Three-dimensional transient thermo-hydro-mechanical fundamental solutions of unsaturated soils
Résumé
The governing differential equations of unsaturated soils considering the thermo-poro-mechanical behaviour consist of equilibrium, moisture air and heat transfer equations. In this paper at first, following some necessary simplifications, the thermal three-dimensional fundamental solution for an unsaturated deformable porous medium with linear elastic behaviour in Laplace transform domain is presented. Subsequently, the closed-form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Then a set of numerical results are presented, which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Finally, the closed-form time domain fundamental solution will be verified mathematically by comparison with the previously introduced corresponding fundamental solution.