Coupled heat-moisture-air transfer in deformable unsaturated media

A mathematical model is developed to simulate coupled heat, moisture, and air transfer in deformable unsaturated porous media. A constitutive model that includes thermo-hydro-mechanical coupling effects for a non-isothermal unsaturated medium and fully coupled heat and moisture transfer is used to establish the coupled nonlinear governing equations. These equations are expressed explicitly using displacements, capillary pressure, air pressure, and temperature (and evaporation rate) as basic variables. This allows the incorporation of porous medium deformation, moisture retention hysteresis, and soil inhomogeneities into the theory. The heat of wetting, heat sink due to thermal expansion of the medium, phase change between liquid water and vapor water, and compressibility of liquid water are also included in the model. A mixed-type finite element formulation of the nonlinear governing equations is presented. The focus of this paper is primarily on the establishment of a consistent set of governing equations. Nonlinear dependencies of some material properties have not been treated due to the lack of experimental data. Numerical solutions for heating, infiltration, and loading of a soil column portray the principal features of the coupled fields and confirm the general validity of the present model.