A two-and-a-half-dimensional finite element method (2.5D FEM) is applied to investigate the dynamic response of an unsaturated ground subjected to moving loads caused by high-speed train. The partial differential equations of unsaturated porous medium in frequency domain are deduced based on the equations of motion and mass conservation of three phases, with consideration of the compressibility of solid grain and pore fluid. Governing equations of unsaturated soil in 2.5D FE form are derived by using the Fourier Transform with respect to the load moving direction. The track structure is simplified as an Euler beam resting on the unsaturated porous half-space and the viscous-elastic artificial boundaries are used to avoid the energy reflection from the boundary. Numerical simulations demonstrate effects of the degree of water saturation and train speed to the ground vibration and the excess pore water pressure. It is concluded that the degree of water saturation has a different influence on the ground displacement and acceleration. The gas phase has varied influence to the ground displacement amplitude at different train speed level at the track center. A very small amount of gas in the saturated ground largely increases the ground acceleration amplitude at a given train speed. Ground displacements attenuate rapidly with almost the same rate for both high and low train speeds near the track center. The maximum amplitude of excess pore water pressure is located at 1.5–۲٫۰ m beneath the ground surface and decreases significantly as the degree of water saturation decreases.

Introduction

In recent years, the high-speed-railway has been developed as a quick and convenient means of mass transportation in China. Evaluating the train-caused ground vibration and its impact on the adjacent environment is hence an important design consideration. Investigations concerning the ground vibration induced by moving loads dated back to 1950s, which have been partly reviewed by Beskou and Theodorakopoulos [1]. Many investigations were conducted by analytical means assuming a homogeneous elastic half-space [2,3] or by using semi-analytical models for a multi-layered ground [4]. The FEM, the BEM or the FEM/BEM hybrid schemes [5–۸] were also widely used considering their advantages at dealing with the irregularities of the geometry and material. By assuming the material and geometric properties to be constant along the load-moving direction, only the profile normal to the load-moving direction needs be considered, which is two-dimensional in nature. However, if the effect of the moving loads is to be considered, then the problem is somewhat between two- and three-dimensional (2.5D) [9,10]. Such an idea was firstly proposed by Hwang and Lysmer [11] in studying the response of an underground structure to traveling seismic waves, and was also used by Barros and Luco [12] to obtain the steady-state displacements and stresses within a multi-layered viscoelastic half-space generated by a buried or surface point load moving with constant speed. Yang and Hung [9,10] used the 2.5D FEM to study the 3D ground dynamic response under train loads, considering the discrete sleeper supports of the train tracks. The same concept was also adopted by Takemiya [13] and Bian et al. [14,15] in the study of the environmental vibration caused by the train loads. These studies simplified the subgrade soil as single-phase elastic or visco-elastic soil.