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Mortar Lining as a Protective Layer for Ductile Iron Pipes

Abstract

The objective of the study is to recognise whether epoxy resin or polyurethane internal linings of ductile iron (DI) pipes create visibly smaller head loss in flow than cement mortar linings. Some data reported by the Ductile Iron Pipes Research Association (DIPRA) was used in the calculations. Only the data from hydraulic tests performed no later than 30 years after the placing of the mortar lining were considered. The average values of the Hazen–Williams roughness coefficients C for each of the internal pipe diameters were calculated, and single experimental data neglected. Two different approaches were taken for interpreting the DIPRA experimental results and omitting the fact that the flow rates during these tests are unknown. The Hazen–Williams roughness coefficients C were used in both for computing the friction factor f from the Moody chart for three values of flow rate: being equal to the optimal value for a given diameter, and then by 50% larger and 50% smaller than this value. Next, the computed friction factors were compared with the values predicted from the Moody chart for smooth pipes. In the first approach, the friction factors f were computed using the Epanet2 software, and in the second approach, a general equation for calculating f from known C and flow parameters was applied. Both approaches resulted in friction factors f very close to those for smooth pipes for the whole range of Q. In conclusion, more smooth plastic linings of DI pipes do not result in a significantly more visible saving of energy for pumping.

Introduction

In most cases, ductile iron pipes require both external and internal protection against corrosion. The most prominent disagreements are concerned with the external protection. In the U.S.A., an approach summarised in the report by the Ductile Iron Pipe Research Association (DIPRA) is based on the principle that bonding cover protection efficiency is doubtful and the cost created by this kind of lining is unreasonably high [1]. To improve the ductile iron structure and, consequently, avoiding mechanical failures; an annealing process is applied in the pipe production foundries. After this process, the wall surface of the pipes is covered by corrosion products being recognised by DIPRA as an efficient protective layer, which should not be removed by sandblasting because of a danger of creating blistering or slivering of the pipe’s surface that may not be totally covered by a thin bonded coating. Because of this DIPRA prefers polyethene encasement for corrosive soil [2]. Several international and national standards have been established for this kind of corrosion protection [3,4,5,6,7,8].

However, the Committee on a Review of the Bureau of Reclamation`s Corrosion Prevention Standards for ductile iron pipe, constituted by the U.S. [9], stated that limited data indicates that ductile iron pipes with polyethene encasement and cathodic protection are not able to serve reliably more than a 50-year life-time in highly corrosive soil (< 2000 Ω-cm). Moreover, the Committee expresses the opinion that bonded dielectric coatings with cathodic protection may provide superior protection to the ductile iron pipe when compared to polyethene encasement with cathodic protection. In contrast to the data included in the DIPRA report [1], the Committee concluded that it was not able to identify any ductile iron pipe (DIP) corrosion control method that would provide reliable 50-year service in highly corrosive soils.

Ductile iron pipe (DIP) producers in Europe rely on zinc passive cathodic protection [10]. However, the galvanic covering is not appropriate because of the oxide layer. Zinc from a zinc wire is continuously supplied at a high temperature by an electric arc where it is melted, atomised, and sprayed on the pipe’s external wall by compressed air, creating a bonded cover from the ferric oxide layer. For non-aggressive soils, 200 g of high purity zinc is applied per 1 m2, and in aggressive soils 400 g/m2 of a mixture consisting of 85% zinc and 15% aluminium [11]. A single zinc–aluminium wire should be used as it gives a more homogeneous distribution of aluminium intrusions into the zinc’s matrix. Most recently, a small amount of copper is added to protect the pipes against external biological pit corrosion. Additional protective coatings are applied on the zinc layer, including; bituminous, or asphaltic layers, petrolatum tapes, plastic adhesive loose encasement, and protective painting. An external cement mortar lining is also offered for aggressive soils. Cathodic protection is known to be an efficient method but requires monitoring and maintenance.

In general, internal DIP protection methods are less contentious. For over 90 years, cement mortar linings have been successfully applied in many countries. The cement mortar adheres well to the DIP wall and it protects the ferric by the high pH of the water from the mortar pores at the boundary between the ductile iron pipe internal wall and the cement mortar lining. This pH ranges between 11 and 13. One of the shortcomings for the application of cement mortar linings is the short time increase in the flowing water pH after an installation, which results in the dissolution of alum and chromium [12]. This problem is mostly prominent in pipes with smaller diameters, slowly transporting soft water of low buffer capacity. If the cement mortar lining is sprayed in situ, the time required for curing is important because it extends the break in the water supply. Because of these shortcomings, epoxy or polyurethane linings are more often used in such cases. These kinds of adhesively bonded linings adhere well to the pipe’s surface and protect it by denying access of oxygen and ions to the ductile iron. However, if not done properly or damaged, the lining loses its protective ability because there is no chemical mechanism protecting the pipe’s internal surface. This difference still makes cement mortar linings an attractive alternative for the internal adhering of linings for ductile and old cast iron pipes.

Polyurethane and epoxy linings are only 2 mm thick [13] compared with the thickness of cement mortar linings starting from 3 to 9 mm, as a function of pipe diameter in the standard [10], or from 3 to 10 mm as specified in the Polish standard [14], or from 5 to 6 mm for Australian standards [15]. For larger diameter pipes, the differences in the lining thicknesses are too small [16] to play any role in predicting the required pump characteristics. The equivalent sand roughness is the second parameter impacting head loss for a turbulent flow and its value and changes in time will be discussed here.

Purpose of the Study

Several choices can be made while selecting materials for water pipelines. For large diameters and high pressures, ductile iron or steel is a likely choice. If so, the next step is to design external and internal protective linings and sometimes cathodic protection as well. Firstly, grey iron and later ductile iron pipes have been protected internally by a cement mortar lining for almost 100 years. However, now some alternatives exist [17] such as epoxy resin linings and polyurethane linings. For new pipes, the choice of the corrosion protective materials depends on; the short- and long-term impact of the water’s quality [12, 18, 19], calcium carbonate equilibrium in flowing water and pipe diameter [20], the preferable mechanism for the protection a pipe’s wall [21], impact on the decay of disinfectant, a tendency to biofilm formation [18], lifetime expectancy [11], price of pipes and surface roughness coefficient. The last factor is essential, especially for the almost turbulent character of the flow, which is typical for pipelines with large diameters. Energy prices have been growing continuously for the last three decades and this trend is expected to continue. The purpose of the study is to discuss whether cement mortar lining creates much higher friction of flow than plastic lining materials, whose surface is characterised with a much lower sand roughness coefficient. The results of the computations presented here are helpful in rational decision-making on choosing materials for the internal ductile iron pipelining, or for considering whether to prefer ductile iron or rather other alternatives for pipe materials being of a smooth surface and resistant to corrosion, therefore, not requiring any internal lining.

Cement Mortar Lining Technology

Whilst not attacked by the water with a low alkalinity and negative Langelier Saturation Index according to Muster et al. [21], cement mortar linings typically have a predicted lifetime exceeding 100 years, so in most cases, longer than the lifespan of the pipe itself. The mortar provides protection due to a high pH environment created by the hydration of cement. Both blast-furnace slag cement and Portland cement are used for cement mortar linings of drinking water pipes while high alumina cement is recommended by Meland [22] for water with a low pH, low concentration of calcium and low alkalinity, used for protecting DI and steel pipes in some industrial applications. According to several guidelines and standards, the cement mortar lining should be characterised by the water to cement ratio w/c 0.25–0.35, and the sand to cement ratio s/c from 1:1 to 3:1. For increased s/c ratio there is less shrinkage and the structure of the lining is more compact, but for s/c above 2, the strength is negatively affected [23]. In a foundry, both the centrifugal and projection methods of applying cement-mortar linings are used. Centrifugal linings produce a centrifugal acceleration of at least 40-times gravity, usually not exceeding 100 times gravity. The bond strength of the cement mortar lining to the inner ductile iron pipe wall is usually not lower than 0.5 MPa for blast furnace slag cement and up to three times higher for high alumina mortar, which gives the best protection for sewerage pipe coatings [24], but leaching of aluminium from cement mortar lining is the main unwanted water quality impact [12]. In contrast, the shear stress along the lining and water boundary is only in the order of a few N/m2 [25].

The curing of the mortar lining is an important process which takes a few days in the foundry and often is shortened to 24 h in field applications, because of practical reasons. In this case, some additives to the cement are used shortening the curing period. During the curing, the humidity of the air has to be very high to avoid rapid evaporation of water from the mortar lining. The drying method is described in the standard ISO 6600. For new pipes, curing tunnels or a sealing coat can be used. Temperatures must be well above freezing point. In field applications just after the curing process, the pipe is washed several times and disinfected. Then it is filled with water without a flow and if after 24 h the physico-chemical water parameters do not fulfil the regulations of the country for drinking water, the whole process of washing and disinfecting has to be repeated.

Other Factors Affecting the Choice of Material

Friction to flow is an important factor in the selection of a pipe’s material, but there are many other facts to be considered. One of them is the mechanism of protection against corrosion. In the case of a cement mortar lining, the protection is of a chemical character. The cement mortar lining is strongly bounded with the thin layer of oxides created during the annealing process and partially divided with pores of a few micrometers. These pores are filled with water of a pH between 11 and 13, which is high enough to protect the ferric matrix and graphite of ductile iron (DI) against corrosion. During the production, transportation, and installation of new DI pipes, some cracks in the cement mortar linings are formed. Cracks in cement mortar linings are generally of two types: surface crazing and circumferential or longitudinal cracks [26]. The standard ANSI/AWWA C104/A21.4 allows any surface crazing without limitation. It also allows any length of circumferential cracks but limits the length of longitudinal cracks. The allowable width of the cracks as a function of pipe diameters are specified. The calcium carbonate equilibrium is dynamical, meaning that in the equilibrium as much of CaCO3 is dissolved as is precipitated. Because of that, self-repairing mechanisms exist and it is believed that the cracks of a width not larger than those specified in the standard are able to be filled with calcium carbonate because of the self-repairing mechanism [27].

The plastic protective covers of DI pipes provide a mechanical barrier against ions and water itself. Their adhesion to a well-prepared pipe’s surface is excellent, but if damage occurs the naked peace of the pipe is subject to intensive corrosion and no self-repairing mechanism exists. Recently, for grey iron water pipes’ renovation in the field, plastic linings are more often chosen instead of cement mortar linings. This is due to the curing process of cement mortar linings, which takes at least 24 h. During the curing process, a mild temperature and high humidity should be maintained inside the renovated pipe, so both entrances of the pipe are covered. Old pipes usually must be cleaned by pigs and then always by a rotating stream of water flowing out of the cleaning machine, this is usually done between a pressure of 1200 and 2400 bars. All unbounded ferric oxides are to be removed, but the pipe’s surface are not cleaned back to its base metal because a higher level of roughness for a pipe’s wall results in better mechanical contact between the metal and a mortar lining. Then, the mortar is sprayed under high pressure in the similar rotating method as was previously used for the pipe cleaning. Drag trowel can be used for a surface polishing process.

Methodology

A large bank of data collected and published by DIPRA [26] was used for investigating if the cement mortar lining sand roughness coefficient predicted in the tests, resulted in much more head losses to flow than created by smoother plastic materials. Firstly, the screening of the data was performed. Observing the trend of the Hazen–Williams roughness coefficient C (see Figs. 1 and 2), it was concluded that for up to 30 years of a pipe’s operation this coefficient can be roughly recognised as not being affected by the pipe’s age. All data for older linings were excluded from the interpretation. Next, the average values of C were calculated for the same pipe’s diameters and they were only used later in the computations. Three single measurements of C for three pipe diameters were discarded as not being representative enough. Then, optimal flow velocities were calculated for all pipe diameters for which the DIPRA [26] experimental values of C remained under consideration after the data screening operation.

Fig. 1
figure1

A graph of the Hazen–Williams roughness coefficients C measured by DIPRA [26]

Fig. 2
figure2

An attempt at predicting a linear correlation between time t and Hazen–Williams roughness coefficient C

In the first approach, the U.S. EPA software Epanet2 was used to compute the relative sand-grain roughness coefficients from the Darcy–Weisbach equation for the internal diameters of these pipes. In the computations, three different cases were taken into account: optimal flow rate Qopt, 50% higher, and 50% lower than optimal flow rates. In these computations, the relative sand-grain roughness coefficients from the Moody chart were predicted in such a way as to result in the identical head loss of flow as calculated previously from the Hazen–Williams equation. The average value of the experimentally predicted C values for a given internal pipe diameter [26] was used in the head loss computations. Then, from the relative sand grain roughness coefficients and the Reynolds number values Darcy friction factors f were predicted and compared with the line describing the smooth surface of pipes on the Moody chart.

In the second approach, the equation developed by Allen [28] was used to calculate directly the friction factor from the Moody chart for the Hazen–Williams roughness coefficient C, water dynamic viscosity μ, pipe internal diameter d, and the Reynolds number Re. Next, the friction factors f (Re) from the Moody chart for smooth pipes were compared with the computed values of f. As previously, the computations were conducted for three values of flow rate: optimal Qopt, 50% higher, and 50% lower than optimal flow rates.

In both approaches, the results of the computations concluded that the friction to flow created by a cement mortar lining is close to that predicted for smooth pipes, so applications of smoother lining materials do not result in substantial saving of energy for the pumping of water.

Not only does the friction factor f impact the value of the head loss, but also the lining thickness. The thickness of the epoxy resin lining or polyurethane lining is about 2 mm only and does not depend on the internal pipe’s diameter. A cement mortar lining’s thickness is a few millimetres thicker for larger pipe diameters. The lining thickness impact on head loss can be easily calculated from the Darcy–Weisbach equation. Despite slightly decreasing the internal pipe diameter, cement mortar lining results usually in higher flow capacity of renovating pipe, especially for large diameters [27, 29].

Optimal Velocities

One of the scopes of the paper is to predict the way in which the relative sand grain roughness changes in time impact the prediction of optimal velocities of flow through cement mortar lining protected ductile or cast iron pipes transporting clean water. This is not an optimisation paper, but it is necessary to describe in general to which kind of problems the considered changes for properties of the mortar lining’s surface are applicable. Usually, the decision variable is the internal pipe’s diameter. The objective function is the equation for the minimised total cost of constructing and operating the pipeline, recalculated for 1 year of the expected life span period. All equations describing head loss in the pipe, cost of construction and cost of energy are boundary conditions to be fulfilled. Formulating an optimisation problem for the pipe’s diameter transporting liquid is a traditional [30] and the simple task looked at from the perspective of optimisation theory. However, it is uncertain in which way energy prices, pipe sand grain roughness, and in some cases even an internal pipe’s diameter, will change in the future. The life span is also predictable with low reliability. Concluding any solution to this simple optimisation problem is uncertain, and reducing the uncertainties is required because underground infrastructure is expensive.

Friction to Flow

For large diameter pipes flowing under pressure, ductile iron seems to be a reasonable choice. Steel and stainless steel can fulfil all the same requirements but are more expensive, so their use is preferable in a difficult soil–water environment such as highly unstable soil when welded connections are the most reliable. Often the same internal linings are applied for steel pipes as for the ductile iron water mains. For low diameters, alternative pipe materials such as polyvinyl chloride (PVC), high-density polyethene (HD PE), or polypropylene (PP) can also be used, especially for diameters lower than 600 mm, above which usually the price—material relations change favourably for ductile iron in the case of transporting water under pressure [11].

DIPRA [26] has analysed data on the Hazen–Williams roughness coefficient C of cement-mortar lined ductile iron pipes from 43 towns. The measurements were done for pipes of nominal diameters ranging from 152 to 914 mm, including ten pipes of the internal diameter d = 152 mm, seven pipes of d = 203 mm, 6 of d = 254 mm, 13 of d = 305 mm, 1 of d = 356 mm, 8 of d = 406 mm, 8 of d = 508 mm, 1 of d = 610 mm, 6 of d = 762 mm and 3 of d = 914 mm. Nominal diameters for ductile iron pipes are predicted while taking into consideration the thickness of the internal lining. The reported values of the Hazen–Williams roughness coefficient C are presented in Fig. 1 as a function of the pipe’s age. Because of the inaccuracy of this equation, it is expected that even for the same pipe lining roughness, the value of C is also to some extent the function of the pipe’s diameter and flow rate.

The results presented in Fig. 1 conclude that the decrease of the roughness coefficient C over time t is moderate. No function to describe this decrease is suggested by the measured points. For the simplest linear correlation, Eq. (1) below determined by the least square’s method describes this decrease with the coefficient of determination R2 equal to 0.3486, where time t is expressed in years. The set of data consisted of 64 values of C factors.

$$C = - 0.19923 \cdot t \, + \, 143.9468.$$
(1)

This equation is uncertain not only because of the low value for the coefficient of determination, but also because only a few points collected for the age above 30 years decide about the regression straight line slope.

For all pipes [26] less than 30 years old, any correlation between time t and the Hazen–Williams friction coefficient C is not clearly visible. An attempt at predicting a linear relation between t and C was made and the result is presented in Fig. 2. The coefficient of determination is only 0.1 and the correlation seems to be coincidental. It is necessary to remember that the Hazen–Williams equation is not accurate for larger diameter pipes and that the correlation between time and the Moody friction factor might be more clearly visible. Let us assume that for the tests considered here [26] the values of C factors for pipes less than 30 years old can be roughly recognised as not being affected significantly by the period of operation. The set of 64 C values from Fig. 1 was reduced to 51 C values by including only the results for pipes not older than 30 years in Fig. 2. Only the average values of k/d for each of the d values were presented. For later interpretations, three single values of C for diameters 356 mm, 457 mm, and 610 mm (14, 18 and 24 inches) were excluded and all the remaining were analysed.

Values of Optimal Velocities

Rationally chosen velocities of flow are higher for larger pipe diameters, but despite this, the hydraulic grade line slopes are smaller. For turbulent flows in steel pipes with diameters above 0.0254 m (1 inch) Peters et al. [31] suggested an equation for predicting optimal pipe diameters. After recalculating it for the flow of water exclusively, it is simplified to Eq. (2):

$$d_{{{\text{opt}}}} = 0.0398 \cdot Q^{0.45} ,$$
(2)

in which dopt is the optimal internal pipe diameter expressed in meters and Q is volumetric flow rate expressed in L/s. The optimal value of pipe diameters for viscous flow is not of interest in water supply systems so the formula for laminar flow optimal pipe diameter is not quoted here. Towler and Sinnott [32] specified two different equations for an optimal pipe diameter dopt in the range between 25–200 mm (Eq. 3a for carbon steel and 3b for stainless steel) and 250–600 mm (Eq. 4a for carbon steel and 4b for stainless steel) written here in a form applicable exclusively for water flow:

$$d_{{{\text{opt}}}} = 0.664 \cdot Q^{0.51} \cdot \rho^{ - 0.36} ,$$
(3a)
$$d_{{{\text{opt}}}} = 0.550 \cdot Q^{0.49} \cdot \rho^{ - 0.35} ,$$
(3b)
$$d_{{{\text{opt}}}} = 0.534 \cdot Q^{0.43} \cdot \rho^{ - 0.30} ,$$
(4a)
$$d_{{{\text{opt}}}} = 0.465 \cdot Q^{0.43} \cdot \rho^{ - 0.31} .$$
(4b)

Density is denoted by ρ, which for all equations from (3a4b) is to be expressed in kg/m3. Genić et al. [30] formulated and solved an optimisation problem on the pipe’s diameter transporting liquid in conditions typical for the chemical industry. The cost of fitting was included in the objective function, but the pipe’s roughness increase over time was not considered and the cost of the pump was assumed to be independent of the pipe’s diameter. Head losses of flow were calculated separately for smooth and rough pipes, in the latter case for complete turbulence. The tables for optimal diameters and flow velocities were presented in the paper [30]. The values of these velocities are presented in Fig. 3 for rough pipes transporting water.

Fig. 3
figure3

Optimal velocities of flow through rough pipes transporting water [30]

The cost of building a pipeline for an urban water supply system differs significantly from the cost of installing the same pipe in a factory. Optimal diameters computed for specific soil–water conditions, depth of soil freezing, pipe life expectancy and the number of hours per year during which the flow is sustained may be critically applied. Materials used for producing pipes differ significantly in surface roughness, but it is necessary to take into account head loss created by pipe connections and the impact of biofilm which makes the surface roughness of different pipe materials more uniform. As a result of all these local circumstances on the impact on the economical velocity of flow, there is no table of economical diameters in water supply systems which is universally applicable. Certainly, creating local guidelines is necessary because designers do not have enough time and access to information, so they are not able to solve the optimisation problem each time themselves.

For water plumbing in houses, usually, velocities not higher than 0.5–0.7 m/s are advised to avoid noise, even if the pressure after the flow meter allows for much higher values.

Lining Roughness

In urban underground infrastructures, plastic pipes are in common use for low diameters, but starting from 300 mm diameter ductile iron is competitive and often is the most likely choice made for main pipes of 600 mm diameter or larger, especially when the pressure is high. These pipes are protected internally against corrosion by a cement mortar lining, and in more recent years by polyurethane or epoxy linings for lower diameter pipes and low buffer capacity water. Cement mortar lining can be made by centrifugal or projection methods which visibly impact not only the cement sand grains’ distribution inside the lining and its porosity but surface roughness as well. In a foundry, the cement spraying tool does not spin but the pipe rotates instead, so the centrifugal force moves the sand grains towards the internal pipe wall and the surface in contact with the water remains smooth. It consists mostly of cement mortar and fine particles of silica from sand [13]. When a cement mortar lining is applied in situ to existing pipelines after cleaning them, the surface of the lining is rougher and the porosity of the whole layer higher. The cleaning process should not remove all the oxides from the inner pipe wall surface because the adhesion of the lining can be improved by higher roughness of ductile/cast iron pipe wall’s surface. However, no loose corrosion products can remain after cleaning.

The prediction for the cement mortar lining sand relative roughness of pipes k/d investigated by DIPRA [26] should be based on measurements done only with a turbulent flow, otherwise, not only surface roughness but also water viscosity would impact the measured head loss, which is unwanted in such measurements. This principle rule, obligatory for corroded pipes of significant roughness, cannot be followed in tests done in situ for pipes of a smooth lining, which will be illustrated by calculations. For a fully turbulent character of flow, the head loss is proportional to the second power of flow velocity according to the Darcy–Weisbach equation, while proportional to the power of 1.85 according to the Hazen–Williams equation. Although it is known that the Hazen–Williams equation is inaccurate for larger diameter pipes [33], it is still overused. To predict the relative sand grain roughness k/d from the value of the Hazen–Williams roughness coefficient C, the flow velocity should be known [28]. Firstly, relative equivalent sand grain roughness has been calculated assuming that during the tests done by DIPRA [26], the optimal velocities were chosen as calculated by Eqs. (3a) and (4a) for rough pipes. The results of these computations are presented in Figs. 4 and 5. Then the uncertainty caused by this assumption was verified based on general relations between the Hazen–Williams roughness coefficient C and equivalent sand grain roughness coefficient [28]. The computations were performed using the Epanet2 software. In the calculations, the value of relative sand grain roughness coefficient has been predicted in such a way as to result in the same friction head loss for each of the pipe diameters as computed using Hazen–Williams equation with the friction coefficient C as specified in the DIPRA report [26]. A temperature of 15 °C was used in the computations. For the fully turbulent character of flow, the temperature has no impact on head losses.

Fig. 4
figure4

Relative sand grain roughness coefficient k/d plotted versus the Hazen–Williams C coefficient. The results of the computations are based on the assumption that the water flow velocities used in the DIPRA tests [26] were identical to those optimally predicted from Fig. 3, depending on the diameters

Fig. 5
figure5

Equivalent sand grain roughness calculated for the DIPRA experiments [26] from Fig. 4

The values of equivalent sand grain roughness coefficient k received from these computations are presented in Fig. 5.

The assumption that the tests [26] were conducted for optimal flow velocities is unrealistic and has been used only for predicting the primary values of k. Now an error resulting from this assumption must be estimated. All the tests should be done under water flow velocity as high as possible to minimise the viscosity impact on the measured friction to flow values. Because of this, it is unlikely that tests with less than 50% of flows corresponding to optimal flow velocities were used. This would correspond to four times smaller head losses if the character of flow was always turbulent and the pipes were considered as having a rough surface—which was not the case as will be shown later.

Calculations of the Reynolds numbers Re, Darcy friction factor f (not the Fanning friction factor), and then the equivalent sand grain roughness k were done for 0.5 Qoptimal (d), Qoptimal (d) and 1.5 Qoptimal (d). By Qoptimal (d) the optimal flow-rate values through pipes of diameters d were denoted. All the values of sand grain roughness coefficients k (Qoptimal (d)), k (1.5 Qoptimal (d)) and k (0.5 Qoptimal (d)) are presented in Fig. 6. For the same values of C, higher k values were received for lower flows, but for the smallest and the largest pipe diameters, the differences were not clearly visible.

Fig. 6
figure6

The range of computed sand roughness coefficients for 0.5 Qoptimal, Qoptimal and 1.5 Qoptimal, where Q is an optimal flow for a rough pipe [28]. The computations were performed for head losses calculated for Hazen–Williams C coefficients predicted by DIPRA tests [26]

Smooth Pipes

DIPRA [26] invoked results of measurements conducted some years ago at the University of Illinois for 102 mm, 152 mm, and 203 mm grey cast iron pipes (4, 6 and 8 inches). From the results of measurements, first Hazen–Williams C, and then the Darcy–Weisbach friction coefficients f were calculated and plotted on the Moody chart, covering mostly the line for smooth pipes. To evaluate the friction created to flow by all cement mortar linings here, only pipes up to 30 years old were considered. For the field tests conducted by DIPRA [26], the results of the calculated Darcy friction coefficients f were compared with the line from the Moody chart, describing friction to flow created by smooth pipes. Before computing the head losses from the Hazen–Williams equation, separately for each of the pipes’ internal diameter the arithmetical average of all C values was calculated, and only this value was used in the computations of head loss. Several explicit equations for the Darcy friction factor exist for smooth pipes. The Blasius and the Nikuradse equations were one of the first examples. All such equations are valid for a given range of Re. For the purpose of this study, our own explicit approximation (5) to the Colebrook equation for f was used. This approximation is accurate for the Reynolds numbers in the range covering the friction tests reported by Bonds [26]. A smooth line has been drawn in Fig. 7 in an ordinary coordinate system Re, f. The exponential approximation of the friction factor f = 0.2179 * Re−0.2103 was characterised by the coefficient of determination R2 = 0.9889, for the Re range from Re = 2320 to 2.4·106.

$$f = 0.2179 * {\text{Re}}^{ - 0.2103} .$$
(5)
Fig. 7
figure7

Exponential approximation to the smooth pipe friction factor from the Moody chart for the range of Re from 2320 to 2.4·106

To present the fit of an approximated Eq. (5) to the friction factors f obtained from the smooth line of the Moody chart for small Re values, a function f{log(Re)} was plotted in Fig. 8 for the whole range of Re from 2320 to 2.4·106.

Fig. 8
figure8

Exponential approximation f{log (Re)} for the data presented in Fig. 7

To plot the values of f computed from Epanet 2 for the head losses calculated from the Hazen–Williams equation for an arithmetical average of C reported for a given internal pipe diameter in the DIPRA report [26], a shorter range of Reynolds number 2320 < Re < 1.5*106 was chosen. For this range of Re, the best fit to the line describing the smooth pipe friction coefficient f was obtained for a slightly different equation giving almost identical results in the whole range of Re numbers of interest.

The computed values of the friction factor f (Qoptimal) are presented in Fig. 9 by the brown squares; they all lie almost exactly on the exponential approximation to the smooth pipeline from the Moody chart. In all the calculations, referring to each of the pipe diameters separately, the same average value of experimentally predicted C (for this diameter) was used. They were calculated as an arithmetical average from all values of C specified for that diameter of pipe not older than 30 years in the DIPRA report [26]. For flow rates 0.5 Qoptimal, the computed friction factors f were lower than predicted from the Moody chart for smooth pipes, which is impossible. For higher flow values (1.5 Qoptimal), the computed friction factors f were a little higher than f (Q) for smooth pipes, but the differences were negligible from a practical point of view. The computations done for 0.5 Qoptimal, Qoptimal, and 1.5 Qoptimal conclude that according to the data measured by DIPRA [26] in 43 towns and interpreted here, the pipes with cement mortar linings should be recognised as smooth pipes for predicting friction to water flow. Because this conclusion is valid for flows 0.5 Qoptimal, Qoptimal, and 1.5 Qoptimal in the range of flow extending from both sides for the values used in water supply systems, there is no need to repeat the computations for optimal smooth pipe flows [30] which are close to the rough pipes’ optimal Q values used here as a starting point in the computations.

Fig. 9
figure9

A comparison of the computed friction factor f values for the results of tests conducted by DIPRA [26] with the exponential approximation (5) to the smooth pipes line from the Moody chart

The conclusion that ductile iron pipes protected with a cement mortar lining create frictions to flow almost identical to hydraulically smooth pipes is important for the evaluation of energy losses caused by this kind of lining in comparison with plastic or GRP pipe walls of a very low sand roughness coefficient. This finding has been verified again using the same set of field data [26] and applying Eq. (6) developed by Allen [28], who compared head losses described by the Darcy–Weisbach and Hazen–Williams equations:

$$f = {{373} \mathord{\left/ {\vphantom {{373} {\left( {C^{1.852} \cdot \mu^{0.148} \cdot d^{0.018} \cdot {\text{Re}}^{0.148} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {C^{1.852} \cdot \mu^{0.148} \cdot d^{0.018} \cdot {\text{Re}}^{0.148} } \right)}}.$$
(6)

In Eq. (6), f is a Darcy friction factor [–], C: Hazen–Williams friction factor, µ: dynamic viscosity of water [kg/(m s)], d: internal diameter [m] and Re: Reynolds number [–]. In the calculations, a constant water temperature t = 15 °C has been assumed arbitrarily. According to the results of a C prediction reported by Bonds [26], the lowest C value was 139.1 and the lowest d value 0.1524 m. Substituting these values to Eq. (5), we received the boundary value of the friction factor f from which all values of f are to be higher for smooth pipes (the lowest f value did not correspond to the lowest diameter d).

Analogously for the highest C and d values equal to 147.83 m and 0.9144 m respectively, the lowest boundary for f was predicted from Eq. (5) for smooth pipes. Next, Eq. (6) was used to calculate f (Re) for boundary Re values, real d and reported C values [26]. The results of the calculations are presented in Fig. 10 for the whole range of Re from Fig. 7. For the smallest Reynolds number, the higher, and even the smaller, boundary values for f exceeded the value calculated from Eq. (5) for smooth pipes. Exceeding the upper boundary value for f can be explained by the unknown water temperature and flow rates used in the measurements reported by DIPRA [26]. For higher Re values, likely for larger pipe diameters of d, the Darcy friction factor f values were settled well between the upper and the lower bounds. Finally, for the highest Re the friction factor f calculated for smooth pipes was practically equal to the lowest bound for f. In conclusion, in the cement mortar lining of ductile iron pipes created in the experiments reported by Bonds [26], friction to flow equals to or is only slightly higher than, the values calculated for hydraulically smooth pipes. If the C values [26] were measured correctly, none or a limited electric energy saving is available by applying pipes made of plastic materials instead of DI pipes.

Fig. 10
figure10

Friction factor f, the upper and lower bounds calculated from Eq. (6). The computations were done for the Reynolds numbers Re, covering the whole range of flow (0.5·Qoptimal, Qoptimal, 1.5·Qoptimal) for the experiments reported by DIPRA [26]

Discussion

Despite at least 175 years [11] of applying cement mortar linings to provide protection to the interior surface of metal pipes from corrosion, a validation of the benefits and short-term water quality risks is being discussed again as nowadays several alternatives exist, e.g., polyurethane linings. All the alternatives have advantages and disadvantages. For example in water samples collected from a polyethene pipeline, which is a part of an existing water supply network, the following organic compounds were identified [18]: benzene, propenenitrile, MTBE, toluene, xylems, styrene, ethylmethylbenzene, phenol, mesitylene, methylstyrene, t-butyl-methylphenol, phenyl-m-dioxane, indane, methylindene, 3-phenyl-1-pentene, naphalene, dihydronaphtalene, 2-phenyl-penthenal, triterbutylphenol. Volatile organic compounds (VOC) were detected in water samples being in contact with HDPD including xylene, styrene, phenols and ethylmethylbenzene [18, 19]. A wide range of heterotrophic bacteria plate counts (HPC) were observed in the samples of biofilm scraped from the inner surface of PE-HD, PEX and PVC-U pipes [18], so biofilm develops on all materials used for the production of pipes. Because of a pH rise, resulting from calcium hydroxide migration to water, cement mortar linings may create the risk of short-term high aluminium leaching after replacing old pipes with new ones, or after making the trenchless renovation of old pipelines [12]. One hot topic is the question about friction to flow created by the lining and increasing the head loss in time for the same flow. From the very beginning [29], it was obvious that pipes protected by cement mortar linings cause much less friction to flow than unprotected pipe surfaces. However, new lining materials have a smooth surface and the thickness of the lining is also reduced. It is easy to calculate the impact of the lining’s thickness on friction to flow, but the impact of a lining’s surface roughness in time is not so clear.

After tests carried out by Dudgeon [34] on cement lined steel pipes for the range of Reynolds number from 4.7∙104 to 8.1∙105, he recommended using the Darcy–Weisbach equation with friction factors given by the Colebrook–White equation. From the empirical results, he predicted a sand roughness value of 0.01 mm for cement mortar linings. In his guide for designers, PAM-Saint Gobain [27] provides a table—including for single pipes measurements—of Hazen–Williams C and Colebrook–White sand roughness coefficients of k. The experiments were performed in 1974 on single pipes with diameters from 150 to 700 mm and aged from 0 to 39 years. The reported range of the Hazen–Williams coefficient C was from 130 to 146. In several cases, older pipes had higher values of the C coefficient because it is not possible to predict the changes of Hazen–Williams C coefficient or Colebrook–White sand roughness coefficient when not taking into consideration the contents of the cement mortar lining and the corrosive properties of transporting water. Single measurements are not informative. The PVC pipe producers publish a list of reports according to which the Hazen–Williams C coefficients for cement mortar lining of DI pipes deteriorate quickly in time, but the sources are not well documented.

Thus, two different approaches seem to be reasonable. The first and the best one takes into consideration different types of cement mortar used in linings, the different manufacturing methods of cement mortar linings and the transported water properties [21]. If necessary, the Langelier Saturation Index (LSI), total alkalinity and buffer capacity of water mixtures from different water intakes can be also calculated [20]. A deterministic life expectancy model was elaborated [21] that accounts for the aggressiveness of water to the cement mortar lining, but it did not include the prediction of the Hazen–Williams C coefficient or Colebrook–White sand roughness coefficient. The values of these coefficients were not investigated as predicting them would require long-term field tests. In the second approach, adopted by us, not only the water chemistry was unknown but even the exact flow rates were unknown for which the Hazen–Williams coefficients C were determined based on the head loss measurements. This approach started with the primary screening of a large bank of data. Then, the optimal flow rates through each of the pipe diameters were calculated and the possible largest and smallest flow rates during the tests predicted. From the calculations, we conclude that in the 30 years almost all cement mortar lined ductile iron pipes reported by Bonds [26] have behaved like hydraulically smooth ones, so it would be a small or almost no saving of energy resulting from using the smoother materials that are available now. Such a conclusion is correct statistically for a large number of cases and is not necessarily applicable for each individual case of specific water chemistry, or in the case of the careless lining.

Applicability of the Results

One commonly accepted rule states that there is no best material for water pipelines regardless of the local circumstances, so the choice should be made individually for a given investment and usually separately for large and small pipe diameters. The choice of the material is usually made by an enlightened investor who prefers to split the tender into two separate parts: one for the design and one for the construction. This approach gives the investor the ability to control the strategic decisions of the investment. Selecting the pipe material is one of several such important decisions. The same goes for the choice of renovation methods and materials for the internal lining of ductile iron or steel pipes. For large investments, a pre-conceptual design study is made to take proper decisions, which must be obligatorily followed later in the design, and formulated in specifications of essential requirements for the tender, forming a part of the contract with the contractors. The present paper contributes to this step of tentative considerations preceding the construction design of water supply systems. The tentative considerations are of crucial importance for a number of factors. These factors include:

  • The lifetime period of pipes and joints, the corrosion intensity of metal pipes, the deterioration over time of the mechanical properties of PE, PVC, GRP,

  • The necessity for the replacement of highly corrosive soil around ductile iron pipes,

  • The application of cathodic protection for steel or ductile iron pipes,

  • The cost of transporting and installing pipes,

  • The protection of pipes during storage outside (for example, the protection of plastic pipes against solar radiation, including the UV component of such radiation),

  • The time period necessary for completing the construction,

  • The minimal air temperature at which the pipelines can be constructed from PVC pipes,

  • The head loss created by water flow,

  • The energy requirements for pumping water,

  • The requirements of compacting the soil backfill,

  • The necessity of using and if necessary the size of water hammer anticipating control valves or water–air surge tanks,

  • The reliability of pipes and water losses,

  • The frequency of pipe failures in different months of the year,

  • The intensity of biofilm growth on internal pipe walls,

  • The short- and long-term interactions between pipe walls and water quality,

  • The methods of pipeline renovation in future, and even the possibilities of recycling materials, etc.

The interpretation of the large bank of head losses measurements caused by friction to flow reported by Bonds [26] which is presented here concludes that in a period of 30 years after constructing grey iron and ductile iron pipes with a cement mortar lining in recent years, a statistically insignificantly larger friction to flow of water was observed than expected for flow through smooth pipes from the Moody chart. Plastic and GRP pipes obviously have physically smoother surfaces than a cement mortar lining, but despite this, the head loss to flow created may not be smaller for any pipe material than that calculated from the Moody chart for hydraulically smooth pipes. In other words, for the data reported by Bonds [26] the head losses in the first 30 years of ductile iron pipes usage were not noticeably higher than would be expected for plastic pipes of the same internal diameters. Moreover, the nominal diameters of plastic pipes are usually measured to the external wall, while for ductile iron pipes this measurement is made to the internal surface of a cement mortar lining. This piece of information may be the reason that ductile iron is the more often chosen material for pipes of slightly lower diameters than up to now. However, it should be remembered that this general conclusion refers to the large bank of data reported by Bonds [26] and is not necessarily correct for cement mortar linings which are not carefully executed or in situations where corrosive waters with negative calcium carbonate saturation indexes and low buffer capacities occur, so perhaps it is not always applicable.

When the construction design is being elaborated, the choice of the material for pipelines is made by the investor based on pre-design studies. This choice is formulated in the specifications of essential requirements for tender to the design. It is obligatory for the designer unless they come to an agreement with the investor about changing the tender requirements for the design, which is a complicated procedure. The designer for the given material specifies requirements regarding the strength and diameters of pipes and all other important construction details, but this specification may significantly limit the number of pipe producers which are eligible to compete during the tender for the construction. If the requirements for the material are too specific and thus result in a small number of producers being able to fulfil them, then because of a lack of competition the price may be extraordinarily high and the construction company may try to save some money using another specification for the pipes. However, first of all, it is necessary to prove that their offer of a substitute is in all categories of quality at least not worse than the product originally specified in the design and that at least one advantage of the new proposal can be proved in comparison with the original version from the design. Such a change requires the approval of the investor and usually the elaboration of new documentation for the design, so it happens only occasionally. The most important factors are that in the primary pre-design studies and in the case of any changes which may however rarely be made, many properties of water transporting pipes are taken into consideration and also the initial friction created to flow as well as changes in this friction to flow over the time of the pipeline’s operation are of importance for the selection of the material.

Conclusions

Elaboration of the set of data published by DIPRA [26] results in the conclusions that:

  • The changes in time of the Hazen–Williams friction factor C for cement mortar lining are small in comparison with the changes reported for unprotected pipes (which was known previously).

  • The set of C values data does not show visible changes in the first 30 years of the pipes’ operation, which provide an opportunity for using the measured C values in this period for interpretation of sand grain roughness coefficients for pipes with internal cement mortar linings,

  • Assuming optimal velocities of flow during the analysed tests, it was predicted that the Darcy friction coefficients f for all the analysed internal diameters of pipes (roughly up to 900 mm) almost followed the line for smooth pipes from the Moody chart,

  • To evaluate if the assumption on the hypothetical flow values in the tests (Bonds [26]) has a crucial impact on the final conclusion that the analysed mortar lining protected pipes were hydraulically smooth for water flow, the same computations were repeated for flows 50% higher and lower than the optimal values. The results confirmed the main conclusion of the paper that ductile iron pipes (DIP) protected internally by cement mortar lining behaved similarly to smooth pipes in the field experiments reported by Bonds [26] from head loss measurements of flow-through 64 pipes of diameters from 152 to 914 mm and aged up to 30 years. This conclusion refers exclusively to the large bank of data published by Bonds [26] and is not always valid in other individual cases, especially when the mortar lining is done roughly.

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Acknowledgements

The first author is grateful to the Gifu University for hiring him for 3 months, as a professor, which created the chance to write this text together with the second author.

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Correspondence to Wojciech Dąbrowski.

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On behalf of both authors, the corresponding author states that there is no conflict of interest. We have never been working for any company producing ductile iron, steel, or plastic pipes and we are not involved in any renovation of pipelines projects.

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Dąbrowski, W., Li, F. Mortar Lining as a Protective Layer for Ductile Iron Pipes. Int J Civ Eng 19, 369–380 (2021). https://doi.org/10.1007/s40999-020-00585-6

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Keywords

  • Cement mortar lining
  • Friction to flow
  • Ductile iron pipes
  • Smooth pipes