True-triaxial strength criteria for rock

Abstract

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 σ oct= f N( σ oct), such as Drucker–Prager, represent a rotation surface in the principal stress space, symmetric to the line σ 1= σ 2= σ 3 in the meridian plane. Because σ oct= f N( σ oct) must fit the pseudo-triaxial compressive strength, it will have a non-physical outcome for triaxial extension. Mogi's criteria, σ oct= g 1( σ m,2) and σ max= g 2( σ β ) 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( σ 1, σ 2, σ 3)= F[ η( σ 1, σ 2, σ 3)], 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 σ 3. Also when σ 2 is high enough to cause failure in the σ 2– σ 3 direction, the strength will decrease with the increasing σ 2. 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].