Brittle Creep and Brittle Failure of Rocks: a reformulation of the wing
crack model
Abstract
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.