Three-Dimensional Failure Criteria for Rocks Based on the Hoek-Brown Criterion and a General Lode Dependence

Three-dimensional (3D) failure criteria based on the Hoek-Brown (HB) criterion and a general Lode dependence for rocks were proposed in this paper. The proposed failure criteria inherited the compression meridian from the HB criterion and can include independent shear meridians to construct the failure envelop surface. Four failure criteria [Rubin-Willam-Warnke (RWW), Rubin-Pan-Hudson, R1.65, and Rubin (R)] with curved-triangular cross sections and two failure criteria with hexagonal cross sections (Rubin-Mohr-Coulomb and Rubin-Hoek-Brown) were shown as examples of applications of the general Lode dependence to demonstrate its versatility. The material parameters involved in the new failure criteria can be easily obtained from conventional triaxial compression (TXC) tests. Polyaxial compression (PXC) test data for six different rocks at a variety of stress states from published literatures were used to validate the proposed failure criteria, in which the best-fitting parameters obtained from the TXC tests were used to predict the rock failure in PXC states of stress. The comparison results demonstrated that three criteria (RWW, R1.65, and R) with similar cross section shapes gave better predictions than the other three criteria. One 3D failure criterion (R1.65) with an empirical factor ( = 1.65) to define the independent shear meridian was considered to be the best among them because the RWW criterion tended to underestimate the strength for some rocks and the R criterion involved an extra parameter , which needed to be fitted from expensive PXC tests. The use of best-fitting parameters obtained from TXC tests can provide satisfactory predictions for rock failure with sigma(2) dependence using the R1.65 criterion.