This article presents a novel mathematical model of hygro-thermal processes in a porous material, partially saturated with liquid water, exposed to temperatures below the freezing point of pore water. Water–ice phase transition is modeled by means of a kinetic approach considering water supercooling and thermodynamic non-equilibrium of the phases, what allows taking into account a hysteresis of ice content during freezing–thawing of moist porous materials. The model equations are solved for two numerical examples. The first one deals with laboratory differential scanning calorimetry test of a cement mortar saturated with water and exposed to temperatures below the freezing point of water (down to −40°C). The results are used for experimental validation of the proposed model, confirming its accuracy and practical usefulness. In the second example, the mesh refinement test is performed and the influence of the solid–liquid water phase change model parameters on the simulation results for a 1D model problem concerning water freezing–thawing are analyzed and discussed.

中文翻译：

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水冻结的非平衡建模滞后：部分饱和多孔建筑材料中的冰融化

本文介绍了多孔材料中湿热过程的新数学模型，部分被液态水饱和，暴露在低于孔隙水冰点的温度下。水-冰相变通过考虑水过冷和相的热力学非平衡的动力学方法建模，这允许考虑潮湿多孔材料冻融过程中冰含量的滞后。针对两个数值示例求解模型方程。第一个涉及用水饱和并暴露于低于水的冰点（低至 -40°C）的温度的水泥砂浆的实验室差示扫描量热法测试。结果用于所提出模型的实验验证，确认其准确性和实用性。在第二个例子中，