The Micromechanics of Westerley Granite at Large Compressive Loads

Abstract

Abstract-The micromechanical damage mechanics formulated by ASHBY and SAMMIS (Pure Appl Geophys 133(3) 1990) has been shown to give an adequate description of the triaxial failure surface for a wide variety of rocks at low confining pressure. However, it does not produce the large negative curvature in the failure surface observed in Westerly granite at high confining pressure. We show that this discrepancy between theory and data is not caused by the two most basic simplifying assumptions in the damage model: (1) that all the initial flaws are the same size or (2) that they all have the same orientation relative to the largest compressive stress. We also show that the stress-strain curve calculated from the strain energy density significantly underestimates the nonlinear strain near failure in Westerly granite. Both the observed curvature in the failure surface and the nonlinear strain at failure observed in Westerly granite can be quantitatively fit using a simple bi-mineral model in which the feldspar grains have a lower flow stress than do the quartz grains. The conclusion is that nonlinearity in the failure surface and stress-strain curves observed in triaxial experiments on Westerly granite at low loading rates is probably due to low-temperature dislocation flow and not simplifying assumptions in the damage mechanics. The important implication is that discrepancies between experiment and theory should decrease with increased loading rates, and therefore, the micromechanical damage mechanics, as formulated, can be expected to give an adequate description of high strain-rate phenomena like earthquake rupture, underground explosions, and meteorite impact.

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“…[2,12,13] calculate the shear (s) and normal (r) stresses on each penny crack from the remote compressive stress field.…”

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