Skip to main content

Thermochemomechanical material model for shotcrete

  • Chapter

Abstract

Employing a thermodynamic framework, thermochemomechanical couplings for shotcrete are treated in this chapter. A material model based on multisurface thermochemoplasticity is presented. It accounts for hydration kinetics, chemomechanical couplings related to strength growth, stiffness properties, and to autogeneous shrinkage in early-age shotcrete. Creep is modeled by means of two mechanisms: stress-induced water movement in the capillary pores of shotcrete, and a relaxation mechanism in the nanopores of the cement gel. The underlying material functions are intrinsic, i.e., independent of field and boundary conditions. They are determined from standard material tests. As for the numerical treatment of the constitutive equations of the material model, an extended form of the return map algorithm is presented. Microcracking is considered by means of a Drucker-Prager failure surface for the compressive load regime and by means of Rankine surfaces for tensile brittle failure.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Acker P. (1988) Comportement mécanique du béton: apports de l’approche physico-chimique [Mechanical behaviour of concrete: a physico-chemical approach]. Technical Report Res. Rep. LCPC 152, Laboratoires des Ponts et Chaussées, Paris, France, in French

    Google Scholar 

  2. Acker P., Ulm F.-J. (2001) Creep and shrinkage of concrete: physical originsand practical measurements. Nuclear Engineering and Design, 203:148–158

    Article  Google Scholar 

  3. Bazant Z.P., (ed) (1988) Mathematical modeling of creep and shrinkage in concrete. Wiley, Chichester

    Google Scholar 

  4. Z.P. Bažant, A.B. Hauggard, S. Baweja, and F.-J. Ulm (1997) Microprestress solidification theory for concrete creep, part I: Aging and drying effects. Jour- nal of Engineering Mechanics, ASCE, 123(11):1188–1194

    Google Scholar 

  5. A. Boumiz, C. Vernet, and F. Cohen Tenoudij (1996) Mechanical properties of cement pastes and mortars at early age. Advanced Cement Based Materials, 3:94–106

    Google Scholar 

  6. J. Byfors (1980) Plain concrete at early ages. Technical report, Swedish Cement and Concrete Research Institute, Stockholm, Sweden

    Google Scholar 

  7. P. Catharin (1978) Hydratationswärme und Festigkeitsentwicklung [Hydration heat and strength evolution]. Technical Report 31, Forschungsinstitut des Vereins der österreichischen Zementfabrikanten, Vienna, Austria, in German

    Google Scholar 

  8. W.F. Chen (1982) Plasticity in reinforced concrete. McGraw-Hill, London,England

    Google Scholar 

  9. O. Coussy (1995) Mechanics of porous continua. Wiley, Chichester

    MATH  Google Scholar 

  10. Guideline (1997) Richtlinie für Spritzbeton [Guideline for shotcrete]. Österreichischer Betonverein, Vienna, Austria, in German

    Google Scholar 

  11. Ch. Hellmich (1999) Shotcrete as part of the New Austrian Tunneling Method: from thermochemomechanical material modeling to structural analysis and safety assessment of tunnels. Ph.D. thesis, Vienna University of Technology, Vienna, Austria

    Google Scholar 

  12. Ch. Hellmich, M. Lechner, R. Lackner, J. Macht, and H.A. Mang (2001) Creep in shotcrete tunnel shells. In S. Murakami and N. Ohno, editors, Creep in Struc- tures 2000 - Proceedings of the 5th IUTAM Symposium on Creep in Structures, pages 217–229, Nagoya, Japan. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  13. Ch. Hellmich, H.A. Mang, E. Schön, and R. Friedle (2003) Materialmodellierung von Spritzbeton - vom Experiment zum konstitutiven Gesetz [Material modeling of shotcrete - from the experiment to the constitutive law]. In Th. Varga, editor, Proceedings of the conference held at the 1998 general assem- bly of the Austrian Society for Material Testing, Vienna, Austria, in print, in German

    Google Scholar 

  14. Ch. Hellmich, F.-J. Ulm, and H. A. Mang (1999) Consistent linearisation in finite element analysis of coupled chemo-thermal problems with exo- or endothermal reactions. Computational Mechanics, 24(4):238–244

    Article  MATH  Google Scholar 

  15. Ch. Hellmich, F.-J. Ulm, and H. A. Mang (1999) Multisurface chemoplasticity I: Material model for shotcrete. Journal of Engineering Mechanics (ASCE), 125(6):692–701

    Article  Google Scholar 

  16. H.G. Huber (1991) Untersuchungen zum Verformungsverhalten von jungem Spritzbeton im Tunnelbau [Investigation of the deformation behavior of young shotcrete in tunneling]. M.Sc. thesis, University of Innsbruck, Innsbruck, Aus- tria, in German

    Google Scholar 

  17. W. Karush (1939) Minima of functions of several variables with inequalities as side constraints. M.Sc. thesis, Department of Mathematics, University of Chicago, Chicago, USA

    Google Scholar 

  18. W.T. Koiter (1960) General theorems for elastic-plastic solids, volume I, Chap- ter IV, pages 167-218. North-Holland Publishing Company, Amsterdam

    Google Scholar 

  19. R. Lackner, Ch. Hellmich, and H.A. Mang (2002) Constitutive modeling of cementitious materials in the framework of chemoplasticity. International Jour- nal for Numerical Methods in Engineering, 53(10):2357–2388

    Article  MATH  Google Scholar 

  20. R. Lackner and H.A. Mang (2003) Chemoplastic material model for the simulation of early-age cracking: from the constitutive law to numerical analyses of massive concrete structures. Cement and Concrete Composites, tentatively accepted for publication

    Google Scholar 

  21. R. Lackner and H.A. Mang (2003) Cracking in shotcrete tunnel shells. Engi- neering Fracture Mechanics, 70(7-8): 1047–1068

    Article  Google Scholar 

  22. M. Lechner, Ch. Hellmich, and H.A. Mang (2001) Short-term creep of shotcrete- thermochemoplastic material modeling and nonlinear analysis of a laboratory test and of a NATM excavation by the finite element method. In P. A. Vermeer, S. Diebels, W. Ehlers, H.J. Herrmann, S. Luding, and E. Ramm, editors, Con- tinuous and discontinuous modeling of cohesive-frictional materials, Lecture Notes in Physics, 568:47–62, Springer, Berlin

    Chapter  Google Scholar 

  23. G. Meschke (1996) Consideration of aging of shotcrete in the context of a 3D viscoplastic material model. International Journal for Numerical Methods in Engineering, 39:3123–3143

    Article  MATH  Google Scholar 

  24. S. Mindess, J.F. Young, and F.-J. Lawrence (1978) Creep and drying shrinkage of calcium silicate pastes. I: specimen preparation and mechanical properties. Cement and Concrete Research, 8:591–600

    Article  Google Scholar 

  25. R. Rokahr and K.H. Lux (1987) Einfluß des rheologischen Verhaltens des Spritzbetons auf den Ausbauwiderstand [Influence of the rheological behavior of shotcrete on the lining resistance]. Felsbau, 5:11–18, in German

    Google Scholar 

  26. W. Ruetz (1966) Das Kriechen des Zementsteins im Beton und seine Beeinflussung durch gleichzeitiges Schwinden [Creep of cement in concrete as influenced by simultaneous shrinkage]. Deutscher Ausschuß für Stahlbeton, Heft 183, in German

    Google Scholar 

  27. P. Schubert (1988) Beitrag zum rheologischen Verhalten von Spritzbeton [Contribution to the rheological behavior of shotcrete]. Felsbau, 6:150–153, in Ger- man

    Google Scholar 

  28. J. Sercombe, Ch. Hellmich, F.-J. Ulm, and H. A. Mang (2000) Modeling of early-age creep of shotcrete. I: model and model parameters. Journal of Engi- neering Mechanics (ASCE), 126(3):284–291

    Article  Google Scholar 

  29. J.C. Simo and T.J.R. Hughes (1998) Computational inelasticity. Springer, Berlin, Germany

    MATH  Google Scholar 

  30. G. Swoboda, A. Moussa, and N. Hafez (1994) Two and three dimensional mod- eling of layered shotcrete lining. In P.K.K. Lee, L.G. Tham, and Y.K. Cheung, editors, Proceedings of the International Conference on Computational Meth- ods in Structural and Geotechnical Engineering, pages 1077–1084, Hong Kong. China Translation and Printing Services, Hong Kong

    Google Scholar 

  31. M. Testor (1995) Trockenspritzbeton mit neuen Bindemitteln - Temperatureinfluss, Staubeinfluss und Rückprallreduktion [Dry-mix shotcrete with new cements - influence of temperature and of dust, reduction of rebound]. M. Sc. thesis, University of Innsbruck, Innsbruck, Austria, in German

    Google Scholar 

  32. P. Torrenti (1992) La resistance du béton au très jeune age [Strength of concrete at very early age]. Bulletin liaison des Laboratoires des Ponts et Chaussées, 179:31–41, in French

    Google Scholar 

  33. F-J. Ulm (1998) Couplages thermochémomécaniques dans les bétons : un premier bilan. [Thermochemomechanical couplings in concretes : a first review]. Technical report, Laboratoires des Ponts et Chaussées, Paris, France, in French

    Google Scholar 

  34. F.-J. Ulm and P. Acker (1998) Le point sur le fluage et la recouvrance des bétons [Concrete creep and recovery: a review]. Special issue of the ”Bulletin des Laboratoires des Ponts et Chaussées”, XX:73–82, in French

    Google Scholar 

  35. F.-J. Ulm and O. Coussy (1995) Modeling of thermochemomechanical couplings of concrete at early ages. Journal of Engineering Mechanics (ASCE), 121(7):785–794

    Article  Google Scholar 

  36. F.-J. Ulm and O. Coussy (1996) Strength growth as chemo-plastic hardening in early age concrete. Journal of Engineering Mechanics (ASCE), 122(12): 1123– 1132

    Article  Google Scholar 

  37. F.-J. Ulm, O. Coussy, and Ch. Hellmich (1998) Chemopla\sticity: a review of evidence. In R. de Borst, N. Bicanić, H. Mang, and G. Meschke, editors, Computational Modeling of Concrete Structures, Proceedings of the EURO-C 1998 Conference, pages 421–440, Bad Gastein, Austria. Balkema, Rotterdam.

    Google Scholar 

  38. F.H. Wittmann (1982) Creep and shrinkage mechanisms, Chapter 6, pages 129-161. Wiley, Chichester

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Wien

About this chapter

Cite this chapter

Hellmich, C., Lackner, R., Mang, H. (2003). Thermochemomechanical material model for shotcrete. In: Beer, G. (eds) Numerical Simulation in Tunnelling. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6099-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-6099-2_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-7221-6

  • Online ISBN: 978-3-7091-6099-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics