A moving-pump model for water migration in unsaturated freezing soil

•A new model is developed for the water migration in unsaturated freezing soil.•Water migration is characterized using an imaginary moving pump and a small reservoir.•Numerical implementation of the new model is straightforward.

This paper presents a new approach for simulating the water migration in freezing soils, in which the pore water migration and heat transfer are characterized using an imaginary pump attached with a small imaginary reservoir. The pump moves with the freezing front as temperature decreases, sucks the liquid water from the unfrozen zone and then stores it in the frozen zone. The reservoir is used to gather the sucked water and store it in the form of pore ice through phase change. Explicit governing equations are developed for describing the water migration, crystallization and/or heat transfer in the soil, the pump and the reservoir. The proposed model is numerically implemented into a commercial code. Compared to the previous approaches used to simulate the soil freezing processes, application of the new approach avoids remeshing and recalculating the moving boundaries, and this feature can drastically simplify the numerical implementation of the theoretical model. The new approach is used to analyze the one-dimensional freezing process in soils. The simulated results are compared with the experimental data available in the literature and the simulations based on other approaches, showing that the new approach is capable of effectively simulating the freezing process of soils.