The relationship between subgrade settlement and rail deformation remains unclear, and the impact of subgrade settlement on dynamic responses of the ballasted track, as well as on the running safety and comfort of high-speed trains, has not been adequately quantified. To address such deficiency, a three-dimensional (3D) numerical model of train-ballasted track-subgrade coupled system considering spatial differential subgrade settlements was established. An innovative iterative algorithm was proposed to determine the real-time track-subgrade contact, enabling the analysis of resulting track irregularities and train-induced vibration. The results show that the number of unsupported sleepers increases with greater settlement amplitudes and shorter settlement wavelengths, while spatial differential subgrade settlement significantly affects wheel-rail interaction. Track structures located at the settlement center area on the side with less settlement, as well as those at the settlement boundary area on the side with greater settlement, are more susceptible to damage. These areas also exhibit higher dynamic vertical subgrade stress, thus aggravating differential settlement. The findings could provide theoretical basis and technical guidance for improving high-speed railway operation and maintenance practices.

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.