Ingenieria Naval

Reliability Engineering and System Safety 86 (2004) 1–10 www.elsevier.com/locate/ress

Probabilistic risk analysis of corrosion associated failures in cast iron water mains
Rehan Sadiq*, Balvant Rajani, Yehuda Kleiner
Institute for Research in Construction, National Research Council, M 20, 1200 Montreal Road, Ottawa, Ont., Canada K1A 0R6 Received 20 September 2003; accepted 13 December 2003Abstract This paper proposes a method using probabilistic risk analysis for application to corrosion associated failures in grey cast iron water mains. External corrosion reduces the capacity of the pipeline to resist stresses. When external stresses exceed the residual ultimate strength, pipe breakage becomes imminent, and the overall reliability of a water distribution network is reduced. Modellingstresses and external corrosion acting on a pipe involves uncertainties inherent in the mechanistic/statistical models and their input parameters. Monte Carlo (MC) simulations were used to perform the probabilistic analysis. The reduction in the factor of safety (FOS) of water mains over time was computed, with a failure defined as a situation in which FOS becomes smaller than 1. The MC simulationsyielded an empirical probability density function of time to failure, to which a lognormal distribution was fitted leading to the derivation of a failure hazard function. A sensitivity analysis revealed that the contribution of corrosion parameters to the variability of time to failure was more significant than the combined contributions of all other parameters. Areas where more research is neededare identified. Crown Copyright q 2004 Published by Elsevier Ltd. All rights reserved.
Keywords: Cast iron; Corrosion; Factor of safety; Monte Carlo simulations; Reliability; Risk; Uncertainty; Water mains

1. Introduction The long-term planning of the renewal of water distribution networks requires the ability to predict system reliability as well as assess the economic impact. A survey of 21cities comprising 11% of Canada’s population revealed that in 1993 approximately 50% of all water distribution pipes were grey cast iron (CI) [18]. A similar study reported that 48% of water distribution networks in the USA consists of grey CI pipes [10]. Grey CI pipes tend to corrode in aggressive environments, resulting in pits or graphitized areas, which weaken the pipe’s structural resiliency[17]. The failure of pipes is mostly the result of this structural weakening coupled with externally (environmental) and internally (operational) imposed stresses. There is a high degree of uncertainty associated with all the factors contributing to pipe failure, and especially corrosion rates because of large spatial (even in moderate size networks) and temporal variabilities. The traditional
*Corresponding author. Tel.: þ 1-613-993-6282; fax: þ1-613-954-5984. E-mail addresses: rehan.sadiq@nrc-cnrc.gc.ca (R. Sadiq), balvant. rajani@nrc-cnrc.gc.ca (B. Rajani), yehuda.kleiner@nrc-cnrc.gc.ca (Y. Kleiner).

deterministic approach, using point estimates (or fixed values) to estimate factor of safety (FOS), is generally not sufficient, and requires a detailed uncertainty analysis to quantify theprobability of pipe failures at a given time in order to plan maintenance and repair strategies. The aims of this paper are to develop a method for evaluating the timedependent reliability of underground grey CI water mains, and to identify which are the major factors that contribute to water main failures. Ahammed and Melchers [1] used an analytical probabilistic technique—First Order ReliabilityMethod to quantify uncertainties. The proposed technique, although probabilistic in nature is numerical rather than analytical, and it permits Monte Carlo (MC) simulations and allows for fitting of results to a probability distribution, which can be used to develop hazard function of time to failure. In this paper, rank correlation coefficients are used to conduct sensitivity analysis to identify...