## 6 Conclusions  
In this paper, the seismic risk analysis of an offshore bridge was investigated based on improved 2D seismic fragility analysis. The adverse effects of chloride ion erosion were considered, and a finite element analysis model of the entire bridge was established based on OpenSees. The seismic response process of the entire bridge was simulated employing the IDA method, and the displacement \(\Delta\) of the plate rubber bearing and the displacement ductility ratio \(\mu\) of the pier were employed as damage indexes. The correlation coefficients of the plate rubber bearing and the pier under different ground motions were proposed based on Pearson correlation analysis, and the accurate 2D seismic fragility curves of the entire bridge were further obtained. The extreme value type II distribution theory was employed to directly derive the calculation formula of the site hazard curve, and the seismic risk probability of the entire bridge was finally achieved. The main conclusions are as follows:  
1. Due to chloride ion erosion, the longitudinal reinforcement of the pier begins to corrode after 19.4 years, resulting in structural seismic performance degradation throughout the life cycle. The time-varying seismic fragility caused by chloride ion erosion must be comprehensively considered for offshore bridges. 2. When comparing the seismic fragility curves of two components, the results show that the plate rubber bearing has a higher exceedance probability than the pier under different seismic performance states. This is because the plate rubber bearing is often \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Performance** & **Basically** & **Slight** & **Moderate** & **Serious** & **Complete** \\
**Limit States** & **Intact (S0)** & **Damage (S1)** & **Damage (S2)** & **Damage (S3)** & **Damage (S4)** \\ \hline Seismic & & & & & \\ hazard & 0.73683 & 0.16821 & 0.06770 & 0.01817 & 0.00908 \\ Seismic risk & & & & & \\ probability & 0 & 0.00505 & 0.00542 & 0.00454 & 0.00608 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The seismic risk probability for the entire bridge. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Performance** & **Basically** & **Slight** & **Moderate** & **Serious** & **Complete** \\
**Limit States** & **Intact (S0)** & **Damage (S1)** & **Damage (S2)** & **Damage (S3)** & **Damage (S4)** \\ \hline Reference & 0 & 0.01–0.03 & 0.02–0.15 & 0.10–0.40 & 0.30–1.00 \\ loss ratio & & & & & \\ loss ratio in & 0 & 0.03 & 0.08 & 0.25 & 0.67 \\ this paper & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The loss ratio under different performance limit states. designed as a protective component in seismic design to ensure overall seismic safety performance. Due to the significant difference in mechanical properties between the plate rubber bearing and the pier, the upper and lower bounds of the 1D seismic fragility curves of the entire bridge based on first-order reliability theory are excessively broad. 3. Considering the seismic correlation between vulnerable components, the correlation coefficients were determined according to the Pearson correlation analysis method, then an improved 2D seismic fragility analysis was developed. The 2D seismic fragility curves for the entire bridge were comprehensively achieved, and are significantly higher than the 1D fragility curves based on first-order reliability theory. The results show that the seismic internal relationship between the plate rubber bearing and the pier cannot be ignored. 4. According to the 2D seismic fragility curves for the entire bridge, the PGA of S\({}_{1}\), S\({}_{2}\), S\({}_{3}\), and S\({}_{4}\) corresponding to 50% exceedance probability for the 2D seismic fragility curves of the entire bridge are 0.19, 0.26, 0.34, and 0.40, respectively, which can provide an important theoretical foundation and technical support for seismic design and performance evaluation of offshore bridges. 5.