American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Longitudinal Mechanics of Buried Thermoplastic Pipe: Analysis of PVC Pipes of Various Joint Types
Shah Rahman1, Reynold K. Watkins2 ABSTRACT The analysis of longitudinal deformations compared to performance limits of deformation in buried pipes is referred to as longitudinal mechanics. Principal causes of longitudinal stress and strain within a pipe system include changes in temperature, internal pressure or vacuum, and beam bending. The widespread use of thermoplastic pipes, namely polyvinyl chloride (PVC), in municipal applications throughout North America in the past four decades has made it necessary to re-visit the topic of longitudinal mechanics for pipes that incorporate various types of joining systems. Typical North American PVC pipe joints are either bell-and-spigot gasket-joint or welded (heat-fused Fusible PVC and solvent-cement joints). Analysis herein focuses on the three main causes of longitudinal stresses and strains in bell-and-spigot gasket joints and welded joints, and includes discussion of theoretical concepts such as the Poisson effect and the Reissner effect. Topics which have raised issues in the field such as ponding due to sags in a PVC gravity line and the occasional cracking of PVC pipe bells during or after installation are also discussed. Current industry and manufacturer recommendations of various design parameters are provided in conjunction with the analysis. INTRODUCTION Buried pipes form the bedrock of civilization’s infrastructure, the arteries of communal life. As the exigency for quality communal life increases, so also does the necessity for buried pipelines. The demand for thermoplastic pipes is noteworthy because of leak resistance, long service life, and adaptability. Structural failures of modern thermoplastic pipes are significantly lowered due to their high flexibility and strainability, which enables them to work in tandem with surrounding soils to support applied loading. Pipe wall cracking due to excessive loading or joint deflection while a pipe is in service is almost eliminated with solid wall thermoplastic pipes.
1

Vice President – Technical Services, S&B Technical Products/Hultec, 1300 E. Berry St., Fort Worth, TX 76119; tel. (817) 923-3344; fax (817) 923-1339; srahman@sbtechprod.com 2 Professor Emeritus, Department of Civil and Environmental Engineering, Utah State University, Logan, UT 84322; tel. (435) 797-2864; fax (435) 797-1185; reynold@cc.usu.edu

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Typical design of buried pipe is based on ring stress due to pressure in and on the pipe. However, from field experience, most gasket-joint thermoplastic pipe troubles emanate from longitudinal stress. Soil embedment is a major component in the analysis of buried thermoplastic pipes. Design must be based on pipe-soil interaction. While the topic of longitudinal stresses in pipelines has been analyzed before (Watkins, 1985), the scope of this paper is longitudinal mechanics as it pertains to flexible thermoplastic PVC pipe (rigid unplasticized-PVC, uPVC). The typical North American PVC municipal pipe joints are either gasket-joint (bell-and-spigot) or welded (heat-fused Fusible PVC and solvent-cement joints). In addition, there are at least two proprietary PVC restrained joints of various designs (Rahman, 2004a), analyses of which are outside the scope of this paper. Bell-and-Spigot Gasket Joints: For purposes of analysis, pipe with gasket-joint is considered free-end pipe, i.e. the pipe can shorten or lengthen within limits of the bell-and-spigot joint. This has been the traditional joint-type associated with PVC pressure and gravity pipes used in municipal open-cut installations. The beveled spigot-end of the adjoining pipe is slipped into the bell up to the guide mark (“witness” mark) indicated on the spigot, Figure 1a; the elastomeric gasket is usually prepositioned in the bell and provides a water-tight compression seal, Figure 1b. The space or gap left between the beveled end of the spigot and the neck of the bell after installation accommodates pipe expansion due to changes in temperature, as well as angular deflection at the joint, figure 1c.

Figure 1a, b, c. PVC Bell-and-Spigot Gasket-Joint (Rahman 2004b, Fisher 1998) Welded Joints: For analysis, pipe with welded joint is considered fixed-end (restrained joint) pipe; the joint resists any change in length of the adjoining pipe sections. There are two types of welded joints in PVC pipe --- heat-fused joints and solvent-cement joints. Heat-fused PVC incorporates a combination of heat and pressure, resulting in two melted surfaces flowing together to produce a joint by fusion bonding when the joint cools below the melt temperature of the material. After cooling, the joint is as strong as the pipe wall. This is a procedure similar to the method for joining polyolefin pipes such as high density polyethylene (HDPE) and polypropylene (PP). Temperatures and pressures applied for fusion of the joint are unique to each material type. Formation of “beads” both on the inside and outside of the joint is characteristic of the fusion process, and may be removed if necessary, Figures 2a, b. Also known as Fusible PVC, the pipe is manufactured to both ASTM

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

and AWWA standards, and is used in pressure and gravity applications for diameters of 4-inch (100 mm) and above. This joint type is most useful for trenchless construction and rehabilitation such as horizontal directional drilling (HDD), sliplining, guided boring, and pipe bursting.

Figure 2a, b. Fusible PVC Pipe with Outside Bead, Cross Sectional Schematic In solvent cement joints, welding is chemical bonding and fusion by application of a translucent chemical between the bell (or coupling) and spigot at the joint, Figures 3a, b. Solvent-cement joints are used typically in small-diameter buried PVC pipes (below 4-inch (100 mm) diameter), and are also widely used in non-buried plumbing applications. Pipes of diameters larger than 4-inch, with solvent cement joints, are also available and are still used in some older utilities for sewer service.

Figure 3a, b. Chemical Bonding and Fusion in Solvent-Cement Joints PROPERTIES OF MATERIAL Analysis of buried thermoplastic pipe must be based on a firm understanding of the properties of the materials. Soil properties range from particulate (grain) to viscous (mud). Pipe properties range from plastic to ductile. Thermoplastics such as PVC are viscoelastic. Viscoelastic materials exhibit elastic as well as viscous-like characteristics. A material that deforms under stress, but regains its original shape and size when the load is removed is classified as elastic. Viscous materials, on the other hand, after being subjected to a deforming load, do not recover their original shape and size once the load is removed. In reality, all materials deviate from the linear relationship between stress and strain (Hooke’s Law) at some point in various ways. The two types of thermoplastics most widely used for pipe manufacture include vinyls (PVC, CPVC) and polyolefins (HDPE, PP, PB). For thermoplastic pipe, the designer must consider viscoelastic properties. This can be illustrated using a plastic candy rope. Under constant force, candy rope stretches (creeps) and decreases in cross section until it breaks in a few seconds. If the force is increased, the time to break decreases. This phenomenon is referred to as strength 3

American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

regression. Under constant strain, i.e. stretched slightly then held at constant elongation, the holding force decreases (relaxes) over time. But if the force is increased suddenly, the resisting strength of the rope is pristine --- not regressed. Short term forces are resisted by pristine strength of the plastic, and are most critical during installation. Under rapid loading the thermoplastic behaves like an elastic solid, so that the ratio of stress to strain is constant and independent of time. For this reason, thermoplastic pipes resist short-duration high surge pressures without strength regression. The analogy of the candy rope is illustrated in Figure 4. Graph A represents the linear relationship between stress-strain in an elastic material, such as steel or iron. A specimen of thermoplastic material such as PVC, when rapidly loaded under testing conditions, will also display this behavior. The set of Graphs B is representative of the behavior of a viscoelastic material such as the candy rope (or a PVC pipe that is put into service) that is loaded gradually. There is no longer a directly linear relationship between stress-strain, and the gradients of the curves depend on the loading time. Creep and the relaxation phenomena are also shown.

Figure 4. Stress-Strain Relationships (Rahman 2005) Properties of pipe-grade thermoplastics can be summarized as follows: 1) Under constant stress, a) Thermoplastic creeps over time b) Strength regresses over time 2) Under constant strain, a) Stress relaxes over time b) Strength remains pristine

Except for strength regression, properties of plastics do not deteriorate over the design life. However, properties may be altered by extreme temperatures and by gross chemical deterioration. It should be noted that within the group of thermoplastics, there is a wide range of behavior of properties. For example, differences in the modulus of elasticity, E, can cause one type of thermoplastic pipe to stretch significantly more than another type in response to longitudinal and/or hoop stresses being applied to it. In the manufacturing process, the outside diameter (OD) of the thermoplastic pipe is the diameter of the extruder. In applications where a pipe’s OD is the controlling factor (as in trenchless 4

American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

construction methods such as directional drilling), a thermoplastic pressure pipe of higher tensile strength would allow thinner walls, and consequently, larger internal flow area than another thermoplastic pipe of an equivalent pressure capacity but a lower tensile strength. Of all thermoplastics used in pipe manufacture, PVC has the highest modulus of elasticity and tensile strength. Plastic pipe under constant internal pressure (constant stress), is designed for strength regression over a long time period --- minimum of 100 years. Strength regression data are available (Uni-Bell, 2001). Design of plastic pipe that is held to constant deformation is based on pristine properties. In good installations, the pipe is held in constant shape and alignment by the embedment --- constant strain. Consequently, stresses relax over the service life of the pipeline (Moser, 2000). PVC pipe that has been buried for a long time will hold most of its deflected shape after removal, proving that a large percentage of the initial internal stresses have disappeared through the process of stress relaxation (Bishop, 1981). Research has shown that after 22 years, PVC pipes maintain the same capacity to resist additional deflection increments as when initially installed, which means that its modulus, E, does not decrease with time (Moser, 2001). Notations and Parameters: Notations and parameters used in the equations and examples that follow are based on the following --- nominal 12-inch (300 mm) diameter, (Ductile Iron Pipe Size – DIPS), AWWA C900 PVC pressure pipe, DR 18, Pressure Class 150 psi, cell class 12454B, with either gasket-joint or heat-fused joint (Fusible PVC). Notations not listed below are explained in the body of the text. OD tmin DR t ID σ S S E ε ν θ α P ∆T Rb = = = = = = = = = = = = = = = = Outside Diameter = 13.20” (335 mm) Minimum wall thickness = 0.733” (18.6 mm) Dimension Ratio = OD/tmin = 18 Wall thickness = 0.8” (20.3 mm) Internal Diameter = OD – (2 x t) = 11.60” (295 mm) Stress (“yield stress” = 7000 psi (48.3 MPa) for cell class 12454B). All North American PVC pressure pipes are manufactured to cell class 12454B only Design strength pristine (allowable) = 4000 psi (27.6 MPa) Long-term allowable strength (with factor of safety of 2.5) = 1600 psi (11 MPa) Modulus of “elasticity” = 400,000 psi (2.8 GPa) Strain (by Hooke’s elastic law, E = σ/ε) Poisson’s Ratio = 0.38 for PVC Joint deflection (offset angle of the two adjoining sections of pipe at a belland-spigot gasket joint) Coeff. thermal expansion / contraction for PVC =3.0(10-5)/oF = 5.4(10-5)/oC Eα = 12 psi/oF = 150 kPa/ oC Internal pressure or vacuum, or external pressure Temperature change (oF) Radius of longitudinal bend of pipe

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

LONGITUDINAL EXPANSION AND CONTRACTION Pipes tend to expand and contract under changes in temperature and internal or external pressure. The effect of temperature change depends on the type of joint. In fixed-end pipe (restrained joint), the joint resists any change in length of the adjoining pipe section; this is representative of a welded joint. In free-end pipe, as is the case with gasket joints, the pipe can shorten or lengthen within limits of the bell-andspigot joint. In the analysis that follows, both stress and strain are considered. In many cases, strain is usually a better basis for analysis than stress. 1. Effect of Temperature Changes

For welded joints in pipe, temperature stress (thermally induced stress) is defined by: σ = Eα (∆T) (1)

Decrease in temperature results in the pipe’s attempt to shorten, but it is restrained by longitudinal tension, Figure 5.

Figure 5. Longitudinal Stress in Welded Joint (Restrained Joint) Pipe For gasket-joints in sections of pipe, temperature strain is defined by: ε = α (∆T) Example: For welded joints in straight sections of pipe, a decrease in temperature of ∆T = 50oF (28oC) causes longitudinal tensile stress of σ = 600 psi (4.1 MPa), using Equation 1. This stress must be resisted by welded joints (Fusible PVC joints and solvent-cement joints). If the change in temperature is permanent, stresses relax over time. If changes in temperature are cyclic, pipe design is based on strength regression which is mitigated by the number of cycles per unit of time. In general, temperature stress, by itself, is not critical, but could add to other longitudinal stresses. (2)

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

In gasket joints, there is no longitudinal restraint at the joints. A free-end pipe of length L = 20 ft (6 m), subjected to a decrease in temperature of ∆T = 50oF (28oC), shortens by ∆L = α(∆T)L = 0.36 inches (9 mm), half at each end. In fact, there is some soil friction resistance to shortening of buried pipe. Gasketed joints must be able to accommodate the changes in length. The coefficient of thermal expansion, α, will vary by the type of thermoplastic pipe. For example, in a polyolefin pipe where α is 1.2x10-4 in/in/oF, there would be an increase in length four times greater than the length increase in an equivalent length of PVC pipe (in PVC α is 3.0x10-5 in/in/oF). However, this would not necessarily result in incrementally higher stresses in the polyolefin since its modulus of elasticity, E, would be sufficiently low. Similarly, temperature decreases would result in overall length contractions. Depending on the sensitivity of the pipe material to temperature change, provisions need to be made to accommodate changes in length. Common problems associated with pipes of high thermal expansion coefficients include “pulling out” of pipe from mechanical joining systems during cold weather. This has never been cited as a problem with Fusible PVC pipe in the field. Changes in length can also be caused by soil movement, bending of the pipe, and pressure. 2. Effect of Internal Pressure on Longitudinal Stress and Strain

The effect of internal pressure results in Poisson’s effect, whereby the diameter of the pipe increases and the length shortens. Poisson’s ratio, ν, is the ratio of longitudinal strain to lateral strain under the condition of uniform and uniaxial longitudinal stress within the proportional limit. For PVC, ν = 0.38. For welded joints in pipe, internal pressure causes longitudinal stress, defined as: σ = νP(ID)/2t (3)

In welded joint pipe (restrained joint), as the pipe tries to shorten, it is restrained by longitudinal tension, Figure 6.

Figure 6. Poisson Effect in Welded Joint (Restrained Joint) Pipe

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

For gasket joints in pipe, internal pressure causes longitudinal strain, defined as: ε = νP(ID)/2Et Example: What is the longitudinal stress for fixed-end, and longitudinal strain for free-end pipe in this 12-inch PVC pipe if internal pressure is P = 100psi? For welded joints, longitudinal stress, σ = 275 psi (1.9 MPa) For gasket joints, the pipe shortens 0.34” per 20 ft, half at each end. Longitudinal strain, ε = 0.07% In the above example, it should be recognized that the longitudinal stress, σ, in a welded system would be lower than 275 psi in reality due to soil friction. The longer the pipeline, the greater would be the reduction of longitudinal stress due to soil friction. The stresses and strains above are not critical, but might add to other longitudinal stresses and strains such as longitudinal beam bending and longitudinal thrust from other sources, and should serve as a caution to designers and installers. Over-Insertion in Gasket Joints: The issue of over-insertion has been one of the most prevalent problems with gasket joint PVC pipes. Numerous pipeline failure analyses have been traced back to excessive stresses on the bell as result of overinsertion. Installers should be aware of the detrimental consequences of this practice. When a gasket joint is “stabbed” (connected), the gasket and spigot are lubricated and aligned; then assembled by thrust Q. Pipe spigots are marked for proper depth of insertion by a witness mark. If exceeded, over insertion could result in excessive longitudinal thrust, Q, of the spigot against the bell, Figure 7. If the connection is tight, internal pressure can not reach the gasket. Consequently internal pressure fluctuations on the spigot cause concentrated stresses against the bell. Moreover, if the spigot is jammed into the throat of the bell during insertion, allowable joint deflection is reduced to approximately half. Longitudinal thrust, Q, imposes radial force, q, on the 45o surface, which wedges the bell outward, and tends to shear the bell off from the pipe. q = Q/πD (5) (4)

Shearing strength of plastic is only about half of the tensile strength. Figure 7. Over-Insertion of Spigot into Bell

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Example: What is the thrust Q at shearing strength of τ = 2 ksi? D = OD = 13.2-in, t = 0.8-in Shearing stress is: τ = q/t (6)

Substituting (5) into (6), at Shear slip, Q = 66 kips (294 kN) From typical pipe installations, welded joint efficiency is 100% for changes in temperature and internal pressure. A solvent cement joint slips only when the joint is not properly cemented. Moreover, the joint, when fully welded, provides a doublethick wall. Consequently, any Reissner effect (the ring deflection due to longitudinal bending) is minimized. Difference in ring deflection of the bell and spigot does not cause disbonding of a good solvent-cement joint. Failure of a heat-fusion welded joint in either Fusible PVC pipe, or polyolefin pipes, can be the result of cold-welding, whereby the applied pressure during joining is so high that it forces the molten material aside. Using incorrect temperatures, pressures or durations can have a negative affect on the strength and long-term performance of a heat-fused joint. 3. Longitudinal Beam Bending in Pipe

If a straight pipe is bent into a circular arc of radius Rb, longitudinal stresses result in the form of tension at the crown and compression at the invert, Figure 8. It is important to be cognizant of the size of Rb; if Rb is too short, the pipe could buckle (crumple at a plastic hinge). If pipe is subjected to two-dimensional stress, such as internal pressure and longitudinal bending (within allowable limits), strength regression is not significantly less than for internal pressure only; i.e. the time to failure of the pipe with the combined loading is the same as that for straight nondeflected pipe subjected to internal hydrostatic pressure only (Alferink et. al., 2004).

Figure 8. Longitudinal Tensile and Compressive Stresses in Bent Pipe The primary stress in bent pipe, or flexural stress, σf, is defined as, σf = E(OD)/2Rb (7)

σf is maximum at the inside and outside of the bend. Rb/OD is called the minimum bending radius ratio of the pipe.

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

The analysis of longitudinal stresses in Fusible PVC pipe is particularly pertinent for trenchless applications such as horizontal directional drilling where the pipe must simultaneously withstand bending (flexural) stresses as well as tensile pull stresses during the installation process. The tensile strength of PVC pipe formulated to cell class 12454B is 7000 psi. For design, factors of safety are used to ensure that the total longitudinal stress (tensile and flexural), experienced by the pipe during pull-in, is sufficiently less than its tensile strength. Based on the tensile strength of 7000 psi, the allowable tensile stress, σa, for Fusible PVC pipe during pull-in is 2800 psi, derived by applying a factor of safety of 2.5 to the tensile strength. This low stress value ensures that any additional stresses due to pipe bending (flexure), as well as other stresses such as those due to temperature changes, soil movements etc., keep the overall longitudinal stresses in the pipe sufficiently lower than the pipe’s tensile strength of 7000 psi. The safe pull force, Fa, is then calculated by multiplying the allowable tensile stress, σa, of 2800 psi, by the cross sectional area of the pipe, Ap. Table 1 shows allowable bend radii and safe pull forces for selected nominal diameters of Fusible C-900 and C-905 pipe, of varying wall thicknesses. Table 1. Allowable Bend Radii and Safe Pull Forces for Select Diameters of Fusible C-900/C-905 Pipe.
Nominal Diameter (in)
4 6 8 10 12 16 24

Dimension Ratio (DR)
14 18 25 14 18 25 14 18 25 14 18 25 14 18 25 14 18 25 18 25 32.5

(mm)
100 150 200 250 300 400 610

Wall Cross Sectional Area, Ap (mm2) 2 (in ) x103
4.81 3.79 2.75 9.89 7.82 5.71 17.04 13.50 9.86 25.64 20.18 14.86 35.71 28.86 21.00 62.50 49.64 36.43 107.14 78.57 76.79 3.10 2.45 1.77 6.38 5.05 3.68 10.99 8.71 6.36 16.54 13.02 9.59 23.04 18.62 13.55 40.32 32.03 23.50 69.12 50.69 49.54

Allowable Bend Radius, Rb (ft)
100 144 188 232 275 363 538

Safe Pull Force, Fa (lbs)
13,460 10,600 7700 27,700 21,900 16,000 47,700 37,800 27,600 71,800 56,500 41,600 100,000 80,800 58,800 175,000 139,000 102,000 300,000 220,000 215,000

(m)
30 44 57 71 84 111 164

(N) x105
0.60 0.47 0.34 1.23 0.97 0.71 2.12 1.68 1.23 3.19 2.51 1.85 4.45 3.59 2.62 7.78 6.18 4.54 13.34 9.79 9.56

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Example: What is the flexural stress, σf, in the 12-inch (300 mm) DR18 Fusible PVC pipe when it is bent to its allowable bend radius, Rb, of 275 feet (84 m), per table 1? Outside diameter, OD = 12.8-inch; E = 400 ksi Solving (7), flexural stress, σf = 800 psi (5.5 MPa) Sags in Pipelines: Longitudinal bends in buried pipe are often recognized as sag. Sag causes longitudinal stress, due to bending and due to increase in length (catenary). The increase in length in PVC pipe is usually negligible; this is however not the case in other thermoplastics such as a polyolefin, where length increases can be significant. Sag can result in a build-up of sediment in low spots (ponding – discussed in greater detail later) and entrapped air in high spots. Sag is limited by specification according to the use of the pipe. However, sag may also be limited by the longitudinal strength of the pipe --- especially at joints. Example: What is the sag at yield stress in a 12 inch (300 mm) diameter gasket-joint PVC pipe and a welded joint PVC pipe, acting as a beam over a 20 ft (6 m) span where bedding settles? The pipe is deflected by uniform load. Joints affect longitudinal strength. Data: y = sag (deflection at mid-length, L/2) L = length of sag (span) = 20 ft (6 m) D = OD of the pipe = 1.1 ft (335 mm) I = moment of inertia of cross section w = load per unit length of pipe M = maximum bending moment in pipe E = modulus of elasticity for PVC = 400 ksi (2.8 GPa) σ = longitudinal stress (top & bottom) = MD/2I = 4 ksi (27.6 MPa) yield at 100 yrs of constant stress E/σ = 100 at 100 yrs of constant stress Rb = ED/2σ = radius of bend in pipe Gasket-Joint PVC Pipe y = 5wL4/384EI; and, M = wL2/8 = σI/r Solving, y/L = (5σ/24/E)(L/D) I cancels. For L/D = 18.2, at 100 year yield, σ = E/100, critical sag y = 9.1 in. (230 mm)

Figure 9. Longitudinal Sag of Fixed-end pipe (welded-joint PVC pipe) Welded-Joint PVC Pipe (see fig. 9) y = wL4/384EI; and M = wL2/12 = σI/r Solving, y/L = (σ/16E)(L/D) I cancels. For L/D = 18.2, at 100 year yield, σ = E/100, critical sag y = 2.7 in. (69 mm)

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

If this pipe were steel, for which yield stress is 42 ksi, and modulus of elasticity is 30,000 ksi, critical sag is, y = 0.34 in. (8.6 mm) REISSNER EFFECT The Reissner Effect is the ring deflection (flattening) of the ring due to longitudinal bending. The decreased vertical diameter results in a smaller minimum radius Rb, of the bend, but could cause different ring deflections of the bell and spigot. Solvent cement bell-and-spigot joints must sustain slight differential ring deflection over the long term that causes tension between the chemically fused bell and spigot. The question arises, will differential ring deflection cause the joint to disbond over the long term due to vibrations? In fact, the joint is doubly stiff (twice as thick) so that differential ring deflection is reduced to as much as one-eighth of the ring deflection of the pipe. According to Reissner (1959), a longitudinal bend in the pipe causes elliptical ring deflection, d, defined by, d = 2Z/3 + 71Z2/135 where, Z = (1.5/16)(1-ν2)(D/t)2(OD/Rb)2 = 0.08021 (D/t)2(OD/Rb)2 for PVC Example: What is the ring deflection at minimum bending radius ratio, Rb/OD of 250, in a 12inch (300 mm) nominal diameter (Iron Pipe Size, IPS) ASTM D 2241 PVC pressure pipe, DR 32.5 (pressure rated 125 psi), with solvent cement joint? d = ring deflection ODpipe = 12.750 in. (324 mm) D/t = SDR–1 = 31.5 DmeanPipe = 12.358 in. (314 mm) t = 0.392 in. (10 mm) IDbell = 12.778 in. (325 mm) (with 0.057 clearance) DmeanBell =13.170 in. (334.5 mm) Ν = Poisson’s ratio = 0.38 for PVC σ = longitudinal stress at the most remote surfaces; S = yield strength at 100 years of constant stress or of intermittent stress = 4 ksi E = modulus of elasticity of the PVC = 400 ksi Rb = radius of bend = 250 OD (8)

For the spigot: Given Rb/OD = 250, solving Z, and substituting into Eq.8, d = 0.085% for the pipe spigot. For the bell: Given Rb/OD = 250, solving Z, and substituting into Eq. 8, d = 0.097% for the pipe bell. ∆d = 0.097 – 0.085 = 0.012 % A solvent cement joint, properly chemically fused, is twice the thickness of the pipe wall; the moment of inertia of the wall section, I = t3/12, increases eight-fold. The

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Reissner effect is not, therefore, a pertinent issue. From field experience, the Reissner effect is a matter of concern for solvent cement joints only under excessive bending. OTHER JOINT-RELATED ISSUES Ponding in Pipelines: For some pipelines, depth of sag must be limited because of ponding. Typical examples are pipes that transport solids and sediments, such as sanitary sewers and storm-water drains. At low points, such as sags, which may occur at a gasket joint or along the length of the pipeline, deposits of solids and sediment can accumulate at low flow. This is typical of gravity-flow pipelines. Excessive deposits can reduce the flow capacity of a pipe. Experience shows that in PVC gravity pipelines, as long as the overall average slope of the line is maintained, its hydraulic capacity is not adversely affected by sags and deposits. In sanitary sewers, putrefaction generates methane and other gases which lead to corrosion in concrete and metallic pipe materials. Due to the non-corrosive nature of thermoplastics such as PVC, septicity is not of concern. In order to limit depth of sediment deposit, from field experience, a typical recommended maximum depth of the pond, y, for a pipe with internal diameter, ID, must be no greater than, typically, y=0.15(ID) (9)

This is shown to scale in Figure 10. At this depth, the reduction in cross-sectional area of the pipe (cross-hatched) is 9.4%. Depth of the pond may be increased where the flow is fast enough to flush out the solids. Intermittent fast flow is typical of force mains and domestic sewer lines.

Figure 10. Maximum Ponding Depth, to Scale Lever Action of Spigot on Bell in Gasket Joints: From field experience, in the case of bell-and-spigot gasket joints, of greater concern than longitudinal bending and ring deflection is the lever action of a spigot in the bell. Lever action is the “prying open” of the bell by the spigot when allowable joint deflection, θ, is exceeded.

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Manufacturers publish values of maximum allowable joint deflection that can be accommodated by the gap between the spigot and bell. When exceeded, the spigot makes direct contact with the bell, and bears on the lip of the bell with pressure, P. The force on the lip of the bell is rougly Q = PD, Figure 11. Hoop tension stress in the bell is σ = PD/2t = Q/2t. Therefore, approximately, Q = 2tσ (10)

Figure 11. Lever Action of Spigot on Bell Example: If force, Q, on the lip of the bell is excessive, a longitudinal crack opens as a result of the hoop tension due to internal pressure, P. Bending moment is ignored because ring deflection is small. D = 13.2 inches (335 mm); t = 0.8 inch (20 mm); yield stress, σ = 7 ksi (48 MPa); and length of the section of pipe is L = 20 ft. (6 m) a) What is the force Q on the lip of the bell at yield stress, σ? From Eq. (10), Q = 11.2 kips (50 MN) b) What is lever force, F, on the end of a 20-ft long pipe that results in yield stress, and a crack? Force, Q, on the lip of the bell is caused by lever action of the spigot pipe, i.e., Q = FL/X per inch where F is the length of the pipe and X is the length of the insertion. If length of insertion is X = 7.5 inches (190 mm), F = QX/L = 11.2 kips(7.5/240). Substituting values, F = 350 lbs (1.6 kN) The insertion-depth, X, varies by manufacturer, and can range from 6.5 inch (165 mm) to 8.8 inch (224 mm). X= 7.5 inch (190 mm) in the above example represents an industry average. The above result shows that the bell could be cracked by rough handling, such as the use of a backhoe to force the spigot into the bell. The use of a “come-along” device is encouraged for joint assembly by manufacturers. It is imperative that joints be in alignment, lubricated, and the spigot inserted into the bell with care. The spigot, in compression, does not crack. CONCLUSION An understanding of the nature of longitudinal stresses in both gasket joint and welded joint PVC pipe can prevent failures during the service life of a pipeline. 14

American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Welded PVC pipe joints include heat-fused Fusible PVC and solvent-cement joints. In a fixed-end pipe, the joint resists any change in length of the adjoining pipe sections; this is representative of a welded joint. In a free-end pipe, as is the case with gasket joints, the pipe can shorten or lengthen within limits of the bell-and-spigot joint. Principal causes of longitudinal stress and strain within a pipe system include changes in temperature, internal pressure or vacuum, and beam bending. PVC is a viscoelastic material; an appreciation of the physical/mechanical properties of viscoelastics results in better designed PVC pipelines. Pipe-grade thermoplastics, under constant stress, creep over time and their strength regresses over time; under constant strain, stress relaxation takes place while strength remains pristine. All PVC pressure pipes manufactured in North America per ASTM and AWWA standards meet cell class 12454B, per ASTM D1784. For design, factors of safety must always be used when considering longitudinal stresses and strains in pipe. In gasket joint PVC pipes, longitudinal stresses due to internal pressure could cause failure if overinsertion of the spigot into the bell is permitted. Excessive bending of welded joint pipe could cause pipe buckling in the worst case. Strict adherence to manufacturer recommendations and considerations of factors of safety will ensure long-term integrity of both pipes and joints and prolong the service life of pipelines. References
Alferink, F., and Wolters. M., Janson, L.E. (2004), Combined Loading of Buried Thermoplastics Pressure Pipes, Proc. (CD-ROM) Plastics Pipes XII, Milan, Italy. American Society of Testing and Materials (ASTM) International (2000), D 2241-00: Standard Specification for Poly(Vinyl Chloride) (PVC) Pressure-Rated Pipe (SDR Series), W. Conshoken, PA. American Society of Testing and Materials (ASTM) International (1999), D 1784-99a: Standard Specification for Rigid Poly(Vinyl Chloride) (PVC) Compounds and Chlorinated Poly(Vinyl Chloride) (CPVC) Compounds, W. Conshoken, PA. American Society of Testing and Materials (ASTM) International (1996), D 2672-96a: Standard Specification for Joints for IPS PVC Pipe Using Solvent Cement, W. Conshoken, PA. American Water Works Association (AWWA) (1997), C900-97: Polyvinyl Chloride (PVC) Pressure Pipe, and Fabricated Fittings, 4 In.-12 In. (100 mm-300 mm), for Water Dist., Denver, CO. Bishop, R. (1981), Time Dependent Performance of Buried PVC Pipe, Proc. International Conference on Underground Plastic Pipe, American Society of Civil Engineers, New York, NY, pp. 202-212. Fisher, C. (1998), Questions About the Gap: Why Does my PVC Sewer Pipe Joint Have a Gap?, Uni-Bell PVC Pipe News, v. 21, no. 2, pp. 4. Moser, A. P. (2000), Long-term (22 years) Stress Relaxation and Strain Limit Testing of PVC Pipes, Utah State University, Logan, UT.

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American Society of Civil Engineers (ASCE) Pipelines Conference 2005, Houston, TX

Moser, A.P. (2001), Testing PVC Pipes, New World Water 2001, Sterling Publications Ltd., London, UK, pp. 67-72. Rahman, S. (2004a), State of the Art Review of Municipal PVC Piping Products, Proc. ASCE International Conference on Pipeline Engineering & Construction, San Diego, CA. Rahman, S. (2004b), Underground Technology: Thermoplastics at Work, Underground Construction Magazine, Oct. 2004, pp.56-61. Rahman, S. (2005), Chapter 6: Pipe Materials in Trenchless Technology: Pipeline and Utility Design, Construction, and Renewal by Mohammed Najafi, New York, NY, pp. 179. Reissner, E. (1959), On Finite Bending of Pressurized Tubes, Journal of Applied Mechanics Transactions of ASME. Sept. 1959, pp. 386-392. Uni-Bell PVC Pipe Association (2001), Handbook of PVC Pipe: Design and Construction, 4th Edition, Dallas, TX. Watkins, R. K. (1985), Longitudinal Stresses in Buried Pipes, Proc. Advances in Underground Pipeline Engineering, Jey Jeyapalan, Ed., American Society of Civil Engineers, New York, NY, pp. 408-416.

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