# Time-Variant Seismic Fragility of Offshore Continuous Beam Bridges Based on Collapse Analysis
## 5 Time-Variant Fragility of Components and System
### Time-Variant Fragility Analysis of System  
To discuss the difference between the exceeding probability of each component and the system, the fragility curves of each representative component and the bridge system in different damage states are compared, as shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Service Period (Years)** & **0** & **30** & **50** & **70** & **100** & **150** \\ \hline
1\({}^{\#}\) Bearing & 0.02108 & 0.02455 & 0.02931 & 0.03531 & 0.04258 & 0.04299 \\
3\({}^{\#}\) Bearing & 0.01621 & 0.01828 & 0.02127 & 0.02555 & 0.03076 & 0.03405 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Exceeding probability of bearing.  
Figure 10: Fragility curves of each representative component and the bridge system: (**a**) Slight damage; (**b**) Moderate damage; (**c**) Extensive damage; (**d**) Complete damage.  
Figure 10 shows that under the four damage states, the exceeding probability of the system is greater than that of each representative component. Therefore, under no circumstances can the fragility of a single component be used to assess the seismic performance of the bridge. Moreover, 2\({}^{\#}\) pier is not discussed because it did not reach complete damage during the service period. However, for other components, in the slight damage (PGA \(<\) 0.575 g), moderate damage (PGA \(<\) 0.67 g), extensive damage (PGA \(<\) 0.69 g), and complete damage (PGA \(<\) 0.835 g), among all the components, exceeding probability of each representative bearing are greater than that of 5\({}^{\#}\) pier. Further, when PGA in four states is greater than the above four values respectively, 3\({}^{\#}\) bearing has the smallest exceeding probability, and the exceeding probability of each representative bearing is less than that of 5\({}^{\#}\) pier. Moreover, the PGA value at the intersection of the fragility curve of 5\({}^{\#}\) pier and representative component increases with the growth of service years. Therefore, the bridge system deformation is mainly borne by the bearing when the earthquake action is small, and the pier dissipates the vast majority of the earthquake energy when the earthquake action is large. With the increase of the service period, the energy dissipation effect of the pier in earthquake also increases gradually.  
Ranking each component from large to small according to the exceeding probability, the bridge system's fragility surface in different states of damage in the whole life cycle is shown in Figure 11.  
Figure 11 shows that the exceeding probability of the bridge system under different damage states is positively correlated with the PGA and service period. PGA = 0.5 g, for example, when the service period of the bridge reaches 30 years, its exceeding probability under four damage states increased by 1.01%, 1.11%, 1.12%, and 1.13%, respectively, compared with 0 years. When the service period of  
Figure 11: Fragility surface of the bridge system: (**a**) Slight damage; (**b**) Moderate damage; (**c**) Extensive damage; (**d**) Complete damage.  
the bridge reaches 100 years, its exceeding probability under four damage states increased by 4.20%, 7.62%, 13.60%, and 77.90%, respectively, compared with 0 years, which are significantly higher than the increment of 30 years. The increment increases with the increasing of PGA, this is because the pier begins to crack when its service period reaches around 30 years under the effect of chloride-induced corrosion. At this time, the seismic performance of the bridge structure is intact, and the increment of exceeding probability is small. However, when service period of the bridge reaches 100 years and each pier has been cracked for 70 years, the seismic performance of the bridge structure is poor and the increment of exceeding probability is large. Therefore, the time varying durability damage in service period have a great influence on the seismic ability of structures.