Sliding crack model for nonlinearity and hysteresis in the uniaxial stress–strain curve of rock

Uniaxial compression tests on rocks, if conducted at stresses below failure, typically exhibit both non-linearity and hysteresis in the stress–strain curve. In a series of three papers in 1965, Walsh explained this behavior in terms of frictional sliding along the faces of closed cracks. Although well known and widely cited, Walsh’s model does not seem to have 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 by examining 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 data on Berea sandstone taken from the literature, and for some new experimental data acquired on thermally cracked La Peyratte granite. ► Walsh's model for the effect of cracks on the uniaxial stress-strain curve of rock has been extended. ► Revised model accounts for the stress required to close cracks, and considers the unloading process. ► Model provides a good fit to loading and unloading portions of stress-strain curves of several rocks. ► Model provides a micromechanical explanation for nonlinear and hysteretic stress-strain behavior.