Technical Papers
Aug 25, 2022

Chloride Diffusion Prediction in Concrete through Mathematical Models Based on Time–Dependent Diffusion Coefficient and Surface Chloride Concentration

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Publication: Journal of Materials in Civil Engineering
Volume 34, Issue 11

Abstract

This paper compared several mathematical models predicting chloride penetration in concrete by employing a time-dependent diffusion coefficient for a number of analytical solutions of Fick’s second law. We propose calibrated models that consider a time-dependent build-up of the surface chloride concentration Cs. Predicted values and measured values of chloride profiles from experimental results were compared, which showed that the calibrated models considering a time-dependent surface chloride concentration could significantly improve the correlation compared with the conventional models employing a constant surface chloride concentration. Moreover, we investigated several factors (i.e., skin effect, aging factor m, exposure conditions, curing conditions, water/binder ratio, and fly ash content) that may affect chloride penetration in concrete by adopting the calibrated models. The results showed conclusively that these factors also significantly affected the accuracy of the chloride penetration obtained by these calibrated models. Finally, the results predicted by the calibrated Tang–Gulikers model were proved to be reasonably accurate in concrete with a small water/binder ratio compared with the experimental data. It is concluded that the calibrated Tang–Gulikers model can be applied for predicting chloride penetration and solving relevant service-life problems resulting from chloride ingress in concrete.

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Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors acknowledge Professor Fekri Meftah for his valuable discussions and constructive suggestions to improve this paper. The authors also are very grateful to all anonymous reviewers for their insightful comments.

References

Al-alaily, H. S., and A. A. A. Hassan. 2016. “Time-dependence of chloride diffusion for concrete containing metakaolin.” J. Build. Eng. 7 (Sep): 159–169. https://doi.org/10.1016/j.jobe.2016.06.003.
Andrade, C., M. A. Climent, and G. de Vera. 2015. “Procedure for calculating the chloride diffusion coefficient and surface concentration from a profile having a maximum beyond the concrete surface.” Mater. Struct. 48 (4): 863–869. https://doi.org/10.1617/s11527-015-0543-4.
Ann, K. Y., J. H. Ahn, and J. S. Ryou. 2009. “The importance of chloride content at the concrete surface in assessing the time to corrosion of steel in concrete structures.” Constr. Build. Mater. 23 (1): 239–245. https://doi.org/10.1016/j.conbuildmat.2007.12.014.
Bamforth, P. B. 1999. “The derivation of input data for modelling chloride ingress from eight-year UK coastal exposure trials.” Mag. Concr. Res. 51 (2): 87–96. https://doi.org/10.1016/j.jclepro.2019.01.335.
Ben Fraj, A., S. Bonnet, and A. Khelidj. 2012. “New approach for coupled chloride/moisture transport in non-saturated concrete with and without slag.” Constr. Build. Mater. 35 (Oct): 761–771. https://doi.org/10.1016/j.conbuildmat.2012.04.106.
Boddy, A., E. Bentz, M. D. A. Thomas, and R. D. Hooton. 1999. “An overview and sensitivity study of a multimechanistic chloride transport model.” Cem. Concr. Res. 29 (6): 827–837. https://doi.org/10.1016/S0008-8846(99)00045-9.
Buenfeld, N. R., G. K. Glass, A. M. Hassanein, and J.-Z. Zhang. 1998. “Chloride transport in concrete subjected to electric field.” J. Mater. Civ. Eng. 10 (4): 220–228. https://doi.org/10.1061/(ASCE)0899-1561(1998)10:4(220).
Cai, R., Y. Hu, M. Yu, W. Liao, L. Yang, A. Kumar, and H. Ma. 2020. “Skin effect of chloride ingress in marine concrete: A review on the convection zone.” Constr. Build. Mater. 262 (Nov): 120566. https://doi.org/10.1016/j.conbuildmat.2020.120566.
Chalee, W., C. Jaturapitakkul, and P. Chindaprasirt. 2009. “Predicting the chloride penetration of fly ash concrete in seawater.” Mar. Struct. 22 (3): 341–353. https://doi.org/10.1016/j.marstruc.2008.12.001.
Cheewaket, T., C. Jaturapitakkul, and W. Chalee. 2010. “Long term performance of chloride binding capacity in fly ash concrete in a marine environment.” Constr. Build. Mater. 24 (8): 1352–1357. https://doi.org/10.1016/j.conbuildmat.2009.12.039.
Chindaprasirt, P., C. Chotithanorm, H. T. Cao, and V. Sirivivatnanon. 2007. “Influence of fly ash fineness on the chloride penetration of concrete.” Constr. Build. Mater. 21 (2): 356–361. https://doi.org/10.1016/j.conbuildmat.2005.08.010.
Costa, A., and J. Appleton. 1999a. “Chloride penetration into concrete in marine environment—Part I: Main parameters affecting chloride penetration.” Mater. Struct. 32 (4): 252. https://doi.org/10.1007/BF02479594.
Costa, A., and J. Appleton. 1999b. “Chloride penetration into concrete in marine environment—Part II: Prediction of long term chloride penetration.” Mater. Struct. 32 (5): 354–359. https://doi.org/10.1007/BF02479627.
Crank, J. 1979. The mathematics of diffusion. Oxford, UK: Clarendon.
Dhir, R. K., and M. R. Jones. 1999. “Development of chloride-resisting concrete using fly ash.” Fuel 78 (2): 137–142. https://doi.org/10.1016/S0016-2361(98)00149-5.
Frederiksen, J. M., L. Mejlbro, and L.-O. Nilsson. 2009. Fick’s 2nd law—Complete solutions for chloride ingress into concrete—With focus on time dependent diffusivity and boundary condition. Division of Building Materials, LTH, Lund Univ.
Glass, G. K., and N. R. Buenfeld. 2000a. “Chloride-induced corrosion of steel in concrete.” Prog. Struct. Mater. Eng. 2 (4): 448–458. https://doi.org/10.1002/pse.54.
Glass, G. K., and N. R. Buenfeld. 2000b. “The influence of chloride binding on the chloride induced corrosion risk in reinforced concrete.” Corros. Sci. 42 (2): 329–344. https://doi.org/10.1016/S0010-938X(99)00083-9.
Huang, H., X. Wang, and X. Ma. 2016. “A comparison study of solving diffusion equations with different algorithm methods.” AIP Adv. 6 (12): 125043. https://doi.org/10.1063/1.4972953.
Huang, Q., Z. Jiang, X. Gu, W. Zhang, and B. Guo. 2015. “Numerical simulation of moisture transport in concrete based on a pore size distribution model.” Cem. Concr. Res. 67 (Jan): 31–43. https://doi.org/10.1016/j.cemconres.2014.08.003.
Liu, Q., D. Easterbrook, J. Yang, and L. Li. 2015. “A three-phase, multi-component ionic transport model for simulation of chloride penetration in concrete.” Eng. Struct. 86 (Mar): 122–133. https://doi.org/10.1016/j.engstruct.2014.12.043.
Lorente, S., M.-P. Yssorche-Cubaynes, and J. Auger. 2011. “Sulfate transfer through concrete: Migration and diffusion results.” Cem. Concr. Compos. 33 (7): 735–741. https://doi.org/10.1016/j.cemconcomp.2011.05.001.
Lu, C., Y. Gao, Z. Cui, and R. Liu. 2015. “Experimental analysis of chloride penetration into concrete subjected to drying–wetting cycles.” J. Mater. Civ. Eng. 27 (12): 04015036. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001304.
Mangat, P. S., and M. C. Limbachiya. 1999. “Effect of initial curing on chloride diffusion in concrete repair materials.” Cem. Concr. Res. 29 (9): 1475–1485. https://doi.org/10.1016/S0008-8846(99)00130-1.
Mangat, P. S., and B. T. Molloy. 1994. “Prediction of long term chloride concentration in concrete.” Mater. Struct. 27 (6): 338. https://doi.org/10.1007/BF02473426.
McPolin, D., P. A. M. Basheer, A. E. Long, K. T. V. Grattan, and T. Sun. 2005. “Obtaining progressive chloride profiles in cementitious materials.” Constr. Build. Mater. 19 (9): 666–673. https://doi.org/10.1016/j.conbuildmat.2005.02.015.
Muthulingam, S., and B. N. Rao. 2016. “Chloride binding and time-dependent surface chloride content models for fly ash concrete.” Front. Struct. Civ. Eng. 10 (1): 112–120. https://doi.org/10.1007/s11709-015-0322-x.
Nielsen, E. P., and M. R. Geiker. 2003. “Chloride diffusion in partially saturated cementitious material.” Cem. Concr. Res. 33 (1): 133–138. https://doi.org/10.1016/S0008-8846(02)00939-0.
Nokken, M., A. Boddy, R. D. Hooton, and M. D. A. Thomas. 2006. “Time dependent diffusion in concrete—Three laboratory studies.” Cem. Concr. Res. 36 (1): 200–207. https://doi.org/10.1016/j.cemconres.2004.03.030.
Pack, S.-W., M.-S. Jung, H.-W. Song, S.-H. Kim, and K. Y. Ann. 2010. “Prediction of time dependent chloride transport in concrete structures exposed to a marine environment.” Cem. Concr. Res. 40 (2): 302–312. https://doi.org/10.1016/j.cemconres.2009.09.023.
Papadakis, V. G. 2000. “Effect of supplementary cementing materials on concrete resistance against carbonation and chloride ingress.” Cem. Concr. Res. 30 (2): 291–299. https://doi.org/10.1016/S0008-8846(99)00249-5.
Petcherdchoo, A. 2013. “Time dependent models of apparent diffusion coefficient and surface chloride for chloride transport in fly ash concrete.” Constr. Build. Mater. 38 (Jan): 497–507. https://doi.org/10.1016/j.conbuildmat.2012.08.041.
Song, L., W. Sun, and J. Gao. 2013. “Time dependent chloride diffusion coefficient in concrete.” J. Wuhan Univ. Technol.-Mater. Sci. Ed. 28 (2): 314–319. https://doi.org/10.1007/s11595-013-0685-6.
Tang, L. 2008. “Engineering expression of the ClinConc model for prediction of free and total chloride ingress in submerged marine concrete.” Cem. Concr. Res. 38 (8): 1092–1097. https://doi.org/10.1016/j.cemconres.2008.03.008.
Tang, L., and M. Frederiksen, U. M. Angst, R. Polder, M. C. Alonso, B. Elsener, D. Hooton, J. Pacheco. 2018. “Experiences from RILEM TC 235-CTC in recommending a test method for chloride threshold values in concrete.” RILEM Tech. Lett. 3: 25–31. https://doi.org/10.21809/rilemtechlett.2018.55.
Tang, L., and J. Gulikers. 2007. “On the mathematics of time-dependent apparent chloride diffusion coefficient in concrete.” Cem. Concr. Res. 37 (4): 589–595. https://doi.org/10.1016/j.cemconres.2007.01.006.
Thomas, M. D. A., and P. B. Bamforth. 1999. “Modelling chloride diffusion in concrete: Effect of fly ash and slag.” Cem. Concr. Res. 29 (4): 487–495. https://doi.org/10.1016/S0008-8846(98)00192-6.
Thomas, M. D. A., and E. G. Moffatt. 2018. Performance of Concrete in Marine Environment. Leeds, West Yorkshire: Univ. of Leeds.
Van den Heede, P., M. De Keersmaecker, A. Elia, A. Adriaens, and N. De Belie. 2017. “Service life and global warming potential of chloride exposed concrete with high volumes of fly ash.” Cem. Concr. Compos. 80 (Jul): 210–223.
Wang, H.-L., J.-G. Dai, X.-Y. Sun, and X.-L. Zhang. 2016. “Time-dependent and stress-dependent chloride diffusivity of concrete subjected to sustained compressive loading.” J. Mater. Civ. Eng. 28 (8): 04016059. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001578.
Xiong, Q. X., and F. Meftah. 2021. “Determination on pore size distribution by a probabilistic porous network subjected to salt precipitation and dissolution.” Comput. Mater. Sci. 195 (Jul): 110491. https://doi.org/10.1016/j.commatsci.2021.110491.
Yuan, Q., C. Shi, G. De Schutter, D. Deng, and F. He. 2011. “Numerical model for chloride penetration into saturated concrete.” J. Mater. Civ. Eng. 23 (3): 305–311. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000168.
Zhang, J.-Z., I. M. McLoughlin, and N. R. Buenfeld. 1998. “Modelling of chloride diffusion into surface-treated concrete.” Cem. Concr. Compos. 20 (4): 253–261. https://doi.org/10.1016/S0958-9465(98)00003-1.
Zhang, Y., J. Zhang, W. Luo, J. Wang, J. Shi, H. Zhuang, and Y. Wang. 2019. “Effect of compressive strength and chloride diffusion on life cycle CO2 assessment of concrete containing supplementary cementitious materials.” J. Cleaner Prod. 218 (May): 450–458. https://doi.org/10.1016/j.jclepro.2019.01.335.

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Go to Journal of Materials in Civil Engineering
Journal of Materials in Civil Engineering
Volume 34Issue 11November 2022

History

Received: Apr 8, 2021
Accepted: Feb 16, 2022
Published online: Aug 25, 2022
Published in print: Nov 1, 2022
Discussion open until: Jan 25, 2023

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Ph.D. Candidate, Laboratoire Génie Civil & Génie Mécanique, Institut National des Sciences Appliquées de Rennes, Rennes 35700, France. ORCID: https://orcid.org/0000-0002-6686-275X. Email: [email protected]
Associate Professor, State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong Univ., Shanghai 200240, China (corresponding author). ORCID: https://orcid.org/0000-0001-5437-4946. Email: [email protected]
Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Case Western Reserve Univ., Cleveland, OH 44106. ORCID: https://orcid.org/0000-0002-3704-6198. Email: [email protected]
Chuan Chen, S.M.ASCE [email protected]
Ph.D. Candidate, Laboratoire Génie Civil & Génie Mécanique, Institut National des Sciences Appliquées de Rennes, Rennes 35700, France. Email: [email protected]

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