An efficient strong seismic analysis model for running safety thresholds of train-track-high pier bridge dynamic system

High-pier bridges, with their strong obstacle-crossing capacity, are vital for high-speed railways (HSR) in rugged mountainous terrains. However high pier flexibility and alignment geometry can critically threaten train safety and substructure stability, risking derailment or rail fracture. This study proposes an efficient dynamics model for running safety assessment of train-track-high pier bridges (TTHPB) system suffering strong earthquakes via the dynamic substructure method (DSM) and hybrid integration time steps. The framework integrates a nonlinear wheel-rail contact model capable of simulating separation, a system longitudinal vibration transmission model for rail stress evaluation, a spatially flexible bridge model, and a novel rigid-flexible coupled large-mass model (RFC-LMM) for seismic excitation input. The employed 3D multipoint seismic algorithm accounts for the travelling wave effect, site effect, coherence effect and non-stationarity. Then The reliability and efficiency of the DSM in formulating bridge dynamic equations, along with the validity of the proposed RFC-LMM in earthquake loading, are well-validated via field experiments and finite element method. Later, a 120 m high-pier bridge (HPB) located in a high-intensity seismic zone (Intensity VIII, PGA = 0.3 g) is investigated. Train safety thresholds are established by varying peak ground acceleration (PGA) and train speed, based on five running safety indicators. Furthermore, this model is extended to the seismic assessment of curved HPB under the limiting curve radius of 5500 m, highlighting the combined effects of ground motion and track curvature. The outcomes provide theoretical support for ensuring the safe operation of HSR trains on straight/curved HPB in mountainous regions and offer a technical framework for seismic control of trains and evaluating post-earthquake residual transport capacity of TTHPB systems.