Numerical Method for Predicting Young’s Modulus of Concrete with Aggregate Shape Effect
Publication: Journal of Materials in Civil Engineering
Volume 23, Issue 12
Abstract
Owing to its importance to the structural analysis and design of cement-based materials, it is essential to determine Young’s modulus of concrete. This paper presents a numerical method for predicting Young’s modulus of concrete with aggregate shape effect. In the numerical method, aggregate particles are assumed to be elliptical and distributed within a rectangular concrete element with periodic boundary conditions by introducing an overlap criterion for two elliptical aggregate particles. The method modifies the lattice model to take account of the mechanical properties of each phase constituent of concrete in the analysis of stress. After the validity of the developed numerical method is verified with three independent sets of experimental results, the effects of the maximum aggregate diameter, aggregate gradation, interfacial transition zone (ITZ) thickness, and aggregate shape on Young’s modulus of concrete are evaluated in a quantitative manner. It is found that Young’s modulus of concrete increases with the increase of the maximum aggregate diameter and aggregate aspect ratio but decreases by increasing the ITZ thickness. It is also found that the aggregate gradation has a significant influence on Young’s modulus of concrete. The paper concludes that the numerical method developed in the paper can predict Young’s modulus of concrete with an average relative error smaller than 7%.
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 Basic Research Program (973 Program) with Grant No. UNSPECIFIED2009CB623200, the National Natural Science Foundation with Grant Nos. NNSFC50878196 and NNSFC50838008, and the State Key Laboratory Open Foundation program of Coastal and Offshore Engineering at Dalian University of Technology with Grant No. UNSPECIFIEDLP1001, of the People’s Republic of China, is greatly acknowledged.
References
Azenha, M., Magalhães, F., Faria, R., and Cunha, A. (2010). “Measurement of concrete -modulus evolution since casting: A novel method based on ambient vibration.” Cem. Concr. Res., 40(7), 1096–1105.
Feng, X. Q., and Yu, S. W. (2001). “Effects of reinforcement shape on the effective moduli of composites (I).” J. Tsinghua Univ., 41(11), 8–14 (in Chinese).
George, E. A., Richard, A., and Ranjan, R. (1999). Special functions, Cambridge University Press, Cambridge.
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 modeling with dilated particles.” Eng. Comput., 21(2–4), 422–430.
Lee, K. M., and Park, J. H. (2008). “A numerical model for elastic modulus of concrete considering interfacial transition zone.” Cem. Concr. Res., 38(3), 396–402.
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.
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.
Neville, A. M. (1995). Properties of concrete, Pitman Publishing, London.
Nilsen, A. U., and Monteiro, P. J. M. (1993). “Concrete: A three phase material.” Cem. Concr. Res., 23(1), 147–151.
Ollivier, J. P., Maso, J. C., and Bourdette, B. (1995). “Interfacial transition zone in concrete.” Adv. Cem. Based Mater., 2(1), 30–38.
Perram, J. W., Rasmussen, J., Prastgaard, E., and Lebowitz, J. L. (1996). “Ellipsoid contact potential: Theory and relation to overlap potentials.” Phys. Rev. E, 54(6), 6565–6572.
Remesh, G., Sotelino, E. D., and Chen, W. F. (1996). “Effect of transition zone on elastic moduli of concrete materials.” Cem. Concr. Res., 26(4), 611–622.
Schlangen, E. (1993). Experimental and numerical analysis of fracture processes in concrete, Delft University Press, Delft.
Scrivener, K. L., and Nemati, K. M. (1996). “The percolation of pore space in the cement paste/aggregate interfacial zone of concrete.” Cem. Concr. Res., 26(1), 35–40.
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 modeling of particle packing for material characterization in concrete technology.” Comput. Concr., 6(2), 133–153.
Tesár, A. (1988). Transfer matrix method, Kluwer Academic Publishers, Dordrecht, Netherlands.
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.
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., 17(5), 498–504.
Wen, G. Z. (2009). Structural mechanics, Higher Education Press, Beijing (in Chinese).
Zheng, J. J., Li, C. Q., and Zhao, L. Y. (2003). “Simulation of two-dimensional aggregate distribution with wall effect.” J. Mater. Civ. Eng., 15(5), 506–510.
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.
Information & Authors
Information
Published In
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jun 28, 2010
Accepted: May 4, 2011
Published online: May 6, 2011
Published in print: Dec 1, 2011
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.