The Coulomb-Navier failure criterion is applied to geological faulting in the general three-dimensional case of rocks containing arbitrarily oriented strength anisotropies and subject to non-Andersonian stress systems (i.e. with none of the principal stresses acting in a vertical direction). General expressions for the critical stress difference necessary to cause failure as a function of depth are given in terms of material parameters, pore fluid pressure, orientation of the stress field and orientation of the strength anisotropy. The range of angles between a plane of anisotropy and the maximum principal stress direction, for which slip occurs along the pre-existing anisotropy rather than along a new fault, is calculated as a function of depth for different stress regimes. When the stress field is non-Andersonian and/or strength anisotropies not containing the intermediate stress direction occur in the rock, faulting generally is oblique-slip. A kinematic classification of faulting is given on the basis of the angle between the strike direction and the slip direction on the fault plane. Triangular diagrams, analogous to those used in petrology, are introduced to describe (i) faulting in isotropic rock subject to arbitrarily oriented stress fields, and (ii) faulting in anisotropic rock when one principal stress direction is vertical. The type of faulting as a function of stress field and anisotropy orientation can be read off directly from these diagrams.

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Journal Journal of Structural Geology
Yin, Z.-M. (Z. M.), & Ranalli, G. (1992). Critical stress difference, fault orientation and slip direction in anisotropic rocks under non-Andersonian stress systems. Journal of Structural Geology, 14(2), 237–244. doi:10.1016/0191-8141(92)90060-A