To explore the influence of spatially varying ground motion on the dynamic behavior of a train passing through a three-tower cable-stayed bridge, a 3D train–track–bridge coupled model is established for accurately simulating the train–bridge interaction under earthquake excitation, which is made up of a vehicle model built by multi-body dynamics, a track–bridge finite element model, and a 3D rolling wheel–rail contact model. A conditional simulation method, which takes into consideration the wave passage effect, incoherence effect, and site-response effect, is adopted to simulate the spatially varying ground motion under different soil conditions. The multi-time-step method previously proposed by the authors is also adopted to improve computational efficiency. The dynamic responses of the train running on a three-tower cable-stayed bridge are calculated with differing earthquake excitations and train speeds. The results indicate that (1) the earthquake excitation significantly increases the responses of the train–bridge system, but at a design speed, all the running safety indices meet the code requirements; (2) the incoherence and site-response effects should also be considered in the seismic analysis for long-span bridges though there is no fixed pattern for determining their influences; (3) different train speeds that vary the vibration characteristics of the train–bridge system affect the vibration frequencies of the car body and bridge.

This study develops a real-time co-simulation solution that combines ANSYS and MATLAB for investigating of the train–track–bridge dynamic interactions, with the aim of providing an effective and robust method for analyzing and assessing the dynamic responses of running train and bridge, considering their complex nonlinear behaviors under extreme excitations such as earthquake and strong wind. The train–track–bridge coupled system consists of the train subsystem, the track subsystem, and the bridge subsystem. With the adoption of a previously developed efficient multi-time-step method, the train subsystem and the track subsystem are analyzed in MATLAB with a small time-step, whereas the bridge subsystem is analyzed in ANSYS using a large time-step. At each large time-step, the train–track subsystem in MATLAB and the bridge subsystem in ANSYS are coupled by communication of the track reaction forces calculated in MATLAB and the dynamic responses at the track–bridge connecting points calculated in ANSYS. The co-simulation procedure is validated through a comparison of the numerical results from computer coding developed by the authors and the measurement data of a cable-stayed bridge. To demonstrate the effectiveness and robustness of the proposed solution, the responses of a train passing through a cable-stayed bridge under earthquake excitation are analyzed, with consideration of the geometrical nonlinearity of the bridge, using the co-simulation solution.

The accurate assessment of running safety during earthquakes is of significant importance for ensuring the safety of railway lines. Currently, assessment methods based on a single index suffer from issues such as misjudgment of operational safety and difficulty in evaluating operational margin, making them unsuitable for assessing train safety during earthquakes. Therefore, in order to propose an effective evaluation method for the running safety of trains during earthquakes, this study employs three indexes, namely lateral displacement of the wheel–rail contact point, wheel unloading rate, and wheel lift, to describe the lateral and vertical contact states between the wheel and rail. The corresponding evolution characteristics of the wheel–rail contact states are determined, and the derailment forms under different frequency components of seismic motion are identified through dynamic numerical simulations of the train–track coupled system under sine excitation. The variations in the wheel–rail contact states during the transition from a safe state to the critical state of derailment are analyzed, thereby constructing the evolutionary path of train derailment and seismic derailment risk domain. Lastly, the wheel–rail contact and derailment states under seismic conditions are analyzed, thus verifying the effectiveness of the evaluation method for assessing running safety under earthquakes proposed in this study. The results indicate that the assessment method based on the derailment risk domain accurately and comprehensively reflects the wheel–rail contact states under seismic conditions. It successfully determines the forms of train derailment, the risk levels of derailment, and the evolutionary paths of derailment risk.

To explore the effect of canyon topography on the seismic response of railway irregular bridge–track system that crosses a V-shaped canyon, seismic ground motions of the horizontal site and V-shaped canyon site were simulated through theoretical analysis with 12 earthquake records selected from the Pacific Earthquake Engineering Research Center (PEER) Strong Ground Motion Database matching the site condition of the bridge. Nonlinear seismic response analyses of an existing 11-span irregular simply supported railway bridge–track system were performed under the simulated spatially varying ground motions. The effects of the V-shaped canyon topography on the peak ground acceleration at bridge foundations and seismic responses of the bridge–track system were analyzed. Comparisons between the results of horizontal and V-shaped canyon sites show that the top relative displacement between adjacent piers at the junction of the incident side and the back side of the V-shaped site is almost two times that of the horizontal site, which also determines the seismic response of the fastener. The maximum displacement of the fastener occurs in the V-shaped canyon site and is 1.4 times larger than that in the horizontal site. Neglecting the effect of V-shaped canyon leads to the inappropriate assessment of the maximum seismic response of the irregular high-speed railway bridge–track system. Moreover, engineers should focus on the girder end to the left or right of the two fasteners within the distance of track seismic damage.