By Robert McKim, Cincinnati, Ohio, 1-513-639-2151, mckim@pbworld.com

Predictive modeling of the degradation of underground pipe systems has often been a hit-or-miss affair, so it has been difficult for utility managers to use their budgets effectively and place the usually scarce resources of labor and dollars where they are most needed. Unlike above ground systems such as highways, bridges and buildings, underground facilities suffer from the “out of sight, out of mind” syndrome. Understanding how much useful life a pipe system has left is a critical issue. This is especially true today in the U.S., where many of the underground systems are approaching the end of their designed service lives.

Underground facilities also suffer from a shortage of useable data because it has been exceedingly difficult to characterize underground systems. Imagine trying to identify the wall thickness, flexural modulus, or even corrosion potential of a pipe located 6 m (20 feet) under a street and 30 m (100 feet) from the nearest access hole. Not impossible, but costly, time consuming and generally inaccurate. Underground pipe systems are noisy, adding to the complexity of obtaining reliable data.

Better information is not likely to become available soon. Often all we have is a history of catastrophic system events, such as collapses, overflows, bursts, or losses of service. Now, however, we can combine this information with a new model developed through PB research to at least obtain definable limitations on accuracy. Such a model is available to those of us in PB Water.

Modeling the Risk of System Failure

The model at left starts with the information that is available. Let us consider collapses as the variable that is best monitored in a sewer system. A simple regression analysis will produce an equation that gives some indication of future collapses, even if the reasons are not understood (Figure 1).

Figure 1: History of Collapses

Figure 2: Risk Ratios

Figure 3: Impact of Rehabilitation Program

Figure 4: Impact of $10M Rehabilitation Program

Figure 5: Impact of $5M Rehabilitation Program

Figure 6: Rehabilitation Budget/System Collapses

Figure 7: Unmaintained sewer collapsing under a road in Dallas(2003) had spectacular results.

Figure 8: Cured-in-place pipe (CIPP) is one of the main tools used in the trenchless technology industry to repair sewers without excavation. Here a falling sewer is being repaired by the CIPP method without the need fir any digging.

Figure 9: Advanced optical systyems are mounted on remotely controlled tractors to explore remote areas of pipelines.

The resulting plot gives a regressions equation (r2 = .9965) that allows a reasonable prediction of future collapses. Nothing new here! Knowing the future collapse rate does not really help us in our planning, though. We know that something needs doing, but what? Do we spend or budget on major problems areas ignoring minor problems? Do we spend money on less expensive minor problems and wait for major problems to occur before we are forced to act?

Now comes the clever part. It involves work that resulted from research from one of my PhD. student’s thesis, but has not yet been incorporated into other models. This research found that sewer defects can be classified in terms of risk: high, medium, or low. High risk defects will have a mean time to collapse of less than 20 years; medium risk defects, 50 years; and low risk defects, greater than 50 years. It was also found that the ratio of high-, medium-, and low-risk defects followed a highly predictable pattern. By plotting a typical pipe system’s ratio of risk defects (Figure 2), we see that a higher proportion of risks enter the “high” category as the service time increases, while the proportions of low and medium risks decrease. This is due to the fact that low and medium risks eventually degrade into high risk defects.

The relative ratios of risks can be predicted at any time in the life cycle of a sewer system. By combining the known risk ratios with the mean time to collapse (the measure of risk), we can calculate the total number of risk elements (defects) in the system at any time. At any point in the service history we can use the risk ratios and defect probabilities to estimate the number of different risks in the system, even if a rehabilitation program is undertaken. Figure 3 shows the impact of undertaking a major rehabilitation program every 5 years after an initial period of 20 years with no rehabilitation program except for collapses.

Determining Optimal Rehabilitation Strategies

This model has been combined with an economic model to provide optimal rehabilitation strategies. For example, with the system described above, if we assume the costs of repairing high, medium, and low risks to be $5,000, $2,000, and $1,000 respectively, and the cost to repair a collapse to be $10,000, then a $10 million rehabilitation program would keep the system collapses over a 50 year service life to fewer than 3,500 (Figure 4).

If only $5 million were spent on rehabilitation from years 20 through 50, the impact on the defects would be as shown in Figure 5. The reduction of the program’s budget from $10 million to $5 million increases the number of system collapses to more than 14,000. The relationship between rehabilitation budget and the number of system collapses is shown in Figure 6.

This demonstration of the power of predictive modeling shows how utility managers can work with their budgets to help optimize resources. It also allows managers and budget administrators to play “what if” scenarios with different budget levels and system performance.

The variables that can be manipulated in this model are:

The output (dependent variables) are the:

Applications for the Model

This model must be considered probabilistic in nature and should be used only when the system information is poor in quantity and quality. It will not replace a deterministic-based model that looks at items such as loads and structural characteristics, which by definition require far more complete information. This model requires a reasonable guesstimate about rehabilitation and collapse costs, and some indication about the standard deviation of the risk elements. It will, however, allow asset managers to prepare long-term plans for underground infrastructure systems that will compliment Capacity, Maintenance, Operation and Management (CMOM) and General Accounting Standards Board Statement #34 (GASB-34) requirements.¹