Riding safety prediction of a high-speed train running on transition zone under foundation settlement

• The settlement threshold of bridge pier for traffic safety at different speeds is determined. • The beveled settlement threshold of subgrade for driving safety under different speed and different length of transition zone is determined. • Time-frequency analysis is used to reveal the dynamic response characteristics of pier settlement and bending deformation of subgrade in frequency domain. The settlement of piers and subgrade bending deformation are widely recognized as common issues in the transition zones of high-speed railway bridges. This study aims to investigate the settlement behavior within these transition zones and its impact on the dynamic interaction between trains and the track. To achieve this, a vehicle-track-transition zone mapping relationship model is developed to analyze both the settlement behavior and the resulting dynamic response characteristics. The study employs the finite element method and multi-body dynamics to construct the simulation model. Settlement effects are simulated using the Newton-Raphson iterative method, with the additional rail deformation caused by foundation settlement serving as the excitation for the vehicle-track-transition zone dynamic interaction system. In the numerical analysis, the dynamic effects of three key factors—train speed, transition zone length, and the amplitude of foundation settlement—are examined based on the performance of the vehicle-track-transition zone interaction. The time-frequency technique is utilized to comprehensively reveal and clarify the spatial-frequency characteristics of system responses influenced by settlement excitation. Moreover, the relationship between the safety-based settlement threshold and these three factors is calibrated.