层状半空间中沉积谷地对斜入射平面SV波的三维散射

3D Scattering of Oblique Incident Plane SV Waves by a Depositional Valley in Layered Half-space

采用间接边界元法,给出了层状半空间中沉积谷地对斜入射平面SV波的三维散射解答,并通过与已有结果的比较,验证了本文解答的正确性。进行数值计算,研究了斜入射角度对散射效应的影响,并以基岩上单一土层为例,讨论了基岩刚度和覆盖土层厚度对沉积谷地附近地表位移的影响。研究表明,三维散射与二维散射之间存在本质差别,不能简单地将斜入射平面SV波分解到沉积谷地横截面的面内方向,然后按平面问题进行计算;基岩与土层刚度比对沉积附近地表位移幅值有着较大的影响,但对位移幅值的空间分布影响不大;土层厚度变化不仅影响地表位移幅值的大小,还会改变地表位移幅值的空间分布。

The solutions of 3D scattering of oblique incident plane SV waves by a depositional val- ley in layered half-space are given in this paper on the basis of the solutions of a canyon. The accu- racy of the method is verified by comparing with related results. It is found there is essential difference between the case of 3D wave scattering and that of 2D. So we canrt simply make the ob- lique incident plane SV wave decompose into inplane and antiplane directions in the cross-section of the valley, then calculate and superpose respectively. At the same time, many numerical cal- culations have been done for the researches of the scattering effect of the incidence angles. Taking an alluvial valley to be a one layer over half-space as an example, the effects of the stiffness and the thickness of the layer on the displacement are discussed.