Lifetime Axial-Bending Capacity of a R.C. Bridge Pier Cross-Section Subjected to Corrosion

  • P. CastaldoEmail author
  • B. Palazzo
  • A. Mariniello
Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 10)


Reinforced concrete structures in service may be affected by aging, which may include changes in strength and stiffness assumed in structural design, in particular when the concrete is exposed to an aggressive environment. In this context, this paper provides a computational probabilistic approach to predict the time-evolution of the mechanical and geometrical properties of a statically determinate r.c. structural system (i.e. bridge pier) subjected to corrosion-induced deterioration, due to diffusive attack of chlorides, in order to evaluate its service life. Adopting appropriate degradation models of the material properties, concrete and reinforcing steel, as well as assuming appropriate probability density functions related to mechanical and deterioration parameters, the proposed model is based on Monte Carlo simulations in order to evaluate time variant axial force-bending moment resistance domains, with the aim to estimate the time-variant reliability index. Finally, an application to estimate the expected lifetime of a r.c. bridge pier is described.


Reinforced concrete Time-variant structural reliability Monte carlo simulations Corrosion-induced deterioration Chlorides attack Lifetime prediction 


  1. Biondini F, Vergani M (2012) Damage modeling and nonlinear analysis of concrete bridges under corrosion. In: Proceedings of the 6th IABMAS 2012 bridge maintenance, safety, management, resilience and sustainability, Stresa, Italy. CRC Press, Taylor and Francis GroupGoogle Scholar
  2. Biondini F, Bontempi F, Frangopol DM, Malerba PG (2004) Cellular automata approach to durability analysis of concrete structures in aggressive environments. ASCE J Struct Eng 130(11):1724–1737CrossRefGoogle Scholar
  3. Biondini F, Bontempi F, Frangopol DM, Malerba PG (2006) Probabilistic service life assessment and maintenance planning of concrete structures. ASCE J Struct Eng 132(5):810–825CrossRefGoogle Scholar
  4. Biondini F, Camnasio E, Palermo A (2014) Lifetime seismic performance of concrete bridges exposed to corrosion. J Struct Eng 10(7):880–900Google Scholar
  5. Biondini F, Frangopol DM, Malerba PG (2008) Uncertainty effects on life time structural performance of cable-stayed bridges. Prob Eng Mech 23(4):509–522CrossRefGoogle Scholar
  6. Broomfield JP (1997) Corrosion of steel in concrete: understanding investigat. and repair. E&FN SPON, New YorkCrossRefGoogle Scholar
  7. Castaldo P, Tubaldi E (2015) Influence of FPS bearing properties on the seismic performance of base-isolated structures. Earthq Eng Struct Dyn 44(15):2817–2836CrossRefGoogle Scholar
  8. Castaldo P, Ripani M (2016) Optimal design of friction pendulum system properties for isolated structures considering different soil conditions. Soil Dyn Earthq Eng 90:74–87CrossRefGoogle Scholar
  9. Castaldo P, Amendola G, Palazzo B (2016a) Seismic fragility and reliability of structures isolated by friction pendulum devices: seismic reliability-based design (SRBD). Earthq Eng Struct Dyn. Scholar
  10. Castaldo P, Palazzo B, Della Vecchia P (2015) Seismic reliability of base-isolated structures with friction pendulum bearings. Eng Struct 95:80–93CrossRefGoogle Scholar
  11. Castaldo P, Palazzo B, Della Vecchia P (2016b) Life-cycle cost and seismic reliability analysis of 3D systems equipped with FPS for different isolation degrees. Eng Struct 125:349–363CrossRefGoogle Scholar
  12. Castaldo P, Palazzo B, Ferrentino T, Petrone G (2016c) Influence of the strength reduction factor on the seismic reliability of structures with FPS considering intermediate PGA/PGV ratios. Compos. Part B. Scholar
  13. CEB-FIB Task Group 5.6 (2006) Model Code for service life design. Fédération Internationale du Béton FIB, Bulletin 31Google Scholar
  14. Collepardi M, Collepardi S, Ogoumah Olagot JJ, Simonelli F, Trioli R (2010) Diagnosi del degrado e restauro delle strutture in c.a.. TintorettoGoogle Scholar
  15. Cornell CA (1969) A probability-based structural code. ACI-J 66:974–985Google Scholar
  16. Coronelli D, Gambarova P (2004) Structural assessment of corroded reinforced concrete beams: modeling guidelines. J Struct Eng 130(8):1214–1224CrossRefGoogle Scholar
  17. Ditlevsen O, Madsen HO (2004) Structural reliability methods. Maritime Engineering, Department of Mechanical Engineering, Technical University of DenmarkGoogle Scholar
  18. DuraCrete (1998) Modelling of Degradation. EU-Project No.BE95-1347, Probabilistic Performance based Durability Design of Concrete Structures, Report 4–5Google Scholar
  19. Ehlen MA, Thomas MDA, Bentz EC (2009) Life-365 service life prediction model version 2.0 – widely used software helps assess uncertainties in concrete service life and life-cycle costs. Concr Int 31(2):41–46Google Scholar
  20. Ellingwood B, MacGregor JG, Galambos TV, Cornell CA (1982) Probability-based load criteria: load factors and load combinations. J Struct Div 108(ST5):978–997Google Scholar
  21. EN 1990 2002: Eurocode 0 - Basis of Structural DesignGoogle Scholar
  22. Etse G, Ripani M, Mroginski JL (2014) Computational failure analysis of concrete under high temperature. Comput Model Concr Struct - Proc EURO-C 2014(2):715–722Google Scholar
  23. Etse G, Vrech SM, Ripani M (2016) Constitutive theory for recycled aggregate concretes subjected to high temperature. Constr Build Mater 111:43–53CrossRefGoogle Scholar
  24. Etse G, Ripani M, Caggiano A, Schicchi DS (2015) Strength and durability of concrete subjected to high temperature: continuous and discrete constitutive approaches. American Concrete Institute, ACI Special Publication 2015-January (SP 305), pp 9.1–9.18Google Scholar
  25. Etse GJ, Ripani M, Vrech, SM (2013) Fracture energy-based thermodynamically consistent gradient model for concrete under high temperature. In: Proceedings of the 8th international conference on fracture mechanics of concrete and concrete structures, FraMCoS 2013, pp 1506–1515Google Scholar
  26. Fitch MG, Weyers RE, Johnson SD (1995) Determination of end of functional service life for concrete bridge decks. Transp Res Rec 1490:60–66Google Scholar
  27. Fotopolulou SD, Karapetrou ST, Pitilakis KD (2012) Seismic vulnerability of RC buildings considering SSI and aging effects. In: 15th world conference on earthquake engineering, Lisbon, PortugalGoogle Scholar
  28. Ghosh J, Padgett JE (2010) Aging considerations in the development of time-dependent seismic fragility curves. J Struct Eng ASCE 136(12):1497–1511 http://www.usclimatedata.comCrossRefGoogle Scholar
  29. Hwang H, Liu JB, Chiu YH (2001) Seismic fragility analysis of highway bridges. Mid-America Earthquake Center, Technical report, MAEC RR-4 Project, Center for Earthquake Research and Information, University of MemphisGoogle Scholar
  30. ISO/DIS 13823 (2006) General principles on the design of structures for durabilityGoogle Scholar
  31. Kashani MM, Crewe AJ, Alexander NA (2012) Durability considerations in performance-based seismic assessment of deteriorated RC bridges. In: 15th world conference on earthquake engineering, Lisbon, PortugalGoogle Scholar
  32. Kent DC, Park R (1971) Flexural members with confined concrete. J Struct Div 97(7):1969–1990Google Scholar
  33. Liu Y, Weyers R (1998) Modeling the time-to-corrosion cracking in chloride contaminated reinforced concrete structures. ACI Mater J 95:675–680Google Scholar
  34. LNEC E-465 (2005) Concrete prescriptive methodology to estimate concrete properties to achieve the design service life under environment conditions XC or XS. National Laboratory of Civil Engineering (LNEC), Lisbon, PortugalGoogle Scholar
  35. Marchand J (2000) Modeling and behaviour of unsaturated cement systems exposed to aggressive chemical environmental. Mater Struct 34:195–200CrossRefGoogle Scholar
  36. Mori Y, Ellingwood BR (1993) Reliability-based service-life assessment of aging concrete structures. J Struct Eng 119:1600–1621CrossRefGoogle Scholar
  37. Mroginski JL, Etse G, Ripani M (2015) A non-isothermal consolidation model for gradient-based poroplasticity. In: PANACM 2015-1st pan-American congress on computational mechanics, in conjunction with the 11th Argentine congress on computational mechanics MECOM 2015, pp 75–88Google Scholar
  38. Norme Tecniche per le Costruzioni (2008) D.M. 14 January 2008Google Scholar
  39. Okamura H, Maekawa K, Sivasubramaniyam S (1985) Verification of modeling for reinforced concrete finite element. In: Finite element analysis of reinforced concrete structures, proceedings of the seminar ASCE, pp 528–543Google Scholar
  40. Palazzo B, Castaldo P, Della Vecchia P (2014) Seismic reliability analysis of base-isolated structures with friction pendulum system, In: IEEE workshop on environmental, energy and structural monitoring systems proceedings, Napoli, 17–18 September 2014Google Scholar
  41. Palazzo B, Castaldo P, Mariniello A (2015b) Time-variant reliability of R.C. structures. In: ACE 2015 - the 2nd international symposium on advances in civil and infrastructure engineering, 12–13 June, pp 1–8Google Scholar
  42. Palazzo B, Castaldo P, Mariniello A (2015a) Time-variant structural reliability of R.C. structures affected by chloride-induced deterioration. American Concrete Institute, ACI Special Publication - January (SP 305), pp 19.1–19.10Google Scholar
  43. Pitiliakis KD, Karapetrou ST, Fotopoulou SD (2014) Consideration of aging and SSi effects on seismic vulnerability assessment of RC buildings. Bull Earthq Eng 12(4):1755–1776CrossRefGoogle Scholar
  44. Ripani M, Etse G, Vrech S, Mroginski J (2014) Thermodynamic gradient-based poroplastic theory for concrete under high temperatures. Int J Plast 61:157–177CrossRefGoogle Scholar
  45. Ripani M, Etse G, Vrech S (2016) Recycled aggregate concrete: localized failure assessment in thermodynamically consistent non-local plasticity framework. Comput Struct 178:47–57. Scholar
  46. Saenz LP (1964) Discussion of “equation for the stress-strain curve of concrete” by Desayi and Krishnan. ACI J 61(9):1229–1235Google Scholar
  47. Samson E, Marchand J, Snyder KA, Beaudoin JJ (2005) Modeling ion and fluid transport in unsaturated cement systems in isothermal conditions. Cem Concr Res 35:141–153CrossRefGoogle Scholar
  48. Thomas MDA, Bentz EC (2000) Life-365: computer program for predicting the service life and life-cycle cost of reinforced concrete exposed to chloride. Prod. ManualGoogle Scholar
  49. Titi A, Biondini F (2016) On the accuracy of diffusion models for life-cycle assessment of concrete structures. Struct Infrastruct Eng 12(9):1202–1215CrossRefGoogle Scholar
  50. Tuutti K (1982) Corrosion of steel in concrete. Swedish Cement and Concrete Research Institute, Stockholm Report 4Google Scholar
  51. UNI EN 206-1 (2006) Specificazione, prestazione, produzione e conformitàGoogle Scholar
  52. Val DV, Stewart MG, Melchers RE (1998) Effect of reinforcement corrosion on reliability of highway bridges. Eng Struct 20(11):1010–1019CrossRefGoogle Scholar
  53. Verma SK, Bhadauria SS, Akhtar S (2014) Probabilistic evaluation of service life for reinforced concrete structures. Chin J Eng 2014:8 Article ID 648438CrossRefGoogle Scholar
  54. Vrech SM, Ripani M, Etse G (2015) Localized versus diffused failure modes in concrete subjected to high temperature. In: PANACM 2015–1st pan-American congress on computational Mechanics, in conjunction with the 11th Argentine congress on computational mechanics, MECOM 2015, pp 225–236Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Structural, Geotechnical and Building Engineering (DISEG)Politecnico di TorinoTurinItaly
  2. 2.Department of Civil EngineeringUniversity of SalernoSalernoItaly

Personalised recommendations