A note on the scaling relations for opening mode fractures in rock

摘要

It is well established that shear cracks in rock (faults) obey linear displacement-length scaling and thus have scale invariant driving stresses. Several recent papers have claimed that for opening mode cracks in rock (joints, veins, and dikes) displacement obeys square root scaling with fracture length. This is a fundamentally different mode of behavior, because, unlike shear cracks, opening mode cracks would then be unstable under constant stress boundary conditions. Here the same data are reexamined and it is found, to the contrary, that for opening mode cracks in rock, fracture toughness K_c scales with √L and hence displacement scales linearly with L. The conflicting view resulted from data misinterpretation. This resolves the discrepancy between the behavior of shear and opening mode cracks in rock.