Skip to main content
Log in

A unified thermoplastic/viscoplastic constitutive model for geomaterials

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

Research on the effect of temperature changes on the behaviour of geomaterials has become increasingly important in recent years. This growing interest is partially due to the recent development of high-level nuclear waste disposals. Because of the complex influence of temperature in these areas, it is necessary to understand the effects of temperature on rock-like materials and use the appropriate constitutive equations to numerically model these phenomena. In this paper, a thermoplastic/viscoplastic constitutive model is developed for this purpose. The model includes thermal softening, the evolution of the yield functions with temperature, and the effects of temperature on the time-dependent behaviour. The model performance is demonstrated by some simple test cases on Tournemire and Bure clayey rocks including triaxial compression tests and creep tests under constant temperatures. The numerical results are discussed using experimental data, which demonstrate that the model can reproduce the overall behaviour of this type of materials under deviatoric loads and non-isothermal conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. Alejano LR, Alonso E (2005) Considerations of the dilatancy angle in rocks and rock masses. Int J Rock Mech Min Sci 42(4):481–507

    Article  Google Scholar 

  2. Arzúa J, Alejano LR (2013) Dilation in granite during servo-controlled triaxial strength tests. Int J Rock Mech Min Sci 61:43–56

    Google Scholar 

  3. Baldi G, Hueckel T, Pellegrini R (1988) Thermal volume changes on the mineral-water system in low porosity clay soils. Can Geotech J 25:807–825

    Article  Google Scholar 

  4. Baldi G, Hueckel T, Peano A, Pellegrini R (1990) Developments in modelling of thermo-hydro-geomechanical behavior of Boom clay and clay based buffer materials. Vol 1 & 2, a report EUR 13365/1&2 EN, Commission of European Communities, Nuclear Science and Technology

  5. Barton N (1976) The shear strength of rock joints. Int J Rock Mech Min & Geomech Abstr 13:255–279

    Article  Google Scholar 

  6. Bergues J, Nguyen MD, Hoteit N (1998) Time dependent behavior of hard marls. In: Proceedings of 2nd international symposium on hard soils, soft rocks, Naples

  7. Biarez J, Hicher PY (1994) Elementary mechanics of soil behaviour. Balkema, Amsterdam

    Google Scholar 

  8. Bigoni D, Piccolroaz A (2004) Yield criteria for quasibrittle and frictional materials. Int J Solids Struct 41:2855–2878

    Article  MathSciNet  MATH  Google Scholar 

  9. Biot MA (1973) Non linear and semilinear rheology of porous solids. J Geophys Res 78(23):4924–4937

    Article  Google Scholar 

  10. Bolton MD (1986) The strength and dilatancy of sands. Géotechnique 36:65–78

    Article  Google Scholar 

  11. Burger A, Recordon E, Bovet D, Cotton L, Saugy B (1985) Thermique des nappes souterraines. Presse Polytechniques Universitaires Romandes, Lausanne

    Google Scholar 

  12. Byerlee JD (1968) Brittle–ductile transition in rocks. J Geophys Res 73(14):4741–4750

    Article  Google Scholar 

  13. Cai M, Kaiser PK, Tasaka Y, Maejima T, Morioka H, Minami M (2004) Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. Int J Rock Mech Min Sci 41:833–847

    Article  Google Scholar 

  14. Cekerevac C, Laloui L (2004) Experimental study on the thermal effects on the mechanical behaviour of a clay. Int J Numer Anal Methods Geomech 28(3):209–228

    Article  Google Scholar 

  15. Chandler NA (2013) Quantifying long-term strength and rock damage properties from plots of shear strain versus volume strain. Int J Rock Mech Min Sci 59:105–110

    Google Scholar 

  16. Chen XT, Davy CA, Skoczylas F, Shao JF (2009) Effects of heat-treatment and hydrostatic loading upon the poro-elastic properties of a mortar. Cem Concr Res 39:195–205

    Article  Google Scholar 

  17. Code\_Aster. http://www.code-aster.org

  18. Coussy O (2004) Poromechanics. Wiley, London

    MATH  Google Scholar 

  19. Cristescu ND, Hunsche U (1998) Time effects in rock mechanics. Wiley, Londone

    Google Scholar 

  20. Darabi MK, Abu Al-Rub RK, Masad EA, Little DN (2012) Thermodynamic-based model for coupling temperature-dependent viscoelastic, viscoplastic, and viscodamage constitutive behavior of asphalt mixtures. Int J Numer Anal Meth Geomech 36:817–854

    Article  Google Scholar 

  21. Delage P, Cui YJ, Tang M (2010) Clays in radioactive waste disposal. J Rock Mech Geotech Eng 2(2):111–123

    Article  Google Scholar 

  22. Diederichs MS, Martin CD (2010) Measurement of spalling parameters from laboratory testing. European rock mechanics symposium EUROCK, Rock Mechanics in Civil and Environmental Engineering, pp 323–326

  23. Dizier A (2011) Caractérisation des effets de température dans la zone endommagée autour de tunnels de stockage de déchets nucléaires dans des roches argileuses. Doctoral thesis, Université de Liège

  24. Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Q Appl Math 10(2):157–165

    MathSciNet  MATH  Google Scholar 

  25. Dupray F, Laloui L, Kazangda A (2014) Numerical analysis of seasonal heat storage in an energy pile foundation. Comput Geotech 55:67–77

    Article  Google Scholar 

  26. Dwivedi RD, Goel RK, Pasad VVR, Sinha A (2008) Thermo-mechanical properties of Indian and other granites. Int J Rock Mech Min Sci 45:303–315

    Article  Google Scholar 

  27. Eberhardt E (2012) The Hoek–Brown failure criterion. Rock Mech Rock Eng 45:981–988

    Article  Google Scholar 

  28. Elamrani K (1992) Contribution à la validation du modèle CJS pour les matériaux granulaires. Doctoral thesis, École Centrale de Lyon

  29. Evans B, Fredrich JT, Wong T-F (2013) The brittle–ductile transition in rocks: recent experimental and theoretical progress. In: Duba AG, Durham WB, Handin JW, Wang HF (eds) The brittle–ductile transition in rocks, vol 86. American Geophysical Union, pp 1–20. doi:10.1029/GM056p0001

  30. Fisher GJ, Paterson MS (1989) Dilatancy during deformation at high temperatures and pressures. J Geophys Res 94(17):607–617

    Google Scholar 

  31. François B (2008) Thermo-plasticity of soils at various saturation state: application to nuclear waste disposal. Doctoral thesis, École Polytechnique Fédérale de Lausanne

  32. François B, Laloui L, Laurent C (2009) Thermo-hydro-mechanical simulation of ATLAS in situ large scale test in Boom clay. Comput Geotech 36:626–640

    Article  Google Scholar 

  33. Gasc-Barbier M, Chanchole S, Bérest P (2004) Creep behavior of Bure clayey rock. Appl Clay Sci 26:449–458

    Article  Google Scholar 

  34. Gens A, Olivella S (2001) Clay barrier in radioactive waste disposal. Revue Française de Génie Civil 5(6):845–856

    Article  Google Scholar 

  35. Grgic D (2014) Constitutive modelling of the elastic-plastic, viscoplastic and damage behaviour of hard porous rocks within the unified theory of inelastic flow. Acta Geotech. doi:10.1007/s11440-014-0356-6

    Google Scholar 

  36. Heuze FE (1983) High-temperature mechanical, physical and thermal properties of granitic rocks—a review. Int J Rock Mech Min Sci & Geomech Abstr 20:3–10

    Article  Google Scholar 

  37. Hicher PY (1974) Étude des propriétés mécaniques des argiles à l’aide d’essais triaxiaux, influence de la vitesse et de la température. Report of the soil mechanics laboratory, École Centrale de Paris, Paris

    Google Scholar 

  38. Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Eng Div ASCE 106(GT9):1013–1035

    Google Scholar 

  39. Hoek E, Carranza-Torres C, Corkum B (2002) Hoek–Brown failure criterion—2002 edition. In: Proceedings of NARSM-TAC conference, Toronto 1:267–273

  40. Homand-Étienne F (1985) Comportement mécanique des roches en fonction de la température. Doctoral thesis, Institut National Polytechnique de Lorraine

  41. Homand-Étienne F, Houpert R (1989) Thermally induced microcracking in granites: characterization and analysis. Int J Rock Mech Min Sci & Geomech Abstr 26(2):125–134

    Article  Google Scholar 

  42. Hueckel T, Peano A, Pellegrini R (1994) A constitutive law for thermoplastic behaviour of rocks: an analogy with clays. Surv Geophys 15:643–671

    Article  Google Scholar 

  43. Hueckel T, Baldi G (1990) Thermoplasticity of saturated clays: experimental constitutive study. J Geotech Eng-ASCE 116(12):1778–1796

    Article  Google Scholar 

  44. Hueckel T, Borsetto M (1990) Thermoplasticity of saturated soils and shales: constitutive equations. J Geotech Eng 116(12):1765–1777

    Article  Google Scholar 

  45. Hueckel T, Peano A (1987) Some geotechnical aspects of radioactive waste isolation in continental clays. Comput Geotech 3(2,3):157–182

    Article  Google Scholar 

  46. Ibsen LB, PV Lade (1999) Effects of nonuniform stresses and strains on measured characteristic states. In: Proceedings of 2nd international symposium on pre-failure deformation characteristics of geomaterials, IS Torino 99, 26–29 Sept, 897:904

  47. Jia Y, Bian HB, Duveau G, Su K, Shao JF (2009) Numerical modelling of in situ behaviour of the Callovo–Oxfordian argillite subjected to the thermal loading. Eng Geol 109:262–272

    Article  Google Scholar 

  48. Jobmann M, Polster M (2007) The response of Opalinus clay due to heating: a combined analysis of in situ measurements, laboratory investigations and numerical calculations. Phys Chem Earth 32:929–936

    Article  Google Scholar 

  49. Kanatani KI (1982) Mechanical foundation of the plastic deformation of granular materials. IUTAM conference on deformation and failure of granular materials, Delft, 31 Aug–3 Sept

  50. Kanatani KI (1983) Macroscopic and microscopic descriptions of the mechanics of granular materials. Advances in the mechanics and flow of granular materials, M. Shahinpoor, Tran Tech Publ, vol 1

  51. Kleine A (2007) Modélisation numérique du comportement des ouvrages souterrains par une approche viscoplastique. Doctoral thesis, Institut National Polytechnique de Lorraine

  52. Koyama T, Chijimatsu M, Shimizu H, Nakama S, Fujita T, Kobayashi A, Ohnishi Y (2013) Numerical modeling for the coupled thermo-mechanical processes and spalling phenomena in Äspö pillar stability experiment (APSE). J Mech Geotech Eng 5:58–72

    Article  Google Scholar 

  53. Laigle F (2003) A new viscoplastic model for rocks: application to the mine-by-test of AECL-URL. Flac and numerical modelling in geomechanics. Balkema, Rotterdam

    Google Scholar 

  54. Laloui L, Nuth M, Vulliet L (2006) Experimental and numerical investigations of the behaviour of a heat exchanged pile. Int J Numer Anal Meth Geomech 30:763–781

    Article  Google Scholar 

  55. Laloui L, Cekerevac C (2003) Thermo-plasticity of clays: an isotropic yield mechanism. Comput Geotech 30(8):649–660

    Article  Google Scholar 

  56. Laloui L, Cekerevac C (2008) Numerical simulation of the non-isothermal mechanical behaviour of soils. Comput Geotech 35:729–745

    Article  MATH  Google Scholar 

  57. Laloui L, Modaressi H (2002) Modelling of the thermo-hydro-plastic behaviour of clays. In: Hoteit N (ed) Hydromechanical and thermohydromechanical behaviour of deep argillaceous rock. Balkema, Amsterdam, pp 161–170

    Google Scholar 

  58. Lion M, Skoczylas F, Ledésert B (2005) Effects of heating on the hydraulic and poroelastic properties of Bourgogne limestone. Int J Rock Mech Min Sci 42:508–520

    Article  Google Scholar 

  59. Lubliner J (2005) Plasticity theory. Revised edition (PDF)

  60. Luong MP (1980) Phénomènes cycliques dans les sols pulvérulents. Revue Française de Génie Civil, Num 10

  61. Maleki M, Dubujet P, Cambou B (2000) Modélisation hiérarchisée du comportement des sols. Revue Française de Génie Civil 4(7–8):895–928

    Article  Google Scholar 

  62. Masri M (2010) Étude expérimentale et modélisation numérique du comportement thermomécanique à haute température de l’argilite de Tournemire. Doctoral thesis, Université Lille 1 des sciences et technologies

  63. Mitchell JK, McMillan JC, Green SL, Sisson RC (1982) Field testing of cable backfill systems. In: Boogs SA et al (eds) Underground cable backfill. Pergamon Press, New York, pp 19–33

    Chapter  Google Scholar 

  64. Modaressi H, Laloui L (1997) A thermo-viscoplastic constitutive model for clays. Int J Numer Anal Meth Geomech 21:313–335

    Article  MATH  Google Scholar 

  65. Pan P, Feng X (2013) Numerical study on coupled thermo-mechanical processes in Äspö pillar stability experiment. J Mech Geotech Eng 2:136–144

    Article  Google Scholar 

  66. Perzyna P (1971) Thermodynamic theory of viscoplasticity. Academic Press, New-York

    Book  Google Scholar 

  67. Picard JM (1994) Écrouissage thermique des argiles saturées: application au stockage des déchets radioactifs. Doctoral thesis, École Nationale des Ponts et Chaussées

  68. Plassart R (2013) Hydromechanical modeling of an excavation in an underground research laboratory with an elastoviscoplastic behaviour law and regularization by second gradient of dilation. Int J Rock Mech Min Sci 58:23–33

    Google Scholar 

  69. Prager W (1958) Non-isothermal plastic deformation. Bol Koninkl Nedrl Akad Wet 8(61/3):176–182

    MATH  Google Scholar 

  70. Schofield AN, Wroth CP (1968) Critical state soil mechanics. McGraw-Hill, London

    Google Scholar 

  71. Sultan N, Delage P, Cui YJ (2002) Temperature effects on the volume changes behaviour of Boom clay. Eng Geol 64:135–145

    Article  Google Scholar 

  72. Terzaghi K (1943) Theoretical soil mechanics. Wiley, New York

    Book  Google Scholar 

  73. Tsang CF, Barnichon JD, Birkholzer J, Li XL, Liu HH, Sillen X (2012) Coupled thermo-hydro-mechanical processes in the near field of high-level radioactive waste repository in clay formations. Int J Rock Mech Min Sci 49:31–44

    Article  Google Scholar 

  74. Vermeer PA (1998) Non-associated plasticity for soils, concrete and rock. In: Herrmann HJ, Hovi J-P, Luding S (eds) Physics of dry granular media, NATO ASI series, vol 350. Springer, Netherlands, pp 163–196. doi:10.1007/978-94-017-2653-5_10

  75. Wilmański K (2005) Continuum theories of mixtures—lecture notes

  76. Wong TF (1982) Effects of temperature and pressure on failure and post-failure behavior of Westerly granite. Mech Mater 1:3–17

    Article  Google Scholar 

  77. Zhang CL, Rothfuchs T, Su K, Hoteit N (2007) Experimental study of the thermo-hydro-mechanical behaviour of indurated clays. Phys Chem Earth 32:957–965

    Article  Google Scholar 

  78. Zhao XG, Cai M (2010) A mobilized dilation angle model for rocks. Int J Rock Mech Min Sci 47(3):368–384

    Article  MathSciNet  Google Scholar 

  79. Zhou H, Hu D, Zhang F, Shao JF (2011) A thermoplastic/viscoplastic damage model for geomaterials. Acta Mech Solida Sin 24:195–208

    Article  Google Scholar 

  80. Zhu C, Arson C (2014) A thermo-mechanical damage model for rock stiffness during anisotropic crack opening and closure. Acta Geotech 9:847–867

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Raude.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raude, S., Laigle, F., Giot, R. et al. A unified thermoplastic/viscoplastic constitutive model for geomaterials. Acta Geotech. 11, 849–869 (2016). https://doi.org/10.1007/s11440-015-0396-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-015-0396-6

Keywords

Navigation