Abstract
Abstract. Heat and water movement in variably saturated freezing soils is a strongly coupled phenomenon. The coupling is a result of the effects of sub-zero temperature on soil water potential, heat carried by water moving under pressure gradients, and dependency of soil thermal and hydraulic properties on soil water content. This study presents a one-dimensional cellular automata (direct solving) model to simulate coupled heat and water transport with phase change in variably saturated soils. The model is based on first-order mass and energy conservation principles. The water and energy fluxes are calculated using first-order empirical forms of Buckingham–Darcy's law and Fourier's heat law respectively. The liquid–ice phase change is handled by integrating along an experimentally determined soil freezing curve (unfrozen water content and temperature relationship) obviating the use of the apparent heat capacity term. This approach highlights a further subtle form of coupling in which heat carried by water perturbs the water content–temperature equilibrium and exchange energy flux is used to maintain the equilibrium rather than affect the temperature change. The model is successfully tested against analytical and experimental solutions. Setting up a highly non-linear coupled soil physics problem with a physically based approach provides intuitive insights into an otherwise complex phenomenon.
Highlights
Saturated soils in northern latitudes undergo repeated freeze–thaw cycles
soil freezing curve (SFC) can be defined because the liquid water content in frozen soils must have a fixed value for each temperature at which the liquid and ice phases are in equilibrium, regardless of the amount of ice present (Low et al, 1968)
Ti for a given cell is such that Tit+ t ≥ Tfw, water cannot freeze; cell temperatures are updated without phase change and the code moves into the time step
Summary
Saturated soils in northern latitudes undergo repeated freeze–thaw cycles. Freezing reduces soil water potential considerably because soil retains unfrozen water (Dash et al, 1995). Mathematical models, describing the mechanism of water and heat movement in variably saturated freezing soils, have been developed to complement these observational studies. Analytical solutions of freezing and thawing front movements have been developed and applied (e.g. Stefan, 1889; Hayashi et al, 2007) and numerical models have replicated the freezing-induced water redistribution with reasonable success This study presents a coupled CA model to simulate heat and water transfer in variably saturated freezing soils. The model was validated against the analytical solutions of (1) the heat conduction problem (Churchill, 1972), (2) steady state convective and conductive heat transport in unfrozen soils (Stallman, 1965), (3) unilateral freezing of a semi-infinite region (Lunardini, 1985), and (4) the experimental results of freezing-induced water redistribution in soils (Mizoguchi, 1990)
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