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.

在本文中，使用非平衡热力学描述了由于边缘温度差引起的过冷水在部分冻结的土壤基质（冻结边缘）上的传输。给出了一组耦合的热与质的输运方程。这意味着，在冰冻边缘中，压力和温度梯度的驱动力同时有助于水和热的传输。温度梯度引起的水流是冻胀现象的主要来源，而霜冻现象为生长的冰晶提供了养分。结果表明，三个可测量的传输系数足以模拟该过程。渗透率（也称为水力传导率），热传导率和交叉耦合系数，可以称为热力学霜冻系数。因此，不需要临时参数设置。本文广泛讨论了传输系数的定义和实验确定。所提出的模型预测了阻止冰晶生长所需的最大压力，即最大霜胀压力。使用文献中的可用数据集，可以计算出相应温度和压力曲线的数值结果。还计算了冻胀率并将其与实验结果进行比较，并取得了合理的一致性。