Analytical solution to mapping rail deformation under bridge transverse deformation using energy variational principle

The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge. This study addresses the mapping relationship between the track deformation and lateral deformations of bridges. Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle, and an analytical solution is derived for the track deformation accounting for lateral bridge deformations. A five-span simply-supported bridge with continuous welded rail has been selected as the case study. The mapping rail deformations are compared to the finite element results, and both results agree well with each other, validating the analytical method proposed in this paper. The influence factors on the mapping rail deformation are further evaluated. Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low. The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.