## 1 Introduction  
The bridge is an important hub of transportation systems, especially the reinforced concrete long-span continuous girder bridge, the most common type on highways in China. In recent years, it has been noticed that the long-period velocity and displacement pulse motion of the near-fault ground motion may adversely affect the seismic performance and design of the bridge [1, 2, 3, 4]. All previous earthquake disaster statistics have shown that these bridges will sustain serious damage from earthquakes [5, 6]. In order to effectively reduce the seismic damage to bridges, the isolation design of lead rubber bearing (LRB) is used in the actual engineering. The seismic responses of such isolated structures have already been widely investigated [7, 8]. It was found that this kind of isolated bridge structure can not only meet the design requirements under various working conditions but can also effectively reduce the seismic effect on the bridge pier under the rare earthquake. However, near-fault ground motion with strong non-stationary characteristics adversely affects the seismic performance and design of the isolated bridge through support shedding, displacement of expansion joints, excessive relative displacement of pier beams, and falling beams caused by the collision of the main beams. What is more, the large bearing displacement and the isolation device failure can cause serious damage to the structure [9, 10]. Therefore, evaluating the seismic performance of isolated bridges under near-fault ground motion is an important subject for study. However, because of the uncertain structural and ground motion parameters, the probabilistic analysis method is generally used to study the seismic performance of bridges. The probabilistic approach offers an efficient way to deal with various uncertainties such as aleatory or epistemic uncertainties in structures and ground motions [11]. Recently, the performance-based seismic design theory of bridges has drawn attention to the probabilistic seismic capacity of structures at multi-performance levels, and the seismic fragility analysis method is the most effective method to evaluate the seismic performance of structures [12; 13]. At present, the seismic fragility analysis of bridges mainly includes empirical analysis and numerical simulation analysis; empirical fragility analysis establishes fragility curves based on the damage to bridge structures in real disasters. However, owing to the lack of disaster damage data for bridge structures, application of this method is extremely limited [14]. The numerical fragility analysis method is based on the numerical simulation and dynamic response analysis of the bridge structure to establish the fragility curve. This method can effectively solve the problems resulting from the empirical method, so it is widely used in the study of the seismic fragility of bridges [15]. In fact, the bridge is a high-order statically indeterminate structure, and the failure of one member of the whole structure does not mean the failure of the whole structure. Compared with those of the individual components, the seismic performance of the whole bridge system deserves more attention [16]. However, under the influence of an earthquake, the main beams, supports, columns, and piers of the bridge system are mutually affected. Therefore, accurate simulation of the correlation between the seismic responses of various components is one of the difficulties in seismic fragility research when shifting from a single component to the whole bridge system [17; 18]. At present, in view of the correlation between the components in the overall bridge structure, it is assumed that the seismic responses of the components are either completely correlated or not, and the upper and lower boundary values of the fragility of the bridge system are obtained by numerical analysis. The upper bound value is conservatively used to describe the seismic fragility of structural systems [19; 20].