Chapter 6 155 Design of PE Piping Systems

Chapter 6

Design of PE Piping Systems

Introduction Design of a PE piping system is essentially no different than the design undertaken with any ductile and flexible piping material. The design equations and relationships are well-established in the literature, and they can be employed in concert with the distinct performance properties of this material to create a piping system which will provide very many years of durable and reliable service for the intended application.

In the pages which follow, the basic design methods covering the use of PE pipe in a variety of applications are discussed. The material is divided into four distinct sections as follows:

Section 1 covers Design based on Working Pressure Requirements. Procedures are included for dealing with the effects of temperature, surge pressures, and the nature of the fluid being conveyed, on the sustained pressure capacity of the PE pipe.

Section 2 deals with the hydraulic design of PE piping. It covers flow considerations for both pressure and non-pressure pipe.

Section 3 focuses on burial design and flexible pipeline design theory. From this discussion, the designer will develop a clear understanding of the nature of pipe/soil interaction and the relative importance of trench design as it relates to the use of a flexible piping material.

Finally, Section 4 deals with the response of PE pipe to temperature change. As with any construction material, PE expands and contracts in response to changes in temperature. Specific design methodologies will be presented in this section to address this very important aspect of pipeline design as it relates to the use of PE pipe.

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This chapter concludes with a fairly extensive appendix which details the engineering and physical properties of the PE material as well as pertinent pipe characteristics such as dimensions of product produced in accordance with the various industry standards.

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Section 1 Design Based on Required Pressure Capacity

Pressure Rating The methodology for arriving at the standard pressure rating, PR, for PE pipe is discussed in detail in Chapter 5. The terms pressure rating (PR), pressure class (PC), are used in various consensus standards from ASTM, AWWA, CSA and others to denote the pipe’s capacity for safely resisting sustained pressure, and typically is inclusive of the capacity to resist momentary pressure increases from pressure surges such as from sudden changes in water flow velocity. Consensus standards may treat pressure surge capacity or allowances differently. That treatment may vary from the information presented in this handbook. The reader is referred to the standards for that specific information.

Equations 1-1 and 1-2 utilize the Hydrostatic Design Stress, HDS, at 73º F (23ºC) to establish the performance capability of the pipe at that temperature. HDS’s for various PE pipe materials are published in PPI TR-4, “PPI Listing of Hydrostatic Design Basis (HDB), Hydrostatic Design Stress (HDS), Strength Design Basis (SDB), Pressure Design Basis (PDB) and Minimum Required Strength (MRS) Ratings for Thermoplastic Piping Materials”. Materials that are suitable for use at temperatures above 100ºF (38ºC) will also have elevated temperature Hydrostatic Design Basis ratings that are published in PPI TR-4.

The PR for a particular application can vary from the standard PR for water service. PR is reduced for pipelines operating above the base design temperatures, for pipelines transporting fluids that are known to have some adverse effect on PE, for pipelines operating under Codes or Regulations, or for unusual conditions. The PR may be reduced by application of a factor to the standard PR. For elevated

temperature applications the PR is multiplied by a temperature factor, FT. For special fluids such as hydrocarbons, or regulated natural gas, an environmental application

factor, AF, is applied. See Tables 1-2 and Appendix, Chapter 3. The reader is alerted to the fact that the form of the ISO equation presented in Equations 1-1 and 1-2 has changed from the form of the ISO equation published in the previous edition of the PPI PE Handbook. The change is to employ HDS rather than HDB, and is necessitated by the additional ratings available for high performance materials. In the earlier form of the ISO equation, PR is given as a function of the HDB, not the HDS as in Equations 1-1 and 1-2. This difference is significant and can result in considerable error if the reader uses the Environmental Applications Factors given in Table 1-2 as the “Design Factor” in the HDB form of the ISO equation.

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Pipe Diameter for OD Controlled Pipe

OD-controlled pipe is dimensioned by outside diameter and wall thickness. Several sizing systems are used including IPS, which is the same OD as IPS steel pipe; DIPS, which is the same OD as ductile iron pipe; and CTS, which is the same OD as copper tubing. For flow calculations, inside diameter is calculated by deducting twice the wall thickness from the outside diameter. OD-controlled pipe standards include ASTM D2513, ASTM D2737, ASTM D2447, ASTM D3035, ASTM F714, AWWA C901, AWWA C906 and API 15LE.(3,4,5,6,7,8,9,10) The appendix provides specific dimensional information for outside diameter158 controlledChapter 6 polyethylene pipe and tubing made in accordance with selected ASTM andDesign AWWA of PE Piping standards. Systems

Equation 1-1 may be used to determine an average inside diameter for OD-controlled polyethylene pipe made to dimension ratio (DR) specifications in accordance with the previously referenced standards. In these standards, pipe dimensions are specified as (1-1) 2 HDS FT AF average outside diameter and, typically,PR = wall thickness is specified as a minimum (DR-1) dimension, and a +12% tolerance is applied. Therefore, an average ID for flow calculation purposes may be determined by deducting twice the average wall thickness (1-2) 2 HDS F A (minimum wall thickness plus half the wallPR = tolerance orT 6%)F from the average outside diameter. (IDR+1)

WHERE § D · PR = Pressure rating, psi O DA DO  2.12¨ ¸ Eq. 1-1 HDS = Hydrostatic Design© DR Stress,¹ psi (Table 1-1) A = Environmental Application Factor (Table 1-2) Where, F NOTE: The environmental application factors given in Table 1-2 are not to be confused with the Design Factor, DF, used in previous editions of the PPI Handbook and in older standards. DA = pipe average inside diameter, in FT = Service Temperature Design Factor (See Appendix to Chapter 3) DO = pipe outside diameter, in DR = OD -Controlled Pipe Dimension Ratio DR = dimension ratio (1-3) D DR O Eq. 1-2 t t = pipe minimum wall thickness, in DO = OD-Controlled Pipe Outside Diameter, in. t = Pipe Minimum Wall Thickness, in. 5 IDR = ID -Controlled Pipe Dimension Ratio Pipe Diameter for ID Controlled Pipe (1-4) D IDR = I Eq. 1-6 Standards for inside diameter controlled pipes tprovide average dimensions for the pipe inside diameter DI =that areID-Controlled used for flow Pipe calculations. Inside Diameter, ID-controlled in. pipe standards include DI = ID-Controlled Pipe Inside Diameter, in. ASTM D2104, ASTM D2239, ASTM F894 and AWWA C901. (11,12,13)

TaBlE 1-1 The terms “DR” and “IDR” are usedHydrostatic with Design outside Stress and Service diameter Temperatures controlled and inside diameterTable controlled 1-1: Hydrostatic pipe respectively. Design Basis Certain Ratings dimension and Service ratios that Temperatures meet an ASTM- ASTM PE 2708, PE 3608, specified numberProperty series are “standardized dimensionPE 3408 ratios,” that is SDRPE 2406 or SIDR. StandardProperty Standard PE 2606, PE2706 PE 3708, PE 4608 PE 3710, PE 4710 Hydrostatic Design Stress, ASTM D2837 & 1000 psi 630 psi (4.6 MPa) 800 psi (5.5 MPa) HDB at 73°F (23°C) HDSD 2837 at 73°F (23°C) 1600 psi (11.04PPI MPa) TR-3 1250 psi (8.62 MPa) (6.9 MPa) Maximum recommended temperature Maximum recommended – 140°F (60°C)* 140°F (60°C) for Pressure Service operating temperature for - 140°F (60°C) 140°F (60°C) 140°F (60°C) Maximum Recommended Temperature Pressure Service* – 180°F (82°C) 180°F (82°C) for Non-Pressure Service Maximum recommended operating temperature for - 180°F (82°C) 180°F (82°C) 180°F (82°C) * Some polyethylene piping materialsNon-Pressure are stress Service rated at temperatures as high as 180° F. For more information regarding these materials and their use, the reader is referred to PPI, TR-4 * Some PE piping materials are stress rated at temperatures as high as 180°F. For more information regarding these materials and their use, the reader is referred to PPI, TR-4. The long-term strength of thermoplastic pipe is based on regression analysis of stress- rupture data obtained in accordance with ASTM D2837. Analysis of the data obtained in this procedure is utilized to establish a stress intercept for the material under evaluation at 100,000 hours. This intercept when obtained at 73° F is called the long- term hydrostatic strength or LTHS. The LTHS typically falls within one of several categorized ranges that are detailed in ASTM D2837. This categorization of the LTHS for a given pipe material establishes154-264.indd 158 its hydrostatic design basis or HDB. The HDB is 1/16/09 9:56:53 AM then utilized in either equation 1-3 or 1-4 to establish the pressure rating for a particular pipe profile by the application of a design factor (DF). The DF for water service is 0.50, as indicated in Table 1-2. Additional information regarding the determination of the LTHS and the D2837 protocol is presented in the Engineering Properties chapter of this handbook.

Table 1-2: PE Pipe Design Factors (DF) Pipe Environment Design Factor (DF) at 73°F (23°C) Water; Aqueous solutions of salts, acids and bases; Sewage; Wastewater; Alcohols; Glycols (anti-freeze solutions); 0.50 Nitrogen; Carbon dioxide; Methane; Hydrogen sulfide; non- federally regulated applications involving dry natural gas 0.50 other non-reactive gases

LPG vapors (propane; propylene; butane) † 0.40

Natural Gas Distribution (Federally regulated under CFR 0.32 ** Tile 49, Part 192)* Fluids such as solvating/permeating chemicals in pipe or soil (typically hydrocarbons) in 2% or greater concentrations, natural or other fuel-gas liquid 0.25 condensates, crude oil, fuel oil, gasoline, diesel, kerosene, hydrocarbon fuels * An overall design factor of 0.32 is mandated by the US Code of Federal Regulations, Chapter 6 159 Design of PE Piping Systems

The Hydrostatic Design Stress, HDS, is the safe long-term circumferential stress that PE pipe can withstand. It is derived by applying an appropriate design factor, DF, to the Hydrostatic Design Basis, HDB. The method for establishing the Hydrostatic Design Stress for PE pipe is described in Chapters 3 and 5.

At the time of this printing, AWWA is in the process of revising AWWA C906 to incorporate PE4710 material and to use the HDS values in Table 1-1. The version in effect at the time of this printing, AWWA C906-07, limits the maximum Hydrostatic Design Stress to 800 psi for HDPE and to 630 psi for MDPE. AWWA C901-08 has been revised to incorporate the materials listed in Table 1-1.

The Environmental Application Factor is used to adjust the pressure rating of the pipe in environments where specific chemicals are known to have an effect on PE and therefore require derating as described in Chapter 3. Table 1-2 gives

Environmental Applications Factors, AF, which should only be applied to pressure equations (see Equations 1-1 and 1-2) based on the HDS, not the HDB.

Ta BlE 1-2 PE Pipe Environmental Application Factors (AF)*

Environmental Application Pipe Environment Factor (AF) at 73ºF (23ºC) Water: Aqueous solutions of salts, acids and bases; Sewage; Wastewater; 1.0 Alcohols; Glycols (anti-freeze solutions) Nitrogen; Carbon dioxide; Methane; Hydrogen sulfide; Non-Federally regulated 1.0 applications involving dry natural gas or other non-reactive gases Fluids such as solvating/permeating chemicals in pipe or soil (typically hydrocarbons) in 2% or greater concentration, natural or other fuel-gas liquids condensates, crude oil, fuel oil, gasoline, diesel, kerosene, hydrocarbon fuels, wet 0.5 gas gathering, multiphase oilfield fluids, LVP liquid hydrocarbons, oilfield water containing >2% hydrocarbons.

* Certain codes and standards include prohibitions and/or strength reduction factors relating to the presence of certain constituents in the fluid being transported. In a code controlled application the designer must ensure compliance with all code requirements.

When choosing the environmental applications factor (AF), consideration must be given to Codes and Regulations, the fluid being transported, the external environment, and the uncertainty associated with the design conditions of internal pressure and external loads.

The pressure rating (PR) for PE pipe in water at 73ºF over the range of typical DR’s is given in Tables 1-3 A and 1-3 B in this chapter.

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Pressure Rating for Fuel Gas Pipe Compared to other common thermoplastic pipes, PE pipe can be used over a broader temperature range. For pressure applications, it has been successfully used from -40º F (-40º C) to 140ºF (60º C). In the case of buried non-pressure applications it has been used for conveying fluids that are at temperatures as high as 180°F (82°C). See Table 1-1. For pressure applications above 80ºF (27º C) the Service Temperature Design Factor is applied to determine the pressure rating. See Table A.2 in the Appendix to Chapter 3.

The pressure rating for gas distribution and transmission pipe in US federally regulated applications is determined by Title 49, Transportation, of The Code of Federal Regulations. Part 192 of this code, which covers the transportation of natural and other gases, requires that the maximum pressure rating (PR) of a PE pipe be determined based on an HDS that is equal to the material’s HDB times a DF of 0.32. (See Chapter 5 for a discussion of the Design Factor, DF.) This is the equivalent of saying that for high density PE pipe meeting the requirements of ASTM D2513 the HDS is 500 psi at 73º F and for medium density PE pipe meeting D2513 the HDS is 400 psi at 73º F. There are additional restrictions imposed by this Code, such as the maximum pressure at which a PE pipe may be operated (which at the time of this writing is 125 psi for pipe 12-in and smaller and 100 psi for pipe larger than 12-in through 24-in.) and the acceptable range of operating temperatures. The temperature design factors for federally regulated pipes are different than those given in Table A.2 in the Appendix to Chapter 3. Consult with the Federal Regulations to obtain the correct temperature design factor for gas distribution piping.

At the time of this writing, there is an effort underway to amend the US federal code to reflect changes already incorporated inASTM F714 and D3035. When amended, these changes will increase the pressure rating (PR) of pipe made with high performance PR resins - those that meet the higher performance criteria listed in Chapter 5 (see “Determining the Appropriate Value of HDS”), to be 25% greater than pressure ratings of pipe made with ‘traditional’ resins.

In Canada gas distribution pipe is regulated per CSA Z662-07. CSA allows a design factor of 0.4 to be applied to the HDB to obtain the HDS for gas distribution pipe.

PE pipe meeting the requirements of ASTM D2513 may be used for the regulated distribution and transmission of liquefied petroleum gas LPG).( NFPA/ANSI 58 recommends a maximum operating pressure of 30 psig for LPG gas applications involving polyethylene pipe. This design limit is established in recognition of the higher condensation temperature for LPG as compared to that of natural gas and, thus, the maximum operating pressure is recommended to ensure that plastic pipe is not subjected to excessive exposure to LPG condensates. The Environmental Application Factor for LP Gas Vapors (propane, propylene, and butane) is 0.8 with

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a maximum HDS of 800 psi at 73º F for HDPE and 630 psi for MDPE. For further information the reader is referred to PPI’s TR-22, Polyethylene Piping Distribution Systems for Components of Liquid Petroleum Gases.

The pressure rating for PE gas gathering lines in the US may differ depending upon the class location (population density) of the gathering line. Gas gathering lines in Class 2, 3 and 4 locations are regulated applications and subject to US federal codes the same as gas distribution and transmission lines. Gas gathering lines in Class 1 locations are not regulated in accordance with US federal codes, and may be operated at service pressures determined using Equation 1-1. Non-regulated gas gathering lines may use PE pipe meeting ASTM F2619 or API 15LE, and may be larger than 24” diameter. PE pipe meeting ASTM D2513 is not required for non- regulated gas gathering lines.

In Canada, PE gas gathering lines are regulated in accordance with CSA Z662 Clause 13.3 and are required to meet API 15LE. PE gas gathering lines may be operated at service pressures equivalent to those determined using Equation 1-1.

Pressure Rating for liquid Flow Surge Pressure Surge pressure events, which give rise to a rapid and temporary increase in pressure in excess of the steady state condition, are the result of a very rapid change in velocity of a flowing liquid. Generally, it is the fast closing of valves and uncontrolled pump shutdowns that cause the most severe changes and oscillations in fluid velocity and, consequently in temporary major pressure oscillations. Sudden changes in demand can also lead to lesser but more frequent pressure oscillations. For many pipe materials repeated and frequent pressure oscillations can cause gradual and cumulative fatigue damage which necessitate specifying higher pressure class pipes than determined solely based on sustained pressure requirements. And, for those pipe materials a higher pressure class may also be required for avoiding pipe rupture under the effect of occasional but more severe high-pressure peaks. Two properties distinguish PE pipes from these other kinds of pipes. The first is that because of their lower stiffness the peak value of a surge pressures that is generated by a sudden change in velocity is significantly lower than for higher stiffness pipes such as metallic pipes. And, the second is that a higher pressure rating (PR), or pressure class (PC), is generally not required to cope with the effects of pressure surges. Research, backed by extensive actual experience, indicates that PE pipes can safely tolerate the commonly observed maximum peak temporary surge pressure of twice the steady state condition. Furthermore, the long-term strength of PE pipes is not adversely affected by repeated cyclic loading – that is, PE pipes are very fatigue resistant.

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In the design of PE pipe, pressure surges are generally classified as Occasional pressure surges, Recurring pressure surges, and Negative pressures.

• Occasional surge pressures are caused by emergency operations such as fire flow or as a result of a malfunction, such as a power failure or system component failure, which includes pump seize-up, valve stem failure and pressure relief valve failure. • Recurring surge pressures are inherent to the design and operation of a system. Recurring surge pressures can be caused by normal pump start up or shut down, normal valve opening and closing, and/or “background” pressure fluctuations associated with normal pipe operation. • Negative pressure may be created by a surge event and cause a localized collapse by buckling. (Negative pressure may also occur inside flowing pipelines due to improper hydraulic design.) In recognition of the performance behavior of PE pipes the following design principles have been adopted by AWWA for all PE pressure class (PC) rated pipes. These design principles, which are as follows, are also applicable to PE water pipes that are pressure rated (PR) in accordance with ASTM and CSA standards:

1. Resistance to Occasional Pressure Surges: • The resultant total pressure – sustained plus surge – must not exceed 2.0 times the pipe’s temperature compensated pressure rating (PR). See Tables 1-3 A and 1-3 B for standard surge allowances when the pipe is operated at its full rated pressure. • In the rare case where the resultant total pressure exceeds 2.0 times the pipe’s temperature adjusted PR, the pipe must be operated at a reduced pressure so that the above criterion is satisfied. In this event the pipe’s reduced pressure rating is sometimes referred to as the pipe’s “working pressure rating” (WPR), meaning that for a specific set of operating conditions (temperature, velocity, and surge) this is the pipe’s pressure rating. AWWA uses the term WPR not just for a reduced pressure rating but for any pressure rating based on application specific conditions. Where the total pressure during surge does not exceed the standard allowance of 2.0 (occasional) and 1.5 (recurring) the WPR equals the temperature adjusted PR. • The maximum sustained pressure must never exceed the pipe’s temperature adjusted pressure rating (PR).

Example: A PE pipe has a DR = 17 and is made from a PE4710 material. Accordingly, its standard pressure rating (PR) for water, at 73°F is 125 psi (See Table A.1 in Appendix to Chapter 3). The maximum sustained water temperature shall remain below 73°F. Accordingly, no temperature compensation is required and therefore, the pipe’s initial WPR is equal to its standard PR or, 125 psi.

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Let us first assume that the maximum occasional surge pressure shall never exceed 120 psi. Since a WPR of 125 psi plus a surge of 120 psi is less than 2 times 125 psi the pipe’s initial WPR of 125 psi remains at that value.

Now let us assume a second case in which the maximum occasional surge pressure can be as high as 150 psi. This pressure plus the pipe’s initial WPR of 125 psi result in a total momentary pressure of 275 psi, which is 25 psi above the limit of 2 x 125 psi = 250 psi. To accommodate this 25 psi excess it is necessary to reduce the pipe’s initial WPR of 125 to a final WPR of 100 psi.

2. Resistance to Recurring Pressure Surges: • The resultant total momentary pressure – sustained plus surge – must not exceed 1.5 times the pipe’s temperature adjusted pressure rating (PR). See Tables 1-3 A and 1-3 B for standard surge allowance when the pipe is operated at its full rated pressure. • In the rare case where the resultant total pressure exceeds 1.5 times the pipe’s temperature adjusted PR the pressure rating must be reduced to the pipe’s WPR so that the above criterion is satisfied. • The maximum sustained pressure must never exceed the pipe’s temperature adjusted PR.

3. Resistance to localized Buckling When Subjected to a Negative Pressure Generated by a Surge Event A buried pipe’s resistance to localized buckling while under the combined effect of external pressure and a very temporary full vacuum should provide an adequate margin of safety. The design for achieving this objective is discussed in a later section of this chapter. It has been shown that a DR21 pipe can withstand a recurring negative pressure surge equal to a full vacuum at 73°F. Higher DR pipes may also be able to withstand a recurring negative surge equal to full vacuum if they are properly installed and have soil support. Their resistance may be calculated using Luscher’s Equation presented later in this chapter.

Estimating the Magnitude of Pressure Surges Regardless of the type of pipe being used surge or water hammer problems can be complex especially in interconnected water networks and they are best evaluated by conducting a formal surge analysis (See References 25 and 32). For all water networks, rising mains, trunk mains and special pump/valve circumstances a detailed surge analysis provides the best way of anticipating and designing for surge.

154-264.indd 163 1/16/09 9:56:53 AM 15 the removal of the load. This temporary elastic strain causes no damage to the polyethylene material and has no adverse effect on the pipe’s long-term strength.(22,23,24)

In order to determine the appropriate DR required for a pressure polyethylene pipe system, the designer must calculate both the continuous working pressure, potential pressure surges and the Working Pressure Rating (WPR) for the pipe.

Surge Pressure

Transient pressure increases (water hammer) are the result of sudden changes in velocity of the flowing fluid. For design purposes, the designer should consider two types of surges:

1. Recurring Surge Pressure (PRS)

Recurring surge pressures occur frequently and are inherent to the design and operation of the system. Recurring surge pressures would include normal pump start up or shutdown, normal valve opening and closing, and/or “background” pressure fluctuation associated with normal pipeline operation.

2. Occasional Surge Pressure (POS)

Occasional surge pressures are caused by emergency operations. Occasional surge pressures are usually164 Chapter the 6result of a malfunction, such as power failure or system component failure, Designwhich of PE includes Piping Systems pump seize-up, valve stem failure and pressure relief valve failure.

To determine the WPR for a selected DR, the pressure surge must be calculated. The following equations may be used to estimate the pressure surge created in pressure water piping systems. Absent a formal surge analysis, an estimate of the magnitude of a surge pressure can be made by evaluating the surge pressure that results from an anticipated sudden An abrupt change in the velocitychange of a flowingin velocity liquid in the watergenera flowingtes a inside pressure a PE pipe. wave. The velocity of the wave may be determinedAn abrupt using change Equation in the velocity 1-21. of a flowing liquid in a pipe generates a pressure wave. The velocity of the wave may be determined using Equation 1-5. (1-5) 4660 a K Eq. 1-21  BULK DR  )2(1 E Where, d

WHERE 16 a = Wave velocity a(celerity), = Wave velocity ft/sec (celerity), ft/sec

KBULK = Bulk modulus KofBULK fluid = Bulk at modulusworking of fluid temperature at working temperature (typically 300,000 psi for water at 73˚F) o Ed = Dynamic (typically instantaneous 300,000Ed = Dynamic psi effectiv for instantaneous watere modulus at effective 73 F) modulus of pipe of pipe material material (typically 150,000 psi(t ypicallyfor PE 150,000 pipe) psi for all PE pipe at 73˚F (23˚C)); see Appendix to Chapter 3 DR = Pipe dimension ratioDR = Pipe dimension ratio The resultant transient surge pressure, Ps, may be calculated from the wave velocity, The resultant transient surge pressure,a, and Ps ,the may sudden be changecalculated in fluid from velocity, the ∆ waveV. velocity, a, and the change in fluid velocity, ∆v. (1-6)  ∆V    Eq. 1-22 s = aP   31.2 g  

Where, WHERE PS = Transient surge pressure, psig a = Wave velocity (celerity), ft/sec Ps = Transient surge pressure, psig a = Wave velocity (celerity),∆V = Sudden ft/sec velocity change, ft/sec g = Constant of gravitational acceleration, 32.2 ft/sec2 ∆V = Sudden velocity change, ft/sec g = Constant of gravitationalFigure 1-1 acceleration, represents the pressure 32.2 ft/sec surge2 curves for all PE pipes as calculated using Equations 1-5 and 1-6 for Standard Dimension Ratios (SDR’s). Figure 1-2 represents the pressure surge curves for PE3408 as calculated using Equations 1-21 and 1-22 for standard Dimension Ratios (DR’s).

140.0

130.0 SDR 7.3 120.0 SDR 9 110.0

100.0 SDR 11 90.0 SDR 13.5

80.0 SDR 17 SDR 21 Pressure Surge, psi Surge, Pressure 70.0 SDR 26 60.0 SDR 32.5 50.0

40.0 154-264.indd 164 1/16/09 9:56:53 AM 30.0

20.0

10.0 0.0 1 2 3 4 5 6 7 Flow Rate, fps Figure 1-2 Sudden Velocity Change vs. Pressure Surge for PE3408

*A value of 150,000 psi and 300,000 psi were used for Ed and K, respectively. **Calculated surge pressure values applicable to water at temperatures not exceeding 80oF (27oC). Chapter 6 165 Design of PE Piping Systems Pressure Surge, psig Pressure Surge,

Sudden Changes in Flow Rate, fps

* A value of 150,000 psi and 300,000 psi were used for Ed and K, respectively. ** Calculated surge pressure values applicable to water at temperatures not exceeding 80ºF (27ºC).

Figure 1-1 Sudden Velocity Change vs. Pressure Surge for All PE Pipes

The surge pressure values in Figure 1-1 are based on a sudden change in velocity, which may more often be the case for events like a sudden pump shut-down or a rapid valve closure. A sudden shut-down or a rapid closure occurs faster than the “critical time” (the time it takes a pressure wave initiated at the beginning of a valve closing to return again to the valve). Under ordinary operations, during which valve closings and pump shut-downs are slower than the “critical time”, the actual pressure surge is smaller than that in Figure 1-1. The “critical time” is determined by means of the following relationship: (1-7) TCR = 2L/a

WHERE TCR = critical time, seconds L = distance within the pipeline that the pressure wave moves before it is reflected back by a boundary condition, ft a = wave velocity (celerity) of pressure wave for the particular pipe, ft/s. (See Equation 1-5)

Generally, PE pipe’s capacity for safely tolerating occasional and frequently occurring surges is such that seldom are surge pressures large enough to require a de-rating of the pipe’s static pressure rating. Tables 1-3 A and 1-3 B show the maximum allowable sudden changes in water flow velocity (ΔV) that are safely tolerated without the need

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to de-rate the pressure rating (PR) or, the pressure class (PC), of a PE pipe. If sudden changes in velocity are expected to be greater than the values shown in these Tables, they then must be accommodated by lowering the pipe’s static pressure rating. As previously discussed, the new rating is called the working pressure rating (WPR).The procedure for establishing a WPR has been discussed earlier in this Section.

TaBlE 1-3a Allowances for Momentary Surge Pressures Above PR or PC for Pipes Made From PE4710 and PE3710 Materials1.

Standard Allowance for Momentary Surge Pressure Above the

Pipe’s PR or PC Standard Static Pressure Rating Allowance for Recurring Surge Allowance for Occasional Surge (PR) or, Standard Resultant Resultant Pipe Standard Pressure Class Allowable Allowable Diameter Ratio (PC) for water @ Allowable Surge Sudden Change Allowable Surge Sudden Change (SDR) 73°F, psig Pressure, psig in Velocity, fps Pressure, psig in Velocity, fps 32.5 63 32 4.0 63 8.0 26 80 40 4.5 80 9.0 21 100 50 5.0 100 10.0 17 125 63 5.6 125 11.2 13.5 160 80 6.2 160 12.4 11 200 100 7.0 200 14.0 9 250 125 7.7 250 15.4 7.3 320 160 8.7 320 17.4

1. AWWA C906-07 limits the maximum Pressure Class of PE pipe to the values shown in Table B. At the time of this printing C906 is being revised to allow PC values in Table A to be used for PE3710 and PE4710 materials. Check the latest version of C906

TaBlE 1-3 B Allowances for Momentary Surge Pressures Above PR or PC for Pipes Made from PE 2708, PE3408, PE3608, PE3708 and PE4708 Materials.

Standard Allowance for Momentary Surge Pressure Above the Pipe’s PR or PC Standard Static Pressure Rating Allowance for Recurring Surge Allowance for Occasional Surge (PR) or, Standard Resultant Resultant Pipe Standard Pressure Class Allowable Allowable Diameter Ratio (PC), for Water @ Allowable Surge Sudden Change Allowable Surge Sudden Change (SDR) 73°F, psig Pressure, psig in Velocity, fps Pressure, psig in Velocity, fps 32.5 50 25 3.1 50 6.2 26 63 32 3.6 63 7.2 21 80 40 4.0 80 8.0 17 100 50 4.4 100 8.8 13.5 125 63 4.9 125 9.8 11 160 80 5.6 160 11.2 9 200 100 6.2 200 12.4 7.3 250 125 6.8 250 13.6

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The surge pressure allowance in Table 1-3 A and 1-3 B are not the maximum surge limits that the pipe can safely withstand. Higher surge pressures can be tolerated in pipe where the working pressure rating (WPR) of the pipe is limited to a pressure less than the pressure rating (PR). This works because the combined total pressure for surge and for pumping pressure is limited to 1.5 times the PR (or PC) for recurring surge and 2.0 times the PR (or PC) for occasional surge. If the pumping pressure is less than the PR (or PC) then a higher surge than the standard allowance given in Table A and B is permitted. The maximum permitted surge pressure is equal to 1.5 x PR – WP for recurring surge and 2.0 x PR – WP for occasional surge, where WP is the pumping or working pressure of the pipeline. For example a DR21 PE4710 pipe with an operating pressure of 80 psi can tolerate a recurring surge pressure of 1.5 x 100 psi – 80 psi = 70 psi. Note that in all cases WP must be equal or less than PR.

Controlling Surge Pressure Reactions Reducing the rate at which a change in flow velocity occurs is the major means by which surge pressure rises can be minimized. Although PE pipe is very tolerant of such rises, other non-PE components may not be as surge tolerant; therefore, the prudent approach is to minimize the magnitude of surge pressures by taking reasonable precautions to minimize shock. Hydrants, large valves, pumps, and all other hydraulic appurtenances that may suddenly change the velocity of a column of water should be operated slowly, particularly during the portion of travel near valve closing which has the larger effect on rate of flow. If the cause of a major surge can be attributable to pump performance – especially, in the case of an emergency stoppage – then, proper pressure relief mechanisms should be included. These can include traditional solutions such as by providing flywheels or by allowing the pumps to run backwards.

In hilly regions, a liquid flow may separate at high points and cause surge pressures when the flow is suddenly rejoined. In such cases measures should be taken to keep the pipeline full at all times. These can consist of the reducing of the flow rate, of the use at high points of vacuum breakers or, of air relief valve.

Also, potential surge pressure problems should be investigated in the design of pumping station piping, force mains, and long transmission lines. Proven and suitable means should be provided to reduce the effect of surges to a minimum that is practicable and economical. Although PE pipe is much more tolerant of the effect of sudden pressure increases traditional measures should be employed for the minimizing of the occurrence of such increases.

154-264.indd 167 1/16/09 9:56:54 AM 168 Chapter 6 Design of PE Piping Systems

Section 2 Hydraulic Design of PE Pipe

This section provides design information for determining the required flow diameter for PE pipe. It also covers the following topics: general fluid flows in pipe and fittings, liquid (water and water slurry) flow under pressure, non-pressure(gravity) liquid flow, and compressible gas flow under pressure. Network flow analysis and design is not addressed. (1,2)

The procedure for piping system design is frequently an iterative process. For pressure liquid flows, initial choice of pipe flow diameter and resultant combinations of sustained internal pressure, surge pressure, and head loss pressure can affect pipe selection. For non-pressure systems, piping design typically requires selecting a pipe size that provides adequate reserve flow capacity and a wall thickness or profile design that sufficiently resists anticipated static and dynamic earthloads. This trial pipe is evaluated to determine if it is appropriate for the design requirements of the application. Evaluation may show that a different size or external load capacity may be required and, if so, a different pipe is selected then reevaluated. The Appendix to Chapter 3 provides engineering data for PE pipes made to industry standards that are discussed in this chapter and throughout this handbook.

Pipe ID for Flow Calculations Thermoplastic pipes are generally produced in accordance with a dimension ratio (DR) system. The dimension ratio, DR or IDR, is the ratio of the pipe diameter to the respective minimum wall thickness, either OD or ID, respectively. As the diameter changes, the pressure rating remains constant for the same material, dimension ratio and application. The exception to this practice is production of thermoplastic pipe in accordance with the industry established SCH 40 and SCH 80 dimensions such as referenced in ASTM D 2447.

Flow Diameter for Outside Diameter Controlled Pipe OD-controlled pipe is dimensioned by outside diameter and wall thickness. Several sizing systems are used including IPS, which specifies the same OD’s as iron pipe sized (IPS) pipe: DIPS pipe which specifies the same OD’s as ductile iron pipe; and CTS, which specifies the same OD’s as copper tubing sizes. For flow calculations, inside diameter is calculated by deducting twice the average wall thickness from the specified outside diameter. OD-controlled pipe standards include ASTM D2513, ASTM D2737, ASTM D2447, ASTM D3035, ASTM F714, AWWA C901, AWWA C906 and API 15LE.(3,4,5,6,7,8,9,10) The Appendix to this chapter provides specific dimensional information for outside diameter controlled PE pipe and tubing that is made to

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Standardized dimension ratios are: 41, 32.5, 26, 21, 17, 13.5, 11, 9, and 7.3. From one SDR or SIDR to the next, there is about a 25% difference in minimum wall thickness.

Pressure Rating for Pressure Rated Pipes

Conventionally extruded (solid wall) polyethylene pipes have a simple cylindrical shape, and are produced to industry standards that specify outside diameter and wall 3 thickness, or inside diameter and wall thickness. OD controlled pressure pipes are pressure rated using Equation 1-3. ID controlled pressure pipes are pressure rated using PipeEquation Diameter 1-4. for OD Controlled Pipe

EquationsOD-controlled 1-3 and 1-4pipe utilize is dimensioned the HDB at by 73°F outside (23°C) diameter to establish and wall the thickness. performance Several capabilitysizing of systems the pipe are profile used at including that temperature. IPS, which Materials is the same that OD are assuitable IPS steel for usepipe; at DIPS, higherwhich temperatures is the same above OD as 100°F ductile (38°C) iron willpipe; also and have CTS, elevated which is temperaturethe same OD HDB’s as copper tubing. For flow calculations, inside diameter is calculated by deducting twice the wall which are published in PPI TR-4. Two design factors, DF and FT, are used to relate environmentalthickness conditions from the outside and service diameter. temperature OD-controlled conditions pipe to standards the product. include See ASTM TablesD2513, 1-2 and ASTM 1-3. D2737, If the HDB ASTM at D2447,an elevated ASTM temperature D3035, ASTM is known, F714, AWWAthat HDB C901, value AWWA C906 and API 15LE.(3,4,5,6,7,8,9,10) The appendix provides specific dimensional Chapter 6 169 should be used in Equation 1-3 or 1-4, and the service temperature design factor, FT, information for outside diameter controlled polyethylene pipe and tubing madeDesign of in PE Piping Systems would then be 1. If the elevated HDB is not known, then FT should be used, but this will generallyaccordance result in witha lower selected or more ASTM conservative and AWWA pressure standards. rating.

Equation 1-1 may be used to determine an average inside diameter for OD-controlled polyethylene pipe made to dimensiondimension ratioratio (DR) (DR) requirements specifications in accordance in accordance with a number with of different the ASTM, previously referenced standards.AWWA,2 HDB In CSAthese x DFand standards, APIx F standards. pipe dimensions are specified as average outside diameter P and, typically, wall T thickness is specified as Eq. a minimum1-3 DR 1 dimension, and a +12% toleranceThe average is inside applied. diameter Therefore, for such pipes an has average been calculated ID forusing flow Equation 2-1. calculation purposes may be determinedTypically, wall bythickness deducting is specified twice as the a minimumaverage dimension, wall thickness and a plus 12% tolerance2 HDB is x applied. DF x InF this equation, the average ID is determined by deducting (minimum wall thickness plusP half the wall toleranceT or 6%) from the averageEq. 1-4 outside diameter. twice the IDR average1 wall thickness (minimum wall thickness plus a tolerance of 6%) from the average outside diameter. Where (2-1)  DO  DA = DO − 2.12  Eq. 1-1 P = Pressure rating, psi I  DR  HDB = Hydrostatic Design Basis, psi Where, DF = Design Factor, WfromHERE Table 1-2 FT = Service TemperatureDI = pipe averageDesign inside Factor, diameter, infrom Table 1-3 DA = pipe average inside diameter, in 1.0 if the elevatedDO = temperature specified average valueHDB of pipeis used.outside diameter, in DO = pipe outside diameter, in DR = dimension ratio DR DR= OD= -Controlleddimension Piperatio Dimension Ratio (2-2) D D DR DRO = O Eq. 1-5Eq. 1-2 t t t = pipe minimum wall thickness, in D O =t OD-Controlled= pipe minimum Pipe Outsidewall thickness, Diameter, in in. t = Pipe Minimum Wall Thickness, in. IDR = ID -Controlled PipePipe DimensionDiameter for Ratio ID Controlled Pipe Standards for inside diameter controlled pipes provide average dimensions for Pipe Diameter for ID Controlledthe Pipe pipe inside diameter that are used for flow calculations. ID-controlled pipe standards include ASTM D2104, ASTM D2239, ASTM F894 and AWWA C901. (11,12,13) Standards for inside diameter controlled pipes provide average dimensions for the pipe The terms “DR” and “IDR” identify the diameter to wall thickness dimension ratios inside diameter that are used for flow calculations. ID-controlled pipe standards include for outside diameter controlled and inside diameter controlled pipe, respectively. ASTM D2104, ASTM D2239, ASTM F894 and AWWA C901. (11,12,13) When those ratios comply with standard values they are called “standard dimension ratios”, that is SDR or SIDR. A discussion of standard dimension ratios is included in The terms “DR” and “IDR” Chapter are used 5. with outside diameter controlled and inside diameter controlled pipe respectively. Certain dimension ratios that meet an ASTM- specified number series are Fluid “standardized Flow in PE dimensionPiping ratios,” that is SDR or SIDR.

Head Loss in Pipes – Darcy-Weisbach/Colebrook/Moody Viscous shear stresses within the liquid and friction along the pipe walls create resistance to flow within a pipe. This resistance results in a pressure drop, or loss of head in the piping system.

The Darcy-Weisbach formula, Equation 2-3., and the Colebrook formula, Equation 2-6, are generally accepted methods for calculating friction losses due to liquids

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Fluid Flow in Polyethylene Piping 7 Head Loss in Pipes – Darcy-Weisbach/Fanning/Colebrook/Moody 7 ViscousFluid shearFlow in stresses Polyethylene within Piping the liquid and friction along the pipe walls create resistance to flow within a pipe. This resistance within a pipe results in a pressure drop, HeadFluid Loss Flow in in Pipes Polyethylene – Darcy-Weisbach/Fanning/Colebrook/Moody Piping or loss of head in the piping system. ViscousHead Loss shear in Pipes stresses – Darcy-Weisbach/Fanning/Colebrook/Moody within the liquid and friction along the pipe walls create Theresistance Darcy-Weisbach to flow within or Fanning a pipe. formula,This resistance Equation within 1-7, a andpipe theresults Colebrook in a pressure formula, drop, EquationorViscous loss 1-10,of head shear are in generally stressesthe piping accepted withinsystem. the methods liquid and for calculating friction along friction the losses pipe walls due to create liquidsresistance flowing in to full flow pipes.(15,16) within a pipe. These This resistanceformulas recognize within a pipedependence results in on a pressurepipe bore drop, and pipe surface characteristics, liquid170 Chapter viscosity 6 and flow velocity. Theor loss Darcy-Weisbach of head in the orpiping Fanning system.Design formula, of PE Piping EquationSystems 1-7, and the Colebrook formula, Equation 1-10, are generally accepted methods for calculating friction losses due to Theliquids Darcy-WeisbachThe Darcy-Weisbachflowing in full formula pipes.(15,16) or is: Fanning These formula, formulas Equation recognize 1-7, and dependence the Colebrook on pipe formula, bore andEquation pipe surface 1-10, characteristics, are generally accepted liquid viscosity methods and forflow calculating velocity. friction losses due to liquids flowing in full pipes.(15,16) TheseL formulasV 2 recognize dependence on pipe bore flowing= in full pipes.(15,16) These formulas recognize dependence on pipe bore and and pipe surface characteristics, hliquidf fviscosity and flow velocity. Eq. 1-7 The Darcy-Weisbach formula is: pipe surfaced 'characteristics,2 g liquid viscosity and flow velocity. The Darcy-Weisbach formula is: TheWhere: Darcy-Weisbach formula is: (2-3) L V 2 hf = friction (head) loss, ft.h of liquidf Eq. 1-7 f d ' 2 g L = pipeline length, ft. L V 2 d’ = pipe inside diameter, ft.h f f Eq. 1-7 Where: WHERE d ' 2 g V = flow velocity, ft/sec. hf = friction (head) loss, ft. of liquid hf = friction (head) loss, ft. of liquid Where: L = pipeline length, ft. L = pipeline length, ft.0 .4085 Q d’ == pipe inside diameter, ft. d’h f = = pipefriction inside (head) diameter,V loss, ft.ft. 2of liquid Eq. 1-8 V = flow velocity,D ft/sec. V L = = flowpipeline velocity, length, f ft/sec.= friction ft. factorl (dimensionless, but dependent upon pipe surface roughness and Reynolds number) 2 g d’= =constant pipe ofinside gravitational diameter,g = constant ofacceleration gravitationalft. acceleration (32.2ft/sec (32.2ft/sec2) ) Q V= =flow rate,flow velocity,gpm ft/sec. 0.4085 Q TheV flow velocity 2may be computed by means of the followingEq. equation 1-8 DI = pipe inside diameter, in D (2-4) 0.4085l Q f = friction factor (dimensionless,V but dependent upon pipe surface Eq. 1-8 g = constant of gravitational acceleration2 (32.2ft/sec2) roughness and Reynolds number)D l Q = flow rate, gpm 2 DIg = = pipeconstant inside of diameter, WgravitationalHERE in acceleration (32.2ft/sec ) fQ == frictionflow rate, factor gpm Q(dimensionless, = flow rate, gpm but dependent upon pipe surface Liquid flow in pipesDI = will roughness assumepipe inside one and diameter,D I of=Reynolds pipe three inside in diameter, flow number) regimes. in The flow regime may be laminar, turbulent f or= infriction transition factor Liquid between (dimensionless, flow in laminar pipes willbut and assume dependent turbulent. one of three upon In flow laminarpipe regimes. surface flow The flow regime may be laminar, (Reynolds number, Re, belowroughness 2000), andturbulent the Reynolds pipe’s or in surfacetransition number) roughnessbetween laminar has and no turbulent. effect and In laminar is flow (Reynolds number, Re, considered negligible. As such, the belowfriction 2000), factor, the pipe’s f, is surfacecalculated roughness using has Equation no effect and 1-9. is considered negligible. As such, the Liquid flow in pipes will assume friction one of factor, three ƒ, is flow calculated regimes. using Equation The flow 2-5. regime may be laminar, turbulent or in transition between laminar and turbulent. In laminar flow (2-5) 64 (ReynoldsLiquid flow number, in pipes Re, will below assume 2000), one fthe = of pipe’s three surface flow regimes. roughness The has flow no regime effectEq. 1-9 mayand is be consideredlaminar, turbulent negligible. or As in such, transition the friction betweenRe factor, laminar f, is calculated and turbulent. using Equation In laminar 1-9. flow (Reynolds number, Re, below 2000), the pipe’s surface roughness has no effect and is For considered turbulent flow negligible. (Reynolds As such, number, W theHERE friction Re, above factor, 4000),f, is calculated the friction using factor, Equation f, 1-9. is Re = Reynolds number,64 dimensionless = < 2000 for laminar flow, see Equation 2-7 dependent on two factors, the Reynolds numberf and pipe surface roughness. Eq. The 1-9 Re > 4000 for turbulent flow, see Figure 2-1 64 For turbulentf flow (Reynolds number, Re, above 4000), the frictionEq. factor,1-9 ƒ, is For turbulent flow (Reynolds number,dependent on Re, two Re above factors, the 4000), Reynolds the number friction and pipe factor, surface f, roughness. is The dependent on two factors, the resultant Reynolds friction number factor may and be pipedetermined surface from roughness.Figure 2-1, the Moody The Diagram. For turbulent flow (Reynolds This number, factor applies Re, to above all kinds 4000), of PE’s and the to all friction pipe sizes factor, (17). In thef, Moody is Diagram, dependent on two factors, therelative Reynolds roughness, number ε/d (see and Table pipe 2-1 for surface ε) is used roughness. which is the ratio The of absolute roughness to the pipe inside diameter. The friction factor may also be determined using the Colebrook formula. The friction factor can also be read from the Moody diagram with enough accuracy for calculation.

154-264.indd 170 1/16/09 9:56:54 AM 8 8 8 frictionfriction factorfriction factor may factor bemay determined bemay determined be determined from fromFigur fromeFigur 1-1, eFigur the1-1, eMoody the1-1, Moody the Dia Moodygram, Diagram, whichDiagram, which can which becan becan be used used for variousused for various for pipe various pipe materials pipe materials materialsand andsizes.(17) sizes.(17)and sizes.(17) In the In Moody the In Moody the Diagram, Moody Diagram, Diagram,relative relative relative roughness,roughness,roughness, İ/d’ (see İ/d’ Table(see İ/d’ Table(see 1-4 forTable 1-4 ɽ) for is 1-4 used.ɽ) foris used. ɽThe) is used.friction The friction The factor friction factor may factor thenmay bethenmay determined bethen determined be determined usingusing the using Colebrook the Colebrook the Colebrook formula. formula. The formula. frictionThe friction The factor friction factor can factor also can alsobe can read alsobe read from be read from the Moody from the Moody the Moody diagramdiagram withdiagram enoughwith enough with accuracy enough accuracy for accuracy calculation. for calculation. for calculation.

The ColebrookThe ColebrookThe Colebrookformula formula is: formula is: is: 8 friction factor may1 be determined1 1 °­ H from ε Figur°­51.2 H °½e 51.2 1-1, 51.2 the °½Moody Diagram, which can be  −=   +  used for various pipe materialslog2 10 ®log2 10  andlog2 10 ® sizes.(17)¾  In ¾ the MoodyEq. Diagram,1-10Eq. 1-10Eq. relative1-10 f f f¯° d'7.3 Red¯°'7.3 fRed¿°'7.3 fRe f ¿° roughness, İ/d’ (see Table 1-4 for ɽ) is used. The friction factor may then be determinedChapter 6 171 For FormulasFor FormulasForusing 1-9Formulas and 1-9 the 1-10, and Colebrook 1-9 1-10, termsand 1-10,terms are formula. asterms are previously as Theare previously as friction previouslydefined, defined, factor and: defined, can and: also and: be read from theDesign of Moody PE Piping Systems diagram with enough accuracy for calculation. İ = İ absolute =İ absolute = roughness, absolute roughness, roughness, ft. ft. ft. Re = Re Reynolds = Re Reynolds = number, Reynolds number, dimensionless number, dimensionless dimensionless The Colebrook formula is: The ColebrookVd Vd Vdformula'' UVd Vdis: '' ρ Vd'' U Re Re Re == Eq. 1-11Eq. 1-11Eq. 1-11 (2-6) v1 vP g vµ g°­ PH g 51.2 °½  log2 10 ®  ¾ Eq. 1-10 f ° d'7.3 Re f ° 3126Q3126Q3126¯ Q ¿ Re Re = Re Eq. 1-12Eq. 1-12Eq. 1-12 For Formulas 1-9 and 1-10, termsI arekD asI kD previouslyI kD defined, and: For Formulas 2-5 and 2-6, terms are as previously defined, and: İ = absolute roughness,ε = absolute roughness, ft. ft. (see Table 2-1) Re = Reynolds Rnumber, = Reynolds dimensionlessnumber, dimensionless (see Equation 2-5) Q = ν kinematic =Q kinematic = viscosity, kinematic viscosity, ft viscosity,2/sece ft 2/sec ft 2/sec Vd Vd'' U Liquid flow* g inReΓ a gpipe * occurs g in one of three flow regimes. It can be laminar,Eq. 1-11 turbulent Q ν = Q v P g Eq. 1-13Eq. 1-13Eq. 1-13 or in transitionU betweenρ U laminar and turbulent. The nature of the flow depends on the pipe diameter, the density and viscosity of the flowing fluid, and the velocity U ρ U 3 3of flow.3 The numerical3126 valueQ of a dimensionless combination of these parameters is = fluid = density, fluid = density, fluid lb/ft density, lb/ft lb/ft Re Eq. 1-12 known2 as the2 Reynolds2 number and the resultant value of this number is a predictor ƥ = ƥ dynamic =ƥ dynamic = viscosity, dynamic viscosity, lb-sec/ft viscosity, lb-sec/ft lb-sec/ft I kD k = k kinematic =k kinematic = viscosity, kinematic viscosity, centistokes viscosity,of the centistokes nature centistokes of the flow. One form of the equation for the computing of this number is as follows: Q (2-7) z 31602 z Q z = kinematic viscosity,kRe =k ft=/sec k Eq. 1-14Eq. 1-14Eq. 1-14 WHERE s k Dis s Q = flow rate, gpm * g z = z dynamic = z dynamic = viscosity, dynamic viscosity, centipoises viscosity, centipoises centipoises Q Eq. 1-13 DI = pipe inside diameter, in 3 WHERE3 3 U s = s liquid = s liquid =density, liquiddensity, gm/cm density, gm/cm Q = gm/cm rate of flow, gallons per minute Liquid flow in pipes will assume one of three flow regimes. The flow regime may be laminar, U = fluid density,k = kinematic lb/ft3 viscosity, in centistokes (See Table 2-3 for values for water) turbulent or in transition between laminar and turbulent. In laminar flow (Reynolds number, Re, Γ = dynamic viscosity,Di = internal diameter lb-sec/ft of pipe,2 in below 2000), the pipe’s surface roughness has no effect and is considered negligible. As such, the WhenWhen the Whenfriction the friction theloss friction throughloss throughloss one through sizeone pipesize one ispipesize known, ispipe known, theis known, friction the friction the loss friction throughloss throughloss another through another another friction factor, ƒ, is calculated using Equation 2-5. k = kinematic viscosity, centistokes pipe ofpipe different ofpipe different of diameter different diameter may diameter bemay found bemayWhen found by: be the found by: friction by: loss through one size pipe is known, the friction loss through (2-5) another pipe of different sizez may be found by: k Eq. 1-14 (2-8) 5 5 5 § d' · d' § ds' · hh ¨= hh 1 ¸ hh 1 ¨ 1 ¸ Eq. 1-15Eq. 1-15Eq. 1-15 z = dynamic viscosity,ff 21 ¨ centipoisesff 21 ¸ ff 21 ¨ ¸ © d'2 ¹ d'2 © d'2 ¹ s = liquid density, gm/cm3

The subscripts 1 and 2 refer to the known and unknown pipes. Both pipes must have the same surface roughness, and the fluid must be the same viscosity and have the When the friction loss throughsame flow one rate. size pipe is known, the friction loss through another pipe of different diameter may be found by:

5 § d' · ¨ 1 ¸ hh ff 21 ¨ ¸ Eq. 1-15 © d'2 ¹

154-264.indd 171 1/16/09 9:56:55 AM 172 Chapter 6 Design of PE Piping Systems

Ta BlE 2-1 Surface Roughness for Various New Pipes

‘ε’ Absolute Roughness of Surface, ft Values for New Pipe and Recommended Design Type of Pipe Values for New Values Reported by Reference (19) Pipe Reported by (18) Recommended Reference Mean Value Design Value Riveted steel 0.03 - 0.003 – – Concrete 0.01 – 0.001 – – Wood stave 0.0003 – 0.0006 – – Cast Iron – Uncoated 0.00085 0.00074 0.00083 Cast Iron – Coated – 0.00033 0.00042 Galvanized Iron 0.00050 0.00033 0.00042 Cast Iron – Asphalt Dipped 0.0004 – – Commercial Steel or Wrought Iron 0.00015 – – 0.000005 corresponds Drawn Tubing – – to “smooth pipe” Uncoated Stee – 0.00009 0.00013 Coated Steel – 0.00018 0.00018 Uncoated Asbestos – Cement – Cement Mortar Relined Pipes – 0.00167 0.00167 (Tate Process) Smooth Pipes “smooth pipe” “smooth pipe” (PE and other thermoplastics, – ( 0.000005 feet) (0.000005) Brass, Glass and Lead) (See Note) (See Note)

Note: Pipes that have absolute roughness equal to or less than 0.000005 feet are considered to exhibit “smooth pipe” characteristics.

Pipe Deflection Effects Pipe flow formulas generally assume round pipe. Because of its flexibility, buried PE pipe will deform slightly under earth and other loads to assume somewhat of an elliptical shape having a slightly increased lateral diameter and a correspondingly reduced vertical diameter. Elliptical deformation slightly reduces the pipe’s flow area. Practically speaking, this phenomenon can be considered negligible as it relates to pipe flow capacity. Calculations reveal that an elliptical deformation which reduces the pipe’s vertical diameter by 7% results in a flow reduction of approximately 1%.

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Pipe flow formulas generally assume round pipe. Because of its flexibility, buried PE pipes tend to deform slightly under earth and other loads to a slightly elliptical shape having a slightly increased lateral diameter and slightly reduced vertical diameter. Elliptical deformation slightly reduces the pipe’s flow area. Practically speaking, this phenomenon can be considered negligible as it relates to pipe flow capacity. Calculations reveal that a deformation of about 7% in polyethylene pipe results in a flow reduction of approximately 1%.

Note for the Moody Diagram: D = pipe inside diameter, ft Figure 1-1: The Moody Diagram

Head Loss in Fittings

Fluids flowing through a fitting or valve will experience a friction loss that canChapter be directly6 173 expressed using a resistance coefficient, K’, for the particular Designfitting.(20) of PE Piping As Systems shown in the discussion that follows, head loss through a fitting can be conveniently added into system flow calculations as an equivalent length of straight pipe having the same diameter as system piping. Table 1-5 presents K´ factors for various fittings.

Wh ere a pip elin e con tain s a lar ge nu mb er of fitti ngs in clo se pro xim ity Note for the Moody Diagram: D = pipe inside diameter, ft to each other, this simplified method of predicting flow loss may not be adequate due to Figure 2-1 The Moody Diagram the cumulative systems effect. Where this is a design consideration, the designer

Head Loss in Fittings Fluids flowing through a fitting or valve will experience a friction loss that can be directly expressed using a resistance coefficient, K’, which represents the loss in terms of an equivalent length of pipe of the same diameter. (20) As shown in the discussion that follows, this allows the loss through a fitting to be conveniently added into the system flow calculations. Table 2-2 presents K’ factors for various fittings.

Where a pipeline contains a large number of fittings in close proximity to each other, this simplified method of predicting flow loss may not be adequate due to the cumulative systems effect. Where this is a design consideration, the designer should consider an additional frictional loss allowance, or a more thorough treatment of the fluid mechanics.

The equivalent length of pipe to be used to estimate the friction loss due to fittings

may be obtained by Eq. 2-9 where LEFF = Effective Pipeline length, ft; D is pipe bore diameter in ft.; and K’ is obtained from Table 2-2.

(2-9) LEFF = K’D

154-264.indd 173 1/16/09 9:56:55 AM 11 should consider an additional frictional loss allowance, or a more thorough treatment of the fluid mechanics.

The equivalent length of pipe to be used to estimate the friction loss due to fittings may be obtained by Eq. 1-18 where LEFF = Effective Pipeline length, ft; D is pipe boro diameter in ft.; and K’ is obtained from Table 1-5.

LEFF = K’D Eq. 1-16

Table 1-5: Representative Fittings Factor, K’, to determine Equivalent Length of Pipe Piping Component K’

90° Molded Elbow 40

174 Chapter 6 45° Molded Elbow Design of PE Piping Systems 21 15° Molded Elbow 6 90° Fabricated Elbow 32

75° Fabricated Elbow Ta BlE 2-2 27 Representative Fittings Factor, K’, To Determine Equivalent Length of Pipe 60° Fabricated Elbow 21 Piping Component K’ 45° Fabricated Elbow 90° Molded Elbow 1640 45° Molded elbow 21 30° Fabricated elbow 15° Molded Elbow 116 15° Fabricated elbow 90° Fabricated Elbow (3 or more miters) 524 90° Fabricated Elbow (2 miters) 30 45° Fabricated Wye 90° Fabricated Elbow (1 miters) 6060 60° Fabricated Elbow (2 or more miters) 25 Equal Outlet Tee, Run/Branch 60° Fabricated Elbow (1 miters) 6016 45° Fabricated Elbow (2 or more miters) 15 Equal Outlet Tee, Run/Run 45° Fabricated Elbow (1 miters) 2012 30° Fabricated Elbow (2 or more miters) 8 Globe Valve, Conventional, Fully Open30° Fabricated Elbow (1 miters) 3408 15° Fabricated Elbow (1 miters) 6 Angle Valve, Conventional, Fully OpenEqual Outlet Tee, Run/Branch 14560 Butterfly Valve, • 8-in , Fully Open Equal Outlet Tee, Run/Run 4020 Globe Valve, Conventional, Fully Open 340 Check Valve, Conventional Swing Angle Valve, Conventional, Fully Open 135145 Butterfly Valve, >8”, Fully Open 40 Check Valve, Conventional Swing 135 - K values are based on Crane Technical Paper No 410-C

Head Loss Due to Elevation Change- K value for Molded Elbows is based on a radius that is 1.5 times the diameter.

- K value for Fabricated Elbows is based on a radius that is approximately 3 times the diameter. Line pressure may be lost or gained from a change in elevation. For liquids, the pressure for a given elevation changeHead is Loss given Due toby: Elevation Change Line pressure may be lost or gained from a change in elevation. For liquids, the pressure for a given elevation change is given by: (2-10) E = − hhh 12 Eq. 1-17 where: hE = Elevation head, ft of liquid WHERE hE = Elevation head, ft of liquid

h1 = Pipeline elevation at point 1, ft

h2 = Pipeline elevation at point 2, ft If a pipeline is subject to a uniform elevation rise or fall along its length, the two points would be the elevations at each end of the line. However, some pipelines may have several elevation changes as they traverse rolling or mountainous terrain. These pipelines may be evaluated by choosing appropriate points where the pipeline slope changes, then summing the individual elevation heads for an overall pipeline elevation head.

154-264.indd 174 1/16/09 9:56:55 AM 12

h1 = Pipeline elevation at point 1, ft h2 = Pipeline elevation at point 2, ft 12 If a pipeline is subject to a uniform elevation rise or fall along its length, the two points would be the elevations at each end of the line. However, some pipelines may have h = Pipeline elevation at point 1, ft several elevation changes1 as they traverse rolling or mountainous terrain. These h = Pipeline elevation at point 2, ft pipelines may be evaluated2 by choosing appropriate points where the pipeline slope changes, then summing the individual elevation heads for an overall pipeline elevation head.If a pipeline is subject to a uniform elevation rise or fall along its length, the two points would be the elevations at each end of the line. However, some pipelines may have several elevation changes as they traverse rolling or mountainous terrain. These In a pipeline conveying liquids and running full, pressure in the pipe due to elevation pipelines may be evaluated by choosing appropriate points where the pipeline slope exists whether or not liquid is flowing. At any low point in the line, internal pressure will changes, then summing the individual elevation heads for an overall pipeline elevationChapter 6 175 be equal to the height of the liquid above the point multiplied by the specific weight of head. Design of PE Piping Systems the liquid. If liquid is flowing in the line, elevation head and head loss due to liquid flow in the pipe are added to determine the pressure in the pipe at a given point in the pipeline.In a pipeline conveying liquids and running full, pressure in the pipe due to elevation exists whether or not liquid is flowing. At any low point in the line, internal pressure will be equal to the height of theIn a pipelineliquid above conveying the liquids point and multiplied running full, by pressurethe specific in the pipeweight due toof the liquid. If liquid is flowingelevation in the exists line, whether elevation or not head liquid and is flowing. head lossAt any due low topoint liquid in the flow line, Pressurein the pipe Flow are of added Water to – internal determineHazen-Williams pressure the will pressure be equal to in the the height pipe of the at liquid a given above point the point in multiplied the pipeline. by the specific weight of the liquid. If liquid is flowing in the line, elevation head and The Darcy-Weisbach methodhead of loss flow due resistanceto liquid flow calculation in the pipe are may added be to applied determine to the liquid pressure and in the pipe at a given point in the pipeline. gases, but its solution can be complex. For many applications, empirical formulas are available and, when used within their limitations, reliable results are obtained with Pressure Flow of Water – Hazen-Williams greater convenience. For example,Pressure FlowHazen of andWater Williams – Hazen-Williams developed Equationan empirical formula for the flow of water in pipesThe at Darcy-Weisbach 60° F. method of flow resistance calculation may be applied to liquid The Darcy-Weisbach methodand gases,of flow but resistance its solution can calculation be complex. may For many be applied applications, to liquid empirical and formulas gases, but its solution can be complex. For many applications, empirical formulas are The Hazen-Williams formulaare foravailable water and, at when60°F used (16°C) within can their be limitations, applied reliableto water results and are other obtained available and, when used within their limitations, reliable results are obtained2 with liquids having the same kinematicwith greater viscosity convenience. of 1.130 For example, centistokes Hazen and (0.00001211 Williams developed ft /sec), an empiricalor greater convenience. For example,formula for Hazenthe flow andof water Williams in pipes developed at 60º F. an empirical formula 31.5for the SSU. flow Theof water viscosity in pipes of waterat 60° varies F. with temperature, so some error can occur at temperatures other than 60°FThe Hazen-Williams(16°C). formula for water at 60º F (16ºC) can be applied to water and other liquids having the same kinematic viscosity of 1.130 centistokes which The Hazen-Williams formula for water at 60°F2 (16°C) can be applied to water and other equals 0.00001211 ft /sec or 31.5 SSU (Saybolt Second Universal). The2 viscosity of liquids having the same kinematicwater varies viscosity with temperature, of 1.130 so centistokes some error can (0.00001211 occur at temperatures ft /sec), other or Hazen-Williams31.5 SSU. The viscosityformula for ofthan frictionwater 60ºF (16ºC).varies(head) with loss temperature,in feet: so some error can occur at temperatures other than 60°FHazen-Williams (16°C). formula for friction (head) loss in feet of water head: (2-11) 1.85 0.002083L §100Q ·

h f 4.8655 ¨ ¸ Eq. 1-18 DI © C ¹ Hazen-Williams formula for friction (head) loss in feet: Hazen-Williams formula forHazen-Williams friction (head) formula forloss friction in (head) psi: loss in psi: (2-12) 1.85 p 0.0009015L0.002083L 100Q  h =   1.85 Eq. 1-18 f 0.00090154.8655 L§100C Q· DI p f 4.8655 ¨ ¸ Eq. 1-19 DI © C ¹ Hazen-Williams formula forTerms friction are as previously(head) defined, loss inand: psi: hf = friction (head) loss, ft. of water. p = friction (head) loss, psi f 1.85 DI = pipe inside0 .diameter,0009015 in L 100Q  p f =   Eq. 1-19 C = Hazen-WilliamsD Friction4.8655 Factor, dimensionlessC  c = 150-155 for PE , (not related to Darcy-Weisbach friction factor, ƒ)I Q = flow rate, gpm

The Hazen-Williams Friction Factor, C, for PE pipe was determined in a hydraulics laboratory using heat fusion joined lengths of pipe with the inner bead present. Other forms of these equations are prevalent throughout the literature.(21) The reader is referred to the references at the end of this chapter.

154-264.indd 175 1/16/09 9:56:56 AM 176 Chapter 6 Design of PE Piping Systems

Ta BlE 2-3 Properties of Water

Kinematic Viscosity, Temperature, °F/°C Specific Weight, lb/ft3 Centistokes 32 / 0 62.41 1.79 60 / 15.6 62.37 1.13 75 / 23.9 62.27 0.90 100 / 37.8 62.00 0.69 120 / 48.9 61.71 0.57 140 / 60 61.38 0.47 14 14 14 14

Water flow through pipes having different Hazen-Williams factors and different UsingUsing equationUsing equationUsing equation 1-21 equation1-21 and 1-21 and C = 1-21 and C150, = C150,and = 150, C = 150, flow diameters may be determined using the following equations:

(2-13) 85.1 85.1 85.1 85.1 )15000(0009015.0 § )15000(0009015.0 D)15000(0009015.0 §)50(100 · )15000(0009015.0 )50(100 §C )50(100 · )50(100 · p p = % flow 100¨  I2 ¸  2 =3.11 psi 3.11 psi f f p f p f 8655.4 8655.4 = 8655.4 8655.4 ¨ ¨ ¸ ¸ 3.11 psi 3.11 psi 938.3 938.3 938.3 ©938.3 150D I1501©¹ 150©C1150¹ ¹ ! To determineTo determineTo determineTo the determine theelevation elevationthe elevation the head, elevation head, assume head, assume head, assume point pointassume 1 ispoint 1at is thepoint 1at is thebottom at1 bottomisthe at ofbottom the the of bottom the of the of the elevation,elevation,elevation, andelevation, and point andpoint 2 Where ispointand 2at is thepoint the2at is thesubscriptstop. at2 top. isthe Using at top. 1theUsing and Equation top.Using 2 referEquation Using toEquation the1-17, Equationdesignated 1-17, 1-17, properties1-17, for two separate pipe profiles, in this case, the pipe inside diameter (DI in inches) of the one pipe (1) versus that of the second=  − pipe= (2) and the Hazen-Williams factor for each respective profile. hE hE hE h1500150 E 1500150 1500150 waterofft waterofft 1500150 waterofft waterofft

Pipe Flow Design Example 3 3 TheThe specific Thespecific specificTheweight weightspecific ofweight water of weight water of at water 60°F atof 60°Fwater atis 60°F62.37 is at 62.37 60°F is lb/ft 62.37 lb/ftis, which62.37 lb/ft, which3 is,lb/ft which a is3pressure, awhich ispressure a pressureis of a 62.37pressure of 62.37 of lb 62.37 oflb 62.37 lb lb 2 2 overover a 1over aft 1square overfta square1 ft a area,square 1 ft area,A square PEor area,pipelinea or pressure aarea, orpressure conveying a pressureor of a 62.37pressure ofwater 62.37 of /at 14462.37 60°F of/ 144 =is62.37 0.43/15,000 144= 0.43 / lb/in feet=144 0.43 lb/inlong .= Therefore, 0.43lb/inand. Therefore, is 2lb/in .laid Therefore, 2on . aTherefore, uniform grade that rises 150 feet. What is the friction head loss in 4” IPS DR 17 PE 3408 pipe 1414 for a 50 gpm flow? What is the elevation head? What is the internal pressure at the14 = ( − ) = bottomhE ofhE theh pipeE h whenE  water 5.6443.00150 ispsi flowing 5.6443.00150 psi5.6443.00150 psi uphill? 5.6443.00150 psi When flowing downhill? When full UsingUsing equationequationUsing 1-21equation1-21 andand but 1-21CC =not= 150, 150, andflowing? C = 150, WhenWhen waterWhen waterWhen is water flowing, is water flowing, isUsing flowing, elevation equation is flowing,elevation 2-12 elevation and head C elevation = head 150 and head and the head and the friction and thefriction frictionhead the head friction are head are added. head are added. added. are The added. The The The maximummaximummaximum frictionmaximum friction headfriction head frictionacts head acts at head theacts at thesour actsat sourthece at point,sour cethe point,85.1 85.1 85.1 cesour and point, ceand the point, andthemaximum maximumtheand maximum the elevation maximum elevation elevation head elevation head head head )15000(0009015.0 )15000(0009015.0 )15000(0009015.0 §§§ )50(100 )50(100 )50(100 ··· 85.1 at theat thelowestat lowesttheat pp point.lowest the point. lowest Therefore, point. Therefore, point. Therefore, when Therefore, when¨¨¨ flowing when flowing )15000(0009015.0 when¸ ¸§¸flowinguphill, uphill, flowing the )50(100 3.11 uphill,3.11 ·psipsi thepressure, uphill, pressure,the pressure, the P, pressure,at P, the at P, thebottom at P, bottomthe at bottom the bottom fff p f 8655.4 8655.4 8655.4 ¨ ¸ 3.11 psi is elevationis elevationis elevation headis elevation head plus head plus the938.3 938.3 head plus thefriction frictionplusthe938.3 headfriction the©©© head8655.4 150 friction150because head because¹¹©¹ head because150 the because theflow¹ flowthe is from flow isthe from theflowis from thebottom is frombottomthe tobottom the the to bottom the to the to the top.top. top. top. ToTo determinedetermineTo determine thethe elevationelevation the elevation head,head, assumeassume head, point pointpointassume 111 isisis point atatat thethethe 1 bottom bottombottomis at the ofofof bottom thethethe of the To determine the elevation head, assume point 1 is at the bottom of the elevation, elevation,elevation,elevation, andand pointpoint and 22 isis point atat thethe 2 top. top.is at UsingUsingthe top. EquationEquation Using Equation1-17,1-17, 1-17, and point= 2 +is at the= top. Using+ Equation= 2-10, phP fE phP fE  phP fE  phP fE  8.753.115.64 psi 8.753.115.64 psi8.753.115.64 psi 8.753.115.64 psi hh E  1500150 1500150 waterofft waterofft EE hE  1500150 waterofft WhenWhen flowing flowing downhill, downhill, water water flows flows from from the the top top to the to the botto bottom. m. Friction Friction head head WhenWhen flowing flowing downhill, downhill, water water flows flows from333 from the top the to top the to botto the bottom. Frictionm. Friction head head TheTheapplies specificspecificappliesThe from weightweight specific from the of theof source weight waterwater sourceThe specific pointat atof 60°F 60°Fwater point atweight isis theat 62.3762.37 60°F theof top, water lb/ft tlb/ftop,is so at62.37 , the60°Fso,, whichwhichwhich theis pressurelb/ft 62.37 is pressureisis3 , alb/ftaawhich pressurepressurepressure3 (see developed isTable developed a pressure of ofof2-3), 62.3762.3762.37 which, from from lb lboflb thefor 62.37 each the foot lb appliesapplies from from the source the source point point at the at t theop, tsoop, the so pressure the222 pressure developed developed from from the the overoverdownhill aadownhill 11 ftftover downhill square square flow a downhill flow1 isftarea, area, square flow applied is or orof flow applied is heada a area, pressure pressure applied inisexerts or theapplied in a thepressure pressureinofof opposite 62.3762.37 the opposite in of theopposite 62.37/ /of 144144 direction 62.37 oppositelb direction= =over 0.43 0.43 / direction a 144 1 as lb/inftlb/in direction square= as the 0.43... Therefore, theasTherefore, Therefore,area, elevation lb/in the as elevationor2 a. pressure theelevationTherefore, head. elevation head.of 62.37/144 head. head. 2 Therefore,Therefore,Therefore, Therefore, = 0.43 lb/in . Therefore, for a 150 ft. head,

hh E  5.6443.00150 5.6443.00150 psipsipsig EE hE  5.6443.00150 psi = − =  − = phP fE phP fE  phP fE  phP fE  2.533.115.64 psi 2.533.115.64 psi 2.533.115.64 psi 2.533.115.64 psi WhenWhen water waterWhen is is flowing,water flowing, is elevation elevation flowing, elevation head head and and head the the friction andfriction the head head friction are are head added. added. are The added.The The maximum friction head acts at the source point, and the maximum elevation head maximummaximumWhenWhen themaximum Whenfrictionfriction thepipeWhen pipethe headishead friction full,pipe isthe acts full,actsbut pipeis head full,but wateratat is the the water but full,acts is soursour water notbut atiscece thenotflowing,water ispoint,point, sourflowing,not is flowing,and ceandnonot point, friction no theflowing,the friction nomaximummaximum and headfriction no the head frictiondevelops. maximum headelevationelevation develops. head develops. elevation headheaddevelops. head atat thethe lowestlowestat the point.point. lowest Therefore,Therefore, point. Therefore, whenwhen flowingflowing when uphill,uphill, flowing thethe uphill, pressure,pressure, the pressure, P,P, atat thethe bottomP,bottom at the bottom isisis elevationelevationelevationis elevation headheadhead154-264.indd plusplusplus head the thethe 176 friction frictionfrictionplus the headheadhead friction becausebecausebecause head thebecausethethe flowflowflow is isisthe fromfromfrom flow thethethe is bottomfrombottombottom the tototo bottom thethethe to the 1/16/09 9:56:56 AM = phP fE + phP fE  =phP  phP + =5.6405.64 psi 5.6405.64  psi5.6405.64 psi 5.6405.64 psi top.top.top. top. fE fE SurgeSurge ConsiderationsSurge ConsiderationsSurge Considerations Considerations  phP phP  8.753.115.64 8.753.115.64 psipsi fE fE fE  phP fE  8.753.115.64 psi A pipingA pipingA system piping systemA piping mustsystem must systembe must designedbe designed mustbe designed forbe designedcontinuousfor continuous for continuous for operating continuous operating operating pressure operatingpressure pressure and pressureandfor transientandfor transient forand transient (surge)for (surge)transient (surge) (surge) pressurespressuresWhenWhenpressures imposed flowing flowingpressures imposed imposed by downhill, downhill, the byimposed particularthe by particular the water water by particular theapplication. flows flows particularapplication. application. from from Surgeapplication. the the Surge topallowance top Surge allowance to to Surge the the allowance and botto botto allowance andtemperaturem.m. andtemperature Friction Friction temperatureand effectstemperature head headeffects vary effects vary effects vary vary fromfrom pipe pipe material materialWhen to pipe flowingto pipe material, material, downhill, and and erroneous water erroneous flows conclusions conclusions from the may top may be to drawn be the drawn botto when whenm. comparing Frictioncomparing head appliesappliesfrom from pipe from materialpipe the the material source source to pipe to point point material,pipe at at material, the the and t top,op, erroneousand so so erroneous the the conclusions pressure pressure conclusions developed developedmay bemay drawn be from from drawn when the the when comparing comparing the Pressurethe Pressurethe Pressure Classtheapplies PressureClass (PC) Class (PC) from of Class different(PC) of the different (PC) of source differentpipe of pipe differentmaterials. point pipematerials. atmaterials.pipe the materials. top, so the pressure developed from the downhilldownhill downhill flow flow is is applied appliedflow is in inapplied the the opposite opposite in the opposite direction direction direction as as the the elevation elevationas the elevation head. head. head.

Therefore,Therefore, Therefore, The Theability Theability to ability Thehandle to handleability to temporary handle totemporary handle temporary pressure temporary pressure pressure surges pressuresurges is surges a ismajor surgesa ismajor aadvantage majoris advantage a major advantage of advantagepolyethylene. of polyethylene. of polyethylene. of polyethylene. Due Due to Dueto toDue to the the viscoelastic viscoelasticthe viscoelasticthe nature viscoelastic nature of nature polyethylene, of nature polyethylene, of polyethylene, of polyethylene, a piping a piping a system piping a system piping systemcan can safelysystem can safely withstand safely can withstand safely withstand momentarily withstand momentarily momentarily momentarily  phP phP fE fE fE  phP   2.533.115.64 2.533.115.64 psipsi 2.533.115.64 psi appliedapplied maximumapplied maximumapplied maximum pressures maximum pressures pressures that pressures that are that are significantly significantlyare that significantlyfE are above significantly above the above the pipe’s above pipe’sthe PC. pipe’s the PC. The pipe’s PC. The strain PC. The strain from strainThe from an strain from an from an an occasional,occasional,occasional, limitedoccasional, limited load limited load of limited short loadof short durationofload short duration of short durationis met isduration metwith is metwith an is elastic withanmet elastic anwith response, elastic an response, elastic response, which response, which is whichrelieved is relieved which is relievedupon is upon relieved upon upon WhenWhen thetheWhen pipepipe is isthe full,full, pipe butbut is waterwater full, but isis not notwater flowing,flowing, is not nono flowing, frictionfriction no headhead friction develops.develops. head develops.

 phP phP  5.6405.64 5.6405.64 psipsi fE fE fE  phP fE  5.6405.64 psi SurgeSurge ConsiderationsConsiderationsSurge Considerations

AA pipingpiping systemsystemA piping mustmust system bebe designed designedmust be fordesignedfor continuouscontinuous for continuous operatingoperating operatingpressurepressure andandpressure forfor transienttransient and for (surge)(surge)transient (surge) pressurespressures pressures imposedimposed by byimposed thethe particularparticular by the application.particularapplication. application. SurgeSurge allowanceallowance Surge allowance andand temperaturetemperature and temperature effectseffects varyvary effects vary fromfromfrom pipepipepipe frommaterialmaterialmaterial pipe toto tomaterial pipepipepipe material,material,material, to pipe andandandmaterial, erroneouserroneouserroneous and erroneous conclusionsconclusionsconclusions conclusions maymaymay bebebe drawndrawndrawn may bewhenwhenwhen drawn comparingcomparingcomparing when comparing thethethe PressurePressurePressurethe ClassClassPressureClass (PC)(PC)(PC) Class ofofof differentdifferentdifferent (PC) of pipepipepipe different materials.materials.materials. pipe materials.

TheThe abilityabilityThe toto handle handleability totemporarytemporary handle temporary pressurepressure surgessurgespressure isis asurgesa majormajor is advantageadvantage a major advantage ofof polyethylene.polyethylene. of polyethylene. DueDue toto Due to thethethe viscoelastic viscoelastic viscoelasticthe viscoelastic nature nature nature of of of nature polyethylene, polyethylene, polyethylene, of polyethylene, a a a piping piping piping system asystem system piping can can can system safely safely safely can withstand withstand withstand safely withstand momentarily momentarily momentarily momentarily appliedapplied maximum maximumapplied maximum pressures pressures pressures that that are are significantly significantly that are significantly above above the the above pipe’s pipe’s the PC. PC. pipe’s The The PC. strain strain The from from strain an an from an occasional,occasional,occasional, limitedlimited loadload limited ofof shortshort load durationduration of short isis duration metmet withwith is an anmet elasticelastic with anresponse,response, elastic response, whichwhich isis relievedrelieved which is uponupon relieved upon 14 14 Using equation 1-21 and C = 150, 14 Using equation 1-21 and C = 150, 85.1 )15000(0009015.0 § )50(100 · p ¨ ¸ 85.1 3.11 psi Using equation 1-21f and 938.3 C = 8655.4 150, ©)15000(0009015.0 § 150 ¹)50(100 · p ¨ ¸ 3.11 psi f 938.3 8655.4 150 To determine the elevation head, assume© point 1¹ is85.1 at the bottom of the )15000(0009015.0  )50(100  elevation,To determine and point thep f elevation =2 is at the head, top. assumeUsing Equation point 1 is1-17,= at the3.11 psi bottom of the 938.3 8655.4  150  elevation, and point 2 is at the top. Using Equation 1-17, h  1500150 waterofft To determine the elevationE head, assume point 1 is at the bottom of the elevation, and point 2 is athE the top. Using 1500150 Equationwaterofft 1-17, The specific weight of water at 60°F is 62.37 lb/ft3, which is a pressure of 62.37 lb over a 1 ft square area, or a pressure of 62.37 / 1443 = 0.43 lb/in2. Therefore, The specific weight of waterhE = at 60°F− = is1500150 62.37 waterofft lb/ft , which is a pressure of 62.37 lb over a 1 ft square area, or a pressure of 62.37 / 144 = 0.43 lb/in2. Therefore, 3 The specific weight of waterhE at 60°F is 62.37 5.6443.00150 lb/ftpsi , which is a pressure of 62.37 lb over a 1 ft square area, or a pressure of 62.37 / 144 = 0.43 lb/in2. Therefore, hE  5.6443.00150 psi When water is flowing, elevation head and the friction head are added. The Chapter 6 177 maximum friction head acts at the source point, and the maximum elevationDesign head of PE Piping Systems When water is flowing,h E elevation= ( − head) = and 5.6443.00150 thepsi friction head are added. The atmaximum the lowest friction point. headTherefore, acts at when the sour flowingce point, uphill, and the the pressure, maximum P, atelevation the bottom head isWhen atelevation the lowest water head ispoint. flowing,plus Therefore,the elevationfriction whenhead head flowingbecause and uphill, the the frictionflow the ispressure, from head the are P, bottom added.at the to bottom the The top.maximumis elevation friction head headplus theacts friction at the headsource because point, and the theflow maximum is from the elevation bottom tohead the attop. the lowest point. Therefore,When water iswhen flowing, flowing elevation uphill, head the and pressure,the friction head P, at are the added. bottom The is elevation head plusmaximum the friction phP frictionfE head head because acts at the 8.753.115.64 thesourcepsi flow point, is fromand the the maximum bottom elevation to the head top. at the lowest phP point.fE Therefore, when flowing8.753.115.64 psi uphill, the pressure, P, at the bottom is When flowing downhill,elevation water head flows plus fromthe friction the head top tobecause the the botto flowm. is from Friction the bottom head to the top. applies from the source point at the top, so the pressure developed from the When flowing downhill,= water+ phP fE flows= from+ the= top8.753.115.64 psig psi to the bottom. Friction head downhillapplies flow from is the applied source inpoint the at opposite the top, so direction the pressure as the developed elevation from head. the Therefore, Whendownhill flowing flow downhill, is appliedWhen water flowing in flows the downhill, opposite from water the directionflows top tofrom the the as bottotop the tom. the elevation bottom. Friction Friction headhead. head appliesTherefore, from the sourceapplies point from the at source the t op,point so at the the top, pressure so the pressure developed developed from from thethe

downhill flow is applieddownhill  in phP flow fE the is applied opposite in the directionopposite2.533.115.64 psi direction as the as the elevation elevation head. head. Therefore, Therefore,  phP fE  2.533.115.64 psigpsi When the pipe is full, but water is not flowing, no friction head develops.

When the pipe is full,When but= thewater− pipephP fE is =is notfull, flowing,but− water= isno not friction2.533.115.64 flowing,psi head no friction develops. head develops.

 phP fE  5.6405.64 psigpsi When the pipe is full, but water is not flowing, no friction head develops.  phP fE  5.6405.64 psi Surge Considerations Pressure Flow of Liquid Slurries Surge Considerations A piping system must be designedLiquid= for slurry continuous+ phP pipingfE = systems operating+ = transport 5.6405.64 pressurepsi solid particles and for entrained transient in (surge)a liquid carrier. pressures imposed by the particularWater application.is typically used Surge as a liquid allowance carrier, and and temperaturesolid particles areeffects commonly vary granular SurgeA piping Considerations system must be designed for continuous operating pressure and for transient (surge) frompressures pipe material imposed to pipeby the material, particularmaterials and application. such erroneous as sand, conclusionsSurgefly-ash allowanceor coal. may Key andbedesign drawn temperature considerations when comparing effects involve vary the nature the Pressure Class (PC) of differentof the pipesolid materials.material, it’s particle size and the carrier liquid. Afrom piping pipe system material must to pipebe designed material, forand continuous erroneous operating conclusions pressure may be and drawn for transientwhen comparing (surge) pressuresthe Pressure imposed Class by(PC) the of particular differentTurbulent application.pipe flow materials. is preferred Surge to allowanceensure that andparticles temperature are suspended effects in the vary liquid. Thefrom ability pipe tomaterial handle to temporary pipe material,Turbulent pressure and flow surgeserroneous also reducesis a conclusions major pipeline advantage wearmay because be of drawnpolyethylene. particles when suspended comparing Due into the carrier the Pressure Class (PC) of differentliquid will pipe bounce materials. off the pipe inside surface. PE pipe has viscoelastic properties theThe viscoelastic ability to handle nature temporary of polyethylene, pressure a surges piping is system a major can advantage safely withstandof polyethylene. momentarily Due to applied the viscoelastic maximum pressuresnature of polyethylene,thatthat arecombine significantly with a pipinghigh molecular above system the weight can pipe’s toughness safely PC. withstand The to provide strain momentarily service from life an that can occasional, limited load of shortsignificantly duration is exceedmet with many an elasticmetal piping response, materials. which Flow velocityis relieved that uponis too low to Theapplied ability maximum to handle pressures temporary that pressure are significantly surges is a above major theadvantage pipe’s PC.of polyethylene. The strain fromDue to an maintain fully turbulent flow for a given particle size can allow solids to drift to the theoccasional, viscoelastic limited nature load of short polyethylene, duration is a met piping with system an elastic can response, safely withstand which is relieved momentarily upon bottom of the pipe and slide along the surface. However, compared to metals, PE is a applied maximum pressures that are significantly above the pipe’s PC. The strain from an occasional, limited load of shortsofter duration material. is Undermet with sliding an elasticbed and response, direct impingement which is conditions, relieved uponPE may wear appreciably. PE directional fittings are generally unsuitable for slurry applications because the change of flow direction in the fitting results in direct impingement. Directional fittings in liquid slurry applications should employ hard materials that are resistant to wear from direct impingement.

Particle Size As a general recommendation, particle size should not exceed about 0.2 in (5 mm), but larger particles are occasionally acceptable if they are a small percentage of the solids in the slurry. With larger particle slurries such as fine sand and coarser particles, the viscosity of the slurry mixture will be approximately that of the carrying liquid. However, if particle size is very small, about 15 microns or less, the slurry viscosity will increase above that of the carrying liquid alone. The rheology

154-264.indd 177 1/16/09 9:56:57 AM 178 Chapter 6 Design of PE Piping Systems

of fine particle slurries should be analyzed for viscosity and specific gravity before determining flow friction losses. Inaccurate assumptions of a fluid’s rheological properties can lead to significant errors in flow resistance analysis. Examples of fine particle slurries are water slurries of fine silt, clay and kaolin clay.

Slurries frequently do not have uniform particle size, and some particle size non- uniformity can aid in transporting larger particles. In slurries having a large proportion of smaller particles, the fine particle mixture acts as a more viscous carrying fluid that helps suspend larger particles. Flow analysis of non-uniform particle size slurries should include a rheological characterization of the fine particle mixture.

Solids Concentration and Specific Gravity Equations 2-14 through 2-17 are useful in determining solids concentrations and 2323 mixture specific gravity. Tables 2-4, 2-5, and 2-6 provide information about2323 specific gravity and particle size of some slurries. (2-14) SS M−SS L M SSMLM SSLL CCV= Eq.Eq. 1-31 1-31 V CCVV Eq.Eq. 1-311-31 SS S−SS L S SSLSS SSLL

(2-15) CCVSS S V S CCVVSSSS CCW= Eq.Eq. 1-32 1-32 W CCWW Eq.Eq. 1-321-32 SS M M SSMM

(2-16) SS M= CCV( SS S−SS L)+ SS L Eq.Eq. 1-33 1-33 M SSMMV CCS VV SSLSS SSLL SSLL Eq.Eq. 1-331-33

(2-17) SS L L SSLL SSMM= Eq.Eq. 1-34 1-34 SSMM  Eq.Eq. 1-341-34 CCWW( SCCSS S− SSSSL L) SS 11− 11 WW SS LL SS S S SSSS Where:Where: Where:Where: WHERE SL = carrier liquid specific gravity SSL L S=SL= L =carrier=carrier carriercarrier liquid liquid liquid liquidspecific specific specificspecific gravity gravity gravitygravity SS = solids specific gravity SSS S SS=S= S =solids=solids solidssolids specific specific specificspecific gravity gravity gravitygravity SM = slurry mixture specific gravity SSM M SS=M= M =slurry=slurry slurryslurry mixture mixture mixturemixture specific specific specificspecific gravity gravity gravitygravity CV = percent solids concentration by volume CCV V CC=V= V =percent=percent percentpercent solids solids solidssolids concentration concentration concentrationconcentration by by volume volume byby volumevolume CW = percent solids concentration by weight CCW W CC=W= W =percent=percent percentpercent solids solids solidssolids concentration concentration concentrationconcentration by by weight weight byby weightweight Critical Velocity

As pointed out above, turbulent flow is preferred to maintain particle suspension. CriticalCritical Velocity Velocity A turbulent flow regime avoids the formation of a sliding bed of solids, excessive CriticalCritical VelocityVelocity pipeline wear and possible clogging. Reynolds numbers above 4000 will generally insure turbulent flow. AsAs pointed pointedAsAs pointed pointed out out above, out above,out above, above, turbulent turbulent turbulent turbulent flow flow flow is flow is preferred preferred is is preferred preferred to to maintain maintain to to maintain maintain particle particle particle particle suspension. suspension. suspension. suspension. A A A A turbulentturbulentturbulentturbulent flow flow regimeflow flowregime regimeregime avoids avoids avoidsavoids the the formation theformationthe formationformation of of a a sliding of ofsliding aa slidingsliding bed bed of bedbedof solids, solids, ofof solids,solids, excessive excessive excessiveexcessive pipeline pipeline pipelinepipeline wear,wear,wear,wear, and and and possible and possible possible possible clogging. clogging. clogging. clogging. Reynolds Reynolds Reynolds Reynolds numbers numbers numbers numbers above above above above 4000 4000 4000 4000 will will generally will will generally generally generally insure insure insure insure turbulentturbulentturbulentturbulent flow. flow. flow. flow. 154-264.indd 178 1/16/09 9:56:58 AM MaintainingMaintainingMaintainingMaintaining the the flow flowthethe velocity flow flowvelocity velocityvelocity of of a a slurry ofofslurry aa slurryslurry at at about about aatt aboutabout 30% 30% 30%above30% above aboveabove the the critical criticalthethe criticalcritical settlement settlement settlementsettlement velocityvelocityvelocityvelocity is is a a good isgoodis aa good goodpractice. practice. practice.practice. This This insuresThis Thisinsures insuresinsures that that the thatthatthe particles particlesthethe particlesparticles will will remain remainwillwill remainremain in in suspension suspension inin suspensionsuspension therebytherebytherebythereby avoiding avoiding avoidingavoiding the the potential potentialthethe potentialpotential for for excessive excessive forfor excessiveexcessive pipeline pipeline pipelinepipeline wear. wear. wear.wear. For For horizontal ForhorizontalFor horizontalhorizontal pipes, pipes, pipes,pipes, critical critical criticalcritical velocityvelocityvelocityvelocity may may bemay maybe estimated estimated bebe estimatedestimated using using using usingEquation Equation EquationEquation 1-35. 1-35. 1-35. 1-35. IndividualIndividualIndividualIndividual experience experience experienceexperience with with this with withthis equation thisequationthis equationequation varies. varies. varies.varies. Other Other OtherOther relationships relationships relationshipsrelationships are are offered areofferedare offeredoffered in in the the inin thethe literature.literature.literature.literature. See See Thompson See SeeThompson ThompsonThompson and and Aude andandAude Aude Aude(26). (26). (26).A(26). A test test AA section testsectiontest sectionsection may may bemay maybe installed installed bebe installedinstalled to to verify verify toto verify verify applicabilityapplicabilityapplicabilityapplicability of of this this ofof equation thisequationthis equationequation for for specific specific forfor specificspecific projects. projects. projects.projects.

VVC= FFL 22gdgd' '( S S S−11) Eq.Eq. 1-35 1-35 C VVCLC FFLL 22gdgdS ' ' SSSS 11 Eq.Eq. 1-351-35 WhereWhereWhereWhere terms terms termsterms are are previously arepreviouslyare previouslypreviously defined defined defineddefined and and andand

VVC C =VV= CC critical==critical criticalcritical settlement settlement settlementsettlement velocity, velocity, velocity,velocity, ft/sec ft/sec ft/sec ft/sec FFL L =FF= LL velocity==velocity velocityvelocity coefficient coefficient coefficientcoefficient (Tables (Tables (Tables(Tables 1-11 1-11 1-11and1-11 and 1-12) andand1-12) 1-12) 1-12) d’d’ =d’d’= pipe==pipe insidepipe pipeinside insideinside diameter, diameter, diameter,diameter, ft ft ftft 23

S M  S L CV Eq. 1-31 S S  S L

CV S S CW Eq. 1-32 S M

S M CV S S  S L  S L Eq. 1-33

S S L Eq. 1-34 M C S  S 1 W S L S S Where:

SL = carrier liquid specific gravity SS = solids specific gravity SM = slurry mixture specific gravity CV = percent solids concentration by volume CW = percent solids concentration by weight

Critical Velocity

As pointed out above, turbulent flow is preferred to maintain particle suspension. A turbulent flow regime avoids the formation of a sliding bed of solids, excessive pipeline Chapter 6 179 wear, and possible clogging. Reynolds numbers above 4000 will generallyDesign insure of PE Piping Systems turbulent flow.

Maintaining the flow velocity of a slurry at about 30% above the critical settlement velocity is a good practice. This insures that the particles will remain in suspension thereby avoiding the potentialMaintaining for excessive the flow pipeline velocity wear.of a slurry For at horizontal about 30% above pipes, the criticalcritical settlement velocity may be estimated usingvelocity Equation is a good 1-35. practice. This insures that the particles will remain in suspension thereby avoiding the potential for excessive pipeline wear. For horizontal pipes, Individual experience with this equation varies. Other relationships are offered in the critical velocity may be estimated using Equation 2-18. literature. See Thompson and Aude (26). A test section may be installed to verify applicability of this equation forIndividual specific experience projects. with this equation varies. Other relationships are offered in the literature. See Thompson and Aude (26). A test section may be installed24 to verify

applicability of this equation for specific projects. (2-18) VC FL 2gd' S S 1 Eq. 1-35 An approximateWhere terms minimum are previously velocity defined for fine and particle slurries (below 50 microns, 0.05 mm) is 4 to 7 ft/sec, provided turbulentWhere flow terms is are maintained. previously defined A and guideline minimum velocity for24 VC = critical settlement velocity, ft/sec larger particleVC slurries= critical (over settlement 150 microns, velocity, 0.15 mm)ft/sec is provided by Equation 1-36. FL = velocity coefficient (Tables 2-7 and 2-8) FL = velocity coefficientd’ = pipe (Tablesinside diameter, 1-11 ft and 1-12) d’ = pipe inside diameter,V ft 14 d' Eq. 1- 36 An approximate minimum velocityAn for approximate finemin particle minimum slurries velocity (below for fine 50 microns,particle slurries 0.05 (below mm) 50 microns, is 4 to 7 ft/sec, provided turbulent0.05 flow mm) is is maintained. 4 to 7 ft/sec, provided A guideline turbulent minimum flow is maintained. velocity forA guideline larger particle slurries (over 150 microns,minimum 0.15velocity mm) for largeris provided particle slurriesby Equation (over 150 1-36. microns, 0.15 mm) is provided Where by Equation 2-19.

Vmin = approximate minimum(2-19) velocity, ft/sec Vmin = 14 d' Eq. 1- 36

WHERE WhereCritical settlement velocity and V minimummin = approximate velocity minimum velocity, for ft/sec turbulent flow increases with increasing pipe bore. The relationshipCritical settlement in Equation velocity 1-37 and minimum is derived velocity from for turbulent the Darcy- flow increases with Vmin = approximate minimum velocity, ft/sec Weisbach equation. increasing pipe bore. The relationship in Equation 2-20 is derived from the Darcy- Weisbach equation. (Equation 2-3) (2-20) Critical settlement velocity and minimum velocityd'2 for turbulent flow increases with V2 V1 Eq. 1- 37 increasing pipe bore. The relationship in Equationd'1 1-37 is derived from the Darcy- Weisbach equation. The subscripts 1 and 2 are for the two pipe diameters.

d'2 V2 = V1 Eq. 1- 37 d'1 The subscripts 1 and 2 are for the two pipe diameters.

Table 1-8: Scale of Particle Sizes Tyler Screen U.S. Standard Inches Microns Class Mesh Mesh The subscripts 1 and 2 are for the two pipe1.3 diameters.– 2.5 33,000 – 63,500 Very coarse gravel 0.6 – 1.3 15,200 – 32,000 Coarse gravel 2.5 Table 1-8: Scale0.321 of Particle Sizes8,000 Medium gravel 5 5 0.157 4,000 Fine gravel Tyler Screen U.S. Standard Mesh9 10 Inches0.079 Microns2,000 VeryClass fine gravel 16 Mesh18 0.039 1,000 Very coarse sand 32 35 1.30.0197 – 2.5 33,000500 – 63,500 VeryCoars coarsee sand gravel 60 154-264.indd60 179 0.60.0098 – 1.3 15,200250 – 32,000 CoarseMedium gravel sand 1/16/09 9:56:58 AM 1152.5 120 0.00490.321 8,000125 MediumFine sand gravel 2505 2305 0.00240.157 4,00062 VeryFine fine gravel sand 4009 10 0.00150.079 2,00037 VeryCoarse fine gravel silt 16 18 0.00060.039 – 0.0012 161,000 – 31 VeryMedium coarse silt sand 32 35 0.0197 8500 – 13 CoarseFine siltsand 60 60 0.0098 4250 – 8 MediumVery fine sand silt 115 120 0.0049 2125 – 4 CoarseFine sand clay 250 230 0.0024 162 – 2 VeryMedium fine sandclay 400 0.0015 0.537 - 1 CoarseFine clay silt 0.0006 – 0.0012 16 – 31 Medium silt 8 – 13 Fine silt 4 – 8 Very fine silt 2 – 4 Coarse clay 1 – 2 Medium clay 0.5 - 1 Fine clay

180 Chapter 6 Design of PE Piping Systems

Ta BlE 2-4 Scale of Particle Sizes

Tyler Screen Mesh U.S. Standard Mesh Inches Microns Class – – 1.3 – 2.5 33,000 – 63,500 Very coarse gravel – – 0.6 – 1.3 15,200 – 32,000 Coarse gravel 2.5 – 0.321 8,000 Medium gravel 5 5 0.157 4,000 Fine gravel 9 10 0.079 2,000 Very fine gravel 16 18 0.039 1,000 Very coarse sand 32 35 0.0197 500 Coarse sand 60 60 0.0098 250 Medium sand 115 120 0.0049 125 Fine sand 250 230 0.0024 62 Very fine sand 400 – 0.0015 37 Coarse silt – – 0.0006 – 0.0012 16 – 31 Medium silt – – – 8 – 13 Fine silt – – - 4 – 8 Very fine silt – – – 2 – 4 Coarse clay – – – 1 – 2 Medium clay – – – 0.5 - 1 Fine clay

Ta BlE 2-5 Typical Specific Gravity and Slurry Solids Concentration (Water Slurries)

Typical Solids Concentration Material Specific Gravity % by Weight % by Volume Gilsonite 1.05 40 –45 39 – 44 Coal 1.40 45 – 55 37 – 47 Sand 2.65 43 – 43 23 – 30 Limestone 2.70 60 – 65 36 – 41 Copper Concentrate 4.30 60 – 65 26 – 30 Iron Ore 4.90 – – Iron Sands 1.90 – – Magnetite 4.90 60 - 65 23 - 27

154-264.indd 180 1/16/09 9:56:58 AM Chapter 6 181 Design of PE Piping Systems

Ta BlE 2-6 Water-Base Slurry Specific Gravities

Concentration by Solid Specific Gravity, S Weight Percent, 1.4 1.8 2.2 2.6 3.0 3.4 3.8 4.2 4.6 5.0 CW 5 1.01 1.02 1.03 1.03 1.03 1.04 1.04 1.04 1.04 1.04 10 1.03 1.05 1.06 1.07 1.07 1.08 1.08 1.08 1.08 1.09 15 1.04 1.07 1.09 1.10 1.11 1.12 1.12 1.13 1.13 1.14 20 1.05 1.10 1.12 1.14 1.15 1.16 1.17 1.18 1.19 1.19 25 1.08 1.13 1.16 1.18 1.20 1.21 1.23 1.24 1.24 1.25 30 1.09 1.15 1.20 1.23 1.25 1.27 1.28 1.30 1.31 1.32 35 1.11 1.18 1.24 1.27 1.30 1.33 1.35 1.36 1.38 1.39 40 1.13 1.22 1.28 1.33 1.36 1.39 1.42 1.44 1.46 1.47 45 1.15 1.25 1.33 1.38 1.43 1.47 1.50 1.52 1.54 1.56 50 1.17 1.29 1.38 1.44 1.50 1.55 1.58 1.62 1.64 1.67 55 1.19 1.32 1.43 1.51 1.58 1.63 1.69 1.72 1.76 1.79 60 1.21 1.36 1.49 1.59 1.67 1.73 1.79 1.84 1.89 1.92 65 1.23 1.41 1.55 1.67 1.76 1.85 1.92 1.98 2.04 2.08 70 1.25 1.45 1.62 1.76 1.88 1.98 2.07 2.14 2.21 2.27

Ta BlE 2-7 Velocity Coefficient, FL (Uniform Particle Size)

Particle Size, Velocity Coefficient, LF

mm CV = 2% CV = 5% CV = 10% CV = 15% 0.1 .76 0.92 0.94 0.96 0.2 0.94 1.08 1.20 1.28 0.4 1.08 1.26 1.41 1.46 0.6 1.15 1.35 1.46 1.50 0.8 1.21 1.39 1.45 1.48 1.0 1.24 1.04 1.42 1.44 1.2 1.27 1.38 1.40 1.40 1.4 1.29 1.36 1.67 1.37 1.6 1.30 1.35 1.35 1.35 1.8 1.32 1.34 1.34 1.34 2.0 1.33 1.34 1.34 1.34 2.2 1.34 1.34 1.34 1.34 2.4 1.34 1.34 1.34 1.34 2.6 1.35 1.35 1.35 1.35 2.8 1.36 1.36 1.36 1.36 ≥ 3.0 1.36 1.36 1.36 1.36

154-264.indd 181 1/16/09 9:56:58 AM 26

1.8 1.32 1.34 1.34 1.34 2.0 1.33 1.34 1.34 1.34 2.2 1.34 1.34 1.34 1.34 2.4 1.34 1.34 1.34 1.34 2.6 1.35 1.35 1.35 1.35 2.8 1.36 1.36 1.36 1.36 • 3.0 1.36 1.36 1.36 1.36

182 Chapter 6 Design of PE Piping Systems

Table 1-12: Velocity Coefficient, FL (50% Passing Particle Size) Velocity Coefficient, F Particle Size, mm L CV = 5% CV = 10% CV = 20% CV = 30% 0.01 0.48 Ta BlE 2-8 0.48 0.48 0.48 0.02 0.58 Velocity Coefficient,0.59 FL (50% Passing Particle Size)1.60 0.61 0.04 0.70 0.72 0.74 0.76 0.06 0.77 Particle Size, 0.79 Velocity Coefficient,0.81 LF 0.83 0.08 0.83 mm 0.86CV = 5% CV = 10% C0.86V = 20% CV = 30% 0.91 0.10 0.85 0.01 0.880.48 0.48 0.920.48 0.48 0.95 0.20 0.97 0.02 1.000.58 0.59 1.050.60 0.61 0.18 0.40 1.09 0.04 1.130.70 0.72 1.180.74 0.76 1.23 0.60 1.15 0.06 1.210.77 0.79 1.260.81 0.83 1.30 0.80 1.21 0.08 1.250.83 0.86 1.310.86 0.91 1.33 1.0 1.24 0.10 1.290.85 0.88 1.330.92 0.95 1.35 2.0 1.33 0.20 1.360.97 1.00 1.381.05 1.08 1.40 3.0 1.36 0.40 1.381.09 1.13 1.391.18 1.23 1.40 0.60 1.15 1.21 1.26 1.30 0.80 1.21 1.25 1.31 1.33 1.0 1.24 1.29 1.33 1.35 Head Loss 2.0 1.33 1.36 1.38 1.40 3.0 1.36 1.38 1.39 1.40 Equation 1-7, Darcy-Weisbach, and Equations 1-18 and 1-19, Hazen-Williams, may be used to determine friction headEquation loss 2-3, for Darcy-Weisbach, pressure slurry and flowsEquations provided 2-11 and 2-12, the Hazen-Williams, viscosity 27may be limitations of the equations are usedtaken to determineinto account. friction Elevationhead loss for head pressure loss slurry is increased flows provided by the viscosity the specificEmpirical gravity Equations of the slurry for High limitationsmixture. Pressure of the equationsGas Flow are taken into account. Elevation head loss is increased by the specific gravity of the slurry mixture. (2-21)  27 Equations 1-39 through 1-42hE areS M empirical h2 h1 equations used in industryEq. for1- 38 pressure greater than 1 psig. (26) Calculated results may vary due to the assumptions inherent inEmpirical the derivation Equations of the for equation. HighCompressible Pressure Gas Gas Flow Flow Flow equations for smooth pipe may be used to estimate compressible gas flow Compressible Gas Flow MuellerEquations Equation 1-39 throughthrough 1-42 PE are pipe. empirical equations used in industry for pressure greater than 1 psig. (26)Empirical Calculated Equations results for High may Pressure vary due Gas toFlow the assumptions inherent Flow equations for smooth pipe may be used to estimate compressible gas flow through in the derivation of the equation. 0.575 polyethylene pipe. Equations 2-22 through2.725 2-25§ are2 empirical2 · equations used in industry for pressure 2826 DI ¨ p1 p2 ¸ greaterQ hthan 1 psig. Calculated results may vary due to the assumptionsEq. inherent 1-39 in S 0.425 ¨ L ¸ Mueller Equation the derivation of gthe equation.© ¹ Mueller Equation (2-22) 0.575 2826 D 2.725  p 2 − p 2  Q = I  1 2  Eq. 1-39 h 0.425   S g  L  Weymouth Equation Weymouth Equation (2-23) 0.5 2034 D 2.667 § p 2  p 2 · Q I ¨ 1 2 ¸ Eq. 1-40 h 0.5 ¨ ¸ S g © L ¹ Weymouth Equation

0.5 2.667  2 2  IGT Distribution Equation 2034 DI p1 − p2 Q =   Eq. 1-40 h 0.5   S g  L  154-264.indd 182 0.555 1/16/09 9:56:59 AM 2679 D 2.667 § p 2  p 2 · Q I ¨ 1 2 ¸ Eq. 1-41 h 0.444 ¨ ¸ S g © L ¹ IGT Distribution Equation

2.667 2 2 0.555 Spitzglass Equation 2679 D  p − p  Q = I  1 2  Eq. 1-41 h 0.444  L  S g   0.5 § · 0.5 ¨ ¸ § 2 2 · 5 3410 p1  p2 ¨ DI ¸ Q ¨ ¸ Eq. 1-42 Spitzglass Equation h 0.5 ¨ ¸ ¨ 3.6 ¸ S g © L ¹ ¨1  0.03DI ¸ © DI ¹ 0.5   0.5   Where: 3410  p 2 − p 2  D 5 =  1 2   I  Qh 0.5 3 Eq. 1-42 Qh = flow, standard ft /hour   3.6  S g  L  1+ + 0.03DI  Sg = gas specific gravity 2  DI  p1 = inlet pressure, lb/in absolute 2 Where:p2 = outlet pressure, lb/in absolute L = length, ft 3 Qh = flow, standard ft /hour DI = pipe inside diameter, in Sg = gas specific gravity 2 p1 = inlet pressure, lb/in absolute 2 p2 = outlet pressure, lb/in absolute L = length, ft DI = pipe inside diameter, in 27 27 Empirical Equations for High Pressure Gas Flow Empirical Equations for High Pressure Gas Flow Equations 1-39 through 1-42 are empirical equations used in industry for pressure greater than 1 psig. (26) Calculated results may vary due to the assumptions inherent Equationsin the 1-39 derivation through of the 1-42 equation. are empirical equations used in industry for pressure greater than 1 psig. (26) Calculated results may vary due to the assumptions inherent in the derivation of the equation. Mueller Equation Mueller Equation 575.0 725.2  2 − 2  2826 DI  1 pp 2  Qh = Eq. 1-39 725.2 425.0 2  2 575.0  2826 D S g§  pp ·L  Q I ¨ 1 2 ¸ Eq. 1-39 h 425.0 ¨ ¸ S g © L ¹

Weymouth Equation

Weymouth Equation 5.0 667.2  2 − 2  2034 DI  1 pp 2  Qh = Eq. 1-40 667.2 5.0 2  2 5.0  S § ·L Chapter 6 183 2034 DI g 1 pp 2  Q ¨ ¸ DesignEq. of PE Piping1-40 Systems h 5.0 ¨ ¸ S g © L ¹ IGT Distribution Equation

IGT Distribution Equation 667.2 2 2 555.0 IGT Distribution Equation  −  2679 DI  1 pp 2  Qh = Eq. 1-41 (2-24) 667.2 444.0 2  2 555.0  2679 D S g§  pp ·L  Q I ¨ 1 2 ¸ Eq. 1-41 h 444.0 ¨ ¸ S g © L ¹ Spitzglass Equation Spitzglass Equation Spitzglass Equation (2-25) 5.0   2 2 5.0  5    5.0 3410 1 − pp 2  DI  Q =  §  · Eq. 1-42 h 5.0  5.0 ¨  ¸ § S 2 2 ·L  5 6.3  3410 1g pp 2 ¨  D1 I ++ ¸03.0 D Q ¨ ¸  I  Eq. 1-42 h 5.0 ¨ ¸ ¨ 6.3  DI ¸  S g © L ¹ ¨1  03.0 DI ¸ Where: © DI ¹ WHERE 28 28 (Equations 2-22 through 2-25) 3 Qh = flow, standard ft /hour Where: 3 Qh = flow, standard ft /hour Sg = gas specific3 gravity Qh = flow,Sg standard= gas specific gravityft /hour 2 p1 = inlet pressure,2 lb/in absolute Sg = gasp specific1 = inlet pressure, gravity lb/in absolute 2 Empirical Equationsp2 = for= outletoutlet Low pressure, pressure, Pressure lb/in22 absolute lb/inGas Flowabsolute Empirical Equationsp1 = for inlet Lowp 2pressure, Pressure lb/in Gas absolute Flow L = L = length, length, ft ft 2 p2 = outlet pressure, lb/in absolute DI = D =pipe pipe inside inside diameter, diameter, in in For applicationsFor applications L = where length, where internalI ft internal pressures pressures are less are than less 1 than psig, 1 such psig, as such landfill as landfill gas gas gathering or wastewater odor control, Equations 1-43 or 1-44 may be used. gathering orD wastewaterI = pipe odorEmpirical inside control, diameter, Equations Equations forin Low 1-43 Pressure or 1-44 Gas may Flow be used. For applications where internal pressures are less than 1 psig, such as landfill gas Mueller Equation Mueller Equation gathering or wastewater odor control, Equations 2-26 or 2-27 may be used. Mueller Equation 725.2 575.0 (2-26) 725.2 575.0 2971DI §  hh 21 · 2971 DI §  hh 21 · Qh 425.0 ¨ ¸ Eq. 1-43 Qh 425.0 ¨ ¸ Eq. 1-43 S g © L ¹ S g © L ¹ Spitzglass Equation Spitzglass Equation Spitzglass Equation (2-27) 5.0 5.0 § § · · 5.0 ¨ 5 ¸ 5.0 ¨ 5 ¸ 3350 §  hh 21 · ¨ DI ¸ 3350 §  hh 21 · ¨ DI ¸ Qh 5.0 ¨ ¸ Eq. 1-44 Qh 5.0 ¨ ¸ ¨ 6.3 ¸ Eq. 1-44 S g © L¨ ¹ 6.3 ¸ S g © L ¹ ¨1  03.0 DI ¸ ¨1  03.0 DI ¸ © DI ¹ © DI ¹

Where terms are previously defined, and WhereWhere terms areterms previouslyh1 are = inlet previously pressure, defined, in H2O defined, and and h2 = outlet pressure, in H2O h1 = inlet pressure, in H2O h1 = inlet pressure, in H2O h2 = outlet pressure, in H2O h2 = outlet pressure, in H2O

Gas PermeationGas Permeation 154-264.indd 183 1/16/09 9:57:00 AM

Long distanceLong distance pipelines pipelines carrying carrying compressed compressed gasses gasses may deliver may deliver slightly slightly less gas less due gas due to gasto permeation gas permeation through through the pipe the wall. pipe Permeation wall. Permeation losses losses are small, are small, but it may but it be may be necessarynecessary to distinguish to distinguish between between permeation permeation losses losses and possible and possible leakage. leakage. Equation Equation 1- 1- 45 may45 be may used be usedto determine to determine the volume the volume of a gas of a that gas wil thatl permeate will permeate through through polyethylenepolyethylene pipe of pipe a given of a wallgiven thickness: wall thickness:

4PAK AsP 4PAK AsP q qP Eq. 1-45Eq. 1-45 P t' t' WhereWhere 3 qP = volume of gas permeated,3 cm (gas at standard temperature and qP = volume of gas permeated, cm (gas at standard temperature and pressure)pressure) KP = permeability constant (Table 1-13) KP = permeability constant (Table 1-13) 2 As = surface area of the outside wall of the pipe, 2100 in As = surface area of the outside wall of the pipe, 100 in 2 PA = pipe internal pressure, atmospheres (1 atmosphere = 14.72 lb/in ) PA = pipe internal pressure, atmospheres (1 atmosphere = 14.7 lb/in ) 28

Empirical Equations for Low Pressure Gas Flow

For applications where internal pressures are less than 1 psig, such as landfill gas gathering or wastewater odor control, Equations 1-43 or 1-44 may be used.

Mueller Equation

575.0 2971D 725.2  − hh  = I 21 Qh 425.0   Eq. 1-43 S g  L  Spitzglass Equation

5.0   5.0  5  3350  − hh 21   DI  Q =   Eq. 1-44 h 5.0  6.3  S g  L  1 ++ 03.0 DI   DI 

Where terms are previously defined, and

h1 = inlet pressure, in H2O h2 = outlet pressure, in H2O 184 Chapter 6 Design of PE Piping Systems

Gas Permeation

Long distance pipelines carryingGas compressed Permeation gasses may deliver slightly less gas due to gas permeation through the Long pipe distance wall. Permeationpipelines carrying losses compressed are small, gasses may but deliver it may slightly be less gas necessary to distinguish betweendue permeation to gas permeation losses through and thepossible pipe wall. leakage. Permeation Equation losses are small,1- but it 45 may be used to determinemay the be necessary volume to distinguish of a gas between that wilpermeationl permeate losses and through possible leakage. polyethylene pipe of a given wallEquation thickness: 2-28 may be used to determine the volume of a gas that will permeate through PE pipe of a given wall thickness: (2-28) ΘPAK q = AsP Eq. 1-45 P t'

Where WHERE 3 qP = volume of gas permeated,3 cm (gas at standard temperature and pressure) qP = volume of gas permeated, cm (gas at standard temperature and Cm3 mil K = permeability constant (Table 2-9); units: pressure) P 100 in2 atm day

KP = permeabilityA constants = pipe outside (Table wall area in1-13) units of 100 square inches 2 2 As = surface areaPA of = pipethe internal outside pressure, wall atmospheres of the (1pipe, atmosphere 100 = in14.7 lb/in ) 2 PA = pipe internalΘ pressure,= elapsed time, atmosdays pheres (1 atmosphere = 14.7 lb/in ) t’ = wall thickness, mils

TaBlE 2-9 Permeability Constants (28)

Gas KP Methane 85 Carbon Monoxide 80 Hydrogen 425

154-264.indd 184 1/16/09 9:57:00 AM Chapter 6 185 Design of PE Piping Systems

Ta BlE 2-10 Physical Properties of Gases (Approx. Values at 14.7 psi & 68ºF)

Chemical Weight Density, Specific Gravity, Gas Molecular Weight Formula lb/ft 3 (Relative to Air) Sg

Acetylene (ethylene) C2H2 26.0 0.0682 0.907 Air – 29.0 0.0752 1.000

Ammonia NH3 17.0 0.0448 0.596 Argon A 39.9 0.1037 1.379

Butane C4H10 58.1 0.1554 2.067

Carbon Dioxide CO2 44.0 0.1150 1.529 Carbon Monoxide CO 28.0 0.0727 0.967

Ethane C2H6 30.0 0.0789 1.049

Ethylene C2H4 28.0 0.0733 0.975

Helium He 4.0 0.0104 0.138 Hydrogen Chloride HCl 36.5 0.0954 1.286 Hydrogen H 2.0 0.0052 0.070

Hydrogen Sulphide H2S 34.1 0.0895 1.190

Methane CH4 16.0 0.0417 0.554

Methyl Chloride CH3Cl 50.5 0.1342 1.785 Natural Gas – 19.5 0.0502 0.667 Nitric Oxide NO 30.0 0.0708 1.037

Nitrogen N2 28.0 0.0727 0.967

Nitrous Oxide N2O 44.0 0.1151 1.530

Oxygen O2 32.0 0.0831 1.105

Propane C3H8 44.1 0.1175 1.562

Propene (Propylene) C3H6 42.1 0.1091 1.451

Sulfur Dioxide SO2 64.1 0.1703 2.264 Landfill Gas (approx. value) – – – 1.00 Carbureted Water Gas – – – 0.63 Coal Gas – – – 0.42 Coke-Oven Gas – – – 0.44 Refinery Oil Gas – – – 0.99 Oil Gas (Pacific Coast) – – – 0.47 “Wet” Gas (approximate value) – – – 0.75

Gravity Flow of liquids In a pressure pipeline, a pump of some sort, generally provides the energy required to move the fluid through the pipeline. Such pipelines can transport fluids across a level surface, uphill or downhill. Gravity flow lines, on the other hand, utilize the energy associated with the placement of the pipeline discharge below the inlet. Like pressure flow pipelines, friction loss in a gravity flow pipeline depends on viscous shear stresses within the liquid and friction along the wetted surface of the pipe bore.

154-264.indd 185 1/16/09 9:57:00 AM 30 30 30 30 Gravity Flow of Liquids GravityGravity Flow Flowof Liquids of Liquids Gravity Flow of Liquids In a pressure pipeline, a pump of some sort, generally provides the energy required to In a pressureIn a pressure pipeline, pipeline, a pump a pump of some of some sort, sort,generally generally provides provides the energy the energy required required to to In a pressuremove the pipeline, fluid through a pump the ofpipeline. some sort, Such generally pipelines provides can transport the energy fluids required across ato level movemove the fluid the throughfluid through the pipeline. the pipeline. Such Suchpipelines pipelines can transportcan transport fluids fluids across across a level a level movesurface, the fluid uphill, through or the downhill. pipeline. Gravity Such flowpipelines lines, can on transport the other fluids hand across utilize a the level energy surface,surface, uphill, uphill, or downhill. or downhill. Gravity Gravity flow lines,flow lines, on the on other the other hand hand utilize utilize the energy the energy surface,associated uphill, orwith downhill. the placement Gravity of flow the lines,pipeline on discharge the other below hand the utilize inlet. the Like energy pressure associatedassociated with thewith placement the placement of the of pipeline the pipeline discharge discharge below below the inlet. the inlet. Like pressureLike pressure associatedflow pipelines, with the frictionplacement loss ofin thea gravity pipeline flow discharge pipeline dependsbelow the on inlet. viscous Like shear pressure stresses flow pipelines,flow pipelines, friction friction loss inloss a gravityin a gravity flow pipelineflow pipeline depends depends on viscous on viscous shear shear stresses stresses flow pipelines,within the liquid,friction and loss friction in a gravity along flowthe wetted pipeline surface depends of the on pipeviscous bore. shear stresses withinwithin the liquid, the liquid, and friction and friction along along the wetted the wetted surface surface of the of pipe the bore.pipe bore. within the liquid, and friction along the wetted surface of the pipe bore. Some gravity flow piping systems186 Chapter may 6 become very complex, especially if the pipeline SomeSome gravity gravity flow pipingflow piping systemsDesign systems ofmay PE Piping becomemay Systems become very complex,very complex, especially especially if the ifpipeline the pipeline Somegrade gravity varies, flow becausepiping systems friction may loss becomewill vary very along complex, with the especially varying grade. if the pipeline Sections of gradegrade varies, varies, because because friction friction loss willloss vary will alongvary along with thewith varying the varying grade. grade. Sections Sections of of gradethe varies, pipeline because may developfriction lossinternal will vary pressure, along orwith vacuum, the varying and maygrade. have Sections varying of liquid the pipelinethe pipeline may maydevelop develop internal internal pressure, pressure, or vacuum, or vacuum, and may and mayhave have varying varying liquid liquid the pipelinelevels in maythe pipe develop bore. internal pressure, or vacuum, and may have varying liquid levelslevels in the in pipe the bore.pipe bore. levels in the pipe bore. Manning ManningManning Some gravity flow piping systems may become very complex, especially if the Manning pipeline grade varies, because friction loss will vary along with the varying grade. For open channel water flow underSections conditions of the pipeline of may constant develop grade,internal pressure,and uniform or vacuum, channel and may have For openFor openchannel channel water water flow underflow under conditions conditions of constant of constant grade, grade, and uniformand uniform channel channel For opencross channel section, waterthe Manning flow under equationvarying conditions mayliquid be levelsof used.constant in the (28,29,30) pipe grade, bore. andOpen uniform channel channel flow exists crosscross section, section, the Manning the Manning equation equation may bemay used. be used. (28,29,30) (28,29,30) Open Open channel channel flow existsflow exists crossin section, a pipe the when Manning it runs equation partially may full. be Like used. the (28,29,30) Hazen-Williams Open channel formula, flow the exists Manning in a in pipe a pipe when when it runs it runs partially Manning partially full. Flow Like full. Equation Like the Hazen-Williams the Hazen-Williams formula, formula, the Manning the Manning in a equation pipe when is limited it runs to partiallywater or full.liquids Like with the a kinematic Hazen-Williams viscosity formula, equal to the water. Manning equationequation is limited is limited to water to water or liquids or liquids with awith kinematic a kinematic viscosity viscosity equal equal to water. to water. equation is limited to water or liquidsFor with open a channel kinematic water viscosity flow under equal conditions to water. of constant grade, and uniform channel cross section, the Manning equation may be used.(29,30) Open channel flow exists in a pipe when it runs partially full. Like the Hazen-Williams formula,

Manning Equation the Manning equation is applicable to water or liquids with a kinematic viscosity ManningManning Equation Equation Manning Equation equal to water. Manning Equation 1.486 2 / 3 1/ 2 (2-29) V 1.4861rH.4862 / 3 S 1/22/ 3 1/ 2 Eq. 1- 46 1V.486= Vn2 / 3 rH1/ 2 SrH S Eq. 1-Eq. 46 1- 46 V rHn S n Eq. 1- 46 Where n WhereWhere Where V = flow velocity,WHE ft/secRE V =V flow= velocity,flow Vvelocity, = flow ft/sec velocity, ft/sec ft/sec V n= =flow velocity,roughness ft/secn coefficient,= roughness coefficient, dimensionless dimensionless n =n roughness= roughness coefficient, coefficient, dimensionless dimensionless n r=H =roughness hydraulic coefficient, radius,rH = hydraulic ft dimensionless radius, ft rH =rH hydraulic= hydraulic radius, radius, ft ft rH = hydraulic radius,SH =ft hydraulic slope, ft/ft AC rH A A Eq. 1- 47 (2-30) rA = Pr C C Eq. 1-Eq. 47 1- 47 r HC WH Eq. 1- 47 H PW PW PW 2 AC = cross-sectional area of pipe bore, ft2 2 AC A=C cross-sectional= cross-sectionalA = cross-sectional area ofarea areapipe ofof flow bore,pipe2 bore, bore, ftft2 ft AC P=W =cross-sectional perimeter wetted areaC of by pipe flow, bore, ft ft PW P=W perimeter= perimeter PwettedW = perimeter wetted by wettedflow, by by flow,ft flow, ft ft PW S=H =perimeter hydraulic wetted slope, by flow,ft/ft ft SH S=H hydraulic= hydraulic slope, slope, ft/ft ft/ft SH = hydraulic slope, ft/ft (2-31) hU  hD h f S H h − hh  h h Eq. 1-48 U hDU Df f ShHU = hSDH L f = L Eq. 1-48Eq. 1-48 S H L L L L Eq. 1-48 31 h = upstream pipe elevation, ft 31 hU = upstream pipeU elevation,L ftL hU h=U upstream= upstream hpipeD = downstream elevation,pipe elevation, pipe elevation, ft ftft hU h=D =upstream downstream pipe elevation, pipe elevation, ft ft It is convenient hD h==D to frictiondownstream=combine downstream (head) thehf = frictionpipeManning loss, (head) elevation,pipe ft of loss, equationelevation, liquid ft of liquidft with ft It is convenient hD =tof combinedownstream the Manning pipe elevation, equation ft with hf =h f friction= friction (head)L = length,(head) loss, ft loss,ft of liquid ft of liquid hf = friction (head) loss,It is convenient ft of liquid to combine the Manning equation with

(2-32) Q ACV Eq. 1-49 Q ACV Eq. 1-49 To obtain To obtain To obtain (2-33) 1.486 AC 2 / 3 1/ 2 1.486Q AC 2 / 3 r1H/ 2 S H Eq. 1-50 Q rH n S H Eq. 1-50 n Where terms are as defined above, and Where terms are as defined above, and Q = flow, ft3/sec Q = flow, ft3/sec When a circular pipe is running full or half-full, When a circular pipe is running full or half-full,

154-264.indd 186 1/16/09 9:57:01 AM d' DI d' rH D I Eq. 1-51 rH 4 48 Eq. 1-51 4 48 where where d’ = pipe inside diameter, ft d’ = pipe inside diameter, ft DI = pipe inside diameter, in DI = pipe inside diameter, in 3 Full pipe fl3ow in ft per second may be estimated using: Full pipe flow in ft per second may be estimated using:

8 / 3 1/ 2 8 / 34 1D/ 2 I S QFPS 6.1436DuI10 S Eq. 1-52 QFPS 6.136u10 n Eq. 1-52 n Full pipe flow in gallons per minute may be estimated using: Full pipe flow in gallons per minute may be estimated using:

8/3 1/ 2 8/3 D S Q' D0.27S51/ 2 I Eq. 1-53 Q' 0.275 I n Eq. 1-53 n Nearly full circular pipes will carry more liquid than a completely full pipe. When slightly Nearly full circular pipes will carry more liquid than a completely full pipe. When slightly less than full, the hydraulic radius is significantly reduced, but the actual flow area is less than full, the hydraulic radius is significantly reduced, but the actual flow area is only slightly lessened. Maximum flow is achieved at about 93% of full pipe flow, and only slightly lessened. Maximum flow is achieved at about 93% of full pipe flow, and maximum velocity at about 78% of full pipe flow. maximum velocity at about 78% of full pipe flow.

Table 1-15: Values of n for Use with Manning Equation Table 1-15: Values of n for Use with Manning Equation n, typical Surface n, typical Surface design Polyethylene pipe design 0.009 Polyethylene pipe 0.009 Uncoated cast or ductile iron pipe 0.013 Uncoated cast or ductile iron pipe 0.013 Corrugated steel pipe 0.024 Corrugated steel pipe 0.024 Concrete pipe 0.013 Concrete pipe 0.013 Vitrified clay pipe 0.013 Vitrified clay pipe 0.013 Brick and cement mortar sewers 0.015 Brick and cement mortar sewers 0.015 31 31 31 It is convenient to combine the Manning equation with It is convenient to combine the Manning equation with It is convenient to combine the Manning equation with Q ACV Eq. 1-49 Q = A V Eq. 1-49 To obtain C Q ACV Eq. 1-49 To obtain 1.486 A To obtain C 2 / 3 1/ 2 Chapter 6 187 Q rH S H Eq.Design 1-50 of PE Piping Systems n 1.486 AC 2 / 3 1/ 2 Q = rH S H Eq. 1-50 1.486 A 2 / 3 1/ 2 Where terms are as defined above,Q and C r nS Eq. 1-50 n H H Where Q terms= areflow, as ftdefined3/sec above, and Where terms are as defined above, 3and When a circular Q pipe =is runningflow,Where ftfull/sec terms or half-full, are as defined above, and Q = flow, ft3/sec When a circular pipe is runningQ = flow, ftfull3/sec or half-full, d' D When a circular pipe is running full or half-full,r I When a circularH pipe is running full or half-full, Eq. 1-51 31 4 48d' DI (2-34) rH = = Eq. 1-51 d' DI 4 48 where rH Eq. 1-51 It is convenient to combine the 4Manning48 equation with d’ where= pipe inside diameter, ft where 31 DI =d’ pipe= insidepipe WHinside diameter,ERE diameter, in ft d’ = pipe inside diameter, ft Q ACV Eq. 1-49 d’ = DIpipe 3 = insidepipe diameter, inside diameter, ft in Full pipe flow in ft per secondD mayI = pipe beinside estimated diameter, in using: It is convenient DI To =obtain to combinepipe inside3 the diameter, Manning equationin with Full pipe 3flow in ft per second may be estimated using: Full pipe flow in ft3 per second may 8be/ 3 estimated1/ 2 using: Full pipe flow in ft per second may be estimated using:D S Q 6.136u10 4 I (2-35)FPS 1.486 AC 28//33 11/ 2/ 2 Eq. 1-52 Q QAC V −4n rDH I SSH Eq. 1-49 Eq. 1-50 = ×8 / 3 1/ 2 QFPS (6.136D 10n S ) Eq. 1-52 To obtain Q 6.136u104 I n Eq. 1-52 Full pipe Whereflow in gallonsterms are per as minuteFPS defined may above, be estimated and n using: Full pipe flow in gallons per minute may be estimated using: Full pipe flow in gallons per minute3 may be estimated using: Q = flow,(2-36) ft1./sec486 A 2 /83/3 11/ 2/ 2 Full pipe flow in gallons per minuteQ may be estimatedC rD SS using: Eq. 1-50 H I H When a circular pipe is runningQ' n0 .275full or half-full,8/ 3 1/ 2 Eq. 1-53 n DI S =8/3 1/ 2 Where terms are as defined above, and QD' 0.275S Eq. 1-53 Q' 0.275 I n Eq. 1-53 Nearly full circular pipes will3 carryNearly more full circular liquid pipesthan willad completely' carryDI more liquid full pipe.than a completelyWhen slightly full pipe. When Q = flow, ft /sec n rH Eq. 1-51 less thanNearly full, full the circular hydraulic pipes radius slightlywill carry isless significantly thanmore full, liquid the perimeter reduced,than4 48a completelywetted but theby flow actual full is reduced,pipe. flow When areabut the isslightlyactual flow Whenonly a slightly circular lessened. pipe is running Maximum full or flow half-full, is achieved at about 93% of full pipe flow, and Nearly fullless circular than full,pipeswhere the will hydraulic carryarea more is radius only liquid slightly is than significantly lessened. a completely This reduced, results full in pipe. a butlarger the Whenhydraulic actual slightly radius flow than area when is lessmaximum thanonly full, velocity slightly the hydraulic lessened.at about radius 78% Maximumthe of ispipe fullsignificantly is piperunning flow flow. is full. achieved reduced, Maximum at butflow about the is achieved actual 93% ofat flow about full area pipe93% of is flow,full pipe and flow, only slightlymaximum lessened. velocityd’ Maximum at= aboutpipeand flow 78% maximum inside is of achieved fulldiameter,d velocity' pipeDI atflow. ftabout about 78% 93% of full of pipe full flow. pipe Manning’s flow, and n is often assumed rH Eq. 1-51 maximum velocity at aboutDI =78% pipeofto befull insideconstant pipe flow.diameter, 4with flow48 depth.in Actually, n has been found to be slightly larger in 3 non-full flow. where Full pipe flow in ft per second may be estimated using: Table 1-15: Values of n for Use with Manning Equation d’ = pipe inside diameter, ft 8 / 3n, typical1/ 2 Table 1-15:Ta B ValueslE 2-11 of n for Use withD ManningS Equation DI = pipe inside diameter,Surface in 4 I Table 1-15: ValuesValues of of n n forforQ UseFPS Use with Manning with6.136 EquationManningu10 Equationdesignn, typical Eq. 1-52 Surface n 3 Polyethylene pipe n, typical0.009 design Full pipe flow in ft per secondSurface may be estimatedSurface using: n, typical design Uncoated cast Polyethyleneor ductile iron pipe pipe design0.013 0.009 Full pipe flow in gallonsCorrugated per steel minutePE pipe pipe may be estimated 0.009using:0.024 PolyethyleneUncoatedUncoated cast pipe cast or or ductile ductile iron iron pipe8 /pipe3 1 / 2 0.0090.013 0.013 Concrete pipe 4 DI S 0.013 Uncoated castQ orCorrugated ductileCorrugated6.136 ironu steel steel 10pipe pipe pipe 0.0130.024 0.024 VitrifiedFPS clay pipe 8/3 1/ 2 0.013 Eq. 1-52 Corrugated steelConcrete Concretepipe pipe n DI S 0.0240.013 0.013 Brick and cement mortar sewersQ' 0 .275 0.015 Eq. 1-53 ConcreteVitrified pipeVitrified clay clay pipepipe n 0.0130.013 0.013 Full pipe flow in gallons perVitrified minuteBrick Brickandclay may and cementpipe cement be estimated mortarmortar sewers sewers using: 0.0130.015 0.015 Nearly fullBrick circular and cement pipes mortarwill carryWood sewers stave more liquid than a0.015 0.011completely full pipe. When slightly Rubble masonry8/3 1/ 2 0.021 less than full, the hydraulic radiusD I is significantlyS reduced, but the actual flow area is Note:Q The' n-value0.275 of 0.009 for PE pipe is for clear water applications. Eq. 1-53 only slightly lessened.An n-value Maximum of 0.010 is flowtypicallyn is utilized achieved for applications at such about as sanitary 93% sewer, of etc. full pipe flow, and maximum velocity at about 78% of full pipe flow. Nearly full circular pipes will carry more liquid than a completely full pipe. When slightly less than full, the hydraulic radius is significantly reduced, but the actual flow area is only slightly lessened. Maximum flow is achieved at about 93% of full pipe flow, and maximum velocity at aboutTable 78% 1-15:of full Valuespipe flow. of n for Use with Manning Equation 154-264.indd 187 n, typical 1/16/09 9:57:02 AM Surface design Polyethylene pipe 0.009 Table 1-15: ValuesUncoated of n forcast Use or ductile with iron Manning pipe Equation 0.013 Corrugated steel pipe 0.024 n, typical Surface Concrete pipe 0.013 design Vitrified clay pipe 0.013 Polyethylene pipe 0.009 Brick and cement mortar sewers 0.015 Uncoated cast or ductile iron pipe 0.013 Corrugated steel pipe 0.024 Concrete pipe 0.013 Vitrified clay pipe 0.013 Brick and cement mortar sewers 0.015 32

188 Chapter 6 Design of PEWood Piping Systemsstave 0.011 Rubble masonry 0.021 Note: The n-value of 0.009 for polyethylene pipe is for clear water applications. An n-value of 0.010 is typically utilized for applications such as sanitary sewer, etc.

Comparative Flows for SliplinersComparative Flows for Slipliners Deteriorated gravity flow pipes may be rehabilitated by sliplining with PE pipe. This Deteriorated gravity flowprocess pipes involves may be the rehabilitated installation of aby PE slipliningliner inside withof the polyethylene deteriorated original pipe. pipe This process involves theas describedinstallation in subsequent of a polyethylene chapters within liner this insidemanual. ofFor the conventional deteriorated sliplining, original pipe as describedclearance in subsequent between the chaptersliner outside within diameter this and manual. the existing For pipe conventional bore is required sliplining, clearance betweento install the the liner; liner thus outside after rehabilitation, diameter and the flow the channel existing is smaller pipe borethan that is of required to install the liner;the originalthus after pipe. rehabilitation,However, it is often the possible flow channelto rehabilitate is smaller with a PE than slipliner, the and original pipe. However, regain it is oftenall or most possible of the original to rehabilitate flow capacity with due a to polyethylene the extremely smooth slipliner, inside and regain all or most ofsurface the originalof the PE pipeflow and capacity its resistance due toto deposition the extremely or build-up. smooth Because inside PE pipe surface of the polyethyleneis mostly joined pipe by and means its of butt-fusion, resistance this toresults deposition in no effective or reduction build-up. of Comparative flow capacitiesflow ofdiameter circular at joint pipes locations may beComparative determined flow bycapacities the following: of circular pipes may be determined by the following: (2-37)  D 8 / 3   I 1    Q  n1  % flow = 100 1 = 100 Eq. 1-54 8 / 3 Q2  D   I 2     n2 

Table 2-12 was developed using Equation 2-36 where DI1 = the inside diameter (ID) Table 1-16 was developed using Equation 1-54 where DI1 = the inside diameter (ID) of of the liner, and DI2 = the original inside diameter of the deteriorated host pipe. the liner, and DI2 = the original inside diameter of the deteriorated host pipe.

Table 1-16: Comparative Flows for Slipliners Liner DR 32.5 Liner DR 26 Liner DR 21 Liner DR 17 Existin Line % flow % % flow % % flow % % flow % g r Line Line Line Line vs. flow vs. flow vs. flow vs. flow Sewer OD, r ID, r ID, r ID, r ID, concre vs. concre vs. concre vs. concre vs. ID, in in. in.† in.† in.† in.† te clay te clay te clay te clay 3.50 3.27 84.5 3.21 80.6 3.14 76.2 3.06 70.9 4 97.5% 93.0% 87.9% 81.8% 0 2 % 5 % 7 % 4 % 4.50 4.20 56.0 4.13 53.5 4.04 50.5 3.93 47.0 6 64.6% 61.7% 58.3% 54.3% 0 6 % 3 % 6 % 9 % 5.37 5.02 90.0 4.93 85.9 4.83 81.1 4.70 75.5 6 103.8% 99.1% 93.6% 87.1% 5 4 % 7 % 2 % 5 % 6.62 6.19 73.0 6.08 69.6 5.95 65.8 5.79 61.2 8 84.2% 80.3% 75.9% 70.7% 5 3 % 5 % 6 % 9 % 7.12 6.66 88.6 6.54 84.5 6.40 79.9 6.23 74.4 8 102.2% 97.5% 92.1% 85.8% 5 0 % 4 % 6 % 6 % 8.62 8.06 81.3 7.92 77.6 7.75 73.3 7.54 68.3 10 93.8% 89.5% 84.6% 78.8% 5 2 % 2 % 4 % 9 % 10.7 10.0 90.0 9.87 85.9 9.66 81.1 9.40 75.5 12 103.8% 99.1% 93.6% 87.1% 50 49 % 3 % 5 % 9 % 12.7 11.9 78.2 11.7 74.6 11.4 70.5 11.1 65.6 15 90.3% 86.1% 81.4% 75.7% 50 18 % 10 % 63 % 60 %

154-264.indd 188 1/16/09 9:57:02 AM Chapter 6 189 Design of PE Piping Systems

Ta BlE 2-12 Comparative Flows for Slipliners

Liner DR 32.5 Liner DR 26 Liner DR 21 Liner DR 17 Existing Liner % flow % flow % flow % flow Liner ID, % flow Liner ID, % flow Liner ID, % flow Liner ID, % flow vs. vs. vs. vs. Sewer OD, in.† vs. clay in.† vs. clay in.† vs. clay in.† vs. clay ID, in in. concrete concrete concrete concrete 4 3.500 3.272 97.5% 84.5% 3.215 93.0% 80.6% 3.147 87.9% 76.2% 3.064 81.8% 70.9% 6 4.500 4.206 64.6% 56.0% 4.133 61.7% 53.5% 4.046 58.3% 50.5% 3.939 54.3% 47.0% 6 5.375 5.024 103.8% 90.0% 4.937 99.1% 85.9% 4.832 93.6% 81.1% 4.705 87.1% 75.5% 8 6.625 6.193 84.2% 73.0% 6.085 80.3% 69.6% 5.956 75.9% 65.8% 5.799 70.7% 61.2% 8 7.125 6.660 102.2% 88.6% 6.544 97.5% 84.5% 6.406 92.1% 79.9% 6.236 85.8% 74.4% 10 8.625 8.062 93.8% 81.3% 7.922 89.5% 77.6% 7.754 84.6% 73.3% 7.549 78.8% 68.3% 12 10.750 10.049 103.8% 90.0% 9.873 99.1% 85.9% 9.665 93.6% 81.1% 9.409 87.1% 75.5% 15 12.750 11.918 90.3% 78.2% 11.710 86.1% 74.6% 11.463 81.4% 70.5% 11.160 75.7% 65.6% 15 13.375 12.503 102.5% 88.9% 12.284 97.8% 84.8% 12.025 92.4% 80.1% 11.707 86.1% 74.6% 16 14.000 13.087 97.5% 84.5% 2.858 93.0% 80.6% 12.587 87.9% 76.2% 12.254 81.8% 70.9% 18 16.000 14.956 101.7% 88.1% 14.695 97.0% 84.1% 14.385 91.7% 79.4% 14.005 85.3% 74.0% 21 18.000 16.826 92.3% 80.0% 16.532 88.1% 76.3% 16.183 83.2% 72.1% 15.755 77.5% 67.1% 24 20.000 18.695 85.6% 74.2% 18.369 81.7% 70.8% 17.981 77.2% 66.9% 17.506 71.9% 62.3% 24 22.000 20.565 110.4% 95.7% 20.206 105.3% 91.3% 19.779 99.5% 86.2% 19.256 92.6% 80.3% 27 24.000 22.434 101.7% 88.1% 22.043 97.0% 84.1% 21.577 91.7% 79.4% 21.007 85.3% 74.0% 30 28.000 26.174 115.8% 100.4% 25.717 110.5% 95.8% 25.173 104.4% 90.5% 24.508 97.2% 84.2% 33 30.000 28.043 108.0% 93.6% 27.554 103.0% 89.3% 26.971 97.3% 84.3% 26.259 90.6% 78.5% 36 32.000 29.913 101.7% 88.1% 29.391 97.0% 84.1% 28.770 91.7% 79.4% 28.009 85.3% 74.0% 36 34.000 31.782 119.5% 103.6% 31.228 114.1% 98.9% 30.568 107.7% 93.4% 29.760 100.3% 86.9% 42 36.000 33.652 92.3% 80.0% 33.065 88.1% 76.3% 32.366 83.2% 72.1% 31.511 77.5% 67.1% 48 42.000 39.260 97.5% 84.5% 38.575 93.0% 80.6% 37.760 87.9% 76.2% 36.762 81.8% 70.9% 54 48.000 44.869 101.7% 88.1% 44.086 97.0% 84.1% 43.154 91.7% 79.4% 42.014 85.3% 74.0% 60 54.000 50.478 105.1% 91.1% 49.597 100.3% 86.9% 48.549 94.8% 82.1% 47.266 88.2% 76.5%

† Liner ID calculated per Equation 2-1.

Flow Velocity Acceptable flow velocities in PE pipe depend on the specific details of the system. For water systems operating at rated pressures, velocities may be limited by surge allowance requirements. See Tables 1-3A and 1-3B. Where surge effects are reduced, higher velocities are acceptable, and if surge is not possible, such as in many gravity flow systems, water flow velocities exceeding 25 feet per second may be acceptable.

Liquid flow velocity may be limited by the capabilities of pumps or elevation head to overcome friction (head) loss and deliver the flow and pressure required for the application. PE pipe is not eroded by water flow. Liquid slurry pipelines may be subject to critical minimum velocities that ensure turbulent flow and maintain particle suspension in the slurry.

Gravity liquid flows of 2 fps (0.6 m/s) and higher can help prevent or reduce solids deposition in sewer lines. When running full, gravity flow pipelines are subject to the same velocity considerations as pressure pipelines.

154-264.indd 189 1/16/09 9:57:02 AM 190 Chapter 6 Design of PE Piping Systems

Flow velocity in compressible gas lines tends to be self-limiting. Compressible gas flows in PE pipes are typically laminar or transitional. Fully turbulent flows are possible in short pipelines, but difficult to achieve in longer transmission and distribution lines because the pressure ratings for PE pipe automatically limit flow capacity and, therefore, flow velocity.

Pipe Surface Condition, aging Aging acts to increase pipe surface roughness in most piping systems. This in turn increases flow resistance. PE pipe resists typical aging effects because PE does not rust, rot, corrode, tuberculate, or support biological growth, and it resists the adherence of scale and deposits. In some cases, moderate flow velocities are sufficient to prevent deposition, and where low velocities predominate, occasional high velocity flows will help to remove sediment and deposits. As a result, the initial design capabilities for pressure and gravity flow pipelines are retained as the pipeline ages.

Where cleaning is needed to remove depositions in low flow rate gravity flow pipelines, water-jet cleaning or forcing a “soft” (plastic foam) pig through the pipeline are effective cleaning methods. Bucket, wire and scraper-type cleaning methods will damage PE pipe and must not be used.

154-264.indd 190 1/16/09 9:57:02 AM Chapter 6 191 Design of PE Piping Systems

Section 3 Buried PE Pipe Design

Introduction This section covers basic engineering information for calculating earth and live-load pressures on PE pipe, for finding the pipe’s response to these pressures taking into account the interaction between the pipe and its surrounding soil, and for judging that an adequate safety factor exists for a given application.

Soil pressure results from the combination of soil weight and surface loads. As backfill is placed around and over a PE pipe, the soil pressure increases and the pipe deflects vertically and expands laterally into the surrounding soil. The lateral expansion mobilizes passive resistance in the soil which, in combination with the pipe’s inherent stiffness, resists further lateral expansion and consequently further vertical deflection.

During backfilling, ring (or hoop) stress develops within the pipe wall. Ring bending stresses (tensile and compressive) occur as a consequence of deflection, and ring compressive stress occurs as a consequence of the compressive thrust created by soil compression around the pipe’s circumference. Except for shallow pipe subject to live load, the combined ring stress from bending and compression results in a net compressive stress.

The magnitude of the deflection and the stress depends not only on the pipe’s properties but also on the properties of the surrounding soil. The magnitude of deflection and stress must be kept safely within PE pipe’s performance limits. Excessive deflection may cause loss of stability and flow restriction, while excessive compressive stress may cause wall crushing or ring buckling. Performance limits for PE pipe are given in Watkins, Szpak, and Allman(1) and illustrated in Figure 3-1.

The design and construction requirements can vary somewhat, depending on whether the installation is for pressure or non-pressure service. These differences will be addressed later in this chapter and in Chapter 7, “Underground Installation of PE Pipe.”

154-264.indd 191 1/16/09 9:57:02 AM 192 Chapter 6 Design of PE Piping Systems

Calculations Section 3 describes how to calculate the soil pressure acting on PE pipe due to soil weight and surface loads, how to determine the resulting deflection based on pipe and soil properties, and how to calculate the allowable (safe) soil pressure for wall compression (crushing) and ring buckling for PE pipe.

Detailed calculations are not always necessary to determine the suitability of a particular PE pipe for an application. Pressure pipes that fall within the Design Window given in AWWA M-55 “PE Pipe – Design and Installation” regarding pipe DR, installation, and burial depth meet specified deflection limits for PE pipe, have a safety factor of at least 2 against buckling, and do not exceed the allowable material compressive stress for PE. Thus, the designer need not perform extensive calculations for pipes that are sized and installed in accordance with the Design Window.

AWWA M-55 Design Window AWWA M-55, “PE Pipe – Design and Installation”, describes a Design Window. Applications that fall within this window require no calculations other than constrained buckling per Equation 3-15. It turns out that if pipe is limited to DR 21 or lower as in Table 3-1, the constrained buckling calculation has a safety factor of at least 2, and no calculations are required.

The design protocol under these circumstances (those that fall within the AWWA Design Window) is thereby greatly simplified. The designer may choose to proceed with detailed analysis of the burial design and utilize the AWWA Design Window guidelines as a means of validation for his design calculations and commensurate safety factors. Alternatively, he may proceed with confidence that the burial design for these circumstances (those outlined within the AWWA Design Window) has already been analyzed in accordance with the guidelines presented in this chapter.

The Design Window specifications are:

• Pipe made from stress-rated PE material. • Essentially no dead surface load imposed over the pipe, no ground water above the surface, and provisions for preventing flotation of shallow cover pipe have been provided. • The embedment materials are coarse-grained, compacted to at least 85% Standard Proctor Density and have an E’ of at least 1000 psi. The native soil must be stable; in other words the native soil must have an E’ of at least 1000 psi. See Table 3-7. • The unit weight of the native soil does not exceed 120 pcf. • The pipe is installed in accordance with manufacturer’s recommendations for controlling shear and bending loads and minimum bending radius, and installed

154-264.indd 192 1/16/09 9:57:02 AM Chapter 6 193 Design of PE Piping Systems

in accordance with ASTM D2774 for pressure pipes or ASTM D2321 for non- pressure pipes. • Minimum depth of cover is 2 ft (0.61 m); except when subject to AASHTO H20 truck loadings, in which case the minimum depth of cover is the greater of 3 ft (0.9 m) or one pipe diameter. • Maximum depth of cover is 25 ft (7.62 m).

Ta BlE 3-1 AWWA M-55 Design Window Maximum and Minimum Depth of Cover Requiring No Calculations

Min. Depth of Min. Depth of Maximum DR Cover With H20 Cover Without Depth of Cover Load H20 Load 7.3 3 ft 2 ft 25 ft 9 3 ft 2 ft 25 ft 11 3 ft 2 ft 25 ft 13.5 3 ft 2 ft 25 ft 17 3 ft 2 ft 25 ft 21 3 ft 2 ft 25 ft

* Limiting depths where no calculations are required. Pipes are suitable for deeper depth provided a sufficient E’ (1,000 psi or more) is accomplished during installations. Calculations would be required for depth greater than 25 ft.

Installation Categories For the purpose of calculation, buried installations of PE pipe can be separated into four categories depending on the depth of cover, surface loading, groundwater level and pipe diameter. Each category involves slightly different equations for determining the load on the pipe and the pipe’s response to the load. The boundaries between the categories are not definite, and engineering judgment is required to select the most appropriate category for a specific installation. The categories are:

1. Standard Installation-Trench or Embankment installation with a maximum cover of 50 ft with or without traffic, rail, or surcharge loading. To be in this category, where live loads are present the pipe must have a minimum cover of at least one diameter or 18” whichever is greater. Earth pressure applied to the pipe is found using the prism load (geostatic soil stress). The ModifiedIowa Formula is used for calculating deflection. Crush and buckling are performance limits as well. The Standard Installation section also presents the AWWA “Design Window.”

2. Shallow Cover Vehicular loading Installation applies to pipes buried at a depth of at least 18” but less than one pipe diameter. This installation category

154-264.indd 193 1/16/09 9:57:03 AM 194 Chapter 6 Design of PE Piping Systems

uses the same equations as the Standard Installation but with an additional equation relating wheel load to the pipe’s bending resistance and the soil’s supporting strength.

3. Deep Fill Installation applies to embankments with depths exceeding 50 ft. The soil pressure calculation may be used for profile pipe in trenches less than 50 ft. The Deep Fill Installation equations differ from the Standard Installation equations by considering soil pressure based on armored, calculating deflection from the Watkins-Gaube Graph, and calculating buckling with the Moore-Selig Equation.

4. Shallow Cover Flotation Effects applies to applications where insufficient cover is available to either prevent flotation or hydrostatic collapse. Hydrostatic buckling is introduced in this chapter because of its use in subsurface design.

Section 3 of the Design Chapter is limited to the design of PE pipes buried in trenches or embankments. The load and pipe reaction calculations presented may not apply to pipes installed using trenchless technologies such as pipe bursting and directional drilling. These pipes may not develop the same soil support as pipe installed in a trench. The purveyor of the trenchless technology should be consulted for piping design information. See the Chapter on “PE Pipe for Horizontal Directional Drilling” and ASTM F1962, Use of Maxi-Horizontal Directional Drilling (HDD) for Placement of Polyethylene Pipe or Conduit Under Obstacles, Including River Crossings for additional information on design of piping installed using directional

drilling. 37

Figu re 2- 1. Perf orm ance Limi ts for Buri ed PE Pipe Figure 3-1 Performance Limits for Buried PE Pipe Design Process

The interaction between pipe and soil, the variety of field-site soil conditions, and the Designrange of Process available pipe Dimension Ratios make the design of buried pipe seem challenging. This section of the Design Chapter has been written with the intent of Theeasing interaction the designer’s between task. While pipe some and very soil, sophisticated the variety design of approachesfield-site for soil conditions, and buried pipe systems may be justified in certain applications, the simpler, empirical themethodologies range of presentedavailable herein pipe have Dimension been proven Ratios by experience make to the provide design reliable of buried pipe seem challenging.results for virtually This all PE section pipe installations. of the Design Chapter has been written with the intent ofThe easing design processthe designer’s consists of the task. following While steps: some very sophisticated design approaches for

1) Determine the vertical soil pressure acting at the crown of the pipe due to earth, live, and surcharge loads.

2) Select a trial pipe, which means selecting a trial dimension ratio (DR) or, in the case of profile pipe, a trial profile as well.

3) Select an embedment material and degree of compaction. As will be described 154-264.indd 194 later, soil type and compaction are relatable to a specific modulus of soil 1/16/09 9:57:03 AM reaction value (E’). (As deflection is proportional to the combination of pipe and soil stiffness, pipe properties and embedment stiffness can be traded off to obtain an optimum design.)

4) For the trial pipe and trial modulus of soil reaction, calculate the deflection due to the vertical soil pressure. Compare the pipe deflection to the deflection limit. If deflection exceeds the limit, it is generally best to look at increasing the modulus Chapter 6 195 Design of PE Piping Systems

buried pipe systems may be justified in certain applications, the simpler, empirical methodologies presented herein have been proven by experience to provide reliable results for virtually all PE pipe installations.

The design process consists of the following steps:

1. Determine the vertical soil pressure acting at the crown of the pipe due to earth, live, and surcharge loads.

2. Select a trial pipe, which means selecting a trial dimension ratio (DR) or, in the case of profile pipe, a trial profile.

3. Select an embedment material and degree of compaction. As will be described later, soil type and compaction are relatable to a specific modulus of soil reaction value (E’) (Table 3-8). (As deflection is proportional to the combination of pipe and soil stiffness, pipe properties and embedment stiffness can be traded off to obtain an optimum design.)

4. For the trial pipe and trial modulus of soil reaction, calculate the deflection due to the vertical soil pressure. Compare the pipe deflection to the deflection limit. If deflection exceeds the limit, it is generally best to look at increasing the modulus of soil reaction rather than reducing the DR or changing to a heavier profile. Repeat step 4 for the new E’ and/or new trial pipe.

5. For the trial pipe and trial modulus of soil reaction, calculate the allowable soil pressure for wall crushing and for wall buckling. Compare the allowable soil pressure to the applied vertical pressure. If the allowable pressure is equal to or higher than the applied vertical pressure, the design is complete. If not, select a different pipe DR or heavier profile or different E’, and repeat step 5.

Since design begins with calculating vertical soil pressure, it seems appropriate to discuss the different methods for finding the vertical soil pressure on a buried pipe before discussing the pipe’s response to load within the four installation categories.

Earth, live, and Surcharge loads on Buried Pipe

Vertical Soil Pressure The weight of the earth, as well as surface loads above the pipe, produce soil pressure on the pipe. The weight of the earth or “earth load” is often considered to be a “dead-load” whereas surface loads are referred to as “surcharge loads” and may be temporary or permanent. When surcharge loads are of short duration they are usually referred to as “live loads.” The most common live load is vehicular load. Other common surcharge loads include light structures, equipment, and piles of stored materials or debris. This section gives formulas for calculating the vertical

154-264.indd 195 1/16/09 9:57:03 AM 196 Chapter 6 Design of PE Piping Systems

soil pressure due to both earth and surcharge loads. The soil pressures are normally calculated at the depth of the pipe crown. The soil pressures for earth load and each surcharge load are added together to obtain the total vertical soil pressure which is then used for calculating deflection and for comparison with wall crush and wall buckling performance limits.

Earth Load In a uniform, homogeneous soil mass, the soil load acting on a horizontal plane within the mass is equal to the weight of the soil directly above the plane. If the mass contains areas of varying stiffness, the weight of the mass will redistribute itself toward the stiffer areas due to internal shear resistance, and arching will occur. Arching results in a reduction in load on the less stiff areas. Flexible pipes including PE pipes are normally not as stiff as the surrounding soil, so the resulting earth pressure acting on PE pipe is reduced by arching and is less than the weight of soil above the pipe. (One minor exception to this is shallow cover pipe under dynamic loads.) For simplicity, engineers often ignore arching and assume that the earth load on the pipe is equal to the weight of soil above the pipe, which is referred to as the “prism load” or “geostatic stress.” Practically speaking, the prism load is a conservative loading for PE pipes. It may be safely used in virtually all designs. Equation 3-1 gives the vertical soil pressure due to the prism load. The depth of cover is the depth from the ground surface to the pipe crown. (3-1) PE = wH

WHERE PE = vertical soil pressure due to earth load, psf w = unit weight of soil, pcf H = depth of cover, ft

UNITS CONVENTION: To facilitate calculations for PE pipes, the convention used with rigid pipes for taking the load on the pipe as a line load along the longitudinal axis in units of lbs/lineal-ft of pipe length is not used here. Rather, the load is treated as a soil pressure acting on a horizontal plane at the pipe crown and is given in units of lbs/ft 2 or psf.

Soil weight can vary substantially from site to site and within a site depending on composition, density and load history. Soil weights are often found in the construction site geotechnical report. The saturated unit weight of the soil is used when the pipe is below the groundwater level. For design purposes, the unit weight of dry soil is commonly assumed to be 120 pcf, when site-specific information is not available.

154-264.indd 196 1/16/09 9:57:03 AM Chapter 6 197 Design of PE Piping Systems

Generally, the soil pressure on profile pipe and on DR pipe in deep fills is significantly less than the prism load due to arching. For these applications, soil pressure is best calculated using the calculations that account for arching40 in the “Deep Fill Installation” section.

FigureFigure 3-2 Prism 2-2. Load Prism Load

Live Load Live Load Even though wheel loadings from cars and other light vehicles may be frequent, these loads generally have little impact on subsurface piping compared to the less frequent but significantly heavier loads from trucks, trains, or other heavy vehicles. Even though wheel loadings from cars and other light vehicles may be frequent, these For design of pipes under streets and highways, only the loadings from these heavier loads generally have little impact on subsurface piping compared to the less frequent vehicles are considered. The pressure transmitted to a pipe by a vehicle depends but significantly heavier loads from trucks, trains, or other heavy vehicles. For design of on the pipe’s depth, the vehicle’s weight, the tire pressure and size, vehicle speed, pipes under streets and highways, then, only the loadings from these heavier vehicles surface smoothness, the amount and type of paving, the soil, and the distance from are considered. The pressure transmitted to a pipe by a vehicle depends on the pipe’s the pipe to the point of loading. For the more common cases, such as AASHTO, H20 depth, the vehicle's weight, the tire pressure and size, vehicle speed, surface HS20 truck traffic on paved roads and E-80 rail loading, this information has been smoothness, the amount and type of paving, the soil, and the distance from the pipe to simplified and put into Table 3-3, 3-4, and 3-5 to aid the designer. For special cases, the point of loading. For the more common cases, such as H20 (HS20) truck traffic on such as mine trucks, cranes, or off-road vehicles, Equations 3-2 and 3-4 may be used. paved roads and E-80 rail loading, this information has been simplified and put into Tables 2-2, 2-3, and 2-4 toThe aid maximum the designer. load under For a wheel special occurs cases, at the surfacesuch asand mine diminishes trucks, with depth. cranes, or off-road vehicles,PE Equati pipes shouldons 2-2 be andinstalled 2-4 amay minimum be used. of one diameter or 18”, whichever is greater, beneath the road surface. At this depth, the pipe is far enough below the wheel load to significantly reduce soil pressure and the pipe can fully utilize the embedment The maximum load under a wheel occurs at the surface and diminishes with depth. soil for load resistance. Where design considerations do not permit installation with Polyethylene pipes should be installed a minimum of one diameter or 18”, whichever is greater, beneath the road surface. At this depth, the pipe is far enough below the wheel load to significantly reduce soil pressure and the pipe can fully utilize the embedment soil for load resistance. Where design considerations do not permit installation with at least one diameter of cover, additional calculations are required and are given in the section discussing154-264.indd "Shallow 197 Cover Vehicular Loading Installation." State highway 1/16/09 9:57:03 AM departments often regulate minimum cover depth and may require 2.5 ft to 5 ft of cover depending on the particular roadway.

During construction, both permanent and temporary underground pipelines may be subjected to heavy vehicle loading from construction equipment. It may be advisable to provide a designated vehicle crossing with special measures such as temporary 198 Chapter 6 Design of PE Piping Systems

at least one diameter of cover, additional calculations are required and are given in the section discussing “Shallow Cover Vehicular Loading Installation.” State highway departments often regulate minimum cover depth and may require 2.5 ft to 5 ft of cover depending on the particular roadway.

During construction, both permanent and temporary underground pipelines may be subjected to heavy vehicle loading from construction equipment. It may be advisable to provide a designated vehicle crossing with special measures such as temporary pavement or concrete encasement, as well as vehicle speed controls to limit impact loads.

The following information on AASHTO Loading and Impact Factor is not needed to use Tables 3-3 and 3-4. It is included to give the designer an understanding of the surface loads encountered and typical impact factors. If the designer decides to use Equations 3-2 or 3-4 rather than the tables, the information will be useful.

AASHTO Vehicular Loading Vehicular loads are typically based on The American Association of State Highway and Transportation Officials AASHTO)( standard truck loadings. For calculating the soil pressure on flexible pipe, the loading is normally assumed to be an H20 (HS20) truck. A standard H20 truck has a total weight of 40,000 lbs (20 tons). The weight is distributed with 8,000 lbs on the front axle and 32,000 lbs on the rear axle. The HS20 truck is a tractor and trailer unit having the same axle loadings as the H20 truck but with two rear axles. See Figure 3-3. For these trucks, the maximum wheel load is found at the rear axle(s) and equals 40 percent of the total weight of the truck. The maximum wheel load may be used to represent the static load applied by either a single axle or tandem axles. Some states permit heavier loads. The heaviest tandem axle loads normally encountered on highways are around 40,000 lbs (20,000 lbs per wheel). Occasionally, vehicles may be permitted with loads up to 50 percent higher.

154-264.indd 198 1/16/09 9:57:03 AM Chapter 6 199 Design of PE Piping Systems

4242

AASHTOAASHTOAASHTO H20 H20 WheelH20 Wheel Wheel Load Load Load AASHTOAASHTOAASHTO HS20HS20 HS20 Wheel Wheel Wheel Load Load Load

Figure 3-3 AASHTO H20 and HS20 Vehicle Loads

FigureFigure 2-3. 2-3. AASHTO AASHTO H20 H20 & &HS20 HS20 Vehicle Vehicle Loads Loads Impact Factor Road surfaces are rarely smooth or perfectly even. When vehicles strike bumps in the road, the impact causes an instantaneous increase in wheel loading. Impact load Impact Factor Impactmay Factor be found by multiplying the static wheel load by an impact factor. The factor varies with depth. Table 3-2 gives impact factors for vehicles on paved roads. For RoadRoad surfaces surfaces are are rarely rarely smooth smooth or orperfectly perfectly even. even. When When vehicles vehicles strike strike bumps bumps in in the the road,unpaved the impact roads, causes impact an factors instantaneous of 2.0 or higher incr easemay occur, in wheel depending loading. on Impact the road load may road, thesurface. impact causes an instantaneous increase in wheel loading. Impact load may be befound found by bymultiplying multiplying the the static static wheel wheel load load by by an an impact impact factor. factor. The The factor factor varies varies with with depth.depth. Table Table 2-1 2-1 gives gives impact impact factors factors for for vehicles vehicles on on paved paved roads. roads. For For unpaved unpaved roads, roads, impact factors of 2.0 or higher may occur, depending on the road surface. impactTa factorsBlE 3 -2of 2.0 or higher may occur, depending on the road surface. Typical Impact Factors for Paved Roads

Cover Depth, ft Impact Factor, If 1 Table1.35 2-1: Typical Impact Factors for Paved Roads Table 2-1: Typical Impact Factors for Paved Roads 2 1.30 3 1.25Cover Depth, ft Impact Factor, If 4 1.20Cover Depth, ft Impact Factor, If

6 1.10 1 1.35 8 1.00 1 1.35

Derived from Illinois DOT dynamic load2 formula (1996). 1.30 2 1.30

3 1.25 Vehicle Loading through Highway3 Pavement (Rigid) 1.25

Pavement reduces the live load4 pressure reaching a pipe.1.20 A stiff, rigid pavement 4 1.20 spreads load out over a large subgrade area thus significantly reducing the vertical 6 1.10 6 1.10

154-264.indd 199 1/16/09 9:57:04 AM 200 Chapter 6 Design of PE Piping Systems

soil pressure. Table 3-3 gives the vertical soil pressure underneath an H20 (HS20) truck traveling on a paved highway (12-inch thick concrete). An impact factor is incorporated. For use with heavier trucks, the pressures in Table 3-3 can be adjusted proportionally to the increased weight as long as the truck has the same tire area as an HS20 truck.

Ta BlE 3-3 Soil Pressure under H20 Load (12” Thick Pavement)

Depth of cover, ft. Soil Pressure, lb/ft2 1 1800 1.5 1400 2 800 3 600 4 400 5 250 6 200 7 175 8 100 Over 8 Neglect

Note: For reference see ASTM F7906. Based on axle load equally distributed over two 18 by 20 inch areas, spaced 72 inches apart. Impact factor included.

Vehicle loading through Flexible Pavement or Unpaved Surface Flexible pavements (or unpaved surfaces) do not have the bridging ability of rigid pavement and thus transmit more pressure through the soil to the pipe than given by Table 3-3. In many cases, the wheel loads from two vehicles passing combine to create a higher soil pressure than a single dual-tire wheel load. The maximum pressure may occur directly under the wheels of one vehicle or somewhere in between the wheels of the two vehicles depending on the cover depth. Table 3-4 gives the largest of the maximum pressure for two passing H20 trucks on an unpaved surface. No impact factor is included. The loading in Table 3-3 is conservative and about 10% higher than loads found by the method given in AASHTO Section 3, LRFD Bridge Specifications Manual based on assuming a single dual-tire contact area of 20 x 10 inches and using the equivalent area method of load distribution.

154-264.indd 200 1/16/09 9:57:04 AM Chapter 6 201 Design of PE Piping Systems

TaBlE 3-4 Soil Pressure Under H20 Load (Unpaved or Flexible Pavement)

Depth of cover, ft. Soil Pressure, lb/ft2 1.5 2000 2.0 1340 2.5 1000 3.0 710 3.5 560 4.0 500 6.0 310 8.0 200 10.0 140

Note: Based on integrating the Boussinesq equation for two H20 loads spaced 4 feet apart or one H20 load centered over pipe. No pavement effects or impact factor included.

Off-Highway Vehicles Off-highway vehicles such as mine trucks and construction equipment may be considerably heavier than H20 trucks. These vehicles frequently operate on unpaved construction or mine roads which may have very uneven surfaces. Thus, except for slow traffic, an impact factor of 2.0 to 3.0 should be considered. For off-highway vehicles, it is generally necessary to calculate live load pressure from information supplied by the vehicle manufacturer regarding the vehicle weight or wheel load, tire footprint (contact area) and wheel spacing.

The location of the vehicle’s wheels relative to the pipe is also an important factor in determining how much load is transmitted to the pipe. Soil pressure under a point load at the surface is dispersed through the soil in both depth and expanse. Wheel loads not located directly above a pipe may apply pressure to the pipe, and this pressure can be significant. The load from two wheels straddling a pipe may produce a higher pressure on a pipe than from a single wheel directly above it.

For pipe installed within a few feet of the surface, the maximum soil pressure will occur when a single wheel (single or dual tire) is directly over the pipe. For deeper pipes, the maximum case often occurs when vehicles traveling above the pipe pass within a few feet of each other while straddling the pipe, or in the case of off-highway vehicles when they have closely space axles. The minimum spacing between the centerlines of the wheel loads of passing vehicles is assumed to be four feet. At this spacing for H20 loading, the pressure on a pipe centered midway between the two passing vehicles is greater than a single wheel load on a pipe at or below a depth of about four feet.

For design, the soil pressure on the pipe is calculated based on the vehicle location (wheel load locations) relative to the pipe that produces the maximum pressure. This

154-264.indd 201 1/16/09 9:57:04 AM 46

46 3 I f W w§ H · PL = ¨ -1 ¸ Eq. 2-2 202 Chapter 6 a ¨ 2 2 1.5 ¸ Design of PE Piping Systems C © ( rT + H ) ¹

3 I f W w§ H · = ¨ -1 ¸ Eq. 2-2 PL ¨ 2 2 1.5 ¸ 46 aC © ( rT + H ) ¹Where: P = vertical soil pressure due to live load, lb/ft2 generally involves comparing the pressure Lunder a single wheel with that occurring with two wheels straddling the pipe. TheI Timoshenko = impact Equationfactor can be used to find Where:§ 3 · f I f W wthe pressureH directly under a single wheel load, whereas the Boussinesq Equation PL = ¨ -1 ¸ 2 Eq. 2-2 can¨ be usedP2L =to verticalfind2 1.5 the¸ soilpressure pressure from wheels Wduew = tonot wheel livedirectly load, load, above lb/ft lb the pipe. aC © ( rT + H ) ¹ 2 46 If = impact factor aC = contact area, ft Timoshenko’s Equation The TimoshenkoWw = wheel Equation load, gives lb the soil pressurerT = equivalent at a point directlyradius, under ft a Where: distributed surface load, neglecting2 any pavement. aC = contact area, ft H = depth of2 cover, ft PL(3-2) = vertical soil pressure due3 to live load, lb/ft I f W w§ H · PLr=T = equivalent ¨ -1 radius, ft¸ Eq. 2-2 I = impact factor¨ 2 2 1.5 ¸ f aC © ( rT + H ) ¹ H = depthThe equivalent of cover, ft radius is given by: Ww = wheel load, lb WHERE 2 2 a PL = vertical soil pressure due to live load, lb/ft C aC = contactWhere: area, ft rT = Eq. 2-3 The equivalentIf =radius impact factor is given by: S rT =W equivalent= wheel load, lb radius, ft 2 w PL = vertical soil pressure due to live load, lb/ft a = contact area, ft2 a H =C depth of cover, ft C I =r Timpact= factor Eq. 2-3 rT = equivalent radius,fFor ft standardS H2O and HS20 highway vehicle loading, the contact area is normally H = depth of cover, ft Wtakenw = wheel for dual load, wheels, lb that is, 16,000 lb over 10 in. by 20 in. area.

The equivalent radius is given by: 2 The equivalent radius a C is= given contact by: area, ft For standard H2O and HS20 highway vehicle loading, the contact area is normally (3-3) a taken for dual wheels, thatrCTTimoshenko is,= equivalent 16,000 lb Example overradius, 10 ft in.Calculation by 20 in. area. rT = Eq. 2-3 S HFind = depth the verticalof cover, pressure ft on a 24" polyethylene pipe buried 3 ft beneath an unpaved

Timoshenko ExampleFor standard Calculation H2Oroad and when HS20 highwayan R-50 vehicle truck loading, is over the the contact pipe. area The is normally manufacturer lists the truck with a gross For standard H2OThe equivalent and takenHS20 for radiushighway dual wheels,weight is givenvehicle that of by: is,183,540 loading, 16,000 lb over lbsthe on acontact 10 21X35in. by 20area E3in. area. istires, normally each having a 30,590 lb load over an imprint taken for Finddual thewheels, vertical that pressure is, 16,000area on lb a overof 24" 370 10polye in in.2. bythylene 20 in. pipe area. buried 3 ft beneath an unpaved Timoshenko Example Calculation road when an R-50 truck is over the pipe.aC The manufacturer lists the truck with a gross Find the verticalSOLUTION: pressurerT = on a 24” Use PE pipeEquations buried 3 ft2-2 beneath and an2-3. unpaved Since road the vehicleEq. is operating2-3 on an unpaved weight of 183,540 lbs on 21X35 E3 tires,S each having a 30,590 lb load over an imprint when2 an R-50 off-roadroad, truckan impact is over thefactor pipe. of The 2.0 manufacturer is appropriate. lists the truck with Timoshenkoarea Example of 370 in Calculation. a gross weight of 183,540 lbs on 21X35 E3 tires, each having a 30,590 lb load over an 2 Find the SOLUTION:vertical pressure Useimprint onEquations area a 24" of 370 polye 2-2in . andthylene 2-3. pipe Since buried the vehicle3 ft beneath is operating an unpaved on an unpaved For standard H2O and HS20 highway vehicle loading, the contact area is normally road whenroad, an R-50an impact truckSOLUTION: factoris over of Usethe 2.0 Equations pipe. is appropriate. The 3-2 andmanufacturer 3-3. Since370 /the 144 vehiclelists the is operatingtruck with on ana grossunpaved taken for dual wheels, that is, 16,000rT lb= over 10 in. =by 0.90ft 20 in. area. weight of 183,540 lbs onroad, 21X35 an impact E3 factor tires, of each2.0 is appropriate. having a 30,590S lb load over an imprint area of 370 in 2. 370 / 144 (2.0)(30,590)§ 33 · = ¨1- ¸ SOLUTION: TimoshenkoUse EquationsrT = Example 2-2 and Calculation 2-3.= 0.90ft Since theP L vehicle is operating on22 an unpaved1.5 47 S 370 © (0.90 + 3 ) ¹ road, an impact factor of 2.0 is appropriate. Find the vertical pressure on a 24" polyethylene144 pipe buried 3 ft beneath an unpaved § 3 · (2.0)(30,590)2 3 road whenP Lan= 2890lbR-50 truck / ft is¨1- over the pipe. ¸ The manufacturer lists the truck with a gross 370 © 221.5 ¹ weight of 183,540 lbs on 21X35(0.90 E3+ tires,3 ) each having a 30,590 lb load over an imprint 370 / 1442 144 arearT = of 370 in . = 0.90ft Boussinesq EquationS SOLUTION: Use Equations 2-2 and 2-3. Since the vehicle is operating on an unpaved 3 road,(2.0)(30,590) an impact factor§ of 2.03 is appropriate.· The BoussinesqP L = Equation¨1- gives22 the1.5 ¸ pressure at any point in a soil mass under a 154-264.indd 202370 © ( + ) ¹ 1/16/09 9:57:04 AM concentrated surface load.0.90 The 3Boussinesq Equation may be used to find the pressure 144 transmitted from a wheel load to a point that is not along the line of action of the load. Pavement effects are neglected.370 / 144 rT = = 0.90ft S

§ 3 · (2.0)(30,590) 3 3 P L = W3I ¨1-wf H 1.5 ¸ 370 © ( 22+ ) ¹ PL = 5 0.90 3 Eq. 2-4 144 2π r

Where: 2 PL = vertical soil pressure due to live load lb/ft

Ww = wheel load, lb H = vertical depth to pipe crown, ft

If = impact factor r = distance from the point of load application to pipe crown, ft

=r X + H 22 Eq. 2-5

47

2 P L = 2890lb / ft

Boussinesq Equation 47

The Boussinesq Equation gives the2 pressure at any point in a soil mass under a concentrated surface Pload.L = 2890lb The /Boussinesqft Equation may be used to find the pressure transmitted from a wheel load to a point that is not along the line of action of the load. Chapter 6 203 Pavement effects are neglected. Design of PE Piping Systems Boussinesq Equation

The Boussinesq Equation gives3 the pressure at any point in a soil mass under a W3I wf H concentrated surfaceP Lload.=Boussinesq The EquationBoussinesq Equation may be used to findEq. the 2-4 pressure 2S r5 transmitted from a wheelThe loadBoussinesq to a Equationpoint that gives is thenot pressure along atthe any line point of in action a soil mass of theunder load. a Pavement effects are neglected.concentrated surface load. The Boussinesq Equation may be used to find the pressure transmitted from a wheel load to a point that is not along the line of action of the Where: load. Pavement effects are neglected. 2 PL = vertical soil (3-4)pressure due to live3 load lb/ft W3I wf H P L = 5 Eq. 2-4 Ww = wheel load, lb 2S r H = vertical depth to pipe crown, ft WHERE 2 PL = vertical soil pressure due to live load lb/ft IWhere:f = impact factor Ww = wheel load, lb 2 r = distancePL = vertical fromH the= verticalsoil point pressure depth of to pipeload crown,due application ftto live load to pipelb/ft crown, ft If = impact factor Ww = wheelr = distance load, fromlb the point of load application to pipe crown, ft

(3-5) 22 4848 H = vertical depth=r Xto pipe+ H crown, ft Eq. 2-5 If = impact factor r = distance from the point of load application to pipe crown, ft

=r X + H 22 Eq. 2-5

Figure 3-4 Illustration of Boussinesq Point Loading FigureFigure 2-4: 2-4: Illustration Illustration of of Boussinesq Boussinesq Point Point Loading Loading

Example Using Boussinesq Point loading Technique ExampleExample Using Using Boussinesq Boussinesq Point Point Loading Loading Technique Technique Determine the vertical soil pressure applied to a 12” pipe located 4 ft deep under a dirt road when two vehicles traveling over the pipe and in opposite lanes pass each DetermineDetermine the the vertical vertical soil soil pressure pressure applied applied to to a a12" 12" pipe pipe located located 4 4ft ftdeep deep under under a adirt dirt other. Assume center lines of wheel loads are at a distance of 4 feet. Assume a wheel roadroad when when two two vehicles vehicles traveling traveling over over the the pipe pipe and and in in opposite opposite lanes lanes pass pass each each other. other. AssumeAssumeload centerof center 16,000 lines lines lb. of of wheel wheel loads loads are are at at a adistance distance of of 4 4feet. feet. Assume Assume a awheel wheel load load of of 16,00016,000 lb. lb.

SOLUTION:SOLUTION: Use Use Equation Equation 2-4, 2-4, and and since since the the wheels wheels are are traveling, traveling, a a2.0 2.0 impact impact factor factor isis applied. applied. The The maximum maximum load load will will be be at at the the center center between between the the two two wheels, wheels, so so X X= =2.0 2.0 ft.ft. Determine Determine r fromr from Equation Equation 2-5. 2-5.

4242 0.2 20.2 2 47.4 47.4 ft=+=r ft=+=r 154-264.indd 203 1/16/09 9:57:05 AM

ThenThen solve solve Equation Equation 2-4 2-4 for for P LP, Lthe, the load load due due to to a asingle single wheel. wheel.

)((( )((( 4000,16)0.23 4000,16)0.23 )3 )3 PLP=L = S(π( 47.42 47.42 )5 )5

2 2 PLPL 548548 /lb= /lb= ftft

TheThe load load on on the the pipe pipe crown crown is is from from both both wheels, wheels, so so 48

48

Figure 2-4: Illustration of Boussinesq Point Loading

Example Using BoussinesqFigure 2-4: Point Illustration Loading of Technique Boussinesq Point Loading

Determine the vertical soil pressure applied to a 12" pipe located 4 ft deep under a dirt Example Using Boussinesq Point Loading Technique road when two vehicles traveling over the pipe and in opposite lanes pass each other. Assume center lines of wheel loads are at a distance of 4 feet. Assume a wheel load of 16,000Determine lb. the vertical soil pressure applied to a 12" pipe located 4 ft deep under a dirt road when two vehicles204 Chapter traveling 6 over the pipe and in opposite lanes pass each other. Assume center lines Designof wheel of PE Piping loads Systems are at a distance of 4 feet. Assume a wheel load of SOLUTION: Use Equation 2-4, and since the wheels are traveling, a 2.0 impact factor 16,000 lb. is applied. The maximum load will be at the center between the two wheels, so X = 2.0 ft. Determine r from Equation 2-5. SOLUTION: Use Equation 2-4, and since the wheels are traveling, a 2.0 impact factor is applied. The maximum load will be at the center between the two wheels, so X = 2.0 ft. Determine r from Equation 2-5. SOLUTION:2 Use2 Equation 3-4, and since the wheels are traveling, a 2.0 impact factor is4 applied.0.2 The 47.4 maximumft=+=r load will be at the center between the two wheels,

so X = 2.0 ft. Determine r from Equation 3-5. 42 0.2 2 47.4 ft=+=r Then solve Equation 2-4 for PL, the load due to a single wheel.

Then solve Equation 3-4 for PL, the load due to a single wheel. Then solve Equation 2-4 for P , the load due3 to a single wheel. L )((( 4000,16)0.23 ) PL = S( 47.42 )5 3 2 )((( 4000,16)0.23 ) 49 PL = 548 /lb= ft π( 47.42 )5

The load on the pipe crown2 is from both wheels, so PL 548 /lb= ft The load on the pipe crown is from both wheels,2 so 2 PL 1096548 /lb=)2(= ft

The load on the pipeThe crown load iscalculated from both in this wheels, example so is higher than that given in Table 3-4 for a comparable depth even after correcting for the impact factor. Both the Timoshenko The load calculated in this example is higher than that given in Table 2-3 for a and Boussinesq Equations give the pressure applied at a point in the soil. In solving comparable depth even after correcting for the impact factor. Both the Timoshenko and for pipe reactions it is assumed that this point pressure is applied across the entire Boussinesq Equations give the pressure applied at a point in the soil. In solving for pipe surface of a unit length of pipe, whereas the actual applied pressure decreases away reactions it is assumed that this point pressure is applied across the entire surface of a from the line of action of the wheel load. Methods that integrate this pressure over unit length of pipe, whereas the actual applied pressure decreases away from the line of the pipe surface such as used in deriving Table 3-4 gives more accurate loading action of the wheel values. load. However, Methods the thaterror integratein the point thispressure pressure equations over is slight the and pipe conservative, surface such as used in derivingso they Table are still 2-3 effective give equations more accurate for design. loading values. However, the error in the point pressure equations is slight and conservative, so they are still effective equations for design.Railroad Loads The live loading configuration used for pipes under railroads is the Cooper E-80 loading, which is an 80,000 lb load that is uniformly applied over three 2 ft by 8 ft areas on 5 ft centers. The area represents the 8 ft width of standard railroad ties and the standard spacing between locomotive drive wheels. Live loads are based on Table 2-4:the axle Live weight Load exerted Pressu on there track for by E-80 two locomotivesRailroad andLoading their tenders coupled togetherDepth in ofdoubleheader cover, ft. fashion. Soil See TablePressure, 3-5. Commercial lb/ft2 railroads frequently require casings for pressure pipes if they are within 25 feet of the tracks, primarily for safety reasons in the event of a washout. Based upon design and permitting requirements,2.0 the designer should determine3800 whether or not a casing is required. 5.0 2400

8.0 1600

10.0 1100

12.0 800

154-264.indd 204 15.0 600 1/16/09 9:57:06 AM

20.0 300

30.0 100

Over 30.0 Neglect

For reference see ASTM A796.

Railroad Loads

The live loading configuration used for pipes under railroads is the Cooper E-80 loading, which is an 80,000 lb. load that is uniformly applied over three 2 ft by 8 ft areas on 5 ft centers. The area represents the 8 ft width of standard railroad ties and the standard 50 spacing between locomotive drive wheels. Live loads are based on the axle weight exerted on the track by two locomotives and their tenders coupled together in doubleheader fashion. See Table 2-4. Commercial railroads frequently require casings for pressure pipes if they are within 25 feet of the tracks, primarily for safety reasons in the event of a washout. Based upon design and permitting requirements,Chapter the 6 designer205 should determine whether or not a casing is required. Design of PE Piping Systems

Surcharge Load

TaBlE 3-5 Live Load Pressure for E-80 Railroad Loading Surcharge loads may be distributed loads, such as a footing, foundation, or an ash pile, Depth of cover, ft. Soil Pressure*, lb/ft 2 or may be concentrated loads,2.0 such as vehicle 3800 wheels. The load will be dispersed through the soil such that there 5.0is a reduction in 2400pressure with an increase in depth or 8.0 1600 horizontal distance from the surcharged10.0 area. Surcharge1100 loads not directly over the pipe may exert pressure on the12.0 pipe as well. 800 The pressure at a point beneath a 15.0 600 surcharge load depends on the20.0 load magnitude 300and the surface area over which the surcharge is applied. Methods 30.0for calculating vertical100 pressure on a pipe either located directly beneath a surcharge orOver located 30.0 near a surchargeNeglect are given below. For referecne see ASTM A796. * The values shown for soil pressure include impact.

Surcharge Load Pipe Directly Beneath aSurcharge Surcharge loads may Load be distributed loads, such as a footing, foundation, or an ash pile, or may be concentrated loads, such as vehicle wheels. The load will be dispersed through the soil such that there is a reduction in pressure with an increase in depth This design method is foror horizontal finding distance the vertic from theal surcharged soil pressure area. Surcharge under loads a not rectangular directly over area with a uniformly distributed surchargethe pipe may exert load. pressure This on the may pipe as be well. used The pressure in place at a point of beneathTables a 2-2 to 2-4 and Equations 2-2 and surcharge2-4 to calculateload depends onvertical the load magnitudesoil pressure and the surface due area to overwheel which loads. To do the surcharge is applied. Methods for calculating vertical pressure on a pipe either this requires knowledgelocated of the directly tire beneathimprint a surcharge area and or located impact near a surchargefactor. are given below.

Pipe Directly Beneath a Surcharge load The point pressure onThis the design pipe method at is for depth, finding the H, vertical is foundsoil pressure by under dividing a rectangular the area rectangular surcharge area (ABCD)with into a uniformly four distributed sub-area surcharge rectangles load. This may (a, be b, used c, in andplace of d) Tables which have a common corner, E, in the3-3 tosurcharge 3-5 and Equations area, 3-3 and and 3-5 toover calculate the vertical pipe. soil pressureThe surcharge due to wheel pressure, loads. This requires knowledge of the tire imprint area and impact factor. PL, at a point directly under E is the sum of the pressure due to each of the four sub- area loads. Refer to FigureThe point 2-5 pressure A. on the pipe at depth, H, is found by dividing the rectangular surcharge area (ABCD) into four sub-area rectangles (a, b, c, and d) which have a common corner, E, in the surcharge area, and over the pipe. The surcharge pressure, P , at a point directly under E is the sum of the pressure due to each of the four The pressure due to eachL sub-area is calculated by multiplying the surcharge pressure sub-area loads. Refer to Figure 3-5 A. at the surface by an Influence Value, IV. Influence Values are proportionality constants that measure what portionThe pressure of a duesurface to each sub-areaload reachesis calculated bythe multiplying subsurface the surcharge point in question. pressure at the surface by an Influence Value, IV. Influence Values are proportionality They were derived usingconstants the Boussinesq that measure what Equation portion of a surfaceand areload reachesgiven the in subsurface Table point2-5. in question. They were derived using the Boussinesq Equation and are given in Table 3-6. (3-6) PL = pa b +p+ p + pdc Eq. 2-6

Where:154-264.indd 205 1/16/09 9:57:06 AM 2 PL = vertical soil pressure due to surcharge pressure, lb/ft 51

2 pa = pressure206 Chapter due 6 to sub-area a, lb/ft Design of PE Piping Systems 2 pb = pressure due to sub-area b, lb/ft 2 pc = pressure due to sub-area c, lb/ft 51 2 pd = pressure due to sub-area d, lb/ft

2 Pressure due to the surchargepa = pressure applied due to thesub-area i-th sub-area a, lb/ft equals: WHERE 2 pb = pressure due to sub-area b, lb/ft 2 PL = vertical soil pressure due to surcharge 2pressure, lb/ft pc = pressure due to sub-area c, 2lb/ft pa = pressure due to sub-area a, lb/ft 2 pd = pressurep = pressure due dueto tosub-area sub-area b, lb/ft d,2 lb/ft b pi I= V wS Eq. 2-7 2 pc = pressure due to sub-area c, lb/ft 2 Pressure due to the surchargep dapplied = pressure dueto tothe sub-area i-th d,sub-area lb/ft equals:

Where: Pressure due to the surcharge applied to the i-th sub-area equals: (3-7) IV = Influence pValuei I= V fromwS Table 2-5 Eq. 2-7 2 wS = distributed pressure of surcharge load at ground surface, lb/ft WHERE IV = Influence Value from Table 3-6 Where: 2 If the four sub-areas are equivalent,wS = distributed then pressure Equation of surcharge 12 mayload at groundbe simplified surface, lb/ft to IV = Influence Value from Table 2-5 If the four sub-areas are equivalent, then Equation 3-7 may be simplified to: 2 wS = distributed pressure of surcharge load at ground surface, lb/ft (3-8) PL 4I= V wS Eq. 2-8 If the four sub-areas are equivalent,The influence then Equationvalue is dependent 12 may upon be thesimplified dimensions to of the rectangular area and upon the depth to the pipe crown, H. Table 3-6 Influence Value terms depicted in

The influence value is dependentFigure upon 3-6, are the defined dimensions as: of the rectangular area and upon H = depth of cover, ft the depth to the pipe crown, H. TablePL 4I= 2-5V wInfluenceS Value terms depicted in FigureEq. 2-5, 2-8 are defined as: M = horizontal distance, normal to the pipe centerline, from the center of the load to the load edge, ft N = horizontal distance, parallel to the pipe centerline, from the center of the load to the load edge, ft

The influence value is dependentInterpolation upon the may dim be usedensions to find of valuesthe rectangular not given in Tablearea 3-6. and The upon influence value H = depth of cover, ft the depth to the pipe crown, H.gives Table the portion 2-5 Influence (or influence) Value of the terms load that depicted reaches ain given Figure depth 2-5, beneath the 5252 M = horizontal distance, normal to the pipe centerline, from the center of the load are defined as: corner of the loaded area. to the load edge, ft N = horizontal distance, parallel to the pipe centerline, from the center of the load H = todepth the loadof cover, edge, ft ft M = horizontal distance, normal to the pipe centerline, from the center of the load to the load edge, ft Interpolation may be used to find values not given in Table 2-5. The influence value gives the N = portionhorizontal (or distance, influence) parallel of the to lo thead pi thatpe centerline, reaches a from given the depth center beneath of the load the corner of theto loadedthe load area. edge, ft

Interpolation may be used to find values not given in Table 2-5. The influence value gives the portion (or influence) of the load that reaches a given depth beneath the corner of the loaded area.

Figure 3-5 Illustration of Distributed Loads

FigureFigure 2-5: 2-5: Illustration Illustration of of Distributed Distributed Loads Loads

154-264.indd 206 1/16/09 9:57:07 AM Table 2-5: Influence Values, IV for Distributed Loads Table 2-5: Influence Values, IV for Distributed Loads N/H N/H M/H 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.5 2.0 ’ M/H 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.5 2.0 ’ 0.1 0.005 0.009 0.013 0.017 0.020 0.022 0.024 0.026 0.027 0.028 0.029 0.030 0.031 0.032 0.1 0.005 0.009 0.013 0.017 0.020 0.022 0.024 0.026 0.027 0.028 0.029 0.030 0.031 0.032 0.2 0.009 0.018 0.026 0.033 0.039 0.043 0.047 0.050 0.053 0.055 0.057 0.060 0.061 0.062 0.2 0.009 0.018 0.026 0.033 0.039 0.043 0.047 0.050 0.053 0.055 0.057 0.060 0.061 0.062 0.3 0.013 0.026 0.037 0.047 0.056 0.063 0.069 0.073 0.077 0.079 0.083 0.086 0.089 0.090 0.3 0.013 0.026 0.037 0.047 0.056 0.063 0.069 0.073 0.077 0.079 0.083 0.086 0.089 0.090 0.4 0.017 0.033 0.047 0.060 0.071 0.080 0.087 0.093 0.098 0.101 0.106 0.110 0.113 0.115 0.4 0.017 0.033 0.047 0.060 0.071 0.080 0.087 0.093 0.098 0.101 0.106 0.110 0.113 0.115 0.5 0.020 0.039 0.056 0.071 0.084 0.095 0.103 0.110 0.116 0.120 0.126 0.131 0.135 0.137 0.5 0.020 0.039 0.056 0.071 0.084 0.095 0.103 0.110 0.116 0.120 0.126 0.131 0.135 0.137 0.6 0.022 0.043 0.063 0.080 0.095 0.107 0.117 0.125 0.131 0.136 0.143 0.149 0.153 0.156 0.6 0.022 0.043 0.063 0.080 0.095 0.107 0.117 0.125 0.131 0.136 0.143 0.149 0.153 0.156 0.7 0.024 0.047 0.069 0.087 0.103 0.117 0.128 0.137 0.144 0.149 0.157 0.164 0.169 0.172 0.7 0.024 0.047 0.069 0.087 0.103 0.117 0.128 0.137 0.144 0.149 0.157 0.164 0.169 0.172 0.8 0.026 0.050 0.073 0.093 0.110 0.125 0.137 0.146 0.154 0.160 0.168 0.176 0.181 0.185 0.8 0.026 0.050 0.073 0.093 0.110 0.125 0.137 0.146 0.154 0.160 0.168 0.176 0.181 0.185 0.9 0.027 0.053 0.077 0.098 0.116 0.131 0.144 0.154 0.162 0.168 0.178 0.186 0.192 0.196 0.9 0.027 0.053 0.077 0.098 0.116 0.131 0.144 0.154 0.162 0.168 0.178 0.186 0.192 0.196 1.0 0.028 0.055 0.079 0.101 0.120 0.136 0.149 0.160 0.168 0.175 0.185 0.194 0.200 0.205 1.0 0.028 0.055 0.079 0.101 0.120 0.136 0.149 0.160 0.168 0.175 0.185 0.194 0.200 0.205 1.2 0.029 0.057 0.083 0.106 0.126 0.143 0.157 0.168 0.178 0.185 0.196 0.205 0.209 0.212 1.2 0.029 0.057 0.083 0.106 0.126 0.143 0.157 0.168 0.178 0.185 0.196 0.205 0.209 0.212 1.5 0.030 0.060 0.086 0.110 0.131 0.149 0.164 0.176 0.186 0.194 0.205 0.211 0.216 0.223 1.5 0.030 0.060 0.086 0.110 0.131 0.149 0.164 0.176 0.186 0.194 0.205 0.211 0.216 0.223 2.0 0.031 0.061 0.088 0.113 0.135 0.153 0.169 0.181 0.192 0.200 0.209 0.216 0.232 0.240 2.0 0.031 0.061 0.088 0.113 0.135 0.153 0.169 0.181 0.192 0.200 0.209 0.216 0.232 0.240 Chapter 6 207 Design of PE Piping Systems

Ta BlE 3-6 Influence Values, IV for Distributed Loads*

N/H M/H 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.5 2.0 ∞ 0.1 0.005 0.009 0.013 0.017 0.020 0.022 0.024 0.026 0.027 0.028 0.029 0.030 0.031 0.032 0.2 0.009 0.018 0.026 0.033 0.039 0.043 0.047 0.050 0.053 0.055 0.057 0.060 0.061 0.062 0.3 0.013 0.026 0.037 0.047 0.056 0.063 0.069 0.073 0.077 0.079 0.083 0.086 0.089 0.090 0.4 0.017 0.033 0.047 0.060 0.071 0.080 0.087 0.093 0.098 0.101 0.106 0.110 0.113 0.115 0.5 0.020 0.039 0.056 0.071 0.084 0.095 0.103 0.110 0.116 0.120 0.126 0.131 0.135 0.137 0.6 0.022 0.043 0.063 0.080 0.095 0.107 0.117 0.125 0.131 0.136 0.143 0.149 0.153 0.156 0.7 0.024 0.047 0.069 0.087 0.103 0.117 0.128 0.137 0.144 0.149 0.157 0.164 0.169 0.172 0.8 0.026 0.050 0.073 0.093 0.110 0.125 0.137 0.146 0.154 0.160 0.168 0.176 0.181 0.185 0.9 0.027 0.053 0.077 0.098 0.116 0.131 0.144 0.154 0.162 0.168 0.178 0.186 0.192 0.196 1.0 0.028 0.055 0.079 0.101 0.120 0.136 0.149 0.160 0.168 0.175 0.185 0.194 0.200 0.205 1.2 0.029 0.057 0.083 0.106 0.126 0.143 0.157 0.168 0.178 0.185 0.196 0.205 0.209 0.21253 1.5 0.030 0.060 0.086 0.110 0.131 0.149 0.164 0.176 0.186 0.194 0.205 0.211 0.216 0.223 2.0 0.031 0.061 0.088 0.113 0.135 0.153 0.169 0.181 0.192 0.200 0.209 0.216 0.232 0.240 ’ 0.032 0.062 0.089 0.116∞ 0.032 0.137 0.062 0.156 0.089 0.116 0.172 0.137 0.1850.156 0.172 0.196 0.185 0.196 0.205 0.205 0.212 0.212 0.223 0.223 0.240 0.240 0.250 0.250 * H, M, and N are per Figure 3-5.

Vertical Surcharge ExampleVertical Surcharge # 1 Example # 1 Find the vertical surcharge load for the 4’ x 6’, 2000 lb/ft2 footing shown below. Find the vertical surcharge load for the 4' x 6', 2000 lb/ft2 footing shown below.

SOLUTION: Use equations 3-6 and 3-7, Table 3-6, and Figure 3-5. The 4 ft x 6 ft footing is divided into four sub-areas, such that the common corner of the sub-areas SOLUTION: Use equations 2-6 and 2-7, Table 2-5, and Figure 2-5. The 4 ft x 6 ft is directly over the pipe. Since the pipe is not centered under the load, sub-areas a footing is divided into four sub-areas, such that the common corner of the sub-areas is directly over the pipe. Since the pipe is not centered under the load, sub-areas a and b have dimensions of 3 ft x 2.5 ft, and sub-areas c and d have dimensions of 3 ft x 1.5 ft.

154-264.indd 207 1/16/09 9:57:07 AM

Determine sub-area dimensions for M, N, and H, then calculate M/H and N/H. Find the Influence Value from Table 2-5, then solve for each sub area, pa, pb, pc, pd, and sum for PL.

Sub-area a b c d M 2.5 2.5 1.5 1.5 N 3.0 3.0 3.0 3.0 M/H 0.5 0.5 0.3 0.3 N/H 0.6 0.6 0.6 0.6

IV 0.095 0.095 0.063 0.063 208 Chapter 6 Design of PE Piping Systems

and b have dimensions of 3 ft x 2.5 ft, and sub-areas c and d have dimensions of 3 ft x 1.5 ft. 54

Determine sub-area dimensions for M, N, and H, then calculate M/H and N/H. Find

pi the 190Influence Value from190 Table 3-6, then solve126 for each sub area, pa126, pb, pc, pd, and sum for PL.

Sub-area a b c d Therefore: P = 632 lbs/ft2 M 2.5 2.5 1.5 1.5 L N 3.0 3.0 3.0 3.0 M/H 0.5 0.5 0.3 0.3 N/H 0.6 0.6 0.6 0.6

Pipe Adjacent to, but Not DirectlyIV Beneath,0.095 a 0.095 Surcharge 0.063 Load 0.063 pi 190 190 126 126

This design method mayTherefore: be usedPL = 632 tolbs/ft find 2 the surcharge load on buried pipes near, but not directly below, uniformly distributed loads such as concrete slabs, footings and floors, or other rectangular area loads, including wheel loads that are not directly over the pipe. Pipe adjacent to, but Not Directly Beneath, a Surcharge load This design method may be used to find the surcharge load on buried pipes near, but The vertical pressure isnot found directly by below, first uniformlyadding an distributed imaginary loads loaded such as concretearea that slabs, covers footings the and pipe, then determiningfloors, the surchargeor other rectangular pressu areare loads, due including to the overwheel allloads load that (actualare not directly and over the pipe. imaginary) based on the previous section, and finally by deducting the pressure due to the imaginary load fromThe that vertical due pressureto the overall is found load. by first adding an imaginary loaded area that covers the pipe, then determining the surcharge pressure due to the overall load (actual and Refer to Figure 2-5 B. imaginary)Since there based is onno the su previousrcharge section, directly and above finally t heby deductingpipe centerline, the pressure an due imaginary surcharge load,to the having imaginary the load same from pressure that due to perthe overallunit area load. as the actual load, is applied to sub-areas c Referand tod. Figure The 3-5 surcharge B. Since there pressure is no surcharge for sub-areas directly above a+d the and pipe b+ccenterline, are determined, then the surchargean imaginary loads surcharge from load, the havingimaginary the same areas pressure c and per d unit are area deducted as the actual to determine the surchargeload, pressure is applied on to sub-areasthe pipe. c and d. The surcharge pressure for sub-areas a+d and b+c are determined, then the surcharge loads from the imaginary areas c and d are

deducted to determine the surcharge pressure on the pipe.

(3-9) PL = p + p - p - pcd+cbd+a Eq. 2-9

Where terms are as previously defined above, and where termsPa+d are = surcharge as previously load of combined defined sub-areas above,a and d, lb/ft and2 Pb+c = surcharge load of combined sub-areas b and c, lb/ft2

2 pa+d = surcharge load of combined sub-areas a and d, lb/ft 2 pb+c = surcharge load of combined sub-areas b and c, lb/ft

Vertical Surcharge Example # 2

154-264.indd 208 1/16/09 9:57:08 AM Chapter 6 209 55 Design of PE Piping Systems

Find the vertical surcharge pressure for the 6' x 10', 2000 lb/ft2 slab shown below.

Vertical Surcharge Example # 2 Find the vertical surcharge pressure for the 6’ x 10’, 2000 lb/ft2 slab shown below.

SOLUTION: Use Equations 3-7 and 3-9, Table 3-6, and Figure 3-5 B. The surcharge area is divided into two sub-areas, a and b. The area between the surcharge and the SOLUTION: Useline Equations of the pipe crown 2-7 isand divided 2-9, into Table two sub-areas, 2-5, and c and Figure d, as well. 2-5 The B. imaginary The surcharge area is divided intoload istwo applied sub-areas, to sub-areas a c andand d. b. Next, The the fourarea sub-areas between are treated the surchargeas a single and the line of the pipe crownsurcharge is area. divided Unlike theinto previous two s example,ub-areas, the pipe c and is located d, asunder well. the edge The imaginary load is applied toof thesub-areas surcharge areac an ratherd d. than Next, the center. the So,four the sub-areas surcharge pressures are treated for the as a single surcharge area. combined Unlike sub-areasthe previous a+d and exampl b+c are determined,e, the pipe and is then located for the sub-areasunder the c and edge of the d. The surcharge pressure is the sum of the surcharge pressure due to the surcharge surcharge area ratheracting on than sub-areas the a+d center. and b+c, So,less the the imaginary surcharge pressure pressures due to the imaginary for the combined sub-areas a+d andsurcharge b+c acting are on determined, sub-areas c and andd. then for the sub-areas c and d. The surcharge pressure is the sum of the surcharge pressure due to the surcharge acting on sub-areas a+d and b+c, less the imaginarySub-area pressure due to the imaginary surcharge a + d b + c c d acting on sub-areas Mc and d.10 10 4 4 N 5 5 5 5 M/H 2.0 2.0 0.8 0.8 N/H 1.0 1.0 1.0 1.0

IV 0.200 0.200 0.160Sub-area 0.160

pi 400 400 (320) (320) a + d b + c c d Therefore PL = 160 lb/ft2 M 10 10 4 4 N 5 5 5 5 M/H 2.0 2.0 0.8 0.8 N/H 1.0 1.0 1.0 1.0

IV 0.200 0.200 0.160 0.160

pi 400 400 (320) (320)

154-264.indd 209 1/16/09 9:57:08 AM 2 Therefore PL = 160 lb/ft 210 Chapter 6 Design of PE Piping Systems

Installation Category 1: Standard Installation - Trench or Embankment

Pipe Reaction to Earth, Live, and Surcharge Loads Now might be a good time to review the “Design Process” that appeared earlier in Section 3. After calculating the vertical pressure applied to the pipe the next design step is to choose a trial pipe (DR or profile). Then, based on the Installation Category and the selected embedment and compaction, calculate the anticipated deflection and resistance to crush and buckling.

The Standard Installation category applies to pipes that are installed between 18 inches and 50 feet of cover. Where surcharge, traffic, or rail load may occur, the pipe must have at least one full diameter of cover. If such cover is not available, then the application design must also consider limitations under the Shallow Cover Vehicular Loading Installation category. Where the cover depth exceeds 50 ft an alternate treatment for dead loads is given under the Deep Fill Installation category. Where ground water occurs above the pipe’s invert and the pipe has less than two diameters of cover, the potential for the occurrence of flotation or upward movement of the pipe may exist. See Shallow Cover Flotation Effects.

While the Standard Installation is suitable for up to 50 feet of cover, it may be used for more cover. The 50 feet limit is based on A. Howard’s (3) recommended limit for use of E’ values. Above 50 feet, the E’ values given in Table B.1.1 in Chapter 3 Appendix are generally thought to be overly conservative as they are not corrected for the increase in embedment stiffness that occurs with depth as a result of the higher confinement pressure within the soil mass. In addition, significant arching occurs at depths greater than 50 feet.

The Standard Installation, as well as the other design categories for buried PE pipe, looks at a ring or circumferential cross-section of pipe and neglects longitudinal loading, which is normally insignificant. They also ignore the re-rounding effect of internal pressurization. Since re-rounding reduces deflection and stress in the pipe, ignoring it is conservative.

Ring Deflection Ring deflection is the normal response of flexible pipes to soil pressure. It is also a beneficial response in that it leads to the redistribution of soil stress and the initiation of arching. Ring deflection can be controlled within acceptable limits by the selection of appropriate pipe embedment materials, compaction levels, trench width and, in some cases, the pipe itself.

The magnitude of ring deflection is inversely proportional to the combined stiffness of the pipe and the embedment soil. M. Spangler (4) characterized this relationship

154-264.indd 210 1/16/09 9:57:08 AM 57 approach for soil characterization, thus developing the Modified Iowa Formula. In 1964,57 Burns and Richards [6] published a closed-form solution for ring deflection and pipe stressapproach based for onsoil classical characterization, linear elasticity. thus developing In 1976 M. the Katona Modified et. al.Iowa [7] Formula.developedChapter 6 211 In a 1964, finite Design of PE Piping Systems elementBurns and program Richards called [6] CANDE published (Culvert a closed-form Analysis and solution Design) for which ring deflection is now available and pipe in astress PC version based andon classical can be usedlinear to elasticity. predict pipe In 1976 deflection M. Katona and stresses. et. al. [7] developed a finite element program called CANDE (Culvert Analysis and Design) which is now available in Thea PC more version recent and solutions can be used may to make predict better pipe predictions deflection thanand stresses.the Iowa Formula, but they require detailedin the Iowa information Formula in 1941.on soil R. Watkins and pipe (5) modified properties, this equation e.g. more to allow soil a labsimpler testing. Often theThe improvementmoreapproach recent forsolutions in soil precision characterization, may is make all butthus better developing lost predictions in construction the Modified than Iowathe variability. IowaFormula. Formula, In Therefore, but they the Modifiedrequire detailed 1964, Iowa Burns Formula information and Richards remains on (6) publishedsoil the and most apipe closed-form frequently properties, solution used e.g. for methodmorering deflection soil of lab determining andtesting. Often ring deflection.the improvementpipe stress based in precision on classical is l inear all but elasticity. lost In in 1976 construction M. Katona et. variability. al. (7) developed Therefore, a the Modified finite Iowa element Formula program remains called CANDE the most (Culvert frequently Analysis usedand Design) method which of is determiningnow ring Sdeflection.pangler'savailable Modified in a PCIowa version Formula and can canbe used be to written predict pipefor usedeflection with andconventionally stresses. extruded DR pipe as:The more recent solutions may make better predictions than the Iowa Formula, Spangler'sbut Modified they require Iowa detailed Formula information can onbe soil written and pipe for properties, use with e.g. conventionally more soil lab extruded

DR pipe as:testing. Often the improvement in precision is all but lost in construction variability. Therefore, the Modified Iowa Formula remains the most frequently used method of

determining ring deflection.    Spangler’s Modified Iowa Formula can be written for use with solid wall PE pipe as: ∆X 1  K BED LDL PE + K BED PL  (3-10) = § 3 · Eq. 2-10 DM 144   ¨ 2E 1 ′ ¸ ' ¨   +0.061FS E ¸ X 1  3KBEDDR L-DL1P E K BED PL  = ¨ 3 ¸ Eq. 2-10 DM 144 § · ¨ 2E 1 c ¸ ¨ ¨ ¸ +0.061FS E ¸ © 3 © DR - 1¹ ¹

and for useand withfor use ASTM with ASTM F894 F894 profile profile wall wall pipe pipe as:as:

(3-11)     and for use with∆X ASTMP F894 profileK L wall pipe as: =  BED DL  Eq. 2-11 § 1.24(RSC) · DI 144 ′ ¨ +0.061FS E ¸ 'X P  DM K BED LDL  = ¨ ¸ Eq. 2-11 ¨ 1.24(RSC) ¸ WHERED I 144 c Where:∆X = Horizontal deflection,¨ in +0.061FS E ¸ © DM ¹ KBED = Bedding factor, typically 0.1 Where:LDL = ǻDeflection X = lag Horizontal factor deflection, in PE = Vertical soil pressure due to earth load, psf K BED = Bedding factor, typically 0.1 PL = Vertical soil pressure due to live load, psf LDL = Deflection lag factor E = ApparentǻX = modulus Horizontal of elasticity ofdeflection, pipe material, lb/in in 2 PE = Vertical soil pressure due to earth load, psf E’ =ModulusKBED of Soil= Bedding reaction, psi factor, typically 0.1 PL = Vertical soil pressure due to live load, psf FS = SoilL DLSupport = Factor Deflection lag factor 2 E = Apparent modulus of elasticity of pipe material, lb/in RSC = PRingE Stiffness= Vertical Constant, soil lb/ft pressure due to earth load, psf E' = Modulus of Soil reaction, psi DR = DimensionPL = VerticalRatio, OD/t soil pressure due to live load, psf FS = Soil Support Factor 2 DM = MeanE = diameter Apparent (DI+2z or DO modulus-t), in of elasticity of pipe material, lb/in z = CentroidRSCE' = of wall= RingModulus section, Stiffness in of Soil Constant, reaction, lb/ft psi = MinimumDR =wall Dimensionthickness, in Ratio, OD/t t FS = Soil Support Factor DI = pipeDRSCM inside = = diameter, Mean Ring Stiffnessin diameter Constant, (DI+2z or lb/ftDO-t), in DO = pipeDR outside = Dimension diameter, in Ratio, OD/t DM = Mean diameter (DI+2z or DO-t), in

154-264.indd 211 1/16/09 9:57:08 AM 212 Chapter 6 Design of PE Piping Systems

Deflection is reported as a percent of the diameter which can be found by multiplying 100 times ∆X/DM or ∆X/DI. (When using RSC, the units of conversion are accounted for in Equation 3-11.)

Apparent Modulus of Elasticity for Pipe Material, E 59 The apparent modulus of PE is dependent on load-rate or, duration of laoding and temperature.Apparent elastic modulus values for high and medium density PE may be found in Table B.1.1 in Chapter 3 Appendix. These values can be used in Spangler’s Iowa Formula. It has long been an industry practice to use the short-term modulus in the Iowa Formula for thermoplastic pipe. This is based on the idea that, in granular embedment soil, deformation is a series of instantaneous deformations Table 2-6: Design Valuesconsisting for of Apparent rearrangement Modulus and fracturing of Elasticity, of grains while E @ the 73°F bending stress in the pipe wall is decreasing due to stress relaxation. Use of the short-term modulus Load Duration Short-has proven10 effective 100and reliable1000 for corrugated 1 year and profile 10 wall 50pipes. These pipes Termtypically hours have pipe hours stiffness valueshours of 46 psi or less whenyears measured years per ASTM D2412. Conventional DR pipes starting with DR17 or lower have significantly higher HDPE 110,000stiffness 57,500 and therefore 51,200 they may 43,700 carry a greater 38,000 proportion 31,600 of the 28,200 earth and live load than corrugated or profile pipe; so it is conservative to use the 50-year modulus for Modulus of DR pipes that have low DR values when determining deflection due to earth load. Elasticity, psi Vehicle loads are generally met with a higher modulus than earth loads, as load MDPE 88,000duration 46,000 may be nearly 41,000 instantaneous 35,000 for 30,400 moving vehicles. 25,300 The 22,600deflection due to a combination of vehicle or temporary loads and earth load may be found by Modulus of separately calculating the deflection due to each load using the modulus appropriate Elasticity, psi for the expected load duration, then adding the resulting deflections together to get the total deflection. When doing the deflection calculation for vehicle load, the Lag Factor will be one. An alternate, but conservative, method for finding deflection for Ring Stiffness Constant, RSCcombined vehicle and earth load is to do one calculation using the 50-year modulus, but separate the vertical soil pressure into an earth load component and a live load Profile wall pipes manufacturedcomponent to ASTM and applyF894, the “Standard Lag Factor only Specificati to the earthon load for component.Polyethylene

(PE) Large Diameter ProfileRing Wall Stiffness Sewer Constant, and Drain RSC Pipe,” are classified on the basis of their Ring Stiffness ConstantProfile (RSC). wall Equation pipes manufactured 2-12 gives to ASTM the F894,RSC. “Standard Specification for Polyethylene (PE) Large Diameter Profile Wall Sewer and Drain Pipe,” are classified on the basis of their Ring Stiffness Constant (RSC). Equation 3-12 gives the RSC. (3-12) 44.6 EI RSC = 2 Eq. 2-12 D M

Where: E = Apparent modulus of elasticity of pipe material (Short-term value Table 2-6) @73oF I = Pipe wall moment of inertia, in4/in (t3/12, if solid wall construction)

154-264.indd z = Pipe212 wall centroid in 1/16/09 9:57:09 AM DI = Pipe Inside diameter in DM = Mean diameter (DI + 2z or DO-t), in t = Minimum wass thickness, in

Chapter 6 213 Design of PE Piping Systems

WHERE E = Apparent modulus of elasticity of pipe material @73°F (See Chapter 3 Appendix) I = Pipe wall moment of inertia, in4/in (t3/12, if solid wall construction) z = Pipe wall centroid in DI = Pipe inside diameter in

DM = Mean diameter (DI + 2z or DO-t), in t = Minimum wall thickness, in

Modulus of Soil Reaction, E’ The soil reaction modulus is proportional to the embedment soil’s resistance to the lateral expansion of the pipe. There are no convenient laboratory tests to determine the soil reaction modulus for a given soil. A. Howard (8) determined E’ values empirically from numerous field deflection measurements by substituting site parameters (i.e. depth of cover, soil weight) into Spangler’s equation and “back- calculating” E’. Howard developed a table for the Bureau of Reclamation relating E’ values to soil types and compaction efforts. See Table 3-7. In back-calculating E’, Howard assumed the prism load was applied to the pipe. Therefore, Table 3-7 E’ values indirectly include load reduction due to arching and are suitable for use only with the prism load. In 2006, Howard published a paper reviewing his original 1977 publication from which Table 3-7 is taken. For the most part the recent work indicates that the E’ values in Table 3-7 are conservative.

Due to differences in construction procedures, soil texture and density, pipe placement, and insitu soil characteristics, pipe deflection varies along the length of a pipeline. Petroff (9) has shown that deflection measurements along a pipeline typically fit the Normal Distribution curve. To determine the anticipated maximum deflection using Eq. 3-10 or 3-11, variability may be accommodated by reducing the Table 3-7 E’ value by 25%, or by adding to the calculated deflection percentage the correction for ‘accuracy’ percentage given in Table 3-7.

In shallow installations, the full value of the E’ given in Table 3-7 may not develop. This is due to the lack of “soil confining pressure” to hold individual soil grains tightly together and stiffen the embedment. Increased weight or equivalently, depth, increases the confining pressure and, thus, the E’. J. Hartley and J. Duncan (10) published recommended E’ values based on depth of cover. See Table 3-8. These are particularly useful for shallow installations.

Chapter 7, “Underground Installation of PE Pipe” covers soil classification for pipe embedment materials and preferred methods of compaction and installation for selected embedment materials. Some of the materials shown in Table 3-7 may not be appropriate for all pipe installation. One example would be fine-grained soils in wet ground, which would not be appropriate embedment, under most circumstances, for either profile pipe or pipes with high DR’s. Such limitations are discussed in Chapter 7.

154-264.indd 213 1/16/09 9:57:09 AM 214 Chapter 6 Design of PE Piping Systems

Ta BlE 3-7 Values of E’ for Pipe Embedment (See Howard (8))

E’ for Degree of Embedment Compaction, lb/in2 Moderate, Slight, High, 85%-95% >95% Proctor, Dumped <85% Proctor, Proctor, >70% Relative Soil Type-pipe Embedment Material <40% Relative 40%-70% Density (Unified Classification System)1 Density Relative Density Fine-grained Soils (LL > 50)2 Soils with No data available: consult a competent soils engineer, medium to high plasticity; CH, MH, CH-MH otherwise, use E’ = 0. Fine-grained Soils (LL < 50) Soils with medium to no plasticity, CL, ML, ML- 50 200 400 1000 CL, with less than 25% coarse grained particles. Fine-grained Soils (LL < 50) Soils with medium to no plasticity, CL, ML, ML-CL, with more than 25% coarse grained 100 400 1000 2000 particles; Coarse-grained Soils with Fines, GM, GC, SM, SC3 containing more than 12% fines.

Coarse-grained soils with Little or No Fines GW, GP, SW, SP3 containing less than 12% 200 1000 2000 3000 fines

Crushed Rock 1000 3000 3000 3000

Accuracy in Terms of Percentage ± 2% ±2% ±1% ±0.5% Deflection4

1 ASTM D-2487, USBR Designation E-3 2 LL = Liquid Limit 3 Or any borderline soil beginning with one of these symbols (i.e., GM-GC, GC-SC). 4 For ±1% accuracy and predicted deflection of 3%, actual deflection would be between 2% and 4%.

Note: Values applicable only for fills less than 50 ft (15 m). Table does not include any safety factor. For use in predicting initial deflections only; appropriate Deflection Lag Factor must be applied for long-term deflections. If embedment falls on the borderline between two compaction categories, select lower E’ value, or average the two values. Percentage Proctor based on laboratory maximum dry density from test standards using 12,500 ft-lb/cu ft (598,000 J/m2) (ASTM D-698, AASHTO T-99, USBR Designation E-11). 1 psi = 6.9 KPa.

154-264.indd 214 1/16/09 9:57:09 AM Chapter 6 215 Design of PE Piping Systems

Ta BlE 3-8 Values of E’ for Pipe Embedment (See Duncan and Hartley(10))

Depth of E’ for Standard AASHTO Relative Compaction, lb/in2 Type of Soil Cover, ft 85% 90% 95% 100% 0-5 500 700 1000 1500 Fine-grained soils with less than 5-10 600 1000 1400 2000 25% sand content (CL, ML, CL-ML) 10-15 700 1200 1600 2300 15-20 800 1300 1800 2600 0-5 600 1000 1200 1900 Coarse-grained soils with fines 5-10 900 1400 1800 2700 (SM, SC) 10-15 1000 1500 2100 3200 15-20 1100 1600 2400 3700 0-5 700 1000 1600 2500 Coarse-grained soils with little or no 5-10 1000 1500 2200 3300 fines (SP, SW, GP, GW) 10-15 1050 1600 2400 3600 15-20 1100 1700 2500 3800

Soil Support Factor, FS Ring deflection and the accompanying horizontal diameter expansion create lateral earth pressure which is transmitted through the embedment soil and into the trench sidewall. This may cause the sidewall soil to compress. If the compression is significant, the embedment can move laterally, resulting in an increase in pipe deflection. Sidewall soil compression is of particular concern when the insitu soil is loose, soft, or highly compressible, such as marsh clay, peat, saturated organic soil, etc. The net effect of sidewall compressibility is a reduction in the soil-pipe system’s stiffness. The reverse case may occur as well if the insitu soil is stiffer than the embedment soil; e.g. the insitu soil may enhance the embedment giving it more

resistance to deflection. The Soil Support Factor, FS, is a factor that may be applied to E’ to correct for the difference in stiffness between the insitu and embedment soils.

Where the insitu soil is less stiff than the embedment, FS is a reduction factor. Where

it is stiffer, FS is an enhancement factor, i.e. greater than one.

The Soil Support Factor, FS, may be obtained from Tables 3-9 and 3-10 as follows:

• Determine the ratio Bd/DO, where Bd equals the trench width at the pipe springline (inches), and DO equals the pipe outside diameter (inches). • Based on the native insitu soil properties, find the soil reaction modulus for the insitu soil, E’N in Table 3-9.

• Determine the ratio E’N/E’.

• Enter Table 3-10 with the ratios Bd/DO and E’N/E’ and find SF .

154-264.indd 215 1/16/09 9:57:09 AM 216 Chapter 6 Design of PE Piping Systems

Ta BlE 3-9 (3) Values of E’N, Native Soil Modulus of Soil Reaction, Howard

Native In Situ Soils Granular Cohesive

Std. Pentration Unconfined E’N (psi) ASTM D1586 Description Compressive Description Blows/ft Strength (TSF)

> 0 - 1 very, very loose > 0 - 0.125 very, very soft 50

1 - 2 very loose 0.125 - 0.25 very soft 200

2 - 4 very loose 0.25 - 0.50 soft 700

4 - 8 loose 0.50 - 1.00 medium 1,500

8 - 15 slightly compact 1.00 - 2.00 stiff 3,000

15 - 30 compact 2.00 - 4.00 very stiff 5,000

30 - 50 dense 4.00 - 6.00 hard 10,000

> 50 very dense > 6.00 very hard 20,000

Rock – – – 50,000

Ta BlE 3-10 Soil Support Factor, FS

B /D B /D B /D B /D B /D B /D E’ /E’ d O d O d O d O d O d O N 1.5 2.0 2.5 3.0 4.0 5.0 0.1 0.15 0.30 0.60 0.80 0.90 1.00 0.2 0.30 0.45 0.70 0.85 0.92 1.00 0.4 0.50 0.60 0.80 0.90 0.95 1.00 0.6 0.70 0.80 0.90 0.95 1.00 1.00 0.8 0.85 0.90 0.95 0.98 1.00 1.00 1.0 1.00 1.00 1.00 1.00 1.00 1.00 1.5 1.30 1.15 1.10 1.05 1.00 1.00 2.0 1.50 1.30 1.15 1.10 1.05 1.00 3.0 1.75 1.45 1.30 1.20 1.08 1.00 5.0 2.00 1.60 1.40 1.25 1.10 1.00

Lag Factor and Long-Term Deflection Spangler observed an increase in ring deflection with time. Settlement of the backfill and consolidation of the embedment under the lateral pressure from the pipe continue to occur after initial installation. To account for this, he recommended applying a lag factor to the Iowa Formula in the range of from 1.25 to 1.5. Lag occurs in installations of both plastic and metal pipes. Howard (3, 11) has shown that the lag factor varies with the type of embedment and the degree of compaction. Many plastic pipe designers use a Lag Factor of 1.0 when using the prism load as it

154-264.indd 216 1/16/09 9:57:09 AM 64 64

Lag Factor and Long-term Deflection Lag Factor and Long-term Deflection Spangler observed an increase in ring deflection with time. Settlement of the backfill Spanglerand consolidation observed of an the increase embedment in ring under deflection the lateral with pressutime. reSettlem from entthe ofpipe the continue backfill andto occur consolidation after initial of installation.the embedment To accountunder the for lateral this, hepressu recommendedre from the applyingpipe continue a lag tofactor occur to theafter Iowa initial Formula installation. in the rangeTo account of from for 1.25 this, to 1.5.he recommended Lag occurs in applyinginstallations a lag of factorboth plastic to the Iowaand metal Formula pipes. in the Howard range [3,of from11] has 1.25 shown to 1.5. that Lag the occurs lag factorin installations varies with of boththe type plastic of embedment and metal pipes.and the Howard degree [3, of 11]compaction. has shown Many that plasticthe lag pipe factor designersChapter varies 6 217 withuse thea Lag type Factor of embedment of 1.0 when and usingthe degree the prism of compaction. load as it accManyounts plastic forDesign pipe backfill of PE Piping designers settlement.Systems use aThis Lag makes Factor even of 1.0 more when sense using the when prism the load Soil as Support it accounts Factor for is backfill included settlement. in the Thiscalculation. makes even more sense when the Soil Support Factor is included in the calculation. Vertical Deflection Example Vertical Deflectionaccounts Example for backfill settlement. This makes even more sense when the Soil Support Estimate the verticalFactor is includeddeflection in the of calculation. a 24” diameter HDPE DR 26 pipe installed under 18 Estimatefeet of cover. the vertical The embedment deflection ofmaterial a 24” diameteris a well-graded HDPE DRsandy 26 pipegravel, installed compacted under to 18 a feetminimum of cover. 90 percent Vertical The embedment Deflection of Standard Example material Proctor is densit a well-gradedy, and the sandy native gravel, ground compacted is a saturated, to a minimumsoft clayey 90 soil. percentEstimate The anticipatedtheof Standardvertical deflection trench Proctor widthof adensit 24” isdiameter 42”.y, and DR the 26 pipe native produced ground from is a PE4710a saturated, material that is installed under 18 feet of cover. The embedment material is a well- soft clayey soil. The anticipated trench width is 42”. graded sandy gravel, compacted to a minimum 90 percent of Standard Proctor

SOLUTION: Usedensity, the and prism the native load, ground Equation is a saturated, 2-1, Tables soft clayey 2-7, soil. 2-9, The and anticipated 2-10, and trench Equation SOLUTION:2-10. Table Use 2-7width the gives is 42”. prism an E'load, for E aquation compacted 2-1, Tables sandy 2-7, gravel 2-9, or and GW-SW 2-10, and soil Equation as 2000 2-10.lb/in2. To Table estimate 2-7 gives maximu an m E' deflection for a compacted due to variability, sandy gravel this orvalue GW-SW will be soil reduced as 2000 by 2 SOLUTION:2 Use the prism load, Equation 3-1, Tables 3-7, 3-9, and 3-10, and Equation lb/in25%,. orTo toestimate 1500 lb/in maximu. Tablem deflection 2-9 gives due an to E’ variability,N of 700 psithis for value soft will clay. be reduced Since2 B dby/D 3-10. Table 23-7 gives an E’ for a compacted sandy gravel or GW-SW soil as 2000 lb/in . 25%,equals or 1.75 to 1500and E’ lb/inN/E’ .equals Table 0.47, 2-9 FgivesS is obtained an E’ ofby 700interpolation psi for soft and clay. equal Since0.60. B /D The Short-Term Apparent Modulus of ElasticityN for PE 4710 material obtained from d equals 1.75 and E’ /E’ equals 0.47, F is obtained by interpolation and equal 0.60. Table B.2.1N equals 130,000 psi.S To estimate maximum deflection due to variability, this value will be reduced by 25%, or to 1500 lb/in2. Table 3-9 gives an E’ of 700 The prism load on the pipe is equal to: N psi for soft clay. Since B /D equals 1.75 and E’ /E’ equals 0.47, F is obtained by The prism load on the pipe is equald to: N S interpolation and equal 0.60. The prism load on the pipe is equal to: 2 PE = (120)(18)= 2160lb / ft = (120)(18)= 2160lb / ft2 PE

Substituting theseSubstituting values these valuesinto intoEquation Equation 3-10 2-10 gives: gives: Substituting these values into Equation 2-10 gives:     ∆X 2160 § 0 )(0.1)(1. · = ¨ ¸ 'X 2160144  (130,000))000,110(2 1 3 0 )(0.1)(1.  DM = ¨ ( (0.061)+ )60.0() (1500)¸ 144 ¨ )000,110(2 1− 3 ¸ DM ¨ 3 ( 126 (0.061)+ )60.0() (1500)¸ © 3 126 ¹

∆X % = 0.0 = = 0.0 = 5.225 % 'X DM = 0.0 = 5.225 % DM Deflection Limits

The designer limits ring deflection in order to control geometric stability of the pipe, wall bending strain, pipeline hydraulic capacity and compatibility with cleaning equipment, and, for bell-and-spigot jointed pipe, its sealing capability. Only the limits for geometric stability and bending strain will be discussed here. Hydraulic capacity is not impaired at deflections less than 7.5%.

Geometric stability is lost when the pipe crown flattens and loses its ability to support earth load. Crown flattening occurs with excessive deflection as the increase in horizontal diameter reduces crown curvature. At 25% to 30% deflection, the

154-264.indd 217 1/16/09 9:57:09 AM 218 Chapter 6 Design of PE Piping Systems

crown may completely reverse its curvature inward and collapse. See Figure 3-1A. A deflection limit of 7.5% provides at least a 3 to 1 safety factor against reverse curvature.

Bending strain occurs in the pipe wall as a result of ring deflection — outer-fiber tensile strain at the pipe springline and outer-fiber compressive strain at the crown and invert. While strain limits of 5% have been proposed, Jansen (12) reported that, on tests of PE pipe manufactured from pressure-rated resins and subjected to soil pressure only, “no upper limit from a practical design point of view seems to exist for the bending strain.” In other words, as deflection increases, the pipe’s performance limit will not be overstraining but reverse curvature collapse.

Thus, for non-pressure applications, a 7.5 percent deflection limit provides a large safety factor against instability and strain and is considered a safe design deflection. Some engineers will design profile wall pipe and other non-pressure pipe applications to a 5% deflection limit, but allow spot deflections up to 7.5% during field inspection.

The deflection limits for pressurized pipe are generally lower than for non- pressurized pipe. This is primarily due to strain considerations. Hoop strain from pressurization adds to the outer-fiber tensile strain. But the internal pressure acts to reround the pipe and, therefore, Eq. 3-10 overpredicts the actual long-term deflection for pressurized pipe. Safe allowable deflections for pressurized pipe are given in Table 3-11. Spangler and Handy (13) give equations for correcting deflection to account for rerounding.

Ta BlE 3-11 Safe Deflection Limits for Pressurized Pipe

DR or SDR Safe Deflection as % of Diameter 32.5 7.5 26 7.5 21 7.5 17 6.0 13.5 6.0 11 5.0 9 4.0 7.3 3.0

* Based on Long-Term Design Deflection of Buried Pressurized Pipe given in ASTM F1962.

154-264.indd 218 1/16/09 9:57:09 AM Chapter 6 219 Design of PE Piping Systems

Compressive Ring Thrust Earth pressure exerts a radial-directed force around the circumference of a pipe that results in a compressive ring thrust in the pipe wall. (This thrust is exactly opposite to the tensile hoop thrust induced when a pipe is pressurized.) See Figure 3-1B. Excessive ring compressive thrust may lead to two different performance limits: crushing of the material or buckling (loss of stability) of the pipe wall. See Figure 3-1C. This section will discuss crushing, and the next section will discuss buckling.

As is often the case, the radial soil pressure causing the stress is not uniform around the pipe’s circumference. However, for calculation purposes it is assumed uniform and equal to the vertical soil pressure at the pipe crown.

Pressure pipes often have internal pressure higher than the radial pressure applied by the soil. As long as there is pressure in the pipe that exceeds the external pressure, the net thrust in the pipe wall is tensile rather than compressive, and wall crush or buckling checks are not necessary. Whether one needs to check this or not can be quickly determined by simply comparing the internal pressure with the vertical soil pressure. 67 Crushing occurs when the compressive stress in the wall exceeds the compressive yield stress of the pipe material. Equations 3-13 and 3-14 give the compressive stress 67 resulting from( earthPEL+ andP ) live DR load pressure for conventional extruded DR pipe and S = Eq. 2-13 for ASTM F894 profile288 wall PE Pipe: (3-13) ( PEL+ P ) DR S = Eq. 2-13 288 :

(3-14) ( P + P )DOLE =S Eq. 2-14 : 288A ( P + P )DOLE WHERE=S Eq. 2-14 288A Where: PE = vertical soil pressure due to earth load, psf PL = vertical soil pressure due to live-load, psf PSE == pipe vertical wall compressive soil pressure stress, lb/in2 due to earth load, psf

Where: PDRL = = vertical Dimension Ratio,soil D pressureO/t due to live-load, psf 2 D = pipe outside diameter (for profile pipe DO = DI + 2HP), in P SE =O pipevertical wall soil compressive pressure due stress, to earth lb/in load, psf DI = pipe inside diameter, in P DRL = =vertical Dimension soil pressure Ratio, D dueO/t to live-load, psf H = profile wall height, in SD =O P pipe= pipe wall outside compressive diameter stress, (for profile lb/in2 pipe DO = DI + 2HP), in A = profile wall average cross-sectional area, in2/in DI = pipe inside diameter, in DR =(O Dimensionbtain the profile Ratio,wall area fromDO the/t manufacturer of the profile pipe.) D HOP = = pipe profile outside wall height, diameter in (for profile pipe DO = DI + 2HP), in (Note: These equations contain a factor of 144 in the denominator for correct2 units conversions.) D AI == profilepipe inside wall averagediameter, cross-sectional in area, in /in HP = profile wall height, in 2 (Note: These equations A = profile contain wall a averagefactor of 144 cross-sectional in the denominator area, for correctin /in units conversions.)

(Note: These equations contain a factor of 144 in the denominator for correct units conversions.) Equation 2-14 may overstate the wall stress in profile pipe. Ring deflection in profile wall pipe induces arching. The "Deep Fill Installation" section of this chapter discusses arching and gives equations for calculating the earth pressure resulting from arching, Equation 2-14 154-264.indd may overstate 219 the wall stress in profile pipe. Ring deflection in profile 1/16/09 9:57:10 AM wallPRD .pipe PRD induces is given arching. by Equation The 2-23"Deep and Fill may Installation" be substituted section for of P thisE to chapterdetermine discusses the wall archingcompressive and gives stress equations when arching for calculating occurs. the earth pressure resulting from arching, PRD. PRD is given by Equation 2-23 and may be substituted for PE to determine the wall compressiveThe compressive stress stress when inarching the pipe occurs. wall can be compared to the pipe material allowable compressive stress. If the calculated compressive stress exceeds the allowable stress, Thethen compressive a lower DR (heavierstress in wallthe pipethickness) wall can or heavierbe compared profile to wall the is pipe required. material allowable compressive stress. If the calculated compressive stress exceeds the allowable stress, then a lower DR (heavier wall thickness) or heavier profile wall is required. Allowable Compressive Stress

AllowableTable 2-12 Compressive gives allowable Stress long-term compressive stress values for PE 3408 and PE 2406 material. Table 2-12 gives allowable long-term compressive stress values for PE 3408 and PE

2406 material. Table 2-12: Long-Term Compressive Stress at 73°F (23°C) Long-Term Compressive Material 2 Table 2-12: Long-Term CompressiveStress, Stress lb/in at 73°F (23°C) PE 3408 Long-Term 1000Compressive Material 2 Stress, lb/in PE 3408 1000 220 Chapter 6 Design of PE Piping Systems

68

Equation 3-14PE may 2406 overstate the wall stress in profile800 pipe. Ring deflection in profile wall pipe induces arching. The “Deep Fill Installation” section of this chapter 68 discusses arching and gives equations for calculating the earth pressure resulting

from arching, PRD. PRD is given by Equation 3-23 and may be substituted for PE to The long-termdetermine compressive thePE wall 2406 stresscompressive value stress should when arching be800 reduced occurs. for elevated temperature pipeline operation. Temperature design factors used for hydrostatic pressure may be used, i.e. 0.5The @ compressive 140°F. Additionalstress in the pipe temper wall aturecan be compared design factorsto the pipe may material be obtained by reference to Tableallowable 1-11 compressive in Section stress. 1 of If thisthe calculated chapter. compressive stress exceeds the The long-termallowable compressive stress, then stress a lower value DR (heavier should wall be thickness) reduced or heavier for elevated profile wall temperature is pipeline operation.required. Temperature design factors used for hydrostatic pressure may be used,Ring Compression i.e. 0.5 @ 140°F. Example Additional temperature design factors may be obtained by Allowable Compressive Stress reference to Table 1-11 in Section 1 of this chapter. Allowable long-term compressive stress values for the several PE material Find the pipe walldesignation compressive codes can ringbe found stress in Appendix, in a DR Chapter 32.5 HDPE 3. pipe buried under 46 ft of cover. The ground water level is at the surface, the saturated weight of the insitu silty- Ring Compression Example clay soil is 120The lbs/ft long-term3. compressive stress value should be reduced for elevated temperature pipeline operation. Temperature design factors used for hydrostatic pressure may be Find the pipe wallused. compressiveSee temperature ringre-rating stress or adjustment in a DR factors32.5 HDPEin the Appendix, pipe buried Chapter under 3. 46 ft of SOLUTION: Find the vertical earth pressure acting on the pipe. Use Equation 2-1. cover. The ground water level is at the surface, the saturated weight of the insitu silty- clay soil is 120Ring lbs/ft Compression3. Example Although the Find net the soil pipe pressure wall compressive is equal ring to stress the in buoyanta DR 32.5 PE4710 weight pipe of buried the soil,under the46 water pressure is alsoft of acting cover. The on groundthe pipe. water Therefore level is at the the surface, total the pressure saturated weight(water of and the insituearth load) SOLUTION: Find the vertical earth pressure acting on the pipe. Use Equation 2-1. can be found usingsilty-clay the soil saturated is 120 lbs/ft unit3. weight of the soil. SOLUTION: Find the vertical earth pressure acting on the pipe. Use Equation 3-1. Although the net soil pressure is equal to the buoyant weight of the soil, the water pressure is alsoAlthough acting the on net the soil pipe. pressure Therefore is equal to thethe buoyant total pressure weight of the (water soil, the and water earth load) PE = (120 pcf)(46 ft) = 5520 psf can be found usingpressure the is alsosaturated acting on unit the pipe.weight Therefore of the the soil. total pressure (water and earth load) can be found using the saturated unit weight of the soil. Next, solve for the compressive stress. Next, solve for the compressive stress. PE = (120 pcf)(46 ft) = 5520 psf

(5520 lb / ft2 )(32.5) S = = 623 lb / inch2 Next, solve for the compressive288 stress.

The compressive stress2 is well below the allowable limit of 1150 psi for the PE4710 (5520 lb / ft )(32.5) 2 The compressivematerialS = stress given in is the within Appendix, the = 1000Chapter 623 lb lb/in 3. / inchallowable2 stress for HDPE given in Table 2-12. 288 Constrained (Buried) Pipe Wall Buckling

Excessive compressive stress (or thrust) may cause the pipe wall to become unstable 2 TheConstrained compressive (Buried)and buckle. stress Pipe Buckling is Wall within fromBuckling thering compressive 1000 lb/in stressallowable initiates locally stress as fora large HDPE given in Table 2-12. “dimple,” and then grows to reverse curvature followed by structural collapse. Resistance to buckling is proportional to the wall thickness divided by the diameter Excessive compressive stress (or thrust) may cause the pipe wall to become unstable and buckle. Buckling from ring compressive stress initiates locally as a large "dimple," Constrained (Buried) Pipe Wall Buckling and then grows to reverse curvature followed by structural collapse. Resistance to buckling is proportional to the wall thickness divided by the diameter raised to a power.

ExcessiveTherefore154-264.indd thecompressive 220 lower the stress DR, the(or thrust) higher maythe resistance.cause the pipe Buried wall to pipe become has an unstable1/16/09 added 9:57:10 AM andresistance buckle. due Buckling to support from (or ring constraint) compressive from strethe sssurrounding initiates locally soil. as a large "dimple," and then grows to reverse curvature followed by structural collapse. Resistance to buckling is proportional to the wall thickness divided by the diameter raised to a power. Therefore the lower the DR, the higher the resistance. Buried pipe has an added resistance due to support (or constraint) from the surrounding soil. Chapter 6 221 Design of PE Piping Systems

69

Non-pressurizedraised pipes to a power.or gravity Therefore flow the pipes lower theare DR, most the higherlikely the to resistance.have a netBuried compressive pipe stress in the has pipe an added wall resistance and, therefore, due to support the (or allowable constraint) from buckling the surrounding pressure soil. should be69 calculated andNon-pressurized compared to pipes the or gravity total (soil flow andpipes are ground most likely water) to have pressure. a net For most pressure pipe compressiveapplications, stress the in fluidthe pipe pressure wall and, in therefore, the pipe the exceedsallowable bucklingthe external pressure pressure, Non-pressurized pipes or gravity flow pipes are most likely to have a net compressive and the net stressshould in be the calculated pipe wall and iscompared tensile. to theBuckling total (soil needs and ground only water)be considered pressure. for that stress in the pipe wall and, therefore, the allowable buckling pressure should be time the pipe isFor not most under pressure pressure, pipe applications, such as the duringfluid pressure and immediately in the pipe exceeds after the construction calculated and compared to the total (soil and ground water) pressure. For most and during systemexternal shut-downs. pressure, and the net stress in the pipe wall is tensile. Buckling needs pressure pipe onlyapplications, be considered the for fluid that timepressure the pipe in is the not underpipe pressure,exceeds such the as external during and pressure, and the net stress in the pipe wall is tensile. Buckling needs only be considered for that This chapter immediately gives two after equations construction for and calculating during system buckling. shut-downs and, The in modifiedcases in Luscher time the pipe iswhich not a undersurge pressure pressure, event such can produce as during a temporary and immediately negative internal after pressure. construction Equationand during is systemfor buried shut-downs. pipes that are beneath the ground water level, subject to vacuum pressure, or underUnder live these load circumstances with a shallow the pipe cover.will react These much stiffer forces to buckling act to increase as its even the modulus is higher under short term loading. When designing, select a modulus slightest eccentricity in the pipe wall by following deformation inward. While soil This chapter appropriate gives two for equations the duration of for the calculating negative external buckling. pressure. For The pipe modified that are Luscher pressure alone can create instability, soil is less likely to follow deformation inward, Equation is forsubjected buried topipes negative that pressure are beneath due to surge, the considerationground water should level, be given subject to to vacuum particularly if it is granular. So, dry ground buckling is only considered for deep pressure, or underselecting live a DRload that with gives a theshallow pipe sufficient cover. unconstrainedThese forces collapse act to strength increase to resist even the applications and is given by the Moore-Selig Equation found in the section, “Buckling of slightest eccentricitythe full applied in the negative pipe pressure wall by without following support deformationfor the soil. This inward.is to insure While soil Pipes in Deep, Dry Fills.” pressure aloneagainst can construction create instability, affects that soilresult is in lessthe embedment likely to material follow not deformation developing its inward, particularly if full it isdesign granular. strength. So, dry ground buckling is only considered for deep applications and is given by the Moore-Selig Equation found in the section, “Buckling of Luscher EquationThis chapterfor Constrained gives two equations Buckling for Belowcalculating Ground buckling. Water The modified Level Luscher Pipes in Deep,Equation Dry Fills.” is for buried pipes that are beneath the ground water level, subject to vacuum pressure, or under live load with a shallow cover. These forces act to

For pipes belowincrease the even ground the slightest water eccentricity level, operating in the pipe under wall by afollowing full or deformation partial vacuum, or subjectLuscher toEquation liveinward. load, for W Constrainedhile Luscher’s soil pressure equationBuckling alone can Below may create be instability,Ground used Watersoil to is determine less Level likely to follow the allowable constrained bucklingdeformation pressure. inward, particularly Equation if it 2-15 is granular. and So, 2-16 dry areground for buckling DR and is only profile pipe respectively. For pipes belowconsidered the ground for deep waterapplications level, and operating is given by the under Moore-Selig a full Equation or partial found vacuum, in or the section, “Buckling of Pipes in Deep, Dry Fills”. subject to live load, Luscher’s equation may be used to determine the allowable constrained bucklingLuscher Equation pressure. for Constrained Equation Buckling 2-15 Below and Ground 2-16 Water are forLevel DR and profile pipe respectively. For pipes below the ground water level, operating under a full or partial vacuum, or subject to live5.65 load, Luscher’s equationE may be used to determine the allowable PWC = RB′E′ Eq. 2-15 constrained bucklingN pressure.12 (EquationDR −1) 33-15 and 3-16 are for DR and profile pipe respectively. (3-15) 5.65 E PWC = RB′E′ Eq. 2-15 N 12(DR −1)3

(3-16) 5.65 EI PWC = RB′ E′ 3 Eq. 2-16 N D M

5.65 EI PWC = RB′ E′ 3 Eq. 2-16 N D M Where: 2 PWC = allowable constrained buckling pressure, lb/in 154-264.indd 221 N = safety factor 1/16/09 9:57:10 AM Where: 2 PWC = allowable constrained buckling pressure, lb/in N = safety factor

222 Chapter 6 Design of PE Piping Systems 70

WHERE 70 P = allowable constrainedH buckling pressure, lb/in2 WC 0.33-1=R GW Eq. 2-17 N = safety factor H

(3-17) H 0.33-1=R GW Eq. 2-17 Where: H R = buoyancy reduction factor WHERE HRGW = buoyancy = height reduction of factorground water above pipe, ft Where:H = depth of cover, ft HGW = height of ground water above pipe, ft RH == depthbuoyancy of cover, ft reduction factor

HGW = height of ground water above pipe, ft H(3-18) = depth of cover,1 ft B=′ Eq. 2-18 1+4 (-0.065H) e

WHERE 1 e = naturalB=′ log base number, 2.71828 Eq. 2-18 Where: 1+4 (-0.065H) E’ = soil reaction modulus,e psi eE = = apparentnatural modulus log baseof elasticity, number, psi 2.71828 E'DR = = soilDimension reaction Ratio modulus, psi

Where:E I == pipe apparent wall moment modulus of inertia, in4 /inof (t elasticity,3/12, if solid wall psi construction) eDRD =M =natural= Mean Dimension diameter log (DbaseI + Ratio 2z or number, DO – t), in 2.71828 4 3 E'I = soil pipe reaction wall modulus, moment psi of inertia, in /in (t /12, if solid wall Econstruction)Although = apparent buckling modulus occurs rapidly, of elasticity, long-term psi external pressure can gradually deform the pipe to the point of instability. This behavior is considered viscoelastic DDRM == MeanDimension diameter Ratio (D I + 2z or DO – t), in I and = can pipe be accounted wall moment for in Equations of inertia,3-15 and 3-16 in4 by/in using (t3/12, the apparent if solid modulus wall of elasticity value for the appropriate time and temperature of the loading. For construction) Although buckling occursinstance, rapidly, a vacuum long-term event is resisted external by thepressure short-term ca valuen gradually of the modulus deform whereas the DcontinuousM = Mean ground diameter water (DpressureI + 2z would or DO be – resistedt), in by the 50 year value. For pipe to the point of instability. This behavior is considered viscoelastic and can be accounted for in Equationsmodulus 2-15values and see Appendix, 2-16 by Chapter using 3.the apparent modulus of elasticity Althoughvalue for thebuckling appropriate occursFor pipes timerapidly, buried and long-term withtemperature less than external 4 ftof or the a fullpressure loading. diameter ca ofForn cover, gradually instance, Equations deform a 3-15 vacuum and the pipeevent to is the resisted point by of 3-16 theinstability. may short-term have limited This value behaviorapplicability. of the is In modulusconsidered this case the wherea designer viscoelastics continuousmay want and to use canground be accountedwater pressure for in would EquationsEquations be resisted 2-15 3-39 and andby 3-40.the 2-16 50 by year using value. the Forapparent modulus modulus values of see elasticity Table 2-6. value for the appropriateThe designer time and should temperature apply a safety of factor the commensurateloading. For with instance, the application. a vacuum A event is resisted by safety the short-term factor of 2.0 has value been ofused the for modulusthermoplastic wherea pipe. s continuous ground Forwater pipes pressure buried would with lessbe resisted than 4 ftby or the a full 50 diyearameter value. of cover, For modulus Equations values 2-15 see and Table 2-16 may2-6. have limited applicability.The allowable In constrainedthis case bucklingthe designer pressure may should want be comparedto use Equations to the total 2-39 and 2-40. vertical stress acting on the pipe crown from the combined load of soil, and ground water or floodwater. It is prudent to check buckling resistance against a ground For pipes buried withwater less levelthan for 4 a ft 100-year-flood. or a full diameter In this calculationof cover, the Equations total vertical 2-15 stress and is typically 2-16 Themay designerhave limited should applicability. takenapply as a the safety In prism this factorload case pressure thecommensurate designer for saturated may soil,with want plus the theto application. usefluid Equations pressure A of safety any2-39 factorand 2-40. of 2.0 has beenfloodwater used for abovethermoplastic the ground pipe.surface.

The designerallowable should constrained apply abuck safetyling factor pressure commensurate should be comparedwith the application. to the total A vertical safety stressfactor of acting 2.0 has on been the pipe used crown for thermoplastic from the combined pipe. load of soil, and ground water or floodwater. It is prudent to check buckling resistance against a ground water level for a 154-264.indd 222 1/16/09 9:57:11 AM The100-year-flood. allowable constrained In this calculation buckling the pressure total vertical should stress be comparedis typically totaken the as total the vertical prism stress acting on the pipe crown from the combined load of soil, and ground water or floodwater. It is prudent to check buckling resistance against a ground water level for a 100-year-flood. In this calculation the total vertical stress is typically taken as the prism 71 71 load pressure for saturated soil, plus the fluid pressure of any floodwater above the groundload pressure surface. for saturated soil, plus the fluid pressure of any floodwater above the71 ground surface. 71 loadFor DR pressure pipes operating for saturated under soil, a va pluscuum, the it fluidis customary pressure to of use any Equation floodwater 2-15 above to check the loadgroundtheFor DR combined pressure surface.pipes operating for pressure saturated under from soil, soil,a va plus cuum, ground the it fluidiswater, customary pressure and vacuum, to of use any Equation floodwater and then 2-15 to above to use check the groundunconstrainedthe combined surface. buckling pressure equation, from soil, Equation ground 2-39,water, to andverify vacuum, that the pipe and can then operate to use with the Fortheunconstrained vacuumDR pipes independent operating buckling equation,under of any a vasoil Equationcuum, support it 2-39,is or customary soil to verifyload, tothatin usecase the Equation constructionpipe can 2-15 operate doesto check with not the vacuum independent of any soil support or soil load, in case construction doesChapter not 6 223 Forthedevelop DR combined pipesthe full operating pressure soil support. under from Wherea soil, va cuum, ground vacuum it iswater, customary load andis short-term, vacuum,to use Equation andsuch thenas 2-15 during to to use checkwater the develop the full soil support. Where vacuum load is short-term, such asDesign during of PE Piping water Systems theunconstrainedhammer combined events buckling pressure two calculations equation, from soil, withEquation ground Equation 2-39,water, 2-14 to andverify are vacuum, thatnecessary. the pipe and Firstcan then operate determine to use with the if hammer events two calculations with Equation 2-14 are necessary. First determine if unconstrainedthe vacuumpipe is sufficient independent buckling for equation,the of groundany soil Equation water support an 2-39, dor soil soil to pressure verifyload, thatin usingcase the constructionpipea long-term can operate modulus;does with not the pipe is sufficient for the ground water and soil pressure using a long-term modulus; thedevelopthen vacuum determine the independentfull ifsoil the support. pipe of is anysufficient Where soil support vacuumfor the orcombined load soil isload, short-term, ground in case water, constructionsuch soil as pressureduring does water andnot then determine if the pipe is sufficient for the combined ground water, soil pressure and develophammervacuum loadingtheevents full soilusingtwo support.calculations the short-term Where with modulus. vacuumEquation load 2-14 is areshort-term, necessary. such First as duringdetermine water if vacuum loading using the short-term modulus. hammerthe pipe isevents sufficient two Forforcalculations DRthe pipes ground operating with water Equation under an da vacuum,soil 2-14 pressure itare is customary necessary. using to a use long-term FirstEquation determine 3-15modulus; to if thethen pipe determine is sufficient if the check forpipe the the is groundcombinedsufficient water pressure for tanhe fromd combined soil soil, pressure ground ground water, using water,and a vacuum, long-term soil pressureand thenmodulus; to and thenvacuum determine loading if using theuse pipe the the s isunconstrainedhort-term sufficient modulus. for buckling the combined equation, Equation ground 3-39, water, to verify soil that pressure the pipe and vacuumConstrained loading Buckling usingcan Examplethe operate short-term with the modulus.vacuum independent of any soil support or soil load, in case Constrained Buckling Example construction does not develop the full soil support. Where vacuum load is short- Does a 36" SDR 26term, HDPE such as pipe during have water satisfactory hammer events resistance two calculations to constrained with Equation buckling 3-14 ConstrainedwhenDoes ainstalled 36" Buckling SDR with 26 are 18 Example HDPE necessary. ft of coverpipe First have indetermine a satisfactory compacted if the pipe soilresistanceis sufficient embedmen for to the constrained groundt. Assume water bucklingand ground soil 2 Constrainedwaterwhen to installed the surfaceBuckling with andpressure 18 Example ftan of usingE' cover of a1500 long-term in alb/in compacted modulus;. then soil determine embedmen if the pipet. is Assume sufficient groundfor the 2 Doeswater ato 36"the surface SDR 26 andcombined HDPE an E' ground pipe of 1500 have water, lb/in satisfactorysoil .pressure and resistance vacuum loading to constrained using the short-term buckling modulus. Doeswhen ainstalled 36" SDR with 26 18 HDPE ft of coverpipe have in a satisfactory compacted resistancesoil embedmen to constrainedt. Assume buckling ground 2 whenwaterSOLUTION: to installed the surface Solve with and 18Constrained Equation ftan of E' cover ofBuckling 2-15. 1500 in Example aSincelb/in compacted. this is asoil long-term embedmen loadingt. Assume condition, ground the stressSOLUTION: relaxation Solve modulus Equation can be 2-15. assumed Since2 to this be 28,200 is a long-term psi. Soil loading cover, H, condition, and ground the water to the surface andDoes ana 36” E' SDR of 150026 PE4710 lb/in pipe. have satisfactory resistance to constrained buckling waterstress height,relaxation H modulus, are both can 18 be feet. assumed Therefore, to be the28,200 soil psi.support Soil factor,cover, B',H, andis found ground as GW when installed with 18 ft of cover in a compacted soil embedment? Assume ground follows;water height, HGW, are both 18 feet. Therefore, the soil2 support factor, B', is found as SOLUTION: Solve water Equation to the surface 2-15. and Since an E’ of this 1500 is lb/in a long-term. loading condition, the follows; SOLUTION:stress relaxation Solve modulus Equation can be1 2-15. assumed Since to this be 28,200 is a long-term psi. Soil loading cover, H, condition, and ground the SOLUTION:B=c Solve Equation = 0.446 3-15. Since this is a long-term loading condition, the stresswater height,relaxation HGW modulus, are both can 18 be-(0.065)(18)1 feet. assumed Therefore, to be the28,200 soil psi.support Soil factor,cover, B',H, andis found ground as 50B=′ year1+4 stresse relaxation = modulus 0.446 for PE4710 material is given in the Appendix to follows; -(0.065)(18) water height, HGW, areChapter both1+4 3 as18e 29,000 feet. psi. Therefore, Soil cover, H, the and soilground support water height, factor, H B',, are is both found 18 feet. as GW follows; Therefore, the1 soil support factor, B’, is found as follows; B=′ = 0.446 and the bouyancy reduction factor,1-(0.065)(18) R, is found as follows: c 1+4e and the bouyancy reductionB= factor,-(0.065)(18) R, is = found 0.446 as follows: 1+4e 18 R = 1-0.3318= 0.67 R = 1-0.3318= 0.67 and the bouyancy reductionand the bouyancy factor,18 reduction R, factor,is found R, is found as asfollows: follows: and the bouyancy reduction factor, R, is found as follows: 18 Solve Equation 2-15 Rfor = the 1-0.33 allowable= 0.67 lo ng-term constrained buckling pressure: 18 Solve Equation 2-15 Rfor = the 1-0.33 allowable= 0.67 lo ng-term constrained buckling pressure:

18 Solve Equation 3-15 for the allowable long-term constrained buckling pressure: Solve Equation 2-15 for the5.65 allowable long-term)0.67(0.446 1500(28,200) constrained buckling pressure: PWC = 5.652 )0.67(0.446 1500(28,200))126(12 (3 29,000) Solve Equation 2-15 forPWC the= allowable long-term constrained buckling pressure: 2 − )126(12 3

5.65 )0.67(0.446 1500(28,200) 72 = PWC 23.5 3387 3 PWC 5.652 33402.23 psf=psi= )0.67(0.446 15−00(28,200) )126(12 PWC = PWC 2 33402.23 psf=psi=  )126(12 3 The earth pressure and ground water pressure applied to the pipe is found using Equation 2-1 (prism load)The earth with pressure a saturated and ground soil water weight. pressure The applied saturated to the pipe soil is weightfound using being Equation 3-1 (prism load) with a saturated soil weight. The saturated soil weight the net weight of bothP WCsoil and water.33402.23 psf=psi= being the net weight of both soil and water. PWC 33402.23 psf=psi= lb PE = (120)(18)= 2160 ft2

Compare this with the constrained buckling pressure. Since PWC exceeds PE, DR 26 has satisfactory resistance to constrained pipe buckling.

154-264.indd 223 1/16/09 9:57:12 AM

AWWA DESIGN WINDOW

The AWWA Committee Report, “Design and Installation of Polyethylene (PE) Pipe Made in Accordance with AWWA C906” describes a Design Window. Applications that fall within this window require no calculations other than constrained buckling per Equation 2-15. It turns out that if pipe is limited to DR 21 or lower as in Table 2-13, the constrained buckling calculation has a safety factor of at least 2, and no calculations are required.

The design protocol under these circumstances (those that fall within the AWWA Design Window) is thereby greatly simplified. The designer may choose to proceed with detailed analysis of the burial design and utilize the AWWA Design Window guidelines as a means of validation for his design calculations and commensurate safety factors. Alternatively, he may proceed with confidence that the burial design for these circumstances (those outlined within the AWWA Design Window) has already been analyzed in accordance with the guidelines presented in this chapter.

The Design Window specifications are: 224 Chapter 6 Design of PE Piping Systems 74

Installation Category # 2: Shallow Cover Vehicular Loading

Compare this with the constrained buckling pressure. Since P exceeds P , DR 26 The Standard Installation methodology assumes that the pipeWC behaves E primarily as a "membrane" structure,has satisfactory that resistance is, the to pipe constrained is almost pipe buckling. perfectly flexible with little ability to resist bending.Installation At shallow Category cover #2:depths, Shallow es peciallyCover Vehicular those llessoading than one pipe diameter, membrane actionThe Standard may not Installation fully develop, methodology and assumes surcharge that the or pipe live behaves loads primarily place a bending load on the pipeas a crown.“membrane” In thisstructure, case that the is, pipe’s the pipe flexural is almost stiffness perfectly flexible carries withpart little of the load and prevents ability the pipeto resist crown bending. from At shallow dimpling cover inwarddepths, especially under thethose load.less than Equation one pipe 2-19, published by diameter, Watkins membrane [14] gives action the may soil not pressurefully develop, that and can surcharge be supported or live loads place at the pipe crown by the acombination bending load on of the the pipe pipe’s crown. flexuralIn this case stiffness the pipe’s (bending flexural stiffness resistance) carries and the soil’s internal part resistance of the load againstand prevents heaving the pipe upwcrownard. from Indimpling addition inward to under checking the load. Watkins' formula, the designerEquation 3-19, should published check by Watkinsdeflection (14) gives using the soilEquations pressure that 2-10 can orbe supported2-11, pipe wall compressive at stress the pipe using crown by Equations the combination 2-13 of orthe pipe’s 2-14, flexural and stiffness pipe wall(bending buckling using Equations 2-15resistance) or 2-16. and the soil’s internal resistance against heaving upward. In addition to checking Watkins’ formula, the designer should check deflection using Equations Watkins' equation3-10 or is 3-11, recommended pipe wall compressive only wherestress using the Equationsdepth of 3-13 cover or 3-14, is andgreater pipe wall than one- half of the pipebuckling diameter using Equations and the 3-15 pipe or 3-16. is installed at least 18 inches below the road surface. In otherWatkins’ words, equation it is isrecommended recommended only that where the thepipe depth regardless of cover is greaterof diameter than always be at least 18”one-half beneath of the the pipe road diameter surface and thewhere pipe isthere installed are at live least load 18 inchess present; below the more may be required dependingroad surface. on In otherthe words,properties it is recommended of the pipe that and the pipeinstallation. regardless ofIn diameter some cases, lesser cover depthsalways be may at least be 18” sufficient beneath the where road surface there where is a there reinforced are live loads concrete present; cap or a reinforced concretemore may pavement be required slab depending over theon the pipe. properties Equation of the pipe2-19 and may installation. be used In for both DR pipe and profilesome cases, pipe. lesser See cover def initiondepths mayof “A” be sufficientbelow. where there is a reinforced concrete cap or a reinforced concrete pavement slab over the pipe. Equation 3-19 may be used for both DR pipe and profile pipe. See definition of “A” below. (3-19) 2 w(KH12 ) 7387(I)  w DO H  PWAT = + 2  MAT -S  Eq. 2-19 N S DO N S DO c 288A 

WHERE Where: PWAT = allowable live load pressure at pipe crown for pipes with one diameter or less of cover, psf w = unit weight of soil, lb/ft3

PDWATO = pipe = outside allowable diameter, livein load pressure at pipe crown for pipes with one diameterH = depth of cover, or less ft of cover, psf 3 wI = pipe= wall unit moment weight of inertia of (t soil,3/12 for lb/ft DR pipe), in4/in 2 DA O= profile= pipe wall averageoutside cross-sectional diameter, area, inin/in, for profile pipe or wall thickness (in) for DR pipe H =(obtain depth the profile of from cover, the manufacturer ft of the profile pipe.) c = outer fiber to wall centroid, in I = pipe wall moment of inertia (t3/12 for DR pipe), in4/in c = HP – z for profile pipe and c = 0.5t for DR pipe, in A = profile wall average cross-sectional area, in2/in, for profile pipe or HP = profile wall height, in z = pipe wallwall centroid, thickness in (in) for DR pipe c = outer fiber to wall2 centroid, in SMAT = material yield strength, lb/in , Use 3000 PSI for PE3408 c = HP – z for profile pipe and c = 0.5t for DR pipe, in HP = profile wall height, in z = pipe wall centroid, in 2 SMAT = material yield strength, lb/in , USE 3000 PSI FOR pe3408 NS = safety factor

154-264.indd 224K = passive earth pressure coefficient 1/16/09 9:57:12 AM 75

SIN I )(+1 =K Eq. 2-20 SIN I )(-1 Chapter 6 225 Design of PE Piping Systems Ɏ = angle of internal friction, deg

75

NS = safety factor 75 K = passive earth pressure coefficient Equation 2-19 is for a point load applied to the pipe crown. Wheel loads should be determined using a point load method such as given by Equations 2-2 (Timeoshenko) (3-20) SIN I )(+1 or 2-4 (Boussinesq). =K Eq. 2-20 SIN φ )(+1 SIN I )(-1 =K Eq. 2-20 When a pipe is installed with shallow cover below an unpaved surface, rutting can occur SIN φ =)(-1 angle of internal friction, deg which will not only reduce cover depth, but also increase the impact factor. Ɏ = angle of internal friction, deg Equation 3-19 is for a point load applied to the pipe crown. Wheel loads should be

Ɏ = angle of internaldetermined friction, using deg a point load method such as given by Equations 3-2 (Timoshenko) Shallow Cover Exampleor 3-4 (Boussinesq).

Equation 2-19When is for a pipe a pointis installed load with applied shallow to cover the below pipe an crown. unpaved Wheelsurface, rutting loads can should be Determine the safety factor against flexural failure of the pipe accompanied by soil determined usingoccur a which point will load not onlymethod reduce such cover asdepth, given but alsoby increaseEquations the impact 2-2 (Timeoshenko) factor. heave, for a 36" RSC 100 F894 profile pipe 3.0 feet beneath an H20 wheel load. or 2-4 (Boussinesq). Equation 2-19 isAssume for a an point asphalt loadShallow surface applied Cover with Example togranular the pipe embedment. crown. Wheel loads should be determined using a point load Determinemethod the such safety as factor given against by flexural Equations failure of the2-2 pipe (Timeoshenko) accompanied by When a pipe is installed with shallow cover below an unpaved surface, rutting can occur SOLUTION: The soillive heave, load for pressure a 36” RSC acting100 F894 atprofile the crownpipe 3.0 feetof thebeneath pipe an can H20 bewheel found load. using or 2-4 (Boussinesq).which will not only reduce cover depth, but also increase the impact factor. Equation 2-4, theAssume Boussinesq an asphalt point surface load with equation. granular embedment. At 3.0 feet of cover the highest live load pressure occursSOLUTION: directly The under live load a singlepressure wheel acting atand the equals:crown of the pipe can be found When a pipe is installed with shallowusing Equation cover 3-4, below the Boussinesq an unpaved point load surface,equation. At rutting 3.0 feet of can cover occur the which will not only Shallowreduce Covercoverhighest Example depth, live load but pressurealso increase occurs directly the under impact a single factor. wheel and equals: (3)(2.0)(16000)(3.0 3 ) = 1697 psf Determine p theWATP L= safety factor against flexural failure of the pipe accompanied by soil S(3.02 )5 Shallow Cover Exampleheave, for a 36" RSC 100 F894 profile pipe 3.0 feet beneath an H20 wheel load. Assume an asphalt surface with granular embedment. WHERE I = 2.0 Where:f Determine the safetySOLUTION: factor The againstW = 16,000live lbsload flexural pressure failure acting of at the the pipecrown accompanied of the pipe can bybe soilfound using heave, for a 36" Equation RSC 100 2-4, F894 Hthe = 3.0 IfBoussinesq ft= profile 2.0 pipe point 3.0 load feet equation. beneath At 3.0 an feet H20 of wheelcover the load. highest live Assume an asphaltload surface pressure with woccurs =granular 120W pcf =directly 16,000 embedment. under lbs a single wheel and equals: H = 3.0 ft The wlive = load 120 pressure pcf is to be compared with the value in Equation 3-19. To solve SOLUTION: The live load pressureEquation acting 3-19, the atfollowing the crown parameters3 of arethe required: pipe can be found using (3)(2.0)(16000)(3.0 ) Equation 2-4, the Boussinesq Ipoint = 0.171 inload4/in equation. At 3.0 feet of cover the highest live The live load pressurepWAT = is to be compared5 with the value in Equation 2-19. To solve 2 S(3.02 load pressure occursEquation directly 2-19, theunderA = following 0.470 a in single/in parameters wheel) and are required:equals: HP = 2.02 in (Profile Wall Height)

DO = DI+2*h = 36.00+2*2.02 = 40.04 in Where:Z = 0.58I =in 0.171 in4/in C = h-z = 1.44 in3 (3)(2.0)(16000)(3.0If =) 2.0 p = S = 3000 psi WAT 5 W = 16,000 lbs π(3.02 φ = )30 deg. H = 3.0 ft w = 120 pcf

Where: The live load pressure is to be compared with the value in Equation 2-19. To solve EquationIf = 154-264.indd2.0 2-19, 225 the following parameters are required: 1/16/09 9:57:12 AM W = 16,000 lbs H = 3.0 ft I = 0.171 in4/in w = 120 pcf

The live load pressure is to be compared with the value in Equation 2-19. To solve Equation 2-19, the following parameters are required:

I = 0.171 in4/in 76

2 76 A = 0.470 in /in 76 HP = 2.02 in (Profile Wall Height) DA O == 0.470DI+2*h in =2/in 36.00+2*2.02 = 40.04 in ZA == 0.580.470 in in 2/in 76 HP = 2.02 in (Profile Wall Height) CH P = = h-z 2.02 = 1.44in (Profile in Wall Height) DO = DI+2*h = 36.00+2*2.02 = 40.04 in S = 3000 psi2 AZD O = = 0.4700.58 DI+2*h in in =/in 36.00+2*2.02 = 40.04 in ĭZ == 0.5830 deg. in HCP = = h-z 2.02 = 1.44in (Profile in Wall Height) C = h-z = 1.44 in DSO == 3000DI+2*h psi = 36.00+2*2.02 = 40.04 in Determine the earth ZĭSpressure === 0.58300030 deg. incoefficient: psi Cĭ == h-z30 deg.= 1.44 in 226 Chapter 6 Determine theDesign earth of PE Spressure Piping = 3000Systems coefficient:psi 1+sin (30) 1+0.5 Determine theK earth = ĭpressure = 30 deg. =coefficient: = 3.0

1-sin (30) 1-0.5 Determine the earth1+ pressuresin (30) coefficient:1+0.5 K = 1+sin (30) = 1+0.5 = 3.0 K = 1-sin (30) = 1-0.5 = 3.0 The live load pressureDetermine1- thesin earthinci (30) pientpressure to coefficient:1-0.5 failure equals: 1+sin (30) 1+0.5 K = = = 3.0 The live load pressure1-sin inci (30)pient to1-0.5 failure equals: The live load pressure incipient to3.0*0(12)120(3. failure)2 equals:0.171*7387 120(40.04)3.0 = = + -(3000 ) PWAT 2 The live load pressure40.04 incipient to failure equals:40.04 (1.44) 0.470*288 The live load pressure incipient to3.0*0(12)120(3. failure)2 equals:0.171*7387 120(40.04)3.0 2 PWAT = 3.0*0(12)120(3. ) + 2 0.171*7387 -(3000 120(40.04)3.0 ) PWAT = 40.04 +40.042 (1.44) -(3000 0.470*288 ) PWAT = 40.041584+2904 = psf4498 40. 04 (1.44) 0.470*288 2 3.0*0(12)120(3. ) 0.171*7387 120(40.04)3.0 PWAT = + 2 -(3000 ) PWAT = 40.041584+2904 = psf4498 40. 04 (1.44) 0.470*288 The resulting safetyPWAT = factor equals:1584+2904 = psf4498

The resulting safety factor equals: The resulting safetyPWAT = factor equals:1584+2904 = psf4498 PWAT 4498 The resulting safetyN = factor = equals: = 2.65 1697 pL 4498 The resulting safetyPWAT factor equals: InstallationN = PWAT = Category4498 = 2.65 #3: Deep Fill Installation 1697 N = pL = = 2.65 The performancepL 1697 limits for pipes in a deep fill are the same as for any buried pipe.

They Pinclude:WAT 4498 Installation CategoryN = = # 3: Deep = 2.65 Fill Installation 1. Compressivep 1697 ring thrust stress L TheInstallation performance Category2. Ri limitsng deflection #for 3: pipes Deep in Fill a deep Installation fill are the same as for any buried pipe. They include:Installation Category # 3: Deep Fill Installation 3. Constrained pipe wall buckling The performance limits for pipes in a deep fill are the same as for any buried pipe. They (1) compressive ring thrust stress, Installationinclude:The performance CategoryThe suggested limits # for 3: calculation pipes Deep in Fill methoda deep Installation for fill pipe ar ein the deep same fill applications as for any involves buried the pipe. They include: (2)introduction ring deflection, of design routinesand for each performance limit that are different than (3) constrained pipe wall buckling The performance(1)those compressive limits previously for pipes given. ring in thrusta deep stress, fill are the same as for any buried pipe. They (1) compressive ring thrust stress, include: (2)Compressive ring deflection, ring thrust and is calculated using soil arching. The arching calculation (2) ring deflection, and (3)may constrained also be used for pipe profile wall pipe buckling designs in standard trench applications. Profile The suggested(3) constrained calculation pipe method wall forbuckling pipe in deep fill applications involves the (1) pipes compressive are relatively low ring stiffness thrust pipes stress, where significantarching may occur at introduction of design routines for each performance limit that are different than those (2)relatively ring deflection,shallow depths and of cover. previouslyThe suggested given. calculation method for pipe in deep fill applications involves the The suggested(3) constrained calculation pipe method wall buckling for pipe in deep fill applications involves the introduction of At design a depth ofroutines around 50 for feet each or so itperf becomesormance impractical limit tothat use arSpangler’se different equation than those previouslyintroduction given. ofas design published routines in this chapter for each because perf it neglectsormance the significantlimit that loadare reductiondifferent due than to those Thepreviously suggested given.arching calculation and the inherent method stiffening for of pipe the embedment in deep and fill consequential applications increase involves in the introduction ofE’ design due to the routines increased for lateral each earth perf pressureormance applied limit to the that embedment. are different This section than those previously given.gives an alternate deflection equation for use with PE pipes. It was first introduced by Watkins et al. (1) for metal pipes, but later Gaube extended its use to include PE pipes. (15)

154-264.indd 226 1/16/09 9:57:13 AM Chapter 6 227 Design of PE Piping Systems

Where deep fill applications are in dry soil, Luscher’s equation (Eq. 3-15 or 3-16) may often be too conservative for design as it considers a radial driving force from ground water or vacuum. Moore and Selig(17) developed a constrained pipe wall buckling equation suitable for pipes in dry soils, which is given in a following section.

Considerable care should be taken in the design of deeply buried pipes whose failure may cause slope failure in earthen structures, or refuse piles or whose failure may have severe environmental or economical impact. These cases normally justify the use of methods beyond those given in this Chapter, including finite element analysis and field testing, along with considerable professional design review.

Compressive Ring Thrust and the Vertical Arching Factor The combined horizontal and vertical earth load acting on a buried pipe creates a radially-directed compressive load acting around the pipe’s circumference. When a PE pipe is subjected to ring compression, thrust stress develops around the pipe hoop, and the pipe’s circumference will ever so slightly shorten. The shortening permits “thrust arching,” that is, the pipe hoop thrust stiffness is less than the soil hoop thrust stiffness and, as the pipe deforms, less load follows the pipe. This occurs much like the vertical arching described by Marston.(18) Viscoelasticity enhances this effect. McGrath(19) has shown thrust arching to be the predominant form of arching with PE pipes. 78

Burns and Richard(6) have published equations that give the resulting stress occurring in a pipe due to arching. As discussed above, the arching is usually78 considered when calculating the ring compressive stress in profile pipes. For deeply S A −1 buried pipesVAF McGrath (19)−= has71.088.0 simplified the Burns and Richard’s equations Eq. 2-21 to derive + a vertical arching factor as givenS A by Equation5.2 3-21. (3-21) S 1   A Where: VAF 71.088.0 Eq. 2-21 S A  5.2 VAFWHE =RE Vertical Arching Factor VAF = Vertical Arching Factor Where: SA = Hoop Thrust Stiffness Ratio SA = Hoop Thrust Stiffness Ratio VAF = Vertical Arching Factor (3-22) SA = Hoop Thrust1.43 M StiffnessS rCENT Ratio S A = Eq. 2-22 EA WHERE 1.43 r rCENT = radius to McentroidalS CENT axis of pipe, in S A = Eq. 2-22 Ms= one-dimensionalEA modulus of soil, psi Where: E = apparent modulus of elasticity of pipe material, psi (See Appendix, Chapter 3) A= profile wall average cross-sectional area, in2/in, or wall thickness (in) for DR pipe rCENT = radius to centroidal axis of pipe, in Where: Ms= one-dimensional modulus of soil, psi E = apparent modulus of elasticity of pipe material, psi r = radius to centroidal axis of pipe, in 2 CENTA= profile wall average cross-sectional area, in /in, or wall M = one-dimensional modulus of soil, psi sthickness (in) for DR pipe E = apparent modulus of elasticity of pipe material, psi 154-264.indd 227 1/16/09 9:57:14 AM A= profile wall average cross-sectional area, in2/in, or wall One-dimensional modulusthickness values (in) for for DR soil pipe can be obtained from soil testing, geotechnical texts, or Table 2-14 which gives typical values. The typical values in Table 2-14 were obtained by converting values from McGrath [20]. One-dimensional modulus values for soil can be obtained from soil testing, geotechnical texts, or Table 2-14 which gives typical values. The typical values in Table 2-14 were obtained by converting values from McGrath [20]. Table 2-14: Typical Values of Ms, One-Dimensional Modulus of Soil

Vertical Soil Gravelly Gravelly Gravelly TableStress 2-14:1 TypicalSand/Gravels Values of M s, One-DimensionalSand/Gravels ModulusSand/Gravels of Soil

(psi) 95% Std. Proctor 90% Std. Proctor 85% Std. Proctor Vertical Soil Gravelly Gravelly Gravelly Stress1 Sand/Gravels(psi) Sand/Gravels(psi) Sand/Gravels(psi)

(psi) 95% Std. Proctor 90% Std. Proctor 85% Std. Proctor 10 3000 1600 550 (psi) (psi) (psi)

20 3500 1800 650 10 3000 1600 550

40 4200 2100 800 20 3500 1800 650

60 5000 2500 1000 40 4200 2100 800

60 5000 2500 1000 228 Chapter 6 Design of PE Piping Systems

79 One-dimensional modulus values for soil can be obtained from soil testing, geotechnical texts, or Table 3-12 which gives typical values. The typical values in Table 3-12 were obtained by converting values from McGrath (20). 80 6000 2900 1300

Ta BlE 3-12 Typical Values of M , One-Dimensional Modulus of Soil 100 6500 s 3200 1450 Gravelly Sand/Gravels Gravelly Sand/Gravels Gravelly Sand/Gravels *Adapted and extended fromVertical values Soil Stressgiven1 (psi)by McGrath [20]. For depths not shown in McGrath [20], the 95% Std. Proctor (psi) 90% Std. Proctor (psi) 85% Std. Proctor (psi) MS values were approximated using the hyperbolic soil model with appropriate values for K and n where n=0.4 and K=200, K=100, and K=45 10for 95% Proctor, 90%3000 Proctor, and 85%1600 Proctor, respectively.550 20 3500 1800 650 1 Vertical Soil Stress (psi) = [ soil depth (ft) x soil density (pcf)]/144 40 4200 2100 800

60 5000 2500 1000 80 6000 2900 1300 100 6500 3200 1450 * Adapted and extended from values given by McGrath(20). For depths not shown in McGrath(20), the MS values were approximated using the hyperbolic soil model with appropriate values for K and n where n=0.4 and K=200, K=100, and K=45 for 95% Proctor, 90% Proctor, and 85% Proctor, respectively. The radial directed earth1 Vertical pressure Soil Stress can (psi) =be [ soil f depthound (ft) byx soil multiplying density (pcf)]/144 the prism load (pressure) by the vertical arching factor as shown in Eq. 2-23. The radial directed earth pressure can be found by multiplying the prism load (pressure) by the vertical arching factor as shown in Eq. 3-23. (3-23) PRD = (VAF)wH Eq. 2-23

WHERE 2 Where: PRD = radial directed earth pressure, lb/ft w = unit weight of soil, pcf 2 PRD = radialH = depth directed of cover, ft earth pressure, lb/ft w = unit weight of soil, pcf H = depth of cover, ft The ring compressive stress in the pipe wall can be found by substituting PRD from Equation 3-23 for PE in Equation 3-13 for DR pipe and Equation 3-14 for profile wall pipe.

The ring compressiveEarth stress Pressure in the Example pipe wall can be found by substituting PRD from Equation 2-23 for PE in Equation 2-13 for DR pipe and Equation 2-14 for profile wall Determine the earth pressure acting on a 36” profile wall pipe buried 30 feet deep. pipe. The following properties are for one unique 36” profile pipe made from PE3608 material. Other 36” profile pipe may have different properties. The pipe’s cross- Radial Earth Pressure Example sectional area, A, equals 0.470 inches2/inch, its radius to the centroidal axis is 18.00 inches plus 0.58 inches, and its apparent modulus is 27,000 psi. Its wall height is 2.02 Determine the radial earthin and pressure its D equals acting 36 in +2on (2.02 a 36" in) orRSC 40.04 100 in. Assume profile the wall pipe pipe is installed buried in 30 a O 2 feet deep. The pipe'sclean cross-sectional granular soil compacted area, A, to equals90% Standard 0.470 Proctor inches (Ms /inch,= 1875 psi),its radiusthe insitu to soil the centroidal axis is 18.00is as stiff inch as thees embedment,plus 0.58 andinches, the backfill and its weighs modulus 120 pcf. is (Where 28,250 the psi.excavation Its wall height is 2.02 in and its DO equals 36 in +2 (2.02 in) or 40.04 in. Assume the pipe is installed in a clean granular soil compacted to 90% Standard Proctor (Ms = 1875 psi), the insitu soil is as stiff as the embedment, and the backfill weighs 120 pcf. (Where the excavation is in a stable trench, the stiffness of the insitu soil can generally be ignored in this calculation.)154-264.indd 228 1/16/09 9:57:14 AM Chapter 6 229 Design of PE Piping Systems

is in a stable trench, the stiffness of the insitu soil can generally be ignored in this calculation.) The following series of equations calculates the hoop compressive stress, S, in the pipe wall due to the earth pressure applied by the soil above the pipe. 80 The earth pressure is reduced from the prism load by the vertical arching factor. (From Equation 3-22) 80

lbs 80 1.43(1875 2 )(18.58inch) = = inchlbs = 3.93 75.3 S A 1.43(1875 )(18.58inch)2 lbs 2 inch (28250 inch)(0.470 ) = = lbs2 = 75.3 S A inchlbs inch2 1.43(1875lbs 2 )(18.58inchinch) (28250 inch)(0.4702 ) = = inch2 = 75.3 S A = inch 75.3  1 inch2 = 75.3 0.71-0.88 = VAF(From Equation = 3-21)0.71-0.88 lbs = inch 0. 572 (28250 75.3 2 )(0.4702.5+ ) 2 75.3 − 1 inch 0.71-0.88 = VAF = 0.71-0.88 inch = inch 0. 0.5657 75.3 2.5+ lb PRD = (57 75.3  1 =ft)pcf)(301200. 2052 0.71-0.88 = VAF = 0.71-0.88 75.3 1 = 0. 57 2 0.71-0.88 = VAF = 0.71-0.88 = 0. 57 ftlb (From Equation 3-23) 75.3 2.5+ PRD = (57 =ft)pcf)(301200. 2052 2 ft lb PRD = (57 =ft)pcf)(301200. 20162052 PRD DP inpsf )04.40(2052 2 ORD ft d S 2 607 psi 1000 psi 288DP A inin inpsf )/470.0(288 )04.40(2052 = ORD = = ≤ (FromS Equation 3-14) 2 607 psi 1000 psi 288DP A inin inpsf )/470.0(288 )04.40(2052 DP ORD inpsf )04.40(2052 d S 2 596607 psi d 1000 psi 288A 2 inin )/470.0(288 Ring Deflection(Allowable of Pipescompressive Using stress Watkins-Gaube per Table C.1, Appendix Graph to Chapter 3)

Ring Deflection of Pipes Using Watkins-Gaube Graph R. WatkinsRing [1] Deflection developed of Pipes an extremelyUsing Watkins-Gaube straight-forward Graph approach to calculating pipe deflectionRing Deflection in a fill of that Pipes(1) does Using not Watkins-Gauberely on E’. It is Graphbased on the concept that the deflection R. WatkinsR. Watkins [1] developed developed an an extremelyextremely straight-forward straight-forward approach approach to calculating to calculating pipe of a pipe embeddedpipe deflection in ina alayer fill that of soildoes isnot proportionalrely on E’. It is based to the on the compression concept that the or settlement of thedeflection soil layer in aand fill that doesthe const not antrely of on proportionality E’. It is based is ona function the concept of the that relative the deflection stiffness R.of a Watkins pipe embeddeddeflection [1] developed of ina pipe a layer embedded an of extremely soil in ais layer proportional straiof soilght-forward is proportional to the approachcompression to the compression to calculatingor settlement or pipe of betweendeflection thesettlementin a pipe fill that of and the does soil soil. layer not Watkins andrely that on the E’. used constant It is laboratory based of proportionality on testing the concept is to a functionestablish that of the and deflection graph proportionalitythe soil layer and constants, that the const calledant Deformation of proportionality Factors, is a Dfunction, for the of the stiffness relative ranges stiffness of ofbetween a pipe embedded the relative pipe stiffness and in a soil. layer between Watkinsof soilthe pipe is usedproportional and soil. laboratory Watkins to usedthe testingF compressionlaboratory to establishtesting or to settlement and graph of metalthe soil pipes. layerestablish andGaube andthat graph[15, the 16]proportionalityconst extendedant of proportionality constants, Watkins' called work Deformationis by a functiontesting Factors, to of include the D relative, for PE pipes. stiffness In theproportionality soil layer and constants, that the const calledant Deformation of proportionality Factors, is a DfunctionF, for the of the stiffnessF relative ranges stiffness of orderbetween to predict the stiffness pipe deflection, and ranges soil. of themetal Watkins designer pipes. Gaube used first (15, 16)determines laboratory extended Watkins’ testingthe amount work to byestablish testingof compression and graph in themetal layer pipes. of soil Gaube in which [15, the 16] pipe extended is installed Watkins' using work conventional by testing geotechnicalto include PE equations. pipes. In proportionalityto include constants, PE pipes. In called order to Deformation predict deflection, Factors, the designer DF, forfirst the determines stiffness ranges of Then,order todeflection predict deflection,equals the thesoil designercompression first multiplieddetermines by t hethe amount D factor. of compression This bypasses in metalthe layer pipes. ofthe soil amount Gaube in which of [15,compression the 16] pipe extended in isthe installed layer Watkins' of soil using in whichwork conventional theby pipetesting is installed Fgeotechnicalto include using PE equations. pipes. In someorder ofto thepredictconventional inherent deflection, geotechnical problem thes equations.associateddesigner Then, first with deflection determines using E'equals val the ues.the amountsoil The compression designerof compression using the in Watkins-GaubeThen, deflection Graphequals should the soil select compression conservative multiplied soil modulus by the D valuesF factor. to Thisaccommodate bypasses thesome layer of theofmultiplied soil inherent in whichby theproblem D theF factor. pipes associated This is installedbypasses with some using using of the conventional inherentE' values. problems geotechnicalThe associated designer equations. using the variance duewith usingto installation. the soil reaction Two modulus, other E’, factors values. Theto considerdesigner using when the Watkins-using this method is Then, deflection equals the soil compression multiplied by the DF factor. This bypasses thatWatkins-Gaube it assumes Graph a constant should Deformation select conservative Factor independent soil modulus of values depth to of accommodate cover and it somevariance of thedueGaube inherent to Graph installation. (Figureproblem 3-6) sTwo should associated other select factorsconservative with using to considersoil E' modulus values. when values The using to designer this method using the is does not addressaccommodate the varianceeffect of due the to installation.presence Twoof ground other factors water to consideron the Defowhen rmationusing Factor. Watkins-Gaubethat it assumes Graph a constant should Deformation select conservative Factor independent soil modulus of values depth to of accommodate cover and it variancedoes not addressdue to installation. the effect of Twothe presence other factors of ground to consider water onwhen the usingDeformation this method Factor. is Tothat use it assumes the Watkins-Gaube a constant Graph,Deformation the designer Factor independent first determines of depth the relative of cover stiffness and it betweendoes not pipeaddress and the soil, effect which of isthe given presence by the of Rigidity ground Factor,water on R Fthe. Equation Deformation 2-24 Factor. and 2- 25To are use for the DR Watkins-Gaube pipe and for profile Graph, pipe the respectively: designer first determines the relative stiffness between154-264.indd 229pipe and soil, which is given by the Rigidity Factor, RF. Equation 2-241/16/09 9:57:15and AM 2- To use the Watkins-Gaube Graph, the designer first determines the relative stiffness To25 are use for the DR Watkins-Gaube pipe and for profile Graph, pipe the respectively: designer first determines the relative stiffness between pipe and soil, which is given by the Rigidity Factor, RF. Equation 2-24 and 2- 3 25 are for DR pipe and for profile pipeS DRE respectively: )1(12 RF Eq. 2-24 E 3 DRE − )1(12 R = S Eq. 2-24 F DRE E  )1(12 3 S DRE  )1(12 RF Eq. 2-24 F E

80

lbs 1.43(1875 )(18.58inch) inch2 S A = = 75.3 lbs inch2 (28250 )(0.470 ) inch2 inch 75.3 − 1 0.71-0.88 = VAF = 0.71-0.88 = 0. 57 75.3 2.5+ lb PRD = (57 =ft)pcf)(301200. 2052 ft 2

DP inpsf )04.40(2052 S = ORD = = 607 psi ≤ 1000 psi 288A 2 inin )/470.0(288

Ring Deflection of Pipes Using Watkins-Gaube Graph

R. Watkins [1] developed an extremely straight-forward approach to calculating pipe deflection in a fill that does not rely on E’. It is based on the concept that the deflection of a pipe embedded in a layer of soil is proportional to the compression or settlement of the soil layer and that the constant of proportionality is a function of the relative stiffness between the pipe and soil. Watkins used laboratory testing to establish and graph proportionality constants, called Deformation Factors, DF, for the stiffness ranges of metal pipes. Gaube [15, 16] extended Watkins' work by testing to include PE pipes. In order to predict deflection, the designer first determines the amount of compression in the layer of soil in which the pipe is installed using conventional geotechnical equations. Then, deflection equals the soil compression multiplied by the DF factor. This bypasses 230 Chapter 6 some of the inherent Designproblem of PE Pipings associated Systems with using E' values. The designer using the Watkins-Gaube Graph should select conservative soil modulus values to accommodate variance due to installation. Two other factors to consider when using this method is that it assumes a constant Deformation Factor independent of depth of cover and it does not address the effect of the presence of ground water on the Deformation Factor. this method is that it assumes a constant Deformation Factor independent of depth To use the Watkins-Gaubeof cover and Graph, it does thenot address designer the effect first of determines the presence of the ground relative water stiffnesson the Deformation Factor. between pipe and soil, which is given by the Rigidity Factor, RF. Equation 2-24 and 812- 25 are for DR pipe andTo usefor theprofile Watkins- pipeGaube respectively: Graph, the designer first determines the relative stiffness between pipe and soil, which3 is given by the Rigidity Factor, RF. Equation 3-24 and E S Dm 3-25 are for DRR pipeF = and for profile pipe respectively: Eq. 2-25 EI (3-24) DRE − )1(12 3 R = S 81Eq. 2-24 F E Where: (3-25) 3 E S Dm DR = RDimensionF = Ratio Eq. 2-25 ES = SecantEI modulus of the soil, psi E = Apparent modulus of elasticity of pipe material, psi IW HE RE= Pipe wall moment of inertia of pipe, in4/in Where: DR = Dimension Ratio DESm = =Secant Mean modulus diameter of the soil, psi(DI + 2z or DO – t), in DR = DimensionE = Apparent modulus Ratio of elasticity of pipe material, psi ES = SecantI = Pipe wall modulus moment of inertiaof the of pipe,soil, in 4psi/in The secant modulus of the soil may be obtained from testing or from a geotechnical E = ApparentDm = Mean diameter modulus (DI + 2z of or elasticityDO – t), in of pipe material, psi engineer’s evaluation.I = Pipe Inwall lieu mom of ent a preciseof inertia determination, of pipe, in4/in the soil modulus may be related to the one-dimensional modulus, M , from Table 2-14 by the following equation Dm = Mean diameter (DI + 2z orS DO – t), in where ȝ is the soil's PoissonThe secant ratio. modulus of the soil may be obtained from testing or from a geotechnical engineer’s evaluation. In lieu of a precise determination, the soil modulus may be related to the one-dimensional modulus, M , from Table 3-12 by the following The secant modulus of the soil may be obtained from testing S or from a geotechnical engineer’s evaluation. In equation lieu of where a precise µ is the determination,soil’s Poisson ratio. the soil modulus may be related to the one-dimensional(3-26) modulus, M(1+S, fromP )(1- Table 2P ) 2-14 by the following equation E SS = M Eq. 2-26 where ȝ is the soil's Poisson ratio. (1-P )

TaBlE 3-13 (21) Typical range of Poisson’s Ratio for Soil (Bowles ) Soil Type (1+P )(1- 2P ) Poisson’s Ratio, μ Table 2-15:E SS Typical= M range of Poisson’s Ratio for Soil (Bowles Eq. [21]) 2-26 Saturated Clay (1-P ) 0.4-0.5 SoilUnsaturated Type Clay 0.1-0.3Poisson Ratio, ȝ Sandy Clay 0.2-0.3 SaturatedSilt Clay 0.3-0.35 0.4-0.5 Sand (Dense) 0.2-0.4 Table 2-15: TypicalUnsaturatedCoarse range Sand Clay (Voidof Poisson’sRatio 0.4-0.7) Ratio for0.15 Soil0.1-0.3 (Bowles [21]) Fine-grained Sand (Void Ratio 0.4-0.7) 0.25 Soil TypeSandy Clay Poisson Ratio,0.2-0.3 ȝ Silt 0.3-0.35 Saturated Clay 0.4-0.5 Sand (Dense) 0.2-0.4 Unsaturated Clay 0.1-0.3 Coarse Sand (Void Ratio 0.4- 0.15 Sandy Clay0.7) 0.2-0.3 Fine-grainedSilt Sand (Void Ratio 0.3-0.35 0.25 0.4-0.7) Sand154-264.indd (Dense) 230 0.2-0.4 1/16/09 9:57:16 AM Coarse Sand (Void Ratio 0.4- Next, the designer determines the Deformation Factor,0.15 DF, by entering the Watkins- Gaube Graph with0.7) the Rigidity Factor. See Fig. 2-6. The Deformation Factor is the proportionalityFine-grained Sand constant (Void betweenRatio vertical deflection (compression) of the soil layer 0.25 containing the0.4-0.7) pipe and the deflection of the pipe. Thus, pipe deflection can be obtained by multiplying the proportionality constant DF times the soil settlement. If DF is less than Next, the1.0 designerin Fig. 2-6, determines use 1.0. the Deformation Factor, DF, by entering the Watkins- Gaube Graph with the Rigidity Factor. See Fig. 2-6. The Deformation Factor is the proportionality constant between vertical deflection (compression) of the soil layer containing the pipe and the deflection of the pipe. Thus, pipe deflection can be obtained by multiplying the proportionality constant DF times the soil settlement. If DF is less than 1.0 in Fig. 2-6, use 1.0. Chapter 6 231 Design of PE Piping82 Systems

The soil layer surrounding the pipe bears the entire load of the overburden above it without arching. Therefore, settlement (compression) of the soil layer is proportional to the prism load and not the radial directed earth pressure. Soil strain, İS, may be Next, the designer determines the Deformation Factor, DF , by entering the Watkins- determined from geotechnicalGaube Graph analysis with the or Rigidity from theFactor. following See Fig. 3-6.equation: The Deformation Factor is the proportionality constant between vertical deflection (compression) of the soil layer wH ε S = containing the pipe and the deflection of the pipe. Thus, pipe deflectionEq. 2-27 can be 82 144ES obtained by multiplying the proportionality constant DF times the soil settlement. Where:If DF is less than 1.0 in Fig. 3-6, use 1.0. The soil layer surrounding the pipe bears the entire load of the overburden above it The soil layer surrounding the pipe bears the entire load of the overburden above it without arching.w = unit weight Theref ofore, soil, settlement pcf (compression) of the soil layer is proportional to Hwithout = depth arching. of cover Therefore, (height settlement of fill above (compression) pipe crown), of the soil ft layer is proportional the prism load and not the radial directed earth pressure. Soil strain, İS, may be to the prism load and not the radial directed earth pressure. Soil strain, εS, may be determinedEs =from secant geotechnical modulus of analysis the soil, psior from the following equation: determined from geotechnical analysis or from the following82 equation: (3-27) The designer can findThe the soil layer pipe surrounding deflectionwH the pipe as bears a theper entirecent load of of the overburden diameter above by it multiplying the without arching.H S = Therefore, settlement (compression) of th e soil layer is proportional to Eq. 2-27 soil strain, in percent,the by prism the load deformation and144 notE theS radial factor: directed earth pressure. Soil strain, İS, may be determined from geotechnical analysis or from the following equation:

WHEREWhere:wH H S = Eq. 2-27 w = unit weight144 ofE soil,S pcf w = unit weight of soil, pcf H = depth ofWhere: cover (height of fill above pipe crown), ft H = depth of cover (height of fill above pipe crown), ft E = secant modulusw = unit of theweight soil, of psi soil, pcf s H = depth of cover (height of fill above pipe crown), ft

F EEs =s secant = secant modulus of modulus the soil, psi of the soil, psi The designer can find the pipe deflection as a percent of the diameter by multiplying Thethe designer soil strain, can find inthe percent,pipe deflection by as the a per deformationcent of the diameter factor: by multiplying the The designersoil strain, can in percent, find by thethe deformation pipe deflectionfactor: as a percent of the diameter by multiplying the soil strain, in percent, by the deformation factor:

F F Deformation Factor, D

F Deformation Factor, D Deformation Factor, Deformation Factor, D

5 10 5 1050 100 50 100 500 1000 1000 5000 10,000 5000 10,000

R(RigidityRigidity Factor) Factor, RF R(Rigidity Factor)Rigidity Factor, RF Figure 2-6: Watkins-Gaube Graph Figure 3-6 Watkins-Gaube Graph 'X Rigidity Factor, RF (100) = DFH S Eq. 2-28 Figure 2-6:D M Watkins-Gaube Graph (3-28) ∆X Deformation Factor, D Where:(100) ǻ X/D =M multipliedDFε S by 100 gives percent deflection. Eq. 2-28 D M

WHERE ∆X/D multiplied by 100 gives percent deflection. Where: ǻ MX/DM multiplied by 100 gives percent deflection. 5 10 50 100 500 1000 5000 10,000

R(Rigidity Factor) Rigidity Factor, RF Figure 2-6: Watkins-Gaube Graph 154-264.indd 231 'X 1/16/09 9:57:16 AM (100) = DFH S Eq. 2-28 D M

Where: ǻ X/DM multiplied by 100 gives percent deflection.

83

83 83 Watkins – Gaube Calculation Technique

83 Find the deflectionWatkins of– Gaube a 6" SDR Calculation 11 pipe Technique under 140 ft of fill with granular embedment Watkinscontaining – Gaube12% or Calculation less fines, Techniquecompacted at 90% of standard proctor. The fill weighs 75 83 pcf. Find the deflection of a 6" SDR 11 pipe under 140 ft of fill with granular embedment FindWatkins the – deflection Gaubecontaining Calculation of 12% a 6" orSDR Techniqueless 11 fines, pipe compacted under 140 at ft 90% of fill of with standard granular proctor. embedment The fill weighs 75 containing SOLUTION: 12%pcf. First, or lesscalculate fines, the compacted vertical soil at 90%pressure of standard equation, proctor. Eq. 2-1. The fill weighs 75 pcf. 232 Chapter 6 WatkinsFind the – deflection Gaube Calculation ofDesign a of 6" PE PipingSDR Technique Systems 11 pipe under 140 ft of fill with granular embedment containing 12%SOLUTION: or lessEq. fines, 2-1:First, P compacted Ecalculate = wH the at vertical90% of soilstandard pressure proctor. equation, The fillEq. weighs 2-1. 75 SOLUTION:pcf. First, calculate the 3vertical soil pressure equation, Eq. 2-1. Find the deflection ofPE a= 6"(75lb/ft SDR )(140 11 pipe ft) under 140 ft of fill with granular embedment Eq. 2-1: P = wH containing 12% or less fines, compacted2 atE 90% of standard proctor. The fill weighs 75 Eq.PE = 2-1: 10,500 PE = lb/ft wH or 72.93 psi pcf.SOLUTION: First, calculate the PverticalE = (75lb/ft soil pressure)(140 ft) equation, Eq. 2-1. 3 PExampleE = (75lb/ft of the)(140 Application ft) of the2 Watkins-Gaube Calculation Technique PE = 10,500 lb/ft or 72.9 psi Eq.Find 2-1:the deflection PE = wH 2of a 6” SDR 11 pipe made from PE4710 materials under 140 ft SOLUTION:The MS is obtained First, calculateP byE = interpol10,500 the verticalationlb/ft or from soil72.9 pressure Table psi 2-14 equation, and equals Eq. 2-1. 2700. The secant of fill with granular3 embedment containing 12% or less fines, compacted at 90% of modulus can be foundPE assuming= (75lb/ft a)(140 Poisson ft) Ratio of 0.30 standard proctor. The fill weighs 75 pcf. The MS Eq. is obtained 2-1: PE psi= bywH 2 interpol ation from))30.0(21)(30.01(2700 Table 2-14 and equals 2700. The secant PE = 10,500 lb/ft or 72.9 psi The MS is modulus obtained SOLUTION:canE byS be interpol found First,3ation assuming calculate from the Tablea vertical Poisson 2-14 soil Ratiopressure 2005 and ofpsi equals equation, 0.30 2700. Eq. 3-1. The secant modulus can be foundPE assuming= (75lb/ft )(140a Poisson ft) )30.01( Ratio of 0.30 Eq. 3-1: PE = wH 2 psi   ))30.0(21)(30.01(2700 PE = 10,5003 E lb/ft or 72.9 psi 2005 psi The MS is obtained PE by = (75lb/ft interpol)(140psi ft)ationS  from Table  2-14))30.0(21)(30.01(2700 )30.01( and equals 2700. The secant ES 2 2005 psi modulus can be foundPE =assuming 10,500 lb/ft or a72.9 Poisson psi )30.01( Ratio of 0.30

The rigidity MS is factor obtained is obtained by interpol frompsiation Equation from 2-24. Table 2-14))30.0(21)(30.01(2700 and equals 2700. The secant TheE MS is obtained by interpolation from Table 3-12 and equals2005 2700.psi The secant modulus can be found modulus can be found Sassuming a Poisson Ratio of 0.30 assuming a Poisson’s Ratio of 0.30.3 )30.01( 200  )111()5(12 The rigidityF factor= is obtained+ from = 8 −52 Equation 2-24. R psi ))30.0(21)(30.01(2700 The rigidity factor is obtainedES = from28250 Equation 2-24. = 2005 psi − )30.01( 3 200  )111()5(12 200RF =  )111()5(12 3 = 8 52 = = 28250 8 52 The rigidity factor is obtainedTheRF rigidity factor from is obtained Equation from Equation 2-24. 3-24. Using Figure 2-6, the deformation28250 factor is found to be 1.2. The soil strain is calculated 3 by Equation 2-27. 200  )111()5(12 RF = = 8308 52 The rigidity Usingfactor isFigure obtained 2-6, fromthe29,00028250 deformation Equation 2-24. factor is found to be 1.2. The soil strain is calculated Using Figureby 2-6, Equation the deformation 2-27. 140ft*75pcf factor 3is found to be 1.2. The soil strain is calculated H S = 200 − )111()5(12 x 100 = 3.6% by Equation 2-27. UsingRF = Figure 3-6, the averagelbs value = of 8 the52 deformation factor is found to be 1.2. The soil strain is calculated by Equation 3-27. 200*144 282505 2 140ft*75pcf Using Figure 2-6, the deformationH = factorinch is found to xbe 100 1.2. = 3.6% The soil strain is calculated S140ft*75pcf lbs by Equation 2-27. H S = x 100 200*144 = 5 3.6% lbs inch2 Using Figure 2-6, the deformation200*144 5 factor2 is found to be 1.2. The soil strain is calculated 140ft*75pcf inch by Equation 2-27. H S = x 100 = 3.6% The deflection is found by multiplyinglbs the soil strain by the deformation factor: The deflection is200*144 found5 by multiplying2 the soil strain by the deformation factor: 140ft*75pcf inch ε'S = • 100 = 3.6% The deflectionX is found bylbs multiplying the soil strain by the deformation factor: (100) 200*144 = 1.2*5 3.6 = 4.4% The deflection is foundD Mby multiplying the2 soil strain by the deformation factor: 'Xinch (100) = 1.2* 3.6 = 4.4% Moore-Selig'X Equation for Constrained Buckling in Dry Ground The deflection is found by(100) multiplying = D1.2*M 3.6the =soil 4.4% strain by the deformation factor: AsD Mdiscussed previously, a compressive thrust stress exists in buried pipe. When this

thrust' stress approaches a critical value, the pipe can experience a local instability X The deflection is foundor large by(100) multiplying deformation = 1.2* 3.6andthe collapse. =soil 4.4% strain In an by earlier the sectiondeformation of this chapter, factor: Luscher’s D M equation was given for constrained buckling under ground water. Moore and Selig(17) ∆X have (100)used an = alternate 1.2* 3.6 approach = 4.4% called the continuum theory to develop design equationsD M for contrained buckling due to soil pressure (buckling of embedded pipes). The particular version of their equations given below is more appropriate for dry

applications than Luscher’s equation. Where ground water is present, Luscher’s equation should be used.

154-264.indd 232 1/16/09 9:57:18 AM 84

Moore-Selig Equation for Constrained Buckling in Dry Ground

As discussed previously, a compressive thrust stress exists in buried pipe. When this thrust stress approaches a critical value, the pipe can experience a local instability or large deformation and collapse. In an earlier section of this chapter, Luscher’s equation was given for constrained buckling under ground water. Moore and Selig [17] have used an alternate approach called the continuum theory to develop design equations for contrained buckling due to soil pressure (buckling of embedded pipes). The particular version of their equations given below is more appropriate for dry applications than Luscher's equation. Where ground water is present, Luscher’s equation should be used.

Chapter 6 233 Design of PE Piping Systems

The Moore-Selig Equation for critical buckling pressure follows: (Critical buckling pressure is the pressure at which buckling will occur. A safety factor should be provided.) The Moore-Selig Equation for critical buckling pressure follows: (Critical buckling pressure is the pressure at which buckling will occur. A safety factor should be provided.) (3-29) 1 2 2.4 M RH * PCR = (EI )3 ( E S )3 Eq. 2-29 DM

Where Where: PCR = Critical constrained buckling pressure, psi ϕ = Calibration Factor, 0.55 for granular soils PCR = CriticalRH = Geometry constrained Factor buckling pressure, psi ij = CalibrationE = Apparent modulusFactor, of elasticity0.55 for of pipe granular material, psi soils RH = GeometryI = Pipe wall moment Factor of Inertia, in4/in (t3/12, if solid wall construction) E = ApparentES* = ES /(1- modulusμ) of elasticity of pipe material, psi 4 3 I =E S Pipe= Secant wallmodulus moment of the soil, psi of Inertia, in /in (t /12, if solid wall μs = Poisson’s Ratio of Soil (Consult a textbook on soil for values. Bowles (1982) gives typical values construction) for sand and rock ranging from 0.1 to 0.4.) ES* = ES/(1-ȝ) The geometry factor is dependent on the depth of burial and the relative stiffness E = Secant modulus of the soil, psi S between the embedment soil and the insitu soil. Moore has shown that for deep 85 ȝs = Poisson's Ratio of Soil burials in uniform fills, HR equals 1.0.

85 SOLUTION: Critical Buckling Example The geometry factor is dependent on the depth of burial and the relative stiffness 85 Determine the critical buckling pressure and safety factor against buckling for the between the embedment soil *and the2000 insitu soil. Moorelbs has shown that for deep burials SOLUTION: 6”E SSDR = 11 pipe (5.987”= 2860 mean diameter) in the previous example. in uniform fills,SOLUTION: RH equals 1.0. (1-0.3) inch2 SOLUTION: * 2000 lbs E S = = 2860 * (1-0.3)2000 lbs 2 E S = = 2860 inch 1 2 Critical Buckling Example (1-0.3)2.4*0.55*1.0 2 lbs PCR = (28250*0.018inch )3 (2860 )3 = 354 5.987 inch2

Determine the critical buckling pressure2.4*0.55*1.0 and safety factor against1 buckling2 forlbs the 6" 3 3 358 PCR = (28250*0.018(29000 )1 (2860 )2 = 354 2 SDR 11 pipe in the previous example.2.4*0.55*1.0 lbsin 2 5.987 3 3 inch Determine theP S.F.CR = against buckling:(28250*0.018 ) (2860 ) = 354 2 5.987 inch

Determine the Safety Factor against buckling:

Determine the S.F. against buckling: PCR 354*144358 Determine the S.F. against buckling: S.F. = = = 4.9 PE 140*75

PCR 354*144 S.F. = = = 4.9 InstallationPCR Category354*144 #4: Shallow Cover Flotation effects S.F. = PE = 140*75 = 4.9

Shallow coverPE presents140*75 some special considerations for flexible pipes. As already

discussed, full soil structure interaction (membrane effect) may not occur, and live

loads are carried in part by the bending stiffness of the pipe. Even if the pipe has

sufficient strength to carry live load, the cover depth may not be sufficient to prevent

Installation Category # 4: Shallow Cover Flotation Effects

InstallationShallow cover Category presents # 4: some Shallow special Cover considerations Flotation Effects for flexible pipes. As already Installationdiscussed, full Category soil structure # 4: Shallowinteraction Cover (membrane Flotation effect) Effects may not occur, and live loads 154-264.indd 233 1/27/09 11:20:22 AM Shalloware carried cover in part presents by the somebending special stiffness considerations of the pipe. forEven flexible if the pipes.pipe has As sufficient already discussed,Shallowstrength to cover fullcarry soil presents live structure load, somethe interaction cover special depth (membrane considerations may not beeffect) sufficient for may flexible not to preventoccur, pipes. and the As livepipe already loads from arediscussed,floating carried upward fullin partsoil or structurebybuckling the bending interactionif the groundstiffness (membrane becomes of the pipe.effect) saturat Even mayed withnotif the occur,ground pipe andhas water. livesufficient loads This strengtharesection carried addresses: to carryin part live by load, the bendingthe cover stiffness depth may of thenot pipe.be sufficient Even ifto the prevent pipe hasthe pipesufficient from floatingstrength upwardto carry orlive buckling load, the if coverthe ground depth becomesmay not be saturat sufficiented with to prevent ground the water. pipe fromThis sectionfloating addresses:upwardx Minimum or buckling soil coverif the requirementsground becomes to prevent saturat flotationed with ground water. This section addresses: x Hydrostatic buckling (unconstrained) x Minimum soil cover requirements to prevent flotation • Minimum soil cover requirements to prevent flotation x Hydrostatic buckling (unconstrained) Design Considerations• Hydrostatic for buckling Ground (unconstrained)Water Flotation

DesignHigh ground Considerations water can forfloat Ground buried Water pipe, causingFlotation upward movement off-grade as well as Designcatastrophic Considerations upheaval. for This Ground is not Wateran issue Flotation for plastic pipes alone. Flotation of metal or Highconcrete ground pipes water may can occur float at buried shallow pipe, cover causing when upwardthe pipes movement are empty. off-grade as well as catastrophicHigh ground upheaval.water can floatThis buried is not pipe,an issue causing for plastic upward pipes movement alone. Floff-gradeotation of as metal well asor concretecatastrophicFlotation pipesoccurs upheaval. may when occur the This atground shallowis not wateran cover issue surrounding when for plastic the pipesthe pipes pi arepe alone. producesempty. Fl otation a buoyant of metal force or concretegreater than pipes the may sum occur of the at shallowdownward cover forces when provided the pipes by are the empty. soil weight, soil friction, Flotationthe weight occurs of the when pipe, the and ground the weightwater surrounding of its contents. the pi pe In produces addition to a thebuoyant disruption force greaterFlotationoccurring than occurs due the to whensumoff-grade ofthe the groundmovem downward waterents, flotationforcessurrounding provided may thealso bypi cape theuse produces soil significant weight, a buoyant reductionsoil friction, force of thegreater weight than of the the sum pipe, of andthe downward the weight forces of its provided contents. by Inthe addition soil weight, to the soil disruption friction, occurringthe weight due of to the off-grade pipe, and movem the weightents, flotation of its contents.may also ca Inuse addition significant to the reduction disruption of occurring due to off-grade movements, flotation may also cause significant reduction of 234 Chapter 6 Design of PE Piping Systems

the pipe from floating upward or buckling if the ground becomes saturated with ground water. This section addresses:

• Minimum soil cover requirements to prevent flotation • Hydrostatic buckling (unconstrained)

Design Considerations for Ground Water Flotation High ground water can float buried pipe, causing upward movement off-grade as well as catastrophic upheaval. This is not an issue for plastic pipes alone. Flotation of 86 metal or concrete pipes may occur at shallow cover when the pipes are empty.

Flotation occurs when the ground water surrounding the pipe produces a buoyant soil support around theforce pipe greater and than allow the sum the of pipethe downward to buckle forces from provided the external by the soil hydrostatic weight, pressure. soil friction, the weight of the pipe, and the weight of its contents. In addition to the disruption occurring due to off-grade movements, flotation may also cause Flotation is generallysignificant not a design reduction consideration of soil support for around buried the pipepipe and where allow the pipe pipeline to buckle runs full or nearly full of liquidfrom theor whereexternal groundhydrostatic water pressure. is always below the pipe invert. Where these conditions are Flotationnot met, is generallya quick not"rule a design of thumb" consideration is that for pipe buried buried pipe where in soil the having pipeline a 3 saturated unit weightruns of atfull least or nearly 120 full lb/ft of liquid with or at where least ground 1½ pipewater isdiameters always below of thecover pipe will not float. However, ifinvert. burial Where is in these lighter conditions weight are soilsnot met, or awith quick lesser “rule of cover,thumb” groundis that pipe water flotation should be checked.buried in soil having a saturated unit weight of at least 120 lb/ft3 with at least 1½ pipe diameters of cover will not float. However, if burial is in lighter weight soils or Mathematically the relationshipwith lesser cover, between ground waterthe buoyant flotation forceshould andbe checked. the downward forces is given in Equation 2-30.Mathematically Refer to Figure the relationship 2-7. For between an empty the buoyant pipe, force flotation and the will downward occur if forces is given in Equation 3-30. Refer to Figure 3-7. For an empty pipe, flotation will occur if: (3-30) F B >W P +W S +W D + WL Eq. 2-30

WHERE Where:F B = buoyant force, lb/ft of pipe WP = pipe weight, lb/ft of pipe FWBS == weight buoyant of saturated force, soil above lb/ft pipe, oflb/ft pipe of pipe WWDP = = weight pipe of dry weight, soil above pipe,lb/ft lb/ft of ofpipe pipe WWLS = = weight weight of liquid ofcontents, saturated lb/ft of pipe soil above pipe, lb/ft of pipe

WD = weight of dry soil above pipe, lb/ft of pipe WL = weight of liquid contents, lb/ft of pipe

154-264.indd 234 1/16/09 9:57:19 AM

Figure 2-7: Schematic of Ground Water Flotation Forces

For a 1 ft length of pipe totally submerged, the upward buoyant force is: 86 soil support around the pipe and allow the pipe to buckle from the external hydrostatic pressure.

Flotation is generally not a design consideration for buried pipe where the pipeline runs full or nearly full of liquid or where ground water is always below the pipe invert. Where these conditions are not met, a quick "rule of thumb" is that pipe buried in soil having a saturated unit weight of at least 120 lb/ft3 with at least 1½ pipe diameters of cover will not float. However, if burial is in lighter weight soils or with lesser cover, ground water flotation should be checked.

Mathematically the relationship between the buoyant force and the downward forces is given in Equation 2-30. Refer to Figure 2-7. For an empty pipe, flotation will occur if

F B >W P +W S +W D  WL Eq. 2-30

Where:

FB = buoyant force, lb/ft of pipe WP = pipe weight, lb/ft of pipe WS = weight of saturated soil above pipe, lb/ft of pipeChapter 6 235 Design of PE Piping Systems WD = weight of dry soil above pipe, lb/ft of pipe WL = weight of liquid contents, lb/ft of pipe

8787

87 Figure 2-7: SchematicFigure 3-7 Schematic of of Ground Water Flotation Water Forces Flotation Forces SS 2 2 FFBB==ZZGG ddOO Eq.Eq. 2-31 2-31 For a 1 ft length of pipe running empty4 4and submerged, the upward buoyant force is: (3-31) π 2 F B = ωG d O Eq. 2-31 4 Where:Where:

For a 1 ft length of pipe totallyWhere submerged, the upward buoyant force is: ddOO = = pipepipe outside outside diameter, diameter, ft ft Where: dO = pipe outside diameter, ft = specific ȦweightȦGG = =of ground specific specific water weight weight of of ground ground water water ωG 33 dO = pipe(fresh wateroutside = 62.4(fresh(fresh lb/ftdiameter,3) water water ft= = 62.4 62.4 lb/ft lb/ft) ) 33 ȦG = specific(sea water = weight 64.0(sea lb/ft(sea3 ) ofwater water ground = = 64.0 64.0 water lb/ft lb/ft ) ) (fresh water = 62.4 lb/ft3) (sea water = 64.0 lb/ft3) TheThe average averageThe pipeaverage pipe weight, weight, pipe weight, W WPP in Win Plbs/ft inlbs/ft lbs/ft may may may be be obtained obtained from from from manufacturers’ manufacturers’ manufacturers’ literature literature or or fromfrom Equation Equationliterature 2-32. 2-32. or from Equation 3-32 or from the Table of Weights in the Appendix to The average pipe weight, WthisP in Chapter. lbs/ft mayThis calculation be obtained is based from on themanufacturers’ use of a pipe material literature density or of from Equation 2-32. 0.955 gm/cc. (3-32) 2 2(1(1.06.06˜ ˜DRDR11.12.12)) WW SSdd 5959.6.6 Eq.Eq. 2-32 2-32 PP OO DRDR2 2 2 (1.06 ⋅ DR −1.12) W = πd 59.6 Eq. 2-32 P O DR 2

EquationEquation 2-33 2-33 gives gives the the weight weight of of soil soil per per lineal lineal foot foot of of pipe. pipe.

Equation 2-33 gives the weight of soil per lineal foot of pipe. 154-264.indd 235 1/27/09 11:22:42 AM WWDD==ZZd d(H(H--HHS S))ddOO Eq.Eq. 2-33 2-33

W D = ωd (H - H S )d O Eq. 2-33 Where:Where:

ȦȦ = = unitunit weight weight of of dry dry soil, soil, pcf pcf (See (See Table Table 2-16 2-16 for for typical typical Where: dd values.)values.) Ȧd = unit weightHH of= = drydepthdepth soil, of of pcfcover, cover, (See ft ft Table 2-16 for typical values.) HHSS = = levellevel of of ground ground water water saturation saturation above above pipe, pipe, ft ft H = depth of cover, ft HS = level of ground water saturation above pipe, ft

87

S 2 F B = ZG d O Eq. 2-31 4

Where:

dO = pipe outside diameter, ft ȦG = specific weight of ground water (fresh water = 62.4 lb/ft3) (sea water = 64.0 lb/ft3)

The average pipe weight, WP in lbs/ft may be obtained from manufacturers’ literature or from Equation 2-32.

2 ˜ DR  )12.106.1( SdW 6.59 Eq. 2-32 P O DR 2 236 Chapter 6 Design of PE Piping Systems 88

Equation 2-33 gives the weight of soil per lineal foot of pipe. Table 2-16: Saturated and Dry Soil Unit Weight Equation 3-33 gives the weight of soil per lineal foot of pipe. Unit Weight, lb/ft3 (3-33) W ZdD -(H= H S )d O Eq. 2-33 Soil Type 88 Saturated Dry Where Sands & GravelWhere: ω d = unit weight of dry118-150 soil, pcf (See Table 3-14 for typical values.) 93-144 H = depthTable of cover, 2-16: ft Saturated and Dry Soil Unit Weight 3 Silts & Clays ȦHdS == level unit of ground weight water87-131 saturation of dryabove pipe, soil, ft pcfUnit (See Weight,37-112 Table lb/ft 2-16 for typical values.) Soil Type Glacial Till H = depth of131-150 cover, ft Saturated 106-144 Dry Table 3-14 SandsHSaturated S& = Gravel leveland Dry ofSoil groundUnit Weight water118-150 saturation above pipe, ft 93-144 Crushed Rock 119-137 94-125 Unit Weight, lb/ft3 Silts & Clays 87-131 37-112 Organic Silts & Clay 81-112 Dry, the weight of31-94 Soil Type Saturated, unit weight of saturated soil above the ground water, pcf Glacial Till 131-150pipe, lbs per foot of pipe 106-144 ω S ω d CrushedSands Rock & Gravel 118-150 119-137 93-144 94-125 Silts & Clays 87-131 37-112 § 2 S )-(4 · Organic SiltsGlacial &¨ dTillClayO 131-150 ¸ 81-112 106-144 31-94 W ZZ GSS )-(= ¨ + d O H S ¸ Eq. 2-34 Crushed© Rock 8 119-137 ¹ 94-125 Organic Silts & 81-112 31-94 Clay

Where: ȦS = saturated unit weight of soil, pcf (3-34)  2 π   d O )-(4  W ωω GSS )-(=  + d O H S  Eq. 2-34  8  When an area is submerged, the soil particles are buoyed by their immersion in the ground water. The effectiveWhere weight of submerged soil, (ȦS – ȦG), is the soil's saturated ω S = saturated unit weight of soil, pcf unit weight less the density of Where: the ground ȦS = water. saturated For unit example, weight of a soil, soil pcf of 120 pcf saturated unit weight has anWhen effective an area isweight submerged, of 57.6 the soilpcf particles when arecompletely buoyed by theirimmersed immersion in in water (120 - 62.4 = 57.6 pcf).the ground water. The effective weight of submerged soil, (WS – WG), is the soil’s When an areasaturated is submerged, unit weight theless the soil density particles of the areground buoyed water. For by example, their immersion a soil of in the 120 pcf saturated unit weight has an effective weight of 57.6 pcf when completely Equation 2-35ground gives thewater. weight The per effective lineal foot weight of the of liquidsubmerged in a full soil, pipe. (Ȧ S – ȦG), is the soil's saturated unit weight lessimmersed the densityin water (120 of - the62.4 = ground 57.6 pcf). water. For example, a soil of 120 pcf saturated unit Equationweight 3-35has gives an effectivethe weight weightper lineal of foot 57.6 of the pcf liquid when in a completelyfull pipe. immersed in water (120 - 62.4 = 57.6 pcf). 2 (3-35) S d' W = Z LL Eq. 2-35 4 Equation 2-35 gives the weight per lineal foot of the liquid in a full pipe.

Where Where:W L = weight of the liquid in the pipe, lb/ft ω L = unit weight of liquid in the pipe, pcf π 2 WL = weight of the liquid in thed' pipe, lb/ft W = ω LL Eq. 2-35 ȦL = unit weight of liquid in4 the pipe, pcf

Where: and if half-full, the liquid weight is WL = weight of the liquid in the pipe, lb/ft 154-264.indd 236 1/27/09 11:26:22 AM ȦL = unit weight of liquid in the pipe, pcf

and if half-full, the liquid weight is Chapter 6 237 Design of PE Piping Systems

89

2 S d' 89 89 W = Z LL Eq. 2-36 8 and if half-full, the liquid weight is 2 (3-36) S d' 2 W = Z LL π Eq. 2-36 Where 8d' W = ω LL Eq. 2-36 3 ȦL = 8 unit weight of the liquid in the pipe, lb/ft Where d’ = pipe inside diameter, ft

Where 3 ȦL = unit weight of the liquid in the pipe, lb/ft ω L = unit weight of the liquid in the pipe, lb/ft3 Where d’ = pipe inside diameter, ft For liquid levelsd’ = pipebetween inside diameter, empty ftand half-full (0% to 50%), or between half-full and full 3 (50% to 100%), the Ȧ followingL = unit formulas weight provide of the an liquid approximate in the liquid pipe, weight lb/ft with an accuracy of about +10%. Please refer to Figure 2-8. For liquid levelsFor between liquidd’ empty levels = andbetween pipe half-full inside empty (0% diameter, toand 50%), half-full or betweenft (0% to half-full 50%), or and between full half-full and (50% to 100%),full the (50% following to 100%), formulas the following provide an formulas approximate provide liquid an weight approximate with an liquid weight accuracy of aboutwith +10%. an accuracy Please refer of about to Figure ±10%. 2-8. Please refer to Figure 3-8. For liquid levels between empty and half-full (0% to 50%), or between half-full and full (50% to 100%), the following formulas provide an approximate liquid weight with an accuracy of about +10%. Please refer to Figure 2-8.

Figure 2-8: Flotation and Internal Liquid Levels

Figure 2-8: Flotation and Internal Liquid Levels Figure 3-8 Flotation and Internal Liquid Levels

For a liquid level between empty and half-full, the weight of the liquid in the pipe is approximately For a liquid levelFor between a liquid emptylevel between and half-full, empty the and weight half-full, of the the liquid weight in the of pipe the liquid is in the pipe is approximately approximately (3-37) 3 4 hl ' - hd l W = Z LL 3 0.392+ Eq. 2-37 4 hl 3 ' - hd l hl W = Z LL 0.392+ Eq. 2-37 3 hl FigureWhere 2-8:Where: Flotation h = liquid level and in Internalpipe, ft Liquid Levels hl = liquid level in pipe,l ft Where: hl = liquid level in pipe, ft

For a liquid level between half-full and full, the weight of the liquid in the pipe is 90 Forapproximately a liquid levelFor betweena liquid level half-full between and full, half-full the weight and full, of the the liquid weight in of the the pipe liquid is in the pipe is For a liquidapproximately level between approximately empty and half-full, the weight of the liquid in the pipe is approximately (3-38) § S 2 · ¨ d' ¸ W = Z LL ¨ 1.573- he ¸ Eq. 2-38 © 4 ¹

3 Where:4 hhle ''-hd= - hd l l W = ω LL 0.392+ Eq. 2-37 3 hl Unconstrained Pipe Wall Buckling (Hydrostatic Buckling)

Where: hl = liquid level in pipe, ft The equation for buckling given in this section is here to provide assistance when designing shallow cover applications. However, it may be used to calculate the buckling resistanceFor a liquid of154-264.indd level above between237 grade pipes half-full subject and full, to ex theternal weight air pressure of the liquid due into thean internal pipe is1/27/09 11:32:44 AM vacuum,approximately for submerged pipes in lakes or ponds, and for pipes placed in casings without grout encasement.

Unconstrained pipe are pipes that are not constrained by soil embedment or concrete encasement. Above ground pipes are unconstrained, as are pipes placed in a casing prior to grouting. Buried pipe may be considered essentially unconstrained where the surrounding soil does not significantly increase its buckling resistance beyond its unconstrained strength. This can happen where the depth of cover is insufficient to prevent the pipe from floating slightly upward and breaking contact with the embedment below its springline. Ground water, flooding, or vacuum can cause buckling of unconstrained pipe.

A special case of unconstrained buckling referred to as "upward" buckling may happen for shallow buried pipe. Upward buckling occurs when lateral pressure due to ground water or vacuum pushes the sides of the pipe inward while forcing the pipe crown and the soil above it upward. (Collapse looks like pipe deflection rotated 90 degrees.) A pipe is susceptible to upward buckling where the cover depth is insufficient to restrain upward crown movement. It has been suggested that a minimum cover of four feet is required before soil support contributes to averting upward buckling; however, larger diameter pipe may require as much as a diameter and a half to develop full support.

A conservative design for shallow cover buckling is to assume no soil support, and design the pipe using the unconstrained pipe wall buckling equation. In lieu of this, a concrete cap, sufficient to resist upward deflection, may also be placed over the pipe and then the pipe may be designed using Luscher's equation for constrained buckling.

Equations 2-39 and 2-40 give the allowable unconstrained pipe wall buckling pressure for DR pipe and profile pipe, respectively.

3 f O 2E § 1 · PWU = 2 ¨ ¸ Eq. 2-39 N S P )-(1 © 1-DR ¹ 90

 π 2   d'  W = ω LL  1.573- he  Eq. 2-38  4  238 Chapter 6 Design of PE Piping Systems 90 Where: he '-hd= l

§ S 2 · ¨ d' ¸ Unconstrained PipeW Wall= Z LL ¨Buckling1.573- (Hydrostatiche ¸ Buckling) Eq. 2-38 © 4 ¹ WHERE

The equationWhere: for buckling he '-hd= givenl in this section is here to provide assistance when designing shallow cover applications. However, it may be used to calculate the buckling resistance of above grade pipes subject to external air pressure due to an internal Unconstrainedvacuum, Pipe for Wallsubmerged BucklingUnconstrained pipes (Hydrostatic in lakes Pipe WallBuckling)or ponds, Buckling and (Hydrostatic for pipes Buckling) placed in casings without grout encasement. The equation for buckling given in this section is here to provide assistance when The equation for buckling givendesigning in shallow this section cover applications. is here toHowever, provide it may assistance be used to calculate when the designingUnconstrained shallow cover pipe applications. arebuckling pipes resistance However, that are of above notit may constrainedgrade be pipes used subject toby calculate soilto external embedment the air pressurebuckling or due concrete to an resistanceencasement. of above grade Above pipesinternal ground subject vacuum, pipes for toare submerged ex unconstraiternal pipes air ned, pressure in lakes as orare ponds, due pipes to and an placedfor internalpipes inplaced a casing in vacuum,prior for submerged to grouting. pipes Buriedcasings in lakes pipe without ormay ponds, grout be encasement. considered and for pipes essentially placed in unconstrained casings without where the grout encasement.surrounding soil doesUnconstrained not sign pipeificantly are pipes increase that are not its constrained buckling by resistance soil embedment beyond or concrete its unconstrained strength.encasement. This Above can happen ground pipes where are unconstrained, the depth of as coverare pipes is placed insufficient in a casing to prevent the pipe from floating slightly upward and breaking contact with the embedment Unconstrained pipe are pipesprior that to aregrouting. not Buriedconstrained pipe may by be consideredsoil embedment essentially or unconstrained concrete where below its springline. Ground water, flooding, or vacuum can cause buckling of encasement. Above ground thepipes surrounding are unconstrai soil does notned, significantly as are pipes increase placed its buckling in a resistance casing beyond unconstrained pipe. prior to grouting. Buried pipeits may unconstrained be considered strength. Thisessentially can happen unconstrained where the depth whereof cover theis insufficient surrounding soil does not signto preventificantly the pipe increase from floating its bucklslightlying upward resistance and breaking beyond contact its with the unconstrainedA special strength. case of Thisunconstrainedembedment can happen below buckling its where springline. re theferred Ground depth to as ofwater, "upward" cover flooding, is insufficientbuckling or vacuum may can to cause happen prevent thefor shallowpipe from buried floating pipe.buckling slightly Upward of upward unconstrained buckling and breaking pipe. occurs whencontact lateral with thepressure embedment due to ground below itswater springline. or vacuum Ground pushesA special water, the case sides flooding, of unconstrained of the orpipe vacuum buckling inward referred while can cause forcingto as “upward” bucklingthe pipe buckling crown of may and unconstrainedthe soil pipe. above it upward.happen (Cfor ollapseshallow buried looks pipe. like Upward pipe deflection buckling occurs rotated when 90lateral degrees.) pressure A pipe is susceptible todue upward to ground buckling water or vacuumwhere pushesthe cover the sides depth of the is pipe insufficient inward while to forcingrestrain upward crown movement. It has been suggested that a minimum cover of four feet is A special case of unconstrainedthe pipe buckling crown andreferred the soil to above as it"upward" upward. (Collapse buckling looks may like happen pipe deflection required before soil rotated support 90 degrees.) contributes A pipe to is susceptible averting to upward upward buckling;buckling where however, the cover larger depth for shallow buried pipe. Upward buckling occurs when lateral pressure due to ground diameter pipe may requireis insufficient as much to restrain as a diupwardameter crown and movement. a half to It develophas been suggested full support. that a water or vacuum pushes the sides of the pipe inward while forcing the pipe crown and minimum cover of four feet is required before soil support contributes to averting the soil above it upward. (Collapse looks like pipe deflection rotated 90 degrees.) A upward buckling; however, larger diameter pipe may require as much as a diameter pipe is susceptibleA conservative to upward design buckling for shallow where cover the cover buckling depth is tois insufficient assume no to soil restrain support, and and a half to develop full support. upward crowndesign movement.the pipe using It has the been unconstrained suggested pipe that walla minimum buckling cover equation. of four In feet lieu is of this, a required concrete before soil cap, support sufficient A contributes conservative to resist design toupward averting for shallowdeflection, upward cover bucklingmay buckling; also is to be however,assume placed no soil largerover support, the andpipe diameterand pipe then may the require pipe mayasto much designbe designed as the a pipe diameter usingusing the Luscher'sand unconstrained a half equationto developpipe wall for bucklingfull constrained support. equation. buckling. In lieu of this, a concrete cap, sufficient to resist upward deflection, may also be placed over the pipe and then the pipe may be designed using Luscher’s equation for constrained A conservativeEquations design 2-39 forand shallow 2-40 give cover the bucklingallowable is unconstrained to assume no pipe soil wall support, buckling and pressure buckling. design thefor pipeDR pipe using and the profile unconstrained pipe, respectively. pipe wall buckling equation. In lieu of this, a concrete cap, sufficient to resistEquations upward 3-39 anddeflection, 3-40 give themay allowable also beunconstrained placed over pipe wallthe bucklingpipe and then the pipe may be designedpressure using for DR Luscher'spipe and profile equation pipe, respectively. for constrained buckling. 3 (3-39) f 2E  1  = O   Eq. 2-39 Equations 2-39 and 2-40 give theP allowableWU unconstrained2 pipe wall buckling pressure N S µ )-(1  1-DR  for DR pipe and profile pipe, respectively.

3 f O 2E § 1 · PWU = 2 ¨ ¸ Eq. 2-39 N S P )-(1 © 1-DR ¹

154-264.indd 238 1/16/09 9:57:22 AM 91

f 24EI = = O Eq. 2-40 PWU 2 3 N S P )-(1 DM Chapter 6 23991 Design of PE Piping Systems

Where:

PWU = allowable unconstrained pipe wall buckling pressure, psi (3-40) f 24EI DR = Dimension = O Ratio Eq. 2-40 PWU 2 3 E = apparentN S modulusµ )-(1 DM of elasticity of pipe material, psi fO = Ovality Correction Factor, Figure 2-9

NWSHE RE = safety factor 4 IP WU == allowable Pipe unconstrainedwall moment pipe wall of buckling inertia, pressure, in /in psi ȝDR = =Dimension Poisson's Ratio ratio Where:E = apparent modulus of elasticity of pipe material, psi DM = Mean diameter, (DI + 2z or DO -t), in fO = Ovality Correction Factor, Figure 3-9 DI = P pipeWU =inside allowable diameter, unconstrained in pipe wall buckling pressure, psi N = safety factor z S = DR wall-section = Dimension centroidal Ratio distance from inner fiber of pipe, in I = Pipe wall moment of inertia, in4/in E = apparent modulus of elasticity of pipe material, psi μ = Poisson’s ratio fO = Ovality Correction Factor, Figure 2-9 DM = Mean diameter, (DI + 2z or DO -t), in NS = safety factor Although buckling occursD = pipe rapidly, inside diameter, long-term in external pressure can gradually deform the I I = Pipe wall moment of inertia, in4/in pipe to the point of z instability. = wall-section centroidal This distance behavior from inner is fiber considered of pipe, in (obtain viscoelastic from pipe producer) and can be ȝ = Poisson's ratio accounted for in Equations 2-39 and 2-40 by using the apparent modulus of elasticity DM = Mean diameter, (DI + 2z or DO -t), in value for the appropriateAlthough time buckling and temperatureoccurs rapidly, long-term of the specificexternal pressure application can gradually as given deform in DI = pipe inside diameter, in Table 2-6. For Poisson'sthe pipe z ratio,to the = point designers wall-section of instability. typically centroidal This behavior use distance a is value considered from of 0.45 viscoelasticinner for fiber long-term and of pipe, in loading on polyethylenecan bepipe, accounted and 0.35 for in for Equations short-term 3-39 and loading. 3-40 by using the apparent modulus of elasticity value for the appropriate time and temperature of the specific application as given in the Appendix, Chapter 3. For Poisson’s ratio, use a value of 0.45 for all PE OvalityAlthough or deflection buckling of the occurs pipe rapidly,diameter long-term increases external the local pressure radius ofca ncurvature gradually of deform the the pipe wall and thus reducespipe materials. buck ling resistance. Ovality is typically reported as the pipe to the point of instability. This behavior is considered viscoelastic and can be percentage reductionOvality in pipe or diameterdeflection or:of the pipe diameter increases the local radius of curvature of accounted for thein pipeEquations wall and 2-39thus reduces and 2-40 buckling by resistance.using the Ovality apparent is typically modulus reported of aselasticity value for the appropriatethe percentage reduction time and in temperaturepipe diameter or: of the specific application as given in Table 2-6. For(3-41) Poisson's ratio, designers typically use a value of 0.45 for long-term § I -D DMIN · loading on polyethylene%DEFLECTIO pipe, and 0.35100=N for¨ short-term¸ loading. Eq. 2-41 © DI ¹ Ovality or deflection of the pipe diameter increases the local radius of curvature of the Where: pipe wall and W thusHERE reduces buckling resistance. Ovality is typically reported as the DI = pipe inside diameter, in percentage reductionD inI pipe = pipe diameter inside or:diameter, in DMIN = pipe minimum inside diameter, in DMIN = pipe minimum inside diameter, in

 I -D DMIN  %DEFLECTIO 100=N   Eq. 2-41  DI  Where:

DI = pipe inside diameter, in DMIN = pipe minimum inside diameter, in

154-264.indd 239 1/16/09 9:57:22 AM 240 Chapter 6 Design of PE Piping Systems

92

Figur e 2-9: Ovalit y Com pens ation Facto r, ƒ0

The desig ner should compare the critical buckling pressure with the actual anticipated pressure, and apply Figure a safety 3-9 factorOvality Compensation commensurate Factor, with į their assessment of the application. A safety factor of 2.5 is common, but specific circumstances may warrant a higher or lower safetyThe factor. designer For should large-diameter compare the submergedcritical buckling pipe, pressure the anticipated with the actual pressure may be conservatively calculated by determining the height of water from the pipe invert anticipated pressure, and apply a safety factor commensurate with their assessment rather than from the pipe crown. of the application. A safety factor of 2.5 is common, but specific circumstances may warrant a higher or lower safety factor. For large-diameter submerged pipe, the anticipated pressure may be conservatively calculated by determining the height of Ground Water Flotation Example water from the pipe invert rather than from the pipe crown.

Find the allowableGround Water flood Flotationwater level Example above a 10" DR 26 HDPE pipe installed with only 2 ft of cover. Assume the pipe has 3 percent ovality due to shipping, handling, and installationFind loads. the allowable flood water level above a 10” DR 26 PE4710 pipe installed with only 2 ft of cover. Assume the pipe has 3 percent ovality due to shipping, handling, and installation loads. SOLUTION:SOLUTION: Use Equation Use Equation 2-39. 3-39. The The pipe pipe wall wall buckling buckling pressure pressure dependsdepends upon upon the the duration ofduration the water of the level water above level theabove pipe. the pipe. If the If thewater water level level is is constant, long lasting, then then a along- term valuelong-term of the stress value relaxationof the stress modulus relaxation should modulus be should used, bebut used, if the but water if the levelwater rises only occasionally,level rises a onlyshorter occasionally, term elastic a shorter modulus term mayelastic be modulus applied. may be applied. Case (a): For the long lasting water above the pipe, the stress relaxation modulus at 50 year, 73ºF is approximately 29,000 lb/in2 for a typical PE4710 material. Assuming Case (a): For the constant water above the pipe, the stress relaxation modulus at 50 93 3% ovality (fO equals 0.76) and a 2.5 to 1 safety factor, the allowable long-term year, 73°ҢF is approximately 28,200 lb/in2 for a typical P3408 material. Assuming 3% pressure, PWU is given by: ovality (fO equals 0.76) and a 2.5 to 1 safety factor, the allowable long-term pressure, 3 PWU is given by: )76.0( 2 (28,200) (29,000) 1  1.4 psig (3.2 ft-hd−= ) PWU = 2   = 2.34.1 Hdftpsi 5.2 0.-(1 45 )  1-26 

Case (b): Flooding conditions are occasional happenings, usually lasting a few days to a week or so. However, ground water elevations may remain high for several weeks following154-264.indd a flood. 240 The 1000 hour (41.6 days) elastic modulus value has been used1/16/09 9:57:22 to AM approximate the expected flood duration.

3 )76.0( 2(43,700)  1  PWU =   = 9.41.2 −= Hdftpsi 5.2 0.-(1 452 )  1-26 

SECTION 3: THERMAL DESIGN CONSIDERATIONS

INTRODUCTION

Like most materials, polyethylene is affected by changing temperature. Unrestrained, 93

3 )76.0( 2 (28,200)  1  −= PWU = 2   = 2.34.1 Hdftpsi 5.2 0.-(1 45 )  1-26  Chapter 6 241 Design of PE Piping Systems

Case (b): Flooding conditions are occasional happenings, usually lasting a few days to a week or so. However, ground water elevations may remain high for several weeks following a flood.Case (b):The Flooding 1000 conditionshour (41.6 are occasionaldays) elastic happenings, modulus usually value lasting has a few been days used to approximate theto a expectedweek or so. floodHowever, duration. ground water elevations may remain high for several weeks following a flood. The 1000 hour elasticmodulus value has been used to approximate the expected flood duration. 3 )76.0( 2(43,700)(46,000)  1  PWU =   = 2.2 5.29.41.2 ft. −= (ofHdftpsi head) 5.2 0.-(1 452 )  1-26 

SECTION 3: THERMAL DESIGN CONSIDERATIONS

INTRODUCTION

Like most materials, polyethylene is affected by changing temperature. Unrestrained,

154-264.indd 241 1/16/09 9:57:23 AM 242 Chapter 6 Design of PE Piping Systems

Section 4 Thermal Design Considerations

Introduction Similar to all thermoplastics, the engineering behavior of PE can be significantly affected by temperature. An increase in temperature causes a decrease in strength and in apparent modulus. A decrease in temperature results in opposite effects. For effective pipeline design these effects must be adequately recognized.

In the case of pressure pipe the highest operating temperature is limited by the practical consideration of retaining sufficient long-term strength or maintaining the pressure rating that is sufficient for the intended application. That maximum temperature is generally 140°F (60°C). De-rating factors for up to 140°F are presented in the Appendix to Chapter 3. If higher temperatures are being considered, the pipe supplier should be consulted for additional information.

In the case of buried applications of non-pressure pipe, in which the embedment material provides a significant support against pipe deformation, the highest operating temperature can be higher –sometimes, as high 180°F (~82°C). The temperature re-rating factors for apparent modulus of elasticity, which are presented in the Appendix, Chapter 3, can be used for the re-rating of a pipe’s 73°F pipe stiffness for any other temperature between -20 to 140°F (-29 to 60°C). For temperatures above 140°F the effect is more material dependent and the pipe supplier should be consulted.

A beneficial feature of PE pipe is that it retains much of its toughness even at low temperatures. It can be safely handled, installed and operated even in sub-freezing conditions. The formation of ice in the pipe will restrict or, stop flow but not cause pipe breakage. Although under sub-freezing conditions PE pipe is somewhat less tough it is still much tougher that most other pipe materials.

Strength and Stress/Strain Behavior As discussed earlier in this Handbook, the engineering properties of PE material are affected by the magnitude of a load, the duration of loading, the environment and the operating temperature. And, also as discussed earlier, the standard convention is to report the engineering properties of PE piping materials based on a standard environment – which is water – and, a standard temperature – which is 73°F (23°C). A design for a condition that departs from this convention requires that an appropriate accommodation be made. This Section addresses the issue of the effect of a different temperature than that of the base temperature.

154-264.indd 242 1/16/09 9:57:23 AM Chapter 6 243 Design of PE Piping Systems

To properly consider the affect of temperature on strength and, on stress/strain properties this must be done based on actually observed long-term strength behavior. Tables which are presented in an Appendix to Chapter 3, list temperature adjustment factors that have been determined based on long-term evaluations.

Thermal Expansion/Contraction Effects Fused PE pipe joints are fully restrained. The pipe and the fused joints can easily accommodate the stress induced by changes in temperature. In general thrust restraints and mechanical expansion joints are not required in a fully fused PE piping system. However, thrust restraint may be necessary where PE pipe is connection to other ‘bell and spigot’ end pipe. Design for this condition is addressed later in this chapter and in PPI’s TN-36.

Because the coefficient of thermal expansion for PE is significantly larger than that of non-plastics, considerations relating to the potential effects of thermal expansion/ contraction may include:

• Piping that is installed when it is warm may cool sufficiently after94 installation to generate significant tensile forces. Thus, the final connection should be made after polyethylene will experience greaterthe pipe expansion has equilibrated and to its contraction operating temperature. than many other materials due to increasing or decreasing• Unrestrained (respectively) pipe may shrink temperatures. enough so that it However, pulls out from its a low mechanical joint elastic modulus eases the challengethat does of arrestingnot provide sufficient this movement, pull-out resistance. and very Methods often used end to connect PE restraints may be employed to eliminatepipe should the provideeffects restraint of temperature against pull-out changes. that is either inherent to the joint design or additional mechanical restraint. See Chapter 9. (Note –specially designed thrust blocks may be needed to restrain movement when mechanical joints are in Polyethylene pipe can be installed and operated in sub-freezing conditions. Ice in the line with PE pipes.) pipe will restrict or stop flow, but not cause pipe breakage. In sub-freezing conditions, polyethylene is not as impact resistant• Unrestrained as it pipeis at that room is exposed temperature. to significant In temperature all cases, swings one will in some should follow the unloading guidelinescombination, in the expand handling and contract, and storage deflect laterally, section or ofapply the compressive PPI or tensile Engineering Handbook chapter “Inspections,loads to constraints Tests, or supports. and Safety Considerations” that calls for use of lifting devices to safeA mitigatingly unload factor polyethylene is PE’s relatively piping low modulus products. of elasticity, which greatly reduces the thrust that is generated by a restrained expansion/contraction. This thrust imposes no problem on thermal fusion connections. See Chapter 8 for additional information on designing above grade pipelines for Unrestrained Thermal Effects thermal effects. The theoretical change in length for an unrestrained pipe placed on a frictionless surface can be determined from UnrestrainedEquation 3-1. Thermal Effects The theoretical change in length for an unrestrained pipe placed on a frictionless surface can be determined from Equation 4-1. (4-1) ∆ = α ∆ TLL Eq. 3-1

Where: ǻL = pipeline length change, in L = 154-264.indd pipe length, 243 ft 1/16/09 9:57:23 AM Į = thermal expansion coefficient, in/in/°F ǻT = temperature change, °F

The coefficient of thermal expansion for polyethylene pipe material is approximately 1 x -4 10 in/in/°F. As a “rule of thumb,” temperature change for unrestrained PE pipe is about “1/10/100,” that is, 1 inch for each 10° F temperature change for each 100 foot of pipe. A temperature rise results in a length increase while a temperature drop results in a length decrease.

End Restrained Thermal Effects

A length of pipe that is restrained or anchored on both ends and placed on a frictionless surface will exhibit a substantially different reaction to temperature change than the unrestrained pipe discussed above. If the pipe is restrained in a straight line between two points and the temperature decreases, the pipe will attempt to decrease in length. Because the ends are restrained or anchored, length change cannot occur, so a 244 Chapter 6 Design of PE Piping Systems

Where ∆ L = pipeline length change, ft L = pipe length, ft α = thermal expansion coefficient, in/in/ºF ∆ T = temperature change,ºF

The coefficient of thermal expansion for PE pipe material is approximately 1 x 10-4 in/in/˚F. As a “rule of thumb,” temperature change for unrestrained PE pipe is about “1/10/100,” that is, 1 inch for each 10˚F temperature change for each 100 foot of pipe. A temperature rise results in a length increase while a temperature drop results in a length decrease.

end restrained Thermal effects A length of pipe that is restrained or anchored on both ends and one placed on a frictionless surface will exhibit a substantially different reaction 95to temperature change than the unrestrained pipe discussed above. If the pipe is restrained in a straight line between two points and the temperature decreases, the pipe will longitudinal tensile stress is createdattempt along to the decrease pipe. in The length. magnitude Because the of ends this are stress restrained can or be anchored, length determined using Equation 3-2. change cannot occur, so a longitudinal tensile stress is created along the pipe. The magnitude of this stress can be determined using Equation 4-2. (4-2) V D 'TE Eq. 3-2

Where terms are as definedWhere above, terms andare as defined above, and σ = longitudinal stress in pipe, psi ı = longitudinal stress in pipe, psi E = apparent modulus elasticity of pipe material, psi E = apparent modulus elasticity of pipe material, psi 47

The value of the apparent modulus of elasticity of the pipe material has a large 2 impactP L = 2890lbon the calculated / ft stress. As with all thermoplastic materials, PE’s modulus, The value of the apparent modulus of elasticity of the pipe material has a large and therefore its stiffness, is dependent on temperature and the duration of the impact on the calculated stressapplied. As with load. allTherefore, thermoplastic the appropriate materials, elastic modulus polyethylene’s should be selected based on modulus, and thereforeBoussinesq its stiffness, Equationthese is two dependent variables. When on temper determiningature the and appropriate the duration time interval, of it is important the applied load. Therefore, the appropriateto consider that elastic heat transfer modulus occurs should at relatively be selected slow rates throughbased the wall of PE on these two variables.The When Boussinesq determining Equation the appropriate gives the pressure time interval, at any pointit is important in a soil mass under a pipe; therefore temperature changes do not occur rapidly. Because96 the temperature to consider that heat concentrated transfer occurschange surface does at load. relativelynot happenThe Boussinesq rapidly, slow ratesthe Equationaverage through temperature may thebe used is wall often to of findchosen the for pressure the transmitted from a wheel load to a point that is not along the line of action of the load. polyethylene pipe; therefore temperaturemodulus selection. changes do not occur rapidly. Because the Pavement effects are neglected. temperature change does not happen(4-3) rapidly, the average temperature is often chosen V AF P Eq. 3-3 for the modulus selection. Where terms are as defined above, and 3 F = end thrust, lb W3I wf H PL = Eq. 2-4 5 2 2 2 Where terms are as defined above,AP = area ofand pipe cross section,(2π /4)(DOr – Di ) in TableF 3-1: = Apparent end thrust, Modulus lb Elasticity for HDPE Pipe Material A = area atof Variouspipe cross Temperatures section,(ʌ/4)(D 2 – D 2) in2 P Where: O i PE 3408 Apparent Elastic Modulus†, 1000 psi (MPa), at Temperature, °F (°C) Load Duration 2 -20 (-29) 0 (-18) 40P L(4) = vertical60 (16) soil pressure 73 (23) due 100to live (38) load 120 lb/ft (49) 140 (60) 300.0 260.0 170.0 130.0 110.0 100.0 65.0 50.0 EquationsShort-Term 3-2 and 3-3 can also be usedWw =to wheel determine load, lb the compressive stress and thrust (2069) (1793)154-264.indd 244(1172) (896) (758) (690) (448) (345) 1/27/09 11:36:22 AM (respectively) from140.8 a temperature122.0 increase.79.8 61.0 57.5 46.9 30.5 23.5 10 h H = vertical depth to pipe crown, ft (971) (841) (550) (421) (396) (323) (210) (162) 125.4 108.7 71.0If = impact54.3 factor 51.2 41.8 27.2 20.9 Although100 h the length change of polyethylene pipe during temperature changes is greater (865) (749) (490) r = distance(374) from the(353) point of load(288) application (188) to pipe (144)crown, ft than many other107.0 materials, 92.8 the amount60.7 of force46.4 required43.7 to restrain35.7 the movement23.2 17.8 is 1000 h less because of its(738) lower modulus(640) of(419) elasticity. (320) (301) (246) (160) (123) 93.0 80.6 52.7 40.3 38.0 31.0 20.2 15.5 1 y =r X + H 22 Eq. 2-5 As pipeline temperature(641) decreases(556) (363)from weather(278) or operating(262) conditions,(214) a(139) longitudinal (107) 77.4 67.1 43.9 33.5 31.6 25.8 16.8 12.9 10 y tensile stress develops(534) along(463) the pipe(303) that can(231) be determined(218) using(178) Equation (116) 3-2. The(89) allowable tensile69.1 stress for59.9 pipe operating39.1 at29.9 its pressure28.2 rating23.0 is determined15.0 using11.5 50 y Equation 3- 4 . (476) (413) (270) (206) (194) (159) (103) (79) † Typical values based on ASTM D 638 testing of molded plaque material specimens. An elastic modulus for PE 2406 may be estimated by multiplying the PE 3408 modulus value by 0.875.

Eq. 3-4 V As longitudinal stress builds in theallow pipe wall, DFxHDB a thrust load is created on the end structures.Where The thrust load is determined by Equation 3-3. 2 ıallow = Allowable tensile stress at 73°F, lb/in HDB = Hydrostatic Design Basis, psi (Table 1-1)* DF = Design Factor, from Table 1-2 * The manufacturer should be consulted for HDB values for temperatures other than 73°F.

Equation 3-3 is used to determine the thrust load applied to structural anchoring devices.

During temperature increase, the pipeline attempts to increase in length, but is restrained by mechanical guides that direct longitudinal compressive thrust to structural anchors that prevent length increase. This in turn creates a longitudinal compressive stress in the pipe and a thrust load against the structural anchors. The compressive stress that develops in the pipe and is resisted by the structural anchors is determined using Equation 3-2. Compressive stress should not exceed the allowable compressive stress per Table 2-12 in Section 2 of this chapter. 96

= σ AF P Eq. 3-3

Where terms are as defined above, and F = end thrust, lb 2 2 2 AP = area of pipe cross section,(ʌ/4)(DO – Di ) in

Chapter 6 245 Design of PE Piping Systems Equations 3-2 and 3-3 can also be used to determine the compressive stress and thrust (respectively) from a temperature increase.

Although the length change of polyethylene pipe during temperature changes is greater Equations 4-2 and 4-3 can also be used to determine the compressive stress and than many other materials, the amount of force required to restrain the movement is thrust (respectively) from a temperature increase. less because of its lower modulus of elasticity. Although the length change of PE pipe during temperature changes is greater than As pipeline temperature decreasesmany from other materials,weather theor amountoperating of force conditions, required to arestrain longitudinal the movement is less tensile stress develops along thebecause pipe ofthat its lowercan modulusbe determined of elasticity. using Equation 3-2. The allowable tensile stress for pipeAs operatingpipeline temperature at its pressuredecreases from rating weather is determinedor operating conditions, using a Equation 3- 4 . longitudinal tensile stress develops along the pipe that can be determined using Equation 4-2. The allowable tensile stress for pipe operating at its pressure rating is determined by the HDS for that temperature. The HDS is that of the pipe material for the base temperature at 73˚F (23˚C) times the temperature adjustment factor listed in Appendix, Chapter 3. Eq. 3-4 (4-4) σ allow == HDS x DFxHDB FT

Where WHERE HDS = Hydrostatic Design Stress, psi (Table 1-1) 2 ıallow = Allowable tensile stress at 73°F, lb/in F = Temperature factor (See Appendix, Chapter 3) HDB = HydrostaticT Design Basis, psi (Table 1-1)* DF = Design Factor, from Table 1-2 Equation 4-3 is used to determine the thrust load applied to structural anchoring * The manufacturer shoulddevices. be consulted for HDB values for temperatures other than 73°F. During temperature increase, the pipeline attempts to increase in length, but is restrained by mechanical guides that direct longitudinal compressive thrust to structural anchors that prevent length increase. This in turn creates a longitudinal Equation 3-3 is used to determine the thrust load applied to structural anchoring compressive stress in the pipe and a thrust load against the structural anchors. devices. The compressive stress that develops in the pipe and is resisted by the structural anchors is determined using Equation 4-2. Compressive stress should not exceed the During temperature increase, allowablethe pipeline compressive attempts stress per to the increase Appendix in in Chapter length, 3. but is restrained by mechanical guides that direct longitudinal compressive thrust to structural anchors that prevent length increase.above Ground This inPiping turn Systemscreates a longitudinal compressive stress in the pipe and a thrust load against the structural anchors. The compressive The design considerations for PE piping systems installed above ground are stress that develops in the pipe and is resisted by the structural anchors is determined extensive and, therefore, are addressed separately in the Handbook chapter on above using Equation 3-2. Compressive stress should not exceed the allowable compressive ground applications for PE pipe. stress per Table 2-12 in Section 2 of this chapter.

Buried Piping Systems A buried pipe is generally well restrained by soil loads and will experience very little lateral movement. However, longitudinal end loads may result that need to be addressed.

Transitions to other pipe materials that use the bell and spigot assembly technique will need to be calculated using the thrust load as delivered by the pressure

154-264.indd 245 1/16/09 9:57:24 AM 97 246 Chapter 6 Design of PE Piping Systems

Above Ground Piping Systems

The design considerationsplus the forpotential polyethyl of theene load duepiping to temperature systems changes.installed Merely above fixing ground the end are extensive and, therefore,of the PE are to the addressed mating material separately may result in in the up PPIstream Engineering joints pulling Handbookapart chapter on “Above Groundunless those Applications connections for are PE restrained. Pipe.” The number of joints that need to be restrained to prevent bell and spigot pull out may be calculated using techniques as recommended by the manufacturer of the alternate piping material. Equation 4-3 Buried Piping Systemsmay be used to calculate the total thrust load due to temperature change. Low thrust capacity connections to manholes or other piping systems as will A buried pipe is generallybe present well in many restrained no pressure by gravity soil flow friction systems along may its be length,addressed andvia a with moderate or low temperaturelongitudinal change, thrust anchor soil suchfriction as shown alone in Fig.is usually 4-1. The sizesufficient of the thrust to prevent block will thermal expansion andvary depending contraction on soil movement. conditions and Consequently, the thrust load as a calculated buried polyethylene via Equation 4-3.

Figure 4-1 Longitudinal Thrust Anchor pipe will usually experience a change in internal stress rather than dimensional change and movement. A very significant temperature decrease may exceed soil friction restraint, and apply Conclusion contraction thrust loads to pipeline appurtenances. Longitudinal thrust anchoring may be used to protect underground connections that have limited The durability and visco-elastic nature of modern PE piping materials makes these resistance to longitudinal movement, but are usually not required unless great products ideally suited for a broad array of piping applications such as: potable temperature change is anticipated. water mains and service lines, natural gas distribution, oil and gas gathering, force main sewers, gravity flow lines, industrial and various mining piping. To this end, fundamental design considerations such as fluid flow, burial design and thermal response were presented within this chapter in an effort to provide guidance to the piping system designer on the use of these tough piping materials in the full array of potential piping applications.

ForFigure the benefit 3-1: of Longitudinalthe pipeline designer, Thrust a considerable Anchor amount of background information and/or theory has been provided within this chapter. However, the designer should also keep in mind that the majority of pipeline installations fall Typically, the soil frictionwithin can the becriteria employed for the AWWA to arrest Design the Window effects approach of operating presented temperature in Section 3 changes. In smaller diameter pipe, the pipe is usually “snaked” from side to side within the ditch to assist in the soil anchoring.

154-264.indd 246 1/16/09 9:57:24 AM Chapter 6 247 Design of PE Piping Systems

of this chapter. Pipeline installations that fall within the guidelines for the AWWA Window, may be greatly simplified in matters relating to the design and use of flexible PE piping systems.

While every effort has been made to be as thorough as possible in this discussion, it also should be recognized that these guidelines should be considered in light of specific project, installation and/or service needs. For this reason, this chapter on pipeline design should be utilized in conjunction with the other chapters of this Handbook to provide a more thorough understanding of the design considerations that may be specific to a particular project or application using PE piping systems. The reader is also referred to the extensive list of references for this chapter as additional resources for project and or system analysis and design.

References for Section 1 Kerr, Logan, “Water Hammer Problems in Engineering Design”, Consulting Engineering, May 1985 Howard; A., “The Reclamation E’ Table, 25 Years Later”, Plastic Pipe XIII, Washington, D. C., Oct. 2-5, 2006. Marshall, G. P., Brogden, S., “Evaluation of the Surge and Fatigue Resistances of PVC and PE Pipe Materials for use in the U.K. Water Industry”, Plastics Pipe X, September ’98, Gotenberg, Sweden. UK Water Industry IGN 4-37-02, “Design Against Surge And Fatigue Conditions For Thermoplastics Pipes”, March 1999.

References for Section 2 1. Jeppson, Roland W., Analysis of Flow in Pipe Networks, Ann Arbor Science, Ann Arbor, MI. 2. Distribution Network Analysis, AWWA Manual M32, American Water Works Association, Denver, CO. 3. ASTM D 2513, Standard Specification for Thermoplastic Gas Pipe, Tubing and Fittings, American Society for Testing and Materials, West Conshohocken, PA. 4. ASTM D 2737, Standard Specification for PE (PE) Tubing, American Society for Testing and Materials, West Conshohocken, PA. 5. ASTM D 2447, Standard Specification for PE (PE) Plastic Pipe, Schedules 40 and 80, Based on Outside Diameter, American Society for Testing and Materials, West Conshohocken, PA. 6. ASTM D 3035, Standard Specification for PE (PE) Plastic Pipe (DR-PR) Based on Controlled Outside Diameter, American Society for Testing and Materials, West Conshohocken, PA. 7. ASTM F 714, Standard Specification for PE (PE) Plastic Pipe (SDR-PR) Based on Controlled Outside Diameter, American Society for Testing and Materials, West Conshohocken, PA. 8. ANSI/AWWA C901, AWWA Standard for PE (PE) Pressure Pipe and Tubing, 1/2 In.(13 mm) Through 3 In. (76 mm) for Water Service, American Water Works Association, Denver, CO 9. ANSI/AWWA C906, AWWA Standard for PE (PE) Pressure Pipe and Fittings, 4 In. Through 63 In. for Water Distribution, American Water Works Association, Denver, CO. 10. API Specification 15LE, Specification for PE Line Pipe (PE), American Petroleum Institute, Washington DC. 11. ASTM D 2104, Standard Specification for PE (PE) Plastic Pipe, Schedule 40, American Society for Testing and Materials, West Conshohocken, PA. 12. ASTM D 2239, Standard Specification for PE (PE) Plastic Pipe (SIDR-PR) Based on Controlled Inside Diameter, American Society for Testing and Materials, West Conshohocken, PA. 13. ASTM F 894, Standard Specification for PE (PE) Large Diameter Profile Wall Sewer and Drain Pipe, American Society for Testing and Materials, West Conshohocken, PA. 14. PPI TR-22, PE Piping Distribution Systems for Components of Liquid Petroleum Gases, Plastics Pipe Institute, Irving, TX. 15. Nayyar, Mohinder L. (1992). Piping Handbook , 6th Edition, McGraw-Hill, New York, NY. 16. Iolelchick, I.E., Malyavskaya O.G., & Fried, E. (1986). Handbook of Hydraulic Resistance, Hemisphere Publishing Corporation. 17. Moody, L.F. (1944). Transactions, Volume 6, American Society of Mechanical Engineers (ASME), New York, NY. 18. Swierzawski, Tadeusz J. (2000). Flow of Fluids, Chapter B8, Piping Handbook, 7th edition, Mohinder L. Nayyar, McGraw-Hill, New York, NY. 19. Lamont, Peter A. (1981, May). Common Pipe Flow Formulas Compared with the Theory of Roughness, Journal of the American Water Works Association, Denver, CO. 20. Flow of Fluids through Valves, Fittings and Pipe. (1957). Crane Technical Paper No 410, the Crane Company, Chicago, IL. 21. Chen, W.F., & J.Y. Richard Liew. (2002). The Civil Engineering Handbook, 2nd edition, CRC Press, Boca Raton, FL.

154-264.indd 247 1/16/09 9:57:24 AM 248 Chapter 6 Design of PE Piping Systems

22. Bowman, J.A. (1990). The Fatigue Response of Polyvinyl Chloride and PE Pipe Systems, Buried Plastics Pipe Technology, ASTM STP 1093, American Society for Testing and Materials, Philadelphia. 23. Marshall, GP, S. Brogden, & M.A. Shepherd, Evaluation of the Surge and Fatigue Resistance of PVC and PE Pipeline Materials for use in the UK Water Industry, Proceedings of Plastics Pipes X, Goteborg, Sweden. 24. Fedossof, F.A., & Szpak, E. (1978, Sept 20-22). Cyclic Pressure Effects on High Density PE Pipe, Paper presented at the Western Canada Sewage Conference, Regian, Saskatoon, Canada. 25. Parmakian, John. (1963). Waterhammer Analysis, Dover Publications, New York, NY. 26. Thompson, T.L., & Aude, T.C. (1980). Slurry Pipelines, Journal of Pipelines, Elsevier Scientific Publishing Company, Amsterdam. 27. Handbook of Natural Gas Engineering. (1959). McGraw-Hill, New York, NY. 28. AGA Plastic Pipe Manual for Gas Service. (2001). American Gas Association, Washington DC. 29. ASCE Manuals and Reports on Engineering Practice No. 60. (1982). Gravity Sewer Design and Construction, American Society of Civil Engineers, New York, NY. 30. Hicks, Tyler G. (1999). Handbook of Civil Engineering Calculations, McGraw-Hill, New York, NY. 31. PPI TR-14, Water Flow Characteristics of Thermoplastic Pipe, Plastics Pipe Institute, Irving, TX. 32. Kerr, Logan, Water Hammer Problems in Engineering Design, Consulting Engineering, May 1985.

References for Section 3 1. Watkins, R.K., Szpak, E., & Allman, W.B. (1974). Structural Design of PE Pipes Subjected to External Loads, Engr. Experiment Station, Utah State Univ., Logan. 2. AWWA (2006), PE Pipe Design and Installation, M55, American Water Works Association, Denver, CO. 3. Howard, A.K. (1996). Pipeline Installation, Relativity Printing, Lakewood, Colorado,ISBN 0-9651002-0-0. 4. Spangler, M.G. (1941). The Structural Design of Flexible Pipe Culverts, Bulletin 153, Iowa Engineering Experiment Station, Ames, IA. 5. Watkins, R.K., & Spangler, M.G. (1958). Some Characteristics of the Modulus of Passive Resistance of Soil—A Study in Similitude, Highway Research Board Proceedings 37:576-583, Washington. 6. Burns, J.Q., & Richard, R.M. (1964). Attenuation of Stresses for Buried Cylinders, Proceedings of the Symposium on Soil Structure Interaction, pp.378-392, University of Arizona, Tucson. 7. Katona, J.G., Forrest, F.J., Odello, & Allgood, J.R. (1976). CANDE—A Modern Approach for the Structural Design and Analysis of Buried Culverts, Report FHWA-RD-77-5, FHWA, US Department of Transportation. 8. Howard, A.K. (1977, January). Modulus of Soil Reaction Values for Buried Flexible Pipe, Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No GT 1. 9. Petroff, L.J. (1995). Installation Technique and Field Performance of PE, Profile Pipe, Proceedings 2nd Intl. Conference on the Advances in Underground Pipeline Engineering, ASCE, Seattle. 10. Duncan, J.M., & Hartley, J.D. (1982). Evaluation of the Modulus of Soil Reaction, E’, and Its Variation with Depth, Report No. UCB/GT/82-02, University of California, Berkeley. 11. Howard, A.K. (1981). The USBR Equation for Predicting Flexible Pipe Deflection, Proceedings Intl. Conf. On Underground Plastic Pipe, ASCE, New Orleans, LA. 12. Janson, L.E. (1991). Long-Term Studies of PVC and PE Pipes Subjected to Forced Constant Deflection, Report No. 3, KP-Council, Stockholm, Sweden. 13. Spangler, M.G., & Handy, R.L. (1982). Soil Engineering, 4th ed., Harper & Row, New York. 14. Watkins, R.K. (1977). Minimum Soil Cover Required Over Buried Flexible Cylinders, Interim Report, Utah State University, Logan, UT. 15. Gaube, E. (1977, June). Stress Analysis Calculations on Rigid PE and PVC Sewage Pipes, Kunstoffe, Vol.67, pp. 353-356, Germany. 16. Gaube, E., & Muller, W. (1982, July). Measurement of the long-term deformation of PE pipes laid underground, Kunstoffe, Vol. 72, pp. 420-423, Germany. 17. Moore, I. D., & Selig, E. T. (1990). Use of Continuum Buckling Theory for Evaluation of Buried Plastic Pipe Stability, Buried Plastic Pipe Technology, ASTM STP 1093, Philadelphia. 18. Marston, A. (1930). Iowa Engineering Experiment Station, Bulletin No. 96. 19. McGrath, T. (1994). Analysis of Burns & Richard Solution for Thrust in Buried Pipe, Simpson Gumpertz & Heger, Inc, Cambridge, Mass. 20. McGrath, T.J. (1998). Replacing E’ with the Constrained Modulus in Flexible Pipe Design, proceedings Pipeline Div. Conf. Pipelines in the Constructed Environment, ASCE, San Diego, CA. 21. Bowles, J.E. (1982). Foundation Analysis and Design, 3rd ed., McGraw-Hill Book Company, New York.

154-264.indd 248 1/16/09 9:57:25 AM Chapter 6 249 Design of PE Piping Systems

appendix a.1

PIPE WEIGHTS aND DIMENSIONS (DIPS) (Black)

Pipe Minimum

inside Wall

diameter Thickness Weight OD (d) (t) (w) Nominal Actual lb. per in. in. DR* in. in. foot 7 2.76 0.566 2.621 9 3.03 0.440 2.119 11 3.20 0.360 1.776 13.5 3.34 0.293 1.476 3 3.960 15.5 3.42 0.255 1.299 17 3.47 0.233 1.192 21 3.56 0.189 0.978 26 3.64 0.152 0.798 32.5 3.70 0.122 0.644

7 3.35 0.686 3.851 9 3.67 0.533 3.114

11 3.87 0.436 2.609 13.5 4.05 0.356 2.168 4 4.800 15.5 4.14 0.310 1.909 17 4.20 0.282 1.752 21 4.32 0.229 1.436 26 4.41 0.185 1.172 32.5 4.49 0.148 0.946

7 4.81 0.986 7.957 9 5.27 0.767 6.434 11 5.57 0.627 5.392 13.5 5.82 0.511 4.480 6 6.900 15.5 5.96 0.445 3.945 17 6.04 0.406 3.620 21 6.20 0.329 2.968 26 6.34 0.265 2.422 32.5 6.45 0.212 1.954

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Pipe Minimum

inside Wall

diameter Thickness Weight OD (d) (t) (w) Nominal Actual lb. per in. in. DR* in. in. foot 7 6.31 1.293 13.689 9 6.92 1.006 11.069 11 7.31 0.823 9.276 13.5 7.63 0.670 7.708 8 9.050 15.5 7.81 0.584 6.787 17 7.92 0.532 6.228 21 8.14 0.431 5.106 26 8.31 0.348 4.166 32.5 8.46 0.278 3.361

7 7.74 1.586 20.593 9 8.49 1.233 16.652 11 8.96 1.009 13.955 13.5 9.36 0.822 11.595 10 11.100 15.5 9.58 0.716 10.210 17 9.72 0.653 9.369 21 9.98 0.529 7.681 26 10.19 0.427 6.267 32.5 10.38 0.342 5.056

7 9.20 1.886 29.121 9 10.09 1.467 23.548 11 10.66 1.200 19.734 13.5 11.13 0.978 16.397 12 13.200 15.5 11.39 0.852 14.439 17 11.55 0.776 13.250 21 11.87 0.629 10.862 26 12.12 0.508 8.863 32.5 12.34 0.406 7.151

7 10.67 2.186 39.124 9 11.70 1.700 31.637 11 12.35 1.391 26.513 13.5 12.90 1.133 22.030 14 15.300 15.5 13.21 0.987 19.398 17 13.39 0.900 17.801 21 13.76 0.729 14.593 26 14.05 0.588 11.907 32.5 14.30 0.471 9.607

154-264.indd 250 1/16/09 9:57:25 AM Chapter 6 251 Design of PE Piping Systems

Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR* in. in. foot 7 12.13 2.486 50.601 9 13.30 1.933 40.917 11 14.05 1.582 34.290 13.5 14.67 1.289 28.492 16 17.400 15.5 15.02 1.123 25.089 17 15.23 1.024 23.023 21 15.64 0.829 18.874 26 15.98 0.669 15.400 32.5 16.26 0.535 12.425

7 13.59 2.786 63.553 9 14.91 2.167 51.390 11 15.74 1.773 43.067 13.5 16.44 1.444 35.785 18 19.500 15.5 16.83 1.258 31.510 17 17.07 1.147 28.916 21 17.53 0.929 23.704 26 17.91 0.750 19.342 32.5 18.23 0.600 15.605

7 15.06 3.086 77.978 9 16.51 2.400 63.055 11 17.44 1.964 52.842 13.5 18.21 1.600 43.907 20 21.600 15.5 18.65 1.394 38.662 17 18.91 1.271 35.479 21 19.42 1.029 29.085 26 19.84 0.831 23.732 32.5 20.19 0.665 19.147

11 20.83 2.345 75.390 13.5 21.75 1.911 62.642 15.5 22.27 1.665 55.159 24 25.800 17 22.58 1.518 50.618 21 23.20 1.229 41.495 26 23.70 0.992 33.858 32.5 24.12 0.794 27.317

154-264.indd 251 1/16/09 9:57:25 AM 252 Chapter 6 Design of PE Piping Systems

Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR* in. in. foot 13.5 26.97 2.370 96.367 15.5 27.62 2.065 84.855 30 32.000 17 28.01 1.882 77.869 21 28.77 1.524 63.835 26 29.39 1.231 52.086 32.5 29.91 0.985 42.023

* These DRs (7.3, 9, 11, 13.5, 17, 21, 26, 32.5) are from the standard dimension ratio (SDR) series established by ASTM F 412.51

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appendix a.2

PIPE WEIGHTS aND DIMENSIONS (IPS) (BLACK)

Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 7 0.59 0.120 0.118 7.3 0.60 0.115 0.114 1/2 0.840 9 0.64 0.093 0.095 9.3 0.65 0.090 0.093 11 0.68 0.076 0.080 11.5 0.69 0.073 0.077

7 0.73 0.150 0.184 7.3 0.75 0.144 0.178 3/4 1.050 9 0.80 0.117 0.149 9.3 0.81 0.113 0.145 11 0.85 0.095 0.125 11.5 0.86 0.091 0.120

7 0.92 0.188 0.289 7.3 0.93 0.180 0.279 1 1.315 9 1.01 0.146 0.234 9.3 1.02 0.141 0.227 11 1.06 0.120 0.196 11.5 1.07 0.114 0.188

7 1.16 0.237 0.461 7.3 1.18 0.227 0.445 9 1.27 0.184 0.372 1 1/4 1.660 9.3 1.28 0.178 0.362 11 1.34 0.151 0.312 11.5 1.35 0.144 0.300 13.5 1.40 0.123 0.259

154-264.indd 253 1/16/09 9:57:25 AM 254 Chapter 6 Design of PE Piping Systems

Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 7 1.32 0.271 0.603 7.3 1.35 0.260 0.583 9 1.45 0.211 0.488 1 1/2 1.900 9.3 1.47 0.204 0.474 11 1.53 0.173 0.409 11.5 1.55 0.165 0.393 13.5 1.60 0.141 0.340 15.5 1.64 0.123 0.299

7 1.66 0.339 0.943 7.3 1.69 0.325 0.911 9 1.82 0.264 0.762 9.3 1.83 0.255 0.741 2 2.375 11 1.92 0.216 0.639 11.5 1.94 0.207 0.614 13.5 2.00 0.176 0.531 15.5 2.05 0.153 0.467 17 2.08 0.140 0.429

7 2.44 0.500 2.047 7.3 2.48 0.479 1.978 9 2.68 0.389 1.656 9.3 2.70 0.376 1.609 11 2.83 0.318 1.387 3 3.500 11.5 2.85 0.304 1.333 13.5 2.95 0.259 1.153 15.5 3.02 0.226 1.015 17 3.06 0.206 0.932 21 3.15 0.167 0.764 26 3.21 0.135 0.623

154-264.indd 254 1/16/09 9:57:25 AM Chapter 6 255 Design of PE Piping Systems

Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 7 3.14 0.643 3.384 7.3 3.19 0.616 3.269 9 3.44 0.500 2.737 9.3 3.47 0.484 2.660 11 3.63 0.409 2.294 4 4.500 11.5 3.67 0.391 2.204 13.5 3.79 0.333 1.906 15.5 3.88 0.290 1.678 17 3.94 0.265 1.540 21 4.05 0.214 1.262 26 4.13 0.173 1.030 32.5 4.21 0.138 0.831

7 3.88 0.795 5.172 7.3 3.95 0.762 4.996 9 4.25 0.618 4.182 9.3 4.29 0.598 4.065 11 4.49 0.506 3.505 5 5.563 11.5 4.54 0.484 3.368 13.5 4.69 0.412 2.912 15.5 4.80 0.359 2.564 17 4.87 0.327 2.353 21 5.00 0.265 1.929 26 5.11 0.214 1.574 32.5 5.20 0.171 1.270

7 4.62 0.946 7.336 7.3 4.70 0.908 7.086 9 5.06 0.736 5.932 9.3 5.11 0.712 5.765 11 5.35 0.602 4.971 6 6.625 11.5 5.40 0.576 4.777 13.5 5.58 0.491 4.130 15.5 5.72 0.427 3.637 17 5.80 0.390 3.338 21 5.96 0.315 2.736 26 6.08 0.255 2.233 32.5 6.19 0.204 1.801

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Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 7 6.01 1.232 12.433 7.3 6.12 1.182 12.010 9 6.59 0.958 10.054 9.3 6.66 0.927 9.771 11 6.96 0.784 8.425 8 8.625 11.5 7.04 0.750 8.096 13.5 7.27 0.639 7.001 15.5 7.45 0.556 6.164 17 7.55 0.507 5.657 21 7.75 0.411 4.637 26 7.92 0.332 3.784

7 7.49 1.536 19.314 7.3 7.63 1.473 18.656 9 8.22 1.194 15.618 9.3 8.30 1.156 15.179 11 8.68 0.977 13.089 10 10.750 11.5 8.77 0.935 12.578 13.5 9.06 0.796 10.875 15.5 9.28 0.694 9.576 17 9.41 0.632 8.788 21 9.66 0.512 7.204 26 9.87 0.413 5.878 32.5 10.05 0.331 4.742

7 8.89 1.821 27.170 7.3 9.05 1.747 26.244 9 9.75 1.417 21.970 9.3 9.84 1.371 21.353 11 10.29 1.159 18.412 12 12.750 11.5 10.40 1.109 17.693 13.5 10.75 0.944 15.298 15.5 11.01 0.823 13.471 17 11.16 0.750 12.362 21 11.46 0.607 10.134 26 11.71 0.490 8.269 32.5 11.92 0.392 6.671

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Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 7 9.76 2.000 32.758 7.3 9.93 1.918 31.642 9 10.70 1.556 26.489 9.3 10.81 1.505 25.745 11 11.30 1.273 22.199 14 14.000 11.5 11.42 1.217 21.332 13.5 11.80 1.037 18.445 15.5 12.09 0.903 16.242 17 12.25 0.824 14.905 21 12.59 0.667 12.218 26 12.86 0.538 9.970 32.5 13.09 0.431 8.044

7 11.15 2.286 42.786 7.3 11.35 2.192 41.329 9 12.23 1.778 34.598 9.3 12.35 1.720 33.626 11 12.92 1.455 28.994 16 16.000 11.5 13.05 1.391 27.862 13.5 13.49 1.185 24.092 15.5 13.81 1.032 21.214 17 14.00 0.941 19.467 21 14.38 0.762 15.959 26 14.70 0.615 13.022

7 12.55 2.571 54.151 7.3 12.77 2.466 52.307 9 13.76 2.000 43.788 9.3 13.90 1.935 42.558 11 14.53 1.636 36.696 18 18.000 11.5 14.68 1.565 35.263 13.5 15.17 1.333 30.491 15.5 15.54 1.161 26.849 17 15.76 1.059 24.638 21 16.18 0.857 20.198 26 16.53 0.692 16.480 32.5 16.83 0.554 13.296

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Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 7 13.94 2.857 66.853 7.3 14.19 2.740 64.576 9 15.29 2.222 54.059 9.3 15.44 2.151 52.541 11 16.15 1.818 45.304 20 20.000 11.5 16.31 1.739 43.535 13.5 16.86 1.481 37.643 15.5 17.26 1.290 33.146 17 17.51 1.176 30.418 21 17.98 0.952 24.936 26 18.37 0.769 20.346 32.5 18.70 0.615 16.415

9 16.82 2.444 65.412 9.3 16.98 2.366 63.574 11 17.76 2.000 54.818 11.5 17.94 1.913 52.677 22 22.000 13.5 18.55 1.630 45.548 15.5 18.99 1.419 40.107 17 19.26 1.294 36.805 21 19.78 1.048 30.172 26 20.21 0.846 24.619 32.5 20.56 0.677 19.863

9 18.35 2.667 77.845 9.3 18.53 2.581 75.658 11 19.37 2.182 65.237 11.5 19.58 2.087 62.690 24 24.000 13.5 20.23 1.778 54.206 15.5 20.72 1.548 47.731 17 21.01 1.412 43.801 21 21.58 1.143 35.907 26 22.04 0.923 29.299 32.5 22.43 0.738 23.638

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Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 11 22.60 2.545 88.795 11.5 22.84 2.435 85.329 13.5 23.60 2.074 73.781 15.5 24.17 1.806 64.967 28 28.000 17 24.51 1.647 59.618 21 25.17 1.333 48.874 26 25.72 1.077 39.879 32.5 26.17 0.862 32.174

11 24.22 2.727 101.934 11.5 24.47 2.609 97.954 13.5 25.29 2.222 84.697 15.5 25.90 1.935 74.580 30 30.000 17 26.26 1.765 68.439 21 26.97 1.429 56.105 26 27.55 1.154 45.779 32.5 28.04 0.923 36.934

13.5 26.97 2.370 96.367 15.5 27.62 2.065 84.855 32 32.000 17 28.01 1.882 77.869 21 28.77 1.524 63.835 26 29.39 1.231 52.086 32.5 29.91 0.985 42.023

15.5 31.08 2.323 107.395 17 31.51 2.118 98.553 36 36.000 21 32.37 1.714 80.791 26 33.06 1.385 65.922 32.5 33.65 1.108 53.186

15.5 36.26 2.710 146.176 17 36.76 2.471 134.141 42 42.000 21 37.76 2.000 109.966 26 38.58 1.615 89.727 32.5 39.26 1.292 72.392

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Pipe Minimum inside Wall OD diameter Thickness Weight (d) (t) (w) Nominal Actual lb. per in. in. DR in. in. foot 17 42.01 2.824 175.205 48 48.000 21 43.15 2.286 143.629 26 44.09 1.846 117.194 32.5 44.87 1.477 94.552

21 48.55 2.571 181.781 54 54.000 26 49.60 2.077 148.324 32.5 50.48 1.662 119.668

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appendix a.3 List of Design Chapter Variables

υ = kinematic viscosity, ft2/sec ρ = fluid density, lb/ft3 μ = dynamic viscosity, lb-sec/ft2 Δ v = Sudden velocity change, ft/sec a = Wave velocity (celerity), ft/sec 2 AC = Cross-sectional area of pipe bore, ft ac = contact area, ft2 A = profile wall average cross-sectional area, in2/in, for profile pipe or wall thickness (in) for DR pipe 2 2 2 AS = Area of pipe cross-section or (∏/4) (DO – Di ), in AP = area of the outside wall of the pipe, 100 in2 C = Hazen-Williams Friction Factor, dimensionless ,see table 1-7. c = outer fiber to wall centroid, in

CV = percent solids concentration by volume CW = percent solids concentration by weight DA = pipe average inside diameter, in DF = Design Factor, from Table 1-2 d’ = Pipe inside diameter, ft

DI = Pipe inside diameter, in DM = Mean diameter (DI+2z or DO-t), in DMIN = pipe minimum inside diameter, in Do = pipe outside diameter, in dO = pipe outside diameter, ft DR = Dimension Ratio, DO/t E = Apparent modulus of elasticity for pipe material, psi e = natural log base number, 2.71828 E’ = Modulus of soil reaction, psi

Ed = Dynamic instantaneous effective modulus of pipe material (typically 150,000 psi for PE pipe) EN = Native soil modulus of soil reaction, psi ES = Secant modulus of the soil, psi ES* = ES/(1-μ) f = friction factor (dimensionless, but dependent upon pipe surface roughness and Reynolds number) F = end thrust, lb

FB = buoyant force, lb/ft FL = velocity coefficient (Tables 1-14 and 1-15) fO = Ovality Correction Factor, Figure 2-9 FS = Soil Support Factor FT = Service Temperature Design Factor, from Table 1-11 g = Constant gravitational acceleration, 32.2 ft/sec2

HP = profile wall height, in H = height of cover, ft

hl = liquid level in the pipe, ft HGW = ground water height above pipe, ft h1 = pipeline elevation at point 1, ft

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h1 = inlet pressure, in H2O hU = upstream pipe elevation, ft

h2 = pipeline elevation at point 2, ft

h2 = outlet pressure, in H2O

dD = downstream pipe elevation, ft HDB = Hydrostatic Design Basis, psi

hE = Elevation head, ft of liquid

hf = friction (head) loss, ft. of liquid

HS = level of ground water saturation above pipe, ft

IV = Influence Value from Table 2-5 I = Pipe wall moment of inertia, in4/in IDR = ID -Controlled Pipe Dimension Ratio

If impact factor k = kinematic viscosity, centistokes

KBULK = Bulk modulus of fluid at workingtemperature

KBED = Bedding factor, typically 0.1 K = passive earth pressure coefficient K’ = Fittings Factor, Table 1-5

KP = permeability constant (Table 1-13)

LEFF = Effective Pipeline length, ft. L = Pipeline length, ft

LDL = Deflection lag factor ∆ L = pipeline length change, in M = horizontal distance, normal to the pipe centerline, from the center of the load to the load edge, ft

Ms = one-dimensional modulus of soil, psi n = roughness coefficient, dimensionless N = horizontal distance, parallel to the pipe centerline, from the center of the load to the load edge, ft

NS = safety factor P = Internal Pressure, psi

PW = perimeter wetted by flow, ft 2 p1 = inlet pressure, lb/in absolute 2 p2 = outlet pressure, lb/in absolute 2 PA = pipe internal pressure, atmospheres (1 atmosphere = 14.7 lb/in ) PC = Pressure Class

PCR = Critical constrained buckling pressure, psi

PE = vertical soil pressure due to earth load, psf

Pf = friction (head) loss, psi

PL = vertical soil pressure due to live load, psf

POS = Occasional Surge Pressure 2 PRD = radial directed earth pressure, lb/ft

PRS = Recurring Surge Pressure

Ps = Transient surge pressure, psig

PWAT = Allowable live load pressure at pipe crowm for pipes with one diameter or less of cover, psf 2 PWC = allowable constrained buckling pressure, lb/in

PWU = allowable unconstrained pipe wall buckling pressure, psi

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2 pi = Pressure due to sub-area i lb/ft Q = flow rate, gpm

3 QFPS = flow, ft /sec 3 Qh = flow, standard ft /hour

qP = volume of gas permeated, cm3 (gas at standard temperature and pressure)

rH = hydraulic radius, ft r = distance from the point of load application to pipe crown, ft R = buoyancy reduction factor

rCENT = radius to centroidal axis of pipe, in Re = Reynolds number, dimensionless

RH = Geometry Factor RSC = Ring Stiffness Constant, lb/ft

r T = equivalent radius, ft RF = Rigidity factor, dimensions s = liquid density, gm/cm3

SH = hydraulic slope, ft/ft S = pipe wall compressive stress, lb/in2 2 SMAT = material yield strength, lb/in

SA = Hoop Thrust Stiffness Ratio

Sg = gas specific gravity

SL = carrier liquid specific gravity

SM = slurry mixture specificgravity

SS = solids specific gravity t = minimum wall thickness, in t’ = wall thickness, mils

TCR = Critical time, seconds V = flow velocity, ft/sec VAF = Vertical Arching Factor

VC = critical settlement velocity, ft/sec ν = kinematic viscosity. ft2/sec

VMin = approximate minimum velocity, ft/sec w = unit weight of soil, pcf w = unit weight of soil, lb/ft3

WD = weight of dry soil above pipe, lb/ft of pipe

Ww = wheel load, lb

WL = weight of liquid contents, lb/ft of pipe

WL = weight of the liquid in contacts, lb/ft of pipe WP = Working Pressure, psi

WP = pipe weight, lb/ft of pipe WPR = Working Pressure Rating, psi 2 wS = distributed surcharge pressure acting over ground surface, lb/ft

WS = weight of saturated soil above pipe, lb/ft of pipe ζ = dynamic viscosity, centipoises Z = Centroid of wall section, in Z = Pipe wall centroid, in

Zi = wall-section centroidal distance from inner fiber of pipe, in α = thermal expansion coefficient, in/in/ºF

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Δ L = length change, in Δ T = temperature change, ºF Δ X = Horizontal deflection, in ΔV = Sudden velocity change., ft/sec ε = absolute roughness, ft. ε s = Soil strain Θ = elapsed time, days

μs = Poisson’s Ratio of Soil μ = Poisson’s ratio σ = longitudinal stress in pipe, psi

σallow = Allowable tensile stress at 73ºF, lb/in ϕ = Calibration Factor, 0.55 for granular soils change in psi 3 ω D = unit weight of dry soil,lb/ft (See Table 2-16 for typical values.) 3 ω G = unit weight of groundwater lb/ft 3 ω L = unit weight of liquid in the pipe, lb/ft 3 ω S = unit weight of saturated soil, pcf lb/ft φ = angle of internal friction, deg Γ = Dynamic viscosity, lb-sec/ft2

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