Analytical Prediction of the Young’s Modulus of Concrete with Spheroidal Aggregates
Publication: Journal of Materials in Civil Engineering
Volume 28, Issue 1
Abstract
The Young’s modulus of concrete is an important mechanical parameter for assessing the stiffness of concrete structures. The objective of this paper is to present an analytical method for evaluating the Young’s modulus of concrete with spheroidal aggregates. In this method, the interfacial transition zone (ITZ) between aggregates and the bulk cement paste is treated as an independent phase. To reduce mathematical complexity, the three-phase concrete is decomposed into two two-phase composite materials and modeled through a two-step procedure. After the validity of the analytical method is verified with three sets of experimental data, a sensitivity analysis is conducted to quantify various factors that affect the Young’s modulus of concrete. The numerical results show that the Young’s modulus of concrete increases with the increase of the maximum size and aspect ratio of aggregate but decreases by increasing the ITZ thickness. It is also shown that the aggregate gradation influences the Young’s modulus of concrete to a certain extent.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The financial support from the National Natural Science Foundation with Grant Nos. 51379188, 51378398, and 51178356 and the Natural Science Foundation of Zhejiang Province with Grant No. LY15E090006 of the People’s Republic of China is greatly acknowledged.
References
Azenha, M., Magalhães, F., Faria, R., and Cunha, A. (2010). “Measurement of concrete E-modulus evolution since casting: A novel method based on ambient vibration.” Cem. Concr. Res., 40(7), 1096–1105.
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), 375–396.
Feng, X. Q., and Yu, S. W. (2001). “Effects of reinforcement shape on the effective moduli of composites (I).” J. Tsinghua Univ., 41(11), 8–10 (in Chinese).
Garboczi, E. J., and Berryman, J. G. (2000). “New effective medium theory for the diffusivity or conductivity of a multi-scale concrete microstructure model.” Concr. Sci. Eng., 2(6), 88–96.
Hashin, Z., and Monteiro, P. J. M. (2002). “An inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste.” Cem. Concr. Res., 32(8), 1291–1300.
Hopkins, M. A. (2004). “Discrete element modelling with dilated particles.” Eng. Comput., 21(2–4), 422–430.
Huang, K. Z., Xue, M. D., and Lu, M. W. (1986). Tensor analysis, Tsinghua University Press, Beijing (in Chinese).
Li, G. Q., Zhao, Y., and Pang, S. S. (1999a). “Four-phase sphere modeling of effective bulk modulus of concrete.” Cem. Concr. Res., 29(6), 839–845.
Li, G. Q., Zhao, Y., Pang, S. S., and Li, Y. (1999b). “Effective Young’s modulus estimation of concrete.” Cem. Concr. Res., 29(9), 1455–1462.
Lutz, M. P., Monteiro, P. J. M., and Zimmerman, R. W. (1997). “Inhomogeneous interfacial transition zone model for the bulk modulus of mortar.” Cem. Concr. Res., 27(7), 1113–1122.
Mura, T. (1987). Micromechanics of defects in solids, Martinus Nijhoff, Dordrecht, Netherlands.
Nadeau, J. C. (2003). “A multiscale model for effective moduli of concrete incorporating ITZ water-cement ratio gradients, aggregate size distributions, and entrapped voids.” Cem. Concr. Res., 33(1), 103–113.
Simeonov, P., and Ahmad, S. (1995). “Effect of transition zone on the elastic behaviour of cement-based composites.” Cem. Concr. Res., 25(1), 165–176.
Stock, A. F., Hannant, D. J., and Williams, R. I. T. (1979). “The effect of aggregate concentration upon the strength and modulus of elasticity of concrete.” Mag. Concr. Res., 31(109), 225–234.
Stroeven, P., Hu, J., and Stroeven, M. (2009). “On the usefulness of discrete element computer modelling of particle packing for material characterization in concrete technology.” Comput. Concr., 6(2), 133–153.
Topcu, I. B., Bilir, T., and Boğa, A. R. (2010). “Estimation of the modulus of elasticity of slag concrete by using composite material models.” Constr. Build. Mater., 24(5), 741–748.
Vilardell, J., Aguado, A., Agullo, L., and Gettu, R. (1998). “Estimation of the modulus of elasticity for dam concrete.” Cem. Concr. Res., 28(1), 93–101.
Wang, J. A., Lubliner, J., and Monteiro, P. J. M. (1988). “Effect of ice formation on the elastic moduli of cement paste and mortar.” Cem. Concr. Res., 18(6), 874–885.
Wang, L. B., Wang, X. R., Mohammad, L., and Abadie, C. (2005). “Unified method to quantify aggregate shape angularity and texture using Fourier analysis.” J. Mater. Civ. Eng., 498–504.
Zheng, J. J., Li, C. Q., and Zhou, X. Z. (2005). “Thickness of interfacial transition zone and cement content profiles around aggregates.” Mag. Concr. Res., 57(7), 397–406.
Zheng, J. J., Li, C. Q., and Zhou, X. Z. (2006). “An analytical method for prediction of the elastic modulus of concrete.” Mag. Concr. Res., 58(10), 665–673.
Zheng, J. J., Xiong, F. F., Wu, Z. M., and Jin, W. L. (2009). “A numerical algorithm for the ITZ area fraction in concrete with elliptical aggregate particles.” Mag. Concr. Res., 61(2), 109–117.
Zheng, J. J., Zhou, X. Z., Wu, Y. F., and Jin, X. Y. (2012). “A numerical method for the chloride diffusivity in concrete with aggregate shape effect.” Constr. Build. Mater., 31(6), 151–156.
Zheng, Q. S., and Du, D. X. (2001). “An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution.” J. Mech. Phys. Solids, 49(11), 2765–2788.
Information & Authors
Information
Published In
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Sep 21, 2014
Accepted: Mar 26, 2015
Published online: May 28, 2015
Discussion open until: Oct 28, 2015
Published in print: Jan 1, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.