Materials and Structures

, 41:431 | Cite as

Specimen shape and the problem of contact in the assessment of concrete compressive strength

Original Article


This paper proposes a critical analysis of the studies which, since the 1950s, have attempted to quantify the influence of specimen shape on the determination of concrete compressive strength, with special regard to the problem of conversion from cylinder to cube strength and vice versa. From such a retrospective analysis, it emerges that the problem of contact between the platens of the testing machine and the concrete specimen plays a crucial role for the explanation of the variability of the concrete compressive strength as a function of specimen shape. To obtain quantitative predictions and to investigate on the influence of the friction coefficient, uniaxial compressive tests are numerically simulated by using a nonlinear finite element model. Both the constitutive nonlinearity of concrete and the nonlinearity due to contact are taken into account in the formulation. The results of the proposed parametric analysis permit to evaluate the evolution of the conversion ratio between cylinder and cube strength as a function of the friction coefficient. This sheds a new light on the complex nature of this nonlinear relationship, whose value approaches 1 for a friction coefficient close to 0.01, simulating the presence of Teflon, and then approaches asymptotically 0.78 for  = 0.60, as is typical of steel-concrete interfaces.


Concrete compressive strength Specimen shape Finite element method Friction Contact mechanics 



The financial support provided by the Italian Ministry of University and Research with the project PRIN2005—Modelling and approximation in advanced mechanical problems—is gratefully acknowledged.


  1. 1.
    L’ Hermite R (1954) Idées actuelles sur la technologie du béton. Bull RILEM 18:27–40Google Scholar
  2. 2.
    Hansen H, Kielland A, Nielsen KEC, Taulow S (1962) Compressive strength of concrete-cube or cylinder. Bull RILEM 17:23–30Google Scholar
  3. 3.
    Thaulow S (1962) Apparent compressive strength of concrete as affected by height of test specimen and friction between loading surfaces. Bull RILEM 17:31–33Google Scholar
  4. 4.
    Leonhardt F (1973) Vorlesungen über Massivbau-Grundlagen zur Bemessung im Stahlbetonbau. Springer Verlag, Berlin, pp 14–15Google Scholar
  5. 5.
    RILEM (1949–1950) Etude comparative des coefficients usuels, et coefficients déduits de notre théorie. Bull RILEM 2(Tome III):89–90Google Scholar
  6. 6.
    L’Hermite R (1950) La résistance du béton et sa mesure. Annales de l’Institut Technique du Batiment et des Travaux Publics 114:1–19Google Scholar
  7. 7.
    Chefdeville J (1953) L’auscultation dynamique du béton. Application de la méthode à l’estimation de la qualité du béton. Bull RILEM 15:60–78Google Scholar
  8. 8.
    Commission Béton RILEM (1957) Coefficients de corrispondace entre les résistances de differents types d’éprouvettes. Bull RILEM 39:81–105Google Scholar
  9. 9.
    Kordina K (1960) RILEM symposium “Influence of time upon the strength and the deformation of concrete”-Final Report. Bull RILEM 9:62–93Google Scholar
  10. 10.
    Commission Béton RILEM (1961) Coefficients de corrispondance entre les differentes types d’éprouvettes. Bull RILEM 12:155–156Google Scholar
  11. 11.
    Kuczynski W (1960) La résistance du béton étudié sur des éprouvettes de différentes formes et de diverses dimensions. Bull RILEM 8:77–92Google Scholar
  12. 12.
    Lyse I, Johansen R (1962) An investigation on the relationship between the cube and the cylinder strengths of concrete. Bull RILEM 14:125–133Google Scholar
  13. 13.
    CEB–Commission Dalles-Planchers-Dalles (1960) La theorie des lignes de rupture. Bulletin d’Information 27:73–78Google Scholar
  14. 14.
    CEB (1972) Proposition de Compléments aux Recommandations Internationales CEB-FIP 1970. Bulletin d’Information 74:17–20Google Scholar
  15. 15.
    Neville AM (1995) Properties of concrete, 4th edn. Longman, Harlow Essex, pp 591–594Google Scholar
  16. 16.
    CEB-FIP (1993) Model Code 1990. Bulletin d’ Information (231/214):33–34Google Scholar
  17. 17.
    EN 1992-1-1 (2003) Eurocode 2: design of concrete structures - Part 1.1: general rules and rules for buildings. pp 27–37Google Scholar
  18. 18.
    EN 13791 (2005) Assessment of in-situ compressive strength in structures and in precast concrete components. pp 7–8Google Scholar
  19. 19.
    RILEM TC 148-SSC (1997) Strain-softening of concrete in uniaxial compression. Mater Struct 30:195–209Google Scholar
  20. 20.
    Drucker DC, Prager W (1952) Soil mechanics and plastic analysis of limit design. Quart J Appl Math 10(2):157–165MATHMathSciNetGoogle Scholar
  21. 21.
    Köksal HO, Karakoç C, Yildirim H (2005) Compression behavior and failure mechanisms of concrete masonry prisms. ASCE J Mater Civil Eng 17(1):107–115CrossRefGoogle Scholar
  22. 22.
    Cela JJL (2002) Material identification procedure for elastoplastic Drucker-Prager model. ASCE J Eng Mech 128(5):586–591CrossRefGoogle Scholar
  23. 23.
    Pietruszczak ST, Mróz Z (1981) Finite element analysis of deformation of strain-softening materials. Int J Numer Methods Eng 17:327–334MATHCrossRefGoogle Scholar
  24. 24.
    Bazant ZP, Pijaudier-Cabot G (1988) Nonlocal continuum damage, localization instability and convergence. J Appl Mech 55:287–293MATHCrossRefGoogle Scholar
  25. 25.
    Zienkiewicz OC, Pastor M, Huang M (1995) Softening, localisation and adaptive remeshing: capture of discontinuous solutions. Comput Mech 17:98–106MATHCrossRefGoogle Scholar
  26. 26.
    Ortiz M, Leroy Y, Needleman A (1987) A finite element method for localized failure analysis. Comput Methods Appl Mech Eng 61:189–214MATHCrossRefGoogle Scholar
  27. 27.
    Simo JC, Oliver J, Armero F (1993) An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Comput Mech 12:277–296MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Borja RI, Regueiro RA, Lai TY (2000) FE modelling of strain localization in soft rock. ASCE J Geotech Geoenviron Eng 126:335–343CrossRefGoogle Scholar
  29. 29.
    Fichera G (1964) Problemi elastostatici con vincoli unilaterali e il problema di Signorini con ambigue condizioni al contorno. Memorie dell’Accademia Nazionale dei Lincei VIII(7):91–140MathSciNetGoogle Scholar
  30. 30.
    Panagiotopoulos PD (1985) Inequality problems in mechanics and applications. Birkhäuser Verlag, BaselMATHGoogle Scholar
  31. 31.
    Kuhn HW, Tucker AW (1951) Nonlinear programming. Proceedings of the 2nd Berkeley symposium. University of California Press, Berkeley, pp 481–492Google Scholar
  32. 32.
    Zavarise G, Wriggers P, Stein E, Schrefler B (1992) Real contact mechanisms and finite element formulation - a coupled thermomechanical approach. Int J Numer Methods Eng 35:767–785MATHCrossRefGoogle Scholar
  33. 33.
    Zavarise G, Wriggers P, Stein E, Schrefler B (1992) A numerical model for thermomechanical contact based on microscopic interface laws. Mech Res Commun 19:173–182MATHCrossRefGoogle Scholar
  34. 34.
    Paggi M, Carpinteri A, Zavarise G (2006) A unified interface costitutive law for the study of fracture and contact problems in heterogeneous materials, In: Wriggers P, Nackenhorst U (eds) Analysis and simulation of contact problems, Lecture Notes in Applied and Computational Mechanics, vol 27. Springer-Verlag, Berlin, pp 297–304Google Scholar
  35. 35.
    Wriggers P (2002) Computational contact mechanics. John Wiley & Sons, Ltd., The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, EnglandGoogle Scholar
  36. 36.
    Wriggers P, Zavarise G (2004) Computational contact mechanics, Encyclopedia of Computational Mechanics. In: Stein E, De Borst R, Huges TJR (eds) Solids and structures, vol 2. John Wiley & Sons, Ltd, Chichester, pp 195–226Google Scholar
  37. 37.
    Wriggers P, Simo JC (1985) A note on tangent stiffness for fully nonlinear contact problems. Commun Appl Numer Methods 1:199–203MATHCrossRefGoogle Scholar
  38. 38.
    Zienkiewicz OC, Taylor RL (1989) The finite element method, 4th edn. McGraw-Hill, LondonGoogle Scholar
  39. 39.
    Gdoutos EE, Theocaris PS (1975) Stress concentrations at the apex of a plane indenter acting on an elastic half plane. ASME J Appl Mech 8:688–692Google Scholar
  40. 40.
    Carpinteri A, Paggi M (2007) Analytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems. Eng Fract Mech 74:59–74CrossRefGoogle Scholar
  41. 41.
    Caner FC, Bažant ZP (2002) Lateral confinement needed to suppress softening of concrete in compression. ASCE J Eng Mech 128(12):1304–1313CrossRefGoogle Scholar
  42. 42.
    Van Vliet MRA, Van Mier JGM (1996) Experimental investigation of concrete fracture under uniaxial compression. Mech Cohesive-Frictional Mater 1:115–127CrossRefGoogle Scholar
  43. 43.
    Carpinteri A, Ciola F, Pugno N (2001) Boundary element method for the strain-softening response of quasi-brittle materials in compression. Comput Struct 79:389–401CrossRefGoogle Scholar
  44. 44.
    Markeset G, Hillerborg A (1995) Softening of concrete in compression – localization and size effects. Cement Concrete Res 25:702–708CrossRefGoogle Scholar
  45. 45.
    Carpinteri A, Ferro G, Monetto I (1999) Scale effects in uniaxially compressed concrete specimens. Mag Concrete Res 51:217–225CrossRefGoogle Scholar

Copyright information

© RILEM has copyright 2007

Authors and Affiliations

  1. 1.Department of Structural and Geotechnical EngineeringPolitecnico di TorinoTorinoItaly

Personalised recommendations