Abstract: In order to calculate the temperature of the one-dimensional soil freezing process, the equivalent heat capacity model which considers the unfrozen water content has been applied; and the semi-analytical solution for the temperature field has been obtained. The solution procedure has been based on the Fourier method, and the solution has been confirmed by comparing with the numerical solution in some references. The comparison between the equivalent heat capacity model and the apparent heat capacity model has been made; and the results indicate that, during the transient stage, the advancing velocity of the freezing front calculated from the apparent heat capacity model is smaller than that of the equivalent heat capacity model; during the steady stage, the thickness of the frozen zone calculated from the apparent heat capacity model is larger than that of the equivalent heat capacity model. Considering the situation that the water flow induced by the freezing process is weak, then the better the soil freezing characteristic is, the larger the error gets when the apparent heat capacity model is used to calculate the temperature field; and the results are unsafe for the design of the artificial ground freezing engineering.

Key words: soil freezing, temperature field, semi-analytical solution, equivalent heat capacity model, apparent heat capacity model, unfrozen water