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A plasticity model for discontinua

Chapter

Abstract

This article is concerned with the development and application of a simple continuum theory for rocks that may contain both randomly as well as preferentially oriented plane discontinuity surfaces. The theory stipulates that displacement discontinuities are independently activated on these surfaces as soon as an appropriate yield criterion is fulfilled; these displacement jumps account for the irreversible, ‘plastic’ part of the bulk deformation. In stress space, the critical conditions for the activation of discontinuous slip or opening displacements define an overall yield envelope that could be initially anisotropic, reflecting for example a weakness of certain orientations due to pre-existing joint sets. For the yield conditions studied in this paper, essentially a Coulomb-type friction law and a simple fracture opening condition, the inferred stress-strain response under typical triaxial loading conditions reveals the sensitivity of the two discontinuous deformation modes to the confining pressure. The incipient growth of a geological fold in such a material is modelled as a problem of plate bending. The slip- and opening-modes of deformation are found to be activated typically in the fold intrados and extrados, respectively. Under certain conditions, both modes will be activated simultaneously at the same locality and contribute to the total deformation. Field observations on a well exposed sandstone anticline are reported here, which support this conclusion. The present plasticity model for discontinua can clearly be explored in more detail for realistic distributions of faults and joints taken from field observations. It could also be improved in various ways in its description of the underlying deformation mechanisms. Apart from its interest as a mechanical constitutive model, it can also serve as a point of departure for studies of stress-sensitive, anisotropic permeability distributions in fractured formations.

Keywords

Rock Mass Representative Elementary Volume Yield Criterion Triaxial Test Plasticity Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Asaro, R.J. (1983). Micromechanics of Crystals and Polycrystals. Advances in Applied Mechanics, 23, 2–111.Google Scholar
  2. Batdorf, S.B. and Budiansky, B. (1949). A mathematical theory of plasticity based on the concept of slip, U.S. N.A.C.A. Technical Note 1871.Google Scholar
  3. Bott, M.H.P. (1959). The mechanics of oblique slip faulting. Geol. Mag., 96, 109–117.CrossRefGoogle Scholar
  4. Bažant, Z.P. and Oh, B.H. (1985). Mieroplane model for progressive fracture of concrete and rock. J. Eng. Mech., A.S.C.E., 111, 559–582.Google Scholar
  5. Drucker, D.C. (1951). A more fundamental approach to plastic stress-strain relations. First U.S. Nat. Congr. Appl. Mech., 487–491.Google Scholar
  6. Dunne, W.M. and Hancock, P.L. (1993). Paleostress analysis of small-scale brittle structures, In: Continental deformation, edited by P.L. Hancock, Chap. 5, pp. 101–120, Pergamon Press.Google Scholar
  7. Gaulier, J.M., Mengus, J.M., Letouzey, J., Lecomte, J.C., Sassi W., Cacas, M.C. and Petit, J.P. (1996). Caractérisation des families de diaclases formées au cours d’un phase de plissement. Cas des plis hercyniens de 1’anti-At las marocain. Internal Report, Institut Frangais du Pétrole, Rueil-Malmaison.Google Scholar
  8. Gauthier, B. and Angelier, J. (1985). Fault tectonics and deformation: a method of quantification using field data. Earth and Planetary Science Letters, 74, 137–148.CrossRefGoogle Scholar
  9. Hafner, W. (1951). Stress distributions and faulting. Geol. Soc. Am. Bull, 62, 373–398.CrossRefGoogle Scholar
  10. Horii, H. and Nemat-Nasser, S. (1983). Overall moduli of solids with microcracks: Load induced anisotropy. J. Mech. Phys. Solids, 31, 155–1–71.CrossRefGoogle Scholar
  11. Jaeger, J.C. (1960). Shear failure of anisotropic rocks, Geol. Mag.. 97, 65–72.CrossRefGoogle Scholar
  12. Kachanov, M.L. (1982). A microcrack model of rock inelasticity. Part I: frictional sliding on microcracks. Mechanics of Materials, 1, 19–27.Google Scholar
  13. Kachanov, M.L. (1982). A microcrack model of rock inelasticity. Part II: propagation of microcracks. Mechanics of Materials, 1, 29–41.Google Scholar
  14. Koiter, W.T. (1953). Stress-strain relations, uniqueness and variational theorem for elastic-plastic materials with a singular yield surface, Quarter. Appl. Math., 11, 350–354.Google Scholar
  15. Lehner, F.K. and Kachanov, M. (1995). On the stress-strain relations for cracked elastic materials in compression. Mechanics of Jointed Faulted Rock, edited by H.-P. Rossmanith, Balkema, Rotterdam.Google Scholar
  16. Leroy, Y.M. and Triantafyllidis, N. (1999). Stability analysis of incipient folding and faulting of an elasto-plastic layer on a viscous substratum. This Volume.Google Scholar
  17. Mandel, J. (1964). Les conditions de stabilité et postulat de Drucker. In: Rheology and Soil Mechanics, IUTAM Symposium Grenoble, edited by J. Kravtchenko and P.M. Sirieys, pp. 58–68.Google Scholar
  18. Mandl, G. (1987). Tectonic deformation by rotating parallel faults - the ’bookshelf’ mechanism. Tectonophysics, 141, 277–316.CrossRefGoogle Scholar
  19. Mandl, G. (1988). Mechanics of tectonic faulting. Elsevier, Amsterdam. Molnar, P. (1983). Average regional strain due to slip on numerous faults of different orientations. J. of Geophys. Res., 88/B8, 6430–6432.Google Scholar
  20. Molnar, P. (1983). Average regional strain due to slip on numerous faults of different orientations. J. of Geophys. Res., 88/B8, 6430–6432.CrossRefGoogle Scholar
  21. Nelson, R.A. (1985). Geologic analysis of naturally fractured reservoirs. Contribution in Petroleum Geology & Engineering, Gulf Publishing Company.Google Scholar
  22. Nieuwland, D.A. and Walters, J.V. (1993). Geomechanics of the South Furious field. An integrated approach towards solving complex structural geological problems, including analogue and finite-element modelling. Tectonophysics, 226, 143–166.CrossRefGoogle Scholar
  23. Oertel, O. (1965). The mechanism of faulting in clay expriments. Tectonophysics, 2, 343–393.CrossRefGoogle Scholar
  24. Odé, H.(1960). Faulting as a velocity discontinuity in plastic deformation. In: Rock Deformation, edited by D. Griggs and J. Handin, Geol. Soc. Am. Memoir 79, pp 293–321.Google Scholar
  25. Pan, J. and Rice, J.R. (1983). Rate sensitivity of plastic flow and implications for yield-surface vertices. Int. J. Solids Structures, 19, 973–987.CrossRefGoogle Scholar
  26. Petit, J.P., Auzias V., Rawnsley, K. and Rives, T. (1999). Development of joint sets in association with faults. This volume.Google Scholar
  27. Reches. Z. (1983). fault ing of rocks in three-dimensional strain-fields II. Theoretical analysis. Teclonophysics. 95. 133–156.CrossRefGoogle Scholar
  28. Rawnsley, K.D., Rives. T., Petit, J.P., Hencher. S.R., and Lumsden A.C. (1992). Joint development in perturbed stress fields near faults. J. Struct. Geol. 11. 939–951.CrossRefGoogle Scholar
  29. Rudnicki, J.W. and Rice, J.R. (1975). Conditions for the localization of the deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids. 23. 371–391.CrossRefGoogle Scholar
  30. Sanders,J.L. (1951). Plastic stress-strain relations based on linear loading functions. In: Proc. Second US Nat. Congress of Applied Mechanics, edited by P.M. Naghdi. ASMK. 455–460.Google Scholar
  31. Wallace. R.W. (1951). Geometry of shearing stress and relation to faulting. J. Geol. 59. 118–130.CrossRefGoogle Scholar
  32. Zienkiewiex, O.C. and Pande, G.N. (1977). Time-dependent multilaminate model of rocks - A numerical study of deformation and failure of rock masses. Inf. J. Num. Anal. Methods in Geomechanics. 1. 219–247.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  1. 1.Laboratoire de Mécanique des Solides, Ecole PolytechniqueU.M.R. C.N.R.S. no. 7649Palaiseau CedexFrance
  2. 2.Institut Français du PétroleRueil-MalmaisonFrance

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