The dynamic response of a railway bridge can be affected by the properties of its foundations, particularly if founded on soft soils. Thus, this work aims to establish a coupled dynamic model to investigate the vibration of train-track-bridge systems considering piled foundations embedded in soft soil. Firstly, to construct the simulation framework, the finite element and multi-body methods are used to model the dynamic behavior of a train-track-bridge interaction (TTBI) system and a pier-cap-pile-soil interaction system. The equilibrium of the two sub-systems is maintained through the bridge's bearing force and a multi-time-step integration strategy is introduced to improve computational efficiency. The proposed model is validated by comparing it to the results from commercial finite element software ABAQUS. Then results are computed using the proposed model and the conventional TTBI model without piles. It is concluded that when considering the piled foundations, the low-frequency vibration of the TTBI system is dominant. Moreover, the vibration energy in the track and bridge below 7 Hz is larger compared with the conventional TTBI model. The influence of train speed on the vibration characteristics of the pile and soil is analyzed. It is found that higher train speeds cause increased pile and soil accelerations at the frequencies associated with the train axle spacing. The novelty of the analysis is providing a new insight into the coupled vibration properties of TTBI systems considering the participation of piled foundations in soft soil.

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.