Abstract This research work introduces a novel phase-field thermo-hydro-mechanical (P-THM) modeling approach that allows to deeply understand and model the freezing–thawing cyclic process in a fluid-saturated porous medium. In this, a biphasic macroscopic, non-isothermal porous media model, augmented by the phase-field method (PFM), is applied to account for the temperature development, the interstitial pore-fluid flow, and the volumetric deformations due to ice formation (phase change). Utilizing the theory of porous media (TPM) in the continuum mechanical formulation provides a well-founded basis for the description of deformable, fluid-saturated, non-isothermal porous solid materials. Of particular importance in the underlying work is the unified kinematics treatment of the ice and water constituents as a single pore-fluid, where the PFM is employed for the description of the phase transition between both constituents. The PFM is a diffuse-interface approach that relies on the specification of the free energy density function as the main driving force in the phase transition. It employs a scalar-valued, phase-field variable to indicate the state of the pore-fluid, i.e., a solid (ice) or a liquid (water). A significant virtue of using the PFM approach is its viability in the implementation within standard finite element frameworks, as no need to explicitly track the moving boundaries (interfaces) of the phase-change constituent. The numerical examples and comparisons presented at the end of the manuscript demonstrate the ability, reliability and usefulness of the proposed modeling framework in describing the freezing–thawing process in a saturated porous solid under thermal loading within an elastic deformation limit.

中文翻译：

---

一种统一的水/冰运动学方法，用于多孔介质中霜冻作用的相场热-水-力学建模

摘要 本研究工作引入了一种新的相场热水力机械 (P-THM) 建模方法，可以深入了解和模拟流体饱和多孔介质中的冻融循环过程。在此，通过相场法 (PFM) 增强的双相宏观非等温多孔介质模型被应用于解释温度发展、间隙孔隙流体流动和由于冰形成而引起的体积变形（相变）。在连续介质力学公式中利用多孔介质 (TPM) 理论为描述可变形、流体饱和、非等温多孔固体材料提供了良好的基础。在基础工作中特别重要的是将冰和水成分作为单一孔隙流体的统一运动学处理，其中 PFM 用于描述两种成分之间的相变。PFM 是一种扩散界面方法，它依赖于作为相变主要驱动力的自由能密度函数的规范。它采用标量值相场变量来指示孔隙流体的状态，即固体（冰）或液体（水）。使用 PFM 方法的一个重要优点是它在标准有限元框架内的实施中的可行性，因为不需要明确跟踪相变成分的移动边界（界面）。手稿末尾的数值例子和比较展示了这种能力，