Finite element implementation of a seepage-stress coupling method for solid-liquid-gas three phases in porous media considering compressible gas

Abstract

Some existing coupling models of porous media ignore the gas phase or gas compressibility, making them inadequate in describing the gas transport process and their effects on water infiltration and solid deformation. However, consideration of gas compressibility becomes crucial when involving the confined gas. Furthermore, the unsteady seepage free surface problem may make the numerical solution of seepage-stress coupling more complicated and difficult. To overcome the above problems, a new coupled seepage-stress method considering compressible gas is proposed. Based on the momentum balance equation of solid–liquid–gas, the three-phase model is constructed by making the pore liquid and compressible gas both satisfy the fluid equilibrium equation and continuity equation. Integration of the interface-correction level set method in the solid–liquid–gas three phases model provides a good solution for representing liquid–gas two-phase flow and solid deformation while describing the unsteady free surface between saturated and unsaturated zones. The primary variables in this model are solid displacement and liquid/gas pressure and its governing equations are discretized by finite element strategy. After comprehensively explaining the mathematical framework and numerical implementation, the reliability and effectiveness of the proposed method are validated through several benchmarking examples.