## 1 Introduction  
Given the intricate temporal and spatial distribution of earthquakes across fault lines, the limited warning time, and the significant risk of earthquake-induced damage, there is an urgent need to address the challenges related to the operational performance of bridges during sudden seismic events and the prompt restoration of bridges post-earthquakes. Consequently, there is a growing demand for enhanced seismic resilience and operational safety of bridges. It is, therefore, essential to undertake comprehensive research on the theoretical framework for seismic resilience of bridges in regions prone to intense seismic activity across fault lines, as well as conduct thorough assessments of their operational safety. While earthquakes have inflicted considerable damage on bridges crossing faults and have the potential to result in derailments, the existing research primarily concentrates on bridge responses. However, there is a paucity of studies investigating the impact of train-bridge coupling vibrations. Nonetheless, researchers worldwide have made notable advancements in this area, yielding a range of valuable scientific research findings. [PERSON] et al. [1] developed near-fault pulse seismic ductility spectra based on machine learning to investigate the influence of pulse parameters on structures in near-fault zones. [PERSON] et al. [2] utilized a parameter sensitivity approach to investigate the influence of the velocity pulse period and velocity pulse count on high-pier bridges. The study involved conducting experiments on a prototype bridge using a shaking table, followed by calibrating and validating the corresponding numerical models based on recorded experimental data. [PERSON] et al. [3] delved into the consequences of a fault rupture zone intersecting a seismically isolated bridge. The research demonstrated that the response of the seismically isolated bridge was notably affected by the position of the fault crossing along the bridge's span and the orientation of the fault relative to the bridge's longitudinal direction. These findings emphasize the criticality of incorporating fault characteristics into the design and analysis of seismically isolated bridges, particularly in areas prone to intense seismic activity. [PERSON] et al. [4] and [PERSON] et al. [5] investigated the impact of FCAs and PGRDs on the seismic responses of bridges. Their investigations revealed that the seismic responses of fault-crossing bridges surpassed those of bridges located near faults, particularly in terms of girder and bearing displacements. Moreover, the results indicated that, among the various FCAs analyzed, a 90\({}^{\circ}\) angle resulted in smaller pylon displacement and longitudinal bearing displacement while leading to larger transverse bearing displacement. [PERSON] et al. [6], [PERSON] et al. [7], and [PERSON] et al. [8] examined both ordinary and seismically isolated bridges crossing strike-slip faults. Their study systematically explored various factors, including FCA and fault-crossing location. Their consistent findings indicated that the most favorable outcomes were generally observed when the FCA was set at 90\({}^{\circ}\) and the fault-crossing location was positioned at the middle span of the bridge. It is worth noting that the majority of existing studies have primarily focused on highway bridges crossing strike-slip fault, with relatively fewer investigations conducted on railway bridges. However, considering the substantial influence of train-bridge interaction on the dynamic characteristics of high-speed railway systems, further research in this domain becomes imperative. As previously mentioned, it is essential to account for the influence of trains when studying bridges crossing slip faults. Given the pressing need to ensure the safety of high-speed railway bridges and traffic, research in this area holds great significance. [PERSON] et al. [9] employed a real-time co-simulation approach to address the train-track-bridge dynamic interaction. [PERSON] et al.