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A Thermal–Mechanical Coupling Elastoplastic Model of Freeze–Thaw Deformation for Porous Rocks

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Abstract

Freeze–thaw (FT) damage and deformation of porous rocks would affect the normal operation or even threaten the safety of rock engineering in cold regions. During the FT process, pore ice pressure induced by temperature variation and phase change of pore water/ice would exceed the yield strength of rocks accompanied by the occurrence of plastic strain. Therefore, an effort that couples thermal mechanism and elastoplastic mechanical process is performed in the study to further understand the deformation process of porous rocks under FT condition. First, experiments on FT deformation of saturated sandstone with different freezing temperature are conducted. Four stages are observed in deformation variation process: thermal contraction stage, frost heaving stage for the freezing process, and thawing shrinkage stage, thermal expansion stage for the thawing process. Besides, significant residual strain remains after FT experiments implying the occurrence of irrecoverable plastic strain. Then, a thermal–mechanical coupling elastoplastic model of FT deformation for porous rocks is proposed, which couples the governing equations of heat transfer considering unfrozen water content and mechanical equilibrium equations based on the poro-elastoplastic approach. Comparisons between the results of thermal–mechanical numerical simulation based on the model and the experimental results show that the model can predict the temperature variation and FT deformation process of porous rocks with desirable accuracy. Moreover, as exhibited in the numerical results, during the freezing process, pore ice pressure increases dramatically as temperature decreases from 0 to  − 5 ℃. The plastic region generates at about − 2 ℃, and its increase rate is greater when the temperature is between − 2 and − 5 ℃. During the thawing process, although pore ice pressure eliminates in the region where the temperature becomes positive, the frost heaving strain there is not completely recovered as the plastic residual strain remains, which is consistent with the experimental phenomenon.

Highlights

  • A thermal-mechanical coupling elastoplastic model of freeze-thaw deformation for porous rocks is proposed.

  • The model couples the governing equations of heat transfer and equilibrium equations with poro-mechanics.

  • Experiments on freeze-thaw deformation of porous sandstone are conducted.

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Abbreviations

\(\omega\) :

Unfrozen water content of porous rocks

\(\omega^{ * }\) :

Residual unfrozen water content at a reference temperature

\(T\) :

Temperature

\(T_{0}\) :

Freezing point

\(C\) :

Volumetric thermal capacity of porous rocks

\(\lambda_{ef}\) :

Effective thermal conductivity of porous rocks

\(L\) :

Specific latent heat of pore water

\(\rho_{w}\) :

Density of pore water

\(\theta_{w}\) :

Volumetric unfrozen water content of porous rocks

\(\theta_{i}\) :

Volumetric ice content of porous rocks

\(n_{0}\) :

Initial porosity of rock

\(d_{s}\) :

Specific gravity of rock

\(C_{s}\) :

Volumetric thermal capacity of sandstone grains

\(C_{w}\) :

Volumetric thermal capacity of pore water

\(C_{i}\) :

Volumetric thermal capacity of pore ice

\(\lambda_{s}\) :

Thermal conductivity of sandstone grains

\(\lambda_{w}\) :

Thermal conductivity of pore water

\(\lambda_{i}\) :

Thermal conductivity of pore ice

\(P_{i}\) :

Pore ice pressure at the interface of pore and rock matrix

\(K_{i}\) :

Bulk modulus of pore ice

\(\alpha_{T}\) :

Thermal expansion coefficient

\(G_{m}\) :

Shear modulus of rock matrix

\(K_{m}\) :

Bulk modulus of rock matrix

\(\sigma_{0}\) :

Tensile strength of rock matrix

\(R_{V}\) :

Volume ratio the plastic zone and the pore

\(\varepsilon_{t}\) :

Total freezing strain of porous rocks

\(\varepsilon_{f}\) :

Frost heaving strain of porous rocks

\(\varepsilon_{T}\) :

Thermal strain of porous rocks

\({\mathbf{C}}\) :

Fourth-order tensor of material stiffness

\({\varvec{\varepsilon}}_{el}\) :

Elastic strain tensor

\({\varvec{\varepsilon}}_{inel}\) :

Initial and inelastic strains

\({\varvec{\varepsilon}}_{0}\) :

Initial strain tensor

\({\varvec{\varepsilon}}_{T}\) :

Thermal strain tensor

\({\varvec{\varepsilon}}_{ft}\) :

Frost heaving strain tensor

\(\varepsilon_{re}\) :

Residual strain during the thawing process

\(P_{u}\) :

Unloading pressure during the thawing process

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (52108370) and Jiangxi Provincial Natural Science Foundation (No. 20212BAB214062).

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Nanchang University, Nanchang, 330031, China

    Zhitao Lv, Sicheng Luo & Xiangtai Zeng

  2. Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, China

    Caichu Xia

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  1. Zhitao Lv
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  2. Sicheng Luo
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  3. Caichu Xia
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  4. Xiangtai Zeng
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Contributions

ZL: funding acquisition, writing—original draft and methodology. SL: data curation and validation. CX: formal analysis and investigation. XZ: conceptualization; writing—review & editing.

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Correspondence to Xiangtai Zeng.

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Lv, Z., Luo, S., Xia, C. et al. A Thermal–Mechanical Coupling Elastoplastic Model of Freeze–Thaw Deformation for Porous Rocks. Rock Mech Rock Eng 55, 3195–3212 (2022). https://doi.org/10.1007/s00603-022-02794-y

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  • DOI: https://doi.org/10.1007/s00603-022-02794-y

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