## 1 Introduction
Ignoring the collision effect will underestimate the seismic demand of the substructure and lead to unsafe results. However, the problem of energy dissipation is not considered in the collision process. [PERSON] et al. [21] established a bridge lateral collision contact element analysis model that can take into account the energy loss during the collision process and investigated the influence of collision stiffness, initial gap, and bridge pier height on the seismic collision effect of a railway RC simply supported beam bridge under shallow source strong earthquake. The results show that when the lateral collision stiffness is 1-2% of the axial stiffness of the beam, the relative balance between force and deformation can be achieved. [PERSON] et al. [22] and [PERSON] et al. [23] studied the simulation model of lateral collision on bridge structure and conducted parameter analysis. They pointed out that the collision parameters have a significant effect on the overall seismic performance of the bridge but did not propose the specific values of the corresponding bridge collision parameters. Therefore, the above scholars only carry out correlation analysis on the transverse collision effect of conventional far-field bridges, and whether it is suitable for bridges near faults needs further study. Compared to conventional bridges, the permanent ground displacement caused by the mutual dislocation of faults will result in different spatial position changes at the bridge support points, which need to be coordinated by the deformation of the bridge structure itself [24; 25]. This often leads to a larger sliding displacement between the main girder and the pier, resulting in a more severe lateral collision with the shear key. Among these, the location of the fault relative to the bridge and the degree of fault displacement are two important factors affecting the mechanical performance of the bridge [26; 27]. At present, many national codes prohibit bridges from directly crossing active faultsor adopting avoidance distance measures, which leads to an insufficient understanding of the seismic response of cross-fault bridges, and their seismic design method needs to be improved [28,29]. Therefore, the study of the influence of lateral collision on the seismic response of cross-fault bridges under fault dislocation can promote the seismic strengthening of such bridges and the formulation of relevant specifications, which is of great importance to avoid or minimize seismic damage. In this paper, based on the contact element theory, the Kelvin-Voigt model is used to establish a cross-fault bridge analysis model considering the lateral collision between the shear key and the beam. A series of cross-fault ground motions with different ground permanent displacements were artificially synthesized using the hybrid simulation method. The effect of lateral collision on the seismic response of a continuous girder bridge is compared from the position and degree of fault dislocation. Finally, the two key parameters of collision stiffness and the initial gap in the collision effect are analyzed in order to provide guidance for improving the seismic safety of cross-fault bridges.