On failure criteria incorporating a scalar anisotropy parameter

This paper provides a discussion on the formulation of failure criteria incorporating a scalar anisotropy parameter. The latter is defined as the ratio of the joint invariant of the stress and microstructure tensors to the second stress invariant. The properties of the directional distribution of anisotropy parameter are examined by using the second-order microstructure tensor as well as its dyadic products. It is shown that, within the present formulation, the strength characteristics evolve towards an isotropic distribution with increase in the confining pressure. The formulation is applied to model the conditions at failure in Tournemire shale. In particular, the procedure involved in identification of material parameters is outlined in details. Some remarks on the description of induced anisotropy are also provided.