Authors: David, E; Brantut, N; Schubnel, A; Zimmerman, RW Purchase Paper |

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),

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.

Bésuelle, P. (1999) Deformation and rupture in soft rocks and indurate solids: homogeneous behaviour and localization. PhD thesis, University Joseph-Fourier, Grenoble.

Darot, M., Guéguen, Y. and Baratin, M-L. (1992) Permeability of thermically cracked granite, Geophysical Research Letters, 19, pp. 869–872.

David, E. (2006) Modeling of the stress–strain behaviour of a rock under uniaxial compression. MSc report, Royal Institute of Technology, Stockholm.

Grechka, V. and Kachanov, M. (2006) Effective elasticity of rocks with closely spaced and intersecting cracks. Geophysics, 71, pp. D85–D91.

Guyer, R.A., McCall, K.R., Boitnott, G.N., Hilbert, L.B. and Plona, T.J. (1997) Quantitative implementation of Preisach-Mayergoyz space to find static and dynamic elastic moduli in rock. Journal of Geophysical Research B 103, pp. 5281–5293.

Hashin, Z. (1988) The differential scheme and its applications to cracked materials. Journal of the Mechanics and Physics of Solids, 36, pp. 719–734.

Horii, H. and Nemat-Nasser, S. (1983) Overall moduli of solids with microcracks: load-induced anisotropy. Journal of the Mechanics and Physics of Solids, 31, pp. 155–171.

Jaeger, J.C., Cook, N.G.W. and Zimmerman, R.W. (2007) Fundamentals of Rock Mechanics, 4th edition, Blackwell, Oxford, 488 p.

Kachanov, M.L. (1982) A microcrack model of rock inelasticity. Part I: Frictional sliding on microcracks. Mechanics of Materials, 1, pp. 19–27.

Lawn, B.R. and Marshall, D.B. (1998) Nonlinear stress–strain curves for solids containing closed cracks with friction. Journal of the Mechanics and Physics of Solids, 46, pp. 85–113.

Morgenstern, N.R. and Tamuly Phukan, A.L. (1969) Non-linear stress strain relations for a homogeneous sandstone. International Journal of Rock Mechanics and Mining Sciences, 6, pp. 127–142.

Morlier, P. (1971) Description de l’etát de fissuration d’une roche à partir d’essais non-destructifs simples (Description of the state of fracturisation of a rock through simple non-destructive tests). Rock Mechanics, 3, pp. 125–138.

Nihei, K.T., Hilbert, L.B., Cook, N.G.W., Nakagawa, S. and Myer, L.R. (2000) Frictional effects on the volumetric strain of sandstones. International Journal of Rock Mechanics and Mining Sciences, 37, pp. 121–132.

Paterson, M.S. and Wong, T.F. (2005) Experimental Rock Deformation – the Brittle Field, 2nd edition, Springer, Berlin, 347 p.

Sneddon, I.N. (1946) The distribution of stresses in the neighbourhood of a crack in an elastic solid. Proceedings Royal Society of London, 187, pp. 229–260.

Stevenson, A.C. (1945) Complex potentials in two-dimensional elasticity. Proceedings Royal Society of London, Vol. 184, pp. 129–179.

Walsh, J.B. (1965a) The effect of cracks on the compressibility of rocks. Journal of Geophysical Research, Vol. 70, pp. 381–389.

Walsh, J.B. (1965b) The effect of cracks on the uniaxial compression of rock. Journal of Geophysical Research, Vol. 70, pp. 399–411.

Walsh, J.B. (1965c) The effect of cracks in rocks on Poisson’s ratio. Journal of Geophysical Research, Vol. 70, pp. 5249–5257.

Zimmerman, R.W. (1985) Effect of microcracks on the elastic moduli of brittle solids. Journal of Materials Science Letters, 4, pp. 1457–1460.

Zimmerman, R.W. (1991) Compressibility of Sandstones. Elsevier, Amsterdam, 173 p.

© Copyright 2019, Australian Centre for Geomechanics (ACG), The University of Western Australia. All rights reserved.

Please direct any queries or error reports to repository-acg@uwa.edu.au

Please direct any queries or error reports to repository-acg@uwa.edu.au