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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。
By using the indirect boundary element method, the three-dimensional scattering solution to the oblique SV plane SV wave in the sedimentary valleys in the layered half-space is given. The correctness of this paper is verified by comparison with the existing results. The influence of oblique incidence angle on the scattering effect is studied. Taking the single soil bed on the bedrock as an example, the effect of bedrock stiffness and the thickness of overburden on the surface displacement near the valley is discussed. The results show that there is an essential difference between the three-dimensional scattering and the two-dimensional scattering. It is not easy to decompose the obliquely incident plane SV wave into the in-plane direction of the valley of the sedimentary valley and then calculate according to the plane problem. However, it has little effect on the spatial distribution of displacement amplitude. The change of soil thickness not only affects the magnitude of surface displacement but also changes the spatial distribution of the amplitude of surface displacement.