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Microstructural modelling of the elastic properties of tricalcium silicate pastes at early ages

  • Do, Huy Q. (Laboratoire des Materiaux de Construction, Ecole Polytechnique Federale de Lausanne (EPFL)) ;
  • Bishnoi, Shashank (Department of Civil Engineering, Indian Institute of Technology Delhi) ;
  • Scrivener, Karen L. (Laboratoire des Materiaux de Construction, Ecole Polytechnique Federale de Lausanne (EPFL))
  • 투고 : 2014.06.20
  • 심사 : 2015.07.10
  • 발행 : 2015.07.25

초록

This paper describes the numerical calculation of elastic properties of a simulated microstructure of cement paste from very early age, when most previous models fail to give accurate results. The development of elastic properties of tricalcium silicate pastes was calculated by discretising a numerical resolution-free 3D vector microstructure to a regular cubic mesh. Due to the connections formed in the microstructure as an artefact of the meshing procedure, the simulated elastic moduli were found to be higher than expected. Furthermore, the percolation of the solids was found to occur even before hydration started. A procedure to remove these artefacts, on the basis of the information available in the vector microstructures was developed. After this correction, a better agreement of the experimental results with calculations was obtained between 20% and 40% hydration. However, percolation threshold was found to be delayed significantly. More realistic estimates of percolation threshold were obtained if either flocculation or a densification of calcium silicate hydrate with hydration was assumed.

키워드

참고문헌

  1. Abrams, D. (1918), Design of Concrete Mixtures, Structural Materials Research Laboratory, Lewis Institute, Chicago, USA.
  2. ACI Committee 318 (2008), Building code requirements for structural concrete (ACI 318-08) and commentary, American Concrete Institute.
  3. Bernard, O., UIm, F.J. and Lemarchand, E. (2003), "A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials", Cement. Concrete. Res., 33(9), 1293-1309. https://doi.org/10.1016/S0008-8846(03)00039-5
  4. Bary, B., Ben, M., Adam, E. and Montarnal, P (2009), "Numerical and analytical effective elastic properties of degraded cement pastes", Cement. Concrete. Res., 39(10), 902-912. https://doi.org/10.1016/j.cemconres.2009.06.012
  5. Bentz, D.P. (1995), A Three-Dimensional Cement Hydration and Microstructure Program. I. Hydration Rate, Heat of Hydration, and Chemical Shrinkage, NISTIR 5756, U.S. Department of Commerce.
  6. Bishnoi, S. and Scrivener, K.L. (2009a), "A new platform for modelling the hydration of cements", Cement. Concrete. Res., 39(4), 266-274. https://doi.org/10.1016/j.cemconres.2008.12.002
  7. Bishnoi, S. and Scrivener, K.L. (2009b), "Studying nucleation and growth kinetics of alite hydration using ${\mu}ic$", Cement. Concrete. Res., 39(10), 849-860. https://doi.org/10.1016/j.cemconres.2009.07.004
  8. Bolomey, J. (1935), "Granulation et prevision de la resistance probable des betons", Travaux, 30, 228-232.
  9. Boumiz, A., Sorrentino, D., Vernet, C. and Tenoudji, F.C. (2000), "Modelling the development of the elastic moduli as a function of the hydration degree of cement pastes and mortars", RILEM Proceedings, PRO 13, Hydration and Setting: Why does Cement Set, an Interdisciplinary Approach, 295-316.
  10. Castaneda, P.P. and Willis, J.R. (1995), "The effect of spatial distribution on the effective behaviour of composite materials and cracked media", J. Mech. Phys. Solids., 43(12), 1919-1951. https://doi.org/10.1016/0022-5096(95)00058-Q
  11. Constantinides, G. and Ulm, F.J. (2004), "The effect of two types of C-S-H on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modeling", Cement. Concrete. Res., 34(1), 67-80. https://doi.org/10.1016/S0008-8846(03)00230-8
  12. Courant, R. (1943), "Variational methods for the solution of problems of equilibrium and vibration", B. Am. Math. Soc., 49, 1-23.
  13. Do, H.Q., Bishnoi, S. and Scrivener, K.L. (2013), "Numerical simulation of porosity in cements", Transport. Porous. Med, 99(1), 101-117. https://doi.org/10.1007/s11242-013-0176-4
  14. Dunant, C.F., Bary, B., Giorla, A.B., Peniguel, C., Sanahuja, J., Toulemonde, C., Tran, A.B., Willot, F. and Yvonnet J. (2013), "A critical comparison of several numerical methods for computing effective properties of highly heterogeneous materials", Adv. Eng. Softw., 58, 1-12. https://doi.org/10.1016/j.advengsoft.2012.12.002
  15. EN 1992-1-1 (2004), Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, CEN Technical Committee 250.
  16. Eshelby, J.D. (1957), "The determination of the elastic field of an ellipsoidal inclusion, and related problems", Proceedings of the Royal Society A, 241, 376-396. https://doi.org/10.1098/rspa.1957.0133
  17. Eshelby, J.D. (1959), "The elastic field outside an ellipsoidal inclusion", Proceedings of the Royal Society A, 252, 561-569. https://doi.org/10.1098/rspa.1959.0173
  18. Feret, R. (1892), "Sur Ie compacite des mortiers", Annales des Pants et Chaussees, 7, 5-164.
  19. Haecker, C.J., Garboczi, E.J., Bullard, J.W., Bohn, R.B., Sun, Z., Shah, S.P. and Voigt, T. (2005), "Modeling the linear elastic properties of Portland cement paste", Cement. Concrete. Res., 35(10), 1948-1960. https://doi.org/10.1016/j.cemconres.2005.05.001
  20. Hain, M. and Wriggers, P. (2008), "Numerical homogenization of hardened cement pastes", Comput. Mech., 42(2), 197-212. https://doi.org/10.1007/s00466-007-0211-9
  21. Hill, R. (1952), "The elastic behaviour of a crystalline aggregate", Proceedings of the Physical Society, 65, 349-354.
  22. Hill, R. (1965), "A self-consistent mechanics of composite materials", J. Mech. Phys. Solids., 13(4), 213-222. https://doi.org/10.1016/0022-5096(65)90010-4
  23. Hrennikoff, A.P. (1940), "Plane stress and bending of plates by method of articulated framework", Doctoral Dissertation, Massachusetts Institute of Technology, Boston.
  24. Huet, C. (1990), "Application of variational concepts to size effects in elastic heterogeneous bodies", Mech. Phys. Solids., 38(6), 813-841. https://doi.org/10.1016/0022-5096(90)90041-2
  25. Jennings, H.M. (2000), "A model for the microstructure of calcium silicate hydrate in cement paste", Cement. Concrete. Res., 30(1), 101-116. https://doi.org/10.1016/S0008-8846(99)00209-4
  26. Jennings, H.M. and Parrott, L.J. (1986), "Microstructural analysis of hardened alite paste, part II: microscopy and reaction products", J. Mater. Sci., 21(11), 4053-4059. https://doi.org/10.1007/BF02431651
  27. Mori, T and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta. Metall. Sin., 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  28. Moulinec, H. and Suquet, P. (1994), "A fast numerical method for computing the linear and nonlinear properties of composites", Comptes Rendus de l'Academie des Sciences Paris, II, 318(11), 1417-1423.
  29. Nguyen, V.P., Stroeven, M. and Sluys, L.J. (2012a), "Multiscale failure modelling of concrete: micromechanical modelling, discontinuous homogenization and parallel computations", Comput. Method Appl. M., 201-204, 139-156. https://doi.org/10.1016/j.cma.2011.09.014
  30. Nguyen, V.P., Stroeven, M. and Sluys, L.J. (2012b), "Multiscale continuous and discontinuous modelling of heterogeneous materials: A review on recent developments", J. Multi. Model., 3(4), 1-42.
  31. Pichler, B., Hellmich, C. and Eberhardsteiner, J. (2009), "Spherical and acicular representation of hydrates in a micromechanical model for cement paste: prediction of early-age elasticity and strength", Acta. Mech., 203(3-4), 137-162. https://doi.org/10.1007/s00707-008-0007-9
  32. Powers, T.C. (1958), "Structure and physical properties of hardened portland cement paste", J. Am. Ceram. Soc., 41(1), 1-6.
  33. Reuss, A. (1929), "Berechnung der fliessgrenze von mischkristallen auf grund der plastizitatsbedingung fur einkristalle", J. Appl. Math. Mech., 9(1), 49-58.
  34. Sanahuja, J., Dormieux, L. and Chanvillard, G. (2007), "Modelling elasticity of a hydrating cement paste", Cement Concrete. Res., 37(10), 1427-1439. https://doi.org/10.1016/j.cemconres.2007.07.003
  35. Scherer, G.W, Zhang, J., Quintanilla, J.A. and Torquato, S. (2012), "Hydration and percolation at the setting point", Cement. Concrete. Res., 42(5), 665-672. https://doi.org/10.1016/j.cemconres.2012.02.003
  36. Smilauer, V. and Bittnar, Z. (2006), "Microstructure-based micromechanical prediction of elastic properties in hydrating cement paste", Cement. Concrete. Res., 36(9), 1708-1718. https://doi.org/10.1016/j.cemconres.2006.05.014
  37. Stefan, L.. Benboudjema. F., Torrenti. J.M. and Bissonnette, B. (2010), "Prediction of elastic properties of cement pastes at early ages", Comput. Mater. Sci. 47(3), 775-784. https://doi.org/10.1016/j.commatsci.2009.11.003
  38. Suquet, P. (1990), "A simplified method for the prediction of homogeneized elastici properties of composites with a periodic structure", Comptes Rendus de l'Academie des Sciences Paris, II, 311, 769-774.
  39. Thomas, J.J., Allen, A.J. and Jennings, H.M. (2009), "Hydration kinetics and microstructure development of normal and CaCl2-Accelerated tricalcium silicate pastes", J. Phys. Chem. C. 113(46), 19836-19844. https://doi.org/10.1021/jp907078u
  40. Vandamme, M. (2008), "The nanogranular origin of concrete creep: A nanoindentation investigation of microstructure and fundamental principles of calcium-silicate-hydrates", Doctoral Dissertation, Massachusetts Institute of Technology, Boston.
  41. Velez, K., Maximilien, S., Damidot, D., Fantozzi, G. and Sorrentino, F. (2001), "Determination by nanoindentation of elastic modulus and hardness of pure constituents of Portland cement clinker", Cement. Concrete. Res. 31(4), 555-561. https://doi.org/10.1016/S0008-8846(00)00505-6
  42. Voidt, W. (1887), "Theoretische studien uber die elasticitatsverhaltnisse der krystalle", Abhandlungen der Koniglichen Gesellschaft der Wissenschaften in Gottingen, 34, 3-51.

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  3. Microstructural modelling of the strength of mortars containing fly ash using µic vol.163, 2018, https://doi.org/10.1016/j.conbuildmat.2017.12.163
  4. Microstructural simulation and measurement of elastic modulus evolution of hydrating cement pastes vol.130, pp.None, 2015, https://doi.org/10.1016/j.cemconres.2020.106007
  5. Microstructural modelling of autogenous shrinkage in Portland cement paste at early age vol.37, pp.9, 2015, https://doi.org/10.1108/ec-08-2019-0353