2.5维有限元分析饱和地基列车运行引起的地面振动

从饱和土的Biot波动方程出发，通过对时间的Fourier变换得出频域内的波动方程，再结合边界条件利用Galerkin法推导出频域内的u–p格式的有限元方程。把轨道视为饱和地基上的Euler梁，通过沿轨道方向的波数变换将三维空间问题降为平面应变问题。将平面应变问题解答沿轨道方向进行波数扩展，最后通过快速Fourier逆变换求得三维时域–空间域内的地面振动响应。假设体波波阵面为半圆柱形式，推导出了适合饱和多孔介质2.5维有限元的黏弹性人工边界。验证了计算模型。结果表明：车速低时，弹性介质的竖向位移大于饱和介质；高速时，饱和介质竖向位移大于弹性介质。车速略微超过饱和土剪切波速时地面产生振动增大现象，随车速进一步增加位移幅值又逐渐减小，但随距离的增加衰减变慢，且得出了不同车速时孔隙水压力随深度的变化曲线。

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.