Applicability of a new modified explicit three-dimensional Hoek-Brown failure criterion to eight rocks

Abstract

It has been well recognized that the performance of a failure criterion to polyaxial strength data depends on both the type of failure criterion and the varying σ2-dependence of the rock. To incorporate the varying influence of the intermediate principal stress on rock failure at true triaxial or polyaxial stress states, a new modified explicit three-dimensional Hoek-Brown failure criterion has been proposed by combining the Mogi (1967) criterion and the generalized Hoek-Brown criterion. The difference between the modified and the original generalized Hoek-Brown criteria is the introduced term nσ2, which may correspond to the contribution of σ2 to the normal stress on the failure plane and directly quantify the amount of σ2-dependence for different rock types. The failure envelope of the modified three-dimensional Hoek-Brown criterion is a circumscribed curved hexagonal pyramid matching with the three outer apices of the original Hoek-Brown criterion in the principal stress space and a parabolic curve in σ1-σ2 or σ1-σ3 space. The applicability analysis of the proposed three-dimensional Hoek-Brown criterion along with five other failure criteria has been performed by applying them to the polyaxial strength data for eight rocks. The proposed modified Hoek-Brown criterion was validated to reproduce the trend of the test data reasonably and to achieve the least mean misfit in six out of eight rocks. The Zhang-Zhu, the Mogi (1971) and the Mogi-Coulomb criteria derived from the Mogi's postulate yielded comparable average fits to the polyaxial strength data compared to other three criteria. The classical two-dimensional Hoek-Brown criterion only worked well for rocks with intermediate or low σ2-dependence, while the Drucker-Prager criterion performed poorly in most cases. Overall, the formulated explicit three-dimensional Hoek-Brown criterion might make accurate predictions of the polyaxial strength for rocks with low to high σ2-dependence property at a variety of stress states. The best-fitting solutions for all the eight rocks indicate that the value of the weighting factor n accounting for σ2-dependence varies from 0.04 to 0.44 relying on the characteristics of rocks tested. Furthermore, it is reliable to appropriately evaluate the influence of σ2 by applying the modified three-dimensional Hoek-Brown criterion to triaxial strength data as was validated for three out of eight rock types.