Most existing empirical formulas and freezing models to describe the process of frost heave are established in saturated soil. However, most frozen soils in situ are unsaturated and vapor phase plays a critical role in the overall water, energy and stress balance. On the basis of existing frost heave models of saturated freezing soil, a mathematical model of coupled water, vapor, stress and heat movement is established here. Void ratio is an important variable adopted in the numerical simulation, which is related to variation of degree of saturation and used to describe the pore pressure distribution. In the proposed model, void ratio is also adopted as a criterion for the ice lens initiation and to establish the stress-deformation relation. The model is validated by comparisons of simulated results with reference model of saturated freezing soil. Seven cases are computed to study the coupled process in unsaturated freezing soil according to different initial and boundary conditions, including various degrees of saturation, temperature gradients and overburden pressures. The result shows that the impacts of different cases on frost heave properties and interactions among liquid water, vapor, temperature and stress fields. Finally, a representative unsaturated freezing case is adopted to investigate the temperature profiles, water and vapor content profiles and pore pressure profiles, respectively.
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