The effect of size and stress concentration on the dilatancy and fracture of rock

Abstract

Uniaxial compression tests were carried out to study the variation of strength and volumetric strain for cylindrical samples of a fine-grained sandstone with varying slenderness ratios (height to diameter). These experiments revealed that the fracture initiation strength is almost unaffected by the sample size. A stress concentration model based on Prandtl's theory of localized plastic deformation is developed for rock-platen contact surfaces of finite rock samples. The model is verified by compression tests on frustum of cone-shaped samples of the same sandstone. This model provides the physical explanation for the commonly reported values of the fracture initiation to failure strength ratio. An attempt was made to relate qualitatively the failure strength to the sample size through a stress concentration strengthening term derived from this model. A relation is also proposed to relate the failure strength and fracture initiation strength by a dilatancy hardening term. The failure strength values calculated from these relations agree fairly well with the experimentally obtained ones. Finally, the reported effects of strain rate and pore pressure, and nature of stress drop are discussed with respect to the stress concentration phenomenon.