Corrosion of steel bars is one of the most significant causes of deterioration of reinforced concrete (RC) structures. The performance of RC structures is affected by many factors such as materials, environments, and load conditions, which usually possess uncertain features. Some of uncertainties may be time- and space-dependent, and the corresponding reliability problems become more challenging. To address these issues, this paper studies the temporal-spatial reliability analysis of RC bridges with corroded steel reinforcement bars. At first, a compound corrosion model is developed in which the combined effects of carbonation (general corrosion) and chloride penetration (pitting corrosion) are considered. In the reliability analysis, both the temporal and spatial variability are accounted through a stochastic process and a random field, respectively. An extended instantaneous response surface (t-IRS) method is then proposed to evaluate the temporal-spatial reliability. Unlike the original t-IRS method, in addition to the original variables, the random variables transformed from the random fields and the space variable are also used as the input variables of the extended surrogate model. When generating sample points, both the time variable and the space variable are treated as uniformly distributed random variables within given intervals. Finally, the proposed method is applied to a RC bridge example with corroded steel reinforcement bars and the results are compared with that of Monte Carlo simulation (MCS) method, demonstrating the effectiveness of the extended t-IRS method.
ElmoatyAEMA. Four-years carbonation and chloride induced steel corrosion of sulfate-contaminated aggregates concrete. Construction Building Mater2018; 163: 539–556.
2.
OtienoMBBeushausenHDAlexanderMG. Modelling corrosion propagation in reinforced concrete structures – A critical review. Cement Concrete Compos2011; 33(2): 240–245.
3.
MangatPSElgarfMS. Flexural strength of concrete beams with corroding reinforcement. ACI Struct J1999; 96: 149–158.
4.
ZhangRCastelAFrançoisR. The corrosion pattern of reinforcement and its influence on serviceability of reinforced concrete members in chloride environment. Cement Concrete Res2009; 39(11): 1077–1086.
5.
Di SarnoLPuglieseF. Numerical evaluation of the seismic performance of existing reinforced concrete buildings with corroded smooth rebars. Bull Earthquake Eng2020; 18(9): 4227–4273.
6.
Di SarnoLPuglieseF. Seismic fragility of existing RC buildings with corroded bars under earthquake sequences. Soil Dyn Earthquake Eng2020; 134: 106169.
7.
PuglieseFDi SarnoL. Effects of mainshock-aftershock sequences on fragility analysis of RC buildings with ageing. Eng Struct2021; 232: 111837.
8.
PuglieseFDi SarnoL. Probabilistic structural performance of RC frames with corroded smooth bars subjected to near- and far-field ground motions. J Building Eng2022; 49: 104008.
9.
PuglieseFDe RisiRDi SarnoL. Reliability assessment of existing RC bridges with spatially-variable pitting corrosion subjected to increasing traffic demand. Reliability Eng Syst Saf2022; 218: 108137.
10.
ChoeDEGardoniPRosowskyD, et al. Seismic fragility estimates for reinforced concrete bridges subject to corrosion. Struct Saf2009; 31(4): 275–283.
11.
PageCLTreadawayKWJ. Aspects of the electrochemistry of steel in concrete. Nature1982; 297(5862): 109–115.
12.
CollepardiMMarcialisATurrizianiR. Penetration of chloride ions into cement pastes and concretes. J Am Ceram Soc1972; 55(10): 534–535.
13.
MangatPSMolloyBT. Predictions of long term chloride con centration in concrete. Mater Struct1994; 27: 338–346.
14.
ChatterjiS. On the applicability of Fick’s second law to chloride ion migration through portland cement concrete. Cement Concrete Res1995; 25(2): 299–303.
15.
SuryavanshiAKSwamyRNCardewGE. Estimation of diffusion coefficients for chloride ion penetration into structural concrete. ACI Mater J2002; 99(5): 441–449.
16.
BaderMA. Performance of concrete in a coastal environment. Cement Concrete Compos2003; 25(4–5): 539–548.
17.
GonzalezJAAlgabaJSAndradeC. Corrosion of reinforcing bars in carbonated concrete. Br Corrosion J1980; 15(3): 135–139.
18.
LiDChenBSunH, et al.Evaluating the effect of external and internal factors on carbonation of existing concrete building structures. Construction Building Mater2018; 167: 73–81.
19.
PaulSCPandaBHuangY, et al.An empirical model design for evaluation and estimation of carbonation depth in concrete. Measurement2018; 124: 205–210.
20.
El HassanJBressolettePChateauneufA, et al.Reliability-based assessment of the effect of climatic conditions on the corrosion of RC structures subject to chloride ingress. Eng Struct2010; 32(10): 3279–3287.
21.
NogueiraCGLeonelED. Probabilistic models applied to safety assessment of reinforced concrete structures subjected to chloride ingress. Eng Fail Anal2013; 31: 76–89.
22.
ZhuWFrançoisR. Structural performance of RC beams in relation with the corroded period in chloride environment. Mater Structures2014; 48(6): 1757–1769.
23.
HongN. Corrosion and protective technology of rebar in concrete (3): rebar corrosion by chloric salt. Ind Construction1999; 29(10): 60–63.
24.
StewartMGAl-HarthyA. Pitting corrosion and structural reliability of corroding RC structures: experimental data and probabilistic analysis. Reliability Eng Syst Saf2008; 93(3): 373–382.
25.
XiaoC. Corrosion of reinforcement in concrete and number theory simulation. Beijing: Tsinghua University, 1995.
26.
LiJChenJZhangX. Time-dependent reliability analysis of deteriorating structures based on Phase-type distributions. IEEE Trans Reliability2020; 69(2): 545–557.
27.
LiJChenJChenZ. Developing an improved composite limit state method for time-dependent reliability analysis. Qual Eng2020; 32(3): 298–311.
28.
LiJChenJChenZ. A new cumulative damage model for time-dependent reliability analysis of deteriorating structures. Proc Inst Mech Eng O: J Risk Reliability2020; 234(2): 290–302.
StewartMG. Spatial and time-dependent reliability modelling of corrosion damage, safety and maintenance for reinforced concrete structures. Struct Infrastruct Eng2012; 8(6): 607–619.
31.
TeixeiraAPGuedes SoaresCWangG. Probabilistic modelling of the ultimate strength of ship plates with non-uniform corrosion. J Mar Sci Technol2013; 18: 115–132.
32.
LiJChenJWeiJ, et al.Developing an instantaneous response surface method t-IRS for time-dependent reliability analysis. Acta Mechanica Solida Sinica2019; 32(4): 446–462.
33.
LiJChenJ. Solving time-variant reliability-based design optimization by PSO-t-IRS: a methodology incorporating a particle swarm optimization algorithm and an enhanced instantaneous response surface. Reliability Eng Syst Saf2019; 191: 106580.
34.
JonesDA. Principles and prevention of corrosion. New York: Macmillan Publishing Co, 1992.
35.
StewartMGMullardJA. Spatial time-dependent reliability analysis of corrosion damage and the timing of first repair for RC structures. Eng Structures2007; 29(7): 1457–1464.
36.
Mohammadi FarsaniAKeshtegarB. Reliability analysis of corroded reinforced concrete beams using enhanced HL-RF method. Civil Eng Infrastructures J2015; 48(2): 315–322.
37.
LiH-NChengHWangD-S. Time-variant seismic performance of offshore RC bridge columns with uncertainty. Int J Struct Stab Dyn2018; 18(12): 1850149.
38.
TarighatAJalalifarF. Assessing the performance of corroding RC bridge decks: a critical review of corrosion propagation models. Civil Eng Infrastructures J2014; 47(2): 173–186.
39.
SuoQStewartMG. Corrosion cracking prediction updating of deteriorating RC structures using inspection information. Reliability Eng Syst Saf2009; 94(8): 1340–1348.
40.
VuKATStewartMG. Structural reliability of concrete bridges including improved chloride-induced corrosion models. Struct Saf2000; 22(4): 313–333.
41.
VuKATStewartMGMullardJA. Corrosion-induced cracking: experimental data and predictive models. ACI Struct J2005; 102(5): 719–726.
42.
SaassouhBLounisZ. Probabilistic modeling of chloride-induced corrosion in concrete structures using first- and second-order reliability methods. Cement Concrete Compos2012; 34(9): 1082–1093.
43.
StewartMG. Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure. Struct Saf2004; 26(4): 453–470.
44.
HuZDuX. First order reliability method for time-variant problems using series expansions. Struct Multidisciplinary Optimiza2015; 51(1): 1–21.
45.
SudretBKiureghianAD. Stochastic finite elements and reliability - A state-of-the-art report. Designing End-User Interfaces2000; 30: 22–25.
46.
LoèveM. Probability theory I. New York: Springer, 1977.
47.
ZhangJEllingwoodB. Orthogonal series expansions of random fields in reliability analysis. J Eng Mech1994; 120(12): 2660–2677.
48.
LiCKiureghianAD. Optimal discretization of random fields. J Eng Mech1993; 119(6): 1136–1154.
49.
AryaiVMahmoodianM. Spatial-temporal reliability analysis of corroding cast iron water pipes. Eng Fail Anal2017; 82: 179–189.
50.
WeiPLuZYuanX. Monte Carlo simulation for moment-independent sensitivity analysis. Reliability Eng Syst Saf2013; 110(2): 60–67.
51.
EchardBGaytonNLemaireM. AK-MCS: an active learning reliability method combining kriging and Monte Carlo simulation. Struct Saf2011; 33: 145–154.
52.
EchardBGaytonNLemaireM, et al.A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models. Reliability Eng Syst Saf2013; 111: 232–240.
53.
XiaoMWWeiQCZhaoTJ, et al.Service life prediction based on carbonation reliability theory for reinforced concrete under mechanical load. Adv Mater Res2011; 243-249: 1156–1162.
54.
ZhangXWangJZhaoY, et al.Time-dependent probability assessment for chloride induced corrosion of RC structures using the third-moment method. Construction Building Mater2015; 76: 232–244.
55.
ShaoWShiDTangP. Probabilistic lifetime assessment of RC pipe piles subjected to chloride environments. J Mater Civil Eng2018; 30(11): 04018297.
56.
Bastidas-ArteagaESánchez-SilvaMChateauneufA, et al.Coupled reliability model of biodeterioration, chloride ingress and cracking for reinforced concrete structures. Struct Saf2008; 30(2): 110–129.
57.
HuZDuX. Reliability-based design optimization under stationary stochastic process loads. Eng Optimization2015; 48(8): 1296–1312.
58.
ZhangDHanXJiangC, et al.Time-dependent reliability analysis through response surface method. J Mech Des2017; 139(4): 041404.
59.
LiQYeX. Surface deterioration analysis for probabilistic durability design of RC structures in marine environment. Struct Saf2018; 75: 13–23.
60.
GjorvOE. Durability of concrete structures. Arabian J Sci Eng2011; 36(2): 151–172.
61.
MelchersREBeckAT. Structural reliability analysis and prediction. 3rd Edition. West Sussex: John Wiley & Sons, 2018.
