Abstract: Based on the statistical theory and damage theory, we establish a statistical damage model under triaxial compression in consideration of residual strength and damage threshold of rock. On the basis of the damage model presented, as well as extreme characteristics of stress-strain relationship at low confining pressure, we derive a unified solution of mechanical parameters of the model. In comparison with the experimental data, we discover that micro-unit strength of rock based on Drucker-Prager criterion or Mohr-Coulomb criterion is better than axial strain in reflecting rock mechanical properties, which shows that the failure and extension of rock is closely relevant with stress state. Then, in light of residual strength of rock, we introduce correction factor of damage variable and propose a new method for solving the factor. The results show that, data from theoretical curve in the damage model is in correspondence with experimental data; by using stress yield point as damage threshold point, we can avoid the situation that value of damage factor is not in the interval from 0 to 1 at low loading. Finally, through analyzing the changing process of rock damage variable, we conclude that the damage model can well reflect the stress-strain relationship of rock under triaxial compression.

Key words: rock mechanics, Weibull distribution, correction factor, threshold, residual strength, stress-strain relationship