Prediction of Elastic Properties of Cementitious Materials Based on Multiphase and Multiscale Micromechanics Theory
Publication: Journal of Engineering Mechanics
Volume 145, Issue 10
Abstract
Prediction of the elastic properties of cementitious materials has been the aim of many researchers. This study developed a new multiscale and multiphase model based on the Mori-Tanaka method for predicting effective elastic properties of hardened cement paste, such as modulus of elasticity. The model considered the microstructural variation in and nonspherical morphology of the hydration products in hardened cement paste. In order to improve prediction accuracy, the model included the effect of ettringite on the elastic properties in addition to the other major hydration products. Instead of considering cement clinker as an isotropic and homogeneous material, this study simulated the clinker as a four-phase composite. In addition, the model used a matrix-inclusion configuration that can include the clinker and ultra-high-density calcium silicate hydrate. Another improvement is that a weakened matrix-inclusion interface was introduced using the modified Eshelby tensor. The prediction results of the model were compared with the experimental data, and good agreement was obtained.
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Acknowledgments
The authors wish to acknowledge the partial support of the US Department of Energy (DOE DE-NE0000659) to University of Colorado at Boulder. Opinions expressed in this paper are those of the authors and do not necessarily reflect those of the sponsor.
References
Acker, P. 2001. “Micromechanical analysis of creep and shrinkage mechanisms.” In Proc., 6th Int. Conf. on Creep, Shrinkage and Durability Mechanics of Concrete and Other Quasi-Brittle Materials, edited by F. J. Ulm, Z. Bazant, and F. Wittmann, 15–26. Amsterdam, Netherlands: Elsevier.
Bentz, D. P., and E. J. Garboczi. 1991. “Percolation of phases in a three-dimensional cement paste microstructural model.” Cem. Concr. Res. 21 (2): 325–344. https://doi.org/10.1016/0008-8846(91)90014-9.
Bogue, R. H. 1929. “Calculation of the compounds in portland cement.” Ind. Eng. Chem. Anal. Ed. 1 (4): 192–197. https://doi.org/10.1021/ac50068a006.
Chen, J., X. Jin, N. Jin, and Y. Tian. 2014. “A nano-model for micromechanics-based elasticity prediction of hardened cement paste.” Mag. Concr. Res. 66 (22): 1145–1153. https://doi.org/10.1680/macr.14.00084.
Chen, J., L. Sorelli, M. Vandamme, F. J. Ulm, and G. Chanvillard. 2010. “A coupled nanoindentation/SEM-EDS study on low water/cement ratio portland cement paste: Evidence for nanocomposites.” J. Am. Ceram. Soc. 93 (5): 1484–1493. https://doi.org/10.1111/j.1551-2916.2009.03599.x.
Constantinides, G., and F. J. Ulm. 2004. “The effect of two types of CSH on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modeling.” Cem. Concr. Res. 34 (1): 67–80. https://doi.org/10.1016/S0008-8846(03)00230-8.
Eshelby, J. D. 1957. “The determination of the elastic field of an ellipsoidal inclusion, and related problems.” Proc. R. Soc. London, Ser. A 241 (1226): 376–396. https://doi.org/10.1098/rspa.1957.0133.
Feldman, R. F. 1972. “Factors affecting Young’s modulus-porosity relation of hydrated portland cement compacts.” Cem. Concr. Res. 2 (4): 375–386. https://doi.org/10.1016/0008-8846(72)90054-3.
Guner, D., H. Ozturk, and M. Erkayaoglu. 2017. “Investigation of the elastic material properties of Class G cement.” Struct. Concr. 18 (1): 84–91. https://doi.org/10.1002/suco.201600020.
Haecker, C. J., E. J. Garboczi, J. W. Bullard, R. B. Bohn, Z. Sun, S. P. Shah, and T. Voigt. 2005. “Modeling the linear elastic properties of Portland cement paste.” Cem. Concr. Res. 35 (10): 1948–1960. https://doi.org/10.1016/j.cemconres.2005.05.001.
Hellmich, C., and H. Mang. 2005. “Shotcrete elasticity revisited in the framework of continuum micromechanics: From submicro to meter level.” J. Eng. Mech. 17 (3): 246–256. https://doi.org/10.1061/(ASCE)0899-1561(2005)17:3(246).
Monteiro, P. J. M., and C. T. Chang. 1995. “The elastic moduli of calcium hydroxide.” Cem. Concr. Res. 25 (8): 1605–1609. https://doi.org/10.1016/0008-8846(95)00154-9.
Mori, T., and K. Tanaka. 1973. “Average stress in matrix and average elastic energy of materials with misfitting inclusions.” Acta Metall. 21 (5): 571–574. https://doi.org/10.1016/0001-6160(73)90064-3.
Mura, T. 2012. Vol. 3 of Micromechanics of defects in solids. Heidelberg, Germany: Springer Science & Business.
Parrot, L. J., and D. C. Killoh. 1984. “Prediction of cement hydration.” In Vol. 35 of Stoke-on-trent, 41–53. Staffs, UK: British Ceramic Society.
Qu, J. 1993. “Eshelby tensor for an elastic inclusion with slightly weakened interface.” J. Appl. Mech. 60 (4): 1048–1050. https://doi.org/10.1115/1.2900974.
Speziale, S., F. Jiang, Z. Mao, P. J. M. Monteiro, H. R. Wenk, T. S. Duffy, and F. R. Schilling. 2008. “Single-crystal elastic constants of natural ettringite.” Cem. Concr. Res. 38 (7): 885–889. https://doi.org/10.1016/j.cemconres.2008.02.004.
Stora, E., Q. C. He, and B. Bary. 2006. “Influence of inclusion shapes on the effective linear elastic properties of hardened cement paste.” Cem. Concr. Res. 36 (7): 1330–1344. https://doi.org/10.1016/j.cemconres.2006.02.007.
Taylor, H. F. W. 1997. Cement chemistry. London: Thomas Telford.
Termkhajornkit, P., Q. H. Vu, R. Barbarulo, S. Daronnat, and G. Chanvillard. 2014. “Dependence of compressive strength on phase assemblage in cement pastes: Beyond gel-space ratio-experimental evidence and micromechanical modeling.” Cem. Concr. Res. 56 (Feb): 1–11. https://doi.org/10.1016/j.cemconres.2013.10.007.
Uchikawa, H., and S. Uchida. 1974. “The analysis of ettringite in hardened cement paste.” Cem. Concr. Res. 4 (5): 821–834. https://doi.org/10.1016/0008-8846(74)90053-2.
Ulm, F. J. 2012. “Nano-engineering of concrete.” Arabian J. Sci. Eng. 37 (2): 481–488. https://doi.org/10.1007/s13369-012-0181-x.
Vandamme, M., and F. J. Ulm. 2009. “Nanogranular origin of concrete creep.” Proc. Natl. Academy Sci. 106 (26): 10552–10557. https://doi.org/10.1073/pnas.0901033106.
Vandamme, M., F. J. Ulm, and P. Fonollosa. 2010. “Nanogranular packing of C─ S─ H at substochiometric conditions.” Cem. Concr. Res. 40 (1): 14–26. https://doi.org/10.1016/j.cemconres.2009.09.017.
Velez, K., S. Maximilien, D. Damidot, G. Fantozzi, and F. Sorrentino. 2001. “Determination by nanoindentation of elastic modulus and hardness of pure constituents of Portland cement clinker.” Cem. Concr. Res. 31 (4): 555–561. https://doi.org/10.1016/S0008-8846(00)00505-6.
Wang, Y., D. Damien, and Y. Xi. 2018. “Micro- and meso-mechanical modeling of effect of freezing on modulus of elasticity of concrete.” Eng. Fract. Mech. 200 (Sep): 401–417. https://doi.org/10.1016/j.engfracmech.2018.08.013.
Zaoui, A. 2002. “Continuum micromechanics: Survey.” J. Eng. Mech. 128 (8): 808–816. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:8(808).
Zheng, J., X. Zhou, L. Shao, and X. Jin. 2010. “Simple three-step analytical scheme for prediction of elastic moduli of hardened cement paste.” J. Mater. Civ. Eng. 22 (11): 1191–1194. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000103.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 10 • October 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Sep 11, 2018
Accepted: Feb 11, 2019
Published online: Jul 24, 2019
Published in print: Oct 1, 2019
Discussion open until: Dec 24, 2019
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