INTRODUCTION
A seismic damage simulation of regional buildings can provide useful information for earthquake disaster prevention and mitigation. The most influential software in the world for such simulation is HAZUS, which was developed by the Federal Emergency Management Agency (FEMA) of the United States (US) (FEMA 1999). In HAZUS, the seismic damage of each building is determined by the intersection of the building capacity curve and the demand spectrum (FEMA 1999). The building capacity curve is obtained through nonlinear static analysis (i.e., first-mode pushover analysis), while the demand spectrum is derived from the 5% damped response spectrum. However, the effects of high-order vibration modes and some characteristics of ground motions (e.g., the near-fault impulse) cannot be taken into consideration when using the HAZUS method (Lu et al. 2014). To overcome the abovementioned problems, the Integrated Earthquake Simulation (IES) by Tokyo University (Sobhaninejad et al. 2011) provides a more reasonable method of seismic damage simulation for regional buildings, which adopts a multi-degree-of-freedom (MDOF) model and nonlinear THA. However, this method significantly increases the computational workload. Hence, only supercomputers have the ability to perform the simulation with IES. In addition, Sobhaninejad¡¯s work focuses on constructing a framework of IES, and the method used to determine the parameters for building models is not provided.
To overcome those problems, a moderate-fidelity model, named the multi-story concentrated-mass shear (MCS) model, and the associated parameter determination approach based on the HAZUS performance database are proposed, with which the seismic responses of each story can be predicted through nonlinear THA. A computer program is developed to implement the simulation. With this program, users can construct numerical models of buildings automatically, select a ground motion of interest, perform nonlinear THA, and observe the simulation results of the whole region. The Tsinghua campus in China has 619 buildings with various structural types. The information of the buildings can be easily accessed. Therefore, the Tsinghua campus is selected to be the case study area to demonstrate the proposed seismic damage simulation. The case study shows that a 40 s nonlinear THA of 619 buildings can be completed in 15 s on a desktop computer. The outcome of this study provides a seismic damage simulation method for regional buildings that balances accuracy and efficiency, which is very important for seismic damage assessment and emergency management of an urban area.
COMPUTATIONAL MODELS
Multi-Story Concentrated-Mass Shear Model
There are numerous buildings in an urban region, so it is very difficult to obtain detailed structural information for every building, such as the reinforcement design of beams, columns and shear walls. Therefore, it is of great importance to establish numerical building models according to some basic and easily accessible information. Meanwhile, the numerical models used should have a reasonable accuracy to simulate the seismic response of buildings. The MCS model is a proper numerical model that satisfies these requirements. In the MCS model, each story of a building is treated as a dynamic degree of freedom (DOF), so the number of DOFs of a building is equal to the number of stories, as shown in Figure 1. The MCS model is a type of MDOF model that can more accurately simulate the nonlinear seismic behavior of low-rise and middle-rise buildings (Lu et al. 2014), compared to the traditional single DOF (SDOF) model in HAZUS.
Figure 1. Multi-story concentrated-mass shear model
The inter-story mechanical behavior of the MCS model can be defined by the backbone curve and the hysteretic curve. The tri-linear backbone curve is adopted as the backbone curve of the MCS model. For the hysteretic curve, three different types of models are adopted to describe the hysteretic behaviors of different types of structures. Specifically, the bilinear elasto-plastic model is suitable for describing steel moment frames (Miranda and Ruiz-Garcia 2002), while the modified-Clough model (Mahin and Lin 1984) is generally used for reinforced concrete (RC) frames for which the flexural failure is significant. For other structures that easily fail by shear, the pinching model (Steelman and Hajjar 2009) is adopted to describe their hysteretic behavior.
Parameter Determination Approach
In the MCS model, the tri-linear backbone curve can be determined by five parameters (Lu et al. 2014). A parameter determination approach is suggested in Lu et al.¡¯s work. In this approach, these five parameters can be determined according to the seismic performance data of typical buildings provided in HAZUS if the structural type, story height, number of stories, construction time and floor area of a building is known. In other words, the numerical model of each building can be easily constructed if the above five basic building properties are available. This method can quickly establish the numerical model for a region with hundreds or thousands of buildings. Detailed parameter determination steps can be accessed in Lu et al. (2014).
Model Validation
A cyclic pushover analysis and a nonlinear THA for a six-story RC frame building are performed to validate the MCS model (Xu et al. 2014). The analysis results (e.g., the time histories of the lateral hysteretic behavior and the top displacement) of the MCS model are compared with those of a refined FE model for the same building, as shown in Figure 2 (Xu et al. 2014). The comparison shows a good agreement between the MCS model and the refined FE model.
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(a) Comparison of the lateral hysteretic properties between the refined FE model and the MCS model on the bottom story |
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(b) Comparison of the top displacement versus time histories between MCS model and the refined FE model |
Figure 2. Validation of the MCS model (Xu et al. 2014)
CASE STUDY: SEISMIC DAMAGE SIMULATION OF BUILDINGS IN TSINGHUA CAMPUS
The Framework of the Seismic Damage Simulation
A computer program is developed to implement the pre-processing, analysis, and post-processing of the regional seismic damage simulation. The program consists of four function modules: (1) determination and editing of the building information, (2) visual selection of ground motion, (3) nonlinear THA of buildings, and (4) visualization of the result of seismic damage simulation, as shown in Figure 3.
Figure 3. Framework of the seismic damage simulation program
Numerical Model Establishment of Buildings
The simulation area is the campus of Tsinghua University, Beijing, China, as shown in Figure 4. According to 3D and 2D maps (Tsinghua University 2014), the geometry properties of the buildings, such as the building shape, floor area and number of stories, can be obtained easily. In addition, to calculate the mechanical properties of the MCS model, a survey of the entire campus is conducted to obtain the structural type, story height and construction time of each building.
Once the above information is obtained, an MCS model for each building can be established through the proposed parameter determination approach. When the textboxes of the basic building information are filled-in, as shown in Figure 5, the inter-story hysteretic parameters as well as the criteria of story drift ratio representing different damage states will be automatically calculated by the program. These automatically generated parameters may be modified manually. When the parameters are changed, the corresponding hysteretic curve shown in the program dialogue (Figure 5) will be updated accordingly, which clearly illustrates how the hysteretic curve is influenced by these parameters. Furthermore, the dynamic properties of building (e.g., the free vibration frequencies and modes) are also calculated automatically by the program to assist in determining whether the parameters of the building are correct or not. For example, if the fundamental period of a three-story masonry structure is greater than 1 s, there may be something wrong with the parameters of the building because this type of building generally cannot be so flexible.
Figure 4. 3D map of the Tsinghua University campus (source: http://map.tsinghua.edu.cn/3d/)
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Figure 5. The parameters of the MCS model for an individual building
Selection of Ground Motions
In the module for the selection of ground motions (Figure 6), several widely used ground motion records (e.g., the El Centro record of Imperial Valley, California, 1940) are readily provided in the program. In addition, user-defined ground motions can be added into the program by providing the file paths of the corresponding ground motion records. The ground motions and their acceleration response spectra can be drawn in different colors so that users can clearly select and compare different ground motions.
Figure 6. Visual selector for seismic waves
Regional Seismic Damage Simulation of Buildings
According to the above MCS models and the selected ground motion, the nonlinear THA of the entire campus is performed. A 40 s ground motion measured in 1999 Taiwan (Chi-Chi) earthquake is selected for demonstration in this section, and the time step is set to a constant, 0.005 s (thus, the total number of computational steps is 8000). There are a total of 619 buildings on the Tsinghua campus. It takes only 15 s to complete the analysis on a desktop computer with a 2.60 GHz Intel G620 CPU, which shows a high computing efficiency of the proposed seismic damage simulation method. Therefore, this program can serve as a useful tool for the quick evaluation of regional seismic damage.
In the visualization module, users can observe the simulation results, including the displacement time-history of each story and the detail damage result of each building on the entire campus, as shown in Figure 7. The damage of each story can be predicted by using the MCS model, which is important in some cases. For example, for some of the classrooms and student apartments, the ground story is used for bicycle parking; therefore, the population of other stories is much larger than the ground story, which implies that a collapse of the other stories will have more casualties than the ground story. Therefore, compared to the SDOF model, which is only able to calculate the damage state of the entire building, the MCS model provides more valuable detailed information for seismic emergency management and loss assessment.
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(a) Displacement time-history of the buildings in the Tsinghua campus |
(b) Detailed damage information of a building |
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(c) Damage and collapse state of the entire campus |
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Figure 7. Visualization of the seismic damage simulation results for the Tsinghua campus
CONCLUSIONS
To balance the efficiency and accuracy of the regional seismic damage simulation for buildings, a moderate-fidelity numerical model for building structures and the associated parameter determination approach based on the HAZUS performance database are proposed. A numerical model for each building can be easily constructed if five basic building properties are available. The seismic response of buildings is simulated through nonlinear THA, and the displacement time-history and damage states of each story can be observed in a visualization module, which provides more detailed information than the results using SDOF models. The case study shows that a 40 s seismic response simulation for the 619 buildings of the Tsinghua campus can be completed in 15 s on a desktop computer, so this method can serve as a useful tool for the quick evaluation of regional seismic damage.
ACKNOWLEDGEMENTS
The authors are grateful for the financial support received from the National Key Technology R&D Program (No. 2013BAJ08B02) and the National Natural Science Foundation of China (No. 51178249).
REFERENCES
FEMA. (1999). ¡°Earthquake loss estimation methodology - HAZUS99. technical manual¡±. Washington, D.C., Federal Emergency Management Agency ¨C National Institute of Building Sciences.