ABSTRACT

EPA’s Drinking Water Infrastructure Needs Survey determined the national capital expenditure need over the next 20 years is approximately $150.9 billion. While this information is noteworthy for individual water system managers, it does not provide a defendable replacement strategy. Using a risk assessment approach enables system managers to base their decisions upon quantitative information rather than the empirical knowledge that “more needs to be done.” This project provides a model that determines the risk associated with various replacement strategies, taking into account local conditions and infrastructure histories.

A BRIEF HISTORY OF WATER PIPE AND DISTRIBUTION

The development of drinking water delivery systems and the science of fluid mechanics took place over the past 4000 years. The earliest systems demonstrated the intuitive genius of the time, as the theories for the underlying science were developed many centuries later.

THE EARLY DEVELOPMENT OF WATER DISTRIBUTION SYSTEMS

The earliest piped water delivery systems date from about 2000 years before Christ on the island of Crete. The remnants of clay pipe have also been discovered in the cities of Ephesus and Perge, in present-day Turkey, that are believed to have been in service several hundred years B.C. The Romans developed the most extensive water distribution systems in ancient times, delivering water by gravity through aqueducts over long distances. Some local water distribution was accomplished through lead pressure pipes, thus providing origin for the modern day word, plumber, which was derived from the Latin word for lead, plumbium. The fall of the Roman Empire also brought the fall of water distribution technology. During the Dark Ages that followed, the development and maintenance of water distribution and sanitation systems regressed resulting in conditions that were poorer than during Roman times. The Renaissance not only ushered in the rebirth of the arts and sciences, but also the rebirth of water distribution development.

The city of London benefited from this burgeoning technology. An early, 13^th century, lead pipeline brought water from the Tybourne Brook to London. This line, plus several others that followed, delivered water to a central point in London where residents collected the water in buckets. One of the earliest water pumps, powered by a water wheel on the Thames, was constructed to pump water through a section of London in 1582.

Cast iron pipe was first developed in Germany and installed at the Dillenburg Castle in 1455. The expense of iron pipe, however, prevented its extensive use as the first major cast iron pipeline was not installed until 1664, a 15-mile water line from Marly-on-Siene to the Palace of Versailles in France.

For the next 200 years most water mains were constructed of wood, cast iron and lead. Small diameter pipelines were often made from bored logs having bell and spigot joints made of lead. Wood-stave pipe was frequently used through the early 1900’s for larger diameter applications, 4-inch and larger. The wood staves were held in place by metal bands. The pipe was then coated in tar, wrapped in tar-paper and coated again in tar. These pipes had relatively long lives under conditions where they remained full of water, (Walski, 2006).

THE DEVELOPMENT OF THE SCIENCE OF FLUID MECHANICS

The underlying theories of water mechanics were developed during the 1700’s and 1800’s. These discoveries are the bases for present day hydraulic models. Haestad, et al (2003), provide the following:

1732 – Pitot invents a velocity-measuring device. Henri Pitot is tasked with measuring the velocity of water in the Seine River. He finds that by placing an L-shaped tube into the flow, water rises in the tube proportionally to the velocity squared, and the Pitot tube is born.

1738 – Bernoulli publishes Hydrodynamica. The Swiss Bernoulli family extends the early mathematics and physics discoveries of Newton and Leibniz to fluid systems. These principals will become the key to energy principles used in hydraulic models and the basis for numerous devices such as the Venturi meter and, most notably, the airplane wing.

1770 – Chezy develops head loss relationship. While previous investigators realized that energy was lost in moving water, it is Anoine Chezy who realizes that V²/RS is reasonably constant for certain situations. This relationship will serve as the basis for head loss equations to be used for centuries.

1839 – Hagen-Poiseuille equation developed. Gotthilf Hagen and Jean Louis Poiseuille independently develop the head loss equations for laminar flow in small tubes.

1845 – Darcy-Weisbach head loss equation developed. Julius Weisbach publishes a three-volume set on engineering mechanics that includes the results of his experiments. The Darcy-Weisach equation comes from this work, which is essentially and extension of Chezy’s work, as Chezy’s C is related to Darcy-Weisbach’s f by C² = 8g/f. Darcy’s name is also associated with Darcy’s law for flow through porous media, widely used in groundwater analysis.

1883 – Laminar/turbulent flow distinction explained. While earlier engineers such as Hagen observed the differences between laminar and turbulent flow, Osborne Reynolds is the first to conduct the experiments that clearly define the two flow regimes. He identifies the dimensionless number, later referred to as the Reynolds number, for quantifying the conditions under which each type of flow exists. He publishes “An Experimental Investigation of the Circumstances which Determine whether the Motion of Water shall be Direct or Sinuous and the Law of Resistance in Parallel Channels.”

1906 – Hazen-Williams equation developed. A. Hazen and G.S. Williams develop an empirical formula for head loss in water pipes. Although not as general or precise in rough, turbulent flow as the Darcy-Weisbach equation, the Hazen-Williams equation proves easy to use and will be widely applied in North America.

--Haestad et al, 2003

WATER DISTRIBUTION SYSTEM DEVELOPMENT IN THE UNITED STATES THROUGH THE EARLY 1900’s

The first cities to install domestic water systems in the United States were Schafferstown, Pennsylvania in 1746 and Bethlehem, Pennsylvania in 1754. Bored logs were used for pipes in these systems. Cast iron pipe was first installed in the United States to serve the city of Philadelphia, Pennsylvania in 1817. Over the next 100 years several other new pipe technologies were developed, wrought iron, galvanized iron and steel, however, the predominant material installed during this period was cast iron. All of these metallic pipe materials have one thing in common, corrosion. The development of cement-mortar lining to help reduce internal corrosion took place in Charleston, South Carolina in 1922. Cement-mortar lining became the standard practice for cast iron pipe in 1947. Polyethylene encasement provides a solution to external corrosion in 1951. It can be included with the installation of cast/ductile iron pipe, establishing a barrier between the external pipe surface and the corrosive environment of the trenchline, (Walski, 2006).

The progression to new pipe technologies included ductile iron pipe in the late 1940’s, which has replaced cast iron due to its greater tensile strength and reduced weight. As a result, the Cast Iron Pipe Research Association’s name was changed to the Ductile Iron Research Association (DIPRA) in 1979. In addition, steel pipe, with cement-mortar lining, along with concrete cylinder pipe, are used predominantly for large diameter applications. These two materials can also be custom manufactured to meet the specifications for more complicated installations, such as water and wastewater treatment plants, pump stations and plant yard piping.

Polyvinyl chloride (PVC) pipe was developed in Germany in the 1930’s. It is now widely used for the installation of new water distribution systems. Its acceptance by the industry was prompted by the development of manufacturing standards making it compatible with standard ductile iron pipe diameters, and the approval of Standard C-900 for PVC pipe by the American Water Works Association (AWWA), which occurred in 1976, (Walski, 2006).

While cast iron pipe was the material of choice, for most cases, through the 1940’s, it was not optimal for small diameter applications due to its brittle character. Galvanized iron pipe (GIP) was used extensively for 2-inch and smaller diameter installations. Consumer water demands were relatively low, by today’s standards, permitting the placement of 2-inch diameter GIP to serve predominantly residential areas. In addition, fire hydrant density requirements were low, allowing extensive networks of small diameter water mains. These small metallic mains now present major maintenance and quality of service problems. The accumulated corrosion and tuberculation over the past 60 to 100 years have lead to high leakage rates, plus frequent discolored water and low-pressure complaints from customers. They are also ineffective for fire protection purposes. As a result, these water mains are typically high on the priority list for replacement. Larger steel and cast iron pipe are also prominent on the list primarily due to their disproportionately high leak histories.

While these pipes present significant problems for water system operators, they represent a small fraction of the nation’s aging infrastructure challenge.

AMERICA’S INFRASTRUCTURE CRISIS

Since the aqueducts that served early Rome to the present day, man has continued to develop new technologies for the delivery of drinking water. As one system aged and eventually failed, it was replaced by another, employing the latest construction materials and techniques of the time. The Twentieth Century saw the greatest expansion of civil projects in the history of the United States. As the century neared its end, the challenge posed by the need to replace the nation’s aging infrastructure became evident. Numerous studies were completed with the purpose of delineating the scope of the impending national crisis. These studies focused not only on highways and bridges but also on drinking water and wastewater systems. The American Society of Civil Engineers (ASCE) notes in its Infrastructure Report Card 2005,

“Congested highways, overflowing sewers and corroding bridges are constant reminders of the looming crisis that jeopardizes our nation’s prosperity and our quality of life.” –ASCE 2005

They also note that the total investment need through the year 2010 is estimated at $1.6 trillion for all infrastructure systems from aviation to wastewater improvements. The concerns prompted by this situation are easily understood by the public as they travel along highways constructed over 50 years ago and cross bridges built by their grandparents. While the roadways, railroads and airports are generally well funded, the deteriorating condition of the nation’s underground infrastructure is not appreciated to the same degree. As a consequence, EPA, in 1999, conducted the Drinking Water Infrastructure Needs Survey (DWINS). This effort revealed that transmission and distribution systems accounted for 56 percent of the capital expenditure need for the next 20 years. The other drinking water infrastructure categories, treatment, finished water storage and source of supply make up the balance of the capital need at 25, 12 and 6 percent respectively. The total capital need over the next 20 years was projected at $150.9 billion, of which, $84.5 billion was estimated for transmission and distribution systems.

EPA, in September 2002, issued, The Clean Water and Drinking Water Infrastructure Gap Analysis. This study was intended to follow up on the conclusions of DWINS and to illustrate the gap in capital and operations & maintenance expenditures if current spending levels are continued into the future. This study reinforced the need, from a national perspective, to acknowledge the risks posed by under-funding the future needs for infrastructure renewal. G. Tracy Mehan, III, EPA’s Assistant Administrator for Water, states,

“The analysis suggests that a large gap will result if the challenge posed by an aging infrastructure network—a significant portion of which is beginning to reach the end of its useful life—is ignored.”—EPA, 2002

ASCE adds,

“The nation’s 54,000 drinking water systems face staggering public investment needs over the next 20 years. Although America spends billions on infrastructure each year, drinking water faces an annual shortfall of at least $11 billion to replace aging facilities that are near the end of their useful life and to comply with existing and future federal water regulations.”—ASCE, 2005

These studies are critical for bringing awareness to the overall problem and helping legislators deal with funding allocation issues. While this knowledge illustrates the scope of the problem, it does not provide local water system managers with the tools needed to assess their particular situation or the strategies needed to establish their replacement programs.

OBJECTIVE

The goal of this paper is to provide a tool to be used in developing water main replacement plans. The following approach will provide an assessment of the future monetary risk associated with several replacement strategies, thus presenting management with improved criteria upon which to base their capital expenditure decisions.

A RISK ASSESSMENT METHOD FOR WATER MAIN RENEWAL

Risk assessment involves the process of quantifying the two key elements of risk, the magnitude of the potential loss and the probability that it will occur. A couple common examples include, the intuitive risk assessments performed by golfers and skiers. Most golfers have determined that the risk associated with golfing in a thunderstorm is too high and, as a result, retreat to the proshop when the thunder clouds move in. Although the potential for being struck by lightning is low, the cost is prohibitively high. By contrast, most skiers feel the risk associated with falling is very low and, consequently, they head for the slopes by the thousands. While the probability for falling is very high, the associated danger is typically low. In both cases the people assess risk based upon past experiences and judgement – not on quantitative data.

This is essentially the same process used for determining the risk associated with different water main replacement strategies. Generally, water system managers assess the potential loss and probability of occurrence based upon past experience and judgement – not on quantitative data. The premise of this project is that the indicators of risk can be quantified. Thus, the likelihood for the development of leaks can be projected for various programs, and when multiplied by the repair cost per leak, the related risk is determined.

A method for determining the probability of occurrence for future water main leaks in year t is provided below. This probability is expressed in the rate of leaks per unit of length of main. (For the purposes of this paper, the unit of length is expressed in 100 miles, i.e., leaks per 100 miles of water main). Multiplying the leakage rate by the year t length of main provides the projected number of leaks. This, multiplied by the normal costs associated with their repair, yields the risk.

PROJECTING LEAKAGE RATES IN PIPELINES

Shamir and Howard (1979) describe the exponential relationship between a pipe’s age and the progression of leakage rates. Their analysis of pipeline failure rates in a particular area of Calgary, Alberta, Canada revealed, “…that an exponential growth equation fits the [historical] data well. The regression is assumed to hold for the existing pipe in future times as well, so that the number of breaks in any future year can be obtained from this equation.” The equation is stated as:

Equation 1: N(t) = N(t₀)e^{A(t – to)}

Where, t = time in years

t_{0 =} base year for the analysis (the year the pipe was installed, or the first year for which data are available)

N(t) = number of breaks per 100 miles of pipe in year t

A = growth rate coefficient (dimension is 1/year)

The leak history for a particular pipe or system of homogenous pipeline segments provides the basis for establishing the growth rate coefficient. The equation will then project the future leak rate in year t. Multiplying the leakage rate by the total footage of pipe determines the number of leaks by year. The data below represents the leak history for small metallic pipe (4-inch diameter and smaller) for United Water Idaho for the period from 1997 through 2006 (the only years for which reliable data is available).

Notes:

¹In 2001 a new pressure boundary was established. The increased pressure resulted in the increase in leaks.

²The values N(t₀) and N(t) for 1997 and 2006 from the exponential regression curve are used in solving the equation as they provide a solution that is less subject to the volatility associated with the variations in leak activity from year to year and better represent an average result for the data.

Solving for Shamir and Howard’s growth coefficient is accomplished by the following:

Equation 2: A = (ln(N(t)/N(t₀))/(t-t₀)

A = (ln(91.41/54.82))/(2006-1997)

A = 0.05681

The resultant theoretical leak rates become:

Table 2

Graphing this data provides the following theoretical versus the actual leakage rates:

Figure 1

It appears that the results from Shamir and Howard’s equation fit the data quite well. Extending the equation over the next 20 years yields the following graphical result:

Figure 2

Shamir and Howard’s leakage growth equation provides the probability component of determining risk. The second component is leak repair cost.

PROJECTING COSTS AGAINST THE EXPONENTIAL INCREASE IN PIPELINE FAILURE RATES FOR 4-INCH AND SMALLER METALLIC WATER MAINS

The following table illustrates the progression of leaks per year in 4-inch and smaller metallic water mains if no main replacement work is done. This, plus an average cost of $1,300 per leak repair as provided below, provides the future maintenance risk.

Average Leak Repair Cost

Excavation Size: 6’ x 8’ x 5’ deep

Installing a Full Seal to repair a leak on a metallic water main

Labor (3-man crew for 4 hours) $ 258

Labor Overheads (60%) 155

Transportation (15% of Labor) 39

Street Cut Permit 75

Avg Full Seal Cost (2” – 12”) 40

Traffic Control (Flaggers) 132

Gravel (9 yds) 95

Pavement Repair 278

Subtotal $1,072

Supervision, Contingencies & Overheads 228

Total Repair Cost Estimate $1,300

Note: The repair cost per leak is in 2006 dollars and is not inflated for this 20-year period

As the above data indicate, the annual maintenance costs are projected to increase by approximately three times over the 20-year period. Managing this risk is one of the key objectives of the main replacement program. Several replacement alternatives are analyzed below.

The above table and the following graph indicate how the four replacement rate strategies effect annual maintenance costs. It is clear that even the 10,000-foot per year alternative is much better than the “do nothing” approach.

Figure 3

The maintenance and capital cost net present values for each program are as follows:

NPV O&M NPV Capital

0 feet/yr: $1,417,000 $ 0

10,000 feet/yr: $721,000 $ 7,444,000

15,000 feet/yr: $506,000 $ 9,556,000

20,000 feet/yr: $385,000 $11,261,000

25,000 feet/yr: $309,000 $12,238,000

Figure 4

Notes:

¹The discount rate used is 8.427%, which is the rate of return on capital allowed by the Idaho Public Utilities Commission at United Water Idaho’s most recent rate case.

²The average construction cost of $70 per foot is used in calculating the capital costs.

LEAKAGE RATES AND COSTS FOR 6-INCH AND 8-INCH STEEL PIPELINES

Steel pipe and cast iron pipe were frequently installed in 6-inch and larger sizes from the late 1800’s through the 1960’s. While both materials provided similar performance initially, the steel pipe has not performed as well as cast iron over time, consequently leading to more frequent leaks. The 6 and 8-inch sizes have the highest leakage frequencies of the steel pipe remaining in service. Analyses of several replacement strategies for this pipe, using the same approach as discussed above for the small metallic pipe, is provided below. See Appendix A for details of the analyses supporting the following conclusions.

There is a significant difference in footages between the two cases with 53,779 feet for the steel pipe versus 280,061 feet of the smaller diameter pipe. This makes the analysis more sensitive to small annual changes in failure rates. It is evident that both models should be reviewed annually and adjustments be made to the growth rate coefficient as the results dictate. However, a degree of caution should be applied to avoid giving credence to a one-year anomaly of either high or low leak counts.

6-INCH AND 8-INCH MAIN REPLACEMENT ANALYSIS

ANNUAL O&M COSTS FOR FOUR REPLACEMENT STRATEGIES

Table 5

The above replacement plans include capital costs of:

1,500 feet per year $105,000

2,500 feet per year $175,000

3,500 feet per year $245,000

4,500 feet per year $315,000

It appears that 3,500 feet per year is the most attractive alternative as the annual maintenance costs peak about 30% higher than the 2005 amount, whereas maintenance costs for replacements of 1,500, 2,500 and 4,500 feet per year rise approximately 490%, 80% and 10% respectively. The difference between the maximum annual maintenance costs for the 3,500 and 4,500 foot per year alternatives is only $2,600 compared to the increased annual capital cost of $70,000.

This approach for 6 and 8-inch steel mains demonstrates the risk associated with under-funding the main replacement program. The annual replacement rate of 1,500 feet per year is not sufficient to control rising pipeline repair costs over the next 25 years.

The actual replacement total over the past six years is 9,365 feet. This results in an average of 1,560 feet per year, clearly insufficient to keep pace with declining integrity of the pipeline materials.

SYSTEM SURVEYS

A cross-section of water systems on the east coast and the west coast were contacted to determine their degree of concern regarding their aging underground infrastructure and the methods used to establish their main replacement strategies. All of the water systems contacted seemed to face similar issues with aging small diameter pipe that was installed when fire protection requirements were low, water demands were low and the best materials available were metallic. As a consequence, they had all arrived at strategies for their main replacement plans. The survey revealed a range of sophistication regarding approaches to establishing these main replacement plans. At the high end, models are used, similar to that described above, to project future leakage trends and to develop medium term capital expenditure plans. On the other end, capital spending levels are frequently based on past history and not upon anticipated future needs.

Two observations seem relevant, future capital expenditures should be based upon future needs, not previous expenditure patterns. Second, data gathering is vital. A data base is needed to capture leak records, capturing, at minimum:

Pipe Size

Pipe Material

Year of Installation

Location / Address of Leak

This data enables the type of analyses described above. This analysis is dependent upon trends of pipeline failure. As a result, the longer the period over which the analysis is performed, the more reliable are the results.

CONCLUSIONS

This risk assessment approach provides the water system manager with quantitative information regarding the risk and mitigation costs related to the alternative plans. There is no clear-cut winner as the priorities regarding O&M costs and capital may vary from system to system. It seems apparent, however, that the lower replacement rates are likely insufficient as the maintenance costs are projected to increase significantly before they begin to drop. On the other hand, the higher footage plans may be too aggressive as they provide relatively small improvement in the O&M costs when compared against the higher capital amount.

This data is essential for establishing the type of model described in this paper. It can also help identify failure trends within these categories. For instance, this investigation has revealed that metallic pipe installed during the 1950’s has the highest overall failure rate of any other decade. This type of information is useful when choosing specific mains for replacement during upcoming budget cycles.

Finally, it should be noted that the financial risk associated with each strategy should not be the lone criteria in determining the plan. As noted earlier, the small water mains are sources for a number of customer service problems: discolored water, low-pressure complaints and the lack of fire protection capabilities. Consequently, the O&M risk cost, capital mitigation cost and other customer service considerations must be taken together to establish the water system’s capital commitment to its transmission and distribution system renewal process.

APPENDIX A

6-INCH AND 8-INCH STEEL PIPE

Solving Shamir and Howard’s equation yields a growth coefficient of 0.10872. The resultant theoretical leak rates become:

Table 7

Graphing this data provides the following:

Figure 5

Figure 6

MAIN REPLACEMENT ANALYSIS

ANNUAL O&M COSTS FOR FOUR REPLACEMENT STRATEGIES

Table 9

BIBLIOGRAPHY

References:

Haestad Methods, Inc., (2003), “Advanced Water Distribution Modeling and Management”, Haestad Press.

United States Environmental Protection Agency, (2002), “The Clean Water and Drinking Water Infrastructure Gap Analysis”, September 2002.

United States Environmental Protection Agency, (2001), “Drinking Water Infrastructure Needs Survey”, February 2001.

Shamir, Uri and Howard, Charles D.D. (1979), “An Analytical Approach to Scheduling Pipe Replacement”, American Water Works Journal, May 1979, pages 248-258.

Rausand, Marvin, (2004), “System Reliability Theory (2^nd Edition)”, Wiley-Interscience.

Cast Iron Soil Pipe Institute, (1994), “Cast Iron Soil Pipe and Fittings Handbook”, Cast Iron Soil Pipe Institute.

AWWA Research Foundation, (2005), “Managing the Future: Trends in Drinking Water”, Drinking Water Research, January/February 2005, pages 2-8.

United State Environmental Protection Agency – Office of Research and Development, (2005), “White Paper on Improvement of Structural Integrity Monitoring for Drinking Water Mains”, March 2005.

American Water Works Association, Hughes, D.M., Technical Editor, (2002), “Assessing the Future: Water Utility Infrastructure Management”, American Water Works Association.

Matichich, M, Allen, J., and Allen , R., (2006), “Asset Management Planning and Reporting Options for Water Utilities”, American Water Works Journal, January 2006, pages 80-87.

Stahr Jr., Richard W., (2006), “Asset Management – One Size Does Not Fit All”, Opflow, January 2006, pages 10-12, American Water Works Association.