# Time-Variant Seismic Fragility of Offshore Continuous Beam Bridges Based on Collapse Analysis
## 6 Conclusions  
In this paper, a four-span offshore continuous beam bridge with rigid pier is selected for a case study. Based on the fragility analysis method and considering the influence factors such as concrete carbonation and chloride-induced corrosion, the time-variant fragility of the bridge is analyzed, and the quantification method in obtaining the coefficient of fragility is proposed. The main conclusions are as follows:  
1. After considering the time-varying damage of material durability, the peak stress of concrete increases with the extension of service period. On the contrary, the peak strain and limit strain of concrete decrease with the extension of service period. Moreover, the yield strength, ultimate strength, and diameter of the reinforcement decreased with the extension of service period. In addition, the stirrup damage degree was worse than the longitudinal reinforcement. As C50 concrete has better material properties than C40 concrete, the longitudinal reinforcement damage degree in 2\({}^{\#}\) pier and 3\({}^{\#}\) pier is lower than that of 1\({}^{\#}\), 4\({}^{\#}\) and 5\({}^{\#}\) piers. Taking 1\({}^{\#}\) pier which is in 100 years as an example, the yield strength of longitudinal reinforcement and stirrup decreases by 2.52% and 7%, respectively, after the repair of concrete damage in the protective layer of the pier
2. When the local vibration intensity is small, the 1\({}^{\#}\) pier in working condition 1 is more fragile to damage at the component level. The bridge system in working condition 2 is more fragile at the system level in small local vibration intensity. According to the time-variant fragility curves of components and bridge system, the fragility of each component and bridge system increases with the extension of the service period. Meanwhile, the exceeding probability of any component is lower than the system in same condition. Therefore, the exceeding probability of component cannot be used to replace the exceeding probability of bridge systems when assessing the seismic performance of a bridge.
3. The time-varying fragility coefficient of each component and system in three working conditions are compared, among which the fragility coefficient of system are the largest values under every working conditions. When the bridge reaches the design service life, the fragility coefficient of the bridge system is 105% of 1\({}^{\#}\) pier and 132% of the bridge system in 0 year. During the whole service period, both WC2 (dismantle 1\({}^{\#}\) pier) and WC3 (dismantle 4\({}^{\#}\) pier) will increase the fragility coefficient of the system compared with WC1 (original state). However, WC2 is the most fragile working condition in the service period of the bridge.  
**Author Contributions:** [PERSON] proposed the topic of this study and performed the finite element analysis; [PERSON] designed the process and wrote the paper; [PERSON] designed the experiments; [PERSON] has done related works in review and editing. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the National Natural Science Foundation of China (Grant No. 51608488), and the Scientific and Technological Project of Henan province, China (192102210185).  
**Conflicts of Interest:** We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.