ABSTRACT
In the axisymmetric compression test, rock samples, even those which are isotropic when unstressed, develop a transversely isotropic structure after a small amount of inelastic deformation due to the preferential growth of microcracks in the axial direction. To examine the effect of this developed anisotropy on faulting, conditions for the localization of deformation are derived for the most general form of stress strain relation for a material exhibiting transversely isotropic incremental response. This constitutive law involves six independent, incremental moduli. Expressions are derived for the predicted slope of the axial stress vs. axial strain curve at faulting and for the predicted fracture angle. Unfortunately, laboratory data are not sufficient to determine the values of all the incremental moduli, specifically, the moduli governing shearing parallel and transverse to the specimen axis. Nevertheless, for a plausible range of these moduli, the predicted fracture angle is relatively insensitive to their exact value and is shown to agree with experimentally observed values. If these shear moduli are interpreted as incremental elastic values, the results for the predicted slope at localization suggest that although stress-induced anisotropy may cause some reduction in the amount of postpeak deformation predicted for localization, it is not sufficient to cause localization to be predicted at peak load. However, it is possible that yield surface vertex effects may cause a further reduction of the amount of postpeak deformation prior to predicted localization.
INTRODUCTION
Although the Griffith theory of fracture has been relatively successful in describing the failure of metals under tensile loads due to the growth of sharp-tipped flaws, attempts to modify the theory to apply to the failure of brittle rock in compression have been less successful. Some authors (e.g. Brace, 1964) have observed that the predictions of the modified Griffith theory agree reasonably well with some data, but others (e.g. Wawersik and Fairhurst, 1970) have noted that the fracture process for brittle rock in compression seems to violate the fundamental premise of the Griffith theory. Failure, that is, "faulting" in brittle rock evidently does not occur by the propagation of a single critical flaw as envisioned by Griffith; rather microcracks grow, interact, and link-up to form the fault which is often not a distinct plane but a rubble-like zone of definite thickness. However, a description of faulting which focuses on the growth and interaction of individual microcracks is likely to be very complex. Brady (1974) has approached the problem by modelling clusters of microcracks as elastic inclusions which are weaker than the surrounding material and by studying the conditions for their growth. Rudnicki and Rice (1975, hereafter abbreviated RR) have adopted an alternative point-of-view that localization of deformation, or faulting, is explainable as a smooth continuation of the response for homogeneous deformation; that is, the constitutive description of homogeneous deformation is such that the incremental boundary value problem admits a bifurcation point for which the nonuniform mode corresponds to localized deformation in a planar band. This approach to localization of deformation has been reviewed by Rice (1976) and its application to describing rupture in geological materials has been reviewed by Cleary and Rudnicki (1976).
