Exact integral solutions for one-dimensional thermal consolidation of semi-infinite saturated soils

Based on the thermo-hydro-mechanical coupled theory for saturated porous media proposed by Coussy, two coupled governing equations for thermal consolidation of saturated soils are presented, taking thermo-osmosis and thermo- filtration into account. The sine and cosine transforms as well as the Hamilton-Cayley law are used to obtain exact integral solutions for one-dimensional thermal consolidation of semi-infinite saturated soils with two types of arbitrary nonhomogeneous boundary conditions. It helps avoid the errors of numerical inverse Laplace transform when dealing with complex boundary conditions. Finally, case studies are provided to validate the proposed analytical solutions and to investigate the thermal responses of saturated soils with seasonal thermal loads on the permeable or impermeable surface. The results show that temperature change, excess pore water pressure and displacement all fluctuate periodically due to seasonal thermal loads. The responses of the excess pore water pressure and displacement of the saturated soils with an impermeable surface are much higher than those with a permeable surface.