Quantifying economic lifetime for asset management ...

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Jul 2, 2008 - diameter main breaks, 14 of which occurred in cast-iron pipes (Gaewski &. Blaha, 2007). Total costs were taken to be the sum of direct costs ...
distribution systems Large-diameter water mains have relatively low failure rates, but significant costs can result when failures do occur. Although economic analyses to schedule water main replacements are available, they rely on historical failure data. In many cases, however, large-diameter

BY PAUL DAVIS AND DAVID MARLOW

mains do not have sufficient failure data to enable confident application of these methods. As an alternative, water authorities can inspect pipes to determine structural condition and assess the need for and timing of future inspections and replacement. Because asset failure depends on a range of factors, however, inspection data alone cannot fully support this type of decision-making. This article describes a methodology that combines asset condition with a physical probabilistic failure model to determine the lifetime of a large-diameter cast-iron pipeline. Net present value calculations are used to determine the timing of future inspections and replacement of the entire pipeline. The authors also present a case study that illustrates the use of the proposed methodology.

Quantifying economic lifetime for asset management of large-diameter pipelines

he effective management of water supply networks is a significant challenge to water authorities. In part, this is because these networks consist of many spatially distributed pipes and fittings that range in size, material, and age and are generally buried and thus hidden from view. Furthermore, the long-term performance of these assets is dependent on complicated interactions among the pipe, the surrounding soil environment, and operational factors. An added complication is that many large-diameter mains do not exhibit sufficient historical failure data to confidently forecast future performance. Large-diameter pipeline assets often have low failure rates but can have severe consequences when they do fail. For example, a case study in the literature detailed the investigations that followed a catastrophic failure of a large-diameter water transmission pipe in a metropolitan area of Australia (Marlow et al, 2007a). This failure resulted in extensive flooding, damage to property, severe disruption to traffic on a freeway, and significant direct and indirect costs. A similar study in the United States examined the total cost associated with 30 largediameter main breaks, 14 of which occurred in cast-iron pipes (Gaewski & Blaha, 2007). Total costs were taken to be the sum of direct costs plus societal costs and ranged from $6,000 to $8.5 million per break, with an arithmetic mean of $1.7 million and a geometric mean of $0.5 million. To put this into context, however, Gaewski and Blaha (2007) also estimated that the total cost of large-diameter main breaks occurring in the United States per year was only one

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twelfth of the cost associated with small-diameter main breaks (with small-diameter main breaks having an estimated total cost of $3 billion per year). Given the relative cost of failures, the effective management of small-diameter mains is essential to the water sector as a whole, and a proactive replacement strategy is desirable (Marlow et al, 2007b; Moglia et al, 2008). On an individual basis, however, these assets can still be allowed to fail because of the relatively low consequences incurred per pipe break, relative to the cost of preventing such breaks across a network. In contrast, because of the higher consequences associated with failure of large-diameter mains, most water authorities would prefer to prevent and/or avoid such failures whenever possible, not the least because of the negative publicity and high direct costs they generate. Therefore, proactive management strategies are needed that allow water authorities to prolong the life of large-diameter pipes and (just as importantly) minimize the probability of these catastrophic asset failures through timely interventions. Advances in asset management approaches and modeling techniques provide the potential for solutions to these problems. In the absence of sufficient historical failure data for future performance prediction, one solution is to adopt a condition-based management approach.

CONDITION-BASED APPROACHES TO ASSET MANAGEMENT Condition-based management strategies for largediameter water pipes have received only limited treatment in the literature. A useful (if somewhat dated) reference is the trunk main manual produced by the Water Research Centre in the United Kingdom (Randall-Smith et al, 1992). The manual provides a framework that allows general conclusions to be drawn about the current and future structural condition of a system of largediameter pipes from a limited number of discrete observations made at a fixed point in time. More generally, condition assessment provides a means of understanding the state of an asset or group of assets. In common with other asset types, the process of condition-based asset management for large-diameter water mains requires that several steps be followed. • Pipes at risk must be identified and targeted for inspection. • Inspection results then must be combined with a physical model to predict the probability of pipe failure over time. • Prediction of failure probability then must be combined with cost consequences to quantify the economic lifetime of the asset. Targeting pipes for inspection. The identification of pipes for inspection can be facilitated by adopting a risk-based ranking procedure. In essence, this involves a systematic (but generally subjective) review of risk factors that influence the probability of failure, such as pipe age, material

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and soil type, and consequence of failure. Failure consequences may be qualitatively indicated by the number of customers supplied by the pipe in question, the potential for road and/or rail disruption, and the potential for property damage. Because of the spatial nature of the problem, manually undertaking this assessment across a network can be a laborious task, but it can be greatly facilitated by the use of geographical information system analysis techniques. Estimating pipe failure probability from condition assessment data. Once identified and accessed, nondestructive condition assessment techniques can be used to determine the level of deterioration that a pipe of interest has experienced (De Silva et al, 2006; Lillie et al, 2004). Use of these tools can be expensive, however, and although they provide information on the condition of the asset (e.g., remaining wall thickness), they do not in themselves provide information on the propensity of the asset to fail. The data arising from asset inspection therefore must be analyzed in some manner to help understand the effect of asset deterioration so that maintenance and rehabilitation can be prioritized. For example, past research demonstrated how measured corrosion depth data for mild steel pipes can be combined with pipe operating loads in a model to predict the time to failure by ductile rupture (Ahammed & Melchers, 1997; Rahman, 1997). Similar studies described how the level of corrosion pitting in cast-iron pipelines can be combined with internal pressure and external loading conditions to predict the time to brittle fracture failure (Moglia et al, 2008; Deb et al, 2002; Rajani et al, 2000). In an investigation of polyvinyl chloride (PVC) pipes, researchers demonstrated how estimates of pipe wall defect size can be combined with material fracture toughness to predict the time to brittle fracture failure (Davis et al, 2007). These researchers also demonstrated how measured rates of strength loss in asbestos–cement pipes can be used to determine failure times (Davis et al, 2008). Although the pipe materials in these investigations differed, the commonality among the approaches was that measurements from some form of condition assessment were combined with a physical (i.e., mechanism-based) model to predict failure. Development of physical probabilistic failure models. Although the literature describes many physical models that predict failure from condition assessment measurements, an additional problem is presented by the inherent uncertainty of the degradation process. For example, although available information may indicate that a uniform soil type exists along a pipe length, local variations in soil electrochemistry will lead to uncertainty in external surface corrosion rates (Moglia et al, 2008). Similarly, variations in the water chemistry in contact with the pipe inner surface will lead to inherently uncertain leaching rates in cement-based pipes (Davis et al, 2008). To help solve these problems, physical probabilistic failure models have been developed for buried pressure pipelines

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manufactured from metallic (Moglia et al, 2008; Sadiq et al, 2004), cement-based (Davis et al, 2008), and plastic (Davis et al, 2007) pipeline materials. These models retained the details of the actual degradation and failure processes that occur in service but also attempted to account for inherent uncertainty in the degradation process. This was achieved by representing model variables by appropriate probability distributions rather than single-value (deterministic) quantities. For example, Moglia and co-workers (2008) demonstrated that the inherent variation in measured maximum corrosion rate along a cast-iron pipeline was well represented by the two-parameter Weibull probability distribution. Rather than a single corrosion rate that was assumed to apply along the entire length, the adoption of the Weibull probability distribution allowed a mean value and a variance to be defined. The two-parameter Weibull distribution also has been applied to measured rates of strength loss in asbestos–cement pipes (Davis et al, 2008) and measured defect sizes in PVC pipes (Davis et al, 2007. Monte Carlo simulation. If a suitable probability distribution can be selected for model variables, a relatively straightforward approach to incorporating this uncertainty into a physical failure model is to use Monte Carlo simulation. In Monte Carlo simulations, a computer program repeatedly generates random values for model variables (e.g., corrosion rate and defect size) from their probability distribution. Each time a random value is generated, it is used in the physical model to predict a failure time. The end result of a Monte Carlo simulation is a set of predicted lifetimes, the number of which corresponds to the number of trials in the simulation. Monte Carlo simulations are run until some form of stopping rule is satisfied. For example, one commonly used rule is that the number of trials must be sufficiently large to ensure that the standard error of the mean predicted lifetime is below a threshold value (Davis et al, 2008). The resulting set of predicted lifetimes is fitted to an appropriate probability distribution, which is then used to estimate failure probability over time. For modeling the structural reliability of pressure pipes, Monte Carlo simulations are simple to set up, and model detail and computer processing time usually are not limiting factors (Moglia et al, 2008; Sadiq et al, 2004). Combining failure probability with costs to estimate economic lifetime. Information on the probable physical lifetime of an asset is useful, but the decision to replace still depends on the level of risk associated with the pipe and the risk aversion level of the water authority. The ability to estimate economic asset lifetimes allows the most costeffective time for intervention to be calculated. A number of researchers have used standard economic approaches such as net present value (NPV) to estimate the economic lifetime of pipeline assets. For example, Shamir and Howard (1979) first recognized that a rational decision to replace a pipe must be based on a com-

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parison of two alternatives: replace the pipe, incurring the replacement cost and whatever future costs are associated with the new pipe, or retain the existing length of pipe, saving the replacement cost but possibly incurring possible future costs of repair. In their analysis, they reasoned that if the costs of pipe replacement and failure are known, then forecasting breakage rates in the existing and new replacement pipeline will allow a cost–benefit comparison to be made. Assuming that historical failure data for a pipeline were available, Shamir and Howard proposed that the expected number of breaks over time for existing and new replacement pipes be represented by time exponential equations. Future failure costs were then expressed in terms of their present day worth, using an appropriate discount rate (Shamir & Howard, 1979). Their analysis produced a curve that showed the present value of all future replacement costs as a function of replacement year. The analysis also produced a second curve showing the present value of maintenance costs (incurred by pipe failures) summed up to the replacement year. By adding these two curves together, it was possible to identify a replacement year when the present value of total cost associated with the pipe was a minimum. This was defined as the economic lifetime of the pipe and the optimum time for replacement (Shamir & Howard, 1979). Walski (1987) extended this approach to cover the cost of broken valves along pipelines and the cost of lost water from pipe leakage. Similar water pipe economic analyses based on historical failure data were also conducted by Deb and colleagues (2002). The identification of optimum replacement times for water pipes has been well documented, but these analyses rely on historical failure data to forecast future failure rates and their associated costs. As noted previously, however, these historical data are rarely available for largediameter water mains, and an alternative, condition-based approach must be adopted. In these cases, actual failure data can be replaced by predictions from a physical probabilistic failure model (Davis et al, 2008). With some simplifying assumptions, an economic analysis similar to that originally proposed by Shamir and Howard (1979) can then be made.

CONDITION-BASED ASSET MANAGEMENT CASE STUDY A case study provides an example of condition-based asset management for a large-diameter cast-iron water pipeline. The main was 0.75-mi long and 120 years old at the time of the study. The main had no previous failure history (and thus no data were available for forecasting) but was considered by the water utility to be in a location where potentially severe consequences would be incurred should the main fail. Several pipeline segments (~ 19.7 ft between joints) had previously been exposed and inspected for pitting corrosion damage. Measured values of minimum remaining wall thickness at

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each inspection site were converted to a maximum corrosion rate on the basis of the main’s age main and an assumed original wall thickness (Moglia et al, 2008). Although anecdotal evidence indicated that the soil type was thought to be similar along the length of the main, significant variation was observed in the measured corrosion rate data at different locations. This variation in maximum corrosion rate was represented using a two-parameter Weibull probability distribution, which has a probability density function given by Eq 1: f(c) = –c–1 exp {– (c/a)}

(1)

in which c is the measured maximum corrosion rate in a pipe segment in units of in. per year,  is the scale parameter for the distribution in units of in. per year, and  is the shape parameter for the distribution and is nondimensional. Eq 1 represents the probability of a particular maximum corrosion rate occurring for a pipe segment chosen at random along the pipeline. As described by Moglia and co-workers (2008), the parameters  and  were obtained by fitting Eq 1 to measured corrosion rate data for the exhumed pipe segments along the length of the pipeline. Standard procedures for identifying and fitting measured data to the appropriate probability distribution are detailed elsewhere (D’Agostino & Stephens, 1986). Estimating failure probability. In the next stage of the process, the probability distribution for maximum corrosion rate was combined with a physical model to predict failure in a cast-iron pipe segment subjected to internal pressure and external loading. Following other researchers, the authors developed the model using Schlick’s failure criterion for cast-iron pipes subjected to combined internal pressure and in-plane bending loading (Rajani et al, 2000; Schlick, 1940); full details of the model development are provided elsewhere (Moglia et al, 2008). The resulting failure criterion for the cast-iron pipe is given by Eq 2: pD  1 age × c 2b0 0 – 120  b0





(2)

冣冧





WD  age × c 1048b02 0 – 120  b0





冣冧



in which p is internal pressure, D is the mean diameter, W is the applied external load from soil and surface loads, b0 is the estimated original pipe wall thickness, age is the pipe age, c is the measured maximum corrosion rate (which is sampled from the two-parameter Weibull distribution in Eq 1), and 0 is the estimated original tensile strength of the uncorroded cast-iron pipe. To account for uncertainty in maximum corrosion rate

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c, a computer program was written to conduct a Monte Carlo simulation of the physical probabilistic model. The simulation comprised eight steps. (1) Set up a trial population of individual pipe segments, each the length between pipe joints. The pipe segment was adopted as the modeling unit because this was the length of pipe exposed for each inspection. The probability distribution for maximum corrosion rate therefore applied directly to this pipe length. (2) Randomly assign initial maximum corrosion rates in each pipe segment on the basis of the Weibull probability distribution function in Eq 1. Steps 4–6 are then used to create a time-marching loop. (3) Calculate and assign operating loads for each pipe segment. (4) Increment time and update pipe age. (5) Check all pipe segments for failure using the criterion in Eq 2. (6) Record all pipe failures before returning to step 4. (7) Check that the number of trials in the simulation is sufficient in accordance with a stopping rule. (8) To account for statistical inference, fit predicted lifetime data to an appropriate probability distribution and estimate its parameters. Steps 1–8 were implemented to simulate the lifetimes of a set of 100 trials with the same operating conditions as the pipelines in the case study. As described previously, the end result of the Monte Carlo simulation was a set of 100 predicted lifetimes, which (as with measured corrosion rate data) could then be fitted to an appropriate probability distribution. In this particular case study, the two-parameter Weibull distribution was also found to be a good representation of the variation in predicted lifetimes from the simulation. Similar to Eq 1, the probability density function, f(t), for pipe lifetime was given by Eq 3: f(t) = –t–1 exp {– (t/)}

(3)

in which t is the predicted pipe lifetime in years. Eq 3 provides the probability that the pipe will fail in the time period between t and t +1. It is obtained by fitting the predicted pipe lifetime data form the Monte Carlo simulation to the Weibull Distribution. The prodecure for this fitting is described by D’Agostino and Stephens (1986). In this case,  and  are now the scale and shape parameters, respectively, of the pipe lifetime probability distribution, with  in units of years and  again nondimensional. For this case study, values of  = 160 years and  = 14 were obtained, and the corresponding probability density function is plotted in Figure 1. In addition to lifetime probability density, another useful measure that can be obtained from Monte Carlo simulations of physical probabilistic models is the so-called hazard (or failure rate) function h(t), which represents the probability that an asset will fail at time t (given that it has not yet failed) and is written as h(t) = –t–1

(4)

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Figure 2 shows the hazard function for this particular case study. In Figure 2, the horizontal axis refers to the time from the present age of the pipeline. Estimating economic lifetime. After the failure probability and hazard function over time for the pipeline have been estimated, the economic lifetime is determined through a cost–benefit analysis. The economic analysis rests on three key assumptions. • The analysis unit for the pipeline is a segment between joints (~ 19 ft in length). For this particular case study, the pipeline was 0.75-mi long, which corresponded to 200 segments. • Each pipe segment has a failure probability (determined from the physical probabilistic failure model), which is independent of other segments along the pipeline. • When a segment of the existing pipeline fails, it is replaced by a new pipe segment that is immune to failure over the period of the analysis. This assumption was also made in the original economic analysis of Shamir and Howard (1979). With these assumptions in place, the expected failure cost of the pipeline over time, EFC(t), is given by Eq 5: EFC(t)  nh(t)CF (t)

(5)

in which n is the current number of original pipe segments that remain along the pipeline at time t, h(t) is the hazard function calculated from Eq 4 (which on a yearly time scale represents the probability of imminent failure in a single segment at time, t), and CF(t) is the failure cost for a single segment of the existing pipeline. For the purposes of this study, an intervention is defined as an inspection of the remaining pipeline that has not yet failed, followed by its complete replacement. It is assumed that an authority would always precede pipe replacement by inspection because new information on the condition of an asset provides valuable input to a physical probabilistic failure model. This would allow the probability distribution for physical lifetime to be refined, which would, in turn, improve the accuracy of the Weibull hazard function h(t). This assumption of inspection preceding replacement was also adopted by Kleiner (2001) in a previous economic analysis of large infrastructure assets. The value (V) of an intervention is defined as its benefits (B) net of costs (C). V=B–C

(6)

Because the decision horizon of buried pipe assets may encompass many years, the time value of money is generally considered by discounting all future cash flows. As outlined by Shamir and Howard (1979), the discount rate, d, accounts for the potential to earn interest on money by deferring current expenditure until a later date. This means that costs for the analysis should be expressed in today’s dollars. The discount rate can be calculated

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from the interest rate normally involved in the utility’s financing and the anticipated cost of inflation (Shamir & Howard, 1979). The present value (PV) of a future cash flow is discounted by factor (1 + d)–t in which t is the time (in years) from the present. Therefore the NPV of intervention is given as NPV  PVB – PVC

(7)

in which PVB is the present value of benefits and PVC is the present value of costs. In order to apply Eq 7 in practice, the costs and benefits of intervention must first be described. The total costs associated with an intervention are considered to be the sum of two components: the expected cost of failures in pipe segments summed up to the scheduled intervention at time t and the sum of the cost of inspection and subsequent replacement of all remaining segments that have not yet failed at time t. The failure costs (CF in Eq 5) include the direct costs of trenching, replacement with a new pipe, and surface reinstatement. Although difficult to quantify, estimates of indirect and social costs such as traffic and customer disruption also should ideally be made. The cost of inspection will depend on the particular technique used for condition assessment (e.g., electromagnetic-based measurements of remaining wall thickness) and the number of condition samples taken during the inspection. The costs associated with intervention at time t can therefore be expressed as: T–1

PVC  冱 [nh(0 t)CF (0 t) (1 d)–t] t0

(8)

[CI CR) (0 T) (1 d)–T]

The first term in Eq 8 represents the discounted expected cost of failures, summed between the current age of the pipe, t0, and the scheduled intervention time, T. In Eq 8, n represents the number of pipe segments from the original cast-iron pipeline that remain after each time step. The second term represents the discounted cost of intervention at time, T. As used in Eq 8, CI and CR represent the cost of inspection and the cost of replacement, respectively, of all remaining pipe segments that have not yet failed. In Eq 8, future failure costs are calculated as the discounted value of current known costs. The discount rate calculation is described in detail elsewhere (Shamir & Howard, 1979), but the current study assumed a discount rate of 7%, which is in the middle of the range currently adopted by Australian water utilities. The benefits of intervention are defined as the future expected failure costs that would be otherwise present if the intervention is deferred. For simplicity it is assumed that, over the assessment period, the new replacement pipe segment does not experience any failures. Therefore the benefit of intervention is given by the avoided failure costs that would be otherwise have accumulated if the

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intervention had not taken place (Shamir & Howard, 1979). The schematic diagram in Figure 3 shows how these benefits are calculated with the benefits of intervention given by Eq 9: TMAX – 

PVB 

冱 tT

0

冤nh (

0

t) CF (0 t) (1 d)–t



(9)

in which TMAX is the upper time limit of the analysis and corresponds to the time when all the original cast-iron pipe segments have been replaced. As with failure costs, n is the current number of original pipe segments that remain at time t. For this particular case study, the amounts in Table 1 are assumed to apply for a single cast-iron pipe segment. The cost of failure, CF, for one pipe segment is given by the sum of the direct and indirect costs. For this particular case study, CF = $4,200 + $9,792 + $10,722 = $24,714 (all in Australian dollars). The cost of inspection, CI, is given by the cost of inspecting the pipe wall for corrosion damage (in this case study, by a commercially available broadband electromagnetic tool). It is assumed that, following the current practices of many Australian water utilities, inspection typically covers 10 individual pipe segments. Therefore, CI = (10 × $5,500) + $4,200 = $59,200 (all in Australian dollars). The plots in Figure 4 were generated assuming a discount rate of 7%. Eqs 8 and 9 were implemented in a spreadsheet program,1 in which the number of remaining pipe segments could be easily updated after each time step in the calculation. Figure 4 plots the present value of cost (PVC), present value of benefit (PVB), and NPV of intervention over time for the cast-iron main. As shown, the cost curve decreases to a minimum and then begins to level out. This reflects the competing influences of the discount rate and the probability of imminent failure. Initially, any increase in expected failure cost—attributable to the increasing hazard, h(t)—is outweighed by the influence of discounting. However, as time progresses, the hazard h(t) begins to increase more rapidly, and the corresponding rate of increase in expected failure cost balances the influence of the discount rate. The benefit curve indicates that as intervention is deferred, there are fewer original pipe segments remaining and therefore fewer potential failures that are avoided. Consequently, the benefit of intervention decreases continually. The Net Present Value of Intervention (NPV) referred back to the present is given by the difference between these two curves. The NPV curve clearly shows a maximum at a time of 11 years from the present. Following the arguments outlined previously, the economic lifetime of the pipe equals 11 years plus the current pipe age of 120 years and is compared with the physical lifetime in Figure 5. In this case, the analysis indicates that the pipe could be allowed to run until it is 131 years old (11 years plus the current pipe age of 120 years), and that from that

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point on, it becomes less cost-effective to intervene. Although the NPV in Figure 4 remains positive until 14 years from the present (and therefore the cost of intervention is still less than the benefit), the NPV decreases from its previous maximum value. The comparison of physical and economic lifetimes in Figure 5 suggests that the consequences of failure are not sufficient to adopt a pessimistic pipe lifetime, i.e., two standard deviations (SD) before the expected lifetime. However, the consequences of failure are sufficiently high that an intervention is required well in advance of the pipe reaching an optimistic physical life (2 SD after the expected lifetime) or indeed, the expected physical lifetime of 154 years. Furthermore, although the pipe is approaching the time where an intervention will be necessary, deferral of intervention is still warranted for the next 10 years. This would suggest that the next inspection and replacement of the asset will not be needed within short-to-mediumterm planning horizons.

DISCUSSION Although the approach described previously may be useful for asset management of large-diameter cast-iron mains with no historical failure data, several areas require further development. Accuracy of pipe inspection tools. The proposed approach relies on condition assessment as input to a physical probabilistic model for pipe failure. In the case study, inspection costs were based on results provided by a commercially available broadband electromagnetic tool that measured the remaining uncorroded wall thickness in metallic pipes. On the basis of previous experience with this tool, a minimum of 10 individual pipe inspections was proposed to accurately define the parameters of the corrosion rate probability distribution (Davis et al, 2004). However, previous research by Sadler and colleagues (2003) demonstrated that different nondestructive inspection techniques produce different correlations with actual measured corrosion damage on Australian cast-iron pipes. This may mean that, depending on the particular technique chosen, a different number of discrete inspections are needed to adequately define the corrosion rate probability distribution, which in turn will change the inspection cost. Further work is required to determine the relationship between the required number of inspections and the corrosion rate distribution accuracy for different inspection tools. Prediction of different failure modes. The physical probabilistic model used to estimate failure probability is currently restricted to internal pressure and in-plane (diametrical) bending only. The resulting failure mode would therefore be one of longitudinal fracture. In reality, however, other failure modes are possible that are not yet captured by the model. For example, lateral pipe deflection under the action of expansive soils can cause excessive bending stress and circumferential fracture. As the

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diameter increases, however, the resistance to bending of an individual pipe segment also increases by virtue of a reduced length-to-diameter ratio. Therefore, for largediameter pipes, circumferential fractures may not be the preferential failure mode, and it is sufficient to model longitudinal fractures only. However, the model does not account directly for those failures that occur as a result of pressure surges. If such failures are governed by the rapid rate of stress increase from a pressure surge (similar to an external impact event), then additional work is required to quantify a new failure criterion for cast-iron pipes under dynamic loading conditions. On the other hand, if failures occur simply because of increased static stress from a higher peak pressure and if the peak pressures are known, then this can readily be included in the current model. Monte Carlo simulation does not restrict the detail of the underlying physical model, and as a result, any changes can be incorporated into the process. Replacement versus rehabilitation decisions. The current analysis defines intervention as an inspection followed by the replacement of the entire remaining cast-iron pipeline. A more flexible approach would allow for different replacement strategies after failure. For example, the asset owner may wish to replace only the problematic pipe segment that has failed, rather then the entire remaining pipeline. Alternatively, construction advantages offered by trenchless technologies may mean that proactive replacement of the problematic segment and its near neighbors is desired. Rather than replacement, options such as rehabilitating pipes using trenchless technologies or reducing corrosion (and extending the pipe lifetime) by cathodic protection should also be considered. For example, Rajani and Kleiner (2007) quantified the effectiveness of cathodic protection in water mains and demonstrated how failure rates and life-cycle costs decrease after the implementation of cathodic protection programs. This previous research provides a useful starting point for incorporating other management strategies into the current study. Quantification of failure consequences. Further work is also needed to accurately quantify the consequences of failure and therefore, the cost and benefit of different management strategies. Although indirect consequences such as those incurred from traffic disruption and customer service interruption are included in the analysis, the consequences upstream or downstream of a failure are not. For example, a failure in a large-diameter water supply main will incur consequences attributable to service interruptions elsewhere in the network in those locations that rely on supply from the failed main. To capture these remote but related consequences of a single main failure, the hydraulic connectivity of the pipe network must be defined and considered in the analysis. Other researchers examined the approaches of various industries to estimation of failure cost consequences (Cromwell et al, 2002). They described methods from the electricity, nat-

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ural gas, and transportation industries and suggested that elements from these approaches could be applied to estimating failure cost consequences in water transmission and distribution lines (Cromwell et al, 2002). Their research may provide a useful guide to accurately quantifying failure consequences for water infrastructure.

CONCLUSION Effective asset management of large-diameter water pipes is necessary because of the high costs and other consequences associated with asset failures, circumstances that most water authorities wish to avoid if possible. Although analytic approaches to scheduling pipe replacements have been widely reported in the literature, previous solutions relied on existing historical failure data to estimate future failure rates. In many cases, however, larger-diameter cast-iron mains do not exhibit sufficient historical failure data, and an alternative approach is required. This study described a proactive management strategy based on condition assessment, failure prediction, and cost–benefit analysis. In summary, the proposed modeling framework involves the following stages: • Stage 1: Assess the condition of the asset, and convert inspection data into a measured corrosion rate. • Stage 2: Represent inherent uncertainty in measured corrosion rate by fitting data to an appropriate probability distribution. • Stage 3: Combine the corrosion rate with a physical failure model, and use Monte Carlo simulation to estimate the increase in failure probability over time. • Stage 4: Combine failure probability with costs to estimate the expected failure costs for a pipeline over time. • Stage 5: Compare expected failure costs with the cost of inspecting and replacing the pipeline in order to determine the NPV of intervention over time. The proposed approach was illustrated for a case study of a large-diameter cast-iron pipeline. The pipeline was 0.75-mi long and 120 years old at the time of the analysis, and no previous failures had been observed. Stages 1 to 3 of the approach resulted in a probability density function for the failure time for a single pipe segment (the length between joints). Results indicated an expected failure time of 154 years, with upper and lower limits of 127 years (– 2 SD) and 181 years (+ 2 SD). In stages 4 and 5, this lifetime distribution for a single segment was aggregated and combined with failure cost data to estimate the expected cost of failures along the entire pipeline over time. A cost–benefit analysis was conducted in which the costs associated with the pipeline comprised the actual failure costs up to the time of intervention and the actual costs of inspecting and replacing the remaining cast-iron pipeline. Following Shamir and Howard (1979), the benefits of intervention included the notional failure costs that would have otherwise been incurred had intervention not taken place. For this particular case study, the max-

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imum NPV of intervention was estimated to be when the pipeline reached an age of 131 years. This suggests that the next inspection and replacement of the asset will not be needed within the short-to-medium-term planning horizons. However, inspection and replacement should be scheduled before the expected physical lifetime of 154 years. Many data issues must be considered when undertaking such an analysis, and the costs of failure are highly uncertain. In light of these admissions, interpretation of the results in an absolute manner would be beyond the scope of the accuracy available. The need for additional work aside, however, the modeling approach presented here allows asset managers to maximize the usefulness of expensive inspection data and has the potential for improving the management of large-diameter water mains, a management challenge that is compounded by an aging asset base and limited budgets.

ACKNOWLEDGMENT The authors gratefully acknowledge the efforts of Roger O’Halloran and John Mashford in reviewing this article. ABOUT THE AUTHORS

Paul Davis (to whom correspondence should be addressed) is a research scientist with the Commonwealth Scientific and industrial Research Organization (CSIRO), Division of land and Water, Graham Rd., Highett, VIC Australia, 3190; e-mail [email protected]. He has more than 15 years of experience in the area of degradation and failure mechanisms of pipeline materials and 8 years of experience in failure prediction, economic modeling, and assessment management of water pipelines. He holds a bachelor’s degree from the University of Liverpool (United Kingdom) and a doctorate from Imperial College, London (United Kingdom). David Marlow is a research scientist at CSIRO. Date of submission: 07/16/07 Date of acceptance: 02/14/08

FOOTNOTES 1Microsoft

Excel, Microsoft, Redmond, Wash.

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REFERENCES Ahammed, M. & Melchers, R.E., 1997. Probabilistic Analysis of Underground Pipelines Subject to Combined Stress and Corrosion. Engrg. Structures, 19:12:988. Burn, L.S.; Davis, P.; DeSilva, D.; Marksjo, B.; Tucker S.N.; & Geehman C., 2001.[MM1] Proc. Plastics Pipes XI, München, Germany. Cromwell, J.; Reynolds, H.; & Young, K., 2002. Cost of Infrastructure Failure. AwwaRF, Denver. D’Agostino, R.B. & Stephens, M.A., 1986. Goodnes-of-Fit Techniques. Marcel Dekker, New York.

Davis, P.; De Silva, D.; Marlow, D.; Moglia, M.; Gould, S.; & Burn, S., 2008 Service Life Prediction and Scheduling Intervention in Asbestos Cement Pipelines. Jour. Water Supply: Research & Technol.— AQUA, in press.[MM2] Davis, P.; Burn, S.; Moglia, M.; & Gould, S., 2007. A Physical Probabilistic Failure Model to Forecast Failure Rates in PVC Pipe Networks. Reliability Engrg. & System Safety, 92:1258. Davis, P.; Moglia, M.; Burn, S.; & Farlie, M., 2004. Estimating Failure Probability From Condition Assessment of Critical Cast-Iron Water Mains. Proc. 6th National Australasian Society for Trenchless Technology Conf., Melbourne, Australia. Deb, A.K.; Grablutz, F.M.; Hasit, Y.J.; Snyder, J.K.; Loganathan, G.V.; & Agbenowski, N., 2002. Prioritizing Water Main Replacement and Rehabilitation. AwwaRF, Denver. DeSilva, D.; Moglia, M.; Davis, P.; & Burn, L.S., 2006. Condition Assessment to Estimate Failure Rates in Buried Metallic Pipelines. . Jour. Water Supply: Research & Technol.—AQUA, 55:179. Gaewski, P.E. & Blaha, F.J., 2007. Analysis of Total Cost of Large-Diameter Pipe Failures. Proc. AWWA Research Symp. Distribution Systems: The Next Frontier, Reno, Nev. Kleiner, Y., 2001. Scheduling Inspection and Renewal of Large Infrastructure Assets. Jour. Infrastructure Systems, 7:4:136. Kleiner, Y.; Sadiq, R.; & Rajani, B., 2006. Modeling Deterioration of Buried Infrastructure as a Fuzzy Markov Process. Jour. Water Supply: Research & Technol.—AQUA, 55:2:67. Lillie, K.; Reed, C.; & Rodgers, M.A.R., 2004. Workshop on Condition Assessment Inspection Devices for Water Transmission Mains. AwwaRF, Denver. Marlow, D.R.; Heart, S.; Burn, S.; Urquhart, A.; Gould, S.; Anderson, M.; Cook, S.; Ambrose, M.; Madin, B.; & Fitzgerald, A., 2007a. Condition Assessment Strategies and Protocols for Water and Wastewater Utility Assets. Project Ref 03-CTS-20CO, Water Environment Research Foundation, Alexandria, Va. Marlow D.; Moglia, M.; & Burn, S., 2007[MM3]b. PARMS-PRIORITY: An Advanced Asset Management Software Tool for Water Distribution Networks. Proc. AWWA Research Symp. Distribution Systems: The Next Frontier, Reno, Nev. Moglia, M.; Davis, P.; & Burn, S., 2008. Exploration of a Physical Probabilistic Model for Cast-Iron Pipe Failure Prediction. Reliability Engrg. & System Safety, 93:885. Rahman, S. 1997. Probabilistic Fracture Analysis of Cracked Pipes With Circumferential Flaws. Intl. Jour. Pressure Vessels & Piping, 70:223. Rajani, B. & Kleiner, Y., 2007. Quantifying Effectiveness of Cathodic Protection in Water Mains: Case Studies. Jour. Infrastructure Systems, 13:1:1. Rajani, B.; Makar, J.; McDonald, S.; Zhan, C.; Kuraoka, S.; Jen, C.K.: & Viens, M., 2000. Investigation of Grey Cast-Iron Water Mains to Develop a Methodology for Estimating Service Life. AwwaRF, Denver.

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Randall-Smith, M.; Russell, A.; & Oliphant, R., 1992. Guidance Manual for the Structural Condition Assessment of Trunk Mains. WRc, Swindon, United Kingdom. Sadiq, R.; Rajani, B.; & Kleiner, Y., 2004. Probabilistic Risk Analysis of Corrosion-Associated Failures in Cast-Iron Water Mains. Reliability Engrg. & System Safety, 86:1. Sadler, P.; Davis, P.; Burn, S.; & Farlie, M., 2003. Benefits and Limitations of Nondestructive Electromagnetic Condition Monitoring Techniques for Ferrous Pipes. Proc. Pipes Wagga Wagga 2003, Wagga Wagga, Australia. Schlick, W.J., 1940. Supporting Strength of Cast Iron Pipe for Gas and Water Service. Bulletin Number 146. Iowa Engineering Experimental Station, Ames, Iowa. Shamir, U. & Howard, C.D.D., 1979. An Analytic Approach to Scheduling Pipe Replacement, Jour. AWWA, 71:5:248. Walski, T.M., 1987. Replacement Rules for Water Mains. Jour. AWWA, 79:11:33.

L

arge-diameter pipeline assets often have low failure rates but can have severe consequences when they do fail.

B

ecause of the higher consequences associated with failure of large-diameter mains, most water authorities would prefer to prevent and/or avoid such failures whenever possible, not the least because of the negative publicity and high direct costs they generate.

I

nformation on the probable physical lifetime of an asset is useful, but the decision to replace still depends on the level of risk associated with the pipe and the risk aversion level of the water authority.

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JULY 2008 | JOURNAL AWWA • 100:7 | PEER-REVIEWED | DAVIS & MARLOW

E

ffective asset management of large-diameter water pipes is necessary because of the high costs and other consequences associated with asset failures, circumstances that most water authorities wish to avoid if possible.

Photo 1

This photo shows the volume of water that may be lost

as a result of a filed case-iron main.

Photo 2

A longitudinal split can result from corrosion and fracture

in a cast-iron pipe.

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TABLE 1

Direct and indirect costs of replacement and cost of inspection for cast-iron main Direct Costs of Replacement

Trench excavation (19-ft long, 6-ft wide, 12-ft deep)

AU$1,500

New pipe installation (19 ft of 10in. diameter plastic pipe)

AU$1,800

Backfill and reinstatement (bitumen surface)

AU$900

Total replacement cost for 6-m length

AU$4,200

Indirect Costs of Replacement Traffic disruption (cost per vehicle per hour)

AU$2.72 (Burn et al, 2001)

Estimated repair time

12 hours (estimate, no data)

Traffic density (vehicles per hour)

300 (estimate, no data)

Total traffic cost over repair time

AU$9,792

Number of connections to main water authority)

23 (estimate based on local

Number of customers per connection water authority)

5 (estimate based on local

Estimated repair time

12 h (estimate, no data)

Failures that lead to interruptions—%

100

Social cost per interruption (cost per customer per hour)

AU$7.77 (Burn et al, 2001)

Total cost per customer interruption

AU$10,722.60

Cost of Inspection Electromagnetic pipe wall inspection

AU$5,500 (estimate, no data)

Adapted from Burn et al (2001)

FIGURE 1 Failure time probability distribution for cast-iron water distribution main

Probability Density, f(t)

0.035

Expected failure time = 154 years

0.030 0.025 0.020 0.015 – 2 SD = 127 years

0.010

+ 2 SD = 181 years

0.005 0 80

100

120

Current age = 120 years

140

160

180

Time to first failure (years)

SD—standard deviation

18

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FIGURE 2 Hazard function (probability of imminent failure) for cast-iron main 10.0

Hazard, h(t)

0.8 0.6 0.4 0.2 0 0

10

20

30

40

50

60

70

80

Time From Current Pipeline Age—years

FIGURE 3 Schematic of costs and benefits associated with intervention

Costs incurred from failures before intervention

τ Current time

τ +1

τ +2… …

Benefits from avoiding failures after intervention

t

Scheduled intervention

$$

.. TMAX

t+1 t+2 Benefit assessment period

Time when all orginal cast-iron pipe segments have been replaced (upper limit of the analysis)

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FIGURE 4 Costs, Benefits and NPV of intervention over time for cast-iron main

Thousands of Dollars

800

PVC PVB

700 600

500 400

0

5

10

15

20

Time From Current Pipeline Age—years

Thousands of Dollars

15

NPV intervention

10

5

0 0

5

10

15

20

Time From Current Pipeline Age—years NPV—net present value, PVB—present value of benefits, PVC— present value of costs

FIGURE 5 Comparison of physical and economic lifetime of the cast-iron main 0.035

Expected failure time = 154 years

Probability Density, f(t)

0.030 0.025 0.020 Max NPV = 131 years

0.015 0.010

–2 SD = 127 years

+ 2 SD = 181 years

0.005 0 80

100

120 Current age = 143 yrs

140

160

180

Time to first failure (years)

NPV—net present value, SD—standard deviation

20

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