Transport coefficients and pressure conditions for growth of ice lens in frozen soil

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.