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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 the Biot theory, the Biot wave equation is transformed into a set of Helmholtz equations by Fourier transform and potential function method. Through the expressions of wave potential functions and the boundary conditions of incident waves and reflected waves, the amplitudes of the wave potential functions can be obtained, and displacement, stress and pore pressure can be obtained. Numerical examples show the wave field solutions of P and SV waves and their variations with the parameters of saturated porous media. The result of this paper is to study the liquefaction of saturated soils under the action of seismic waves and to use the integral equation or boundary element method to study the dynamic response of piles under seismic waves.