Coupled Model for Heat, Moisture, Air Flow, and Deformation Problems in Unsaturated Soils

Abstract

Through extensive review and study on the different aspects of coupled processes in unsaturated soil, a general three-dimensional mathematical model for coupled heat, moisture, air flow, and deformation problems in unsaturated soils is proposed in a consistent and unified manner. In the proposed model, both pore-water and air transfers are assumed to be governed by the generalized Darcy’s law and pore-vapor transfer is considered to occur due to two effects: first, under molecular diffusion and, second, as part of the bulk flow of the pore-air. The pore-vapor transfer due to the molecular diffusion is described using Fick’s law. Heat transfer is formulated to include the effects of conduction, convection, and latent heat of vaporization. An elastoplastic framework is used to describe the deformation behavior of the unsaturated soil structure where linear elastic and nonlinear elastic models are two special cases. In particular, a generalized nonlinear constitutive model proposed earlier by the first writer is introduced and incorporated into the framework to predict the soil deformation with modification to account for the effect of temperature changes on deformation. The determination of the soil parameters involved in the coupled model is carefully discussed. Fully coupled, nonlinear differential equations are established and then solved by using a Galerkin weighted residual approach in space domain and an implicit integrating scheme in time domain. Finally, robust new three-dimensional finite-element numerical computer program, C-HWAM-3D, is developed to incorporate the proposed mathematical model for analyzing the transient coupled flows of heat, moisture, and air, and the stress and strain in unsaturated soils.