The theoretical frame of multi-phase porous medium for the freezing soil

Based on the equilibrium, continuity and energy principles of the multi phase porous medium, the heat moisture deformation (HMD) coupled theoretical frame is established for the freezing soil in this paper, with the consideration of the force interaction between the soil skeleton and ice particle, and the energy jump behaviors during the phase changing between ice and water. The proposed model is more advanced than the commonly used Hydrodynamic models,Rigid ice models and Thermomechanical models.