What Magnitude Of Earthquake Was My Structure Designed For? Naveed Anwar Vice President for Knowledge Transfer, Asian Institute of Technology, Thailand (nanwar@ait.ac.th) Wamiq Ahmed Master Student, Department of Structural Engineering, Asian Institute of Technology, Thailand (wamiqahmad17@gmail.com) ABSTRACT – This article discusses one of the most commonly asked questions by the general public relating to earthquake magnitude that a structure can safely resist. It explains the problems in measuring earthquakes and the large number of variables involved in the interpretation of earthquake hazards. It then presents possible ways in which this question can be answered and proposes site-specific analysis and a performance-based design approach as one of the most effective methods to do so. Understanding the problem One of the questions that the public or clients would often like to know the answer to is: What level of an earthquake or what magnitude of an earthquake is their structure designed for? This seems like a simple and valid question from their point of view, but unfortunately, the structural engineers may not have a clear or simple answer to that. The main reason for asking this question is probably because whenever there is a strong earthquake anywhere in the world, the pictures of destruction like those displayed in Fig.1 are commonly seen. In such pictures, the buildings have either fallen or severely damaged, people have been injured or have lost their lives, or the whole community has been destroyed. This makes the clients or public get worried about the behavior of standing or new structures if a similar earthquake happens in their area, which prompts the question: what magnitude of earthquake the structure can resist? In this article, we are trying to address this question. Fig.1. A view of an earthquake destruction Page 1 of 7 To understand the problem, let’s first talk about one very simple case. Assume that you are interested in reading a book in a dark room. So, you want to buy the light bulb with appropriate wattage to lighten this room. For this, you may need a recommendation from a lighting engineer. Now, it seems like a simple question, and you would assume there would be a simple answer to this. However, instead of providing the expected answer of some bulb specifications, the lighting engineer might ask you for many further details. He might ask questions like how far you will be sitting from the light bulb, will you be facing the light bulb, or will the book be facing the light bulb, how good is your eyesight, what will be the color of the page that you'll be reading, will it be white or black, what will be the font size and so on, before giving you any information you initially requested. All these factors were necessary to ask as they will have an impact on the light coming to the book from the bulb. In the same way, earthquake design also depends upon a multitude of factors without which it will be difficult for any engineer to properly satisfy or answer the concerns of the public and clients. Why do earthquakes happen? Before we delve into answering what level of an earthquake any structure is designed for, first go back to the basics of what causes an earthquake. The reason the earthquake happens is primarily due to the relative movement of faults in tectonic plates. When these faults break, move, or slip against each other, a large amount of energy is released which results in earthquakes. Another important thing about the Moment Magnitude scale is that this scale goes even beyond the logarithmic scale, as shown in Fig.3. Every step in the scale represents about 31 times more energy than the previous value in that scale (USGS) which means that the energy released goes from a very small value initially to billions of times as we go up. Fig.2. World tectonic plates and fault lines As can be seen in Fig.2. there are many plates on earth each of which has its movements that can develop into an earthquake of varying magnitude. Earthquake measurement and perception Once an earthquake happens, then four things can be related to that earthquake event. First is, how an earthquake is measured or what is the measure of an earthquake. The second one is how it is going to be reported in the news and the third is how it was experienced by the people near the earthquake location. Every person’s experience can be different based upon where exactly that person was at the time of seismic activity. A person on the top floor of a tall building, the person standing on the ground floor, or a person in a car, every one of them will have different perceptions of the earthquake. The last point related to an earthquake event is how the structures are designed for it. So, the perception of the earthquake, how it is reported, and how it is measured are all essential in their regard and they also influence how the structures are designed. The measurement of an earthquake is the measurement of energy released at the source of the earthquake. To measure the energy, we put a network of seismographs on the ground which reports the energy level detected when an earthquake event occurs. This energy is then quantified based on a scale that represents the level of energy from minimum zero level to the maximum possible energy that can be generated. The most common scale for this purpose is called the Moment Magnitude scale. When we see any news reporting the magnitude of an earthquake as any number between 0 to 10, that is based on the output of the Moment Magnitude scale. The Richter scale was an earlier version of the same scale, but it could not measure large earthquakes. There are many other types of scales as well which cover the local, body, and surface waves, however, the Moment Magnitude Scale is the most comprehensive measure of the earthquake. Page 2 of 7 Fig.3. Moment magnitude Scale On the other hand, the number of earthquakes that happens corresponding to any energy level reduces as the magnitude level rises. In simple terms, a lot of earthquakes happen with lower magnitude and very few earthquakes happen which are of a higher magnitude. It is assumed that beyond the magnitude 10 levels there is no earthquake computationally possible so that is the maximum limit of the scale. Moreover, a lot of earthquakes can be seen listed on the figure which reflects that this is the scale usually referred to when reporting the earthquake and both designers and clients are concerned about where the design earthquake lies on this scale. Coming to the next point of how the earthquake is reported, let’s again refer to Fig.1 which shows the after-effects of a 6.2 magnitude earthquake that happened in Indonesia. It can be seen that many people died, bodies are still being discovered and it shows the building that is completely collapsed. That is the image that people get of a strong earthquake and it sparks fear in them about their houses and communities., even when their houses might not be in any particular danger. How people feel about the earthquake is another issue entirely and may not exactly go hand in hand with the magnitude of the reported earthquake. The feeling of an earthquake is more related to the shaking of structure or ground under the earthquake. During an earthquake, every person might have differing views on the intensity of the earthquake depending upon where that person was, whether he/she was awake or asleep, moving or standing still, on a tall building or on the ground. All these conditions affect the feeling of shaking experienced by a person and hence change their perceptions of the earthquake. A high magnitude earthquake happening very far from the building may not be felt as strongly as any low magnitude earthquake nearby. The scales like the Modified Mercalli scale and Rossi-Forel scale are used to measure the amount of shaking at a particular location and they range from ‘Not felt’ at one end to ‘Extreme’ at the other end. These scales are all related to how a person feels and not to the earthquake magnitude and are therefore called intensity scales. Fig.4. An example of an intensity scale The building’s modal time period also influences the earthquake motion felt. Some buildings are triggered due to short period earthquakes whereas others are susceptible to long-period earthquakes. In Bangkok a few years back, for example, a building swayed so much so that the occupants had to evacuate the building and the water pipes broke in the elevator shaft, even though the earthquake happened very far in Indonesia. Surprisingly, occupants of other neighboring buildings did not even feel this earthquake. It was mainly because that particular building was susceptible to that particular period of the earthquake. Generally, when people say that the earthquake was mild or strong, it is not based on magnitude but on how they experienced it. Page 3 of 7 How do earthquakes affect structures? How earthquakes affect structure is a complex phenomenon. As mentioned in an example earlier, the same earthquake can have different effects on different structures at the same location. A tall building will respond differently than a short or midrise building, which in turn will respond entirely differently from a single-story building. Conversely, it is also true that the same structures perform differently for different earthquake effects. Structures also perform differently depending on whether the earthquake shock was fast-moving or slow-moving, the frequency content of the earthquake, the type of earthquake waves, and whether the earthquake has a vertical component or not. Each magnitude of earthquake has a different probability of occurrence and a different frequency which needs to be considered as well. The design earthquake loading is derived from several earthquakes from different sources having different magnitudes with different probability of occurrence. All this information is then collected and analyzed for the development of seismic hazard maps by the code authorities or the building officials for each country and locality. How do structural engineers see earthquakes? Structural engineers use the design of earthquake loading and convert that into a numerical input for the structural analysis process. For the most basic analysis, this input could be as simple as an equivalent static force applied at each floor level. Another form of this input is to convert earthquake force into response accelerations for short periods and long periods effects to cover buildings of different heights, stiffnesses, masses, and natural frequencies. Similarly, this input could also be a base acceleration imparted as time history. For more rigorous analysis, we could go for an experimental approach where we shake the scaled-down building model by a simulated ground motion to see the dynamics and even the non-linear effects of an earthquake. We can employ any of these methods while designing and analyzing depending on the type of structure, available tools, and experiences that we have. Most codes let us use all three numerical approaches. However, it must be noted that none of these approaches have a direct correlation with the magnitude of the earthquake. Nevertheless, to get a clear picture of the current state of concepts and methods, some brief descriptions of these three methods are given below. return period and response parameters including short-period response and long-period response. The equivalent force concept and seismic hazard maps Earthquake as response spectrum or acceleration time history In this approach, we start with Newton's law of motion where force is a product of mass and acceleration. Since the earthquake is an acceleration, we can relate the mass of the building with the earthquake to get an equivalent force that can be applied to a structure. There are several equations available in different codes which combine this simple concept with various factors like the R factor, Cd factor et cetera to account for different influences and design methodologies. Response spectrum can also be developed for a particular region and modified by a few factors for the local conditions. It covers a longer range of the initial periods and can be applied to tall and short buildings equally. Fig.5. An example of an equation in ASCE-7-16 As new research and understandings are being included in building codes, these factors are now becoming a more accurate representation of actual seismic loading, albeit increasingly complex to determine. Whatever the form of the equation is, at the root of it is the relation F=ma attempting to convert the acceleration to an equivalent force. Fig.7. Earthquake as response spectrum Similarly, we can also apply seismic shaking on the building by a simulated time history or series of time histories of ground accelerations. We can then let the structure determine the forces itself using the nonlinear dynamic equilibrium equation shown below which incorporates damping and time history of accelerations in it. Fig.6. Single response hazards map (UBC-97) Many of the factors used in the above-mentioned equations require corresponding seismic maps. Fig.6 shows a map developed with the older version of these equations where the countries or the regions are divided into zones from 0 to 4 or 5 indicating the severity of the hazard. A newer version of maps often incorporates more details like the earthquake Page 4 of 7 Nonlinear dynamic equilibrium equation This is a more accurate representation of actual loading and response conditions and from this equation, we can have all forms of outputs like the free vibration, the equilibrium static force mentioned before, the pushover analysis, the response spectrum analysis as well as the time history linear and nonlinear analysis. Fig.8. Earthquake as acceleration time history What happened to the earthquake magnitude question and the possible answers? The magnitude of the earthquake got absorbed in so many factors like hazard maps, ground acceleration, response acceleration, importance factor, structure type, modification factor ‘R’, damping ratios, stiffness assumptions, load combinations, design philosophy, and many others that it is now very hard to correlate the earthquake magnitude we started with to the final design outcome. So, how can we possibly answer our original question? One way to look at it is to say that if you have followed the design codes and design approaches, the possible answer can be that the structure has been designed for the appropriate earthquake magnitude for the location where it is built and it has a reasonable margin of safety against collapse. However, we cannot say exactly which magnitude of the earthquake will collapse the structure. On the other hand, we can try to answer that the structure has been designed for an acceleration of 0.6g or 0.8g, corresponding to a very strong earthquake, with an adequate margin of safety against collapse. It can also be referred to as the hazard map because the acceleration is part of this map, but again this acceleration is not directly related to the earthquake magnitude and hence the question remains. Both answers try to address the question; first in a more general way while the other is more technical. Whether these are enough to satisfy the public, however, cannot be ensured. Page 5 of 7 The seismic design intent in the codes and the performance-based design approach The code-based design approach has a good intent to cover three levels of earthquake loading in design, although not explicitly. It includes service level earthquakes (SLE), moderate level or design level earthquakes, and the maximum considered earthquake (MCE). Performance-based design (PBD), on the other hand, can make the checks at each of the earthquake levels more explicitly. Can performance-based design help to improve the answer to the problem? The answer to this question can surely be in the affirmative. One of the pre-requisites of PBD is a site-specific study through which we can get specific and realistic information about the earthquake hazard at the site of the building. Then we do the initial design of the structure and then we model it so we can check its performance. We do not design the reinforcement to come to one solution but rather we check what has been designed through a more detailed and comprehensive analysis involving explicit evaluation of serviceability and collapse prevention levels. So, what PBD does is that by using a sitespecific study it can correlate the hazard levels with their performance levels making it much easier to determine which hazard will fail the structure. Fig.9. Linking hazards to performance levels The site-specific hazard studies The site-specific study considers all the relevant earthquake sources with their potential maximum magnitude with different return periods. It also considers the attenuation or the effect of that earthquake on the site depending on what is in between and the bedrock structure together with the amplification or the damping effects. This knowledge can help tremendously in determining the hazards for sites that are not generally considered susceptible to earthquakes. For example, buildings in Bangkok were, for a long time, not designed for an earthquake because people believed that since there was no fault nearby, there was no earthquake hazard. However, as the knowledge developed it was realized that earthquakes happening in very far regions like in Myanmar region or the Northern Thailand region, can still affect the buildings in Bangkok, mostly midrise buildings in the range of 25 to 30 floors, due to the soft soil of the bed. magnitude, corresponding to a return period of say 50 years or 2475 years, without any damage thereby satisfying the serviceability and collapse prevention requirements respectively. In this way, the safety of the structure is directly connected to the magnitude, location, and occurrence interval of an earthquake which is difficult to gather from code recommended procedures unless we know a lot of background information on the development of the seismic risk maps. Moreover, through this study, we can see the relative contribution to the total risk at any site from different sources which are located at different locations with different magnitude. This results in a clear understanding of what magnitude of earthquake originating at what distance can cause a critical impact on our structure. Conclusion Providing an answer to the question of ‘which magnitude of earthquake the structure can safely resist’ based solely on design codes can be difficult and inconclusive because code-based seismic maps do not clearly reflect the earthquake’s magnitudes and locations. It is therefore hard to link safety with a particular seismic hazard. By using a site-specific study and performancebased design approach we can overcome this problem by identifying the controlling earthquake for any performance level. This is usually done by looking at the time history response of structure from every earthquake, through which it is easy to identify which maximum response controls the design. Fig.10. An example of de-aggregation of the hazard by Magnitude and Distance From all this data, we have now more or less identified the magnitude of the earthquake for which the structure is primarily designed, including the effects of all other earthquakes that might occur. An alternate answer to the question All the detailed information that we have looked at so far can now help us in coming up with an alternate answer which might be more in line with what the public expected to get. We are now able to provide information about any considered structure in terms of its capability of resisting an earthquake of specific magnitude happening at a location some specific distance away with a specific probability of occurrence. In other words, we can say with confidence that this structure can resist an earthquake of any particular Page 6 of 7 Acknowledgment The authors would like to thank Dr. Salman Ali Suhail, Engr. Ashish Sapkota, the structural engineering team of AIT solutions, and the academic programs of the Asian Institute of Technology for their contributions to publishing this article. References Anwar, N. (2021, July 5). What Magnitude of Earthquake was my Structure designed for? . [Video] YouTube.https://www.youtube.com/watch ?v=Qmmq8-MbBNA&t=610s Anwar.N & Najam.F (2016). Structural CrossSections: Analysis and Design, 1st Edition. Anwar, N. CE 72.52: Advanced Concrete Structures, Asian Institute of Technology, Thailand. Class Lectures. Anwar, N. CE 72.33: Structural Design of tall buildings, Asian Institute of Technology, Thailand. Class Lectures. FEMA 451 B. NEHRP Recommended Provisions for New Buildings and Other Structures: Training and Instructional Materials,2007. ASCE/SEI 7-16, Minimum Design Loads and Associated Criteria for Buildings and Other Structures, 2016. U.S. Geological Survey (USGS) Page 7 of 7