Predicting the Remaining Useful Life of Corroding Bridge Girders Using Bayesian Updating
Publication: Journal of Performance of Constructed Facilities
Volume 35, Issue 5
Abstract
This paper developed a model for predicting the temporal failure probability of prestressed concrete (PC) highway bridges. The model updates predictions based on data from nondestructive testing and visual inspections. Chloride-induced corrosion is taken as the main cause for deterioration, and a gamma process describes the reduction in structural capacity. A nonhomogeneous Poisson process models vehicle arrival, in which the vehicle load variability follows a two-peak lognormal mixture distribution. After each inspection, Bayesian inference updates select model parameters and, consequently, the associated temporal structural resistance. Bridge managers can use the updated failure probability predictions to evaluate the remaining useful life of the bridge and determine the maintenance scheme and budget accordingly. A real bridge example illustrated the methodology and justified the probability distributions used for deterioration and vehicle load. Through comparisons with three existing methods, we argued that the proposed model provides more-conservative recommendations, yet existing methods tend to underestimate failure probabilities.
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 (the bridge design drafts and the inspection data).
Acknowledgments
The authors thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for the financial support under Grant No. RGPIN-2018-0.
References
AASHTO. 2002. Standard specifications for highway bridges. AASHTO HB-17. Washington, DC: AASHTO.
Abdel-Hameed, M. 1975. “A gamma wear process.” IEEE Trans. Reliab. R-24 (2): 152–153. https://doi.org/10.1109/TR.1975.5215123.
Ahmad, S. 2003. “Reinforcement corrosion in concrete structures, its monitoring and service life prediction––A review.” Cem. Concr. Compos. 25 (4–5): 459–471. https://doi.org/10.1016/S0958-9465(02)00086-0.
Akiyama, M., D. M. Frangopol, and I. Yoshida. 2010. “Time-dependent reliability analysis of existing RC structures in a marine environment using hazard associated with airborne chlorides.” Eng. Struct. 32 (11): 3768–3779. https://doi.org/10.1016/j.engstruct.2010.08.021.
Alonso, C., C. Andrade, and J. A. Gonzalez. 1988. “Relation between resistivity and corrosion rate of reinforcements in carbonated mortar made with several cement types.” Cem. Concr. Res. 18 (5): 687–698. https://doi.org/10.1016/0008-8846(88)90091-9.
Crank, J. 1979. The mathematics of diffusion. New York: Oxford University Press.
CSA (Canadian Standards Association). 2019. Canadian highway bridge design code. Mississauga, ON: CSA Group.
Dai, K., B. H. Smith, S.-E. Chen, and L. Sun. 2014. “Comparative study of bridge management programmes and practices in the USA and China.” Struct. Infrastruct. Eng. 10 (5): 577–588. https://doi.org/10.1080/15732479.2012.757332.
Darmawan, M. S., and M. G. Stewart. 2007. “Spatial time-dependent reliability analysis of corroding pretensioned prestressed concrete bridge girders.” Struct. Saf. 29 (1): 16–31. https://doi.org/10.1016/j.strusafe.2005.11.002.
Du, Y. G., L. A. Clark, and A. H. C. Chan. 2005. “Residual capacity of corroded reinforcing bars.” Mag. Concr. Res. 57 (3): 135–147. https://doi.org/10.1680/macr.2005.57.3.135.
Ellingwood, B. R., and Y. Mori. 1993. “Probabilistic methods for condition assessment and life prediction of concrete structures in nuclear power plants.” Nucl. Eng. 142 (2–3): 155–166. https://doi.org/10.1016/0029-5493(93)90199-J.
Enright, M. P., and D. M. Frangopol. 1999. “Condition prediction of deteriorating concrete bridges using Bayesian updating.” J. Struct. Eng. 125 (10): 1118–1125. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:10(1118).
Enright, M. P., and D. M. Frangopol. 2000. “Survey and evaluation of damaged concrete bridges.” J. Bridge Eng. 5 (1): 31–38. https://doi.org/10.1061/(ASCE)1084-0702(2000)5:1(31).
Estes, A. C., and D. M. Frangopol. 2003. “Updating bridge reliability based on bridge management systems visual inspection results.” J. Bridge Eng. 8 (6): 374–382. https://doi.org/10.1061/(ASCE)1084-0702(2003)8:6(374).
Fouladirad, M., and A. Grall. 2011. “Condition-based maintenance for a system subject to a non-homogeneous wear process with a wear rate transition.” Reliab. Eng. Syst. Saf. 96 (6): 611–618. https://doi.org/10.1016/j.ress.2010.12.008.
Frangopol, D. M., J. S. Kong, and E. S. Gharaibeh. 2001. “Reliability-based life-cycle management of highway bridges.” J. Comput. Civ. Eng. 15 (1): 27–34. https://doi.org/10.1061/(ASCE)0887-3801(2001)15:1(27).
Gerlough, D. L., and A. Schuhl. 1955. Use of Poisson distribution in highway traffic. Saugatuck, CT: Eno Foundation for Highway Traffic Control.
Hong, F., and J. A. Prozzi. 2006. “Estimation of pavement performance deterioration using Bayesian approach.” J. Infrastruct. Syst. 12 (2): 77–86. https://doi.org/10.1061/(ASCE)1076-0342(2006)12:2(77).
Jacinto, L., L. C. Neves, and L. O. Santos. 2016. “Bayesian assessment of an existing bridge: A case study.” Struct. Infrastruct. Eng. 12 (1): 61–77. https://doi.org/10.1080/15732479.2014.995105.
Jiang, J., F. Ni, L. Gao, and S. Lou. 2016. “Developing an optional multiple repeated load test to evaluate permanent deformation of asphalt mixtures based on axle load spectrum.” Constr. Build. Mater. 122 (Sep): 254–263. https://doi.org/10.1016/j.conbuildmat.2016.05.006.
Khanzada, K. M. 2013. “State of bridge management in Canada.” M.S. thesis, Construction Management and Engineering, North Dakota State Univ.
Li, D., M. Tan, S. Zhang, and J. Ou. 2018. “Stress corrosion damage evolution analysis and mechanism identification for prestressed steel strands using acoustic emission technique.” Struct. Control Health Monit. 25 (8): e2189. https://doi.org/10.1002/stc.2189.
Li, F., Y. Yuan, and C.-Q. Li. 2011. “Corrosion propagation of prestressing steel strands in concrete subject to chloride attack.” Constr. Build. Mater. 25 (10): 3878–3885. https://doi.org/10.1016/j.conbuildmat.2011.04.011.
Li, Q., C. Wang, and B. R. Ellingwood. 2015. “Time-dependent reliability of aging structures in the presence of non-stationary loads and degradation.” Struct. Saf. 52 (Jan): 132–141. https://doi.org/10.1016/j.strusafe.2014.10.003.
Liu, M., and D. M. Frangopol. 2005. “Bridge annual maintenance prioritization under uncertainty by multiobjective combinatorial optimization.” Comput.-Aided Civ. Infrastruct. Eng. 20 (5): 343–353. https://doi.org/10.1111/j.1467-8667.2005.00401.x.
Liu, T., and R. W. Weyers. 1998. “Modeling the dynamic corrosion process in chloride contaminated concrete structures.” Cem. Concr. Res. 28 (3): 365–379. https://doi.org/10.1016/S0008-8846(98)00259-2.
Lu, Z.-H., F. Li, and Y.-G. Zhao. 2016. “An investigation of degradation of mechanical behaviour of prestressing strands subjected to chloride attacking.” In Proc., 5th Int. Conf. on Durability of Concrete Structures, 57–65. Shenzhen, China: Purdue Scholarly Publishing Services.
Macea, L. F., L. Márquez, and H. LLinás. 2015. “Improvement of axle load spectra characterization by a mixture of three distributions.” J. Transp. Eng. 141 (12): 04015030. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000801.
Mejlbro, L. 1996. “The complete solution of Fick’s second law of diffusion with time-dependent diffusion coefficient and surface concentration.” Durability Concr. Saline Environ. 25 (3): 127–158.
Menn, C. 2012. Prestressed concrete bridges. Basel, Switzerland: Birkhäuser.
Ministry of Transport of the People’s Republic of China. 1999. Unified standard for reliability design of highway engineering structures. [In Chinese.] GB/T 50283-1999. Beijing: China Planning Press.
Ministry of Transport of the People’s Republic of China. 2004. Code for maintenance of highway bridges and culverts. [In Chinese.] JTG H11-2004. Beijing: CCCC Highway Consultants.
Ministry of Transport of the People’s Republic of China. 2014. Technical standard of highway engineering. [In Chinese.] JTG B01-2014. Beijing: China Communications Press.
Ministry of Transport of the People’s Republic of China. 2018. Specifications for design of highway reinforced concrete and prestressed concrete bridges and culverts. [In Chinese.] JTG 3362-2018. Beijing: China Communications Press.
Mirza, S. A., D. K. Kikuchi, and J. G. MacGregor. 1980. “Flexural strength reduction factor for bonded prestressed concrete beams.” ACI J. Proc. 77: 237–246.
Neville, A. 1995. “Chloride attack of reinforced concrete: An overview.” Mater. Struct. 28 (2): 63. https://doi.org/10.1007/BF02473172.
Otieno, M., H. Beushausen, and M. Alexander. 2016. “Chloride-induced corrosion of steel in cracked concrete—Part II: Corrosion rate prediction models.” Cem. Concr. Res. 79 (Jan): 386–394. https://doi.org/10.1016/j.cemconres.2015.08.008.
Ramseyer, C., and T. H.-K. Kang. 2012. “Post-damage repair of prestressed concrete girders.” Int. J. Concr. Struct. Mater. 6 (3): 199–207. https://doi.org/10.1007/s40069-012-0019-7.
Rehman, S. K. U., Z. Ibrahim, S. A. Memon, and M. Jameel. 2016. “Nondestructive test methods for concrete bridges: A review.” Constr. Build. Mater. 107 (Mar): 58–86. https://doi.org/10.1016/j.conbuildmat.2015.12.011.
Shipman, C. L. 2014. “Finding maximum moment: Determining HL-93 truck position on simple spans.” J. Bridge Eng. 19 (6): 06014003. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000591.
Srikanth, I., and M. Arockiasamy. 2020. “Deterioration models for prediction of remaining useful life of timber and concrete bridges: A review.” J. Traffic Transp. Eng. 7 (2): 152–173. https://doi.org/10.1016/j.jtte.2019.09.005.
Stewart, M. G. 2004. “Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure.” Struct. Saf. 26 (4): 453–470. https://doi.org/10.1016/j.strusafe.2004.03.002.
Stewart, M. G., and D. V. Rosowsky. 1998. “Time-dependent reliability of deteriorating reinforced concrete bridge decks.” Struct. Saf. 20 (1): 91–109. https://doi.org/10.1016/S0167-4730(97)00021-0.
Suo, Q., and M. G. Stewart. 2009. “Corrosion cracking prediction updating of deteriorating RC structures using inspection information.” Reliab. Eng. Syst. Saf. 94 (8): 1340–1348. https://doi.org/10.1016/j.ress.2009.02.011.
Tu, B., Y. Dong, and Z. Fang. 2019. “Time-dependent reliability and redundancy of corroded prestressed concrete bridges at material, component, and system levels.” J. Bridge Eng. 24 (9): 04019085. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001461.
Val, D. V., and R. E. Melchers. 1997. “Reliability of deteriorating RC slab bridges.” J. Struct. Eng. 123 (12): 1638–1644. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:12(1638).
Val, D. V., and P. A. Trapper. 2008. “Probabilistic evaluation of initiation time of chloride-induced corrosion.” Reliab. Eng. Syst. Saf. 93 (3): 364–372. https://doi.org/10.1016/j.ress.2006.12.010.
van Noortwijk, J. M. 2009. “A survey of the application of gamma processes in maintenance.” Reliab. Eng. Syst. Saf. 94 (1): 2–21. https://doi.org/10.1016/j.ress.2007.03.019.
van Noortwijk, J. M., J. M. van der Weide, M. J. Kallen, and M. D. Pandey. 2007. “Gamma processes and peaks-over-threshold distributions for time-dependent reliability.” Reliab. Eng. Syst. Saf. 92 (12): 1651–1658. https://doi.org/10.1016/j.ress.2006.11.003.
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.
Xu, G., and V. Makis. 2019. “Bayesian update of the residual life of a concrete structure using inspection data.” In Proc., 4th Int. Conf. on Civil, Structural and Transportation Engineering. Ottawa: ICCSTE.
Yanaka, M., S. H. Ghasemi, and A. S. Nowak. 2016. “Reliability-based and life-cycle cost-oriented design recommendations for prestressed concrete bridge girders.” Struct. Concr. 17 (5): 836–847. https://doi.org/10.1002/suco.201500197.
Yanweerasak, T., W. Pansuk, M. Akiyama, and D. M. Frangopol. 2018. “Life-cycle reliability assessment of reinforced concrete bridges under multiple hazards.” Struct. Infrastruct. Eng. 14 (7): 1011–1024. https://doi.org/10.1080/15732479.2018.1437640.
Zhang, S., W. Zhou, M. Al-Amin, S. Kariyawasam, and H. Wang. 2014. “Time-dependent corrosion growth modeling using multiple in-line inspection data.” J. Press. Vessel. Technol. 136 (4): 041202. https://doi.org/10.1115/1.4026798.
Information & Authors
Information
Published In
Journal of Performance of Constructed Facilities
Volume 35 • Issue 5 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Oct 19, 2020
Accepted: Apr 21, 2021
Published online: Jul 20, 2021
Published in print: Oct 1, 2021
Discussion open until: Dec 20, 2021
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.
Cited by
- Manuel Salmeron, Nichole Criner, Xin Zhang, Shirley J. Dyke, Julio A. Ramirez, B. Eric Wogen, Anne Rearick, Mechanistic Modeling of Construction Defects in Concrete Decks Subject to Corrosion-Induced Deterioration, Journal of Bridge Engineering, 10.1061/JBENF2.BEENG-6636, 29, 9, (2024).
- Jin Collins, Jeffrey Weidner, Comparison of Markovian-Based Bridge Deterioration Model Approaches, Journal of Bridge Engineering, 10.1061/JBENF2.BEENG-5920, 28, 8, (2023).
- Gaowei Xu, Fae Azhari, Data-driven optimization of repair schemes and inspection intervals for highway bridges, Reliability Engineering & System Safety, 10.1016/j.ress.2022.108779, 228, (108779), (2022).