Unsaturated thermal consolidation around a heat source

Abstract

Thermal loadings in saturated (two-phase) clays induce excess pore water pressure due to the difference in the thermal expansion coefficient of the pore volume and the pore water. The gradual dissipation of the excess pore water pressure causes thermal volume reduction which is known as thermal consolidation. However, thermal consolidation in a three-phase soil system such as unsaturated soil is more sophisticated. In this paper, an analytical model for thermal consolidation around a heat source embedded in unsaturated clay or in calyey soils containing two immiscible fluids is developed based on the effective stress concept. Governing equations, including energy, mass, and momentum balance equations are developed. Coexisting solid and pore fluids are assumed to be in local thermal equilibrium. First, a solution is provided using Fourier-Laplace transformation by considering constant coefficients. The inverse transformation is carried out fully analytically and thus, a closed-form solution is proposed. Then, the variations of soil properties during the thermal consolidation process are considered through a temporal discretization process. The developed model is validated using Green’s function theory and the equations and results are compared with the available models in the literature. Results indicate the capability of the model to accurately predict thermal consolidation in a three-phase clayey soil.