关于传递矩阵法分析饱和成层介质响应问题的讨论

DISCUSSION ON THE MATRIX PROPAGATOR METHOD TO ANALYZE THE RESPONSE OF SATURATED LAYERED MEDIA

水平成层土体的地震响应分析(自由场分析)是地震工程领域地震波散射问题的前提基础,由于饱和多孔方程的复杂性,以往的研究大多集中于干土情形,对于饱和土情形的研究相对较少.而实际工程中,地下水位以下,土体孔隙中充满流体,应考虑饱和多孔介质模型.基于Biot多孔介质模型,考虑饱和土中固液相对运动引起的衰减,采用Thomson--Haskell传递矩阵方法得到了饱和成层土体在地震波入射情形时的稳态反应,经傅里叶反变换,可得到时域暂态反应.通过SV波从基岩入射至上覆饱和土层的数值算例,验证了该方法的有效性.发现和初步阐明了计算中出现的两类违背因果律(即响应先于输入)的现象:(1)当SV波入射角度大于导致基岩中反射P波为非均匀波的临界角时,会使得计算结果违背因果律.因此,当入射角超过临界角时,非均匀波的表示尚需进一步完善;(2)由于P2波的衰减,当与稳态波衰减有关的渗透率、土层厚度、入射波频率等参数导致衰减系数超过计算机表示精度时,会出现结果违背因果律现象,并据此得到了满足因果律的参数范围,该范围可作为实际计算时的一个上界.该工作为采用传递矩阵法分析水平饱和土层自由场响应提供了指导依据,且地下水位以上可采用干土模型,水位以下采用饱和土模型,更符合实际情形.

Seismic response analysis of horizontal layered soil is the precondition of the seismic wave scattering problem.The previous studies mostly focused on the dry soil condition, but in practical engineering, below the underground water level, the soil is filled with fluid. So the saturated porous media model should be considered. Based on the Biot model,considering the attenuation caused by the relative motion of solid and liquid, the steady-state response of saturated layered soil subjected to oblique incident seismic wave is obtained by using the Thomson--Haskell propagator matrix method. The time-domain transient response can be obtained by inverse Fourier transform. This method is validated by a numerical example that SV wave is incident from the bedrock to the overlying saturated soil layers. Two kinds of contraries to law of causality are found in numerical analysis, and their reasons are explained preliminarily：（1） When the incident angle of SV wave is larger than the critical angle for the reflection P wave in the bedrock becoming non-uniform, it leads to noncausality;（2） Due to the attenuation of P2 wave, when the attenuation coefficient associated with the parameters such as permeability, the thickness of the soil layer and the frequency of the incident wave is beyond the computer accuracy, it leads to noncausality either. The range of parameters necessary for causality is obtained accordingly, which can be used as an upper bound in practice. This work provides guidance for the analysis of free field response of saturated soil layer.