Journal of Failure Analysis and Prevention

, Volume 13, Issue 5, pp 634–642 | Cite as

Multi-Failure Mode Assessment of Buried Concrete Pipes Subjected to Time-Dependent Deterioration, Using System Reliability Analysis

  • M. Mahmoodian
  • A. M. Alani
Technical Article---Peer-Reviewed


This article presents a reliability-based methodology for assessment of corrosion-affected, reinforced concrete sewers, considering serviceability and ultimate strength as limit state functions for multi-failure mode assessment. A stochastic model for system failure analysis is developed, which relates to key factors that affect concrete corrosion in a concrete sewer system in Harrogate in the United Kingdom. A time-dependent Monte Carlo simulation method is employed to quantify the probability of failure of concrete sewers with 70-cm diameter due to two categories of failure modes (serviceability and ultimate strength). Factors that affect the failure due to concrete corrosion are also studied by way of parametric sensitivity analysis.


System reliability analysis Multi-failure mode assessment Time-dependent deterioration Concrete sewers Monte Carlo simulation Concrete durability 

List of Symbols


Depth of the equivalent rectangular stress block (mm)


Acid-consuming capability of the wall material

\( A_{\text{s}} \)

Area of tension reinforcement in length b (mm2/m)


Unit length of pipe (1000 mm)

\( B_{1} \)

Crack control coefficient for effect of spacing and number of layers of reinforcement


Average rate of corrosion (mm/year)

\( C_{1} \)

Crack control coefficient for type of reinforcement

\( d \)

Distance from compression face to centroid of tension reinforcement (mm)

\( d_{\text{b}} \)

Diameter of rebar in inner cage (mm)


Dissolved sulfide concentration (mg/l)

\( f^{\prime}_{\text{c}} \)

Design compressive strength of concrete (MPa)

\( f_{\text{y}} \)

Design yield strength of reinforcement (MPa)


Crack width control factor

\( F_{\text{c}} \)

Factor for effect of curvature on diagonal tension (shear) strength in curved components

\( F_{\text{d}} \)

Factor for crack depth effect resulting in increase in diagonal tension (shear) strength with decreasing \( d \)

\( F_{\text{N}} \)

Coefficient for effect of thrust on shear strength

\( h \)

Overall thickness of member (wall thickness) (mm)

\( i \)

Coefficient for effect of axial force at service load stress


Acid reaction factor


pH-dependent factor for proportion of H2S


Width of the stream surface


Perimeter of the exposed wall

\( M_{\text{s}} \)

Service load bending moment acting on length b (N mm/m)

\( M_{u} \)

Factored moment acting on length b (N mm/m)

\( N_{\text{s}} \)

Axial thrust acting on length b, service load condition (+ when compressive, − when tensile) (N/m)

\( N_{u} \)

Factored axial thrust acting on length b (+ when compressive, − when tensile) (N/m)


Slope of the pipeline


Elapsed time


Velocity of the stream (m/s)

\( V_{\text{b}} \)

Basic shear strength of length b at critical section

\( {{\Upphi}} \)

Average flux of H2S to the wall

\( \phi_{\text{f}} \)

Strength reduction factor for flexure

\( \phi_{\text{v}} \)

Strength reduction factor for shear

\( \Updelta \)

Reduction in wall thickness due to corrosion (mm)

\( \Updelta_{\hbox{max} } \)

Maximum permissible reduction in wall thickness (structural resistance or limit) (mm)


  1. 1.
    OFWAT, Maintaining Water and Sewerage Systems in England and Wales, Our Proposed Approach for the 2004 Periodic Review (Office of Water Services, London, 2002)Google Scholar
  2. 2.
    The Urban Waste Water Treatment Directive, 91/271/EEC, Waste Water Treatment in the United Kingdom—2012 Implementation of the European Union Urban Waste Water Treatment Directive—91/271/EEC (Department for Environment, Food and Rural Affairs, London, 2012)Google Scholar
  3. 3.
    L. Zhang, P. De Schryver, B. De Gusseme, W. De Muynck, N. Boon, W. Verstraete, Chemical and biological technologies for hydrogen sulphide emission control in sewer systems: a review. J. Water Res. 42, 1–12 (2008)CrossRefGoogle Scholar
  4. 4.
    E. Vincke, Biogenic sulfuric acid corrosion of concrete: microbial interaction, simulation and prevention. Ph.D. Thesis, Faculty of Bio-engineering Science, University Ghent, Ghent, 2002, pp. 7–9Google Scholar
  5. 5.
    N.S. Grigg, Infrastructure management systems, in Water, Wastewater, and Stormwater Infrastructure Management (Lewis Publishers, Boca Raton, 2003), pp. 1–17Google Scholar
  6. 6.
    B. Salman, O. Salem, Modeling failure of wastewater collection lines using various section-level regression models. ASCE J. Infrastruct. Syst. 18(2), 146–154 (2012)CrossRefGoogle Scholar
  7. 7.
    P. Davis, D. De Silva, S. Gould, S. Burn, Condition assessment and failure prediction for asbestos cement sewer mains, in Proceedings of the Pipes Wagga Wagga Conference, Wagga Wagga, 17–20 Oct 2005Google Scholar
  8. 8.
    P. Davis, D. De Silva, D. Marlow, M. Moglia, S. Gould, S. Burn, Failure prediction and optimal scheduling of replacements in asbestos cement water pipes. J. Water Supply Res. Technol.—AQUA 57(4), 239–252 (2008)CrossRefGoogle Scholar
  9. 9.
    N. De Belie, J. Monteny, J.A. Beeldens, E. Vincke, D. Van Gemert, W. Verstraete, Experimental research and prediction of the effect of chemical and biogenic sulfuric acid on different types of commercially produced concrete sewer pipes. J. Cem. Concr. Res. 34, 2223–2236 (2004)CrossRefGoogle Scholar
  10. 10.
    Y. Kleiner, R. Sadiq, B. Rajani, Modelling the deterioration of buried infrastructure as a fuzzy Markov process. J. Water Supply Res. Technol.—AQUA 55(2), 67–80 (2006)Google Scholar
  11. 11.
    R. Sadiq, B. Rajani, Y. Kleiner, Probabilistic risk analysis of corrosion associated failures in cast iron water mains. Reliab. Eng. Sys. Saf. 86(1), 1–10 (2004)CrossRefGoogle Scholar
  12. 12.
    A.M. Freudenthal, Safety and the probability of structural failure. ASCE Trans. 121, 1337–1397 (1956)Google Scholar
  13. 13.
    M. Ahammed, R.E. Melchers, Reliability of underground pipelines subject to corrosion. J. Transp. Eng. 120(6), 989–1002 (1994)CrossRefGoogle Scholar
  14. 14.
    M. Ahammed, R.E. Melchers, Probabilistic analysis of pipelines subjected to pitting corrosion leaks. Eng. Struct. 17(2), 74–80 (1995)CrossRefGoogle Scholar
  15. 15.
    M. Ahammed, R.E. Melchers, Probabilistic analysis of underground pipelines subject to combined stresses and corrosion. Eng. Struct. 19(12), 988–994 (1997)CrossRefGoogle Scholar
  16. 16.
    A. Benmansour, Z. Mrabet, Reliability of Buried pipes, in Asranet (Integrating Advanced Structural Analysis with Structural Reliability Analysis) International Colloquium, Glasgow, 8–10 July 2002Google Scholar
  17. 17.
    S.X. Li, S.R. Yu, H.L. Zeng, J.H. Li, R. Liang, Predicting corrosion remaining life of underground pipelines with a mechanically-based probabilistic model. J. Petrol. Sci. Eng. 65(3–4), 162–166 (2009)CrossRefGoogle Scholar
  18. 18.
    L.S. Lee, H. Estrada, M. Baumert, Time-dependent reliability analysis of FRP rehabilitated pipes. ASCE J. Compos. Constr. 14(3), 272–279 (2010)CrossRefGoogle Scholar
  19. 19.
    M. Mahmoodian, C.Q. Li, Service life prediction of underground concrete pipes subjected to corrosion, in 4th International Conference on Concrete Repair, Dresden, 26–28 Sept 2011Google Scholar
  20. 20.
    P. Davis, S. Burn, M. Moglia, S. Gould, A physical probabilistic model to predict failure rates in buried PVC pipelines. Reliab. Eng. Syst. Saf. 92, 1258–1266 (2007)CrossRefGoogle Scholar
  21. 21.
    F.H. Olmsted, H. Hamlin, Converting portions of the Los Angeles outfall sewer into a septic tank. Eng News 44(19), 317–318 (1900)Google Scholar
  22. 22.
    F.D. Bowlus, A.P. Banta, Control of anaerobic decomposition in sewage transportation. Water Works Sewerage 79(11), 369 (1932)Google Scholar
  23. 23.
    C.C. James, Sewers and their construction, in Drainage Problems of the East (A Revised and Enlarged Edition of Oriental Drainage) (Bennett, Coleman & Company, Bombay, 1917)Google Scholar
  24. 24.
    C.D. Parker, The corrosion of concrete 1. The isolation of a species of bacterium associated with the corrosion of concrete exposed to atmospheres containing hydrogen sulfide. Aust. J. Exp. Biol. Med. Sci. 23, 81–90 (1945)CrossRefGoogle Scholar
  25. 25.
    C.D. Parker, The corrosion of concrete 2. The function of Thiobacillus concretivorus nov. spec. in the corrosion of concrete exposed to atmospheres containing hydrogen sulphide. Aust. J. Exp. Biol. Med. Sci. 23, 91–98 (1945)CrossRefGoogle Scholar
  26. 26.
    C.D. Parker, Species of sulphur bacteria associated with the corrosion of concrete. Nature 159(4039), 439–440 (1947)CrossRefGoogle Scholar
  27. 27.
    R. Pomeroy, F.D. Bowlus, Progress report on sulfide control research. Sew Works J. 18(4), 597–640 (1946)Google Scholar
  28. 28.
    K.-S. Cho, T. Mori, A newly isolated fungus participates in the corrosion of concrete sewer pipes. Water Sci. Technol. 31(7), 263–271 (1995)CrossRefGoogle Scholar
  29. 29.
    M. Hernandez, E.A. Marchand, D. Roberts, J. Peccia, In situ assessment of active Thiobacillus species in corroding concrete sewers using fluorescent RNA probes. Int. Biodeterior. Biodegrad. 49(4), 271–276 (2002)CrossRefGoogle Scholar
  30. 30.
    D. Nica, J.L. Davis, L. Kirby, G. Zuo, D.J. Roberts, Isolation and characterization of microorganisms involved in the biodeterioration of concrete in sewers. Int. Biodeterior. Biodegrad. 46(1), 61–68 (2000)CrossRefGoogle Scholar
  31. 31.
    S. Okabe, M. Odagiri, T. Ito, H. Satoh, Succession of sulfur-oxidizing bacteria in the microbial community on corroding concrete in sewer systems. Appl. Environ. Microbiol. 73(3), 971–980 (2007)CrossRefGoogle Scholar
  32. 32.
    C.D. Parker, J. Prisk, The oxidation of inorganic compounds of sulphur by various sulphur bacteria. J. Gen. Microbiol. 8(3), 344–364 (1953)CrossRefGoogle Scholar
  33. 33.
    ASCE 60, Manuals and Reports of Engineering Practice, Gravity Sanitary Sewers, 2nd edn. (American Society of Civil Engineers, Reston, 2007)Google Scholar
  34. 34.
    ASCE 15-98, Standard Practice for Direct Design of Buried Precast Concrete Pipe Using Standard Installations (SIDD) (American Society of Civil engineers, Reston, 2000)Google Scholar
  35. 35.
    O. Ditlevsen, H.O. Madsen, Structural Reliability Methods (Chichester, New York, 1996)Google Scholar
  36. 36.
    R.E. Melchers, Structural Reliability Analysis and Prediction, 2nd edn. (Wiley, Chichester, 1999)Google Scholar
  37. 37.
    R.Y. Rubinstein, D.P. Kroese, Simulation and the Monte Carlo Method, 2nd edn. (Wiley, New York, 2008)Google Scholar

Copyright information

© ASM International 2013

Authors and Affiliations

  1. 1.School of EngineeringUniversity of GreenwichLondonUK

Personalised recommendations