Preliminary Study on Modeling Thermo-Hydro-Mechanical Coupling Behavior of Unsaturated Soils Based on Hybrid Mixture Theory

Abstract

Thermo-hydro-mechanical (THM) coupling processes in unsaturated soils are very important in both theoretical and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from the Taylor's series expansions. Constitutive relationships of the THM coupled behavior for unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closed problem is formed. In addition to the modification of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling of elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are derived.

A Coupling Difference Scheme of Thermo-Hydro-Mechanical Model on Unsaturated Porous Media

“…Unsaturated soils are composed of a solid skeleton, a liquid, and a gas, represented by s, l, and g, respectively. The THM coupled equations are given as following [4].…”

“…The mixture theory was initially proposed to analyze multi-constituent gas mixtures. A nonlinear multi-field coupled framework for multi-constituent three-phase soils was derived by Cai et al using HMT [4]. And with development of the application, it successively appeared all kinds of grid difference methods [5], discontinuous grid [6], and staggered grid finite difference method [7] and so on.…”

“…Based on the HMT framework, the formulas of the THM coupling behavior for unsaturated soils has been established. The closed field equations include 10 equations and 10 unknown variables .Then the number of unknown variables is equal to equations, thus the closure of this coupling problem is set up [4,8].…”