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Brittle Creep and Brittle Failure of Rocks: a reformulation of the wing crack model
  • Yves Bernabe,
  • Matej Pec
Yves Bernabe
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Matej Pec
Massachusetts Institute of Technology

Corresponding Author:mpec@mit.edu

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We propose a reformulation of the wing crack model of brittle creep and brittle 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 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 deformation (i.e. wing crack growth). In this approach, the dimensionless shear band half-length A is related to the dimensionless wing crack length L by a function, A(L) = 1 + f(L), where f(L) embodies the entire process of shear band formation, growth and interaction with other shear bands and flaws and the problem is then to identify its proper form. We compare the model predictions for various classes of functions f(L) to experimental brittle creep data. Although a very large class of functions reproduce the classic sequence of tri-modal creep, we found that only the simple power law f(L) = (L/Λ)q generated creep curves consistent with published creep data of rocks. Similar accord was also obtained with experimental brittle failure data.