基于2.5维有限元法分析横观各向同性地基上列车运行引起的地面振动

Study on Ground Vibration Induced by Train Load in Transversely Isotropic Soil Using 2.5D Finite Element Method

根据2.5维有限元原理,从横观各向同性土体弹性本构方程出发,推导出横观各向同性土体2.5维有限元弹性波动方程。轨道简化成铺设在横观各向同性地基上的Euler梁。在轨道方向的垂直截面上,将轨道结构和地基进行有限元离散,采用八节点单元,每个节点包含三个自由度,从而使复杂的三维问题转化为平面应变问题,再通过FFT逆变换将转换为沿轨道方向三维空间中的时域振动响应。分别基于上海和北京地区的典型土质参数,进行场地动力响应分析。结果表明:列车运行引起的北京地区场地的加速度响应幅值及位移响应幅值均大于上海地区场地;随着距轨道中心处距离的增加,两地区土体的动力响应频率均衰减到简谐荷载的自振频率周围,反映出横观各向同性土体的滤波作用;列车运行引起的地面振动衰减曲线会出现反弹增大的现象,其反弹特性及出现的位置与地基土体参数及列车运行速度密切相关。

2.5D finite element equations for elastic waves of transversely isotropic soil was derived by means of 2.5D FEM from elastic constitutive equation of the transversely isotropic soil. The track was simplified as an Euler beam resting on the transversely isotropic ground. Through finite element discretization, the track structure and the foundation in the section perpendicular to track direction were modeled with 8-node elements. Each node consists of three degrees of freedom so the 3D problem was reduced to a plane strain problem, and the results could be obtained by inverse FFT. Dynamic responses of the ground were analyzed based on typical soil parameters of Shanghai and Beijing. The results indicated that the amplitude of acceleration and displacement response amplitude caused by train traveling in Beijing was higher than that of Shanghai. With the distance increase to the track center, dynamic response frequencies of the ground in both areas declined to the free vibration frequency of simple harmonic vibration, so the filtering of soil was obvious. The rebound phenomenon in the attenuation curve of the ground vibration had the tendency to increase, which was closely relevant to the parameters of the soil and the speed of the train.