一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论，在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下，建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型，利用Laplace变换，求得了原初边值问题在变换空间中的解析解，并利用Laplace逆变换的Crump数值反演方法，得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应，分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明，与不可压流体饱和弹性多孔介质相同，不可压流体饱和粘弹性多孔介质中亦只存在一个纵波，并且固相骨架的粘性对动力行为有显著的影响。

Dynamical Response of One Dimension Liquid Saturated Viscoelastic Porous Medium Layer

Based on the theory of porous media and Viscoelasticity, the dynamical responses of a fluid saturated viscoelastic porous medium layer were investigated, in which the saturated porous material was modeled as a two phase system composed of an incompressible solid phase and an incompressible fluid phase. The Laplace transformation technique was applied to the initial boundary problem for the dynamical behaviour of one dimensional liquid saturated viscoelastic porous medium layer, and the analytical solution in the transformed space was obtained.The Crump numerical method for the inverse Laplace transformation was adopted to obtain the numerical results of the dynamical behaviour. A transient behaviour of fluid saturated standard linear viscoelastic porous medium layer was examined numerically, and the porous solid displacement, seepage velocity of the pore liquid, pore pressure and the effective stress were obtained. It has been shown that only one longitudinal wave in the incompressible fluid-saturated viscoelastic media is existed, and the influences of the viscosity of the porous solid on the dynamical behaviour are remarkable.