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The smoothness of the high-speed railway (HSR) on the bridge may exceed the allowable standard when an earthquake causes vibrations for HSR bridges, which may threaten the safety of running trains. Indeed, few studies have evaluated the exceeding probability of rail displacement exceeding the allowable standard. The purposes of this article are to provide a method for investigating the exceeding probability of the rail displacement of HSRs under seismic excitation and to calculate the exceeding probability.

In order to investigate the exceeding probability of the rail displacement under different seismic excitations, the workflow of analyzing the smoothness of the rail based on incremental dynamic analysis (IDA) is proposed, and the intensity measure and limit state for the exceeding probability analysis of HSRs are defined. Then a finite element model (FEM) of an assumed HSR track-bridge system is constructed, which comprises a five-span simply-supported girder bridge supporting a finite length CRTS II ballastless track. Under different seismic excitations, the seismic displacement response of the rail is calculated; the character of the rail displacement is analyzed; and the exceeding probability of the rail vertical displacement exceeding the allowable standard (2mm) is investigated.

The results show that: (1) The bridge-abutment joint position may form a step-like under seismic excitation, threatening the running safety of high-speed trains under seismic excitations, and the rail displacements at mid-span positions are bigger than that at other positions on the bridge. (2) The exceeding probability of rail displacement is up to about 44% when PGA = 0.01g, which is the level-five risk probability and can be described as 'very likely to happen'. (3) The exceeding probability of the rail at the mid-span positions is bigger than that above other positions of the bridge, and the mid-span positions of the track-bridge system above the bridge may be the most hazardous area for the running safety of trains under seismic excitation when high-speed trains run on bridges.

The work extends the seismic hazardous analysis of HSRs and would lead to a better understanding of the exceeding probability for the rail of HSRs under seismic excitations and better references for the alert of the HSR operation.

This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.

The track and substructure are decomposed into the rail subsystem and substructure subsystem, in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener. The rail is treated as a continuous beam with elastic discrete point supports, and spring-damping elements are used to simulate the constraints between rail and fastener. Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system, while the external load is used to deal with the reverse effect. The fastener failure is simulated with the methods that cancel the forced vibration transmission, namely take no account of the substructure–rail interaction at that position.

The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method. Local fastener failure will slightly affect the vibration of substructure and carbody, but it will significantly intensify the vibration response between wheel and rail. The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value, respectively, under the train speed of 350 km·h⁻¹. At the same time, the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%, respectively, from the normal value.

This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.

This paper aims to study the influence of aerodynamics force of trains passing each other on the dynamic response of vehicle bridge coupling system based on numerical simulation and multi-body dynamics and put forward the speed threshold for safe running of train under different crosswind speeds.

The computational fluid dynamics method is adopted to simulate the aerodynamic force in the whole process of train passing each other by using dynamic grid technology. The dynamic model of vehicle-bridge coupling system is established considering the effects of aerodynamic force of train passing each other under crosswind, the dynamic response of train intersection on the bridge under crosswind is computed and the running safety of the train is evaluated.

The aerodynamic force of trains' intersection has little effects on the derailment factor, lateral wheel-rail force and vertical acceleration of train, but it increases the offload factor of train and significantly increases the lateral acceleration of train. The crosswind has a significant effect on increasing the derailment factor, lateral wheel-rail force and offload factor of train. The offload factor of train is the key factor to control the threshold of train speed. The impact of the aerodynamic force of trains' intersection on running safety cannot be ignored. When the extreme values of crosswind wind speed are 15 m·s⁻¹, 20 m·s⁻¹ and 25 m·s⁻¹, respectively, the corresponding speed thresholds for safe running of train are 350 km·h⁻¹, 275 km·h⁻¹ and 200 km·h⁻¹, respectively.

The research can provide a more precise numerical method to study the running safety of high-speed trains under the aerodynamic effect of trains passing each other on bridge in crosswind.