Three-Phase Composite Sphere Model for the Prediction of Chloride Diffusivity of Concrete
Publication: Journal of Materials in Civil Engineering
Volume 20, Issue 3
Abstract
In predicting the chloride diffusivity of concrete as a three-phase material, the morphological characteristics of the three phases, the physical properties of each phase constituent material, and the interactions of the three phases in the concrete matrix should all be taken into account. The present paper attempts to develop an analytical method to achieve this. A three-phase composite sphere model for the concrete matrix is proposed to represent the heterogeneous nature of concrete and a closed form solution for the chloride diffusivity of concrete is derived. After verifying the derived closed form solution with experimental results, the effects of key factors that affect the chloride diffusivity of concrete, namely the chloride diffusivity and thickness of the interfacial transition zone (ITZ), the maximum aggregate diameter, and the aggregate gradation are examined in a quantitative manner. It is found in the paper that the most important factor influencing the chloride diffusivity of concrete is the chloride diffusivity of ITZ. When the aggregate volume fraction is equal to 0.8, the relative chloride diffusivity of concrete to cement paste for a given relative chloride diffusivity of ITZ to cement paste at 10 is almost four times that for a given relative chloride diffusivity of ITZ to cement paste at 2. The second most important factor is the thickness of ITZ. When the aggregate volume fraction is equal to 0.8, the relative chloride diffusivity of concrete to cement paste for a given ITZ thickness at increases by 76% as compared to that for a given ITZ thickness at . The least important factors are the maximum aggregate diameter and aggregate gradation. The extent to which they influence the chloride diffusivity of concrete is in the range of 10–55%. The paper concludes that the closed form solution derived here can predict the chloride diffusivity of concrete with reasonable accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The financial support of the National Natural Science Foundation via Grant No. NNSFC50578147 and the Natural Science Foundation of Zhejiang Province via Grant No. UNSPECIFIEDY107638, both of the P. R. China, is greatly acknowledged. All reviewers’ constructive comments and suggestions are gratefully appreciated.
References
Bourdette, B., Ringot, E., and Ollivier, J. P. (1995). “Modelling of the transition zone porosity.” Cem. Concr. Res., 25(4), 741–751.
Caré, S. (2003). “Influence of aggregate on chloride diffusivity into mortar.” Cem. Concr. Res., 33(7), 1021–1028.
Crank, J. (1975). The mathematics of diffusion, Clarendon, Oxford.
Delagrave, A., Bigas, J. P., Ollivier, J. P., Marchand, J., and Pigeon, M. (1997). “Influence of the interfacial zone on the chloride diffusivity of mortars.” Adv. Cem. Based Mater., 5(3-4), 86–92.
Devore, J. L. (1995). Probability and statistics for engineering and the sciences, Duxbury, Belmont, Calif.
Garboczi, E. J., and Bentz, D. P. (1997). “Analytical formulas for interfacial transition zone properties.” Adv. Cem. Based Mater., 6(3-4), 99–108.
Garboczi, E. J., Schwartz, L. M., and Bentz, D. P. (1995). “Modeling the influence of the interfacial zone on the DC electrical conductivity of mortar.” Adv. Cem. Based Mater., 2(5), 169–181.
Li, C. Q., Zheng, J. J., Zhou, X. Z., and McCarthy, M. J. (2003). “A numerical method for the prediction of elastic modulus of concrete.” Mag. Concrete Res., 55(6), 497–506.
Li, G., Zhao, Y., and Pang, S. S. (1999). “Four-phase sphere modelling of effective bulk modulus of concrete.” Cem. Concr. Res., 29(6), 839–845.
Lu, B. L., and Torquato, S. (1992). “Nearest-surface distribution functions for polydispersed particle system.” Phys. Rev. A, 45(8), 5530–5544.
Mindess, S. (1989). “Interface in concrete.” Materials science of concrete I, J. P. Skalny, ed., American Ceramic Society, Westerville, 163–180.
Mura, T. (1987). Micromechanics of defects in solids, Martinus Nijhoff, Dordrecht, The Netherlands.
Neville, A. M. (1995). Properties of concrete, Pitmann, 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.
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.
Shah, S. P. (2000). “High performance concrete: Past, present and future.” High performance concrete—Workability, strength and durability, S. P. Shah, C. K. Y. Leung, Z. Li, and J. T. Ding, eds., Hong Kong University of Science and Technology, Hong Kong, 3–29.
Yang, C. C., and Cho, S. W. (2003). “Influence of aggregate content on the migration coefficient of concrete materials using electrochemical method.” Mater. Chem. Phys., 80(3), 752–757.
Yang, C. C., and Su, J. K. (2002). “Approximate migration coefficient of interfacial transition zone and the effect of the aggregate content on the migration coefficient of mortar.” Cem. Concr. Res., 32(10), 1559–1565.
Zheng, J. J. (2000). Mesostructure of concrete—Stereological analysis and some mechanical implications, Delft University Press, Delft, The Netherlands.
Zheng, J. J., and Li, C. Q. (2002). “Three-dimensional aggregate density in concrete with wall effect.” ACI Mater. J., 99(6), 568–575.
Zheng, J. J., Li, C. Q., and Zhao, L. Y. (2003). “Simulation of 2D aggregate distribution with wall effect.” J. Mater. Civ. Eng., 15(5), 506–510.
Zheng, J. J., Li, C. Q., and Zhou, X. Z. (2005). “Characterization of the microstructure of interfacial transition zone in concrete.” ACI Mater. J., 102(4), 265–271.
Information & Authors
Information
Published In
Journal of Materials in Civil Engineering
Volume 20 • Issue 3 • March 2008
Pages: 205 - 211
Copyright
© 2008 ASCE.
History
Received: Nov 16, 2005
Accepted: Jun 8, 2007
Published online: Mar 1, 2008
Published in print: Mar 2008
Notes
Note. Associate Editor: Jason Weiss
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.