Abstract A thermodynamics-based mathematical model is presented for unsaturated freezing soils. The proposed model describes the contributions of the film water, capillary water and vapor in unsaturated freezing soils, based on hybrid mixture theory and phase field theory. A new parameter, namely φB, is introduced to describe the freezing state of the capillary water in the pore space. The proposed model can describe the primary and secondary frost heave in a consistent manner. To illustrate the proposed model, expressions for the free energy function and the dissipative potential are formulated. The surface energy potential and the strain energy that is associated with the phase transition of pore fluid are considered. The stress tensors and constitutive relationships are then derived. Finally, the undercooling of the pore fluid and its moisture migration in freezing unsaturated soils are discussed.

中文翻译：

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基于热力学的非饱和冻结土冻胀数学模型

摘要 提出了一种基于热力学的非饱和冻结土数学模型。所提出的模型基于混合混合理论和相场理论，描述了非饱和冻结土壤中薄膜水、毛细管水和蒸汽的贡献。引入了一个新参数 φB 来描述孔隙空间中毛细管水的冻结状态。所提出的模型可以以一致的方式描述一次和二次冻胀。为了说明所提出的模型，制定了自由能函数和耗散势的表达式。考虑了与孔隙流体相变相关的表面能势和应变能。然后导出应力张量和本构关系。最后，