A theoretical investigation of the sliding crack model of dilatancy

Laboratory measurements of volumetric strain and velocity in Westerly granite are analyzed to determine the physical nature of microcracks in the rock. The commonly used factional ‘sliding crack’ model of dilatancy is examined in detail. The characteristics of an ensemble of sliding cracks are determined from the characteristics of the individual sliding surfaces. It is found that sliding cracks which open with a stick slip motion cannot account for the observed ‘memory’ of the peak stress in cycling experiments. A system of stably sliding cracks would have the required memory but would also produce a very long dead band at the beginning of sample unloading during which no change in inelastic volumetric strain could take place. An analysis of the elastic constants at the beginning of unloading shows that this dead band is not observed in laboratory experiments. This analysis shows that the sliding crack is an unlikely mechanism for dilatancy. An alternative is developed in the following paper.