Because of the limitations and deficiencies of rock damage model based on Lemaitre's strain equivalence. Our study is firstly concerned with the evolution rule of damage variable during the process of rock strain softening, considering the influence of damage threshold. Secondly, as Mogi-Coulomb strength criterion can better describe the failure features of rocks under high geostress and rock micro-unit strength obeys the Weibull distribution, a new statistical damage constitutive model is established. Then, comparing the new model based on Mogi-Coulomb criterion with the Drucker-Prager model and Mohr-Coulomb model, the new model can fit well experimental data. Finally, the new model is applied to the study of sudden change in rock permeability. Theoretical prediction is in good agreement with experimental result and is better than the existing results through a comparative analysis. The validity and feasibility of the model are verified.
Rock is a inhomogeneous and anisotropic material, containing a large number of pores, joints, cracks and other defects. Rock failure process is the evolution of crack propagation, showing the complex stress strain relationship. Krajcinovic (1982) establishes a statistical damage constitutive model with the strain equivalence theory and statistical damage theory. The model includes the following three important parts. The first part is the damage constitutive relation. The strain equivalence damage model has a clear physical meaning and is widely used (Lemaitre 1984). Xie (1990), Cao et al. (2008), Yang et al. (2010), Li et al. (2006). The second part is micro-unit strength distribution function. Krajcinovic (1982),Tang et al. (1993), Cao et al. (2005) describe micro-unit strength with the Weibull distribution and normal distribution. The third part is the measure of micro unit strength, Krajcinovic (1982), Zhou et al. (1989), Tang et al. (1993) measure the strength of the micro unit with Strain, while Cao et al. (1998, 2005, 2008), Xu et al. (2002) use stress to measure it.
Hence, it is critical to reasonably measure rock micro-unit strength. Classic Mohr-Coulomb criterion doesn't consider the effect of intermediate principal stress on rock strength and is a linear failure criterion. However, the deep high stress rock has nonlinear characteristics (Zhou et al. 2005, Lü et al. 2005). The Drucker-Prager criterion considers the intermediate principal stress, but too conservative. Mogi (1971) established a new failure criterion through a large number of experiments, which appropriately considers the influence of intermediate principal stress. Adel Met al. (2005) studied the relation between Mogi criterion and Coulomb criterion. According to Lü et al. (2010), Zhang et al. (2010), the Mogi-Coulomb failure criterion can better reflect the failure characteristics of deep rock.