Three-dimensional strength estimation of intact rocks using a modified Hoek-Brown criterion based on a new deviatoric function

Hoek-Brown criterion has been applied widely in a large number of rock projects around the world and has the main advantage that its input data can be determined from the uniaxial compressive strength, mineralogy and structural properties of the rock. However, there also exist demerits that neglect the effects of the intermediate principal stress and represent a non-smoothness shape in the deviatoric plane. After reviewing the history of the development of the Hoek-Brown criterion briefly, a modified Hoek-Brown criterion was proposed by the combination of a versatile deviatoric function and a meridian function of the original Hoek-Brown criterion. The new deviatoric function, which was proposed by introducing an extra strength parameter a into the one of Matsuoka-Nakai (MN) criterion and behaviors as well as the one proposed by Bigoni and Piccolroaz, is a generalization of deviatoric shapes belonging to several classic strength criteria, i.e. Drucker-Prager (DP), Tresca, Mohr-Coulomb (MC), Lade-Duncan (LD), Matsuoka-Nakai (MN) and Ottosen strength criterion. The procedure for determination of the strength parameters was demonstrated in detail. Comparisons between the derived criterion and true triaxial test data of KTB amphibolite, Westerly granite, Dunham dolomite, Mizuho Trachyte were presented in three-dimensional principal stress space qualitatively and quantitatively. Overall predicted errors were also compared with the ones obtained by the generalized Zhang-Zhu criterion (Z-Z) as well as its modifications (S-D, E-D, H-D), which showed least error for each rock type by the modification in this paper. The effect of the intermediate principal stress was also discussed for these four rock types, confirming that the intermediate principal stress is included in the strength criterion. The derived criterion not only maintains the features in the meridian plane of the original Hoek-Brown criterion, but solves the non-smoothness problem in the deviatoric plane and shows an excellent performance for describing brittle and ductile rock types considered.