Dynamic Response of a Bridge–Embankment Transition with Emphasis on the Coupled Train–Track–Subgrade System

Dynamic response of a bridge–embankment transition is determined by, and therefore an indicator of, the coupled train–track–subgrade system. This study aims to investigate the approach of coupling the train–track–subgrade system to determine the dynamic response of the transition. The coupled system is established numerically based on the weak energy variation, the overall Lagrange format of D’Alembert’s principle and dynamics of the multi-rigid body, which is verified by in-site measurements. With this model, the influence of rail bending, differential settlement and other factors on the dynamic performance of the transition system is analyzed. The results show that when the train driving speed is 350 km/h, basic requirements should be satisfied. These requirements include that the irregularity bending of the bridge–embankment transition section should be less than 1/1000, the rigidity ratio should be controlled within 1:6, and the length of the transition section should be more than 25 m. In addition, the differential settlement should not exceed 5 mm. Among these factors, the differential settlement and the bending of the rail surface are the main ones to cause the severe dynamic irregularity of the transition section. Our analysis also indicates a requirement to strengthen the 18 m and 25–30 m distance from the abutment tail and the bed structure.