An analytical model for the thermal conductivity of soils during a freezing process

The thermal conductivity of freezing soils (λ) plays a vital role in the analysis of heat and water transfer in cold engineering regions. However, models for describing the variations in λ with subzero temperatures are still scarce. In this study, we proposed an analytical model to estimate λ based on heat conduction theory and a simplified microstructure. Variations in the phases and frost heave at different subzero temperatures were applied to divide the freezing process into three stages. The void ratio, initial volumetric water content and subzero temperature were considered in the analytical model. A flow chart was designed to describe the calculation process for λ at different subzero temperatures. The new theoretical model was evaluated with experimental λ data from the published literature. The results showed that the calculated λ values matched the measured λ values well. The theoretical model accurately captures the variation in λ with subzero temperature. In addition, the performance of the new model was evaluated and compared with 5 other thermal conductivity models under positive temperatures. The results showed that the new model performed best among the 6 thermal conductivity models. •An analytical model for the thermal conductivity of freezing soils was proposed.•The void ratio, initial volumetric water content and temperature were considered in the model.•The model has physical meaning and good performance in modelling the relationship between thermal conductivity and subzero temperature.