Heat and water flows in freezing and thawing soils numerical modelling, laboratory and field observations
Abstract: A laboratory study of infiltration rates into frozen and unfrozen fine sand, including temperature effects of both soil and infiltration water, is reported. The average infiltration rate varied from about 10.6 mm/min for unfrozen conditions, to about 1-2 mm/min for frozen conditions. A new numerical method for solving the phase change in unsaturated freezing and thawing soils is presented. The governing equations are solved by a two-step approach. In the first step, the heat and water flow equations, neglecting changes in ice content, are solved using a fully implicit numerical scheme. In the second step, the phase change is directly solved using a total energy balance and a relationship between unfrozen water content and freezing temperature (SWFC). Simulations of three horizontal freezing experiments using different time-dependent temperature boundary conditions (T b.c) are evaluated and discussed. Results from a simulated freezing and thawing cycle are also discussed. A good agreement between measured and calcuted temperature and moisture content profiles for different temperature boundary conditions was achieved. The freezing and thawing simulation demonstrated how the ice growth continued during thawing at the cold side of the ice zone, caused by a very small freezing temperature, and how the frost (ice) depth differed considerably from the depth at which 0°Coccurred. Moreover, in the melt zone, water moved from the melt front towards the zone with the maximum ice content. Some characteristic parameters in the modelling of unsaturated freezing and thawing silt loam were studied. Closed-form expressions for soil-hydraulic properties were combined with the concept that relates soil water potential to freezing-point depression, to obtain the SWFC. The highest sensitivities resulted from variations of T b.c and initial moisture contents. For example, freezing-induced moisture accumulation only occurred in the initially wettest soil profile by the largest amounts for T b.c of less strength. Significant discrepancies occurred, in several phenomena, between soil types. One soil type had direct solid-to-solid contacts (SS) and the other had particles which were always separated by liquid water (SLS). The phenomena were ice contents, differences between the position of 0°C and frost depth, melt zones, and the time of thawing. A similar sensitivity pattern was found when comparing wetting and drying characteristics, although the sensitivities were low. Freezing-induced moisture and ice accumulations, penetration rate of maximum frost depth and melt zone extension were strongly dependent of the hydraulic conductivity. For example, total moisture and ice contents changed by about ±4.5% and ±10%, respectively, for T b.c. of the lowest strength, based on conductivity changes of ±50%, which e.g. is the changes of the conductivity when comparing the effects of the water viscosity for temperatures between 0 and +20°C. Studied phenomena during freezing, including time of thawing,were insensitive to changes of an impedence parameter, which is normally used in numerical modelling to reduce the hydraulic conductivity close to the freezing front.
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