SH波作用下地表软覆盖层中浅埋圆孔的动力分析

Dynamic analysis for a shallow buried circular cavity impacted by SH-Wave in a soft layered half-space

利用复变函数法和波函数展开法对地表软覆盖层中浅埋圆形孔洞在稳态SH波作用下的动应力集中问题进行了研究并给出了解析解。根据SH波散射时的衰减特性,采用了大圆弧假定的方法,即利用一个半径很大的圆来近似表示地表覆盖层的直线边界,将半空间覆盖层直线边界问题转化为曲面边界问题。首先根据Helmholtz定理预先给出了待求波函数的一般形式解,再根据边界条件并利用复数Fourier-Hankel级数展开的方式把所求问题转化为求解波函数中未知系数的无穷线性代数方程组问题,对该无穷代数方程组截取有限项求得该问题的数值结果。通过算例分析了SH波垂直入射时,覆盖层和半空间介质的波数差异、覆盖层厚度的变化、圆孔埋置深度等因素对地表软覆盖层中浅埋圆形孔洞周边动应力集中系数的影响。

The issue of dynamic stress concentration for shallow buried circular cavity in a soft layered half-space under steady SH-wave has been studied based on the complex function and wave function expansion method. An analytical solution was obtained. According to the attenuation characteristic of SH-wave scattering,using the large-arc assumption method,which was,straight boundary of the surface layer was approximated by a circle with large radius,which led to a surface boundary problem. Firstly,the general forms of unknown wave function were given based on the Helmholtz theorem. Then,according to the boundary conditions and the complex Fourier-Hankel series expansion method,the problem was transformed into the infinite linear algebraic equations of unknown coefficients in the solution of the wave function. From the finite terms,the numerical results could be obtained. Through examples,it is analyzed the influence on the distribution of dynamic stress concentration factor around the shallow buried circular cavity in a soft layered halfspace when SH-Wave is normal incidence,including the wave number difference between overburden layer and half space medium in different incident frequencies,the variation on the cover thickness and the buried depth of the circular cavity.