The process of water migration in variably-saturated soils during imposed freezing/thawing cycles is significant with respect to a number of practical problems including frost heaving of structures, stability of hillslopes, migration of agrichemicals in soils during winter, and migration/capture of hazardous compounds in soils during cryogenic remediation. Water fluxes in variably-saturated soils occur due to gradients in hydraulic potential, thermal potential, and osmotic potential, and can be quantified in terms of linear flux laws containing measured transport coefficients. Formulation of a mathematical description of the process of water migration in variably-saturated, variably- frozen soils is based on a conservation equation for each of the quantities of water mass, heat and solute mass. These three conservation equations, with the flux equations for water mass, heat and solute mass form a coupled set of equations for simultaneous heat, water and solute transport. These coupled equations are supplemented by appropriate boundary conditions and initial conditions, a mathematical description of the process of solute exclusion, and with appropriate descriptions of porous media properties of including unsaturated hydraulic conductivity, liquid water retention, solute sieving potential and solute dispersion. These equations form a complete mathematical description of coupled heat, water and solute transport for a particular physical setting. Due to the nonlinearity of these equations and the potential complexity of flow region geometries it is necessary to use numerical methods to solve the coupled set of equations. Here we propose to solve the equations using the finite element method for two- dimensional domains. A code has been developed using triangular elements to facilitate simulations on complex geometries. Conservative formulations of the governing equations are used with fully-implicit time discretization. A modified Picard scheme is applied for solving the nonlinear iteration step, as an alternative to a Newton iteration scheme. The iterative matrix solver, GMRES, is applied to solve the set of nonsymmetric matrix equations arising from the finite element discretizations. The model is applied to the simulation of heat, water and solute transport in selected practical problems relating to variably-saturated, variably-frozen soils.

Dr. John L. Nieber
Department of Biosystems and Agricultural Engineering
University of Minnesota
St. Paul, MN 55108
(612)-625-6724
(612)-624-3005 (fax)
E-mail: nieber@gaia.bae.umn.edu