When vehicles interact with a bridge, a vehicle–bridge interaction (VBI) system is created. The frequency and modal shape of VBI systems have been widely studied, but the damping of VBI systems has not been adequately investigated. In recent years, several incidents of abnormal bridge vibration due to changes in bridge damping have occurred and aroused widespread concern in society. Damping is an important evaluation index of structural dynamic performance. Knowing the damping ratio of a VBI system is useful for analyzing the damping changes while a bridge is in service. This paper presents a method to extract bridge damping values from a VBI system, which can serve as a guide for bridge damping evaluation. First, a double-beam theoretical model was used to simplify the VBI system for cases involving uniform traffic flow. The damping ratio equation for the simplified VBI system was obtained using the extended dynamic stiffness method (EDSM). A double-beam finite element model and a VBI finite element model were established. The damping ratios of the two models were separately calculated and then compared with the simplified VBI model results. The results verified the accuracy of the simplified method. This paper then explains that bridge damping values can be extracted by estimating the equivalent traffic flow parameters and using the damping formula for the simplified VBI system. The bridge damping ratios extracted using this method in an engineering case ranged from 0.75% to 0.78%, which is smaller than the range that was directly identified using monitoring data (0.83–1.19%). The results show that the method can effectively extract bridge damping ratios and improve damping ratio identification.

In this study, the dynamic response of a vehicle with flexible car body moving on a ballasted track is investigated. The vehicle/track interaction model is divided into two sub-systems, namely the vehicle and the ballasted track sub-system. The vehicle sub-system is composed by one flexible car body, two bogies and four wheel sets. The car body is created using flexible multibody dynamics. The ballasted track consists of rail, sleeper, ballast and sub-grade. For its representation the simplified 2D discrete support model (DSM) is used and modelled by finite elements. The connection between the two sub-systems, i.e. between the moving wheels and the track is ensured by a linearized Hertzian spring. The dynamic response of the vehicle/track system is computed by the Newmark-β integration method. The effect of the car body flexibility on the dynamic response of this system is analyzed and evaluated based on the maximum car center acceleration. It is concluded that the increase in flexural stiffness of the car body can lead to a notable decrease of its maximum acceleration.

Railway culverts and their transition zones constitute mechanically heterogeneous systems in which abrupt variations in structural and geotechnical stiffness disrupt the symmetry of train–track–soil–structure interaction (TTSSI). The resulting stiffness asymmetry alters load transfer within the TTSSI system and contributes to dynamic amplification, differential settlement, vibration concentration, and progressive track deterioration. Although substantial research has been conducted on railway transition zones, a systematic synthesis from a symmetry-oriented perspective remains lacking. This review critically examines studies published between 2000 and 2026 on railway culvert dynamics, transition-zone design, TTSSI mechanisms, numerical modeling, field monitoring, international design standards, and emerging digital-twin technologies. Particular attention is given to the influence of stiffness asymmetry on load-transfer mechanisms, vibration propagation, soil–structure interaction, and long-term infrastructure performance. Numerical approaches ranging from simplified analytical formulations to fully coupled three-dimensional TTSSI models are assessed alongside experimental evidence and field observations. The review demonstrates that the dynamic behavior of railway transition zones is fundamentally governed by stiffness discontinuities that break the mechanical symmetry between embankments and buried structures. Despite significant advances in vehicle–track interaction modeling and digital monitoring, important challenges remain in nonlinear soil behavior, hydro-mechanical coupling, resilience quantification, and long-term field validation. To address these limitations, a system-oriented digital-twin framework is proposed that integrates sensing, data assimilation, physics-based simulation, and predictive maintenance. The framework provides a pathway toward resilient, intelligent, and data-driven management of railway culvert transition zones while identifying key priorities for future research.