A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks

Abstract

Abstract In this study we examine seven different failure criteria by comparing them to published polyaxial test data (σ1>σ2>σ3) for five different rock types at a variety of stress states. We employed a grid search algorithm to find the best set of parameters that describe failure for each criterion and the associated misfits. Overall, we found that the polyaxial criteria Modified Wiebols and Cook and Modified Lade achieved a good fit to most of the test data. This is especially true for rocks with a highly σ2-dependent failure behavior (e.g. Dunham dolomite, Solenhofen limestone). However, for some rock types (e.g. Shirahama Sandstone, Yuubari shale), the intermediate stress hardly affects failure and the Mohr–Coulomb and Hoek and Brown criteria fit these test data equally well, or even better, than the more complicated polyaxial criteria. The values of C0 yielded by the Inscribed and the Circumscribed Drucker–Prager criteria bounded the C0 value obtained using the Mohr–Coulomb criterion as expected. In general, the Drucker–Prager failure criterion did not accurately indicate the value of σ1 at failure. The value of the misfits achieved with the empirical 1967 and 1971 Mogi criteria were generally in between those obtained using the triaxial and the polyaxial criteria. The disadvantage of these failure criteria is that they cannot be related to strength parameters such as C0. We also found that if only data from triaxial tests are available, it is possible to incorporate the influence of σ2 on failure by using a polyaxial failure criterion. The results for two out of three rocks that could be analyzed in this way were encouraging.