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将轨道模拟为铺设在地基上的欧拉梁,对高速列车荷载作用下的欧拉梁动力方程进行双重傅里叶变换,得到地基振动的隐式边界条件。保留每个结点为3个自由度,通过常规u-p格式有限元推导,得到横观各向同性饱和地基有限元控制方程。分别考虑外行SH波、SV波、P波,推导相应的2.5维有限元格式的黏弹性动力边界来模拟人工截断边界。通过与已有文献的对比分析,验证本文理论及计算程序的正确性。算例分析结果表明:随着距离轨道中心距离的增加,土体振动位移减小,加速度衰减减缓;随着深度的增加,孔隙水压力减小,孔隙水压力曲线第一个拐点出现在第1,2层土的分界面上,在深度为10 m处,孔隙水压力减小至0。
The orbit is modeled as an Eulerian beam laid on the foundation. The Euler beam dynamic equation under the action of high-speed train loads is double-Fourier transformed to obtain the implicit boundary conditions of foundation vibration. Each node is kept at 3 degrees of freedom, and the governing equations of the finite element of the transversely isotropic saturated soil are obtained by the conventional u-p finite element method. Considering the lay SH wave, SV wave and P wave respectively, the corresponding 2.5-D finite element finite element viscoelastic dynamic boundary is deduced to simulate the artificial truncation boundary. Through the comparison with the existing literature, this paper verifies the correctness of the theory and calculation procedure. The results of numerical examples show that with the increase of the distance from the center of the orbit, the vibration displacement of the soil decreases and the acceleration attenuation slows down. As the depth increases, the pore water pressure decreases and the first inflection point of the pore water pressure curve appears in the first At the depth of 10 m, the pore water pressure decreases to 0 at the interface between the two layers of soil.