Compressive failure of rocks by shear faulting

Abstract

A model for the compressive failure of rocks via the process of shear faulting is presented. The model addresses the progressive growth of damage that leads to the formation of a critical fault nucleus which grows 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 initial damage, followed by the use of stress enhancement factors for addressing the increased probability of failure in the vicinity of already cracked grain boundaries. These factors essentially involve surface averaging of enhanced stresses in the neighboring grains with the appropriate strength distribution as the weighting function. As the stress is further increased, similar correlated fracturing events get preferentially 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 effect of which, mechanistically, is to lower the shear modulus compared with the uncracked material on the outside. The shear stress concentration resulting from this moduli mismatch is calculated and used to compute the stress enhancement factors for defining the nucleation of additional 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 accordance 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 predict 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 predicted failure envelopes compare rather well with the failure data available in the literature.