Analytical Solutions Under Half-Space Condition

This chapter investigates the responses of a semi-infinite saturated, porous material subjected to a time-dependent local heat source applied on its free surface, based on the method of elementary solutions. The thermal consolidation behavior of the saturated porous medium under harmonic thermal loading is systematically examined. The coupled heat-water transport induced by non-conjugate thermodynamic forces is often disregarded. This type of coupling arises from the framework of irreversible thermodynamics, in contrast to the mathematical coupling embedded in Biot-type governing equations, which primarily describe flows driven by conjugate forces. The effects of thermal gradients on pore water migration (thermo-osmosis) and the influence of pore pressure gradients on heat transfer (thermal filtration) are incorporated into the formulation of governing equations for linear, isotropic, thermo-elastic porous media. A closed-form theoretical solution is developed for the thermal consolidation behavior of layered porous media subjected to time-dependent thermal loading.