Determination of the complete stress-strain characteristics of rock is an essential issue in rock mechanics and plays an important role in solving excavation problems. To reflect the whole damaging process, a three-dimensional damage-softening statistical constitutive model for rock was established based on the Weibull distribution of mesoscopic element strength and by adopting the Generalized Zhang-Zhu (GZZ) criterion as the distribution parameter. The GZZ criterion is a three-dimensional Hoek-Brown strength criterion taking account of the influence of the intermediate principal stress. The results from the model were compared with existing experimental data, indicating that the model is feasible to describe the mechanical behavior of brittle rock. The influence of the Weibull distribution parameters on the constitutive model was studied and the results were generally consistent with physical interpretations of the Weibull parameters. A computer program for this constitutive model was developed, providing an easy way for simulating true triaxial tests under different conditions.


During underground excavations, a situation can arise where the rock material surrounding the excavation has failed but the excavation, as a structure, remains stable (Tiwari and Rao, 2006). It has been suggested (Bieniawski, 1967) that the most effective way to study this problem is through determination of the complete stress-strain characteristics of rock. The study of damage-softening constitutive model for rock can reflect the damaging process and complete stress-strain relationship of rock and is an essential issue in rock mechanics.

In the study of damage-softening constitutive model for rock, Krajcinovic and Silva (1982) introduced statistical damage theory and established a damage-softening constitutive model for rock at a certain confining pressure based on distribution randomness of internal defects in rock materials and hypothesis of rock particles obeying Weibull random distribution. This model was further developed by Tang (1993) and Cao and Fang (1998). There is an important parameter, namely the distribution parameter of mesoscopic element strength in this model. Cao and Fang (1998) adopted the Drucker-Pager (D-P) criterion as this distribution parameter. Wang et al. (2007) introduced the classical Mohr-Coulomb (M-C) criterion into the statistical constitutive model of rock to improve the model accuracy in damage-softening and residual strength, and concluded that the use of D-P criterion normally produces larger damage zone and the classical M-C criterion is more suitable. Shi et al. (2011) used Hoek-Brown criterion as the distribution parameter and discussed the influence of Weibull distribution parameters and Hoek-Brown criterion parameters on the rock damage-softening constitutive model.

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