## 4 Results and Discussion  
### The Seismic Fragility Analysis of Isolated Bridge Components  
As an example, owing to limited space, only the No. 3 pier is provided, based on the damage index. The pier and isolation bearing of the seismic fragility curves under different damage conditions are plotted (obtained from Equation (3)) in Figures 5 and 6, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Correlation Coefficient** & **In\(\mu\)(\(\varphi\))** & **In\(\mu\)(\(d_{\Delta}\))** & **In\(\mu\)(Gap)** \\ \hline \(\ln\mu\)(\(\varphi\)) & 1 & 0.892 & 0.753 \\ \(\ln\mu\)(\(d_{\Delta}\)) & 0.892 & 1 & 0.892 \\ \(\ln\mu\)(Gap) & 0.753 & 0.813 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation coefficients of structure seismic demands. In order to analyze the structure under the earthquake action, it was assumed that when the ground motion intensity was 0.11 g (PGA = 0.11 g), it was a frequent earthquake, and when the ground motion intensity was 0.51 g (PGA = 0.51 g), it was a rare earthquake. As is shown in Figure 5, the No. 3 pier with isolated bridges remained intact under frequent earthquake action (PGA = 0.11 g). In the case of rare earthquake action (PGA = 0.51 g), the probability of minor damage to the bridge pier was 4%, but without moderate damage, severe damage, complete destruction, or other incidents. Minor damage did not occur in the frequent earthquake, and it had only a small probability of occurring from the rare earthquake. This was because the pier could bear a greater force, which reflected the requirements of ductility design of bridge components. It showed that the seismic demand on the bridge pier was greatly reduced in the isolation bearing structure. According to the data shown in Figure 6, under frequent earthquake action (PGA = 0.11 g), the isolated bearing was not easily damaged. However, under rare earthquake action (PGA = 0.51 g), damage to the bearing occurred; the probability of minor, moderate, and severe damage was 52, 11, and 4%, respectively, but a collapse of the isolated bearing did not happen. Compared with the bridge pier, the seismic fragility of the isolated bearing played a key role in the safety control of the isolated continuous girder bridge. This was mainly because the isolated continuous girder bridge canceled the braking pier, the  
Figure 5: The seismic fragility curves of the pier. Figure 6: The seismic fragility curves of the isolated bearing. deformation of the isolated bearing was relatively large, so the seismic fragility of the isolated bearing was large. In order to compare the failure probability of collision between the girder end and the abutment of the general bridge (without isolation device) and of the isolated bridge, the seismic fragility curves of the collisions between the girder and the abutment of two different bridges are given in Figure 7. Under the frequent earthquake action (PGA = 0.11 g), there was no collision between the girder end and abutment of these two types of bridges. However, in the case of rare earthquake action (PGA = 0.51 g), the probability of collision between the girder end and the abutment of the general bridge was about 78%, and the probability of collision between the girder end and the abutment of the isolated bridge was 63%. Therefore, for the bridge constructed using the isolation technology, the probability of collision was 15% lower than that of the general bridge. The main reason was that the relative displacement of the beam members from the earthquake was greatly reduced because of the isolation bearings. Comparative Analysis of the Seismic Fragility of the Bridge Structure System Based on First-Order Reliability Theory and Copula Technique  
In order to verify the accuracy of the copula function method, the upper and lower limits of the seismic fragility of bridge structures based on the first-order reliability theory were considered.