Thermochemomechanical material model for shotcrete

  • Christian Hellmich
  • Roman Lackner
  • Herbert Mang


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.


Material Model Autogeneous Shrinkage Chemical Shrinkage Principal Stress Space Viscous Strain 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [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 FrenchGoogle Scholar
  2. [2]
    Acker P., Ulm F.-J. (2001) Creep and shrinkage of concrete: physical originsand practical measurements. Nuclear Engineering and Design, 203:148–158CrossRefGoogle Scholar
  3. [3]
    Bazant Z.P., (ed) (1988) Mathematical modeling of creep and shrinkage in concrete. Wiley, ChichesterGoogle Scholar
  4. [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):1188–1194Google Scholar
  5. [5]
    A. Boumiz, C. Vernet, and F. Cohen Tenoudij (1996) Mechanical properties of cement pastes and mortars at early age. Advanced Cement Based Materials, 3:94–106Google Scholar
  6. [6]
    J. Byfors (1980) Plain concrete at early ages. Technical report, Swedish Cement and Concrete Research Institute, Stockholm, SwedenGoogle Scholar
  7. [7]
    P. Catharin (1978) Hydratationswärme und Festigkeitsentwicklung [Hydration heat and strength evolution]. Technical Report 31, Forschungsinstitut des Vereins der österreichischen Zementfabrikanten, Vienna, Austria, in GermanGoogle Scholar
  8. [8]
    W.F. Chen (1982) Plasticity in reinforced concrete. McGraw-Hill, London,EnglandGoogle Scholar
  9. [9]
    O. Coussy (1995) Mechanics of porous continua. Wiley, ChichesterMATHGoogle Scholar
  10. [10]
    Guideline (1997) Richtlinie für Spritzbeton [Guideline for shotcrete]. Österreichischer Betonverein, Vienna, Austria, in GermanGoogle Scholar
  11. [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, AustriaGoogle Scholar
  12. [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, DordrechtGoogle Scholar
  13. [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 GermanGoogle Scholar
  14. [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):238–244MATHCrossRefGoogle Scholar
  15. [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):692–701CrossRefGoogle Scholar
  16. [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 GermanGoogle Scholar
  17. [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, USAGoogle Scholar
  18. [18]
    W.T. Koiter (1960) General theorems for elastic-plastic solids, volume I, Chap- ter IV, pages 167-218. North-Holland Publishing Company, AmsterdamGoogle Scholar
  19. [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):2357–2388MATHCrossRefGoogle Scholar
  20. [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 publicationGoogle Scholar
  21. [21]
    R. Lackner and H.A. Mang (2003) Cracking in shotcrete tunnel shells. Engi- neering Fracture Mechanics, 70(7-8): 1047–1068CrossRefGoogle Scholar
  22. [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, BerlinCrossRefGoogle Scholar
  23. [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, 39:3123–3143MATHCrossRefGoogle Scholar
  24. [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, 8:591–600CrossRefGoogle Scholar
  25. [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 GermanGoogle Scholar
  26. [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 GermanGoogle Scholar
  27. [27]
    P. Schubert (1988) Beitrag zum rheologischen Verhalten von Spritzbeton [Contribution to the rheological behavior of shotcrete]. Felsbau, 6:150–153, in Ger- manGoogle Scholar
  28. [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):284–291CrossRefGoogle Scholar
  29. [29]
    J.C. Simo and T.J.R. Hughes (1998) Computational inelasticity. Springer, Berlin, GermanyMATHGoogle Scholar
  30. [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 KongGoogle Scholar
  31. [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 GermanGoogle Scholar
  32. [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 FrenchGoogle Scholar
  33. [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 FrenchGoogle Scholar
  34. [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 FrenchGoogle Scholar
  35. [35]
    F.-J. Ulm and O. Coussy (1995) Modeling of thermochemomechanical couplings of concrete at early ages. Journal of Engineering Mechanics (ASCE), 121(7):785–794CrossRefGoogle Scholar
  36. [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– 1132CrossRefGoogle Scholar
  37. [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. [38]
    F.H. Wittmann (1982) Creep and shrinkage mechanisms, Chapter 6, pages 129-161. Wiley, ChichesterCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • Christian Hellmich
    • 1
  • Roman Lackner
    • 1
  • Herbert Mang
    • 1
  1. 1.Institute for Strength of MaterialsVienna University of TechnologyAustria

Personalised recommendations