## 4 Model Establishment
### Experimental Validation of the Model
Figure 6:1 Earthquake probability demand model for structures with different numbers of dropped layers: (**a**) the probability demand model for the C1K2 YBR structure in civil engineering, (**b**) the probability demand model for the C2K2 YBR structure in civil engineering, and (**c**) the probability demand model for the C3K2 YBR structure in civil engineering. The Impact of the Number of Dropped Stories and Dropped Spans on the Structural Vulnerability Function  
According to the structural failure probability formula, vulnerability function curves for structures with six different numbers of dropped stories and dropped spans can be obtained for IO, LS, and CP states. The vulnerability curves for structures with different numbers of dropped spans are shown in Figure 14, while the vulnerability curves for structures with different numbers of dropped stories are shown in Figure 6:2 The horizontal axis represents the seismic intensity value (peak ground acceleration, PGA), and the vertical axis represents the exceedance probability of the limit state. From Figures 14 and 15, it can be observed that under frequent earthquakes, the exceedance probability of structures with different numbers of dropped stories and dropped spans beyond the IO limit state was less than 2%. This indicates that the structures can be safely used without the need for repair after an earthquake. For the LS and CP limit states, the exceedance probability of structures was 0, indicating that they did not exceed the life safety and collapse prevention limit states, meeting the performance requirements of \"no damage for small earthquakes\". 1. Under the design earthquake, for the C2 KXYBR structures with the same number of dropped stories but different numbers of dropped spans, the exceedance probability of surpassing the IO limit state gradually increased with the number of dropped spans. Figure 6:3 Vulnerability curves for structures with different numbers of dropped spans: (**a**) the vulnerability curve for the C2K1 YBR structure in civil engineering, (**b**) the vulnerability curve for the C2K2 YBR structure in civil engineering, and (**c**) the vulnerability curve for the C2K3 YBR structure in civil engineering. Figure 6:4 Vulnerability curves for structures with different numbers of dropped layers: (**a**) the vulnerability curve for the C1K2 YBR structure in civil engineering, (**b**) the vulnerability curve for the C2K2 YBR structure in civil engineering, and (**c**) the vulnerability curve for the C3K2 YBR structure in civil engineering. Specifically, it increased to 23.73%, 24.53%, and 30.55% as the number of dropped spans increased. Similarly, for the CXK2 YBR structures with the same number of dropped spans but different numbers of dropped stories, the exceedance probability of surpassing the IO limit state gradually increased with the number of dropped stories, reaching 9.79%, 24.53%, and 30.67%, respectively. These probabilities are all less than 50%, indicating that the structures can still be safely used, although minor repairs may be required after the earthquake. The exceedance probability of surpassing the LS limit state for all five structures was less than 5%, indicating that the structures had just begun to undergo damage, with low levels of damage. The exceedance probability of surpassing the CP limit state for all structures was very low, less than 1%. 2. Under a rare earthquake event, for the C2 KXYBR structures with the same number of dropped stories but different numbers of dropped spans, the exceedance probability of surpassing the IO limit state gradually increased with the number of dropped spans. Specifically, it increased to 79.98%, 81.54%, and 85.65% as the number of dropped spans increased. Similarly, for the CXK2 YBR structures with the same number of dropped spans but different numbers of dropped stories, the exceedance probability of surpassing the IO limit state gradually increased with the number of dropped stories, reaching 63.00%, 81.54%, and 85.38%, respectively.