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<p>Freeze–thaw (F–T) cycling is a significant factor contributing to the rapid deterioration of the mechanical properties of rocks, posing a threat to the stability and durability of rock engineering in cold regions. To establish a uniaxial compression constitutive model that reflects the evolution of micro-structural damage in rocks under F–T action, this study focused on sandstone as the research object. The evolution of pore structure was quantitatively characterized after different numbers of F–T cycles using nuclear magnetic resonance (NMR) tests. The results showed that F–T cycling increased porosity and caused a transition in the pore size distribution from bimodal to unimodal, with micro-damage tending to stabilize as the number of cycles increases. Based on internal variable thermodynamics, the micro-scale porosity changes induced by F–T cycles were transformed into a macroscopic damage variable, and an F–T damage function is incorporated into the constitutive model. This approach establishes a cross-scale theoretical link from microstructural evolution to macroscopic mechanical response, overcoming the limitations of traditional statistical damage models, such as unclear physical mechanisms and ambiguous parameter meanings. Furthermore, by introducing internal variables for strain-hardening and uniaxial compression damage, the constitutive equations for the elastic, strain-hardening, and strain-softening stages were constructed in segments. This resulted in a unified constitutive model capable of describing the entire uniaxial compression process under the combined effects of F–T and loading damage. The model is validated against experimental data, accurately representing the complete stress–strain response of rocks at different F–T stages. It significantly improves the simulation accuracy of the post-peak softening stage and effectively captures the enhanced ductility of rocks caused by F–T cycling. This study establishes a theoretical link between micro-structural damage and macroscopic mechanical behavior, providing a micro-mechanical basis for the stability analysis and prediction of rock engineering in cold regions.</p>

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A Constitutive Model of Rock Freeze–Thaw Damage Based on Irreversible Thermodynamics

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Yifan Zhang,
  • Huiming Tang,
  • Luobin Zheng,
  • Chunyan Tang,
  • Sixuan Sun,
  • Qihang Gong,
  • Chenlu Wang,
  • Chengcheng Gao

摘要

Freeze–thaw (F–T) cycling is a significant factor contributing to the rapid deterioration of the mechanical properties of rocks, posing a threat to the stability and durability of rock engineering in cold regions. To establish a uniaxial compression constitutive model that reflects the evolution of micro-structural damage in rocks under F–T action, this study focused on sandstone as the research object. The evolution of pore structure was quantitatively characterized after different numbers of F–T cycles using nuclear magnetic resonance (NMR) tests. The results showed that F–T cycling increased porosity and caused a transition in the pore size distribution from bimodal to unimodal, with micro-damage tending to stabilize as the number of cycles increases. Based on internal variable thermodynamics, the micro-scale porosity changes induced by F–T cycles were transformed into a macroscopic damage variable, and an F–T damage function is incorporated into the constitutive model. This approach establishes a cross-scale theoretical link from microstructural evolution to macroscopic mechanical response, overcoming the limitations of traditional statistical damage models, such as unclear physical mechanisms and ambiguous parameter meanings. Furthermore, by introducing internal variables for strain-hardening and uniaxial compression damage, the constitutive equations for the elastic, strain-hardening, and strain-softening stages were constructed in segments. This resulted in a unified constitutive model capable of describing the entire uniaxial compression process under the combined effects of F–T and loading damage. The model is validated against experimental data, accurately representing the complete stress–strain response of rocks at different F–T stages. It significantly improves the simulation accuracy of the post-peak softening stage and effectively captures the enhanced ductility of rocks caused by F–T cycling. This study establishes a theoretical link between micro-structural damage and macroscopic mechanical behavior, providing a micro-mechanical basis for the stability analysis and prediction of rock engineering in cold regions.