The sliding wing crack—again!

Abstract

We present accurate numerical calculations for the opening and extension of tensile wing cracks driven by sliding on an oblique crack with Coulomb friction. In contrast to previous analyses, the portions of the crack system that are open or closed and slipping or stuck are determined as part of the solution. Calculations reveal that reduction of the compressive normal stress accompanying opening of the wing cracks causes considerable opening of the sliding crack providing an additional component of macroscopic dilatancy. Immediately upon unloading the central portion of the planar crack is locked but there is closure of the open portions of the crack causing a decrease in inelastic volume strain as observed in laboratory experiments. Reverse slip begins near the open portion of the crack and spreads toward the center. The rate of decrease of inelastic volume strain with axial stress remains small, causing an apparent “dead band” until the axial stress is sufficiently reduced to cause reverse slip on the entire crack. This apparent “dead band” is small because opening reduces the compressive normal stress on the planar crack. These calculations demonstrate that the behavior of this model is consistent with measurements of inelastic volume strain and acoustic velocity on laboratory rock specimens.