An analytical solution to the mapping relationship between bridge structures vertical deformation and rail deformation of high-speed railway

This paper describes a study of the mapping relationship between the vertical deformation of bridge structures and rail deformation of high-speed railway, taking the interlayer interactions of the bridge subgrade CRTS II ballastless slab track system (HSRBST) into account. The differential equations and natural boundary conditions of the mapping relationship between the vertical deformation of bridge structures and rail deformation were deduced according to the principle of stationary potential energy. Then an analytical model for such relationship was proposed. Both the analytical method proposed in this paper and the finite element numerical method were used to calculate the rail deformations under three typical deformations of bridge structures and the evolution of rail geometry under these circumstances was analyzed. It was shown that numerical and analytical calculation results are well agreed with each other, demonstrating the effectiveness of the analytical model proposed in this paper. The mapping coefficient between bridge structure deformation and rail deformation showed a nonlinear increase with increasing amplitude of the bridge structure deformation. The rail deformation showed an obvious "following feature"; with the increase of bridge span and fastener stiffness, the curve of rail deformation became gentler, the track irregularity wavelength became longer, and the performance of the rail at following the bridge structure deformation was stronger.