Establishment of damage statistical constitutive model of loaded rock and method for determining its parameters under freeze-thaw condition

It is of great significance to analyze and predict the deformation characteristics of rock engineering materials by establishing a universal damage constitutive model under freeze-thaw and loading conditions. Based on the study of statistical damage constitutive model founded under freeze-thaw and loading condition, analytical expressions of the model parameters and characteristic parameters in the stress-strain curves (i.e., elastic modulus, stress and corresponding strain at the peak point) were established under specific freeze-thaw cycles. Then, an attenuation model that complies with Newton's material cooling law was introduced to develop the relationship among elastic modulus, stress at peak point and freeze-thaw cycles. Thirdly, the formula of the peak strain under different freeze-thaw cycles was proposed by exploring the correlation between the peak strain of stress-strain curves and freeze-thaw cycles. Therefore, the determination method of the unified model parameters under different freeze-thaw cycles is proposed, then, statistical damage constitutive model under freeze-thaw and loading conditions is generalized, and the freeze-thaw mechanics test with marble was performed to verify the rationality of the model. The results show that stress-strain curves described by presented model under different freeze-thaw cycles have a good agreement with the experimental curves, especially at the peak strength point. The results can provide theoretical reference for the study of rock mechanical properties under different freeze-thaw cycles