流体饱和弹性半空间裂隙对平面P_I波的衍射

Scattering of plane P_I waves by a crack in poroelastic half-space

采用间接边界元法,求解了饱和半空间裂隙对平面PI波的二维衍射问题。基于单层位势理论,将边界离散并直接在边界单元上施加虚拟荷载(水平作用力、竖向作用力和流量源的叠加)以构造散射波场,并由边界条件确定虚拟荷载密度,总波场由自由波场和散射波场共同组成。通过参数分析研究了入射波频率、入射倾角、埋深、孔隙率、边界渗透条件等因素对饱和半空间中裂隙对平面PI波衍射的影响规律。结果表明:裂隙随埋深增大,地表位移谱振荡加剧,峰值有所降低;随着入射频率增加,孔隙率影响逐渐增大;垂直入射时,水平位移的放大区域主要分布在裂隙两端,斜入射时,主要集中在裂隙正上方地表附近;透水和不透水两种情况下的地表位移幅值和相位差别较小,但干土情况与饱和情况下的位移幅值相差较大。

Presents an indirect boundary element method(IBEM)for solving the scattering of plane PI waves by a crack in permeable and poroelastic half-space.The basic idea of this method is based on the single layer potential theory,and the scattering wave field is constructed by discretizing boundaries and applying virtual loads(horizontal force,vertical force,flow source)to the boundary elements.The magnitudes of the fictitious wave sources are determined by boundary conditions,and then the total response can be obtained by superposing of the free field and the scattered field.The effects of the depth of the crack,the frequency and the incident angle of wave,the porosity and the boundary permeability on the scattering of plane PI waves are discussed by parametric analysis.The results show that:as the depth increases,the surface displacement spectrum fluctuates and the peak value decreases.With the increase of incident frequency,the influence of porosity increases gradually.Under normal incidence,the horizontal displacement is mainly distributed at both ends of the crack,when obliquely incident;it mainly concentrates near the surface above the crack.The difference between displacement amplitude and phase of the surface is not very remarkable in both water-permeable and impermeable cases,but the difference between the saturated and the dry soil conditions is very large.