An analytical model for ground vibrations from accelerating trains

An analytical approach is used to investigate ground vibrations due to accelerating and decelerating trains. The ground is modelled as a stratified half-space with linearly viscoelastic layers. On top of the ground, a rectangular embankment is placed, supporting the rails and the sleepers. The rails are modelled as Euler–Bernoulli beams where the propagating forces (wheel loads) are acting and the sleepers are modelled with an anisotropic Kirchhoff plate. The solution is based on Fourier transforms in time and along the track. In the transverse direction the field in the embankment is developed in Fourier series and the fields in the ground with Fourier transforms. The resulting numerical scheme is efficient and displacements for a wide frequency spectrum can be considered. Numerical examples are given for an X2 train that operates at the site Ledsgard in Sweden. In particular, the effects of the wheel traction from the driving wheel pairs or the braking wheels (all wheels) are accounted for. The results at some instantaneous train speeds are compared to corresponding constant train speeds.