摘要
针对饱和半空间中任意形状不均质体对地震波的散射问题,采用一种新型基本解方法(MFS)进行求解分析。该方法结合饱和半空间中膨胀波源和剪切波源的格林函数,首先由分布在不均质体和半空间交界面附近两虚拟波源面上的PI、PII、SV波源分别构造了不均质体内外的散射波场,然后由交界面连续性条件建立方程并求解确定了虚拟波源密度,总波场反应由自由波场和散射波场叠加而得,最后在精度检验的基础上,通过一组典型算例研究了平面P波在饱和半空间中不均质体周围散射的基本规律。研究结果表明:两相介质波动的MFS模拟具有极高的数值精度和高频稳定性;波在饱和不均质体中的散射特征取决于入射波的频率和方向、边界渗透条件、介质孔隙率等参数,与在单相介质中的情况具有很大差别;地表位移特征反映了波的散射和饱和不均质体的自振特性,随着介质孔隙率增大,位移幅值谱振荡更为剧烈,且不均质体刚度越小,地表位移放大效应越显著,但最大不超过自由场反应的2倍。
A novel Method of Fundamental Solution(MFS) for scattering of seismic waves by a two-dimensional inclusion of arbitrary shape in poroelastic half-space is presented. Based on the Green's functions of compressional and shear wave source in poroelastic half-space, the scattered waves in inclusion and half space are constructed using the fictitious wave sources close to the interface between the inclusion and the half-space respectively, and the magnitude of the fictitious wave sources are determined by continuous boundary conditions, then the total response can be obtained by the superposition of the free field and the scattered field. Based on the accuracy verification, the nature of diffraction of P-waves around an inclusion in poroelastic half-space is investigated in detail. It is shown that the MFS is of high precision for solving the wave motion in poroelstic twophase medium and is stable for high frequency wave incident. There is large difference between the wave diffraction around the fluid-poroelastic inclusion and the corresponding single phase case. The dynamic response depends on the incident frequency, drainage condition, porosity, etc. The surface displacement characteristics reflect the wave scattering and free vibration characteristics of saturated inclusion. As the porosity increases, the displacement amplitude spectrum oscillates more rapidly, and the surface displacement amplification effect seems more pronounced, but always less than two times of the free field response.
出处
《应用力学学报》
CAS
CSCD
北大核心
2013年第6期815-821,948-949,共7页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(51008210
50978183)
关键词
饱和半空间
不均质体
散射
基本解方法(MFS)
地震波
poroelastic half-space,inclusion,diffraction,Method of Fundamental Solution,seismic waves
