Abstract

In the case of a fast drainage process, water movements result in a rapid change in capillary pressure and shrinkage of a porous material. Until now the models used to predict the deformation of most porous media are based on the quasi-static behaviour laws, and dynamic effects are completely neglected. In this paper, a fully coupled model with dynamic capillarity effect considered is proposed for unsaturated water-air flow within deforming porous media. Then, this model is validated with respect to documented experiment on investigation of dynamic capillarity effect in unsaturated sand. The Finite Element Method (FEM) and backward Euler method are used for the discrete approximation of the partial differential equations in space and time, respectively. Numerical results provided by dynamic model have high agreement with recorded experiment data. Moreover, numerical results also reveal that dynamic effects on capillary pressure could cause unexpected deformation (shrinkage) for porous media. All investigations suggest that dynamic effects on capillary pressure should be taken into account to predict unsaturated water-air flow and shrinkage for porous media.

摘要

在快速排水过程的情况下，水运动导致毛细管压力的快速变化和多孔材料的收缩。迄今为止，用于预测大多数多孔介质变形的模型都是基于准静态行为定律，而完全忽略了动力效应。本文针对变形多孔介质中的非饱和水-空气流动提出了一种考虑动态毛细效应的全耦合模型。然后，该模型在非饱和砂中动态毛细作用研究的记录实验中得到验证。有限元法 (FEM) 和反向欧拉法分别用于空间和时间偏微分方程的离散逼近。动态模型提供的数值结果与记录的实验数据高度吻合。此外，数值结果还表明，对毛细管压力的动态影响可能导致多孔介质意外变形（收缩）。所有研究表明，在预测多孔介质的不饱和水-空气流动和收缩时，应考虑对毛细管压力的动态影响。