Abstract The paper presents a novel mathematical model of coupled hygro-thermo-mechanical processes in a porous material, partially saturated with liquid water and exposed to temperatures below the freezing point of pore water. Water – ice phase change is modelled by means of a non-equilibrium approach considering both water supercooling and a hysteresis of ice content during freezing and thawing of moist porous materials. The hysteresis results in different crystallization pressure and material strains during freezing and thawing processes at a given temperature. The latter effect is modelled by means of the effective stress principle, considering crystallization pressure of ice in the material pores. Methods used for discretization of the model equations and their numerical solution are described. The model is applied for solving the numerical example dealing with laboratory Dynamic Mechanical Analysis test of two different cement mortars saturated with water and exposed to temperatures below the freezing point of water (down to −15 °C) where hysteresis of strains was observed. The results are used for experimental validation of the proposed model. Then, for a 1-D case concerning water freezing-thawing of a wall, the effects on the simulation results of the phase-change model parameters, of the material hygro-thermal state, of the supercooling phenomenon and finally of the rate of temperature variation, are analyzed and discussed.

中文翻译：

---

部分饱和多孔介质中循环水冻结引起的应变滞后的多孔力学模型

摘要 本文提出了一种多孔材料中湿-热-机械耦合过程的新数学模型，该材料部分被液态水饱和并暴露在低于孔隙水冰点的温度下。水-冰相变是通过非平衡方法模拟的，同时考虑了水过冷和潮湿多孔材料在冷冻和解冻过程中冰含量的滞后现象。在给定温度下的冷冻和解冻过程中，滞后导致不同的结晶压力和材料应变。后一种效应是通过有效应力原理建模的，考虑了材料孔隙中冰的结晶压力。描述了模型方程的离散化方法及其数值解。该模型用于求解处理两种不同水泥砂浆的实验室动态力学分析试验的数值示例，这些水泥砂浆用水饱和并暴露于低于水的冰点（低至 -15 °C）的温度，观察到应变滞后。结果用于所提出模型的实验验证。然后，对于壁的水冻融的一维情况，相变模型参数、材料湿热状态、过冷现象以及最终的温度变化率对模拟结果的影响变化，进行分析和讨论。