关于传递矩阵法分析饱和成层介质响应问题的讨论

发布时间：2018-03-01 14:27

本文关键词： 成层饱和土自由场响应传递矩阵法衰减波因果律　出处：《力学学报》2016年05期 　论文类型：期刊论文

【摘要】：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.
[Abstract]:The seismic response analysis of horizontal layered soil (free field analysis) is the premise of seismic wave scattering problem in seismic engineering field. Due to the complexity of saturated porous equation, most of the previous studies focused on dry soil case. The study of saturated soil is relatively few. But in practice, under the groundwater level, the soil pore is filled with fluid, so the saturated porous media model should be considered. Based on the Biot porous media model, the saturated porous media model should be considered. Considering the attenuation caused by the relative motion of solid and liquid in saturated soil, the steady-state response of saturated layered soil in the case of seismic wave incidence is obtained by using Thomson--Haskell transfer matrix method, which is inversely transformed by Fourier transform. The transient response in time domain can be obtained. A numerical example of SV wave incident from bedrock to saturated soil layer is presented. The validity of the method is verified. Two kinds of phenomena that violate causality law (i.e. response before input) are found and preliminarily explained when the incident angle of SV wave is greater than that of critical angle of inhomogeneous wave reflected in bedrock. Therefore, when the angle of incidence exceeds the critical angle, the representation of the non-uniform wave needs to be further improved) because of the attenuation of P2 wave, when the permeability and the thickness of soil layer are related to the attenuation of steady wave, When the attenuation coefficient of incident wave frequency exceeds the accuracy of the computer representation, the result will violate the causality law, and the parameter range satisfying the causality law will be obtained. The range can be used as an upper bound in practical calculation. This work provides a guide for the analysis of free field response of horizontal saturated soil layer by transfer matrix method, and the dry soil model can be used above the groundwater level and the saturated soil model can be used below the water level. More in line with the actual situation.
【作者单位】：南京航空航天大学土木工程系;
【基金】：国家自然科学基金资助项目(51178222,51378260)
【分类号】：TU435

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