Abstract: In this paper, the dissipative energy in the damage process was employed to solve the damage variable while the damage constitutive model was established. In this model, the Mohr-Coulomb criterion and the energy dissipation theory were introduced. Considering the hardening and softening characteristics of rock during loading, the non-associated plastic flow rule was applied to describe the plastic deformation of rock, and the damage variable was calculated by quoting the dissipation energy and damage energy dissipation rate in the damage process. Based on the conventional triaxial loading-unloading experiments, the energy consumption and damage evolution law of rock was analyzed. The expression of damage energy dissipation rate was established, and the parameters in the model were calibrated. Simulation was conducted by this model and the simulation results were compared with the experimental results to validate the model. In this process, the following conclusions were obtained: (1) in the elastic stage, the damage dissipation energy increases slowly with the axial strain, showing an upward concave curve, and the growth rate reaches the maximum near the peak-stress. In the residual stage, the relationship between damage dissipation energy and axial strain is linear; (2) based on elastic modulus associated damage definition, the experimental results show that there is a damage variable limit less than 1, and the damage variable limit gradually decreases with the increase of confining pressure; (3) the model in this paper can be used to investigate the strength, hardening, softening characteristics and strain law of rock under different confining pressures during the loading process. The numerical simulation results can describe the stress-strain relationship and damage evolution law of rock.

Key words: damage, energy dissipation, Mohr-Coulomb criterion, constitutive model, damage energy consumption rate