Brittle Creep and Failure: A Reformulation of the Wing Crack Model

We propose a reformulation of the wing crack model of brittle creep and failure. Experimental studies suggest that the mechanical interactions of sliding and tensile wing cracks are complex, involving formation, growth, and coalescence of multiple tensile, shear and mixed-mode cracks. Inspired by studies of failure in granular media, we propose that these complex mechanical interactions lead to the formation of micro shear-bands, which, in turn, develop longer wing cracks and interact with a wider volume of rock to produce larger shear bands. This process is assumed to indefinitely continue at greater scales. We assume that the original wing crack formalism is applicable to micro shear-band formation, with the difference that the half-length, a, of the characteristic micro shear band is allowed to increase with wing crack growth. In this approach, the functional relationship of a with the wing crack length l embodies the entire process of shear band formation, growth and interaction with other shear bands and flaws. We found that the function a(l)/a(0) = 1 + (l/lambda)(q), where lambda and q are constant parameters, generated creep curves consistent with published creep data of rocks. Similar accord was also obtained with experimental brittle failure data. Furthermore, we found that the Mohr-Coulomb behavior emerged from our model, allowing estimation of the cohesion and angle of internal friction in materials for which lambda and q are independently known.