SH波对浅埋裂纹的半圆形凹陷地形的散射

Scattering of a semi-cylindrical canyon and a crack with incident SH waves

采用Green函数方法,研究浅埋裂纹和含有圆形凹陷的弹性半空间对入射SH波的散射。首先取含有半圆形凹陷的弹性半空间,任意一点承受时间谐和的出平面线源荷载作用时的位移函数基本解作为Green函数;然后求解含半圆形凹陷的弹性半空间对SH波的散射问题;最后在裂纹实际存在位置利用Green函数实施裂纹的人工切割以恢复存在的裂纹,给出浅埋裂纹的半圆形凹陷弹性空间内的位移函数,进而求解裂纹存在对地表位移的影响。

The scattering of a semi-cylindrical canyon and a crack with incident SH waves was studied based on Green＇s function. A special Green＇s function which was a fundamental solution of displacement field for a half-elastic space with a semi-cylindrical canyon bearing an anti-plane harmonic linesource force at any point was proposed for the present problem. And the scattering problem of SH- wave by a half-elastic space with semi-cylindrical canyon was solved. Then, at the actual position of cracks, the existent cracks could be reverted by using Green＇s function and the method of crack-division. Integration for the obtained solution of the whole problem was established, and the solution of the ground surface＇s displacement amplitude was concluded.