Mechanics of Time-Dependent Materials

, Volume 17, Issue 3, pp 481–499 | Cite as

Relevance of a mesoscopic modeling for the coupling between creep and damage in concrete

  • J. Saliba
  • F. Grondin
  • M. Matallah
  • A. Loukili
  • H. Boussa


In its service-life concrete is loaded and delayed strains appear due to creep phenomenon. Some theories suggest that micro-cracks nucleate and grow when concrete is submitted to a high sustained loading, thereby contributing to the weakening of concrete. Thus, it is important to understand the interaction between the viscoelastic deformation and damage in order to design reliable civil engineering structures. Several creep-damage theoretical models have been proposed in the literature. However, most of these models are based on empirical relations applied at the macroscopic scale. Coupling between creep and damage is mostly realized by adding some parameters to take into account the microstructure effects. In the authors’ opinion, the microstructure effects can be modeled by taking into account the effective interactions between the concrete matrix and the inclusions. In this paper, a viscoelastic model is combined with an isotropic damage model. The material volume is modeled by a Digital Concrete Model which takes into account the “real” aggregate size distribution of concrete. The results show that stresses are induced by strain incompatibilities between the matrix and aggregates at mesoscale under creep and lead to cracking.


Tensile creep Mesoscopic model Damage Concrete 



The experimental part of this study has been performed in the project MEFISTO which is supported by the French National Research Agency (ANR—Agence Nationale pour la Recherche) in the program “Villes Durables” (Sustainable Cities) under grant number VD08_323065. And the modeling part of this study is supported by the Scientific and Technical Centre for Building (CSTB).


  1. Altoubat, S.A., Lange, D.A.: A new look at tensile creep of fiber reinforced concrete. In: Banthia, N. (ed.) ACI Special Publication on Fiber Reinforced Concrete (2003) Google Scholar
  2. Barpi, F., Valente, S.: A fractional order rate approach for modeling concrete structures subjected to creep and fracture. Int. J. Solids Struct. 41, 2607–2621 (2004) CrossRefMATHGoogle Scholar
  3. Barpi, F., Valente, S.: Lifetime evaluation of concrete structures under sustained post-peak loading. Eng. Fract. Mech. 72(16), 2427–2443 (2005) CrossRefGoogle Scholar
  4. Bazant, Z.P.: Creep and damage in concrete. In: Svalny, J., Mindess, S. (eds.) Materials Science of Concrete, pp. 355–389. American Ceramic Society, Westerville (1995) Google Scholar
  5. Bazant, Z.P., Ozbolt, J.: Nonlocal microplane model for fracture, damage, and size effect in structures. J. Eng. Mech. 116, 2485–2505 (1990) CrossRefGoogle Scholar
  6. Bazant, Z.P., Li, Y.: Cohesive crack with rate-dependent opening and viscoelasticity: I. Mathematical model and scaling. Int. J. Fract. 86, 247–265 (1997) CrossRefGoogle Scholar
  7. Benboudjema, F., Torrenti, J.M.: Early age behavior of concrete nuclear containments. Nucl. Eng. Des. 238, 2495–2506 (2008) CrossRefGoogle Scholar
  8. Berthollet, A.: Contribution à la modélisation du béton vis-à-vis du vieillissement et de la durabilité: interaction des déformations de fluage et du comportement non-linéaire du matériau. PhD thesis of the Institut National des Sciences Appliquées de Lyon (2003) Google Scholar
  9. Bissonnette, B., Pigeon, M.: Tensile creep at early ages of ordinary, silica fume and fiber reinforced concretes. Cem. Concr. Res. 25(5), 1075–1085 (1995) CrossRefGoogle Scholar
  10. Bissonnette, B., Pigeon, M., Vaysburd, A.: Tensile creep of concrete: study of its sensitivity to basic parameters. ACI Mater. J. 104(4), 360–368 (2007) Google Scholar
  11. Brooks, J.J., Neville, A.M.: A comparison of creep, elasticity and strength of concrete in tension and in compression. Mag. Concr. Res. 29(100), 131–141 (1977) CrossRefGoogle Scholar
  12. Carpinteri, A., Valenten, S., Zhou, F.P., Ferrara, G., Melchiorri, G.: Tensile and flexural creep rupture tests on partially-damaged concrete specimens. Mater. Struct. 30, 269–276 (1997) CrossRefGoogle Scholar
  13. Challamel, N., Lanos, C., Casandjian, C.: Creep damage modeling for quasi-brittle materials. Eur. J. Mech. A, Solids 24, 593–613 (2005) CrossRefMATHGoogle Scholar
  14. Cook, D.J., Haque, M.N.: The tensile creep and fracture of desiccated concrete and mortar on water sorption. Mater. Struct. 7(3), 191–196 (1974) Google Scholar
  15. Denarié, E., Cécot, C., Huet, C.: Characterization of creep and crack growth interactions into fracture behavior of concrete. Cem. Concr. Res. 36(3), 571–575 (2006) CrossRefGoogle Scholar
  16. Dupray, F., Malecot, Y., Daudeville, L., Buzaud, E.: A mesoscopic model for the behavior of concrete under high confinement. Int. J. Numer. Anal. Methods 33, 1407–1423 (2009) CrossRefMATHGoogle Scholar
  17. Fichant, S., Pijaudier-Cabot, G., La Borderie, C.: Continuum damage modeling: approximation of crack induced anisotropy. Mech. Res. Commun. 24(2), 109–114 (1997) CrossRefMATHGoogle Scholar
  18. Fichant, S., La Borderie, C., Pijaudier-Cabot, G.: Isotropic and anisotropic descriptions of damage in concrete structures. Mech. Cohes.-Frict. Mater. 4(4), 339–359 (1999) CrossRefGoogle Scholar
  19. Garas, V.Y.: Multi-scale investigation of tensile creep of ultra-high performance concrete for bridge applications. Ph.D. Thesis, Georgia Institute of Technology (2009) Google Scholar
  20. Granger, L.: Comportement différé du béton dans les enceintes de centrales nucléaires analyse et modélisation. Ph.D. Thesis, Laboratoire Central des Ponts et Chaussées, Paris (1996) Google Scholar
  21. Granger, S., Loukili, A., Pijaudier-Cabot, G., Chanvillard, G.: Experimental characterization of the self-healing of cracks in an ultra high performance cementitious material: mechanical tests and acoustic emission analysis. Cem. Concr. Res. 37, 519–527 (2007) CrossRefGoogle Scholar
  22. Grassl, P., Jirasek, M.: Meso-scale approach to modeling the fracture process zone of concrete subjected to uniaxial tension. Int. J. Solids Struct. 47, 957–968 (2010) CrossRefMATHGoogle Scholar
  23. Grondin, F., Dumontet, H., Ben Hamida, A., Mounajed, G., Boussa, H.: Multi-scales modeling for the behavior of damaged concrete. Cem. Concr. Res. 37, 1453–1462 (2007) CrossRefGoogle Scholar
  24. Grondin, F., Dumontet, H., Ben Hamida, A., Boussa, H.: Micromechanical contributions to the behavior of cement-based materials: two-scale modeling of cement paste and concrete in tension at high temperatures. Cem. Concr. Compos. 33(3), 424–435 (2011) CrossRefGoogle Scholar
  25. Haidar, K., Pijaudier-Cabot, G., Dubé, J.F., Loukili, A.: Correlation between the internal length, the fracture process zone and size effect in model materials. Mater. Struct. 38, 201–210 (2005) Google Scholar
  26. Le, Q.V., Meftah, F., He, Q.-C., Le Pape, Y.: Creep and relaxation functions of a heterogeneous viscoelastic porous medium using the Mori–Tanaka homogenization scheme and a discrete microscopic retardation spectrum. Mech. Time-Depend. Mater. 11, 309–331 (2007) CrossRefGoogle Scholar
  27. Lopez, C.M., Carol, I., Aguado, A.: Meso-structural study of concrete fracture using interface elements. I: Numerical model and tensile behavior. Mater. Struct. 41, 583–599 (2008) CrossRefGoogle Scholar
  28. Matallah, M., La Borderie, C., Maurel, O.: A practical method to estimate crack openings in concrete structures. Int. J. Numer. Anal. Methods 34, 1615–1633 (2010) MATHGoogle Scholar
  29. Mazzotti, C., Savoia, M.: Non linear creep damage model for concrete under uniaxial compression. J. Eng. Mech. 129(9), 1065–1076 (2003) CrossRefGoogle Scholar
  30. Mihashi, H., Nomura, N.: Correlation between characteristics of fracture process zone and tension-softening properties of concrete. Nucl. Eng. Des. 65, 359–376 (1996) CrossRefGoogle Scholar
  31. Mounajed, G.: Exploitation du nouveau modèle Béton Numérique dans Symphonie: Concept, homogénéisation du comportement thermomécanique des BHP et simulation de l’endommagement thermique. Cahiers du CSTB No 3421 (2002) Google Scholar
  32. Nguyen, T.D., Lawrence, C., La Borderie, C., Matallah, M., Nahas, G.: A mesoscopic model for a better understanding of the transition from diffuse damage to localized damage. Eur. J. Environ. Civ. Eng. 14(6–7), 751–776 (2011) Google Scholar
  33. Omar, M.: Déformations différées du béton: Etude expérimentale et modélisation numérique de l’interaction fluage – endommagement. PHD thesis, Ecole Centrale de Nantes (2004) Google Scholar
  34. Omar, M., Loukili, A., Pijaudier-Cabot, G., Le Pape, Y.: Creep-damage coupled effects: experimental investigation on bending beams with various sizes. J. Mater. Civ. Eng. 21(2) (2009) Google Scholar
  35. Otsuka, K., Date, H.: Fracture process zone in concrete tension specimen. Eng. Fract. Mech. 65, 111–131 (2000) CrossRefGoogle Scholar
  36. Ozbolt, J.: Sustained loading strength of concrete modeled by creep-cracking interaction. Otto Graf J. 12 (2001) Google Scholar
  37. Reviron, N., Benboudjema, F., Torrenti, J.-M., Nahas, G., Millard, A.: Coupling between creep and cracking in tension. In: The Sixth Int. Conf. in Frac. Mech. of Concr. and Concr. Struct. (Framcos-6), Catania, Italy, June 17–22 (2007) Google Scholar
  38. RILEM TC212-ACD: Acoustic emission and related NDE techniques for crack detection and damage evaluation in concrete. Mater. Struct. 43, 1177–1181 (2010) CrossRefGoogle Scholar
  39. Rossi, P., Godart, N., Robert, J.L., Gervais, J.P., Bruhat, D.: Investigation of the basic creep of concrete by acoustic emission. Mater. Struct. 27, 510–514 (1994) CrossRefGoogle Scholar
  40. Rossi, P., Tailhan, J.-L., Le Maou, F., Gaillet, L., Martin, E.: Basic creep behavior of concretes investigation of the physical mechanisms by using acoustic emission. Cem. Concr. Res. 42, 61–73 (2012) CrossRefGoogle Scholar
  41. Ruiz, M.F., Muttoni, A., Gambarova, P.G.: Relationship between nonlinear creep and cracking of concrete under uniaxial compression. J. Adv. Concr. Technol. 5(3), 1–11 (2007) Google Scholar
  42. Saliba, J., Grondin, F., Loukili, A.: Coupling creep and damage in concrete under high sustained loading. In: The Seventh Int. Conf. in Frac. Mech. of Concr. and Concr. Struct. (Framcos-7), Jeju, Korea, May 23–28 (2010) Google Scholar
  43. Saliba, J., Loukili, A., Grondin, F.: Study of creep-damage coupling in concrete by acoustic emission technique. Mater. Struct. 45(9), 1389–1401 (2012) CrossRefGoogle Scholar
  44. Saliba, J.: Contribution of the acoustic emission technique in the understanding and the modeling of the coupling between creep and damage in concrete. Ph.D. Thesis at Ecole Centrale de Nantes (in French) (2012) Google Scholar
  45. Torrenti, J.M., Nguyen, V.H., Colina, H., Le Maou, F., Benboudjema, F., Deleruyelle, F.: Coupling between leaching and creep of concrete. Cem. Concr. Res. 38, 816–821 (2008) CrossRefGoogle Scholar
  46. Verpaux, P., Charras, T., Millard, A.: Une approche moderne du calcul des structures. In: Fouet, J., Ladevèze, P., Ohayon, R. (eds.) Calculs des Structures et Intelligence Artificielle. Pluralis, Paris (1988) Google Scholar
  47. Zhu, W.C., Tang, C.A.: Numerical simulation on shear fracture process of concrete using mesoscopic mechanical model. Constr. Build. Mater. 16, 453–463 (2002) CrossRefGoogle Scholar
  48. Zhu, W.C., Zhao, X.D., Kang, Y.M., Wei, C.H., Tian, J.: Numerical simulation on the acoustic emission activities of concrete. Mater. Struct. 43, 633–650 (2010) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • J. Saliba
    • 1
  • F. Grondin
    • 1
  • M. Matallah
    • 2
  • A. Loukili
    • 1
  • H. Boussa
    • 3
  1. 1.LUNAM Université, Ecole Centrale de Nantes, Institut de Recherche en Génie Civil et Mécanique (GeM)UMR-CNRS 6183NantesFrance
  2. 2.Risk Assessment and Management (RiSAM)Université de TlemcenTlemcenAlgeria
  3. 3.Centre Scientifique et Technique du BâtimentDivision MOD-EVEMarne-la-ValléeFrance

Personalised recommendations