Investigation of the Failure of Large-Diameter Cast-Iron Water Mains Using a Stochastic, Physical Model
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Cast-iron water mains are still in use in water distribution systems across North America. These pipes are now reaching the end of their expected service lives and are becoming a concern to water utilities. Large-diameter water mains (defined as water mains with a diameter greater than 500 mm (20”)) are particularly important because of they can entail severe consequences when they fail. A physical model is presented to estimate the time-dependent factor of safety and probability of failure of large-diameter cast-iron water mains. Failure is assumed to occur by longitudinal cracking caused by tensile hoop stress and a reduction in the strength of the pipe due to corrosion pitting. Six sources of loading are considered in the model, including: earth load, live load, frost load, internal water pressure, and the curvature caused by the live load. The model is used in a two-part sensitivity analysis to determine the influence of each input of the model outputs. The first part of the analysis is a one-way deterministic sensitivity analysis of all 28 input variables. This identified six variables as having a high impact: the pipe wall thickness, the pitting depth scaling constant, the corrosion rate inhibition factor, the fracture toughness, the constant S in the residual tensile strength calculation, and the pipe diameter. The second part is a stochastic sensitivity analysis to further investigate the sensitivity of the model to those variables identified in the deterministic analysis. The mean factor of safety and probability of failure were determined to be sensitive to the pipe wall thickness, corrosion rate, and the constants used to calculate the residual tensile strength, but were relatively insensitive to the diameter of the pipe. A case study of the City of Hamilton water distribution system was performed to characterize the failure of 20 large-diameter cast-iron water mains. Due to the uncertainty in the accuracy of the model, the pipes were assigned ranks relative to each other rather than an absolute probability of failure. The diameter, burial depth and soil type were all determined to have an effect on the ranking of each pipe.