# A Story-Based Random Structure Modeling Method for Regional Buildings Earthquake Loss Estimation
## 4 Case Study
### Earthquake Loss of Regional Buildings  
After the SBRS models of all the buildings are established, the predicted values of the loss ratio of each building under different seismic intensities can be obtained using the method described in Section 3.3. Due to the relatively poor seismic performance of RC frame and reinforced masonry structures, most collapsed when the PGA reached 0.5 g, as shown in Figure 18.  
In contrast, the total loss ratio of wall-frame structures in the range of a PGA of 0.5-1.0 g is small and does not change much, so only the PGA \(\leq\) 0.5 g results are shown. The damage state of the building is represented by taking the damage state of the most damaged story. The damage distribution of the buildings at different intensities is shown in Figure 19. The \(M_{building}\) values of the total loss ratio of each building are shown in Figure 20.  
Figure 17: Prediction curve of the total loss ratio. Figure 18: The peak IDR on a typical building: (**a**) RC frame structure and (**b**) RM structure. Figure 19: The damage distribution of the buildings in the study area: **(a)** PGA = 0.1 g; **(b)** PGA = 0.2 g; **(c)** PGA = 0.3 g; **(d)** PGA = 0.4 g; and **(e)** PGA = 0.5 g.  
Figure 20: \(M_{building}\) values of loss ratio for each building in the area: **(a)** PGA = 0.1 g; **(b)** PGA = 0.2 g; **(c)** PGA = 0.3 g; **(d)** PGA = 0.4 g; and **(e)** PGA = 0.5 g.  
It can be seen that, when PGA \(\leq\) 0.2 g, none of the buildings in the region produced serious damage or collapsed; the loss ratio was at a low level. The generated SBRS models could meet the three-level defense requirements of \"no collapse in large earthquakes, repairable in medium earthquakes, and no damage in small earthquakes\" required by the specification. As the ground motion intensity continued to increase, the loss ratio of the reinforced masonry structure rose the fastest, and when PGA = 0.3 g, the structure was basically in a more serious damage state or even collapse. When PGA = 0.5 g, the loss ratio of most of the buildings in the region was close to or reached 1, while the buildings showing a dark green color and lower loss ratio were all wall-frame structures. The findings of this study suggest that the impact of earthquakes on buildings varies depending on the level of ground motion intensity and the type of structure. These results are consistent with previous seismic hazard surveys, demonstrating the validity of the SBRS models used in this paper for estimating the earthquake losses in regional buildings. Figure 21 displays the loss ratios based on the HASUZ method. In this study, the RM, RC frame, and RC wall-frame structures are comparable to the HAZUS structural types of RM2, C3, and C2, respectively. According to [PERSON] et al. [46], the seismic design code of the buildings matches the Low-code in HAZUS. The study area includes buildings with various occupancy types, such as RES3 af, RES5, COM1, COM4, COM5, COM6, EDU1, and EDU2. The structural repair cost ratio was standardized to facilitate easy comparison with the results presented in this paper. Upon examination, it appears that the disparity in loss ratios for various building types at the same seismic intensity is not readily apparent. Upon comparing Figures 20 and 21, it becomes clear that, while the difference between the two methods is not immediately noticeable at lower seismic intensities, there is a significant difference in loss ratios when the earthquake intensity is high (PGA \(\geq\) 0.4 g). This is due to the fact that this paper's method is based on the loss ratio ascertained from individual stories, while HAZUS, as a single-degree-of-freedom system, may underestimate the overall seismic loss at higher intensities.