Three‐dimensional coupled heat,moisture, and air transfer in a deformable unsaturated soil

A three‐dimensional numerical model is presented for three‐phase flow (moisture, air, and heat) in a deformable partly saturated soil with deformation calculated via a non‐linear elastic theory. The present work is an extension of a two‐dimensional analysis presented by Thomas and He. The objective of this work is the solution of problems of greater geometric complexity. The mathematical formulation of this coupled problem consists of four governing equations, developed from the principles of mass and energy conservations as well as the stress equilibrium equation. Darcy's flow law is used to describe the motion of liquid and air in the porous medium, and a Philip and de Vries type vapour flow approach is employed in the formulation. A Galerkin finite element method coupled with a finite difference recurrence relationship is used to obtain simultaneous solutions to the governing equations where pore liquid, pore air pressures, temperature and displacements are the primary variables. The method allows the non‐linear nature of the soil parameters to be modelled. Three‐dimensional 20‐noded isoparametric elements are used to simulate different types of cases for the verification of the work. Results are presented of the application of the new model to four problems, two of which are isothermal and two heating simulations. The three‐dimensional nature of the results achieved is highlighted. Copyright © 1999 John Wiley & Sons, Ltd.