2.5D有限元分析列车荷载引起非饱和土地面振动

Ground vibration induced by moving train loads on unsaturated soil using 2.5D FEM

摘要:

为研究高速列车荷载引起非饱和土地面振动,将地基视为三相介质,开发非饱和地基2.5维有限单元方法.用Euler梁模型模拟轨道系统,对控制方程进行时间Fourier变换和轨道方向波数变换,结合边界条件和Galerkin法推导出频域内2.5维有限元方程,频域-波数域内解答通过快速Fourier逆变换得到时域-空间域结果,通过数值分析考察车速和路基饱和度对地面振动及超静孔隙水压力影响.结果表明:车速较低时,路基从近饱和到完全饱和轨道中心处地面竖向振动位移幅值显著增加；同一速度下非饱和路面加速度幅值大于饱和路面,其地面振动位移和加速度随时间更快衰减.同一车速下距轨道中心8 m处非饱和路基地面振动加速度峰值远大于饱和路基,车速超过300 km/h后两者地面振动位移幅值趋于相等.近轨道处地面振动幅值快速衰减,远轨道处衰减变慢.轨道中心下超静孔隙水压力分布深度为地表下0~4.5 m,最大峰值约在1.8 m,且随路基饱和度降低显著减少.

Abstract:

To investigate the ground vibration of unsaturated ground subjected to moving loads caused by high-speed train,a two-and-a-half-dimensional finite element method (2.5D FEM) was deduced. The foundation was considered as three-phase medium, and the Euler beam model was used to simulate the track system. The 2.5D FEM equations were derived by using the Galerkin method and the Fourier transform with respect to time and load moving direction. The solution in the frequency-wave number domain was transformed to the time-space domain through the Fast Fourier Transform (FFT). The influences of train speed and water saturation on ground vibration and excess pore water pressure were analyzed. Results show that at the track center, ground vibration displacement amplitude increased significantly as the soil varied from near saturated (S_r=99%) to fully saturated state.At a given speed, the unsaturated ground acceleration amplitude was larger than that of the saturated ground,and it decreased more rapidly over time than the saturated ground. At 8 m away from the track center, the unsaturated ground acceleration amplitude was far greater than that of the saturated ground at the same speed. but, when the train speed was beyond 300 km/h, their displacement amplitudes tended to be equal. The ground vibration amplitude attenuated rapidly near the track center, while it attenuated slowly beyond 5 m. The excess pore water pressure of the unsaturated ground under the track center was mainly distributed in shallow depth (0~4.5 m beneath the ground surface) and the peak value appeared at about 1.8 m, which decreased sharply as the ground saturation decreases.