True-triaxial strength criteria for rock

This paper reviews some strength criteria which include the role of the intermediate principal stress, and proposes a new criterion. Strength criteria of the form σoct=fN(σoct), such as Drucker–Prager, represent a rotation surface in the principal stress space, symmetric to the line σ1=σ2=σ3 in the meridian plane. Because σoct=fN(σoct) must fit the pseudo-triaxial compressive strength, it will have a non-physical outcome for triaxial extension. Mogi's criteria, σoct=g1(σm,2) and σmax=g2(σβ) are able to fit experimental data reasonably well, but the prediction of strength is not good and sometimes problematic. Strength criterion with the form λ(σ1, σ2, σ3)=F[η(σ1, σ2, σ3)], or a curve of two variables which can be decided by fitting pseudo-triaxial experimental data, is not expected to describe the strength under various stress states, no matter how high the correlation coefficient of λ and η is, or how low the misfit of the equation λ=F(η) is, as these seemingly good correlations usually result from the dominant influence of the maximum principal stress in the metrics of λ and η. The intermediate principal stress may improve the strength of rock specimen, but its influence will be restricted by σ3. Also when σ2 is high enough to cause failure in the σ2–σ3 direction, the strength will decrease with the increasing σ2. The new strength criterion with exponent form has just such a character, and gives much lower misfits than do all seven criteria discussed by Colmenares and Zoback [Colmenares LB, Zoback MD. A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 2002;39:695–729].