Heat and mass transfer in unsaturated soils during freezing
Newman, Greg P.
Experimental and field data have shown that large amounts of water can be redistributed from warmer soils to and behind an advancing freezing front. The mechanisms by which this occurs are becoming more understood, but the most appropriate method for analysing these mechanisms is not yet known. Various researchers have developed soil freezing models, but they are all limited to some extent and are not practical tools from a design or predictive modelling perspective. The objective of this research program is to develop unsaturated soil freezing theory from a geotechnical engineering perspective, and to verify the theory by modifying an existing non-freezing soil heat and mass transfer model. In this study the SoilCover (MEND, 1993) model is modified to verify the theory and numerical solution. SoilCover (MEND, 1993) is a one-dimensional soil heat flow and mass transfer computer model used for designing protective covers over waste rock and tailings. These covers, if they remain saturated, significantly reduce oxygen infiltration into the waste material where it can combine with water to produce acid mine drainage. SoilCover (MEND, 1993) is not capable of modelling through the winter months when upper regions of the covers become subjected to freezing temperatures. Unique to the modified soil freezing model is the method by which the coupled heat and mass equations are combined and solved. The numerical model uses a single, unique expression which describes the heat flow, mass transfer, and phase change phenomenon in the frozen or partially frozen soil zones. To derive the modified equation, the dependent suction variable in the mass transfer equation is re-written as a function of freezing point depression temperature using a Clapeyron type relationship that is obtained by combining soil freezing curve data with soil water characteristic curve data. The mass transfer equation is then re-written as a function of change in ice content and substituted into the ice content term of the heat transfer equation. The result is a single combined heat and mass transfer equation with one unknown variable, i.e., temperature. Once new temperatures are solved for over the current time step, suctions and ice contents are computed using back-substitution. The revised model was verified using laboratory freezing test data collected at the University of Saskatchewan in 1977. During laboratory data modelling of three freezing tests, the average percent difference between measured and computed frost front positions was approximately 6%. The average difference between measured and computed ice contents was approximately 7%, and the average difference between measured and computed liquid water contents was approximately 14%. These discrepancies were primarily due to errors in the estimated and measured soil thermal and hydraulic property functions. Results of the laboratory data simulations suggest that the permeability versus suction relationship for an unsaturated soil also applies as soil pore-water freezes. This finding is contrary to the findings of other researchers who had to introduce an arbitrary ice impedance factor to make computed and measured ice contents agree. The ice impedance factor has the effect of reducing the permeability by several orders of magnitude as the volumetric pore-ice content increases. In this study, good agreement between computed and measured ice contents was obtained without the use of an impedance factor. To demonstrate an application of the revised model, a simulation of freezing and thawing in a soil cover system was carried out and compared to field data collected during the winter of 1993/1994 at a silver mine near Houston, B.C. For comparisons between the field data and simulations, the soil surface temperature beneath the snow pack had to be estimated as the numerical model does not account for heat and mass flux through snow layers. Daily infiltration during the spring thaw was also estimated based on averaged meteorological data provided by Equity Mine.