横观各向同性饱和土体三维粘弹性动力分析  

Three dimensional 3-D viscoelastic dynamic analysis of transversely isotropic fluid-saturated poroelastic soil in time domain

作　　者：祝彦知[1] 李冬霞[2] 方志[1] 

机构地区：[1]同济大学地下建筑与工程系,上海200092 [2]中原工学院土木建筑系,郑州450007

出　　处：《岩土力学》2005年第10期1557-1564,共8页Rock and Soil Mechanics

基　　金：上海市重点学科建设项目资助。

摘　　要：采用针对横观各向同性饱和土体u-w形式三维粘弹性动力方程,考虑土骨架的粘弹性性质且基于粘弹性理论,通过运用Fourier展开、Laplace和Hankel积分变换方法和引入中间变量,将含有粘弹性参数的六元二阶偏微分运动控制方程组,化为2组各含4个未知变量的常微分方程组,从而给出了柱坐标系下粘弹性横观各向同性饱和土体在非轴对称动力荷载作用下的瞬态反应的土骨架位移分量、孔隙流体相对于土骨架的位移分量瞬态反应一般解。在此基础上,引入初始条件和边界条件,对垂直向和水平向动力荷载作用下半空间边值问题进行了求解。根据动力时域解答的一般解,利用Laplace和Hankel数值逆变换技术,编制了相应的数值计算程序。并进行了实例验证和弹性、粘弹性解的对比分析。结果表明,在进行横观各向同性饱和土体动力分析时,考虑土骨架的粘弹性是必要的。Based on 3D viscoelastic dynamic equations for transversely isotropic fluid-saturated soil, the Fourier expansion approach and Laplace-Hankel transformation are used to solve the viscoelastic dynamic response of the transversely isotropic fluid-saturated soil. Through strictly theoretical deduction, the closed-form solutions are derived in terms of solid matrix displacements and fluid displacements relative to the soil matrix. According to initial condition and boundary condition, the boundary-value problems of transversely isotropic saturated viscoelastic half-space under the action of vertical and horizontal dynamic loads are solved. The solutions in time domain can be obtained by using Laplace-Hankel inverse transforms. The computer programs are developed for calculating the stress and diaplacement of transversely isotropic fluid-saturated soil. Selected numerical results are presented. The results show that it is necessary to take into account viscoelasticity of saturated soil.

关 键 词：BIOT波动方程 横观各向同性 饱和土体 粘弹性模型 动力分析 LAPLACE-HANKEL变换 数值解 

分 类 号：TB115[理学—数学] TU435[理学—应用数学]