Theoretical frame of the saturated freezing soil

Based on the equilibrium, continuity and energy principles of the soil particle, ice and water three-phase porous medium, the theoretical frame for the heat–moisture deformation (HMD) coupling behaviors of the freezing soil is established 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 has more advantages compare to the commonly used hydrodynamic models, rigid-ice models and thermomechanical models.