Downscaling Based Identification of Nonaging Power-Law Creep of Cement Hydrates
Publication: Journal of Engineering Mechanics
Volume 142, Issue 12
Abstract
Creep of cementitious materials results from the viscoelastic behavior of the reaction products of cement and water, called hydrates. In the present paper, a single isochoric creep function characterizing well-saturated portland cement hydrates is identified through downscaling of 500 different nonaging creep functions derived from three-minute-long tests on differently young cement pastes with three different initial water-to-cement mass ratios. A two-scale micromechanics representation of cement paste is used for downscaling. At a scale of 700 microns, spherical clinker inclusions are embedded in a continuous hydrate foam matrix. The latter is resolved, at the smaller scale of 20 microns, as a highly disordered arrangement of isotropically oriented hydrate needles, which are interacting with spherical water and air pores. Homogenization of viscoelastic properties is based on the correspondence principle, involving transformation of the time-dependent multiscale problem to the Laplace-Carson space, followed by quasi-elastic upscaling and numerical back-transformation. With water, air, and clinker behaving elastically according to well-accepted published data, the hydrates indeed show one single power-law-type creep behavior with a creep exponent being surprisingly close to those found for the different cement pastes tested. The general validity of the identified hydrate creep properties is further corroborated by using them for predicting the creep performance of a 30-year-old cement paste in a creep test lasting 30 days: the respective model predictions agree very well with results from creep experiments published in the open literature.
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Acknowledgments
The second author wishes to thank Higher Education Commission (HEC) Pakistan and University of Engineering and Technology, Lahore, Pakistan, for their support.
References
Abate, J., and Valkó, P. (2004). “Multi-precision Laplace transform inversion.” Int. J. Numer. Methods Eng., 60(5), 979–993.
Acker, P. (2001). “Micromechanical analysis of creep and shrinkage mechanisms.” Creep, shrinkage and durability mechanics of concrete and other quasi-brittle materials, F.-J. Ulm, Z. Bažant, and F. Wittmann, eds., Elsevier, Amsterdam, Netherlands, 15–26.
Acker, P., and Ulm, F.-J. (2001). “Creep and shrinkage of concrete: Physical origins and practical measurements.” Nucl. Eng. Des., 203(2), 143–158.
Bažant, Z., Hubler, M., and Yu, Q. (2011). “Pervasiveness of excessive segmental bridge deflections: Wake-up call for creep.” ACI Struct. J., 108(6), 766–774.
Bažant, Z., and L’Hermite, R. (1988). Mathematical modeling of creep and shrinkage of concrete, Wiley, Chichester, U.K.
Bažant, Z., and Prasannan, S. (1989a). “Solidification theory for concrete creep. I: Formulation.” J. Eng. Mech., 1691–1703.
Bažant, Z., and Prasannan, S. (1989b). “Solidification theory for concrete creep. II: Verification and application.” J. Eng. Mech., 1704–1725.
Benveniste, Y. (1987). “A new approach to the application of Mori-Tanaka’s theory in composite materials.” Mech. Mater., 6(2), 147–157.
Bernard, O., Ulm, F., and Lemarchand, E. (2003a). “A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials.” Cem. Concr. Res., 33(9), 1293–1309.
Bernard, O., Ulm, F.-J., and Germaine, J. (2003b). “Volume and deviator creep of calcium-leached cement-based materials.” Cem. Concr. Res., 33(8), 1127–1136.
Beurthey, S., and Zaoui, A. (2000). “Structural morphology and relaxation spectra of viscoelastic heterogeneous materials.” Eur. J. Mech. A/Solids, 19(1), 1–16.
Carrier, B., et al. (2016). “Effect of water on elastic and creep properties of self-standing clay films.” Langmuir, 32(5), 1370–1379.
Delsaute, B., et al. (2016). “Testing concrete E-modulus at very early ages through several techniques: An inter-laboratory comparison.” Strain, 52(2), 91–109.
Delsaute, B., and Staquet, S. (2014). “Monitoring of the creep and the relaxation modelling of concrete under tension and compression.” RILEM International Symp. on Concrete Modelling—CONMOD 2014, RILEM, Paris, 168–175.
Eshelby, J. (1957). “The determination of the elastic field of an ellipsoidal inclusion, and related problems.” Proc. R. Soc. London Ser. A, 241(1226), 376–396.
Fritsch, A., Dormieux, L., and Hellmich, C. (2006). “Porous polycrystals built up by uniformly and axisymmetrically oriented needles: Homogenization of elastic properties.” Comptes Rendus Mécanique, 334(3), 151–157.
Fritsch, A., Hellmich, C., and Young, P. (2013). “Micromechanics-derived scaling relations for poroelasticity and strength of brittle porous polycrystals.” J. Appl. Mech., 80(2), 020905.
Gurtin, M., and Sternberg, E. (1962). “On the linear theory of viscoelasticity.” Arch. Ration. Mech. Anal., 11(1), 291–356.
Hashin, Z. (1983). “Analysis of composite materials.” J. Appl. Mech., 50(3), 481–505.
Hellmich, C., Barthélémy, J.-F., and Dormieux, L. (2004). “Mineral-collagen interactions in elasticity of bone ultrastructure—A continuum micromechanics approach.” Eur. J. Mech. A/Solids, 23(5), 783–810.
Hershey, A. (1954). “The elasticity of an isotropic aggregate of anisotropic cubic crystals.” J. Appl. Mech. Trans., 21(3), 236–240.
Hill, R. (1965). “A self-consistent mechanics of composite materials.” J. Mech. Phys. Solids, 13(4), 213–222.
Ioannidou, K., et al. (2016). “Mesoscale texture of cement hydrates.” Proc. Natl. Acad. Sci., 113(8), 2029–2034.
Irfan-ul-Hassan, M., Pichler, B., Reihsner, R., and Hellmich, C. (2016). “Elastic and creep properties of young cement paste, as determined from hourly repeated minute-long quasi-static tests.” Cem. Concr. Res., 82, 36–49.
Kröner, E. (1958). “Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einheitskristalls [Computation of the elastic constants of a polycrystal based on the constants of the single crystal].” Zeitschrift für Physik. A: Hadrons and Nuclei, 151(4), 504–518 (in German).
Laws, N. (1977). “The determination of stress and strain concentrations at an ellipsoidal inclusion in an anisotropic material.” J. Elast., 7(1), 91–97.
Laws, N., and McLaughlin, R. (1978). “Self-consistent estimates for the viscoelastic creep compliances of composite materials.” Proc. R. Soc. London A: Math. Phys. Eng. Sci., 359(1697), 251–273.
Lin, F., and Meyer, C. (2009). “Hydration kinetics modeling of portland cement considering the effects of curing temperature and applied pressure.” Cem. Concr. Res., 39(4), 255–265.
Manzano, H., Masoero, E., Lopez-Arbeloa, I., and Jennings, H. (2013). “Shear deformations in calcium silicate hydrates.” Soft Matter, 9(30), 7333–7341.
Manzano, H., Moeini, S., Marinelli, F., Van Duin, A., Ulm, F.-J., and Pellenq, R.-M. (2012). “Confined water dissociation in microporous defective silicates: Mechanism, dipole distribution, and impact on substrate properties.” J. Am. Chem. Soc., 134(4), 2208–2215.
MATLAB [Computer software]. MathWorks, Natick, MA.
Mori, T., and Tanaka, K. (1973). “Average stress in matrix and average elastic energy of materials with misfitting inclusions.” Acta Metall., 21(5), 571–574.
Neville, A. (1964). “Creep of concrete as a function of its cement paste content.” Mag. Concr. Res., 16(46), 21–30.
Pichler, B., et al. (2013). “Effect of gel-space ratio and microstructure on strength of hydrating cementitious materials: An engineering micromechanics approach.” Cem. Concr. Res., 45, 55–68.
Pichler, B., and Hellmich, C. (2011). “Upscaling quasi-brittle strength of cement paste and mortar: A multi-scale engineering mechanics model.” Cem. Concr. Res., 41(5), 467–476.
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.
Powers, T. (1958). “Structure and physical properties of hardened portland cement paste.” J. Am. Ceram. Soc., 41(1), 1–6.
Powers, T., and Brownyard, T. (1946). “Studies of the physical properties of hardened portland cement paste.” Am. Concr. Inst. J. Proc., 43(9), 101–992.
Read, W., Jr. (1950). “Stress analysis for compressible viscoelastic materials.” J. Appl. Phys., 21(7), 671–674.
Sadowski, P., Kowalczyk-Gajewska, K., and Stupkiewicz, S. (2015). “Classical estimates of the effective thermoelastic properties of copper-graphene composites.” Compos. Part B: Eng., 80, 278–290.
Sanahuja, J., and Dormieux, L. (2010). “Creep of a C-S-H gel: A micromechanical approach.” Anais da Academia Brasileira de Ciências, 82(1), 25–41.
Sanahuja, J., Dormieux, L., Meille, S., Hellmich, C., and Fritsch, A. (2010). “Micromechanical explanation of elasticity and strength of gypsum: From elongated anisotropic crystals to isotropic porous polycrystals.” J. Eng. Mech., 239–253.
Scheiner, S., and Hellmich, C. (2009). “Continuum microviscoelasticity model for aging basic creep of early-age concrete.” J. Eng. Mech., 307–323.
Schwarzl, F., and Struik, L. (1968). “Analysis of relaxation measurements.” Adv. Mol. Relax. Processes, 1(3), 201–255.
Shahidi, M., Pichler, B., and Hellmich, C. (2014). “Viscous interfaces as source for material creep: A continuum micromechanics approach.” Eur. J. Mech. A/Solids, 45, 41–58.
Shahidi, M., Pichler, B., and Hellmich, C. (2015a). “Interfacial micromechanics assessment of classical rheological models—I: Single interface size and viscosity.” J. Eng. Mech., 04015092.
Shahidi, M., Pichler, B., and Hellmich, C. (2015b). “Interfacial micromechanics assessment of classical rheological models—II: Multiple interface sizes and viscosities.” J. Eng. Mech., 04015093.
Shahidi, M., Pichler, B., Wendner, R., Scheiner, S., and Hellmich, C. (2015c). “Interfacial micromechanics assessment of rheological chain models and their application to early-age creep of concrete.” 10th Int. Conf. on Mechanics and Physics of Creep, Shrinkage, and Durability of Concrete and Concrete Structures (CONCREEP-10), ASCE, Reston, VA, 260–269.
Sips, R. (1951). “General theory of deformation of viscoelastic substances.” J. Polym. Sci., 7(2–3), 191–205.
Tamtsia, B., and Beaudoin, J. (2000). “Basic creep of hardened cement paste: A re-examination of the role of water.” Cem. Concr. Res., 30(9), 1465–1475.
Tamtsia, B., Beaudoin, J., and Marchand, J. (2004). “The early age short-term creep of hardening cement paste: Load-induced hydration effects.” Cem. Concr. Compos., 26(5), 481–489.
Thomas, J., and Jennings, H. (2006). “A colloidal interpretation of chemical aging of the C-S-H gel and its effects on the properties of cement paste.” Cem. Concr. Res., 36(1), 30–38.
Torquato, S. (2013). Random heterogeneous materials: Microstructure and macroscopic properties, Vol. 16, Springer, New York.
Valkó, P., and Abate, J. (2004). “Comparison of sequence accelerators for the Gaver method of numerical Laplace transform inversion.” Comput. Math. Appl., 48(3), 629–636.
Vandamme, M., and Ulm, F.-J. (2013). “Nanoindentation investigation of creep properties of calcium silicate hydrates.” Cem. Concr. Res., 52, 38–52.
Zaoui, A. (2002). “Continuum micromechanics: Survey.” J. Eng. Mech., 808–816.
Zhang, Q., Le Roy, R., Vandamme, M., and Zuber, B. (2014). “Long-term creep properties of cementitious materials: Comparing microindentation testing with macroscopic uniaxial compressive testing.” Cem. Concr. Res., 58, 89–98.
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Published In
Journal of Engineering Mechanics
Volume 142 • Issue 12 • December 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 26, 2016
Accepted: Aug 2, 2016
Published online: Oct 14, 2016
Published in print: Dec 1, 2016
Discussion open until: Mar 14, 2017
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