Reliability algorithms for calculating and predicting the durability of reinforced concrete under chloride aggression: analysis of methodology and applications
https://doi.org/10.31659/0005-9889-2022-614-6-40-50
Abstract
The article deals with the analysis of the probabilistic onset of corrosion in reinforced concrete structures subject to the penetration of chloride ions. Structural strength is an important criterion that must be evaluated in every type of structure, especially when these structures are operated in aggressive environments. When considering reinforced concrete members, the chloride diffusion process is widely used to evaluate durability. Therefore, by simulating this phenomenon, reinforcement corrosion can be better assessed and prevented. These processes begin when a threshold level of chloride concentration on the steel reinforcement bars is reached. Despite the reliability of several models proposed in the literature, deterministic approaches cannot accurately predict the time of onset of corrosion due to the randomness observed in this process. In this regard, durability can be more realistically represented using probabilistic approaches. The article presents a probabilistic analysis of the penetration of chloride ions. The penetration of chloride ions is modeled using Fick’s second law of diffusion. This law represents the diffusion process of chlorides, taking into account time-dependent effects. The failure probability is calculated using Monte Carlo simulation and first order reliability method (FORM) with a feed-forward approach. To study these phenomena, some examples are considered and a simplified method is proposed for determining the optimal values for the concrete cover.
About the Authors
S. N. Leonovich
Belarusian National Technical University
Belarus
Belarus
Doctor of Sciences (Engineering), Foreign Academician of the RAACS, Chief Researcher of the Center for Scientific Research and Testing of Building Structures branch of the BNTU “Research Polytechnic Institute”
e-mail: sleonovich@mail.ru
E. E. Shaly
D. A. Litvinovsky
InzhSpetsStroyProekt LLC
Belarus
Belarus
Main engineer
A. V. Stepanova
Belarusian National Technical University
Belarus
Belarus
Engineer
V. V. Malyuk
Transstroy-Trest LLC
Russian Federation
Russian Federation
General director
A. V. Kolodey
Belarusian National Technical University
Belarus
Belarus
Engineer
References
1. Ueli Angst, Bernhard Elsener, Claus K. Larsen, Øystein Vennesland. Critical chloride content in reinforced concrete – A review. <i>Cement and Concrete Research</i>. 2009. Vol. 39, pp. 1122–1138. https://doi.org/10.1016/j.cemconres.2009.08.006
2. Santiago Guzmán, Jaime C.Gálvez, José M. Sancho. Cover cracking of reinforced concrete due to rebar corrosion induced by chloride penetration. <i>Cement and Concrete Research.</i> 2011. Vol. 41, Iss. 8, pp. 893–902. https://doi.org/10.1016/j.cemconres.2011.04.008
3. Tianyu Xiang, Renda Zhao Evaluation of the reliability of diffusion of chlorides in fatigue-damaged concrete. <i>Engineering Structures</i>. 2007. Vol. 29. Iss. 7, pp. 1539–1547. https://doi.org/10.1016/j.engstruct.2006.09.002
4. Izabela Skrzypczak, Marta S owik, Lidia Buda-O g. The Application of reliability analysis in engineering practice – reinforced concrete foundation. <i>Procedia Engineering</i>. 2017. Vol. 193, pp. 144–151. https://doi.org/10.1016/j.proeng.2017.06.197
5. Jung S. Kong, Ayman N. Ababneh, Dan M. Frangopol, Yunping Xi. Reliability analysis of chloride penetration in saturated concrete. <i>Probabilistic Engineering Mechanics</i>. 2002. Vol. 17. Iss. 3, pp. 305–315. https://doi.org/10.1016/S0266-8920(02)00014-0
6. Trevor J Kirkpatrick, Richard E Weyers, Christine M Anderson-Cook, Michael M Sprinkel. Probabilistic model for the chloride-induced corrosion service life of bridge decks. <i>Cement and Concrete Research.</i> 2002. Vol. 32. Iss. 12, pp. 1943–1960. https://doi.org/10.1016/S0008-8846(02)00905-5
7. Woo-Yong Jung, Young-Soo Yoon, Young-Moo Sohn Predicting the remaining service life of land concrete by steel corrosion. <i>Cement and Concrete Research</i>. 2003. Vol. 33. Iss. 5, pp. 663–677. https://doi.org/10.1016/S0008-8846(02)01034-7
8. Tuutti Kyösti Corrosion of steel in concrete. 1982. [Doctoral Thesis (monograph), Division of Building Materials]. Swedish Cement and Concrete Research Institute, Stockholm.
9. Thirumalai Parthiban, R. Ravi, G.T. Parthiban Potential monitoring system for corrosion of steel in concrete. <i>Advances in Engineering Software.</i> 2006. Vol. 37. Iss. 6, pp. 375–381. https://doi.org/10.1016/j.advengsoft.2005.09.004
10. Michael P. Enright, Dan M. Frangopol. Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion. <i>Engineering Structures</i>. 1998. Vol. 20. Iss. 11, pp. 960–971. https://doi.org/10.1016/S0141-0296(97)00190-9
11. Duracrete, “Statistical Quantification of the Variables in the Limit Stat Functions,” Contract BRPR-CT95-0132, Project BE95-1347, The EU-Brite EuRam III, January 2000.
12. Kim Anh T. Vu, Mark G. Stewart. Structural reliability of concrete bridges including improved chlorideinduced corrosion models. <i>Structural Safety</i>. 2000.
13. Vol. 22. Iss. 4, pp. 313–333. https://doi.org/10.1016/S0167-4730(00)00018-7
14. Sanjeev Kumar Verma, Sudhir Singh Bhadauria, Saleem Akhtar. Estimating residual service life of deteriorated reinforced concrete structures. <i>American Journal of Civil Engineering and Architecture</i>. 2013. Vol. 1 (5), pp. 92–96. DOI: 10.12691/ajcea-1-5-1
15. Stewart M.G., Rosowsky D.V. Structural safety and serviceability of concrete bridges subject to corrosion. <i>Journal of Infrastructure Systems</i>. 1998. Vol. 4, pp. 146-155.
16. Allen C. Estes, Dan M. Frangopol. Updating bridge reliability based on bridge management systems visual inspection results. <i>Journal of Bridge Engineering</i>. 2003. Vol. 8 (6). DOI: 10.1061/(ASCE)1084-0702(2003)8:6(374)
17. Q. Suo, M. Stewart. Corrosion cracking prediction updating of deteriorating RC structures using inspection information. <i>Materials Science.</i> 2009. Vol. 94, pp. 1340–1348, DOI:10.1016/j.ress.2009.02.011
18. Crank J. The Mathematics of Diffusion. 2nd ed. Clarendon Press, Oxford, London. 1975. 414 p.
19. Dhir R.K., Jones M.R., Ng S.L.D. Prediction of total chloride content profile and concentration/time-dependent diffusion coefficients for concrete. <i>Magazine of Concrete Research</i>. 1998. Vol. 50. Iss. 1, pp. 37–48. https://doi.org/10.1680/macr.1998.50.1.37
20. Ditlevsen O., Madsen H.O. Structural reliability methods. Department of mechanical engineering technical university of Denmark. June-September, 2007.
21. Abraham M. Hasofer, Niels C. Lind. Exact and invariant second-moment code format. <i>Journal of the Engineering Mechanics Division</i>. 1974. Vol. 100. Iss. 1.
22. LiuyangFengXudongQian An adaptive learning approach to determine and update crack sizes from strain relaxation data for welded plate joints. <i>Engineering Fracture Mechanics</i>. 2022. Vol. 259. 108165. https://doi.org/10.1016/j.engfracmech.2021.108165
23. Edson Denner Leonel, Alaa Chateauneuf, Wilson Sergio Venturini. Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems. <i>Engineering Analysis with Boundary Elements</i>. 2012. Vol. 36. Iss. 6, pp. 944–959. https://doi.org/10.1016/j.enganabound.2011.12.016
24. Leonela E.D., Chateauneuf A., Venturini W.S., Bressolette P. Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation. <i>International Journal of Fatigue</i>. 2010. Vol. 32. Iss. 11, pp. 1823–1834. https://doi.org/10.1016/j.ijfatigue.2010.05.001
25. Rüdiger Rackwitz, Bernd Flessler. Structural reliability under combined random load sequences. <i>Computers & Structures</i>. 1978. Vol. 9. Iss. 5, pp. 489–494. https://doi.org/10.1016/0045-7949(78)90046-9
26. Andrzej S. Nowak, Kevin R. Collins. Reliability of structures. CRC Press. 2019 407 p.
27. Brazilian Association of Technical Standards. ABNTNBR 6118. Concrete Structural Design – Procedures. Rio de Janeiro, 2003.
28. Papadakis V.G., Roumeliotis A.P., Fardis M.N., Vagenas C.G. Mathematical modelling of chloride effect on concrete durability and protection measures. <i>Concrete repair, rehabilitation and protection</i>. 1996. No. 6, 165–174.
29. Edson Denner Leonel, Wilson SergioVenturini, Alaa Chateauneuf A BEM model applied to failure analysis of multi-fractured structures. <i>Engineering Failure Analysis</i>. 2011. Vol. 18. Iss. 6, pp. 1538–1549 https://doi.org/10.1016/j.engfailanal.2011.05.014
30. JCSS Probabilistic Model Code. ISBN 978-3-909386-79-6. jcss-lc.org/jcss-probabilistic-model-code/
31. Leonovich S.N. Durability of centrifuged reinforced concrete structures during cyclic freezing and thawing. <i>Beton i zhelezobeton</i> [Concrete and reinforced concrete]. 1988. No. 10.
32. Leonovich S.N. Fracture Mechanics Parameters of Concrete: «Test Methods Development and Harmonization of Standards», 1996. <i>Intern. Congress «Concrete in The Service of Mankind»</i>. Dundee, Scotland, UK.
33. Guzeev E.A., Leonovich S.N., Milovanov A.F., Piradov K.A., Seilanov L.A. Razrusheniye betona i yego dolgovechnost’ [Destruction of concrete and its durability]. Minsk: Tydzen. 1997. 170 p.
34. Leonovich S.N. The non-destructive diagnostic methods of concrete-lined tunnels, <i>Proc. of World Tunnel Congress</i>. Wienna, Austria. 1997.
35. Leonovich S.N. The influence of structure of concrete on frost-salt resistance. <i>Proc. of 13-th International Conference of Building Materials (13 IBAUSIL).</i> Weimar, Germany. 1997. Vol. 2.
36. Leonovich S.N. Calculation of durability of concrete monuments using fracture mechanics. <i>Internationale Zeitschrift für Baudenkmalpflege</i>. Aedificatio Publishers. 1999. Helt 6.
37. Leonovich S.N. Treshchinostoykost’ i dolgovechnost’ betonnykh i zhelezobetonnykh elementov v terminakh silovykh i energeticheskikh kriteriyev mekhaniki razrusheniya. [Crack resistance and durability of concrete and reinforced concrete elements in terms of force and energy criteria of fracture mechanics]. Minsk: Tydzen. 2000. 266 p.
38. Leonovich S.N. Algorithm for calculating the durability of reinforced concrete structures during carbonization. <i>Materials of the 6th International scientific and methodological seminar “Prospects for the development of new technologies in construction and training of engineering personnel in the Republic of Belarus</i>. Minsk. 2000. (In Russian).
39. Leonovich S.N. Hypotheses of frost destruction and fracture mechanics of concrete. <i>Proc. 24 – 2nd Int. RILEM Workshop Frost Resistance of concrete: from nanostructure and Pore Solution to Macroscopic Behaviout and Testing</i>. Essen, Germany. 2002.
40. Leonovich S.N. Frost-resistance of expansive (selfstressed) concrete (Fracture mechanics Approach). <i>Prof. of Intern. Conference «Non-traditional Concrete».</i> Brno, Czechia. 2002.
41. Leonovich S.N. Facture mechanism for estimation of freeze – thaw resistance of concrete. <i>15. Internationale Baustofftagung.</i> 24–27 September 2003. Weimar.
42. RILEM Technical Committee 200-HTC. Recommendation of RILEM TC 200-HTC: mechanical concrete properties at high temperatures – modelling and applications. <i>Mater Struct</i>. 40, 841–853 (2007). https://doi.org/10.1617/s11527-007-9285-2
43. Leonovich S.N., Snezhkov D.Yu., Zaitsev Yu.V. About the use of non-destructive testing of concrete at the Minsk-Arena monolithic construction facility (Republic of Belarus). <i>Vestnik of the Department of Construction Sciences</i>. 2008. Iss. 12. Belgorod, pp. 113–124. (In Russian).
44. Leonovich S.N. Method of determining the state of reinforcement of operated reinforced concrete structures. <i>Stroitel’naya nauka i tekhnika</i>. 2008. No. 4 (19).
45. Leonovich S.N. Fracture resistance and durability of NPP supporting structures from the point of view of fracture mechanics. <i>Vestnik of the Belarusian National Technical University</i>. 2009. No. 4, pp. 13–15. (In Russian).
46. Leonovich S.N., Snezhkov D.Yu. Manufactured reinforced concrete structures and products. Method for determining the state of reinforcement (potentiometric method). <i>Izvestiya vysshikh uchebnykh zavedeniy. Stroitel’stvo</i>. 2009. No. 8. (In Russian).
47. Zaitsev Yu.V., Leonovich S.N., Schneider U. Struktura, prochnost’ i mekhanika razrusheniya betonov pri dvukhosnom i trekhosnom szhatii [Structure, strength and fracture mechanics of concrete under biaxial and triaxial compression]. Minsk: BNTU, 2011. 382 p.
48. Leonovich S.N., Prasol A.V. Models of the period of reinforcement corrosion initiation. <i>Stroitel’nye Materialy</i> [Construction Materials]. 2012. No. 9, pp. 74–75. (In Russian).
49. Leonovich S.N., Prasol A.V. The impact of hlorides on reinforced concrete structures: modeling of penetration into concrete. <i>Science and Technology</i>. 2012. No. 2, p. 34.
50. Rudnitsky V.A., Kren A.P., Leonovich S.N. Method for determining the strength class of reinforcement in reinforced concrete: Pat. 16278 Rep. Belarus: IPC(2006.01) G 01N 3/40/; applicant State scientific institution «Institute of Applied Physics of the National Academy of Sciences of Belarus»; Publication date: 2012.08.30 (In Russian).
51. Leonovich S.N., Litvinovsky D.A., Chernyakevich O.Yu., Stepanova A.V. Prochnost’, treshchinostoykost’ i dolgovechnost’ konstruktsionnogo betona pri temperaturnykh i korrozionnykh vozdeystviyakh: monografiya [Strength, crack resistance and durability of structural concrete under temperature and corrosion effects: monograph: in 2 hours. Part 1]. Minsk: BNTU, 2016. 390 p. (In Russian).
52. Shaly E.E., Kim L.V., Leonovich S.N. Probabilistic calculation of the depth and propagation of the carbonization front in the concrete of hydraulic structures of the Khabarovsk Territory. <i>Innovations in concrete science, construction production and training of engineering personnel: a collection of articles based on the materials of the International Scientific and Technical Conference dedicated to the 100th anniversary of the birth of I.N. Akhverdov and S.S. Ataev</i>. Minsk, June 9–10, 2016. Belarusian National Technical University. Part 1, pp. 243–247. (In Russian).
53. Leonovich S.N. Modeling of capillary shrinkage and cracking of concrete at an early age. <i>Nauka i tekhnika</i>. 2018. Vol. 17. No. 4, pp. 265–277. (In Russian).
54. Leonovich S.N. Algorithm for calculating the crack resistance of concrete at an early age with capillary shrinkage according to a generalized criterion. <i>Nauka i tekhnika</i>. 2018. Vol. 17. No. 6, pp. 502–507. (In Russian).
55. Leonovich S.N., Shalyi E.E., Kim L.V. Reinforced concrete under the influence of carbonization and chloride aggression: a probabilistic model for calculating and predicting service life. <i>Nauka i tekhnika</i>. 2019. Vol. 18. No. 4, pp. 284–291. (In Russian).
56. Shaly E.E., Leonovich S.N., Budrevich N.A. Service life prediction algorithm: load, carbonization, chloride aggression. <i>Vestnik of the Brest State Technical University</i>. 2021. No. 3 (126), pp. 17–20. DOI: https://doi.org/10.36773/1818-1112-2021-126-3-17-20
57. Leonovich S.N., Shalyi E.E., Polonina E.N. Dolgovechnost’ portovykh zhelezobetonnykh konstruktsiy (Dal’niy Vostok i Sakhalin): monografiya [Durability of port reinforced concrete structures (Far East and Sakhalin): monograph]. Moscow: INFRA-M. 2022. 315 p.
58. Zhdanok S.A., Polonina E.N., Leonovich S.N. Synergistic effect of SiO<sub>2</sub> nanoparticles and carbon nanotubes on the properties of concrete. <i>Reports of the National Academy of Sciences of Belarus.</i> 2022. Vol. 66. No. 1, pp. 109–112. (In Russian).
Review
For citations:
Leonovich S.N., Shaly E.E., Litvinovsky D.A., Stepanova A.V., Malyuk V.V., Kolodey A.V. Reliability algorithms for calculating and predicting the durability of reinforced concrete under chloride aggression: analysis of methodology and applications. Concrete and Reinforced Concrete. 2022;614(6):40-50. (In Russ.) https://doi.org/10.31659/0005-9889-2022-614-6-40-50
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