A quantitative model of dilatancy in dry rock and its application to westerly granite

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Abstract
A general model of dilatancy was developed based on the behavior of individual microcracks. Macroscopic effects were described by combining the effects of individual cracks using a statistical approach. The model was developed using distribution functions for crack size, crack strength, and local stress. Hysteresis in volumetric strain and stress‐strain data for partial unloading and reloading and general loading paths can be described. The model is best suited to describing rock which has been subjected to a number of loading cycles sufficient to remove the residual volumetric strain that is present in the initial cycles. This makes the rock more representative of the real earth and removes transient effects that obscure the dilatant effect. Volumetric strain data from triaxial experiments on Westerly granite were well described by the model for confining pressures from 0 to 4.11 kbar. Only one parameter was needed to describe the effect of changing the confining pressure, and this can be interpreted as an elastic effect on the crack volume. Some aspects of the crack behavior that were necessary to explain the data are incompatible with the usual sliding crack model of dilatancy. Combined with the lack of observable shear cracks, this casts serious doubts on the validity of the sliding crack model.

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