained using the software MATLAB R2019a and the results from the energy-based method are compared with those obtained from the field test data as well as the Finite Element Analysis (FEA) based on the software ANSYS 2019R3. The non-linear elastic constitutive relationship which described the variation of secant shear modulus with strain through a power law has shown reasonably accurate predictions when compared to the published field test data and the FEA. The developed mathematical framework is also more computationally efficient than the three-dimensional (3D) FEA. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>An axially loaded pile in an isotropic non-linear elastic medium.</p> Full article ">Figure 2
<p>Stresses and displacements within a soil continuum (<b>a</b>) stresses within a soil continuum and (<b>b</b>) displacements within a soil continuum.</p> Full article ">Figure 3
<p>Discretization of the soil (<b>a</b>) top view and (<b>b</b>) front view (adapted from Basu et al. [<a href="#B7-geotechnics-02-00027" class="html-bibr">7</a>]).</p> Full article ">Figure 4
<p>The variation of normalizing shear secant with logarithmic strain <span class="html-italic">ε_q</span> or normalized displacement (adapted from Atkinson [<a href="#B33-geotechnics-02-00027" class="html-bibr">33</a>]).</p> Full article ">Figure 5
<p>Degradation of tangent with deviatoric strain (Adapted from Dasari [<a href="#B50-geotechnics-02-00027" class="html-bibr">50</a>]).</p> Full article ">Figure 6
<p>Logarithmic scale of degradation of tangent stiffness with strain level (Adapted from Osman et al. 2007 [<a href="#B39-geotechnics-02-00027" class="html-bibr">39</a>] after Dasari [<a href="#B51-geotechnics-02-00027" class="html-bibr">51</a>]).</p> Full article ">Figure 7
<p>Flowchart depicting the iterative solution procedure (Adapted from Fidel [<a href="#B30-geotechnics-02-00027" class="html-bibr">30</a>] after Basu et al. [<a href="#B7-geotechnics-02-00027" class="html-bibr">7</a>]).</p> Full article ">Figure 8
<p>(<b>a</b>) Normalized pile head stiffness versus <span class="html-italic">h/L</span> (with and <span class="html-italic">E_p/G</span>₀₂ = 1000) and (<b>b</b>) Normalized pile head stiffness versus <span class="html-italic">E_p/G</span>₀₂ (with <span class="html-italic">h</span> = 0.5 L).</p> Full article ">Figure 9
<p>(<b>a</b>) Normalized pile head stiffness as a function of the pile slenderness ratio <span class="html-italic">L/D</span> with <span class="html-italic">E_p/G</span> =1000 (for all the three cases). (<b>b</b>) Normalized pile head stiffness as a function of <span class="html-italic">E_p/G</span> with <span class="html-italic">L/D</span> = 25 (for all the three cases).</p> Full article ">Figure 10
<p>The soil profile and elastic properties of each layer (adapted from Russo [<a href="#B51-geotechnics-02-00027" class="html-bibr">51</a>]).</p> Full article ">Figure 11
<p>Response of the pile due to axial load.</p> Full article ">Figure 12
<p>Pile Profile at TCD in Dublin.</p> Full article ">Figure 13
<p>(<b>a</b>) Variation of soil stiffness with strains for Upper Brown Boulder Clay. (<b>b</b>) Variation of soil stiffness with strains for Upper Black Boulder Clay.</p> Full article ">Figure 13 Cont.
<p>(<b>a</b>) Variation of soil stiffness with strains for Upper Brown Boulder Clay. (<b>b</b>) Variation of soil stiffness with strains for Upper Black Boulder Clay.</p> Full article ">Figure 14
<p>Response of the axially loaded pile head versus the axial load.</p> Full article ">Figure 15
<p>(<b>a</b>) Input stress–strain relationship curve of soil layer 1 for the software ANSYS. (<b>b</b>) Input stress–strain relationship curve of soil layer 2 for the software ANSYS.</p> Full article ">Figure 16
<p>A mesh representation of the FEM Model (ANSYS 2019 R3).</p> Full article ">Figure 17
<p>Pile displacements resulting from FEM Analysis.</p> Full article ">

31 pages, 6494 KiB  

Open AccessArticle

Dynamic Response of Lining Structure in a Long Tunnel with Different Adverse Geological Structure Zone Subjected to Non-Uniform Seismic Load

by Yongqiang Zhou, Hongchao Wang, Dingfeng Song, Qian Sheng, Xiaodong Fu, Haifeng Ding, Shaobo Chai and Wei Yuan

Energies 2022, 15(13), 4599; https://doi.org/10.3390/en15134599 - 23 Jun 2022

Cited by 4 | Viewed by 1695

Abstract

The damage of a long tunnel is found in parts with an adverse geological structure zone under an earthquake. The phenomenon is normally the consequence of a non-uniform seismic load. Thus, to reveal the mechanism of the phenomenon, the dynamic response of the [...] Read more.

The damage of a long tunnel is found in parts with an adverse geological structure zone under an earthquake. The phenomenon is normally the consequence of a non-uniform seismic load. Thus, to reveal the mechanism of the phenomenon, the dynamic response of the lining structure in a long tunnel passing through an adverse geological structure zone subjected to a non-uniform seismic load is mainly studied in this paper. Firstly, based on the random ground motion synthesis theory, the non-uniform ground motion acceleration–time history curves that reflect local site effects, such as traveling wave effects and attenuation effects, are generated. Secondly, the behavior of the tunnel with a different adverse geological structure zone (including different inclinations, thicknesses, and lithologies) under non-uniform seismic input is studied. Then, the impact of the different adverse geological structure zone on the internal force and safety factor of the tunnel lining is analyzed. Finally, the failure characteristics of the lining structure in the tunnel crossing through the adverse geological structure zone subjected to a non-uniform seismic load are revealed. The results show that the seismic dynamic responses significantly increase under non-uniform seismic input compared with the results under uniform seismic input, and the dynamic responses distribution along the tunnel axial is distinctly different under non-uniform seismic input. The inclination and thickness of the adverse geological structure zone have a significant influence on the internal force and safety factor of the tunnel lining, while the lithology mainly acts around the adverse geological structure zone. When the inclination angle of the adverse geological structure zone is 45°, a large number of compression-bending cracks appear in the entrance and exit sections of the tunnel, and the tunnel is in the most dangerous state. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Adverse geological structure zone and numerical model of the tunnel.</p> Full article ">Figure 2
<p>Flow chart of synthesis method for non-uniform ground motion acceleration.</p> Full article ">Figure 3
<p>Acceleration–time history curves of non-uniform seismic load.</p> Full article ">Figure 4
<p>The input method of non-uniform seismic.</p> Full article ">Figure 5
<p>Bending moment of lining of the tunnel passing through adverse geological structure zone with different inclinations for each cross section along the tunnel axial direction. (It is noted that “No” represents that there is no adverse geological structure zone. Consistency means uniform seismic input and inconsistency means non-uniform seismic input).</p> Full article ">Figure 5 Cont.
<p>Bending moment of lining of the tunnel passing through adverse geological structure zone with different inclinations for each cross section along the tunnel axial direction. (It is noted that “No” represents that there is no adverse geological structure zone. Consistency means uniform seismic input and inconsistency means non-uniform seismic input).</p> Full article ">Figure 6
<p>Bending moment of the lining monitoring points of the tunnel passing through adverse geological structure zone with different inclinations along the tunnel axial direction.</p> Full article ">Figure 6 Cont.
<p>Bending moment of the lining monitoring points of the tunnel passing through adverse geological structure zone with different inclinations along the tunnel axial direction.</p> Full article ">Figure 7
<p>Bending moment of lining of the tunnel passing through adverse geological structure zone with different thicknesses for cross section at y = 500 m.</p> Full article ">Figure 8
<p>Bending moment of the lining monitoring points of the tunnel passing through adverse geological structure zone with different thicknesses along the tunnel axial direction.</p> Full article ">Figure 8 Cont.
<p>Bending moment of the lining monitoring points of the tunnel passing through adverse geological structure zone with different thicknesses along the tunnel axial direction.</p> Full article ">Figure 9
<p>Bending moment of the lining monitoring points of the tunnel passing through adverse geological structure zone with different lithologies.</p> Full article ">Figure 10
<p>Shear force of lining of the tunnel passing through adverse geological structure zone with different inclinations for each cross section along the tunnel axial direction.</p> Full article ">Figure 10 Cont.
<p>Shear force of lining of the tunnel passing through adverse geological structure zone with different inclinations for each cross section along the tunnel axial direction.</p> Full article ">Figure 11
<p>Shear force of the lining monitoring points of the tunnel passing through adverse geological structure zone with different inclinations along the tunnel axial direction.</p> Full article ">Figure 11 Cont.
<p>Shear force of the lining monitoring points of the tunnel passing through adverse geological structure zone with different inclinations along the tunnel axial direction.</p> Full article ">Figure 12
<p>Shear force of lining of the tunnel passing through adverse geological structure zone with different thicknesses for cross section at y = 500 m.</p> Full article ">Figure 13
<p>Shear force of the lining monitoring points of the tunnel passing through adverse geological structure zone with different thicknesses along the tunnel axial direction.</p> Full article ">Figure 13 Cont.
<p>Shear force of the lining monitoring points of the tunnel passing through adverse geological structure zone with different thicknesses along the tunnel axial direction.</p> Full article ">Figure 14
<p>Shear force of the lining monitoring points of the tunnel passing through adverse geological structure zone with different lithologies.</p> Full article ">Figure 15
<p>Safety factor distribution of cross section at y = 500 m.</p> Full article ">Figure 15 Cont.
<p>Safety factor distribution of cross section at y = 500 m.</p> Full article ">Figure 16
<p>Schematic diagram of lining failure crossing different inclinations of adverse geological structure zone at different sections along the tunnel axis.</p> Full article ">Figure 17
<p>Schematic diagram of longitudinal cracks along the axial lining of the tunnel crossing different inclinations of adverse geological structure zones.</p> Full article ">

21 pages, 8075 KiB  

Open AccessArticle

Design of a Biaxial Laminar Shear Box for 1g Shaking Table Tests

by Francesco Castelli, Salvatore Grasso, Valentina Lentini and Maria Stella Vanessa Sammito

Geotechnics 2022, 2(2), 467-487; https://doi.org/10.3390/geotechnics2020023 - 16 Jun 2022

Cited by 3 | Viewed by 2551

Abstract

In this paper, the design of a new laminar shear box at the Laboratory of Earthquake Engineering and Dynamic Analysis (L.E.D.A.) of the University of Enna “Kore” (Sicily, Italy), is presented. The laminar box has been developed to investigate the liquefaction phenomenon and [...] Read more.

In this paper, the design of a new laminar shear box at the Laboratory of Earthquake Engineering and Dynamic Analysis (L.E.D.A.) of the University of Enna “Kore” (Sicily, Italy), is presented. The laminar box has been developed to investigate the liquefaction phenomenon and to validate advanced numerical models and/or the numerical approaches assessed to simulate and prevent related effects. The first part of the paper describes in detail the types of soil containers that have been used in the last three decades around the world. Particular attention is paid to laminar shear box and liquefaction studies. Moreover, the most important factors that affect the performance of a laminar shear box are reported. The last part of the paper describes components, properties, and design advantages of the new laminar shear box for 1g shaking table tests at L.E.D.A. The new laminar box has a rectangular cross section and consists of 16 layers. Each layer is composed of two frames: an inner frame and an outer frame. The inner frame has an internal dimension of 2570 mm by 2310 mm, while the outer frame has an internal dimension of 2700 mm by 2770 mm. Between the layers, there is a 20 mm gap, making the total height 1600 mm. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>View of the model: (<b>a</b>) before shaking, (<b>b</b>) after shaking (From [<a href="#B39-geotechnics-02-00023" class="html-bibr">39</a>]; modified).</p> Full article ">Figure 2
<p>General view of the experimental test (From [<a href="#B40-geotechnics-02-00023" class="html-bibr">40</a>]; modified).</p> Full article ">Figure 3
<p>Rigid box with absorbent boundaries (From [<a href="#B42-geotechnics-02-00023" class="html-bibr">42</a>]; modified).</p> Full article ">Figure 4
<p>Schematic diagram of rigid container with hinged end-walls (from [<a href="#B29-geotechnics-02-00023" class="html-bibr">29</a>]; modified).</p> Full article ">Figure 5
<p>General view of the shear stack (From [<a href="#B5-geotechnics-02-00023" class="html-bibr">5</a>]; modified).</p> Full article ">Figure 6
<p>Active boundaries container (From [<a href="#B29-geotechnics-02-00023" class="html-bibr">29</a>]; modified).</p> Full article ">Figure 7
<p>General view of the laminar box (From [<a href="#B28-geotechnics-02-00023" class="html-bibr">28</a>]; modified).</p> Full article ">Figure 8
<p>General view of the laminar box (From [<a href="#B25-geotechnics-02-00023" class="html-bibr">25</a>]; modified).</p> Full article ">Figure 9
<p>General view of the laminar box (From [<a href="#B27-geotechnics-02-00023" class="html-bibr">27</a>]; modified).</p> Full article ">Figure 10
<p>(<b>a</b>) Laminae (<b>b</b>) skeleton for laminae (From [<a href="#B20-geotechnics-02-00023" class="html-bibr">20</a>]; modified).</p> Full article ">Figure 11
<p>Laminar box system (From Thevanayagam et al. [<a href="#B57-geotechnics-02-00023" class="html-bibr">57</a>]; modified).</p> Full article ">Figure 12
<p>General view of the laminar container (From [<a href="#B36-geotechnics-02-00023" class="html-bibr">36</a>]; modified).</p> Full article ">Figure 13
<p>General view of the laminar container (From Jafarzadeh [<a href="#B30-geotechnics-02-00023" class="html-bibr">30</a>]; modified).</p> Full article ">Figure 14
<p>Schematic drawings of the biaxial laminar box (From [<a href="#B60-geotechnics-02-00023" class="html-bibr">60</a>]; modified): (<b>a</b>) top view and (<b>b</b>) side view.</p> Full article ">Figure 15
<p>Laboratory of Earthquake Engineering and Dynamic Analysis (L.E.D.A.) of “Kore” University of Enna (Sicily, Italy): (<b>a</b>) external view; (<b>b</b>) internal view (From [<a href="#B62-geotechnics-02-00023" class="html-bibr">62</a>]).</p> Full article ">Figure 16
<p>Plan view of the shaking tables system (From [<a href="#B62-geotechnics-02-00023" class="html-bibr">62</a>]).</p> Full article ">Figure 17
<p>Photographic view of the shaking tables system (From [<a href="#B62-geotechnics-02-00023" class="html-bibr">62</a>]).</p> Full article ">Figure 18
<p>Isometric view of the inner and outer frames.</p> Full article ">Figure 19
<p>Isometric view of the rigid steel walls.</p> Full article ">Figure 20
<p>Plan view of the steel frame.</p> Full article ">Figure 21
<p>Plan view of the laminar shear box: (<b>a</b>) back view; (<b>b</b>) right view; (<b>c</b>) front view; (<b>d</b>) left view.</p> Full article ">Figure 22
<p>Profile views of the laminar shear box: (<b>a</b>) back view; (<b>b</b>) right view; (<b>c</b>) front view; (<b>d</b>) left view.</p> Full article ">Figure 22 Cont.
<p>Profile views of the laminar shear box: (<b>a</b>) back view; (<b>b</b>) right view; (<b>c</b>) front view; (<b>d</b>) left view.</p> Full article ">Figure 23
<p>(<b>a</b>) The isometric and (<b>b</b>) 3D views of the laminar shear box.</p> Full article ">Figure 24
<p>Laminar shear box at the Laboratory of Earthquake engineering and Dynamic Analysis (L.E.D.A.).</p> Full article ">

23 pages, 3730 KiB  

Open AccessArticle

Analytical Approach Based on Full-Space Synergy Technology to Optimization Support Design of Deep Mining Roadway

by Shike Zhang and Shunde Yin

Minerals 2022, 12(6), 746; https://doi.org/10.3390/min12060746 - 12 Jun 2022

Cited by 4 | Viewed by 1925

Abstract

The stability of surrounding rock is the basic guarantee of underground space engineering safety. The large deformation of a roadway’s surrounding rock is a very common phenomenon during the underground excavation of coal mine roadways or coal mining, especially in deep soft rock [...] Read more.

The stability of surrounding rock is the basic guarantee of underground space engineering safety. The large deformation of a roadway’s surrounding rock is a very common phenomenon during the underground excavation of coal mine roadways or coal mining, especially in deep soft rock mining roadways. With the increase in mining depth and mining stress, it is very important to prevent disasters caused by surrounding rock deformation. This work aims to conduct an optimization design of roadway support for deep soft rock in coal mines using a full-space synergy control technology. FLAC3D-based orthogonal numerical experiments are adopted to study the influence of bolt parameters and plastic yield zone variation on the deformation of roadway surrounding rock, which provides a basis for optimizing the support design of coal mine roadways. According to the results of the numerical analysis, the optimal support parameters are determined as 20 mm, 2.2 m and 700–900 mm for diameter, length and interval of the bolt, respectively. Finally, the determined bolt-shotcrete net beam support scheme from the full-space synergy control idea is used in a study case. Results illustrate that this study can provide reliable guidance for the stability control of deep soft rock roadways in mining fields under high stress, and it can work well to keep the surrounding rock deformation within the safe limits. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>The comprehensive histogram of No. 3 coal seam and rock strata.</p> Full article ">Figure 2
<p>The roadway roof fall and flow floor heave with rock squeezing.</p> Full article ">Figure 3
<p>The optimization process of roadway support mode and parameters.</p> Full article ">Figure 4
<p>The mechanical representation of the fully anchored reinforcement element system.</p> Full article ">Figure 5
<p>The mechanical model of the improved element.</p> Full article ">Figure 6
<p>The boundary condition of numerical calculation model and roadway geometric size.</p> Full article ">Figure 7
<p>The three-dimensional numerical model based on FLAC3D.</p> Full article ">Figure 8
<p>Deformation of roadway surrounding rock with excavation length without support.</p> Full article ">Figure 9
<p>The variation curve of roadway convergence under the different influencing factors. (<b>a</b>) Bolt diameter influence; (<b>b</b>) Bolt length influence; (<b>c</b>) Bolt interval influence; (<b>d</b>) Pretension influence.</p> Full article ">Figure 10
<p>The variation of plastic zone size of surrounding rock under the different factors. (<b>a</b>) Bolt diameter influence; (<b>b</b>) Bolt length influence; (<b>c</b>) Bolt interval influence; (<b>d</b>) Pretension influence.</p> Full article ">Figure 11
<p>FLAC3D model of bolt-shotcrete net combined support.</p> Full article ">Figure 12
<p>Roof and floor displacement contour of test roadway at an excavation depth of 12 m.</p> Full article ">Figure 13
<p>Two sides displacement contour of the test roadway at an excavation depth of 12 m.</p> Full article ">Figure 14
<p>The plastic yield zone of roadway surrounding rock at an excavation length of 12 m.</p> Full article ">Figure 15
<p>Bolt-shotcrete net support structure of the test roadway (mm).</p> Full article ">

15 pages, 5741 KiB  

Open AccessArticle

Effect of the Particle Size Composition and Dry Density on the Water Retention Characteristics of Remolded Loess

by Xin-Qing Wang, Xiao-Chao Zhang, Xiang-Jun Pei and Guo-Feng Ren

Minerals 2022, 12(6), 698; https://doi.org/10.3390/min12060698 - 31 May 2022

Cited by 3 | Viewed by 2726

Abstract

The experimental study on the water-holding characteristics of remolded loess was carried out, revealing the variation of water-holding characteristics with particle size composition and dry density. The results show that the air-entry value is positively correlated with the silt-sized content and negatively correlated [...] Read more.

The experimental study on the water-holding characteristics of remolded loess was carried out, revealing the variation of water-holding characteristics with particle size composition and dry density. The results show that the air-entry value is positively correlated with the silt-sized content and negatively correlated with the sand-sized content. During the dehumidification of the specimens at a fixed dry density, when the air-entry value is between 9 and 10 Kpa, it is strongly influenced by the silt-sized content; however, beyond 10 Kpa, the sand-sized content is an important influencing factor. Changes in particle size composition have less influence on the residual water content. There is a non-linear relationship between the particle size composition and the slope λ of the dehumidification curve in the transition zone. Air-entry values, residual water content, saturated volumetric water content, and λ correlate well with dry density. Simulation tests were carried out using two power function models, including three variables. It was found that the VG model is a better fit than the Gardner model. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Geographical location of the sampling point.</p> Full article ">Figure 2
<p>Particle size distribution of Yan’an Loess samples.</p> Full article ">Figure 3
<p>Compaction curve for the Yan’an loess.</p> Full article ">Figure 4
<p>(<b>a</b>) Geotechnical sieve; (<b>b</b>) oedometer-type pressure plate SWCC apparatus.</p> Full article ">Figure 5
<p>S0–S5 particle size characteristics of sample. (<b>a</b>) Particle size distribution curves of remolded loess samples; (<b>b</b>) cumulative particle size distribution curves of remolded loess samples.</p> Full article ">Figure 6
<p>SWCC of loess samples. (<b>a</b>) Loess samples with different particle size compositions; (<b>b</b>) loess samples with different dry densities.</p> Full article ">Figure 7
<p>(<b>a</b>) Correlation between air-entry value and sand-sized content; (<b>b</b>) correlation between air-entry value and silt-sized content; (<b>c</b>) relationship between air-entry value and sand-sized and silt-sized content; (<b>d</b>) single-factor correlation between air-entry value and clay-sized content.</p> Full article ">Figure 8
<p>(<b>a</b>) Correlation between residual water content and sand-sized content; (<b>b</b>) correlation between residual water content and silt-sized content.</p> Full article ">Figure 9
<p>(<b>a</b>) Correlation between λ and sand-sized content; (<b>b</b>) correlation between λ and silt-sized content; (<b>c</b>) correlation between drying-cycle slope (λ) and clay-sized content.</p> Full article ">Figure 10
<p>Correlation between SWCC parameters and dry density. (<b>a</b>) Relationship between value of air-entry suction, VWC and dry density. (<b>b</b>) Relationship between residual water content, λ and dry density.</p> Full article ">Figure 11
<p>Experimental data and simulated SWCC of loess samples with different particle size compositions.</p> Full article ">Figure 12
<p>Experimental data and simulated SWCC of loess samples with different dry densities.</p> Full article ">

21 pages, 14252 KiB  

Open AccessArticle

Spatial Distribution Characteristics of Plastic Failure and Grouting Diffusion within Deep Roadway Surrounding Rock under Three-Dimensional Unequal Ground Stress and Its Application

by Yaoguang Huang, Wanxia Yang, Yangyang Li and Weibin Guo

Minerals 2022, 12(3), 296; https://doi.org/10.3390/min12030296 - 26 Feb 2022

Cited by 11 | Viewed by 2336

Abstract

To explore the bolt-grouting method of the deep roadway under three-dimensional unequal ground stress, a unidirectional coupling model of surrounding rock plastic failure and grouting diffusion considering the influence of excavation disturbance stress was established. Spatial evolution characteristics of plastic failure and grouting [...] Read more.

To explore the bolt-grouting method of the deep roadway under three-dimensional unequal ground stress, a unidirectional coupling model of surrounding rock plastic failure and grouting diffusion considering the influence of excavation disturbance stress was established. Spatial evolution characteristics of plastic failure and grouting diffusion, and the impact of the spacing and row spacing of grouting bolts/cables on grout diffusion, were simulated by using the numerical method. The results revealed that the horizontal ground stress perpendicular to the axial direction of the roadway was the main factor inducing roadway damage. Moreover, the more significant the difference of the ground stress in three directions, the larger the plastic zone of the roof corner and floor corner of the roadway. Under different lateral pressure coefficients, the grout diffused can be approximate ellipsoid and cylinders. Furthermore, the larger the ratio of lateral pressure coefficients perpendicular to and parallel to the axial direction of roadway, the larger the diffusion length of grout in each spatial direction in the surrounding rock. In bolt-grouting support, the length of the grouting bolts/cables should be greater than the plastic zone of the surrounding rock, and the optimal relationship between their spacing and row spacing and diffusion length of grout is determined. The research results were applied in the bolt-grouting engineering for the three-level main roadway in the Haizi Coal Mine, and a good support effect was achieved. This can provide technical guidance and a method of reference for the design and parameter optimization of bolt-grouting support for roadways under deep high ground stress. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Unidirectional coupling numerical model.</p> Full article ">Figure 2
<p>Distribution characteristics of plastic failure of roadway surrounding rock. (<b>a</b>) Plastic zone on <span class="html-italic">xz</span> plane, (<b>b</b>) plastic zone on <span class="html-italic">yz</span> plane, (<b>c</b>) plastic zone on <span class="html-italic">xy</span> plane. (a₁) <span class="html-italic">λ_{x =}</span> 1, <span class="html-italic">λ_y</span> = 1; (a₂) <span class="html-italic">λ_x</span> = 2, <span class="html-italic">λ_y</span> = 2; (a₃) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y</span> = 3; (a₄) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y</span> = 0.75; (a₅) <span class="html-italic">λ_x</span> = 2, <span class="html-italic">λ_y</span> = 0.75; (a₆) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y</span> = 0.75; (a₇) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 1; (a₈) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 2; (a₉) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 3; (b₁) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y</span> = 1; (b₂) <span class="html-italic">λ_x</span> = 2, <span class="html-italic">λ_y</span> = 2; (b₃) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y</span> = 3; (b₄) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y</span> = 0.75; (b₅) <span class="html-italic">λ_x</span> = 2, <span class="html-italic">λ_y</span> = 0.75; (b₆) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y</span> = 0.75; (b₇) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 1; (b₈) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 2; (b₉) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 3; (c₁) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y</span> = 1; (c₂) <span class="html-italic">λ_x</span> = 2, <span class="html-italic">λ_y</span> = 2; (c₃) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y</span> = 3; (c₄) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y</span> = 0.75; (c₅) <span class="html-italic">λ_x</span> = 2, <span class="html-italic">λ_y</span> = 0.75; (c₆) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y</span> = 0.75; (c₇) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 1; (c₈) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 2; (c₉) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 3.</p> Full article ">Figure 3
<p>Plastic zone of surrounding rock in different locations of the roadway. (<b>a</b>) <span class="html-italic">λ</span><span class="html-italic">_x</span> = <span class="html-italic">λ_y</span>; (<b>b</b>) <span class="html-italic">λ_x</span> &gt; <span class="html-italic">λ_y</span>, <span class="html-italic">λ_y =</span> 0.75; (<b>c</b>) <span class="html-italic">λ_x</span> &lt; <span class="html-italic">λ_y</span>, <span class="html-italic">λ_x =</span> 0.75.</p> Full article ">Figure 4
<p>Diffusion morphology of grout under different lateral coefficients. (<b>a</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y =</span> 3; (<b>b</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y</span> = 0.75; (<b>c</b>) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y</span> = 3.</p> Full article ">Figure 5
<p>Spatial distribution characteristics of grout pressure head. (<b>a</b>) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y =</span> 1; (<b>b</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y =</span> 3; (<b>c</b>) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y =</span> 1; (<b>d</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y =</span> 3; (<b>e</b>) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y =</span> 1; (<b>f</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y =</span> 3; (<b>g</b>) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y =</span> 0.75; (<b>h</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y =</span> 0.75; (<b>i</b>) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y =</span> 0.75; (<b>j</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y =</span> 0.75; (<b>k</b>) <span class="html-italic">λ_x</span> = 1, <span class="html-italic">λ_y =</span> 0.75; (<b>l</b>) <span class="html-italic">λ_x</span> = 3, <span class="html-italic">λ_y =</span> 0.75; (<b>m</b>) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y =</span> 1; (<b>n</b>) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y =</span> 3; (<b>o</b>) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y =</span> 1; (<b>p</b>) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y =</span> 3; (<b>q</b>) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y =</span> 1; (<b>r</b>) <span class="html-italic">λ_x</span> = 0.75, <span class="html-italic">λ_y =</span> 3.</p> Full article ">Figure 6
<p>Cut-off diagram of diffusion length of grout.</p> Full article ">Figure 7
<p>Change curve of grout pressure head with distance from the grouting borehole surface. (<b>a</b>) <span class="html-italic">λ_x</span> = <span class="html-italic">λ_y</span>, vertical borehole in <span class="html-italic">x</span>-direction; (<b>b</b>) <span class="html-italic">λ_x</span> = <span class="html-italic">λ_y</span>, vertical borehole in <span class="html-italic">y</span>-direction; (<b>c</b>) <span class="html-italic">λ_x</span> = <span class="html-italic">λ_y</span>, parallel borehole in <span class="html-italic">z</span>-direction; (<b>d</b>) <span class="html-italic">λ_x</span> &gt; <span class="html-italic">λ_y</span>, vertical borehole in <span class="html-italic">x</span>-direction; (<b>e</b>) <span class="html-italic">λ_x</span> &gt; <span class="html-italic">λ_y</span>, vertical borehole in <span class="html-italic">y</span>-direction; (<b>f</b>) <span class="html-italic">λ_x</span> &gt; <span class="html-italic">λ_y</span>, parallel borehole in <span class="html-italic">z</span>-direction; (<b>g</b>) <span class="html-italic">λ_x</span> &lt; <span class="html-italic">λ_y</span>, vertical borehole in <span class="html-italic">x</span>-direction; (<b>h</b>) <span class="html-italic">λ_x</span> &lt; <span class="html-italic">λ_y</span>, vertical borehole in <span class="html-italic">y</span>-direction; (<b>i</b>) <span class="html-italic">λ_x</span> &lt; <span class="html-italic">λ_y</span>, parallel borehole in <span class="html-italic">z</span>-direction.</p> Full article ">Figure 8
<p>Diffusion length of grout under different lateral pressure coefficients. (<b>a</b>) Diffusion range of grout on <span class="html-italic">yz</span> plane; (<b>b</b>) diffusion range of grout on <span class="html-italic">xz</span> plane; (<b>c</b>) diffusion range of grout on <span class="html-italic">xy</span> plane.</p> Full article ">Figure 9
<p>Grouting bolt layout and grout diffusion effect in cross-section (i.e., <span class="html-italic">xz</span> plane) of roadway. (<b>a</b>) Spacing 2.68 m; (<b>b</b>) spacing 1.79 m; (<b>c</b>) spacing 1.53 m; (<b>d</b>) spacing 1.34 m.</p> Full article ">Figure 10
<p>Grouting bolt layout and grout diffusion effect in horizontal and vertical longitudinal section (i.e., <span class="html-italic">xy</span> plane and <span class="html-italic">yz</span> plane) of roadway. (<b>a</b>) Row spacing of 2.0 m; (<b>b</b>) row spacing of 2.5 m; (<b>c</b>) row spacing of 3.0 m; (<b>d</b>) row spacing of 3.5 m.</p> Full article ">Figure 11
<p>Numerical model and plastic failure characteristics of the three-level main roadway. (<b>a</b>) Numerical model; (<b>b</b>) spatial distribution of plastic failure; (<b>c</b>) plastic zone in <span class="html-italic">yz</span> plane; (<b>d</b>) plastic zone in <span class="html-italic">xz</span> plane; (<b>e</b>) plastic zone in <span class="html-italic">xy</span> plane.</p> Full article ">Figure 12
<p>Bolt-grouting support scheme for roadway. 1—Sprayed concrete; 2—<span class="html-italic">Φ</span>22 × <span class="html-italic">L</span> 2000 mm high-strength resin bolt; 3—grouting bolt.</p> Full article ">Figure 13
<p>Gout diffusion effect within surrounding rock after grouting. (<b>a</b>) Cross section (<span class="html-italic">xz</span> plane) of roadway; (<b>b</b>) vertical section (<span class="html-italic">yz</span> plane) of roadway; (<b>c</b>) vertical section (<span class="html-italic">yx</span> plane) of roadway.</p> Full article ">Figure 14
<p>Deformation and convergence of roadway surrounding rock. (<b>a</b>) Roadway rib. (<b>b</b>) roadway roof and floor.</p> Full article ">

20 pages, 12799 KiB  

Open AccessArticle

A New Load-Transfer Factor to the Slipping Analytical Formulation in Axially Loaded Piles

by Kelvin Lo, Erwin Oh, Darren Newell and Choo Yong

Geotechnics 2022, 2(1), 171-190; https://doi.org/10.3390/geotechnics2010008 - 17 Feb 2022

Viewed by 2491

Abstract

The load-transfer factor ($\zeta$) in the concentric cylinder approach is often used in analytical formulation in axially loaded piles. The factor is a constant value (in a given pile slenderness ratio and soil condition) devised under the elastic and ‘pre-failure’ perfect [...] Read more.

The load-transfer factor ($\zeta$) in the concentric cylinder approach is often used in analytical formulation in axially loaded piles. The factor is a constant value (in a given pile slenderness ratio and soil condition) devised under the elastic and ‘pre-failure’ perfect pile–soil bonding conditions (a non-slip analytical model). Given most numerical methods have already considered the pile–soil slipping in the ‘pre-failure’ stage, the limitations of non-slip analytical models have recently been discussed, and slipping analytical models have been recommended. Therefore, this research aims to investigate the load-transfer factor in slipping analytical models. This paper reviews that the factor in slipping analytical models is only constant in linear elastic and some Gibson soil conditions. Beyond these conditions, the factor varies as the pile-head load increases in some cohesionless soils. Adopting the existing constant factor in slipping analytical models will deviate the load–displacement results, as supported by numerical results. Therefore, a new equation is proposed to the load-transfer factor, and a new analytical method is proposed by varying the load-transfer factor during loading for improvement. Results presented in this paper demonstrate improved load–displacement results. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Load transfer factor and pile head stiffness versus relative element size factor.</p> Full article ">Figure 2
<p>Load transfer factor and pile head stiffness, versus <math display="inline"><semantics> <mrow> <mi>H</mi> <mo>/</mo> <mi>L</mi> </mrow> </semantics></math> ratio.</p> Full article ">Figure 3
<p>Load-transfer factors (<math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math>) from <span class="html-italic">PLAXIS 2D</span> versus equivalent <math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math> factors from Randolph [<a href="#B11-geotechnics-02-00008" class="html-bibr">11</a>], for about 100 cases (<math display="inline"><semantics> <mi>L</mi> </semantics></math> = 10–25 m, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> </mrow> </semantics></math> = 20–90, <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">υ</mi> <mi>s</mi> </msub> </mrow> </semantics></math> = 0.2–0.3, <math display="inline"><semantics> <mi>G</mi> </semantics></math> = 3.8–7.7 GPa).</p> Full article ">Figure 4
<p>Pile head load (P) versus pile head displacement (<math display="inline"><semantics> <mrow> <msub> <mi>w</mi> <mi>p</mi> </msub> </mrow> </semantics></math>), comparison of the analytical closed-form solution suggested from Guo [<a href="#B14-geotechnics-02-00008" class="html-bibr">14</a>] and the adopted FE model in elastic soil.</p> Full article ">Figure 5
<p>Load transfer factor versus stress ratio at mid-depth for Models 1 to 3.</p> Full article ">Figure 6
<p>Shear stress and modulus profile along the pile shaft.</p> Full article ">Figure 7
<p>Normalized depth versus shear stress at the pile shaft in a load step, from FE analysis.</p> Full article ">Figure 8
<p>Normalized depth versus shear strain, from FE analysis.</p> Full article ">Figure 9
<p>Load-transfer factor versus stress ratio at the mid-depth level of the pile as head load increases in Models 1, 4, 5.</p> Full article ">Figure 10
<p>Shear stress versus pile–soil relative displacement.</p> Full article ">Figure 11
<p>Soil displacement in the mid-depth level of the pile versus radial distance from pile center, from FE analysis.</p> Full article ">Figure 12
<p>Slip ratio (slip depth to pile length) versus stress ratio at the mid-depth level of the pile.</p> Full article ">Figure 13
<p>(<b>a</b>) Shaft strength profile, (<b>b</b>) transition between elastic and plastic portions.</p> Full article ">Figure 14
<p>Flowchart for the iterative analytical procedure.</p> Full article ">Figure 15
<p>Pile head load versus pile head displacement, improvement of the load–displacement curve (<math display="inline"><semantics> <mrow> <mi>L</mi> <mtext> </mtext> </mrow> </semantics></math>= 30 m, <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>G</mi> <mo>=</mo> <mn>3846</mn> <mtext> </mtext> </mrow> </semantics></math>kPa).</p> Full article ">Figure 16
<p>Coefficient of determination (<math display="inline"><semantics> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> </mrow> </semantics></math>) of load–displacement curves versus pile length (analytical against FE analysis results).</p> Full article ">Figure 17
<p>Change of the <math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>m</mi> </msub> </mrow> </semantics></math> values as head load increases (slenderness ratio: <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> and soil shear modulus: <span class="html-italic">G</span> = 3846 kPa).</p> Full article ">Figure 18
<p>Change of the <math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>m</mi> </msub> </mrow> </semantics></math> values as head load increases (slenderness ratio: <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>60</mn> </mrow> </semantics></math> and soil shear modulus: <span class="html-italic">G</span> = 3846 kPa).</p> Full article ">Figure 19
<p>Change of the <math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>m</mi> </msub> </mrow> </semantics></math> values as head load increases (slenderness ratio: <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>/</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math> and soil shear modulus: <span class="html-italic">G</span> = 7962 kPa).</p> Full article ">Figure 20
<p>Change of the <math display="inline"><semantics> <mrow> <mi>ζ</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>m</mi> </msub> </mrow> </semantics></math> values as head load increases (slenderness ratio: <math display="inline"><semantics> <mrow> <mfrac> <mi>L</mi> <mi>r</mi> </mfrac> <mo>=</mo> <mn>60</mn> </mrow> </semantics></math> and soil shear modulus: <span class="html-italic">G</span> = 7962 kPa).</p> Full article ">Figure 21
<p>Adopted strength profile of the interface in the proposed analytical and FE models.</p> Full article ">Figure 22
<p>Load–displacement curve at the pile head in the case study P1 of Sowa [<a href="#B28-geotechnics-02-00008" class="html-bibr">28</a>].</p> Full article ">Figure 23
<p>Further improvement by using a nonlinear hyperbolic analytical model.</p> Full article ">

10 pages, 2718 KiB  

Open AccessArticle

A Simulation Experimental Study on the Advance Support Mechanism of a Roadway Used with the Longwall Coal Mining Method

by Hui Liu, Zhenhua Jiang, Wansheng Chen, Fei Chen, Fenglin Ma, Donghao Li, Zhaoyang Liu and Hongke Gao

Energies 2022, 15(4), 1366; https://doi.org/10.3390/en15041366 - 14 Feb 2022

Cited by 8 | Viewed by 1637

Abstract

Aiming to advance a support problem for roadways used with the longwall coal mining method, the S1202 working face of the Ningtiaota Coal Mine is taken as the engineering background. The monitoring and analysis of bolt force, anchor cable force and surrounding rock [...] Read more.

Aiming to advance a support problem for roadways used with the longwall coal mining method, the S1202 working face of the Ningtiaota Coal Mine is taken as the engineering background. The monitoring and analysis of bolt force, anchor cable force and surrounding rock deformation of two types of roadways within the whole advance pressure influence range are carried out in the present paper. Based on this, a numerical calculation model consistent with the field is established, and numerical comparison tests under different influencing factors are carried out. The rationality of the numerical test results is verified by using the field monitoring data. At the same time, quantitative evaluation indexes, such as characterization deformation, are established, and the deformation law of roadways surrounding rocks under different advance passive support forces is analyzed. The advance support mechanism of the roadway used with the longwall coal mining method is clarified. The test shows that under the condition of no advance passive support, the maximum characteristic deformation of surrounding rock in the haulage roadway and ventilation roadway is 7.1 cm and 10.1 cm, respectively. The above surrounding rock deformation still meets the requirements of on-site safety production. The research results can provide experimental support for the advance support parameters of the roadway used with the longwall coal mining method. Full article

(This article belongs to the Topic Support Theory and Technology of Geotechnical Engineering)

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Figure 1

Figure 1
<p>Working face parameters and rock stratum histogram.</p> Full article ">Figure 2
<p>Roadway support parameter.</p> Full article ">Figure 3
<p>Roadway surrounding rock monitoring within the advance pressure influence range. (<b>a</b>) Displacement curve of the surrounding rock. (<b>b</b>) Force variation curve of the anchor cable. (<b>c</b>) Force variation curve of the bolt.</p> Full article ">Figure 3 Cont.
<p>Roadway surrounding rock monitoring within the advance pressure influence range. (<b>a</b>) Displacement curve of the surrounding rock. (<b>b</b>) Force variation curve of the anchor cable. (<b>c</b>) Force variation curve of the bolt.</p> Full article ">Figure 4
<p>Numerical calculation model.</p> Full article ">Figure 5
<p>Comparison curve between the numerical test and field test. (<b>a</b>) Deformation of the haulage roadway. (<b>b</b>) Deformation of the ventilation roadway.</p> Full article ">Figure 6
<p>Comparison of the surrounding rock deformation of the haulage roadway in each scheme. (<b>a</b>) Roof and floor convergence deformation. (<b>b</b>) Convergence deformation of the two sides. (<b>c</b>) Comparison of the quantitative evaluation index of each scheme.</p> Full article ">Figure 7
<p>Comparison of the surrounding rock deformation of the ventilation roadway in each scheme. (<b>a</b>) Roof and floor convergence deformation. (<b>b</b>) Convergence deformation of the two sides. (<b>c</b>) Comparison of the quantitative evaluation index of each scheme.</p> Full article ">

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