单层不可压缩饱和多孔介质一维瞬态响应精确解

基于Biot理论,考虑惯性、黏滞和机械耦合作用,假定固体颗粒和流体均不可压缩,得到了表面任意竖向荷载作用下单层饱和多孔介质一维瞬态响应的精确解。导出了以固体骨架位移表示的无量纲控制方程,并将边界条件齐次化。求解对应无黏滞耦合作用的特征值问题,得到一组满足齐次边界条件、关于空间坐标的正交函数基。利用变异系数法和基函数的正交性,得到一系列相互解耦的、关于时间的二阶常微分方程及相应的初始条件,并采用状态空间法求解常微分方程,得到位移分量。对整体平衡方程关于空间坐标积分,根据边界条件可确定总应力,并进而求得孔隙压力。通过算例验证所得解法的正确性。

Exact solution for one-dimensional transient response of single-layer incompressible fluid-saturated porous media under arbitrary vertical loadings

Based on the Biot theory,exact solution for one-dimensional transient response of single-layer fluid-saturated porous media loaded arbitrarily at its top surface is developed,where the inertial,viscous and mechanical couplings are taken into account and the solid particles and fluid are assumed to be incompressible.Firstly,the dimensionless governing equations in terms of displacement of solid skeleton are derived;and the boundary conditions are homogenized.Then,the eigen-value problem for the corresponding...