半圆形凸起地形对SH波的散射与地震动 --有多个浅埋圆孔情形

采用"契合"的思想,给出了地下多个孔洞与地面上的半圆形凸起地形对SH波散射问题的解答.将整个求解区域分割成两部分来处理,其一为包括半圆形凸起地形在内的一个圆形区域I,其余为区域Ⅱ.在区域Ⅰ中,构造了一个上半部边界应力为零,而其余部分位移、应力任意的驻波解;在区域Ⅱ中,构造了半圆形凹陷和浅埋圆孔的散射波,且要求它满足水平界面上应力为零的约束条件.然后再通过移动坐标,满足"公共边界"的"契合"条件和地下孔洞的边界条件,建立起求解该问题的无穷代数方程组.最后,给出了分析例题和数值结果,并对地表位移幅值进行了讨论.

Scattering of SH-waves by a semi-cylindrical hill above multiple subsurface cavities

The interaction between a semi-cylindrical hill and the subsurface multiple circular cavities with incident SH-wave is studied in this paper. The method of complex function and multi-polar coordinate is employed here. During the solution, the model is divided into two domains, domain I is a circle including boundary of the hill, and the rest is regarded as domain II, which is an elastic half-space including a canyon whose boundary is the shared line of the two domains and the circular cavities below. A standing wave function which satisfies the condition of stress free at the hill edge is constructed in domain I, while scattered wave functions satisfying the zero-stress condition at the horizontal surface is constructed in another part. By employing zero-stress condition around the circular cavities and displacement-stress continuity on the domains' shared line, the problem is solved. Numerical examples and relative discussion is provided finally.