pure and applied geophysics

, Volume 143, Issue 1–3, pp 483–510 | Cite as

A thermo-plastic constitutive law for brittle-plastic behavior of rocks at high temperatures

  • Tomasz Hueckel
  • Alberto Peano
  • Rita Pellegrini
Rock Friction and Shear Zone Mechanics: Laboratory Studies


Mechanical properties of rocks change under the influence of, temperature. Stress at the onset of yielding, ultimate strength, dilatancy, strain hardening and softening, and the confining pressure at brittle-ductile transition are all reduced by the increasing temperature. This study presents a framework of constitutive modeling of thermo-brittle-plastic behavior of rocks which encompasses these changes. The constitutive law is based on a thermo-plasticity theory first proposed for metals byPrager (1958). Two phenomenological mechanisms have been identified as central for the modeling: temperature dependence of the yield locus (thermal softening), and temperature dependence of the strain-hardening function (thermally enhanced ductility). Material parameters for two rocks, Carrara marble and Westerly granite, were determined on the basis of additional hypotheses. These parameters are used in numerical simulations of triaxial tests at different temperatures. The obtained stress-strain curves compare well to the experimental results. The changes with temperature in the stress at the onset of yielding are more accurately reproduced that the evolution of hardening or softening. Suggestions for possible improvements and future research directions are indicated.

Key words

Temperature strength thermo-plasticity brittle-plastic transition 


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  1. Anderson, R. N., De Long, S. E., andSchwarz, W. M. (1990),Dehydration, Astenospheric Convection and Seismicity in Subduction Zones, J. Geology88, 445–451.Google Scholar
  2. Baldi, G., Hueckel, T., Peano, A., andPellegrini, R. (1990),Developments in Modeling of Thermo-hydro-geoinechanical Behavior of Boom Clay and Clay Based Buffer Materials, Nuclear Science and Technology, Commission of European Communities, EUR 13365/1&2 EN.Google Scholar
  3. Blanpied, M. L., Lockner, D. A., andByerlee, J. D. (1991),Fault Stability Inferred from Granite Sliding Experiments at Hydrothermal Conditions, Geophys. Res. Lett.18, (4), 609–612.Google Scholar
  4. Boland, J. N., andTullis, J.,Deformation behavior of wet and dry clinopyroxenite in the brittle to ductile transition region. InMineral and Rock Deformation, v. 36 (eds, Hobbs, B. E., and Heard, H. C.) (AGU 1986), pp. 35–50.Google Scholar
  5. Byerlee, J. D. (1968),Brittle-ductile Transition in Rocks, J. Geoph. Res.73, 4741–4750.Google Scholar
  6. Byerlee, J. D. (1967),Frictional Characteristics, of Granite under High Confining Stress, J. Geophs. Res.72, 3639–3648.Google Scholar
  7. Campanella, R. G., andMitchell, J. K. (1968),Influence of Temperature Variations on Soil Behavior, ASCE J. of Soil Mech. and Found. Eng.94, (3), 709–734.Google Scholar
  8. Carter, N. L., andKirby, S. H. (1978),Transient Creep and Semi-brittle Behavior of Crystalline Rocks, Pure and Appl. Geophys.116, 807–839.Google Scholar
  9. Carter, N. L., andTsenn, M. C. (1987),Flow Properties of Continental Lithosphere, Tectonophys.136, 27–63.Google Scholar
  10. Carter, N. L., Kronenberg, A. K., Ross, J. V., andWiltschko, D. V.,Control of fluids on deformation of rocks. InDeformation Mechanisms, Rheology and Tectonics GSSP No. 54 (ed. Knipe, R. J., and Rutter, E. H.) (Academic Press, London 1990) pp. 1–13.Google Scholar
  11. Chopra, P. N., andPaterson, M. S. (1981),The Experimental Deformation of Dunite, Tectonophys.78, 453–473.Google Scholar
  12. Crouch, S. L. (1970),Experimental Determination of Volumetric Strains in Failed Rock, Int. J. Rock Mechanics Min. Sci.7, 589–603.Google Scholar
  13. Desai, C. S., andSiriwardane, H. J.,Constitutive Laws for Engineering Materials with Emphasis on Geologic Materials (Prentice-Hall, Englewood Cliffs, NJ 1984).Google Scholar
  14. Derski, W., Izbicki, R., Kisiel, I., andMroz, Z.,Rock and Soil Mechanics (Elsevier Amsterdam 1988).Google Scholar
  15. Dragon, A., andMroz, Z. (1978),A Continuum Model for Plastic-brittle Behaviour of Rock and Concrete, Int. J. Engineering Sci.17, 121–137.Google Scholar
  16. Edmond, J. M., andPaterson, M. S. (1972),Volume Changes during the Deformation of Rocks at High Pressures, Int. J. Rock Mech. and Min. Sci.9, 161–182.Google Scholar
  17. Evans, B., Fredrich, J. T., andWong, T-f. (1990),Brittle-ductile transition in rocks: Recent experimental and theoretical progress. InThe Brittle-ductile Transition in Rocks American Geophysical Union, v. 86 (The Heard Volume) (eds. A. G. Dubaet al.) (Washington 1990) pp. 1–22.Google Scholar
  18. Fischer, G. J., andPaterson, M. S. (1989),Dilatancy during Rock Deformation at High Temperatures and Pressures, J. Geoph., Res.49 (B12), 17607–17617.Google Scholar
  19. Friedman, M..,Handin, J., Higgs, N. G., andLantz, J. R. Strength and ductility of four igneous rocks at low pressures and temperatures to partial, melting, Proc. 20th Symp.Rock Mech., Austin TX, (ASCE, New York, 1979). pp. 35–50.Google Scholar
  20. Gerogiannopoulos, N. G., andBrown, E. T. (1978),The Critical State Concept Applied to Rock, Int. J. Rock Mech. Min. Sci.15, 1–10.Google Scholar
  21. Goto, K., Hamaguchi, H., andSuzuki, Z. (1985),Earthquake Generating Stresses in a Descending Slab, Tectonophys.112, 111–128.Google Scholar
  22. Griffith, A. A. The theory of rupture, Proc. 1st Int. Congr.Applied Mech. (eds. Biezeno, C. B., and Burgers, J. M.) (Tech. Boekhandel en Drukerij J. Walter Jr., Delft 1924) pp. 54–63.Google Scholar
  23. Griggs, D. T., andBlacic, J. D. (1965),Quartz: Anomalous Weakening of Synthetic Crystals, Science147, 292–295.Google Scholar
  24. Griggs, D. T., Turner, F. J., andHeard, H. C.,Deformation of rocks at 500 to 800° C. InRock Deformation, Memoir 79 (eds. Griggs, D. T. and Handin, J.) (GSA, NY 1960) pp. 39–103.Google Scholar
  25. Heuze, F. E. (1983),High Temperature Mechanical Physical and Thermal Properties of Granitic Rocks—A Review, Int. J. Rock Mech. Min. Sci.20, (1), 3–10.Google Scholar
  26. Hueckel, T. (1992),Water-mineral Interaction in Hygro-mechanics of Clays Exposed to Environmental Loads: A Mixture Approach, Canadian Geotech. J.29, 1071–1086.Google Scholar
  27. Hueckel, T., andBorsetto, M., andPeano, A. Modeling of coupled thermo-elastoplastic-hydraulic response of clays subjected to nuclear waste heat. InNumerical. Methods in Transient and Coupled Problems (eds. Lewis, R. W. et al.) (J. Wiley, Chichester, UK 1987) pp. 213–235.Google Scholar
  28. Hueckel, T., andPellegrini, R. (1991),Thermoplastic Modelling of Undrained Failure of Saturated Clay due to Heating, Soils and Foundations31 (3), 11–16.Google Scholar
  29. Hueckel, T., andPellegrini, R. (1992),Effective Stress and Water Pressure in Saturated Clays during Heating-Cooling Cycles, Canadian Geotech. J.29, 1095–1102.Google Scholar
  30. Hueckel, T., andBaldi, G. (1990),Thermoplasticity of Saturated Soils and Shales: Constitutive Equations, J. Geotech. Engineering116 (12), 1765–1777.Google Scholar
  31. Hueckel, T., andBorsetto, M. (1990),Thermoplasticity of Saturated Clays: Experimental Constitutive Study, J. Geotech. Engin.116 (12), 1778–1798.Google Scholar
  32. Hueckel, T., Peano, A., andPellegrini, R. (1994),A Constitutive Law for Thermo-plastic Behavior of Rocks: An Analogy with Clays, Surveys in Geophys.16, in print.Google Scholar
  33. Jaeger, J. C., andCook, N. G. W.,Fundamentals of Rock Mechanics, 2nd ed. (Chapman and Hall, London 1976).Google Scholar
  34. Kirby, S. H., andKronenberg, A. K. (1984),Deformation of Clinopyroxenite: Evidence for a Transition in Flow Mechanisms and Semibrittle Behavior, J. Geophys Res.8 (89), 3177–3292.Google Scholar
  35. Maier, G., andHueckel, T. (1979),Non-associated and Coupled Flow Rules of Elastoplasticity for Geotechnical Media, Int. J. Rock Mech. Min. Sci.16, (2), 77–92.Google Scholar
  36. Meade, C., andJeanloz, R. (1990),Experimental Studies of Deep-focus Earthquakes: Implications for the Recycling of Water into the Mantle, EOS, 1587.Google Scholar
  37. Michelis, P. (1987),True Triaxial Cyclic Behavior of Concrete and Rock in Compression, Int. J. Plasticity3, 249–270.Google Scholar
  38. Mroz, Z. Current problems and new directions in mechanics of geomaterials. InMechanics of Geomaterials: Rocks, Concretes, Soils (ed. Bazant, Z. P.) (Wiley and Sons, Chichester 1985) pp. 539–557.Google Scholar
  39. Murrell, S. A. F., andIsmail, I. A. H. (1976),The Effect of Decomposition of Hydrous Minerals on the Mechanical Properties of Rocks at High Pressures and Temperatures, Tectonophys.31, 207–258.Google Scholar
  40. Olgaard, D. L., Ko, S.-c., andWong, T-f. (1993),Weakening and embrittlement caused by excess pore pressure in dehydrating gypsum, Proc. Int. Workshop onThermomechanics of Clays, Bergamo, Italy.Google Scholar
  41. Paterson, M. S. The interaction of water with quartz and its influence in dislocation flow—an overview. InRheology of Solids and of the Earth (eds. Karato, S-I., and Toriumi, M.) ch. 7 (Oxford Science Press 1990) pp. 107–142.Google Scholar
  42. Prager, W. (1958),Non-isothermal Plastic Deformation, Bol. Koninke Nedrl. Akad. Wet.8, (61/3), 176–182.Google Scholar
  43. Raleigh, C. B., andPaterson, M. S. (1965),Experimental Deformation of Serpentinite and its Tectonic Implications, J. Geoph. Res.70, 3965–1985.Google Scholar
  44. Rudnicki, J. W. (1983),Physical Models of Earthquake Instability and Precursory Processes, Pure Appl. Geophys.126, 531–554.Google Scholar
  45. Rudnicki, J. W., andRice, J. C. (1975),Condition for the Localization of Deformation in Pressuresensitive Dilatant Materials, J. Mech. Phys. Solids23, 371–394.Google Scholar
  46. Rutter, E. H., (1974),The Influence of Temperature, Strain Rate and Interstitial Water in the Experimental Deformation of Calcite Rocks, Tectonophys.22, 311–334.Google Scholar
  47. Rutter, E. H., andBrodie, K. H. (1988),Experimental “syntectonic” Dehydration of Serpentinite under Conditions of Controlled Pore Water Pressure, J. Geoph. Res.93, (85), 4907–4932.Google Scholar
  48. Rutter, E. H., andBrodie, K. H. (1992),Rheology of the lower crust, in Continental Lower Crust. InDevelopments in Geotectonics (eds. Fountain, D. M., Arculus, R., and Kay, R. W.)23, (6), 201–257.Google Scholar
  49. Schofield, A., andWroth, P.,Critical State Soil Mechanics (Cambridge University Press, Cambridge 1968).Google Scholar
  50. Scholz, C. H. The Mechanics of Earthquakes and Faulting (Cambridge University Press, Cambridge 1990).Google Scholar
  51. Sleep, N. H. (1975),Stress and Flow beneath Island Arc, Geoph. J. R. Astron. Soc.42, 827–857.Google Scholar
  52. Stesky, R. M., Brace, W. F., Riley, D. K., andRobin, P.-Y.F. (1974),Friction in Faulted Rock at High Temperature and Pressure, Tectonophs.23, 177–203.Google Scholar
  53. Tullis, J., andYund, R. Y. (1977),Experimental Deformation of Dry Westerly Granite, J. Geophs. Res.82, (36), 5705–5718.Google Scholar
  54. Van der Molen, I., andPaterson, M. S. (1979),Experimental Deformation of Partially Melted Granite, Contr. Mineral. Petrol.70, 399–418.Google Scholar
  55. Wawersik, W. R., andBrace, W. F. (1971),Post-failure Behavior of a Granite and Diabase, Rock Mech.3 (6) 85.Google Scholar
  56. Wong, T-f. (1982),Effects of Temperature and Pressure on Failure and Post-failure Behavior of Westerly Granite, Mech. of Mater.1, 3–17.Google Scholar
  57. Wood, D. M.,Soil Behaviour and Critical State Soil Mechanics (Cambridge University Press, Cambridge 1990).Google Scholar
  58. Zoback, M. D., andByerlee, J. D. (1975),The Effect of Cyclic Differential Stress on Dilatancy in Westerly Granite, J. Geophys. Res.80 (11), 1526–1530.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Tomasz Hueckel
    • 1
  • Alberto Peano
    • 2
  • Rita Pellegrini
    • 2
  1. 1.Duke UniversityDurhamU.S.A.
  2. 2.ISMESBergamoItaly

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