Damage constitutive prediction model for rock under freeze–thaw cycles based on mesoscopic damage definition

Predicting deformation and failure of rock is vital to ensure the safety of engineering in cold regions. The existing constitutive models were established based on specific freeze–thaw cycles, and cannot obtain stress–strain curves of rock under different freeze–thaw cycles. Therefore, in this study, rock was abstracted into non-damage, initial damage, freeze–thaw damage, load damage, and coupled damage to simulate the deformation and failure processes of rock under freeze–thaw cycles and load, and on the basis of determining the relationship between mechanical parameters and the number of freeze–thaw cycles, a damage constitutive prediction model of frozen–thawed rock was established based on the strain equivalent hypothesis. The changes in the microstructure and macroscopic mechanical properties of red sandstone with the number of freeze–thaw cycles were analyzed through freeze–thaw cycles, nuclear magnetic resonance (NMR), and uniaxial compression tests, and the rationality of the model was verified. Results show that as the number of freeze–thaw cycles increases, the internal microstructure of rock is penetrated and expands, porosity increases, and damage is aggravated. This proves that the compressive strength and resistance to deformation of rock decrease. Furthermore, the corresponding peak stress, and elastic modulus decrease, and the peak strain and Poisson's ratio increase. The constitutive model established in this study can predict the deformation and failure characteristics of rock under different freeze–thaw cycles. The theoretical data obtained by the model is in good agreement with experimental data, which verified the rationality of the model and indicated that it can predict the deformation and failure characteristics of rock under different freeze–thaw cycles. The relationship between mechanical parameters and the number of freeze–thaw cycles was determined using theoretical expressions, solving the problem of determining mechanical parameters and model parameters under different freeze–thaw cycles. This method effectively reduces the amount of experimental mechanical parameter data, rendering the constitutive model more adaptive.