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.

The mechanical behavior of frozen soils is strongly affected by the amount of ice. The amount of ice depends on the temperature and the applied mechanical stresses. The influence of ice content and temperature on the mechanical behavior and the coupling effects on the reverse direction can be mentioned as the main difference between frozen and unfrozen soils. In the light of this difference, an elastoplastic constitutive model for describing the stress-strain behavior of saturated frozen soils is proposed. By dividing the total stress into fluid pressure and solid phase stress, in addition to consideration of the cryogenic suction, the model is formulated within the framework of two-stress state variables. The proposed model is able to represent many of fundamental features of the behavior of frozen soils such as ice segregation phenomenon and strength weakening due to pressure melting. In unfrozen state the model becomes a conventional critical state model. Typical predictions of the model for simulating the characteristic trends of the frozen soil behavior is described qualitatively. Model predictions are also compared with the available test results and reasonable agreement is achieved.

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This paper reviews eight geoacoustic models applied to frozen soils: crystal growth models (grain cementing, grain coating, matrix supporting, and pore filling), the weighted equation (WE) model, Zimmerman and King's model (KT), the Biot-Gassmann theory modified by Lee (BGTL), and a two-end member model. We verify the capacity of these models to estimate unfrozen water content (UWC) based on "reference" UWC results and joint P and S wave velocities for different soil types. The satisfactory UWC estimates of saline unconsolidated sand and overconsolidated clay based on V p data prove that the KT, BGTL, and two-end member models are capable of modeling "smooth" transitions in the ice crystal growth mode, while they may provide less accurate UWC values when abrupt change of crystallization mode occurs. None of the tested soil types show a single crystallization mode throughout the freezing process, as assumed by individual crystal growth models. V s-based UWC estimates are less accurate due to significant but difficult-to-estimate influence of effective stress and soil initial cementation. All models, except pore filling and matrix supporting, can match V s versus V p measurement results for sands and silts but gradually provide inconsistent estimates with increasing clay content. We conclude that model validation by independent UWC measurements is necessary and that consistency between UWC values estimated from V s and V p is insufficient to ensure proper model validation.

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.