ABSTRACT:
Uniaxial compression tests on rocks, if conducted at stresses below failure, typically show nonlinearity in the stress-strain curve, and hysteresis. Walsh (J. Geophys. Res., 1965) explained this behavior 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 experimental data on sandstones taken from the literature.
1 INTRODUCTION
The mechanical behavior of rocks is to a great extent controlled by the presence of cracks and crack-like voids. This is true both with regards to the elastic behavior of the rock (see Jaeger et al. 2007), and with regards to inelastic processes such as yielding and failure (Paterson & Wong 2005). In 1965, Walsh (1965a, b ,c) published a set of three papers that provide the conceptual basis of much of our understanding of the influence of cracks on elastic rock deformation. Under hydrostatic loading (Walsh 1965a), open cracks initially (i.e., at low stresses) contribute an excess compliance to the rock. But each crack closes up at a stress that is roughly equal to aE , where E is the Young’s modulus of the uncracked rock, and a is the initial aspect ratio of the crack.
