Investigation of ground vibration due to trains moving on saturated multi-layered ground by 2.5D finite element method
A two-and-a-half-dimensional finite element model (2.5D FEM) was developed to investigate dynamic responses of the tracks and saturated porous ground subjected to moving loads caused by high-speed trains. The governing equation was derived from the Boit's theory in frequency domain by applying the Fourier transform with respect to time, and 2.5D finite element equations in u-p format were then established using Galerkin method. The track structure was simplified as an Euler beam resting on a saturated layered porous half-space. The wave-number transform in the load moving direction was employed to reduce the three-dimensional (3D) dynamic problem to a two-dimensional one. The visco-elastic artificial boundary was derived for the saturated soil in the 2.5D FEM by assuming a semi-cylindrical wave front of body wave. The proposed approach was verified by the semi-analytical solutions for a 3D saturated half space subjected to a moving load. The results show that the vertical displacement of elastic medium is greater than that of saturated medium when the train speed is low, while smaller when the train speed becomes high. A large vertical displacement occurs when the train speed is greater than or approaches the shear-wave velocity of the saturated ground. The ground vibration is dominated by either the track resonance in the near-track zone or the train speed in the far-track zone. The attenuation of vertical displacement becomes much slow along distance for high-speed moving trains, and the decay can hardly take place beyond a certain distance from the track center.