Critical review of the Mogi failure criterion based on true-triaxial laboratory data analysis and theoretical considerations

The influence of the intermediate principal stress, σ2, is disregarded when rock strength is analyzed using the Mohr-Coulomb or Hoek-Brown criteria. Several polyaxial strength criteria have been proposed to account for the influence of σ2. One of the methods that received considerable attention is the Mogi criterion. The criterion modifies the Nadai or Drucker-Prager approaches by exchanging the normal octahedral stress with what is introduced as the mean effective stress, σm,2. This change is based on experimental evidence that the influence of the intermediate principal stress on strength is less pronounced than the influence of the minimum principal stress. However, the Mogi criterion was derived somewhat empirically and consequently it is essential to analyze its potential theoretical deficiencies. In the current note, we analyzed the Mogi failure criterion, describing its characteristics in both τoct–σm,2 and σ1-σ2 spaces. We investigated the relation between Mohr-Coulomb and Mogi criteria, which marks the basis for the commonly used Mogi-Coulomb approach. We compared the performance of the Mogi criterion against available polyaxial strength data using three fitting approaches: Mogi-Coulomb based on triaxial compression results only, linear Mogi based on all polyaxial strength results, and power law Mogi also based on all data. The analysis reveals several serious deficiencies of the Mogi approach which all suggest that the Mogi criterion cannot properly represent the σ2 dependence of rock strength in many cases.