半空间饱和土中的圆形孔洞对稳态剪切波的散射  

Scattering of steady shear waves around a circular cavity in half-space of saturated soil

作　　者：姜领发[1] 王建华[1] 周香莲[1] 

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200030

出　　处：《岩土工程学报》2007年第3期366-371,共6页Chinese Journal of Geotechnical Engineering

基　　金：教育部留学人员科研启动基金资助项目

摘　　要：采用复变函数和多级坐标的方法并借助在非耗散情况下的Biot波动理论,对半无限饱和土中稳态剪切SV波在一个圆形孔洞周围的散射和动应力集中的问题提出了一种近似求解分析方法。其中利用一个半径很大的圆弧来逼近半空间的直边界,将半空间直边界问题转化为曲面边界问题。首先将饱和土中的Biot波动方程解耦成Helmhotz势方程并预先写出问题波函数的一般形式解,再利用边界条件并借助复数傅立叶级数展开把问题化为求解波函数中未知系数的无穷线性代数方程组,通过变换不同的条件组合,得出半空间的圆形孔洞周围的动应力集中系数的数值解的分布和变化情况。由具体算例及分析可知:本文方法对研究与稳态剪切波有关的散射问题是可行的,并对工程实践有一定的指导作用。In terms of Biot＇s dynamic theory, the multi-polar coordinate and complex function were used to put forward an approximate analysis method for scattering and dynamic stress concentration of steady SV wave around a circular cavity in half space of saturated soil, where a circular cavity with large radius was used to replace the straight boundary of the half space of saturated soil. By using the theory of Helmholtz, the general solution of the Biot＇s wave function was given and a system of infinite linear algebraic equations of the problem studied in this paper could be given by means of the complex series expansion technology and the boundary conditions of the solid matrix and the fluid. Then the variation of the coefficient of dynamic stress concentration at boundaries of the cavity was discussed with different parameter conditions. The results of the given example indicated that the method used in this paper was useful and efficient to the scattering and dynamic stress concentration of shear waves in which the straight boundary existed.

关 键 词：半空间 多级坐标 饱和土 非耗散 散射 复变函数 孔洞 

分 类 号：TU43[建筑科学—岩土工程]