非饱和多孔介质有限元分析的基本控制方程与变分原理

Governing Equations and Variational Principle for the Finite Element Analysis of Unsaturated Porous Media

本文在对问题研究现状进行阐述的基础上较系统地给出了骨架可变形非饱和多孔介质的全耦合分析模型,模型中考虑了孔隙气体、水(油)流动对介质力学性能的影响,多孔介质的饱和度、渗透系数与毛吸压力的关系。由实验给出,所导出的控制方程以固体骨架的位移与孔隙流体压力为基本未知量。由于问题的非自共轭特征,文中构造了非饱和介质动力问题的参数变分形式,并在此基础上给出有限元离散方程。

The description of the advances achieved in the past years is given at first, and a fully coupled model is systematically presented for the analysis of skeleton deformable porous media, where the air (gas) and water (oil) are considered in fully or partially saturated conditions. The relationships between saturation, permeability and capillary pressures in porous media are given through the way of laboratory test. The solid displacements and the pressures of fluids are taken as primary unknowns in the governing equations of the model. Due to the non-conjugate behaviour of the problem, the parametric variational principle is derived and then used for the establishment of the finite element formulations.