横观各向同性含液饱和多孔介质黏弹性瞬态反应  

Viscoelastic transient solution of transversely isotropic fluid-saturated porous media

作　　者：王俊林[1] 祝彦知[2] 张天航[1] 

机构地区：[1]郑州大学环境与水利学院,郑州450002 [2]中原工学院土木建筑系,郑州450007

出　　处：《岩土力学》2007年第7期1315-1322,共8页Rock and Soil Mechanics

基　　金：河南省科技攻关项目(No.0624250008)资助

摘　　要：在考虑横观各向同性含液饱和多孔介质固体骨架和流体可压缩性以及固体骨架的黏弹性特征下,基于横观各向同性含液饱和多孔介质u-w形式的三维动力控制方程,以固相位移u、液相相对位移w为基本未知量,综合运用Laplace变换、双重Fourier变换等方法,在直角坐标系下通过引入中间变量,将六元2阶动力控制方程组化为两组各含4个未知变量的常微分方程组,给出了直角坐标系下横观各向同性含液饱和多孔介质三维黏弹性动力反应的积分形式一般解;作为理论推导的验证,通过引入初始条件和边界条件,对横观各向同性含液饱和多孔介质半空间黏弹性瞬态反应问题进行了求解。解答的退化验证表明,所推导的理论解是正确的。The viscoelastic transient dynamic response of transversely isotropic fluid-saturated poro-elastic half-space for non-axisymmetrical dynamic load applied on surface is studied under rectangular coordinates. Based on Biot＇s theory of porous media, the three dimension u-w type dynamic equations are drawn for transversely isotropic fluid-saturated porous media. Through rigorous theoretical deduction, the closed-form solutions for transversely isotropic fluid-saturated poro-viscoelastic media excited by non- axisymmetrical dynamic forces is derived by means of Laplace transform and double Fourier transform. The transient dynamic response of transversely isotropic fluid-saturated poro-viscoelastic half-space media is studied using initial and boundary conditions. The solution in time domain can be evaluated by the numerical Laplace transforms and Fourier inverse transforms. Comparisons with the existing closed-form solutions for rectangular foundation loaded steady vibration on an elastic half-space are made to confirm the accuracy of the present solutions. This study is reasonable for engineering practice and provides an effective method for transversely isotropic fluid-saturated poro-elastic media.

关 键 词：BIOT波动方程 横观各向同性 含液饱和介质 黏弹性 动力反应 

分 类 号：TU443[建筑科学—岩土工程]