Technical Papers
Nov 7, 2023

Machine Learning–Based Reliability Analysis of Structural Concrete Cracking Considering Realistic Nonuniform Corrosion Development

Publication: Journal of Structural Engineering
Volume 150, Issue 1

Abstract

Corrosion-induced concrete cracking significantly weakens the integrity, serviceability and durability of reinforced concrete (RC) structures. Existing reliability analysis of corrosion-induced concrete cracking often considers the corrosion of reinforcement as a uniform process, in favor of implementing the analytical formulation of corrosion rust progression. However, corrosion distribution in RC structures is seldom uniform around the steel reinforcement, hence the corrosion-induced pressure. Thus, considering the nonuniform corrosion process in the reliability analysis becomes important. This paper develops a time-dependent reliability methodology, combining mesoscale heterogeneous fracture modeling and a state-of-the-art machine learning algorithm, to assess the serviceability of the RC structures subjected to nonuniform development of corrosion. The effects of critical crack width, corrosion nonuniformity, chloride content, temperature, and relative humidity on the failure probability are investigated. The worked example demonstrates the importance of considering the nonuniformity of the corrosion product distribution, which provides reliable evaluation of the remaining safe life of RC structures compared with the use of a uniform corrosion model. The developed unified assessing methodology for corrosion of RC structures can serve as a useful tool for engineers, designers, and asset managers for their decision making with regard to repair and maintenance of corrosion-affected RC structures.

Get full access to this article

View all available purchase options and get full access to this article.

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

Financial support from the UK Engineering and Physical Sciences Research Council (EP/S005560/1 and EP/W027763/1) is thankfully acknowledged. Contributions and useful discussions from Dr. Shen Li and Professor Feargal Brennan from the Department of Navel Architecture, Ocean and Marine Engineering, University of Strathclyde, through the Strathwide funding scheme, are also thankfully acknowledged. This work is also supported by the Fundamental Research Funds for the Central Universities in China (No. 00007738).

References

ACI (American Concrete Institute). 2008. Control of cracking in concrete structures (reapproved 2008). Technical. Lansing, MI: ACI.
Andrade, C., F. J. Molina, and C. Alonso. 1993. “Cover cracking as a function of rebar corrosion: Part 1—Experiment test.” Mater. Struct. 26 (Nov): 453–464. https://doi.org/10.1007/BF02472805.
Angst, U. M. 2018. “Challenges and opportunities in corrosion of steel in concrete.” Mater. Struct. 51 (Feb): 1–20. https://doi.org/10.1617/s11527-017-1131-6.
Baji, H., C.-Q. Li, S. Scicluna, and J. Dauth. 2017. “Risk-cost optimised maintenance strategy for tunnel structures.” Tunnelling Underground Space Technol. 69 (Oct): 72–84. https://doi.org/10.1016/j.tust.2017.06.008.
Best, D. J., and N. I. Fisher. 1979. “Efficient simulation of the von Mises distribution.” J. R. Stat. Soc. C 28 (2): 152–157. https://doi.org/10.2307/2346732.
Biondini, F., and D. M. Frangopol. 2009. “Lifetime reliability-based optimization of reinforced concrete cross-sections under corrosion.” Struct. Saf. 31 (6): 483–489. https://doi.org/10.1016/j.strusafe.2009.06.008.
Chen, E., and C. K. Y. Leung. 2015. “Finite element modeling of concrete cover cracking due to non-uniform steel corrosion.” Eng. Fract. Mech. 134 (Jan): 61–78. https://doi.org/10.1016/j.engfracmech.2014.12.011.
Chen, F., C.-Q. Li, H. Baji, and B. Ma. 2019a. “Effect of design parameters on microstructure of steel-concrete interface in reinforced concrete.” Cem. Concr. Res. 119 (May): 1–10. https://doi.org/10.1016/j.cemconres.2019.01.005.
Chen, J., W. Zhang, and X. Gu. 2019b. “Modeling time-dependent circumferential non-uniform corrosion of steel bars in concrete considering corrosion-induced cracking effects.” Eng. Struct. 201 (Dec): 109766. https://doi.org/10.1016/j.engstruct.2019.109766.
Chen, J., W. Zhang, Z. Tang, and Q. Huang. 2020. “Experimental and numerical investigation of chloride-induced reinforcement corrosion and mortar cover cracking.” Cem. Concr. Compos. 111 (Aug): 103620. https://doi.org/10.1016/j.cemconcomp.2020.103620.
Du, X., L. Jin, and R. Zhang. 2014. “Modeling the cracking of cover concrete due to non-uniform corrosion of reinforcement.” Corros. Sci. 89 (Dec): 189–202. https://doi.org/10.1016/j.corsci.2014.08.025.
fib (Internation Federation for Structural Concrete). 2013. fib model code for concrete structures 2010. Lausanne, Switzerland: fib.
Fu, C., N. Jin, H. Ye, X. Jin, and W. Dai. 2017. “Corrosion characteristics of a 4-year naturally corroded reinforced concrete beam with load-induced transverse cracks.” Corros. Sci. 117 (Mar): 11–23. https://doi.org/10.1016/j.corsci.2017.01.002.
Grassl, P., and T. Davies. 2011. “Lattice modelling of corrosion induced cracking and bond in reinforced concrete.” Cem. Concr. Compos. 33 (9): 918–924. https://doi.org/10.1016/j.cemconcomp.2011.05.005.
Gu, X., H. Guo, B. Zhou, W. Zhang, and C. Jiang. 2018. “Corrosion non-uniformity of steel bars and reliability of corroded RC beams.” Eng. Struct. 167 (Jul): 188–202. https://doi.org/10.1016/j.engstruct.2018.04.020.
Haldar, A., and S. Mahadevan. 2000. Reliability assessment using stochastic finite element analysis. New York: Wiley.
Jamali, A., U. Angst, B. Adey, and B. Elsener. 2013. “Modeling of corrosion-induced concrete cover cracking: A critical analysis.” Constr. Build. Mater. 42 (May): 225–237. https://doi.org/10.1016/j.conbuildmat.2013.01.019.
Jang, B. S., and B. H. Oh. 2010. “Effects of non-uniform corrosion on the cracking and service life of reinforced concrete structures.” Cem. Concr. Res. 40 (9): 1441–1450. https://doi.org/10.1016/j.cemconres.2010.03.018.
Li, C. Q., and R. E. Melchers. 2005. “Time-dependent reliability analysis of corrosion-induced concrete cracking.” ACI Struct. J. 102 (4): 105–116. https://doi.org/10.14359/14558.
Li, C. Q., R. E. Melchers, and J. J. Zheng. 2006. “Analytical model for corrosion-induced crack width in reinforced concrete structures.” ACI Struct. J. 103 (4): 479–487. https://doi.org/10.14359/16423.
Li, C. Q., and S. T. Yang. 2011. “Prediction of concrete crack width under combined reinforcement corrosion and applied load.” J. Eng. Mech. 137 (11): 722–731. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000289.
Li, K., D. Zhang, Q. Li, and Z. Fan. 2019. “Durability for concrete structures in marine environments of HZM project: Design, assessment and beyond.” Cem. Concr. Res. 115 (Jun): 545–558. https://doi.org/10.1016/j.cemconres.2018.08.006.
Liu, Y., and R. E. Weyers. 1998. “Modelling the time-to-corrosion cracking in chloride contaminated reinforced concrete structures.” ACI Mater. J. 95 (6): 675–681. https://doi.org/10.14359/410.
Lu, Z.-H., P.-Y. Lun, W. Li, Z. Luo, Y. Li, and P. Liu. 2018. “Empirical model of corrosion rate for steel reinforced concrete structures in chloride-laden environments.” Adv. Struct. Eng. 22 (1): 223–239. https://doi.org/10.1177/1369433218783313.
Lun, P.-Y., Z.-H. Lu, X.-G. Zhang, Q. Zhang, and R. Zhao. 2021. “Experimental study and suggested mathematical model for chloride-induced reinforcement corrosion rate.” Structures 34 (Dec): 2014–2029. https://doi.org/10.1016/j.istruc.2021.08.099.
Marquardt, D. W. 1963. “An algorithm for least-squares estimation of nonlinear parameters.” J. Soc. Ind. Appl. Math. 11 (2): 431–441. https://doi.org/10.1137/0111030.
Melchers, R. E., and A. T. Beck. 2018. Structural reliability analysis and prediction. New York: Wiley.
Melchers, R. E., C. Q. Li, and M. A. Davison. 2009. “Observations and analysis of a 63-year-old reinforced concrete promenade railing exposed to the North Sea.” Mag. Concr. Res. 61 (4): 233–243. https://doi.org/10.1680/macr.2007.00093.
Mullard, J. A., and M. G. Stewart. 2011. “Corrosion-induced cover cracking: New test data and predictive models.” ACI Struct. J. 108 (1): 71–79. https://doi.org/10.14359/51664204.
Neville, A. M. 2006. Properties of concrete. London: Pearson Education Limited.
Niu, D., S. Wang, Y. Hui, and F. Xing. 2019. Standard for durability assessment of existing concrete structures. GB/T 51355-2019. Beijing: Chinese Standard.
Pan, T., and Y. Lu. 2012. “Stochastic modeling of reinforced concrete cracking due to nonuniform corrosion: FEM-based cross-scale analysis.” J. Mater. Civ. Eng. 24 (6): 698–706. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000427.
Qiao, D., H. Nakamura, Y. Yamamoto, and T. Miura. 2016. “Crack patterns of concrete with a single rebar subjected to non-uniform and localized corrosion.” Constr. Build. Mater. 116 (Jul): 366–377. https://doi.org/10.1016/j.conbuildmat.2016.04.149.
Ren, W., Z. Yang, R. Sharma, C. Zhang, and P. J. Withers. 2015. “Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete.” Eng. Fract. Mech. 133 (Jan): 24–39. https://doi.org/10.1016/j.engfracmech.2014.10.016.
Rosenblatt, F. 1958. “The perceptron: A probabilistic model for information storage and organization in the brain.” Psychol. Rev. 65 (6): 386. https://doi.org/10.1037/h0042519.
Rumelhart, D. E., G. E. Hinton, and R. J. Williams. 1986. “Learning representations by back-propagating errors.” Nature 323 (6088): 533–536. https://doi.org/10.1038/323533a0.
Šavija, B., M. Luković, J. Pacheco, and E. Schlangen. 2013. “Cracking of the concrete cover due to reinforcement corrosion: A two-dimensional lattice model study.” Constr. Build. Mater. 44 (Jul): 626–638. https://doi.org/10.1016/j.conbuildmat.2013.03.063.
Val Dimitri, V. 2007. “Deterioration of strength of RC beams due to corrosion and its influence on beam reliability.” J. Struct. Eng. 133 (9): 1297–1306. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:9(1297).
Vu, K., M. G. Stewart, and J. Mullard. 2005. “Corrosion-induced cracking: Experimental data and predictive models.” ACI Struct. J. 102 (5): 719–726. https://doi.org/10.14359/14667.
Vu, K. A. T., and M. G. Stewart. 2000. “Structural reliability of concrete bridges including improved chloride-induced corrosion models.” Struct. Saf. 22 (4): 313–333. https://doi.org/10.1016/S0167-4730(00)00018-7.
Wong, H. S., Y. X. Zhao, A. R. Karimi, N. R. Buenfeld, and W. L. Jin. 2010. “On the penetration of corrosion products from reinforcing steel into concrete due to chloride-induced corrosion.” Corros. Sci. 52 (7): 2469–2480. https://doi.org/10.1016/j.corsci.2010.03.025.
Xi, X., and S. Yang. 2019. “Investigating the spatial development of corrosion of corner-located steel bar in concrete by X-ray computed tomography.” Constr. Build. Mater. 221 (Oct): 177–189. https://doi.org/10.1016/j.conbuildmat.2019.06.023.
Xi, X., S. Yang, and C.-Q. Li. 2018a. “A non-uniform corrosion model and meso-scale fracture modelling of concrete.” Cem. Concr. Res. 108 (Jun): 87–102. https://doi.org/10.1016/j.cemconres.2018.03.009.
Xi, X., S. Yang, C.-Q. Li, M. Cai, X. Hu, and Z. K. Shipton. 2018b. “Meso-scale mixed-mode fracture modelling of reinforced concrete structures subjected to non-uniform corrosion.” Eng. Fract. Mech. 199 (Aug): 114–130. https://doi.org/10.1016/j.engfracmech.2018.05.036.
Xiao, J., W. Li, D. J. Corr, and S. P. Shah. 2013. “Effects of interfacial transition zones on the stress–strain behavior of modeled recycled aggregate concrete.” Cem. Concr. Res. 52 (Oct): 82–99. https://doi.org/10.1016/j.cemconres.2013.05.004.
Yang, S., X. Xi, K. Li, and C.-Q. Li. 2018. “Numerical modeling of nonuniform corrosion-induced concrete crack width.” J. Struct. Eng. 144 (8): 04018120. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002108.
Ye, H., N. Jin, C. Fu, and X. Jin. 2017. “Rust distribution and corrosion-induced cracking patterns of corner-located rebar in concrete cover.” Constr. Build. Mater. 156 (May): 684–691. https://doi.org/10.1016/j.conbuildmat.2017.09.033.
Yuan, Y., and Y. Ji. 2009. “Modeling corroded section configuration of steel bar in concrete structure.” Constr. Build. Mater. 23 (6): 2461–2466. https://doi.org/10.1016/j.conbuildmat.2008.09.026.
Yuan, Y., Y. Ji, and Y. Mu. 2007. “Propagation and model of distribution for corrosion of steel bars in concrete.” China Civ. Eng. J. 40 (7): 5–10. https://doi.org/10.1016/S1672-6529(07)60007-9.
Zhang, K., and J. Xiao. 2018a. “Prediction model of carbonation depth for recycled aggregate concrete.” Cem. Concr. Compos. 88 (Apr): 86–99. https://doi.org/10.1016/j.cemconcomp.2018.01.013.
Zhang, K., and J. Xiao. 2018b. “Time-dependent reliability analysis on carbonation behavior of recycled aggregate concrete based on gamma process.” Constr. Build. Mater. 158 (Jan): 378–388. https://doi.org/10.1016/j.conbuildmat.2017.09.191.
Zhang, K., J. Xiao, and Q. Zhang. 2021a. “Time-dependent reliability analysis of recycled aggregate concrete cover cracking induced by reinforcement corrosion.” J. Build. Eng. 39 (Jul): 102320. https://doi.org/10.1016/j.jobe.2021.102320.
Zhang, K., J. Xiao, Y. Zhao, and Q. Zhang. 2019. “Analytical model for critical corrosion level of reinforcements to cause the cracking of concrete cover.” Constr. Build. Mater. 223 (Oct): 185–197. https://doi.org/10.1016/j.conbuildmat.2019.06.210.
Zhang, M., M. Akiyama, M. Shintani, J. Xin, and D. M. Frangopol. 2021b. “Probabilistic estimation of flexural loading capacity of existing RC structures based on observational corrosion-induced crack width distribution using machine learning.” Struct. Saf. 91 (Jul): 102098. https://doi.org/10.1016/j.strusafe.2021.102098.
Zhang, Q., P.-Y. Lun, and X. Li. 2021c. “A simplified approach for prediction of concrete resistivity: Experimental study and mathematic model.” Mater. Struct. 54 (Aug): 155. https://doi.org/10.1617/s11527-021-01688-9.
Zhao, Y., B. Hu, J. Yu, and W. Jin. 2011a. “Non-uniform distribution of rust layer around steel bar in concrete.” Corros. Sci. 53 (12): 4300–4308. https://doi.org/10.1016/j.corsci.2011.08.045.
Zhao, Y., A. R. Karimi, H. S. Wong, B. Hu, N. R. Buenfeld, and W. Jin. 2011b. “Comparison of uniform and non-uniform corrosion induced damage in reinforced concrete based on a Gaussian description of the corrosion layer.” Corros. Sci. 53 (9): 2803–2814. https://doi.org/10.1016/j.corsci.2011.05.017.
Zhao, Y., X. Xu, Y. Wang, and J. Dong. 2020. “Characteristics of pitting corrosion in an existing reinforced concrete beam exposed to marine environment.” Constr. Build. Mater. 234 (Feb): 117392. https://doi.org/10.1016/j.conbuildmat.2019.117392.
Zhao, Y., J. Yu, B. Hu, and W. Jin. 2012. “Crack shape and rust distribution in corrosion-induced cracking concrete.” Corros. Sci. 55 (Feb): 385–393. https://doi.org/10.1016/j.corsci.2011.11.002.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 150Issue 1January 2024

History

Received: Nov 15, 2022
Accepted: Sep 6, 2023
Published online: Nov 7, 2023
Published in print: Jan 1, 2024
Discussion open until: Apr 7, 2024

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Xun Xi
Associate Professor, School of Civil and Resource Engineering, Univ. of Science and Technology Beijing, Beijing 100083, China.
Ziqing Yin
Ph.D. Student, Dept. of Civil and Environmental Engineering, Univ. of Strathclyde, Glasgow G1 1XJ, UK.
Senior Lecturer, Dept. of Civil and Environmental Engineering, Univ. of Strathclyde, Glasgow G1 1XJ, UK (corresponding author). ORCID: https://orcid.org/0000-0001-9977-5954. Email: [email protected]
Chun-Qing Li
Professor, School of Engineering, Royal Melbourne Institute of Technology Univ., Melbourne, VIC 3001, Australia.

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.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share