A numerical model for water and heat transport in freezing soils with nonequilibrium ice‐water interfaces

Abstract

A one‐dimensional numerical model of heat and water transport in freezing soils is developed by assuming that ice‐water interfaces are not necessarily in equilibrium. The Clapeyron equation, which is derived from a static ice‐water interface using the thermal equilibrium theory, cannot be readily applied to a dynamic system, such as freezing soils. Therefore, we handled the redistribution of liquid water with the Richard's equation. In this application, the sink term is replaced by the freezing rate of pore water, which is proportional to the extent of supercooling and available water content for freezing by a coefficient, β. Three short‐term laboratory column simulations show reasonable agreement with observations, with standard error of simulation on water content ranging between 0.007 and 0.011 cm3 cm−3, showing improved accuracy over other models that assume equilibrium ice‐water interfaces. Simulation results suggest that when the freezing front is fixed at a specific depth, deviation of the ice‐water interface from equilibrium, at this location, will increase with time. However, this deviation tends to weaken when the freezing front slowly penetrates to a greater depth, accompanied with thinner soils of significant deviation. The coefficient, β, plays an important role in the simulation of heat and water transport. A smaller β results in a larger deviation in the ice‐water interface from equilibrium, and backward estimation of the freezing front. It also leads to an underestimation of water content in soils that were previously frozen by a rapid freezing rate, and an overestimation of water content in the rest of the soils.

A Multi‐Phase Heat Transfer Model for Water Infiltration Into Frozen Soil

“…The presented model has been compared to laboratory experiments reproducing freeze and thaw behavior presented in Watanabe and Kugisaki (2017) and Hansson et al (2004). In the freezing experiments, the model agrees well with the experimental data, similar to other models (e.g., Dall'Amico et al, 2011;Hansson et al, 2004;Peng et al, 2016). Based on the different parameterization used in this model with respect to the hydraulic parameters strongly coupled to heat transfer, the obtained parameters to match the experiments of Hansson et al (2004) slightly diverge from values used by other studies, though a spread in used parameters as well as a variation in thermal boundary conditions is common across studies (cf.…”

Soil evaporation and its impact on salt accumulation in different landscapes under freeze–thaw conditions in an arid seasonal frozen region

“…This movement then results in increased total soil water content in the topsoil. However, for SFS, with the further increase of frost depth, ice in the soil pores significantly decreases hydraulic conductivity, which reduces the water supply from the deeper unfrozen layers to the topsoil (Peng et al, 2016). In addition, evaporation from the frozen topsoil is relatively low in SFS (Wu et al, 2016).…”

Rain, Snow and Frozen Soil: Open Questions from a Porescale Perspective with Implications for Geohazards

“…Interactive forces between soil, water, and ice are used to describe the moisture movement [70]. Peng et al [72] introduced a thermal non-equilibrium between the ice and the liquid water. While the Richards equation is used to describe liquid water movement in frozen and unfrozen soil, it is modified with a sink term coupled to the freezing of liquid water.…”