Thermo-hydro-mechanical models for saturated and unsaturated porous media

Abstract

Problems encountered in many branches of engineering, such as geotechnical engineering, geoenvironmental engineering, agricultural engineering, etc., involve the study of deformation, heat and fluid flow in saturated and unsaturated porous media. Although, mathematical models are reported in the literature for porous media, the analyses using those models are often limited to conditions such as rigid media, neglecting thermo-osmosis and thermal filtration, constant material properties, ignoring deformation effects on mass balance and heat balance equations, etc. Most of these conditions are not justifiable for porous materials with very low hydraulic conductivity and high deformability and porosity such as clay buffers used in geoenviromnental applications. Motivated by these observations, this thesis develops fully coupled mathematical models for saturated and unsaturated porous media under thermal, hydraulic and mechanical loading. In a study of saturated media, a set of governing equations accounting forcompressibility and thermal expansion of constituents, convective heat flow and changing porosity and related properties is presented in terms of displacements, temperature and pore water pressure. The governing equations are nonlinear and also consider thermodynamically coupled water and heat flow (thermo-osmosis and thermal-filtration). The advantages of this model over existing saturated models are discussed. Analytical solutions are presented in the Laplace transform space for one dimensional soil columns, spherically symmetric and radially symmetric problems for a linearized version of the model. Time domain analytical solutions are obtained for one dimensional columns and a spherical cavity in a homogeneous media. A numerical inverse scheme is used to obtain time domain solutions for radially symmetric problems. A mixed finite element formulation is presented to solve non-linear problems. Selected numerical results for a soil column, and spherical and cylindrical cavity problems are presented to demonstrate the principal features of the coupled model and the significance of thermo-osmosis and material nonlinearity. A second part of the thesis deals with unsaturated media. Here, a set of governing equations is developed to simulate coupled heat, moisture, and air transfer in deformable porous media. A constitutive model that includes hermo-hydro-mechanical coupling effects for a non-isothermal unsaturated medium and fully coupled heat and moisture transfer accounting for thermo-osmosis and thermal-filtration is used to establish the coupled nonlinear governing equations which are expressed in terms of displacement, temperature, capillary pressure, air pressure (and evaporation rate). 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 applicability and accuracy of the present model is demonstrated by comparisons with an analytical solution for infiltration into a soil column, experimental results for drying and rewetting of a soil column which include hysteresis, and an experiment involving heating of a clay cylinder. Predictions are also made for a one dimensional soil column under various loading, and heating and combined heating-infiltration of a thick clay cylinder to portray the principal features of the coupled fields. The significances of mechanical deformation , thermo-osmosis and thermal-filtration are discussed.