This paper aims to address the potentially inappropriate application of triaxial rock strength criteria to the polyaxial stress states calculated during 3d numerical analysis. We review some existing well-known polyaxial criteria, and discuss the advantage and disadvantage of each. Smoothness and convexity, 3d geometrical representation, the strengthening effect of σ2, and ease-of-use are some of the major requirements that are examined here. We show that accuracy may be achieved at the expense of mathematical complexity and advanced laboratory testing. However, such testing has not yet been accepted as a feasible common practice in rock engineering.

1 Introduction

Determining the peak strength of rock has always been an essential problem in characterization of material behaviour in rock engineering practice. The most common approach in measurement and prediction of peak strength is to utilize a generally accepted strength criterion, such as the well-known triaxial Mohr-Coulomb and Hoek-Brown criteria.

Although the conventional triaxial strength criteria perform well in certain circumstances, they suffer from neglecting the simultaneous influence of all three principal stress components. That is mainly because of the triaxial nature of their empirical derivation methods, and thus being written in terms of σ1 and σ3, and not taking into account the intermediate principal stress σ2.

Studies on the effect of the intermediate principal stress started by conducting triaxial compression and triaxial extension tests on same materials. These results show that the peak strength of the rock in a triaxial extension stress state (σ1= σ2> σ3) is slightly higher than that in triaxial compression (σ1> σ2= σ3) (Figure 1.b). This testing was followed, after appropriate advances in testing equipment, by the true triaxial or the so-called ‘polyaxial’ tests on different rock types.

Results from polyaxial tests show that when the stress state deviates from triaxial compression (σ1> σ2= σ3) to polyaxial (σ1> σ2> σ3), the strength of the rock reaches a peak before it falls to a value in the triaxial extension stress state (σ1= σ2> σ3) that is slightly higher than that in triaxial compression (Figure 1.a). This confirms the earlier results of triaxial compression versus triaxial extension tests.

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