In this paper, the transport of sub-cooled water across a partially frozen soil matrix (frozen fringe) caused by a temperature difference over the fringe, is described using non-equilibrium thermodynamics. A set of coupled transport equations of heat and mass is presented; implying that, in the frozen fringe, both driving forces of pressure and temperature gradients simultaneously contribute to transport of water and heat. The temperature-gradient-induced water flow is the main source of frost heave phenomenon that feeds the growing ice lens. It is shown that three measurable transport coefficients are adequate to model the process; permeability (also called hydraulic conductivity), thermal conductivity and a cross coupling coefficient that may be named thermodynamic frost heave coefficient. Thus, no ad hoc parameterizations are required. The definition and experimental determination of the transport coefficients are extensively discussed in the paper. The maximum pressure that is needed to stop the growth of an ice lens, called the maximum frost heave pressure, is predicted by the proposed model. Numerical results for corresponding temperature and pressure profiles are computed using available data sets from the literature. Frost heave rates are also computed and compared with the experimental results, and reasonable agreement is achieved.

This paper presents a fully coupled thermo‐hydro‐mechanical (THM) model which simulates frost heave in fully saturated soils. The model is able to simulate the formation and growth of multiple distinct ice lenses. The basic equations of the system were derived using the continuum theory of mixtures, nonequilibrium thermodynamics, and fracture mechanics, considering skeleton deformation, water flow and heat transport. Central to this model is the coupled transport of mass due to the temperature gradient across the frozen fringe, which acts as the main driving force of the phenomenon. The model is formulated in terms of measurable physical properties and thus no ad hoc parametrization is required. In an ice‐lens‐free state, the system is solved as a continuum using the finite element method (FEM). It is then locally treated as a discontinuous system upon the formation of ice lens, by enriching the elements carrying the embedded ice lens(es) using the extended finite element method (X‐FEM). The accuracy and efficiency of the proposed model has been verified using several laboratory tests on Devon silt samples at different overburden pressures and thermal boundary conditions. Shut‐off pressures have been also estimated and compared with the experimental results.

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