Theoretical modeling framework for an unsaturated freezing soil

Based on the authors' theoretical modeling framework of the saturated freezing soil, this paper further discusses the air phase in the unsaturated freezing soil in two ideal situations: air in the soil is linked to the atmosphere (the open porous medium) and air in the soil is isolated from the atmosphere (the sealed porous medium). The corresponding theoretical modeling framework for a multi-phase porous medium with interaction of water, heat and deformation is established in this paper. The proposed theoretical model is then extended to the general case (unsaturated half-open and half-sealed porous medium). Also, a finite element numerical solution to the heat-moisture-deformation coupling behavior of the unsaturated freezing soil is obtained. The computer software for solving this problem is also developed. The in-situ measurements for Hua Shixia highway roadbed located in Qinghai–Tibetan Plateau are introduced to compare with the numerical results obtained by the proposed model. The measurement results indicate that the numerical results for the temperature field variations with time are found to be in good correlation with the roadbed depth, just as the relative freezing deformations are correlated with road surface. Numerical modeling results, when compared to field measurements of temperature and deformation, are within 10 to 20%. The comparative analysis shows that proposed theoretical modeling framework and its numerical solution for the temperature–moisture-deformation coupling behavior is suitable and acceptable.