Simple three-dimensional Mohr-Coulomb criteria for intact rocks

A major component of the Mohr-Coulomb (M-C) criterion is that the failure of the material is independent of the intermediate principal stress σ2 along the potential planes of sliding. To account for the effect of σ2, a linear relationship between the octahedral shear stress τoct and the mean stress σm,2 on the plane of failure (called the Mogi-Coulomb criterion) is widely used to represent rock failure in polyaxial compression (PXC) in practice. In this research, a linear relationship between the equivalent stress σe (or τoct) and major principal stress σ1 (or minor principal stress σ3) is proposed, which has a similar expression as the Mogi-Coulomb criterion. The relationship between the proposed failure criteria and M-C criterion is like the relationship between the Tresca and Von-Mises criteria. The material parameters can be related to the M-C strength parameters, and can be easily obtained from conventional triaxial tests. The proposed criteria are numerically calibrated against triaxial compression (TXC) and PXC data sets using three different methods. Sensitivity of the range of TXC stress data employed for fitting on the prediction results in PXC are further discussed. Comparisons of two proposed criteria with the Mogi-Coulomb criterion for rocks in PXC demonstrate that one new criterion with convex failure envelope gives the best performance for seven rock types and provides an acceptable modelling for the rest of rock types. Another new criterion and the Mogi-Coulomb criterion result in large prediction error for three (or two) rock types though they can give best performance for some rock types.