2.5维有限元分析高铁荷载诱发非饱和土地面振动

Unsaturated Ground Vibration Induced by High-speed Train Loads Based on 2.5D Finite Element Method

摘要:

开发一种非饱和地基2.5维有限单元方法研究高速列车荷载引起的地面振动.对时间进行Fourier变换并沿轨道方向进行波数变换将三维空间问题降为二维平面问题，结合边界条件和Galerkin法推导控制方程2.5维有限元格式.轨道结构视为非饱和地基上的Euler梁，所得频域波数域内解答通过快速Fourier逆变换得到三维时域空间域内结果.分析了车速和路基液体饱和度对地面振动及超静孔隙水压力的影响.结果表明，路基从完全饱和转为近饱和状态轨道中心处地面振动位移幅值变化显著；非饱和路基地面振动位移随时间衰减更快.距轨道中心8 m远处，同一速度下饱和路基路面振动持时大于非饱和路基；车速提高非饱和土振动持续时间变短，而饱和土地面振动持时变长.近轨道处200 km?h-1下地面振动位移幅值大于其他速度且均以相当速率快速衰减；地面振动加速度级在某些车速下的衰减会出现反弹增大现象，其位置与车速密切相关.轨道中心处超静孔隙水压力主要分布在地表下4.5 m内，最大幅值出现在1.5~2.0 m深，且随路基饱和度降低显著减小.

Abstract:

A two-and-a-half-dimension finite element method (2.5D FEM) was established to investigate the surface vibration of the unsaturated ground subjected to moving loads caused by high-speed trains. The track structure was simplified as an Euler beam resting on an unsaturated porous half-space. The Galerkin method was used and the governor equations of unsaturated soil of 2.5D in frequency-wavenumber domain was derived by applying the Fourier transform with respect to time and the load moving direction. The influences of train speed and water saturation of unsaturated ground on ground vibration and excess pore water pressure are analyzed. Results show that, at the track center, the displacement amplitude largely decreases when the water saturation decreases from 100% (fully saturated) to 99% (nearly saturated); for a given speed, the ground vibration displacement of unsaturated ground attenuates faster with time than the saturated ground. At 8 m away from the track center, the displacement amplitude of the unsaturated ground is larger than that of the saturated ground when the train speed is below 250 km?h-1; as the speed increasing, the duration time of the unsaturated ground vibration displacement becomes shorter as the speed increases, while of the saturated ground it becomes longer. The displacement amplitude at 200 km?h-1 is larger than the other speed near the track (less than 5m) and attenuates rapidly at an equal rate. The rebound phenomenon of acceleration may occur at some train speed, and the location is strongly related to the train speed. The excess pore water pressure is mainly distributes within 4.5 m below the ground surface and the maximum amplitude is located at 1.5~2.0 m depth and decreases significantly as the water saturation decreases.