Heat-Mass Migration of Unsaturated Lead-contaminated Loess under Unidirectional Freezing Conditions

[Objective] The western regions of China are home to vast seasonal frozen soil areas. The unregulated discharge of industrial wastewater in these regions has resulted in soil contamination with heavy metal ions. Under negative temperature conditions, unsaturated soils exhibit complex water migration and phase transition processes. This study aims to study the heat-mass migration and soil deformation in unsaturated lead-contaminated liess under undirectional freezing conditions. [Methods] We utilized theoretical modelling together with laboratory test to investigate the heat, moisture, and pollutant migration patterns and the associated soil deformation characteristics in unsaturated lead-contaminated loess under unidirectional freezing conditions. First, based on the principles of mass conservation, energy conservation, and stress equilibrium, the study developed the water mass conservation equation, pollutant mass conservation equation, energy conservation equation, and soil stress equilibrium equation for lead-contaminated loess under unidirectional freezing conditions. Special attention was given to the impact of the pollutant crystallization process on moisture and heat, as well as the hindrance effect of liquid water phase changes on the soil’s hydraulic conductivity. In addition, the elastic modulus of the soil under freezing conditions was reasonably corrected, and the dynamic transformation of lead acetate crystals during the cooling process was incorporated. Key linking variables, such as the solubility of pollutants and solid-liquid ratio, were introduced. This led to the construction of a multi-field coupling mathematical model that fully reflected the heat-mass migration laws and soil deformation characteristics in contaminated soils. Next, a three-dimensional soil column calculation model was established using COMSOL Multiphysics simulation software to simulate the redistribution processes of moisture, heat, and pollutants in contaminated loess under unidirectional freezing conditions. The study particularly examined the changes in temperature, volumetric water content, and lead ion volumetric molar concentration. Simultaneously, the initial and boundary conditions used in the numerical calculation were applied to actual soil columns, with the model’s reliability verified by laboratory soil column test results. Finally, parameterized analysis systematically explored the impact of factors such as temperature gradient, soil initial saturation, and initial pollutant concentration on pollutant migration, crystallization, and soil deformation. [Conclusion] The study found that: (1) the water-heat-pollutant-force coupling model established in this paper effectively simulated the dynamic migration processes of the temperature field, moisture field, and lead ions in unsaturated loess under negative temperature conditions. Negative temperature induced complex physical and chemical processes within the soil, causing water and pollutant redistribution.(2) Under negative temperature conditions, ice-water phase transitions occurred at the freezing front, with the air pressure slightly lower than the atmospheric pressure. This generated a vacuum suction effect, causing moisture to migrate from the unfrozen zone into the freezing region, further promoting the freezing phase transition. During this migration, pollutants also accumulated in the freezing zone. As the temperature continued to drop, pollutants concentrated, reaching a peak before gradually stabilizing.(3) With an increase in the negative temperature gradient, the intensity of the ice-water phase transition at the freezing front increased, making the vacuum suction effect more pronounced. This led to an increase in the migration of pollutants toward the negative temperature end, causing the pollutants to gradually accumulate in the freezing zone and significantly increasing the amount of pollutant crystallization.(4) Under the same saturation conditions, as the initial concentration of pollutants within the soil increased, the volume of pollutant crystallization under negative temperature conditions also rose. The expansion of pollutant crystals also increased, but compared to the expansion of ice crystals, the effect of pollutant crystallization expansion on soil displacement was not significant.