Comparison of six major intact rock failure criteria using a particle flow approach under true-triaxial stress condition

Suitability of six major intact rock failure criteria: Mohr–Coulomb, Hoek–Brown, Modified Lade, Modified Wiebols and Cook, Mogi and Drucker–Prager in representing the intact rock strength under the true-triaxial stress condition (σ₁ ≥ σ₂ ≥ σ₃) is examined in this paper. Because the true-triaxial experimental test data available in the literature are limited and do not cover a wide range of confining stresses, the particle flow code (PFC^3D) software was used to simulate synthetic rock material failure of cubic samples of side dimension 160 mm under a broad confining stress range. The synthetic rock was made out of a mixture of gypsum, sand and water. The parallel bond model (PBM) available in PFC^3D with the associated micro parameters was chosen to represent the behavior of the synthetic material. As the first step, uniaxial, triaxial and Brazilian tests were performed in the laboratory to find the macro properties of the synthetic material. As the second step, the effect of some of the micro properties: particle size, coefficient of variation of the normal and shear bond strengths and friction coefficient on the macro properties of the synthetic rock was investigated. Then, the micro parameters of PBM were calibrated based on the aforementioned macro parameter results. Using the calibrated PFC^3D model 29 true-triaxial tests were simulated. All six failure criteria were fitted to these PFC data. Among these criteria, Modified Lade, Mogi and Modified Wiebols and Cook found to be the best failure criteria producing lower root mean square error (RMSE) values of 0.212, 0.219 and 0.304, respectively. Thus those three criteria are recommended for prediction of intact rock strength under true-triaxial stress condition. Another fitting analysis was conducted using only 12 of the 29 data to find the effect of the limited data on the prediction accuracy of the three failure criteria through the RMSE value. The predictions based on these analyses produced RMSE values of 0.40, 0.23 and 0.47 for Modified Lade, Mogi and Modified Wiebols and Cook criteria, respectively. This indicated that the Mogi criterion is the most stable among the three criteria with respect to the prediction accuracy.