含孔半圆形凸起地形及多个孔洞对SH波的散射

Scattering of SH-waves by a semi-cylindrical hill with a hole and multiple cavities around it in half-space

应用"契合"、复变函数及多极坐标法研究在平面SH波的作用之下,含有圆形孔洞的半圆形凸起地形与其附近的多个圆形孔洞的散射问题,研究了SH波对其动应力集中及地震动的影响.对问题求解时,将所研究的区域一分为二,成2个区域,并分别构造其波函数.最后在2个区域的公共边界上实施"契合",而得到问题的解答.最后给出了算例,分析讨论了地表位移幅值及圆形孔洞周边上的动应力集中系数的变化规律.结果表明,浅埋多圆孔的间距越小,对地表位移幅值和动应力集中系数的影响越大,当浅埋圆孔间距与凸起半径的比值达到400时,对地表位移的影响基本消失.

The antiplanar SH-deformation of a semi-cylindrical hill with a hole and several concentric circular cavities around it, and the influence of SH-waves on dynamic stress concentrations and ground motion were studied by using a ＂conjunction＂, complex functions, and the multi-polar-coordinate method. During the solving process, the domain was divided into two regions, and the scattering wave functions were constructed separately in each one. Then a conjunction was made at the common boundaries to find the solution to the problem. Computational examples are presented. Variation rules are discussed for the amplitudes of surface displacements and the dynamic stress concentration factors around the edges of circular cavities. It was concluded that the smaller the distances between the cavities, the greater the influences of displacement amplitude and the dynamic stress concentration factor （DSCF）. When the ratio of the distances between cavities to the radius of the hill is more than 400, their inter-influence on displacements and DSCF basically dies away.