David, E, Brantut, N, Schubnel, A & Zimmerman, RW 2008, 'Sliding Crack Model for the Uniaxial Stress–Strain Curve of Rock', in Y Potvin, J Carter, A Dyskin & R Jeffrey (eds), Proceedings of the First Southern Hemisphere International Rock Mechanics Symposium
, Australian Centre for Geomechanics, Perth, pp. 553-561.
Uniaxial compression tests on rocks, if conducted at stresses below failure, typically exhibit both non-linearity and hysteresis in the stress–strain curve. Walsh (1965b) explained this behaviour in terms of frictional sliding along the faces of closed cracks. Although well known and widely cited, Walsh’s model has not previously been developed in sufficient detail to be used for quantitative predictions. We revisit and extend his model, by including the effect of the stress required to close an initially open crack, and we examine the unloading process in detail. Our analysis leads to closed-form expressions for the loading and unloading portions of the stress–strain curve, as functions of elastic modulus of the uncracked rock, the crack density, the characteristic aspect ratio, and the crack friction coefficient. The model provides a good fit to the loading and unloading portions of the stress–strain curves, for some new experimental data acquired on thermally-cracked La Peyratte granite.
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