# Braking Performance and Response Analysis of Trains on Bridges Under Seismic Excitation
## 1 Introduction  
Urban rail transit systems, particularly subway and light rail networks, have become indispensable components of modern urban infrastructure, offering unparalleled convenience, efficiency, and sustainability for urban mobility [1]. As the backbone of public transportation in densely populated cities, subway systems play a crucial role in alleviating traffic congestion and reducing carbon emissions; however, operational safety remains a major challenge, especially under dynamic scenarios such as acceleration, deceleration, and emergency braking [2, 3]. These operations induce complex longitudinal forces at the wheel-rail interface [4, 5], which, if not properly managed, can jeopardize vehicle stability, track integrity, and passenger safety. Over the past few decades, several catastrophic accidents related to braking failure have underscored the urgency of addressing these issues. For example, in 2009, a collision occurred in the Shanghai subway system due to signal errors and miscalculated braking distance, resulting in casualties and operational disruption. Similarly, a rear-end collision in Beijing in 2023, during snowy conditions, revealed the inadequacy of braking performance caused by reduced wheel-rail adhesion. Meanwhile, although light rail transit (LRT) systems are highly integrated with subway networks, they present distinct challenges and opportunities [6, 7]. LRT is characterized by higher speed, mixed traffic adaptability, and lower construction costs, and often runs on elevated bridges through urban environments. While elevated design optimizes land use and reduces construction expenses, it also increases vulnerability during seismicevents. In earthquake-prone regions such as China, the suddenness and unpredictability of seismic hazards pose serious threats to rail transit systems [8; 9]. [PERSON] et al. [10] analyzed derailment mechanisms of trains on bridges subjected to strong seismic excitation and found that resonance-induced vibration in bridges could significantly aggravate wheel-rail separation, presenting a critical risk to running safety during earthquakes. [PERSON] et al. [11] conducted probabilistic safety analysis of high-speed trains on bridges under near-fault pulse-type ground motions, emphasizing that ground motion uncertainty and running velocity jointly influence the probability distribution of train instability. Historical earthquake disasters, such as the 2008 Wenchuan earthquake, have demonstrated that seismic energy release can lead to track displacement, bridge collapse, and train derailment [12; 13]. For subway and light rail systems operating on elevated structures, ground motions induced by earthquakes may destabilize the wheel-rail interaction, alter adhesion conditions, and trigger emergency braking [14]. In such cases, drivers or automated systems must rapidly implement deceleration strategies to avoid collisions. However, the coupling mechanisms among seismic excitation, dynamic wheel-rail interaction, and braking performance remain inadequately understood [10; 15; 16], particularly regarding the influence of residual track irregularities on post-earthquake operational safety [17; 18]. In recent years, researchers have begun to investigate the running stability of trains during earthquakes. [PERSON] et al. [19; 20] conducted a comprehensive review of methods for assessing the running safety of trains on bridges subjected to seismic excitation, noting that traditional indices fail to capture nonlinear dynamic behavior under seismic loading and calling for the development of physically consistent and vibration-sensitive assessment frameworks. [PERSON] et al. [4; 21] proposed a multi-body dynamic model for train-track-bridge-coupled seismic response analysis and pointed out that under strong earthquakes, braking has a significant impact on both bridge and vehicle response.