Ground vibration induced by trains moving on saturated ground using 2.5D FEM

Based on the Biot’s wave propagation equations and boundary conditions, the Galerkin method is used to derive the u-p format finite element equation in the frequency domain by the Fourier transform. The track and the attached sleepers are simplified as the Euler beams resting on saturated half-space, and the wave-number transform in the load moving direction is applied to reduce the three-dimensional (3D) dynamic problem to a two-dimensional (2D) problem. The dynamic problem is solved in a section perpendicular to the track direction, and the 3D responses of the track and the ground are obtained from the inverse wave-number expansion. Assuming that the wavefront of body wave is the semi-cylindrical form, the visco-elastic artificial boundary which is suitable for 2.5D finite element method (2.5D FEM) is obtained for the saturated soil. The model of 2.5D FEM is verified. The results show that the vertical displacement of elastic medium is greater than that of poroelastic medium when the train speed is low, but the latter is greater than the former as the train speed is high. The track and the ground have produced greater vibration when the train speed is slightly more than the shear wave velocity of the saturated ground. The ground vibration decreases gradually with the further increase of the train speed, but the decay becomes slowly with the distance. The pore water pressure curves with depth are also presented.