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A methodology to evaluate corroded RC structures using a probabilistic damage approach

  • Coelho, Karolinne O. (School of Civil Engineering, Architecture and Urban Design, University of Campinas) ;
  • Leonel, Edson D. (Department of Structural Engineering, Sao Carlos School of Engineering, University of Sao Paulo) ;
  • Florez-Lopez, Julio (School of Civil Engineering, Chongqing University)
  • Received : 2021.01.05
  • Accepted : 2021.12.28
  • Published : 2022.01.25

Abstract

Several aspects influence corrosive processes in reinforced concrete (RC) structures such as environmental conditions, structural geometry and mechanical properties. Since these aspects present large randomnesses, probabilistic models allow a more accurate description of the corrosive phenomena. Besides, the definition of limit states in the reliability assessment requires a proper mechanical model. In this context, this study proposes a straightforward methodology for the mechanical-probabilistic modelling of RC structures subjected to reinforcements' corrosion. An improved damage approach is proposed to define the limit states for the probabilistic modelling, considering three main degradation phenomena: concrete cracking, rebar yielding and rebar corrosion caused either by chloride or carbonation mechanisms. The stochastic analysis is evaluated by the Monte Carlo simulation method due to the computational efficiency of the Lumped Damage Model for Corrosion (LDMC). The proposed mechanical-probabilistic methodology is implemented in a computational framework and applied to the analysis of a simply supported RC beam and a 2D RC frame. Curves illustrate the probability of failure evolution over a service life of 50 years. Moreover, the proposed model allows drawing the probability of failure map and then identifying the critical failure path for progressive collapse analysis. Collapse path changes caused by the corrosion phenomena are observed.

Keywords

Acknowledgement

The financial support from the Brazilian National Council for Scientific and Technological Development (CNPq) is gratefully acknowledged.

References

  1. ABNT NBR 6118 (2014), Projeto de estruturas de concreto-procedimento, Associacao Brasileira de Normas Tecnicas, Rio de Janeiro, RJ, Brazil. (in Portuguese)
  2. ACI 318 (2019), Building Code Requirements for Structural Concrete and Commentary, American Concrete Institute, Farmington Hills, MI, USA.
  3. ACI Committee (2020), Literature Review of Concrete Durability and Service Life Requirements in Global Codes and Standards, ACI Foundation, Pivot Engineers, and CVM Engineers, Farmington Hills, MI, USA.
  4. Albuquerque, A.T. and Otoch, S. (2005), "Proposta de classificacao da agressividade do ambiente na cidade de Fortaleza", Proceedings of the 47° in Congresso Brasileiro do Concreto, Recife, PE, Brazil, November. (in Portuguese)
  5. Amorim, D.L.N. de F., Proenca, S.P.B. and Florez-Lopez, J. (2014), "Simplified modelling of cracking in concrete: Application in tunnel linings", Eng. Struct., 70(1), 23-35. https://doi.org/10.1016/j.engstruct.2014.03.031.
  6. Angst, U., Elsener, B., Larsen, C. and Vennesland, O. (2009), "Critical chloride content in reinforced concrete-A review", Cement Concrete Res., 39(12), 1122-1138. https://doi.org/10.1016/j.cem conres.2009.08.006.
  7. Angst, U.M., Geiker, M.R., Alonso, M.C., Polder, R., Isgor, O.B., Elsener, B., Wong, H., Michel, A., Hornbostel, K., Gehlen, C. and Francois, R. (2019), "The effect of the steel-concrete interface on chloride-induced corrosion initiation in concrete: A critical review by RILEM TC 262-SCI", Mater. Struct., 52(4), 88-113. https://doi.org/10.1617/s11527-019-1387-0.
  8. Astroza, R., Alessandri, Andres and Conte, J.P. (2019), "A dual adaptive filtering approach for nonlinear finite element model updating accounting for modelling uncertainty", Mech. Syst. Signal Process., 115(1), 782-800. https://doi.org/10.1016/j.ymssp.2018.06.014.
  9. Bai, Y., Kurata, M., Florez-Lopez, J. and Nakashima, M. (2016), "Macromodelling of crack damage in steel beams subjected to nonstationary low cycle fatigue", J. Struct. Eng., 142(10), 04016076. https://doi.org/10.1061/(ASCE)ST. 1943-541X.0001536.
  10. Barrios, S.K.M. and Florez-Lopez, J. (2020), "Numerical quantification of damage reduction in frames retrofitted with FRP bands as bracing elements", Eng. Struct., 223(1), 111178. https://doi.org/10. 1016/j.engstruct.2020.111178. https://doi.org/10.1016/j.engstruct.2020.111178
  11. Bastidas-Arteaga, E. (2018), "Reliability of reinforced concrete structures subjected to corrosion-fatigue and climate change", Int. J. Concrete. Struct. Mater., 12(1), 10. https://doi.org/10.1186/ s40069-018-0235-x.
  12. Beirlant, J., Goegebeur, Y., Segers, J. and Teugels, J.L. (2006), Statistics of Extremes: Theory and Applications, John Wiley and Sons, Chichester, West Sussex, England.
  13. Benkemoun, N, Hammood, M.N., and Amiri, O. (2017), "Embedded finite element formulation for the modelling of chloride diffusion accounting for chloride binding in meso-scale concrete", Finite Elem. Anal. Des., 130(1), 12-26. https://doi.org/10.1016/j.finel. 2017.03.003.
  14. Cairns, J., Gehlen, C., Andrade, C., Bartholomew, M., Gulikers, J., Leon, F.J., Matthews, S., McKenna, P., Osterminski, K., Paeglitis, A. and Straub, D. (2017), "Condition control and assessment of reinforced concrete structures exposed to corrosive environments", fib Bulletin, 59.
  15. Chen, E., and Leung, C.K.Y. (2017), "A coupled diffusion-mechanical model with boundary element method to predict concrete cover cracking due to steel corrosion", Corros. Sci., 126(1), 180-196. https://doi.org/10.1016/j.corsci.2017.07.001.
  16. Coelho, K.O. and Leonel, E.D. and Florez-Lopez, J. (2017), "The Mechanical behaviour modelling of Reinforced Concrete Structures by the Lumped Damage Model", Reinf. Concrete, 49.
  17. Di-Sarno, L. and Elnashai, A.S. (2021), "Seismic Fragility Relationships for Structures", Adv. Assess. Model. Earthq. Loss, 189-222.
  18. Estes, A.C and Frangopol, D.M. (1998), "RELSYS: A computer program for structural system reliability", Struct. Eng. Mech., 6(8), 901-919. https://doi.org/10.12989/sem.2000.9.6.557.
  19. Florez-Lopez, J. (1998), "Frame analysis and continuum damage mechanics", Eur. J. Mech. A/Solids, 17(2), 269-283. https://doi.org/10.1016/S0997-7538(98)80086-7.
  20. Goctermann, P. (2000), "Dura crete-probabilistic performance based durability design of concrete structure: General guidelines for durability design and redesign", BE9521347, 14.
  21. Griffith, A.A. (1921), "VI. The phenomena of rupture and flow in solids", Philosophical Transactions of The Royal Society of London, Series A, Containing Papers of a Mathematical or Physical Character, 221(582-593), 163-198. https://doi.org/10.1098/rsta. 1921.0006.
  22. Huang, L., Jin, X., Fu, C., Ye, H. and Dong, X. (2020), "Stochastic characteristics of reinforcement corrosion in concrete beams under sustained loads", Comput. Concrete, 25(5), 447-460. https://doi.org/10.12989/cac.2020.25.5.447.
  23. Jia, G., Gardoni, P., Trejo, D. and Mazarei, V. (2020), "Stochastic modelling of deterioration and time-variant performance of reinforced concrete structures under joint effects of earthquakes, corrosion, and ASR", J. Struct. Eng., 147(2), 04020314. https://doi.org/10.1061/(ASCE)ST.1943-541X.00028 84.
  24. Kiani, K. and Shodja, H. (2012), "Response of reinforced concrete structures to macrocell corrosion of reinforcements Part II: After propagation of microcracks via a numerical approach", Nucl. Eng. Des., 242, 7-18. https://doi.org/10.1016/j.nucengdes.2011.09. 018.
  25. Liberati, E.A.P, Nogueira C.G. and Leonel, E.D. (2014), "Nonlinear formulation based on FEM, Mazars damage criterion and Fick's law applied to failure assessment of reinforced concrete structures subjected to chloride ingress and reinforcements corrosion", Eng. Fail. Anal., 46(1), 247-268. https://doi.org/10.1016/j.engfailanal.2014.09.006.
  26. Marante, M.E. and Florez-Lopez, J. (2003), "Three-dimensional analysis of reinforced concrete frames based on lumped damage mechanics", Int. J. Solids Struct., 40, 5109-5123. https://doi.org/10.1016/S0020-7683(03)00258-0.
  27. Marcelo P. da, S. (1993), "Study of a damage model for concrete: Formulation, parametric identification and application using the finite element method", Ph.D. Dissertation of Philosophy, University of Sao Paulo. (in Portuguese)
  28. Monteiro, P.J.M., Miller, S.A. and Horvath, A. (2017), "Towards sustainable concrete", Nat. Mater., 16(7), 698-699. https://doi.org/10.1038/nmat4930.
  29. Nogueira, C.G., Venturini, W.S. and Coda, H.B. (2013), "Material and geometric nonlinear analysis of reinforced concrete frame structures considering the influence of shear strength complementary mechanisms", Lat. Am. J. Solids Struct., 10(5), 953-980. https://doi.org/10.1016/S0020-7683(03)00258-0.
  30. Otieno, M., Beushausen, H. and Er, M. (2012), "Prediction of corrosion rate in reinforced concrete structures-a critical review and preliminary results", Mater. Corros., 63(9), 777-790. https://doi.org/10.1002/maco.201106282.
  31. Oudah, F. and Norlander, F. (2017), "Design philosophy and requirements of granular wear surface thickness for bridges subjected to extreme truck load", Can. J. Civil Eng., 44(9), 727-735. https://doi.org/10.1139/cjce-2017-0023.
  32. Papadakis, V.G., Fardis, M.N. and Vayenas, C.G. (1992), "Effect of composition, environmental factors and cement-lime mortar coating on concrete carbonation", Mater. Struct., 25(5), 293-304. https://doi.org/10.1007/BF02472670.
  33. Papadakis, V.G., Roumeliotis, A.P., Fardis, M.N. and Vagenas, C.G. (1996), "Mathematical modelling of chloride effect on concrete durability and protection measures", Concrete Repair Rehabilitation Protect., 165-174.
  34. Pellizzer, G.P., Kroetz, H.M., Leonel, E.D. and Beck, A.T. (2020), "Time-dependent reliability of reinforced concrete considering chloride penetration via boundary element method", Lat. Am. J. Solid. Struct., 17(8), 1-17. https://doi.org/10.1590/1679-78255885.
  35. Pellizzer, G.P., Leonel, E.D. and Nogueira, C.G. (2015), "Influence of reinforcement's corrosion into hyperstatic reinforced concrete beams: a probabilistic failure scenarios analysis", IBRACON Struct. Mater. J., 8(4), 479-490. https://doi.org/10.1590/S1983- 41952015000400004.
  36. Santoro, M.G. and Kunnath, S.K. (2013), "Damage-based RC beam element for nonlinear structural analysis", Eng. Struct., 49(1),733-742. https://doi.org/10.1016/j.engstruct.2012.12.026.
  37. Shafikhani, M. and Chidiac, S.E. (2019), "Quantification of concrete chloride diffusion coefficient-A critical review", Cement Concrete Compos., 99(1), 225-250. https://doi.org/10.1016/j.cemconcomp. 2019.03.011.
  38. Shah, V. and Bishnoi, S. (2018), "Carbonation resistance of cements containing supplementary cementitious materials and its relation to various parameters of concrete", Constr. Build. Mater., 178(1), 219-232. https://doi.org/10.1016/j.conbuildmat.2018.05.162.
  39. Shaikh, F.U.A. (2018), "Effect of cracking on corrosion of steel in concrete", Int. J. Concrete Struct. Mater., 12(1), 1-12. https://doi.org/10.1186/s40069-018-0234-y.
  40. Silva, A., Neves, R. and De Brito, J. (2014), "Statistical modelling of carbonation in reinforced concrete", Cement Concrete Compos., 50(1), 73-81. https://doi.org/10.1016/j.cemconcomp.2013.12.001.
  41. Stewart, M.G. (2014), "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.
  42. Tuutti, K. (1982), "Corrosion of steel in concrete", Cement-och betonginst, Stockholm, Sweden.
  43. Ueda, T. and Takewaka, K. (2007), "Performance-based standard specifications for maintenance and repair of concrete structures in Japan", Struct. Eng. Int., 17(4), 359-366. https://doi.org/10.2749/101686607782359119.
  44. Val, D.V., Stewart, M.G. and Melchers, R.E. (1998), "Effect of reinforcement corrosion on reliability of highway bridges", Eng. Struct., 20(11), 1010-1019. https://doi.org/10.1016/S0141-0296(97)00197-1.
  45. Vecchio, F.J. and Emara, M.B. (1992), "Shear deformations in reinforced concrete frames", ACI Struct. J., 89(1), 46-56. https://doi.org/10.14359/1283.
  46. Vennesland, O., Climent, M.A . and Andrade, C. (2013), "Recommendation of RILEM TC 178-TMC: Testing and modelling chloride penetration in concrete", Mater. Struct., 46(12), 337-344. https://doi.org/10.1617/s11527-012-9968-1.
  47. Vu, K.A.T. and Stewart, M.G. (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.
  48. Xiao, J., Ying, J. and Shen, L. (2012), "FEM simulation of chloride diffusion in modeled recycled aggregate concrete", Constr. Build. Mater., 29(1), 12-23. https://doi.org/10.1016/j.conbuildmat. 2011.08.073.
  49. Xu, F., Xiao, Y., Wang, S., Li, W., Liu, W. and Du, D. (2018), "Numerical model for corrosion rate of steel reinforcement in cracked reinforced concrete structure", Constr. Build. Mater., 180(1), 55-67. https://doi.org/10.1016/j.conbuildmat.2018.05.215.
  50. Yu, Y., Gao, W., Castel, A., Chen, X. and Liu, A. (2021), "An integrated framework for modelling time-dependent corrosion propagation in offshore concrete structures", Eng. Struct., 228(1), 111482. https://doi.org/10.1016/j.engstruct.2020.111482.
  51. Zhou, Y., Gencturk, B., Willam, K. and Attar, A. (2015), "Carbonation-induced and chloride-induced corrosion in reinforced concrete structures", J. Mater. Civ. Eng., 27(9), 04014245. https://doi.org/10.1061/(ASCE)MT.1943-5533.0001209.