This paper presents a comprehensive computational model for analyzing thermo‐hydro‐mechanical coupled processes in unsaturated porous media under frost actions. The model employs the finite element method to simulate multiphase fluid flows, heat transfer, phase change, and deformation behaviors. A new soil freezing characteristic curve model is proposed to consider the suctions from air‐water capillary pressure and water‐ice cryosuction. A total pore pressure with components from liquid water pressure, air pressure, and ice pressure is used in the effective stress law. Vapor and dry air are considered miscible gases, utilizing the ideal gas law and Dalton's law. The governing equations encompass the linear momentum balance equation, the energy balance equation, and mass conservation equations for water species (ice, liquid, and vapor) and dry air. Weak forms are formulated based on primary variables of displacement, water pressure, air pressure, and temperature. The spatial discretization is achieved through the finite element method, while temporal discretization employs the fully implicit finite difference method, resulting in a system of fully coupled nonlinear equations. To verify the proposed computational model, a numerical implementation is developed and validated against a set of experimental data from the literature. The successful verification demonstrates the robustness of the model. A detailed discussion of the contributions from phase change strain and different sources of pore pressure is also addressed.

中文翻译：

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考虑空气-水毛管压力和低温吸力的非饱和冻土中热-水-力耦合过程的有限元建模


本文提出了一个综合计算模型，用于分析霜冻作用下不饱和多孔介质的热-水-力耦合过程。该模型采用有限元方法来模拟多相流体流动、传热、相变和变形行为。提出了一种新的土壤冻结特征曲线模型来考虑空气-水毛细管压力和水-冰低温吸力的吸力。有效应力定律中使用了由液态水压力、气压和冰压力组成的总孔隙压力。利用理想气体定律和道尔顿定律，蒸气和干燥空气被认为是可混溶的气体。控制方程包括线性动量平衡方程、能量平衡方程以及水物质（冰、液体和蒸汽）和干燥空气的质量守恒方程。弱形式是根据位移、水压、气压和温度等主要变量制定的。空间离散化是通过有限元方法实现的，而时间离散化则采用全隐式有限差分法，从而形成一个完全耦合的非线性方程组。为了验证所提出的计算模型，开发了数值实现并根据文献中的一组实验数据进行了验证。成功的验证证明了模型的稳健性。还详细讨论了相变应变和不同孔隙压力来源的贡献。