## 4 Validation and Case Study
### Collapse and Ruins Simulation of a Real-World Library Building  
To demonstrate the applicability of the proposed hybrid method to real-world complex structures, a case study of a multi-story reinforced concrete library building is performed. The building is a seven-story frame-shear wall structure, with a total height of 19.8 m and a building area of 15,938 m\({}^{2}\). The total mass of the library building is \(3.17\times 10^{7}\) kg. All reinforcement consists of HRB400 reinforcing bars, whose strength is 400 MPa. The material properties and dimensions of the main structural members are shown in Table 4. Specifically, the library is located on a site class III in GB50011-2010 [44], with an approximate equivalent shear wave velocity of 200 m/s for 30-m soil (VS30). The characteristic period of the site is 0.45 s. The building has an 8-degree seismic design intensity, where the peak ground acceleration is 200 cm/s\({}^{2}\) for a design basis earthquake (DBE) with a return period of 475 years. There is no R-factor, coefficient of displacement or overstrength factor in Chinese seismic design code. However, according to [PERSON] et al. [51] and American Society of Civil Engineers (ASCE) 7-10 [52], the design information of the building is similar to the following seismic design parameters: R factor = 4.5; overstrength factor = 2.5 and deflection amplification factor = 4. Three element types are used in this model: (a) fiber beam elements for beams and columns, (b) multilayer shell elements for shear walls, and (c) membrane elements for floor slabs. Details of these element models have been reported in the published work [35]. Figure 12a illustrates the three-dimensional FE model. The first mode of the model is a translational mode, with a fundamental period (elastic period) \(T_{1}\) = 0.37 s.  
The widely used El-Centro ground motion record, the same as that in Section 4.1, is adopted. To simulate the collapse behavior, the PGAs of the input motions along the X- and Y-directions are scaled to 4000 cm/s\({}^{2}\). The nonlinear time history analysis results show that the maximum vertical displacement of the structural component reaches 1 m at 1.76 s, and the corresponding maximum lateral displacement is 0.97 m. The corresponding deformed shape of the structure is shown in Figure 12b. The colored contours in Figure 12 represent the longitudinal reinforcement yielding in the elements. The amount of shear walls on the third story is much lower than on the first and second stories, which results in a sudden change of stiffness. Therefore, the third story is the weak story of the building. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Element** & **Member Location** & **Strength of Concrete (MPa)** & **Size of Elements (m)** \\ \hline Walls & 1 st floor & 40 & \(8\times 2.25\)–\(2\times 2.25\) \\  & 2 nd floor & 40 & \(8\times 2.07\)–\(2\times 2.07\) \\  & Others & 35 & \(8\times 2\)–\(2.5\times 2\) \\ Beams & 1 st floor & 40 & 4–\(1.25\) \\  & 2 nd floor & 40 & 4–\(0.707\) \\  & Others & 35 & 4–\(0.707\) \\ Columns & 1 st floor & 40 & 2.25 \\  & 2 nd floor & 40 & 2.07 \\  & Others & 35 & 2 \\ Slabs & All floors & elastic & \(8\times 7.45\)–\(2\times 1.5\) \\ \hline \hline \end{tabular} Note that the sizes of walls mean \(X\)-direction/\(Y\)-direction \(\times\)\(Z\)-direction.  
\end{table} 
Table 4: The material properties and dimensions of the main structural members in the library building. The geometric and material information of the FE model, and its displacement and velocity results, are mapped into Blender using the mapping methods discussed in Section 3. After pre-processing with BCB, a collapse simulation is performed using the Bullet physics engine. The collapse process of the library building is then determined, as shown in Figure 13.  
Figure 12: FE model and simulation results of the library building: (**a**) FE model of the library building; (**b**) simulation results (\(t=1.76\) s). Figure 13: _Cont._  
The damage first occurs at the soft story of the structure, as shown in Figure 12b.