半球形凹陷饱和土半空间对入射平面SV波三维散射问题的解析解

An analytic solution for the three-dimensional diffraction of plane SV-waves by hemispherical canyons in a fluid-saturated porous medium half space

以Biot饱和多孔介质动力学理论为基础,利用Fourier-Bessel级展开法,给出了饱和多孔介质半空间中半球形凹陷地形对入射平面SV波散射问题的解析解.利用这一解析解数值计算地表位移幅值,分析入射角、入射波频率对地表位移幅值的影响,并与现存的单相介质情况下三维半球形凹陷问题解析解进行对比得出如下结论:(1)本文两相介质模型与单相介质模型有很大区别;(2)入射角、入射频率对场地表面位移分量有重要影响;(3)随着入射角、入射频率的增大,地表位移分布变得更复杂,且放大效应比单相介质模拟结果更加显著.

In this paper, an analytic solution for the three-dimensional scattering and diffraction of plane SVwaves by a hemispherical canyon in fluid saturated porous media haft space is derived by using the Biot dynamic theory. The Fourier-Bessel series expansion technique is used to get the analytic solution for the first time. The results of surface displacement amplitudes are presented, the effects of frequency and angles of incident waves on the surface displacement amplitudes are discussed. These results are compared with those from the same situation but with an elastic one-phase medium. Based on numerical results, we conclude： （1）there is a significant difference between the previous single-phase model and the present two-phase model; （2） the normalized displacements on the free surface of alluvial valley are mainly dependent on the incident wave angles, the dimensionless frequency of the incident SV-waves; （3）with the increases of the incident angle, frequency, the displacements become more complicated ; and the amplification of the displacement on the free surface of alluvial valley is more prominent than that modeled by single-phase.