Abstract
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.
Highlights
Frost heave, i.e. the transport of sub-cooled water to a growing ice lens, occurs when three conditions coincide: the temperature is below the normal freezing point of water, the sub-cooled water is connected to a water reservoir, and the soil is susceptible to formation of ice lens
It is shown that three measurable transport coefficients are adequate to model the process; permeability, thermal conductivity and a cross coupling coefficient that may be named thermodynamic frost heave coefficient
I.e. the transport of sub-cooled water to a growing ice lens, occurs when three conditions coincide: the temperature is below the normal freezing point of water, the sub-cooled water is connected to a water reservoir, and the soil is susceptible to formation of ice lens
Summary
I.e. the transport of sub-cooled water to a growing ice lens, occurs when three conditions coincide: the temperature is below the normal freezing point of water, the sub-cooled water is connected to a water reservoir, and the soil is susceptible to formation of ice lens. In a series of papers, Konrad and Morgenstern [17, 19, 18] elaborated on a physical model for frost heave They divided the soil into three layers; (1) a layer of unfrozen soil, (2) a partially frozen layer, called the frozen fringe, and (3) a practically completely frozen one. As shown, for a well-defined measurement, it is critical to specify a constant pressure along the frozen fringe To implement this modification, we propose that the thermodynamic frost heave coefficient, s, replaces SP. The rigid-ice model of Miller [21] described the transport of heat and mass through a frozen soil using similar equations from irreversible thermodynamics. A practical set of the transport equation, tailored for frost heave phenomena, is introduced in Sect. 4, and is followed by discussion and numerical examples illustrated with data from literature
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
