Constitutive Model of Rock Uniaxial Damage Based on Rock Strength Statistics

Based on the assumption that rock strength follows the log normal distribution statistically, this paper establishes a damage constitutive model of rock under uniaxial stress conditions in combination with the Mohr–Coulomb strength criterion and damage mechanical theory. Experiments were carried out to investigate the damage evolution process of rock material, which can be categorized into nondamaging, accelerated growth, constant-speed, similar growth, and speed-reducing growth stages. The evolution process had a good corresponding relationship with the rock stress-strain curves. Based on the statistical damage constitutive model proposed in this paper, a numerical fitting analysis was conducted on the uniaxial compression testing data of laboratory sand rock and on experimental data from other literature, in order to validate the rationality of the constitutive equation and the determination of its parameters and to analyze the effect of internal friction variables on damage variables and compression strength. The research outcomes presented in this paper can provide useful reference for the theory of rock mechanics and for rock engineering.