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

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.