An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation

Abstract

A rigorous and unified treatment of the theory of non-isothermal flow and deformation in unsaturated porous media is presented. The governing equations based on the equations of equilibrium, the effective stress concept, Darcy's law, Fourier's law and the conservation equations of mass and energy are derived using a systematic macroscopic approach. The thermo-hydro-mechanical coupling processes taken into account include: thermal expansion, thermal convection by moving fluid, fluid flux due to temperature gradient (Soret effect), phase exchange (vaporisation, condensation), heat exchange between the phases, heat of wetting, and heat due to phase compression. Both elastic and elasto-plastic constitutive equations are developed. All model coefficients are identified in terms of measurable parameters. The governing equations derived are general in nature, embodying all previously presented formulations in the field. For example, when the heat of wetting, and that heat due to phase compression are neglected, and it is assumed that the vapour is at the saturated liquid pressure, with all phases in thermal equilibrium, and that the forced convection is negligible, the theory of heat and mass transfer presented by Thomas and his coworkers is obtained. Also when the pore air volume reduces to zero and the thermal equilibrium is assumed, the thermo-elastic model for fluid saturated media presented by McTigue [J. Geophys. Res. 91 (B9) (1986) 9533] is recovered.