Stochastic Analysis and Time-Dependent Reliability of Reinforced Concrete Beams Considering Spatially Distributed Corrosion Deterioration
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 2
Abstract
Reinforcement corrosion is an important part of durability research of concrete structures. The process of reinforcement corrosion is highly random due to various factors, and the effect of spatial distribution of reinforcement corrosion is obvious in practical structures. This paper took corroded reinforced concrete beams as the research object, summarized the numerical characteristics of reinforcement corrosion in the test, and then established cross section corrosion extent random field models. Finally, this paper carried out a time-varying reliability analysis of the bending and shear capacity of the corroded reinforced concrete beams considering the time-varying effect of corrosion. The results showed that the failure probability of the flexural and shear bearing capacity of corroded RC beams is close to zero at the early stage of corrosion, the reliability index of the flexural bearing capacity is lower than the recommended value of 3.2 after 30 years, and the failure probability increases rapidly after 40 years. The shear capacity is lower than the reliability index 3.7 after 20 years, and the failure probability is greater than 0.3844 after 25 years.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
The authors greatly appreciate the financial support from the Project of National Key Research and Development Program of China (Grant No. 2022YFC3803004), the National Natural Science Foundation of China (Grant No. 52311540017), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20211564).
References
Balabanic, G., N. Bicanic, and A. Durekovic. 1996. “The influence of w/c ratio, concrete cover thickness and degree of water saturation on the corrosion rate of reinforcing steel in concrete.” Cem. Concr. Res. 26 (5): 761–769. https://doi.org/10.1016/S0008-8846(96)85013-7.
Bažant, Z. P. 1979a. “Physical model for steel corrosion in concrete sea structures—Application.” J. Struct. Div. 105 (6): 1155–1166.
Bažant, Z. P. 1979b. “Physical model for steel corrosion in concrete sea structures—Theory.” J. Struct. Div. 105 (6): 1137–1153. https://doi.org/10.1061/JSDEAG.0005169.
Biswas, R. K., M. Iwanami, N. Chijiwa, and K. Uno. 2020. “Effect of non-uniform rebar corrosion on structural performance of RC structures: A numerical and experimental investigation.” Constr. Build. Mater. 230 (Jan): 116908. https://doi.org/10.1016/j.conbuildmat.2019.116908.
Chen, J., J. He, X. Ren, and J. Li. 2018. “Stochastic harmonic function representation of random fields for material properties of structures.” J. Eng. Mech. 144 (7): 04018049. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001469.
Chen, J., and J. Li. 2011. “Stochastic harmonic function and spectral representations.” Chin. J. Theor. Appl. Mech. 43 (3): 505–513. https://doi.org/10.6052/0459-1879-2011-3-lxxb2010-375.
Chinese Standard. 2018. Unified standard for reliability design of building structures. GB 50068-2018. Beijing: China Architecture and Building Press.
DuraCrete. 2000. Statistical quantification of the variables in the limit state functions. European Union-Brite EuRam III-Contract BRPR-CT95-0132-Project BE95-1347/R9. Amsterdam, Netherlands: Gouda.
Du, Y. G., L. A. Clark, and A. 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.
fib (Fédération internationale du béton). 2010. Vol. 1 of model code 2010—First complete draft., 318. Vienna, Austria: fib. https://doi.org/10.35789/fib.BULL.0055.
Ghanem, R. G., and P. D. Spanos. 2003. Stochastic finite elements: A spectral approach. Chelmsford, MA: Courier Corporation.
Gonzalez, J. A., W. Lopez, and P. Rodriguez. 1993. “Effects of moisture availability on corrosion kinetics of steel embedded in concrete.” Corrosion 49 (12): 1004–1010. https://doi.org/10.5006/1.3316021.
He, J., J. Chen, X. Ren, and J. Li. 2021. “Uncertainty quantification of random fields based on spatially sparse data by synthesizing Bayesian compressive sensing and stochastic harmonic function.” Mech. Syst. Sig. Process. 153 (May): 107377. https://doi.org/10.1016/j.ymssp.2020.107377.
He, J., R. Gao, and H. Zhou. 2023. “A nonparametric seismic reliability analysis method based on Bayesian compressive sensing—Stochastic harmonic function method and probability density evolution method.” Mech. Syst. Sig. Process. 196 (Aug): 110339. https://doi.org/10.1016/j.ymssp.2023.110339.
Jin, W., and Y. Zhao. 2002. “State-of-the-rat on durability of concrete structures.” J. Zhejiang Univ. 36 (4): 371–380. https://doi.org/10.3969/j.issn.2095-2104.2015.36.817.
JSCE (Japan Society of Civil Engineers). 2007. Standard specifications for concrete structures 2007: Design. Tokyo: JSCE.
Kashani, M. M., A. J. Crewe, and N. A. Alexander. 2013. “Use of a 3D optical measurement technique for stochastic corrosion pattern analysis of reinforcing bars subjected to accelerated corrosion.” Corros. Sci. 73 (Aug): 208–221. https://doi.org/10.1016/j.corsci.2013.03.037.
Liang, S., W. Sun, and J. Li. 2012. “Simulation of multi-dimensional random fields by stochastic harmonic functions.” J. Tongji Univ. (Natl. Sci.) 40 (7): 965–970. https://doi.org/10.3969/j.issn.0253-374x.2012.07.001.
Lim, S., M. Akiyama, D. M. Frangopol, and H. Jiang. 2017. “Experimental investigation of the spatial variability of the steel weight loss and corrosion cracking of reinforced concrete members: Novel x-ray and digital image processing techniques.” Struct. Infrastruct. Eng. 13 (1): 118–134. https://doi.org/10.1080/15732479.2016.1198397.
Lin, D. 2002. “Random field discretization method for finite element reliability analysis.” J. Tsinghua Univ. (Sci. Technol.) 42 (6): 839–842. https://doi.org/10.3321/j.issn:1000-0054.2002.06.035.
Liu, J., X. Luo, and Y. Xiao. 2021. “Non-uniform corrosion and distribution models of residual cross-sectional areas of rebars.” J. Huazhong Univ. Sci. Technol. (Nat. Sci.) 49 (11): 83–88. https://doi.org/10.13245/j.hust.211114.
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.
Lubliner, J., J. Oliver, S. Oller, and E. Oñate. 1989. “A plastic-damage model for concrete.” Int. J. Solids Struct. 25 (3): 299–326. https://doi.org/10.1016/0020-7683(89)90050-4.
Morinaga, S. 1988. Prediction of service lives of reinforced concrete buildings based on rate of corrosion of reinforcing steel. Special Report of Institute of Technology. Tokyo: Shimizu Corporation.
Ozbolt, J., F. Orsanic, and G. Balabanic. 2017. “Modelling processes related to corrosion of reinforcement in concrete: Coupled 3d finite element model.” Struct. Infrastruct. Eng. 13 (1): 135–146. https://doi.org/10.1080/15732479.2016.1198400.
Shinozuka, M., and G. Deodatis. 1996. “Simulation of multi-dimensional gaussian stochastic fields by spectral representation.” Appl. Mech. Rev. 49 (1): 29. https://doi.org/10.1115/1.3101883.
Tang, F., Z. Lin, G. Chen, and W. Yi. 2014. “Three-dimensional corrosion pit measurement and statistical mechanical degradation analysis of deformed steel bars subjected to accelerated corrosion.” Constr. Build. Mater. 70 (Nov): 104–117. https://doi.org/10.1016/j.conbuildmat.2014.08.001.
Teng, J. G., S. S. Zhang, J. G. Dai, and J. F. Chen. 2013. “Three-dimensional meso-scale finite element modeling of bonded joints between a near-surface mounted FRP strip and concrete.” Comput. Struct. 117 (Feb): 105–117. https://doi.org/10.1016/j.compstruc.2012.12.002.
Vu, K., 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.
Wang, X.-G., W.-P. Zhang, X.-L. Gu, and H.-C. Dai. 2013. “Determination of residual crosssectional areas of corroded bars in reinforced concrete structures using easy-to-measure variables.” Constr. Build. Mater. 38 (Jan): 846–853. https://doi.org/10.1016/j.conbuildmat.2012.09.060.
Xia, J., W.-L. Jin, and L.-Y. Li. 2012. “Effect of chloride-induced reinforcing steel corrosion on the flexural strength of reinforced concrete beams.” Mag. Concr. Res. 64 (6): 471–485. https://doi.org/10.1680/macr.10.00169.
Xia, J., W.-L. Jin, Y.-X. Zhao, and L.-Y. Li. 2013. “Mechanical performance of corroded steel bars in concrete.” Proc. Inst. Civ. Eng. Struct. Build. 166 (5): 235–246. https://doi.org/10.1680/stbu.11.00048.
Ye, Z., W. Zhang, and X. Gu. 2018. “Deterioration of shear behavior of corroded reinforced concrete beams.” Eng. Struct. 168 (Aug): 708–720. https://doi.org/10.1016/j.engstruct.2018.05.023.
Zhang, M., N. Nishiya, M. Akiyama, S. Lim, and K. Masuda. 2020. “Effect of the correlation of steel corrosion in the transverse direction between tensile rebars on the structural performance of RC beams.” Constr. Build. Mater. 264 (Dec): 120678. https://doi.org/10.1016/j.conbuildmat.2020.120678.
Zhang, M., H. Song, S. Lim, M. Akiyama, and D. M. Frangopol. 2019. “Reliability estimation of corroded rc structures based on spatial variability using experimental evidence, probabilistic analysis and finite element method.” Eng. Struct. 192 (Aug): 30–52. https://doi.org/10.1016/j.engstruct.2019.04.085.
Zhang, W., B. Zhou, X. Gu, and H. Dai. 2014. “Probability distribution model for cross-sectional area of corroded reinforcing steel bars.” J. Mater. Civ. Eng. 26 (5): 822–832. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000888.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10 • Issue 2 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 13, 2023
Accepted: Dec 1, 2023
Published online: Mar 4, 2024
Published in print: Jun 1, 2024
Discussion open until: Aug 4, 2024
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