# The Micromechanics of Westerley Granite at Large Compressive Loads

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## Abstract

The micromechanical damage mechanics formulated by Ashby and Sammis (Pure Appl Geophys 133(3) 489–521, 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.

## Keywords

Stress Intensity Factor Failure Surface Strain Energy Density Wing Crack Penny Shaped Crack## Notes

### Acknowledgments

The authors would like to thank Yehuda Ben-Zion and three anonymous reviewers for their constructive reviews. This research was funded through the National Science Foundation collaborative grant EAR-0711171 to the University of Southern California and the California Institute of Technology, the National Science Foundation for the research grant (award no. EAR-0911723), provided under the American Recovery and Reinvestment Act of 2009 (ARRA) (Public Law 111-5) and the Department of the Air Force though Grant #FA8718-08-C-0026.

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