Relation between the Mogi and the Coulomb failure criteria

We have shown that linear Mogi criterion does a good job in representing rock failure under polyaxial stress states. When σ₂ = σ₃ the linear version of Mogi's triaxial failure criterion reduces exactly to the Coulomb criterion. Hence, the linear Mogi criterion can be thought of as a natural extension of the Coulomb criterion into three dimensions (i.e., polyaxial stress space). As Mohr's extension of the Coulomb criterion into three dimensions is often referred to as the Mohr-Coulomb criterion, we propose that the linear version of the Mogi criterion be known as the "Mogi-Coulomb" failure criterion. The classical Coulomb failure criterion can therefore be thought of as a special case, which applies only when σ₂ = σ₃ of the more general linear Mogi failure criterion. Furthermore, we found that the numerical values of the parameters that appear in the Mogi-Coulomb criterion can be estimated from conventional triaxial test data. Thus, this polyaxial failure criterion can be applied even in the absence of polyaxial (true triaxial) data. This offers a great advantage, as most laboratories are equipped to conduct only traditional σ₂ = σ₃ tests. Finally, we showed that if the linear form of the Mogi criterion is used, the parameters that appear in it can be unambiguously related to the traditional parameters appearing in the Coulomb failure law. The lack of such a relationship for the parameters appearing in the power-law Mogi criterion has been cited in [8] as a major drawback to the use of that model.