Increases in Poisson’s ratio due to cyclic deformation in cracked rock

Abstract

Quantifying the changes in elastic properties of rocks during deformation is an important task. Effective Medium Theory (EMT), as formulated by Sayers & Kachanov (1995) relates the crack fabric (or damage) to the elastic properties. EMT has been successfully applied in the forward sense to predict the evolution of elasticity and related acoustic velocities in response to prescribed changes in crack density; and in the inverse sense to recover crack densities from laboratory measurements of acoustic velocities.  However, EMT fails to predict an important observation from laboratory studies of rock deformation: cyclic loading under uniaxial and conventional triaxial loads of rock samples can produce significant increases in Poisson’s ratio. These increases correlate with increasing number of cycles and with increasing crack density. This phenomenon has been known since the work of Walsh (1965), Brace et al. (1966) and Zoback & Byerlee (1975). More recent work by Heap & Faulkner (2008) and Heap et al. (2009; 2010) has extended the findings across a range of different lithologies. Published EMT equations predict Poisson’s ratios that stay constant or decrease with increasing crack density. Resolving this discrepancy is important because Poisson’s ratio may play a key role in producing stress rotations in the damage zones of faults, thereby making them ‘weak’ and prone to slip even when the normal stress is high e.g. the San Andreas Fault (Faulkner et al., 2006; Healy, 2008). Building on the work of David et al. (2012 & 2020) incorporating the effects of crack closure, sliding on cracks (Kachanov, 1992) and grain boundaries (Sayers, 2018) during loading, and delayed back-sliding during unloading, closed form micromechanical equations have been derived to describe increases of Poisson’s ratio with increasing number of cycles. Critically, increases in Poisson’s ratio are predicted even without including the effects of new cracks. Examples are shown comparing the predicted changes in Poisson’s ratio using the newly derived equations to data from uniaxial and triaxial laboratory tests on cracked rocks.