# Time-Variant Seismic Fragility of Offshore Continuous Beam Bridges Based on Collapse Analysis
## 1 Introduction  
Due to the influence of concrete carbonation and chloride-induced corrosion, the seismic performance of reinforced concrete bridge decreases continuously in the whole life cycle [1; 2]. For the bridge located in the seismic belt, the durability damage will cause the change of dynamic characteristics and seismic response due to the decreasing of seismic performance and the change of bridge structure stiffness and damping, which increase the level of its damage state under earthquake. Hence, the reinforced concrete bridge that reaches the requirements of seismic design in the original state may not maintain safe operation in the earthquake disaster. In recent years, the influence of durability damage on the seismic performance of concrete structure has been paid more and more attention. A large number of experiments have been carried out on the reinforced concrete components around the world. Concrete carbonation degrades the mechanical properties and surface alkalinity of concrete, resulting in cracking of concrete protective layer and corrosion of reinforcement [3; 4; 5; 6]. [PERSON] et al. [7] used XRD and ESEM to analyze concrete carbonation. The relationship between temperature, CO\({}_{2}\) concentration, relative humidity, and carbonation depth of concrete was obtained. Their relations are linear, power function, and polynomial, respectively. Based on diffusion-limited aggregation (DLA) model. [PERSON] et al. [8] dynamically and deeply simulated the durability evolution process of the reinforced concrete structure after the coupling of chloride-induced corrosion and carbonation effects. [PERSON] et al. [9] explored the influence of carbonation on the presence of water and acid-soluble chlorides, and the test results showed that the chloride-induced corrosionwas more obvious when it was combined with the carbonization process. However, it is more reasonable to use probabilistic analysis to evaluate the time-varying seismic performance of the bridge due to the uncertainty of structure and corrosion-related parameters [10]. As a probabilistic method, seismic fragility analysis has been widely used in the last few decades [11; 12]. In recent years, some scholars have explored the time-variant seismic fragility of offshore bridges under chloride corrosion [13; 14; 15]. [PERSON] et al. [16; 17] proposed a probabilistic method of time-variant chloride-induced corrosion that is applied to reinforced concrete columns, and considered the reduction of their seismic performance. To identify the parameters which have the greatest influence on the fragility vulnerability of bridges, the sensitivity and importance analysis are carried out by using the nonlinear dynamic analysis. [PERSON] [18] established a time-variant fragility curve of multi-span continuous steel bridge by considering different seismic effects and corrosion parameters. [PERSON] and [PERSON] [19] also considered the influence of reinforcement corrosion and steel bearing deterioration of bridge pairs and established the time-variant fragility curve of the bridge. [PERSON] et al. [20] proposed a framework by considering the impacts of structural deterioration associated with multiple hazards to assess the time-variant seismic performance of bridges. The authors considered the impact of flood scour, reinforcement bars corrosion and the concrete cover cracking on seismic fragility. However, these studies mainly discussed the time-variant seismic fragility of individual components. [PERSON] and [PERSON] [21] analysed the influence of the main components on the fragility of bridge system based on the typical bridge, and utilized probabilistic method to directly assess the fragility of bridge system according to the individual component fragilities. The results show that the fragility of bridge system assessment by the first-order bounds could lead to errors of up to 40% when the fragility of bridge system is higher than that of any individual component. Based on the second-order bounds method, [PERSON] et al.