半空间饱和孔隙介质在P、SV波入射下的波场解

The Wave Fields Solution of Half Space Saturated Porous Medium when Incident P,SV Waves

基于Biot理论,利用Fourier变换和势函数方法,将Biot波动方程化为一组Helmholtz方程。通过入射波和反射波的波势函数表达式及边界条件,可得波势函数的幅值,进而可得位移、应力、孔压。数值算例给出了P和SV波入射的波场解及其随饱和孔隙介质参数的变化。本文的结果是研究饱和土在地震波作用下土的液化以及利用积分方程或边界元方法研究桩在地震波作用下的动力响应的基础。

Based on Biot＇s theory,using Fourier transform and potential function,the wave dynamic equations for Biot＇s theory can be deduced to several Helmholtz equations. The amplitudes of the potentials function can be determined using the expression formula for the potential function of incident wave and reflected wave and the boundary conditions. Then the displacement, the stresses and the pore pressure can be calculated. By numerical examples wave field solution for the incident P and SV waves and their chang with the parameters of saturated porous medium are presented in the paper. The results are basis of the liquefaction for a saturated soil under the action of seisimic waves. Also, it is crucial for the solution of the pile dynamic response problem by integral equation method and boundary elelment method numerical solution under the action of seismic waves.