The normal stress space and its application to constructing a new failure criterion for cross-anisotropic geomaterials

The principal stress space has been traditionally used to describe and formulate isotropic strength criteria for materials, but it has limited functionality for anisotropic behavior, as it does not incorporate any information on material structure. In this paper we introduce a Normal Stress Space (NSS) comprising three normal stresses in the material coordinate system to represent interactions between the stress tensor and material structure. Using NSS we then develop an extension of the well-known isotropic Matsuoka-Nakai (MN) criterion to describe the anisotropic shear strength of rock based on geometric considerations rather than algebraic tensor manipulations. This new criterion, called Anisotropic Matsuoka-Nakai (AMN) criterion, describes failure across bedding and foliation planes, while sliding along these planes of weakness is well described by the Coulomb criterion. True triaxial test data on chlorite schist and Chichibu Green schist obtained from the literature are then used to validate the proposed criterion. Reasonable agreement is obtained for both true triaxial datasets, providing encouraging validations of the proposed AMN-Coulomb failure criterion for describing both the strength and failure mode of cross-anisotropic rocks under complex stress conditions.