A paraboloid failure surface for transversely isotropic materials

Abstract

An invariant 3-D failure criterion for transversely isotropic solids is presented. For isotropic conditions, this criterion reduces to Mises–Schleicher 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 value of the hydrostatic tensile strength as well as of the biaxial tensile strength is less than the uniaxial tensile strength in any direction. The intersections of the AMS failure surfaces with the octahedral plane demonstrates the ability of the criterion to describe the directional character of the strength of transversely isotropic materials under general loading conditions. The application of this criterion to conventional triaxial compression, reduced triaxial extension, and biaxial conditions, shows that this criterion captures the influence of the magnitude of the intermediate principal stress on strength. Representative sets of data from tests on rock have been 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 AMS criterion is applied to rock materials; however, it can be used to describe the strength anisotropy of any material exhibiting transverse isotropy.