Abstract
This chapter reviews and extends analyses of diffusive instabilities in inelastically deforming geomaterials. The onset of these instabilities is connected with the conditions for shear localization in the limiting cases of drained (constant pore pressure) and undrained (constant fluid mass) deformation and depends on whether inelastic volume change is dilation or compaction. Rice [1975] showed that homogeneous shear deformation of a layer was stiffer for undrained than for drained conditions but was unstable in the sense that the magnitude of infinitesimal spatial nonuniformities begins to grow exponentially in time when the condition for localization is met in terms of the underlying drained response. As the condition for localization in terms of the undrained response is passed, infinitesimal spatial perturbations experience infinitely rapid decay and then infinitely rapidly growth. For materials that dilate with inelastic shearing the condition for localization is met for the drained response before it is met for the undrained response. For materials that compact and for which the shear yield stress increases with normal stress, the undrained response is softer than the drained and conditions for localization are met for undrained response before drained. If the shear yield stress decreases with normal stress, as for materials modeled by a “cap” on the yield surface, results for compacting materials are identical to those for the dilating materials. Generalization of the layer results to arbitrary deformation states reveals the same relation for the onset of diffusive instability: spatial nonuniformities begin to grow exponentially when the condition for localization is met in terms of the underlying drained response. In contrast to the result for the layer, the growth rate of perturbations does not necessarily become unbounded when the condition for localization is met in terms of the undrained response. The difference is due to a lack of symmetry in the constitutive tensors that is typical of geomaterials. Explicit expressions are given for the undrained response in terms of the drained for an elastic-plastic relation with yield stress and flow potential depending on first and second stress invariants. For this relation and the limit of incompressible solid constituents, the lack of symmetry just-mentioned disappears. If the fluid constituent is also incompressible, the analysis confirms a result of Runesson et al. [1996] that the undrained response is independent of mean stress and the predicted direction of shear bands is 45° to the principal axes of stress.
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References
Baud, P. Alexandre Schubnel and T.-F. Wang, Dilatancy, compaction and failure model in Solnhofen limestone, J. Geophys. Res., in press, 2000.
Brace, W. F. and R. J. Martin, III, A test of the law of effective stress for crystalline rocks of low porosity, Int. J. Rock Mech. Mining Sci., Vol. 5, 415–436, 1968.
Cleary, M. P. Elastic and dynamic response regimes of fluid-impregnated solids with diverse microstructures, Int. J. Solids Structures, 795–819, 1978.
Coussy, O. Mechanics of Porous Media, John Wiley and Sons, Ltd., Chichester, 1995.
Dimaggio, F. L. and I. S. Sandler, Material model for granular soils, J. Eng. Mech. Div. ASCE, Vol. 97, 935–950, 1971.
Finno, R. J., W. W. Harris, M. A. Mooney, and G. Viggiani, Shear bands in plane strain compression of loose sand, Géotechnique, Vol. 47, 149–165, 1997.
Garagash, D. and J. W. Rudnicki, Stability of undrained deformation of fluid-saturated dilating/compacting solids (Abstract), 20th Int. Cong. of Theor. and Appl. Mech., Chicago, II, Aug. 27–Sept. 2, 2000.
Han, C. and I. G. Vardoulakis, Plane strain compression experiments on water-saturated fine-grained sand, Géotechnique, Vol. 41, 49–78, 1991.
Issen, K. A. and J. W. Rudnicki, Conditions for compaction bands in porous rock, J. Geophys. Res., in press, 2000.
Marone, C., C. B. Raleigh, and C. H. Scholz, Frictional behavior and constitutive modeling of simulated fault gouge, J. Geophys. Res., Vol. 95, 7007–7025, 1990.
Martin, R. J. III, Pore pressure stabilization of failure in Westerly granite, Geophys. Res. Letters, Vol. 7, 404–406, 1980.
Mokni, M. and J. Desrues, Shear localization measurements in undrained plane-strain biaxial tests on Hostun RF sand, Mech. of Cohesive-Frictional Materials, Vol. 4, 419–441, 1999.
Mollema, P. N. and M. A. Antonellini, Compaction bands: a structural analog for antimode I cracks in aeolian sandstone, Tectonophysics, Vol. 267, 209–228, 1996.
Nur, A. and J. D. Byerlee, An exact effective stress law for elastic deformation of rock with fluids. J. Geophys. Res., Vol. 76, 6414–6419, 1971.
Olsson, W. A., Theoretical and experimental investigation of compaction bands, J. Geophys. Res., Vol. 104, 7219–7228, 1999.
Paterson, M. S. Experimental Rock Deformation: The Brittle Field, New York: Springer-Verlag, 1978.
Reynolds, O., On the dilatancy of media composed of rigid particles in contact, with experimental illustrations, Phil. Mag. (reprinted in Papers on Mechanical and Physical Subjects by O. Reynolds, Cambridge University Press, New, York, 1901, Vol.2, pp. 203–216), 1885.
Rice, J. R. On the stability of dilatant hardening for saturated rock masses. J. Geophys. Res., Vol. 80, 1531–1536, 1975.
Rice, J. R. The localization of plastic deformation, in Proceedings of the 14th Int. Union Theor. and Applied Mech. Congress, ed. W. T. Koiter, pp. 207–220, North Holland, Amsterdam, 1976.
Rice, J. R. Pore pressure effects in inelastic constitutive formulations for fissured rock masses. In Advances in Civil Engineering through Engineering Mechanics, pp. 360–363. New York: American Society of Civil Engineers, 1977.
Rice, J. R. and M. P. Cleary, Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressible constituents, Rev. Geophys. Space Phys., Vol. 14, pp. 227–241, 1976.
Rudnicki, J. W. and J. R. Rice, Conditions for the localization of deformation in pressuresensitive dilatant materials. J. Mech. Phys. Solids, Vol. 23, 371–394, 1975.
Rudnicki, J. W. A formulation for studying coupled deformation-pore fluid diffusion effects on localization. In Geomechanics, Proceedings of the Symposium on the Mechanics of Rocks, Soils and Ice, Applied Mechanics Division, Vol. 57 (edited by S. Nemat-Nasser), pp. 35–44, American Society of Mechanics Engineers, New York, 1983.
Rudnicki, J. W. A class of elastic-plastic constitutive laws for brittle rock, J. of Rheology, Vol. 28, 759–778, 1984a.
Rudnicki, J. W. Effects of dilatant hardening on the development of concentrated shear deformation in fissured rock masses, J. Geophys. Res., Vol. 89, 9259–9270, 1984b.
Rudnicki, J. W. Effect of pore fluid diffusion on deformation and failure of rock, in Mechanics of Geomaterials (edited by Z. P. Bažant), pp. 315–347, John Wiley &Sons, Ltd., New York, 1985.
Rudnicki, J. W. and C.-H. Chen, Stabilization of rapid frictional slip on a weakening fault by dilatant hardening, J. Geophys. Res., Vol. 93, 4745–4757, 1988.
Rudnicki, J. W., R. J. Finno, M. A. Alarcon G. Viggiani, and M. A. Mooney, Coupled deformation-pore fluid diffusion effects on the development of localized deformation in fault gouge, in Predictions and Perfomance in Rock Mechanics and Rock Engineering, EUROCK’96, edited by G. Barla, pp.1261–1268, Balkema, 1996.
Runesson, K., D. Perić and S. Sture, Effect of pore fluid compressibility on localization in elastic-plastic porous solids under undrained conditions, Int. J. Solids Structures, Vol. 33, 1501–1518, 1996.
Runesson, K. R. Larsson, and S. Sture, Localization in hyperelasto-plastic porous solids subjected to undrained conditions, Int. J. Solids Structures, Vol. 35, 4239–4255, 1998.
Schrefler, B. A., L. Sanavia and C. E. Majorana, A multiphase medium model for localisation and post localization simulation in geomaterials, Mech. of Cohesive-Frictional Materials, Vol. 1, 95–114, 1996.
Vardoulakis, I. Stability and bifurcation of undrained, plane rectilinear deformations on water-saturated granular soils, Int. J. Num. and Anal. Meth. Geomech., Vol. 9, 399–414, 1985.
Vardoulakis, I. Dynamic stability analysis of undrained simple shear on water-saturated granular soils, Int. J. Num. and Anal. Meth. Geomech., Vol. 10, 177–190, 1986.
Vardoulakis, I. Deformation of water-saturated sand: I. uniform undrained deformation and shear banding, Géotechnique, Vol. 46, 441–456, 1996a.
Vardoulakis, I. Deformation of water-saturated sand: II. effect of pore water flow and shear banding, Géotechnique, Vol. 46, 457–472, 1996b.
Wang, T.-F., C. David, and W. Zhu, The transition from brittle faulting to cataclastic flow in porous sandstones: Mechanical deformation, J. Geophys. Res., Vol. 102, 3009–3025, 1997.
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Rudnicki, J.W. (2000). Diffusive Instabilities in Dilating and Compacting Geomaterials. In: Chuang, T.J., Rudnicki, J.W. (eds) Multiscale Deformation and Fracture in Materials and Structures. Solid Mechanics and Its Applications, vol 84. Springer, Dordrecht. https://doi.org/10.1007/0-306-46952-9_10
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DOI: https://doi.org/10.1007/0-306-46952-9_10
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