平面SV波在饱和半空间中沉积谷地周围的散射

Diffraction of plane SV waves by an alluvial valley in poroelastic half-space

采用一种特殊的间接边界积分方程法,求解了平面SV波在饱和半空间中任意形状沉积谷地周围的二维散射问题。结合饱和半空间中膨胀波源和剪切波源格林函数,由分布在沉积和半空间交界面附近两虚拟波源面上的波源分别构造沉积内外的散射波场,由交界面连续条件建立方程并求解确定虚拟波源密度,总波场反应即可由自由波场和散射波场叠加而得。然后通过边界条件验算、退化解答与现有结果的比较以及稳定性检验,验证了方法的计算精度。通过一组典型算例,研究了平面SV波在饱和半空间中沉积谷地周围散射的基本规律,详细给出了不同参数情况沉积谷地附近地表位移幅值和孔隙水压,着重分析了入射SV波频率和角度、边界渗透条件、沉积孔隙率等因素对场地反应的影响,得出了一些有益的结论。

This paper presents a special indirect boundary integration equation method for scattering of plane SV waves by a two-dimensional alluvial valley of arbitrary shape in poroelastic half-space.Based on the Green＇s functions of compressional and shear wave source in poroelastic half-space,the scattered waves in valley and half space are constructed by using the fictitious wave sources close to the interface between the valley and the half-space respectively,and the magnitude of the fictitious wave sources are determined by boundary conditions for continuity.Then the total response can be obtained by the superposition of the free field and the scattered field.The precision of the method is verified by the satisfaction extent of boundary conditions,the verification of numerical stability and the comparison between the degenerated solutions of single-phased half-space and the well-known solutions.This paper investigates in detail the nature of diffraction of SV waves around alluvial valley in poroelastic half-space,and discusses the effects of incident frequency,drainage condition,porosity,etc.on the diffraction of waves.Finally,some conclusions are drawn.