Correction method of Mohr-Coulomb strength criterion for rock based on freeze-thaw and residual effects

Under confining pressure, rocks transition from brittle failure to plastic failure, and residual strength exists after complete failure. However, in the process of establishing rock damage constitutive models, the strength criteria used usually do not consider residual stress. In cold region engineering, the freeze-thaw effect caused by temperature changes should be considered in the constitutive model, and strength criteria should also be introduced. Considering the failure characteristics of micro element when rock is subjected to freeze-thaw and load, and based on the impact of reducing the effective bearing area on each damage, the total damage variable and constitutive model of rock under freeze-thaw and load are established. Starting from the characteristics of the entire process of rock deformation, the revised Mohr-Coulomb (M-C) strength criterion of rock is established by considering freeze-thaw cycles and residual effects. The results show that: The theoretical curve and test curve of the constitutive model are not completely consistent, but the variance R² between the two does not exceed 0.6, indicating that the theoretical curve is in good agreement with the test curve and can reflect the entire process of rock deformation and failure, verifying the rationality of the constitutive model and damage variable description. With the increasing of freeze-thaw cycles, the strength decreases and the deformation increases of rock. As the number of freeze-thaw cycles increases, the strength decreases and deformation increases. When the freeze-thaw cycle reaches 40 cycles, the strength decreases by more than 60%. With the increasing of confining pressure, the strength and deformation also increase. When the confining pressure increases from 0 to 6 MPa, the strength of red sandstone increases by more than 80% under the same freeze-thaw cycles, which is consistent with the actual situation. The revised M-C strength criterion data does not exceed the test data and is relatively close to the test data. The difference between the two is less than 25%, indicating that the established strength criteria can be safely used as a basis for rock elemental failure, verifying the rationality of the strength standard considering freeze-thaw and residual effects. This Revised M-C strength criterion introduces the influence of freeze-thaw cycles and residual stress factors, which not only characterizes the relationship between internal stress parameters in rock limit states under different freeze-thaw cycles, but also addresses the disadvantage of Drucker-Prager (D-P) criterion being more conservative. This method is based on the measured results of rock triaxial test, which makes it more flexible and the calculation results closer to reality.