Compressive failure of rocks

Abstract

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 the defining 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. As the stress is further increased, similar correlated fracturing events gets preferentially aligned to the crack cluster, resulting in an echelon of cracks. This crack cluster is modeled as an elliptical inhomogeneity with a lower shear modulus compared with the uncracked material on the outside. The shear stress concentration resulting from this moduli mismatch was 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 such that it carries a stress concentration high enough to fracture all grain boundary elements in front of it in an increasingly rapid succession. The stress associated with this event is taken as the failure stress. The model is applied to a variety of rocks, including granite, eclogite, gabbro, aplite, rocksalt, sandstone, dunite, limestone, and marble, and the results compare rather well with the failure data from the literature.