A paraboloid failure surface for transversely isotropic materials

An invariant 3-D failure criterion for transversely isotropic solids is pre sented. For isotropic conditions, this criterion reduces to Mises-Schleiche r failure criterion. It is shown that the anisotropic Mises-Schleicher (AMS ) criterion can accurately describe the observed failure characteristics of transversely isotropic rocks under both compressive and tensile stresses. This criterion predicts that the application of multiaxial tensile stresses on rock reduces the value of the failure strength, i.e., the predicted val ue of the hydrostatic tensile strength as well as of the biaxial tensile st rength is less than the uniaxial tensile strength in any direction. The int ersections of the AMS failure surfaces with the octahedral plant demonstrat es the ability of the criterion to describe the directional character of th e strength of transversely isotropic materials under general loading condit ions. The application of this criterion to conventional triaxial compressio n, reduced triaxial extension, and biaxial conditions, shows that this crit erion captures the influence of the magnitude of the intermediate principal stress on strength. Representative sets of data from tests on rock have be en analyzed and comparison between the theoretical predictions and the data appears to be quite good with the accuracies generally within the natural scatter of test data. In this paper, the AIMS criterion is applied to rock materials; however, it can be used to describe the strength anisotropy of a ny material exhibiting transverse isotropy. (C) 1999 Elsevier Science Ltd. All rights reserved.