Statistical damage constitutive model for rocks based on triaxial compression tests

Based on the triaxial compression tests, a statistical damage constitutive model for rock materials is established using the continuum damage mechanics theory and the statistical strength theory. The mathematical and physical meanings of the model are discussed. It is known from the discussion that the statistical damage constitutive equation in essence is the damage evolution equation in terms of the equivalent stress of a yield criterion. It can describe well the nonlinear mechanical behaviors of rock-like materials and approach their elastic stress-strain relationship. The statistical parameters of the statistical damage constitutive model can be obtained through uniaxial or triaxial compression tests, while the model may be rewritten when using the measured stresses and strains in the compression direction of triaxial tests. An evaluation method for the initial damage variable with the stress-strain curve of uniaxial tests is proposed as well. The model in terms of the log-normally distributed damage and the equivalent stress of the Mohr-Coulomb yield criterion is verified through some uniaxial and triaxial compression tests on rocks. The theoretical fitting curves agree well with the test data, which shows the validity of the statistical damage constitutive equation including the determination method for its parameters and the reasonability of the proposed modification to the model equation. The lognormal distribution and the Mohr-Coulomb yield criterion can be chosen to establish the statistical damage constitutive model for rocks.