Skip to main content

Advertisement

SpringerLink
Log in

Corrosion initiation in marine concrete members considering spatial correlation of porosity: a mesoscale probabilistic analysis

  • Original Article
  • Published:
Materials and Structures Aims and scope Submit manuscript

Abstract

The random field theory has been primarily applied to consider the porosity randomness in the mesoscopic model for cement-based materials. The scale of fluctuation (SOF) of cement-based materials' porosity is the basis of studying the spatial variability of durability performance under the framework of mesoscale modeling of reinforced concrete (RC) structures. In this paper, an approach for SOF and the associated spatial distribution estimation of porosity for cement-based materials are presented with the aid of two-dimensional (2D) image processing technique. The ordinary Kriging interpolation method is employed to determine the porosity at unsampled position. The SOF of porosity for the cement-based materials is calculated using the curve-fitting method based on image data analysis. The results indicate that the obtained SOF in this study is significantly smaller than that assumed in the previous literature. Then, probabilistic evaluation of the time to corrosion initiation was carried out for a reinforced concrete beam in a marine environment. A comparative study is presented to examine the effect of spatial correlation of porosity in cement paste on the corrosion initiation of RC members under chloride attack. The results show that using larger SOF in a random field for modeling the spatial distribution associated with porosity in the cement paste results in a higher probability of corrosion initiation, eventually leading to unconservative estimates of the probability of the rebar corrosion initiation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Stewart MG, Al-harthy A (2008) Pitting corrosion and structural reliability of corroding RC structures: experimental data and probabilistic analysis. Reliab Eng Syst Saf 93:373–382. https://doi.org/10.1016/j.ress.2006.12.013

    Article  Google Scholar 

  2. Li D, Wei R, Li L, Guan X, Mi X (2019) Pitting corrosion of reinforcing steel bars in chloride contaminated concrete. Constr Build Mater 199:359–368. https://doi.org/10.1016/j.conbuildmat.2018.12.003

    Article  Google Scholar 

  3. Lim S, Akiyama M, Frangopol DM (2016) Assessment of the structural performance of corrosion-affected RC members based on experimental study and probabilistic modeling. Eng Struct 127:189–205. https://doi.org/10.1016/j.engstruct.2016.08.040

    Article  Google Scholar 

  4. Gu X, Guo H, Zhou B, Zhang W, Jiang C (2018) Corrosion non-uniformity of steel bars and reliability of corroded RC beams. Eng Struct 167:188–202. https://doi.org/10.1016/j.engstruct.2018.04.020

  5. Zhang M, Song H, Lim S, Akiyama M, Frangopol DM (2019) Reliability estimation of corroded RC structures based on spatial variability using experimental evidence, probabilistic analysis and finite element method. Eng Struct 192:30–52. https://doi.org/10.1016/j.engstruct.2019.04.085

    Article  Google Scholar 

  6. Biswas RK, Iwanami M, Chijiwa N, Uno K (2020) Effect of non-uniform rebar corrosion on structural performance of RC structures: a numerical and experimental investigation. Constr Build Mater 230:116908. https://doi.org/10.1016/j.conbuildmat.2019.116908

    Article  Google Scholar 

  7. Yu Y, Gao W, Castel A, Liu A, Feng Y, Chen X, Mukherjee A (2020) Modelling steel corrosion under concrete non-uniformity and structural defects. Cem Concr Res 135:106109. https://doi.org/10.1016/j.cemconres.2020.106109

    Article  Google Scholar 

  8. Baji H (2020) Stochastic modelling of concrete cover cracking considering spatio-temporal variation of corrosion. Cem Concr Res 133:106081. https://doi.org/10.1016/j.cemconres.2020.106081

    Article  Google Scholar 

  9. Zacchei E, Nogueira CG (2021) 2D/3D Numerical analyses of corrosion initiation in RC structures accounting fluctuations of chloride ions by external actions, KSCE. J Civ Eng 25:2105–2120. https://doi.org/10.1007/s12205-021-1242-z

    Article  Google Scholar 

  10. Kwon SJ, Na UJ, Park SS, Jung SH (2009) Service life prediction of concrete wharves with early-aged crack: Probabilistic approach for chloride diffusion. Struct Saf 31:75–83. https://doi.org/10.1016/j.strusafe.2008.03.004

    Article  Google Scholar 

  11. Leng Y, Lu ZH, Li CQ, Zhao YG (2021) Time-variant probabilistic assessment of corrosion initiation of marine concrete structures considering maximum phenomenon. Constr Build Mater 272:121967. https://doi.org/10.1016/j.conbuildmat.2020.121967

    Article  Google Scholar 

  12. Lu ZH, Zhao YG, Yu ZW, Ding FX (2011) Probabilistic evaluation of initiation time in RC bridge beams with load-induced cracks exposed to de-icing salts. Cem Concr Res 41:365–372. https://doi.org/10.1016/j.cemconres.2010.12.003

    Article  Google Scholar 

  13. Val DV, Trapper PA (2008) Probabilistic evaluation of initiation time of chloride-induced corrosion. Reliab Eng Syst Saf 93:364–372. https://doi.org/10.1016/j.ress.2006.12.010

    Article  Google Scholar 

  14. Frier C, Sørensen JD (2007) Finite element reliability analysis of chloride ingress into reinforced concrete structures. Struct Infrastruct Eng 3:355–366. https://doi.org/10.1080/15732470600557688

    Article  Google Scholar 

  15. Zofia S, Adam Z (2013) Theoretical model and experimental tests on chloride diffusion and migration processes in concrete. Procedia Eng 57:1121–1130. https://doi.org/10.1016/j.proeng.2013.04.141

    Article  Google Scholar 

  16. Yang CC, Chiang CT (2009) Relation between the chloride migration coefficients of concrete from the colourimetric method and the chloride profile method. J Chinese Inst Eng 32:801–809. https://doi.org/10.1080/02533839.2009.9671564

    Article  Google Scholar 

  17. Zhang Z, Song X, Liu Y, Wu D, Song C (2017) Three-dimensional mesoscale modelling of concrete composites by using random walking algorithm. Compos Sci Technol 149:235–245. https://doi.org/10.1016/j.compscitech.2017.06.015

    Article  Google Scholar 

  18. Thilakarathna PSM, Kristombu Baduge KS, Mendis P, Vimonsatit V, Lee H (2020) Mesoscale modelling of concrete—a review of geometry generation, placing algorithms, constitutive relations and applications. Eng Fract Mech 231:106974. https://doi.org/10.1016/j.engfracmech.2020.106974

    Article  Google Scholar 

  19. Pan Z, Ruan X, Chen A (2014) Chloride diffusivity of concrete: probabilistic characteristics at meso-scale. Comput Concr 13:187–207. https://doi.org/10.12989/cac.2014.13.2.187

  20. Du X, Jin L, Ma G (2014) A meso-scale numerical method for the simulation of chloride diffusivity in concrete, Finite Elem. Anal Des 85:87–100. https://doi.org/10.1016/j.finel.2014.03.002

    Article  Google Scholar 

  21. Zheng JJ, Zhou XZ (2007) Prediction of the chloride diffusion coefficient of concrete. Mater Struct 40:693–701. https://doi.org/10.1617/s11527-006-9182-0

    Article  Google Scholar 

  22. Zheng JJ, Zhou XZ, Wu YF, Jin XY (2012) A numerical method for the chloride diffusivity in concrete with aggregate shape effect. Constr Build Mater 31:151–156. https://doi.org/10.1016/j.conbuildmat.2011.12.061

    Article  Google Scholar 

  23. Ruan X, Li Y, Zhou X, Jin Z, Yin Z (2020) Simulation method of concrete chloride ingress with mesoscopic cellular automata. Constr Build Mater 249:118778. https://doi.org/10.1016/j.conbuildmat.2020.118778

    Article  Google Scholar 

  24. Li LY (2014) A pore size distribution-based chloride transport model in concrete. Mag Concr Res 66:937–947. https://doi.org/10.1680/macr.14.00032

    Article  Google Scholar 

  25. Ning J, Zha X, Ren C (2020) Mesoscale approach for estimating carbonation depth affected by random aggregates under supercritical conditions. Constr Build Mater 263:120633. https://doi.org/10.1016/j.conbuildmat.2020.120633

    Article  Google Scholar 

  26. Lin L, Chen J, Zhang X, Li X (2011) A novel 2-D random void model and its application in ultrasonically determined void content for composite materials. NDT E Int 44:254–260. https://doi.org/10.1016/j.ndteint.2010.12.003

    Article  Google Scholar 

  27. Vanmarcke E (2010) Random fields: analysis and synthesis. World Scientific, Singapore

  28. Yu M, Bao H, Ye J, Chi Y (2017) The effect of random porosity field on supercritical carbonation of cement-based materials. Constr Build Mater 146:144–155. https://doi.org/10.1016/j.conbuildmat.2017.04.060

    Article  Google Scholar 

  29. Hernández MG, Izquierdo MAG, Ibáñez A, Anaya JJ, Ullate LG (2000) Porosity estimation of concrete by ultrasonic NDE. Ultrasonics 38:531–533. https://doi.org/10.1016/S0041-624X(99)00095-5

    Article  Google Scholar 

  30. Chandrappa AK, Biligiri KP (2018) Pore structure characterization of pervious concrete using X-ray microcomputed tomography. J Mater Civ Eng 30:04018108. https://doi.org/10.1061/(asce)mt.1943-5533.0002285

    Article  Google Scholar 

  31. Zhang M, Zhou B, Ruan X, Li Y (2022) A 3D random porous media model for cement mortar based on X-ray computed tomography. Constr Build Mater 341:127750. https://doi.org/10.1016/j.conbuildmat.2022.127750

  32. Liu J, Tang K, Qiu Q, Pan D, Lei Z, Xing F (2014) Experimental investigation on pore structure characterization of concrete exposed to water and chlorides. Materials (Basel) 6:6646–6659. https://doi.org/10.3390/ma7096646

    Article  Google Scholar 

  33. Ruan X, Li Y, Jin Z, Pan Z, Yin Z (2019) Modeling method of concrete material at mesoscale with refined aggregate shapes based on image recognition. Constr Build Mater 204:562–575. https://doi.org/10.1016/j.conbuildmat.2019.01.157

    Article  Google Scholar 

  34. Cressie N (1988) Spatial prediction and ordinary Kriging. Math Geol 20:405–421. https://doi.org/10.1007/BF00892986

  35. Deutsch CV, Journel AG (1997) GSLIB geostatistical software library and user’s guide. Oxford University Press, New York

  36. Der Kiureghian A, Ke J (1988) The stochastic finite element method in structural reliability. Probabilistic Eng Mech 3:83–91. https://doi.org/10.1016/0266-8920(88)90019-7

  37. Matthies HG, Brenner CE, Bucher CG, Soares CG (1997) Uncertainties in probabilistic numerical analysis of structures and solids—stochastic finite elements. Struct Saf 19:283–336. https://doi.org/10.1016/S0167-4730(97)00013-1

    Article  Google Scholar 

  38. Noh Y, Liu KKC (2009) Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula. Struct MultidiscOptim 38:1–16. https://doi.org/10.1007/s00158-008-0277-9

    Article  Google Scholar 

  39. Tang X, Li D, Zhou C, Phoon K (2015) Copula-based approaches for evaluating slope reliability under incomplete probability information. Struct Saf 52:90–99. https://doi.org/10.1016/j.strusafe.2014.09.007

    Article  Google Scholar 

  40. Lebrun R, Dutfoy A (2009) An innovating analysis of the Nataf transformation from the copula viewpoint, Probabilistic Eng. Mech 24:312–320. https://doi.org/10.1016/j.probengmech.2008.08.001

    Article  Google Scholar 

  41. Reddy JN, Gartling DK (2010) The finite element method in heat transfer and fluid dynamics. CRC Press, Cambridge

  42. Bajja Z, Dridi W, Larbi B, Le Bescop P (2015) The validity of the formation factor concept from through-out diffusion tests on Portland cement mortars. Cem Concr Comp 63:76–83. https://doi.org/10.1016/j.cemconcomp.2015.07.014

  43. Qiao C, Coyle AT, Isgor OB, Weiss WJ (2018) Prediction of chloride ingress in saturated concrete using formation factor and chloride binding isotherm. Adv Civ Eng Mat 7(1):206–220

    Google Scholar 

  44. Jafari Azad V, Erbektas AR, Qiao C, Isgor OB, Weiss WJ (2019) Relating the formation factor and chloride binding parameters to the apparent chloride diffusion coefficient of concrete. Jour Mat Civ Eng 31(2):04018392

    Article  Google Scholar 

  45. Weiss WJ, Spragg RP, Isgor OB, Ley MT, Dam TV (2018) Toward performance specifications for concrete: linking resistivity, RCPT and diffusion predictions using the formation factor for use in specifications, In High tech concrete: where technology and engineering meet. Springer, Cham, pp 2057–2065

    Google Scholar 

  46. Baten B, Manzur T (2022) Formation factor concept for non-destructive evaluation of concrete’s chloride diffusion coefficients. Cem Conc Comp 128:104440

    Article  Google Scholar 

  47. Snyder K (2001) The relationship between the formation factor and the diffusion coefficient of porous materials saturated with concentrated electrolytes: theoretical and experimental considerations. Conc Sci Eng 3:216–224

    Google Scholar 

  48. Sakai Y (2019) Relationship between pore structure and chloride diffusion in cementitious materials. Constr Build Mater 229:116868. https://doi.org/10.1016/j.conbuildmat.2019.116868

  49. Zheng J, Zhou X (2008) Analytical solution for the chloride diffusivity of hardened cement paste. J Mater Civ Eng 20:384–391. https://doi.org/10.1061/(asce)0899-1561(2008)20:5(384)

    Article  Google Scholar 

  50. Shi M, Chen Z, Sun J (1999) Determination of chloride diffusivity in concrete by AC impedance spectroscopy. Cem Concr Res 29:1111–1115. https://doi.org/10.1016/S0008-8846(99)00079-4

    Article  Google Scholar 

  51. Tang L, Nilsson LO (1992) Rapid determination of the chloride diffusivity in concrete by applying an electrical field. ACI Mater J 89:49–53. https://doi.org/10.14359/1244

  52. Cao C, Cheung MMS (2014) Non-uniform rust expansion for chloride-induced pitting corrosion in RC structures. Constr Build Mater 51:75–81. https://doi.org/10.1016/j.conbuildmat.2013.10.042

    Article  Google Scholar 

  53. Chen J, Zhang W, Gu X (2019) Modeling time-dependent circumferential non-uniform corrosion of steel bars in concrete considering corrosion-induced cracking effects. Eng Struct 201:109766. https://doi.org/10.1016/j.engstruct.2019.109766

    Article  Google Scholar 

  54. Chen E, Leung CKY (2015) Finite element modeling of concrete cover cracking due to non-uniform steel corrosion. Eng Fract Mech 134:61–78. https://doi.org/10.1016/j.engfracmech.2014.12.011

    Article  Google Scholar 

  55. Zhang M, Lim S, Akiyama M, Frangopol DM (2019) Modeling spatial variability of steel corrosion using Gumbel distribution. In: 13th Int. Conf. Appl. Stat. Probab. Civ. Eng., Seoul, South Korea. https://doi.org/10.22725/ICASP13.274

  56. Lim S, Akiyama M, Frangopol DM, Jiang H (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 13:118–134. https://doi.org/10.1080/15732479.2016.1198397

    Article  Google Scholar 

  57. Chiu CK, Tu FJ, Hsiao FP (2015) Lifetime seismic performance assessment for chloride-corroded reinforced concrete buildings. Struct Infrastruct Eng 11:345–362. https://doi.org/10.1080/15732479.2014.886596

    Article  Google Scholar 

  58. Val DV, Stewart MG (2003) Life-cycle cost analysis of reinforced concrete structures in marine environments. Struct Saf 25:343–362. https://doi.org/10.1016/S0167-4730(03)00014-6

    Article  Google Scholar 

  59. Akiyama M, Frangopol DM, Suzuki, (2012) Integration of the effects of airborne chlorides into reliability-based durability design of reinforced concrete structures in a marine environment. Struct Infrastruct Eng 8:125–134. https://doi.org/10.1080/15732470903363313

    Article  Google Scholar 

  60. Ge B, Kim S (2021) Probabilistic service life prediction updating with inspection information for RC structures subjected to coupled corrosion and fatigue. Eng Struct 238:112260. https://doi.org/10.1016/j.engstruct.2021.112260

    Article  Google Scholar 

  61. He ZS, Supasit S, Akiyama M, Frangopol DM (2020) Life-cycle reliability-based design and reliability updating of reinforced concrete shield tunnels in coastal regions. Struct Infrastruct Eng 16:726–737. https://doi.org/10.1080/15732479.2019.1674343

    Article  Google Scholar 

  62. Akiyama M, Frangopol DM, Yoshida I (2010) Time-dependent reliability analysis of existing RC structures in a marine environment using hazard associated with airborne chlorides. Eng Struct 32:3768–3779. https://doi.org/10.1016/j.engstruct.2010.08.021

    Article  Google Scholar 

  63. Zhang M, Nishiya N, Akiyama M, Lim S, Masuda K (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 264:120678. https://doi.org/10.1016/j.conbuildmat.2020.120678

    Article  Google Scholar 

  64. Srivaranun S, Akiyama M, Bocchini P, Christou V, Frangopol DM, Fukushima H, Masuda K (2021) Effect of the interaction of corrosion pits among multiple tensile rebars on the reliability of RC structures: Experimental and numerical investigation. Struct Saf 93:102115. https://doi.org/10.1016/j.strusafe.2021.102115

    Article  Google Scholar 

Download references

Acknowledgements

The financial supports from National Key R&D Program of China under Grant 2018YFB1600100, Natural Science Foundation of China under Grant 51678435 and 52078367, and Shanghai Sailing Program under Grant 21YF1449300 are gratefully acknowledged. The support provided by Shandong Transportation Research Institute for the experiments is also acknowledged.

Author information

Authors and Affiliations

  1. Department of Bridge Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, China

    Mingyang Zhang, Xin Ruan & Yue Li

  2. Key Laboratory of Performance Evolution and Control for Engineering Structures (Ministry of Education), Tongji University, Shanghai, China

    Xin Ruan

Authors
  1. Mingyang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xin Ruan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yue Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xin Ruan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, M., Ruan, X. & Li, Y. Corrosion initiation in marine concrete members considering spatial correlation of porosity: a mesoscale probabilistic analysis. Mater Struct 55, 168 (2022). https://doi.org/10.1617/s11527-022-01994-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1617/s11527-022-01994-w

Keywords

Search

Navigation