饱和土与衬砌动力相互作用的圆柱形孔洞内源问题解答

考虑饱和土与衬砌结构的动力相互作用,该文研究了内源荷载作用下圆柱形孔洞的动力响应问题.将饱和土体和衬砌结构分别视为流固耦合介质和弹性均匀介质,通过引入势函数将位移控制方程化为二维轴对称波动方程.采用拉普拉斯变换,得到饱和土体位移应力的表达式及衬砌的位移应力的表达式.利用土体与衬砌结构之间的连续性条件和衬砌结构内边界上的边界条件,确定表达式的未知系数.采用逆拉普拉斯变换的数值方法,给出了问题的数值解.分析了饱和土中圆形衬砌结构随土体和衬砌结构参数变化的动力响应规律.

A SOLUTION ON THE INTERNAL SOURCE PROBLEM OF A CYLINDRICAL CAVITY COSIDERING THE DYNAMIC INTERACTION BETWEEN LINING AND SATURATED SOIL

Considering the dynamic interaction between the lining and saturated soil, this paper presents the dynamic response of a cylindrical cavity subjected to an internal loading. The lining structure and saturated soil are respectively treated as fluid-solid coupling medium and homogeneous elastic one. Two-dimensional axi-symmetric wave equation is derived from the governing equation of displacement by introducing the potentials functions. The expressions of the displacement and stress for both the saturated soil and the lining structure have been obtained using Laplace transform. Utilizing the inner boundary condition of the lining and the continuity conditions between the soil and the lining, the unknown coefficients in the expressions can be determined. With the inverse Laplace transform, the numerical solution of the problem is presented. The dynamic responses of the lining structure in saturated soil are analyzed for the different parameters of the soil and the lining.