COMPRESSIVE FAILURE OF ROCKS BY SHEAR FAULTING

A model for the compressive failure of rocks via the process of shear faulting is presented. The model addresses the progressive growth of d amage that leads to the formation of a critical fault nucleus which gr ows unstably in its own plane by fracturing the grain boundaries in an increasingly rapid succession. The model uses a two-parameter Weibull -type shear strength distribution for defining the nucleation of initi al damage, followed by the use of stress enhancement factors for addre ssing the increased probability of failure in the vicinity of already cracked grain boundaries. These factors essentially involve surface av eraging of enhanced stresses in the neighboring grains with the approp riate strength distribution as the weighting function. As the stress i s further increased, similar correlated fracturing events get preferen tially aligned to the crack cluster, resulting in en echelon of cracks . This crack cluster is modeled as an elliptical inhomogeneity within which the cracks interact and lead to material pulverization, the effe ct of which, mechanistically, is to lower the shear modulus compared w ith the uncracked material on the outside. The shear stress concentrat ion resulting from this moduli mismatch is calculated and used to comp ute the stress enhancement factors for defining the nucleation of addi tional cracking events near the crack cluster. Eventually, the size of the crack cluster becomes sufficiently large that it carries a stress concentration high enough to fracture all grain boundary elements in from of it in an increasingly rapid succession. The stress associated with this event is taken as the failure stress. Since the model allows other cracking events to occur within the material volume in accordan ce with the assumed strength distribution function, formation of other competing but subcritical shear faults naturally occurs. Besides the faulting stress for a prescribed confinement, the model is able to pre dict the angle of the shear fault fairly well. The model is applied to a variety of rock types, including granite, eclogite, gabbro, aplite, rock salt, sandstone, dunite, limestone, and marble, and the predicte d failure envelopes compare rather well with the failure data availabl e in the literature.