Modeling Coupled Water and Heat Transport in a Freezing Soil Using the Modified HYDRUS-1D Code.

Coupled water and heat flow in freezing soils is generally modeled assuming that the suction of unfrozen water in the frozen soil can be related to temperature using the Clausius-Clapeyron equation. The hydraulic conductivity of a frozen soil generally decreases very significantly during freezing because of ice formation and, as such, is practically impossible to measure directly. For this reason an impedance function is often used to account for the reduction in the conductivity, with the impedance parameters estimated inversely from observed total (liquid and ice) water content profiles. We performed laboratory freezing experiments for three different unsaturated soils (a sand, a loam, and a silt loam) to test applicability of the impedance function. The soils were packed in 35-cm long vertical acrylic columns to uniform bulk densities and water contents.  The soils were allowed to freeze from the top by controlling the temperature at both ends of the columns. Liquid water contents, suctions and temperatures were monitored using 7 TDR sensors, 7 tensiometers and 32 thermocouples installed in soil columns. Total water contents were measured by sectioning the columns after 0, 6, 12, 24 and 48 h. Using a modified version of HYDRUS-1D, calculated temperature, suction and water content profiles in the frozen loam soil agreed reasonably well with the observed data sets when the impedance function was estimated accurately. However, water fluxes in the frozen silt loam were underestimated, while water contents at or near the freezing front in the sand column were overestimated. The Clausius-Clapeyron equation generally estimated unfrozen water contents well unless the freezing rate was relatively fast.