A semi-analytical method for vibrations of a layered transversely isotropic ground-track system due to moving train loads

Abstract

The vibrations of a ground-track system subjected to moving train loads are investigated by using a semi-analytical method combining with the substructure technique. In the coupled system, the ground is modeled as a multi-layered transversely isotropic (TI) half-space, and the track is modeled as a three-layered beam structure, which consists of the rails, sleepers and ballast. The two substructures are coupled by the compatibility condition of vertical displacement at the ballast centerline. The displacement and stress responses of the layered TI ground due to the reaction of the track are then obtained by employing the stiffness method. And solutions in the physical domain are recovered by Fourier synthesis of the frequency-wavenumber domain responses. The proposed semi-analytical model has the merits of all parameters having explicit physical meaning, which is very convenient for engineering application, and of the accuracy being not affected by the layers’ thickness because of the exact dynamic stiffness matrix. The derived formulations are verified by comparison with the existing solutions for the isotropic medium that is a special case of the more general problem addressed. Numerical calculations are first performed for the case of a single wheel axle load moving at subsonic, transonic and supersonic speeds, and then for the case of the X-2000 high speed train of the Swedish National Railway travelling at a speed of 200 km/h. Numeric results show that the vibrations of the ground-track system can be very different when soil anisotropy is considered. And the variation of the TI parameters alters the resonance frequencies of the ground, which in turn alters the interaction between the track and ground.