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Rigid and Flexible PipesAn Objective Understanding of Pipe-Soil Interaction,Design and Installation By Shah Rahman

[ID uried pipelines for the conveyance of potable watero and sanitary sewers form the bedrock of our civilization.The very baSic services that we take for granted,such as a running faucet with clean drinking water and theability of our wastewater to be transported away from ou rhomes and businesses for treatment and release into theenvirolUnent, are possible because of the vast network ofburied pipes that lie hidden beneath roads and the concrete jungles that define the large urban centers that areour cities .These intricate networks consist of various types of pipematerials that range from metals to concrete to plastics tocomposites .Whatever the material type, all are expected toprovide some minimum service qualities: prevention ofleaks, which ensure that potable water isn't compromisedby contaminants entering a piping system and that wastewaters do not pollute soils and existing sources of groundwater, and most importantly, that the structural soundnessof a buried pipe system results in a minimum service life of50 to 100 years. The latter can only be ensured through athorough understanding of and designing for the loa'ds towhich a buried pipe will be exposed, its response to theloading, and the interaction mechanism between the pipeand surrounding soils.While an understanding of pipe-soil interaction is important for the sound structural design of pipelines , it shouldbe noted that the concern for soil pressure on a pipe islinlited to empty pipe or gravity flow pipelines where theconduit never flows full . In municipal pressure piping systems, the internal pressure is typically much greater thansoil pressure on the pipe; internal pressure essentially supports the soil load when the line is placed into service.

The story of tlle formal study of buried pipe structures inorth America begins in Ames, Iowa, at th e turn of the 20m

Century,when Dr.Anson Marston, then Dean of Engineeringat the Iowa State College (now Iowa State University) andthe first Cha irman of the Iowa State Highway CommisSion ,analyzed oil pressures on buried culverts in an effort todrain muddy rural roads. Research was also necessary asmousands of small wooden bridges were being replaced byconcrete and clay pipes placed in stream beds underneathroadway embankments . I t was necessary to design themproperly so that they would not fail .Buried pipe deSign, then, was inextricably connected tothe development of highway systems in the United States.Marston was the first Chairman of the federal HighwayResearch Board. Ou r knowledge of pipe-soil interaction, aswell as the development of ne w pipe materials and theimprovement of traditional ones , has grown by leaps andbounds since those early days, leading to a multi-billion dol-36 TRENCHlESS TECHN OLOGY November 2010

lar global pipe materials industry. Another relatively newconstruction method in buried pipeline construction andrehabilitation is the advent of trenchless technology.While trenchless technology is no longer' in its infancy,the only known and practiced trenchless constructionmethods during Marston's lifetime included jacking andtunneling, and little else . But a tremendous anlount ofresearch in the last two decades no w provides design engineers and contractors with an understanding of the pipesoil mechanics of pipelines built by methods other thantraditional open-trench methods.Classical Pipe-Soil Interaction Theory

In 1913 , and 1930, Marston published his originalpapers "The Theory of Loads on Pipes in Ditches andTests of Cement and Clay Drain Tile an d Sewer Pipe"and"The Theory of External Loads on Closed Conduits in theLight of the Latest Experiments ," respectively, markingth e earliest systematic approach of studying th e structural mechanics of buried pipes . Thus was defined theMarstonTheory of Loads on buried conduitsThis became,in part , the very foundation on which much of the laterwork around the world on earth loading technology ofburied pipes wa s based. In 1941 , Marston 's studentMerlin Spangler, known today as "the father of buriedflexible pipe design ," published another ground-breakingpaper, "Th e Structural Design of Flexible Pipe Culverts ,"in which he derived an equation , the Iowa Formula, forpredicting th e ring deflection of buried flexible pipes .Spangler would later become chairman of the CulvertCommittee of th e federal Transportation Research Board .In 1958, Spangler's student , Reynold Watkins , published"Some Characteristics of th e Modulus of PassiveResistance of Soil - A study in Similitude," in which hesolved a fundamental flaw in th e dimensions of a modulus of passive resistance in Spangler 's Iowa Formula,defUling a ne w modulus of horizontal soil reaction, E', inthe Modified Iowa Equation. In later years , other significant contributions came from A. Howard , ]. Duncan, ].Hartley, F. Heger, T. McGrath, M. Zargbamee, and othersthat now enable th e external load design of rigid andflexible pipes to be an even more exact science..,The Marston Load Theory

In his analysis of external loads on buried pipe , Marstondefined two main types of loading conditions of buriedpipes , a ditch conduit (referred to as trench load conditionin present day nomenclature), and a projecting conduit(referred to as an embankment condition in present dayliterature),Table 1.

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Tab le 1: Marston's Buried Pipe In sta lla tionlLoadine Cond itions load of the central prism due tothe direction in which the shearing stresses or friction forcesdevelop as a result of the differential settlement of tl1e central prismin relation to the external prisms.Pipes that display this behaviorwhen buried are referred to asFlexible Pipes. Use of the prismload is conservative becauseinstallers do no t compact soilagainst the pipe . The pipe isembedded in a "packing" of lessdense soil that erves the sameway as does packing around anitem in a shipping container.Thepipe is relieved of part of theprism load which the soil thenpicks up in arching action overthe pipe.

Marston' s Present DayCo nduit Description Diagra mInstallat ion Ty pe Nomenclatu reDitch Conduit I Trench Load ConditionDitch Conduit Trench Load Pipe is insta lled in a narrow trench NanlcroundMoril(tgondition (generally', trench width :::; 2 x pipediameter) in undisturbed soil , thenr backfi lled to natural groundsurface levelProiecting Conduit I Embankment ConditionPositive Projecting Positive Pipe is insta lled underneath an "" .--",..,--.-Conduit Embankment embankment, in shallow bedding,Condition t wi its top project ing above the -0-ositive surface of the natural groundProjecting .....""'"EmbankmentNegative Projecting Negative Pipe is installed underneath an r o p o l m ~ 1 I l Conduit Embankment embankment, in narrow and """"'''''''''Condition I shallow trench with its top at an lOr As a general rule, flexible pipeswill deflect at least 2 percentwithout structural distress . Most

flexible pipe material standardsallow up to 5 percent deflection.Deflection is limited to 2 percenti f the flexible pipe has a rigid lining and coating and 3 percent fora rigid lining and flexible coating.Flexible pipes include steel, duc-

Negative elevation below natural groundProjecting surfaceEmbankment

Imperfect Ditch Induced Trench Special case, sim ilar to Negative ... ~ [ ) o ; c - . d " " ' ~ ' f f I Conduit Condition Embankment Condition, but more .......-- ,---- . .40r-favorable from standpoint of load ' Ill_wreduction on pipe, used in very ..deep insta llations. Di ffi cult toachieve for large-diameter pipes.

The basic concept of the Marston Load Theory is that theload on a buried pipe, because of the weight of the columnof soil ,or central prism, directly above the pipe , is modifiedby the response of the pipe and the relative movement ofthe side columns of oil,or external prisms (adjacent to thepipe , between the pipe and the trench walls on either side),to the central prism.The relative movement of the centralprism and the side prisms result in shearing stresses or frictional forces, calculated using Rankine's theory.Rigid PipeMarston recognized that in a trench (generally, trenchwidth 2 x pipe diameter), when the side columns of soilor the external prism are more compressible than the pipedue to its inherent rigidity, this causes the pipe to assumeload generated across the width of the trench .The shearingstresses or friction forces that develop due to the differential settlement of the external prisms and tl1e central prismare additive to the load of the central prism alone. Pipesthat behave in this manner are referred to as Rigid Pipes.Generally, rigid pipes start showing signs of structural distress before being vertically deflected 2 percent. Rigidpipes include reinforced non-cylinder concrete , reinforcedconcrete cylinder, prestressed concrete cylinder, vitrifiedclay, polymer concrete , cast iron, asbestos cement and castin-place pipes.Flexible Pipe

On the other hand , i f a pipe is more compressible thanthe external soil COJtU11l1S , without any structural damagecaused to the pipe as a result of its vertical deflectionallowing the central prism to settle more in relation to t h ~ external prisms , the actual load on the pipe is less than thewww.trenchlessonline.com

. tile iron, thermoplastics such asPolyvinyl Chloride (PVC) and HighDensity Polyethylene (HDPE) thermosetting plastics suchas fiberglass-reinforced polymer (FRP), bar-wrapped concrete cylinder pipe , and corrugated steel pipes.Semi-Rigid PipeSome pipe materials exhibit characteristics of both rigidand flexible pipes , primarily controlled by tl1eir diameters,and are referred to as semi-rigid. Attempts have been madeto define semi-rigid pipes as those that will deflec t between0.1 percent and 3.0 percent without causing harmful orpotentially harmful cracks. Bar-wrapped concrete cylinderpipe is an example. But sin

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ground or bedding surface divided by the diameter of thepipe, Be. sm is the compression strain of the side columnsof soil of height pB , s is the settlement of the naturale gground surface adjacent to the pipe , sf is the settlement ofthe pipe into its foundation, and dc is the shortening of thevertical height of the conduit.A settlement ratio, rsd , is thendefined using the formula:

rsd = Settlement Ratio (Eq uation 1)

Since it was almost impossible to predetermine the settlement ratio that would develop in a specific case,Marstontabulated it as an empirical quantity, based on the type ofpipe material (rigid or flexible), and foundation conditionsfor rigid pipe and side-fill soil condition for flexible pipe.

The critical plane is the horizontal plane through the topof the pipe when the fill is level with its top. At criticalplane, H=O. During and after construction , if this criticalplane settles more than the top of the pipe, as shown forrigid pipe in figure 3a, the settlement ratio is positive(prsd>O). For flexible pipes, figure 3b , the critical plane settles less than the top of the pipe, indicating the settlementratio is negative (p rsd

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equal to the ratio of the pipe diameter to the width bf thetrench.

(We)Rigid Pipe(We )Flexible Pipe C d roB d B e

I f the trench is twice as wide as the buried pipe , the loadimposed on a rigid pipe will be twice the load imposed ona flexible pipe with side fills having the same degree ofstiffness as the flexible pipe itself.Load Calculations in Embankment ConditionFor pipe installed under an embankment,Marston derivedanother formula, equation 4.

(Equation 4)where Wc is the load on the pipe under embankment Cc

is a dimensionless load coefficient for embankment condition that accounts for the ratio of the height of fill to pipediameter, the shearing forces between interior and adjacentsoil prisms, and the direction and amount of relative settlement between interior and adjacent soil prismsw is the unit weight of soil, andBc is the pipe diameterSince tllere is no trench by definition of a positive embankment condition, the trench width , Bd , is not a part of equation 4 . For Cc' when the product of tlle settlement ratio, rsd ,and the projection ratio , p, equals zero, i.e. prSd= 0, then Cc=HIBc' I f this is substituted into Equation 4, the load on apipe underneath an embankment is defmed as

(Equation 5)

where , H is the burial depth of the pipeEquation 5 is referred to as the prism 10ad.As stated earlier, for rigid pipes , settlement ratio under an embankmentis positive (p r",>O) and for flexible pipes,settlement ratio isnegative (p r",

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bore subtracted from the weight of the prism above the bore.The 2eC,B, in Equation 6 represents the cohesion of undismrbed soils.In North America, the field of horizontal directional drilling(HDD) has made significant progress due to extensive researchby Tom Iseley, referred by some as "the father of trenchlesstechnology," Ray Sterling, Larry Petroff, Mohammed Najafi,SamuelAriaratnum, Larry Slavin,Erez AIIouche,Alan Atalah, IanMoore, Mark Knight and others . HDD is the most widely uti-lized method of trend1kss constmction in North America.

ASTM F1962, Standard Guide for Use of Maxi-HorizontalDirectional Drilling for Placement of Polyethylene Pipe orConduit Under Obstacles, including River Crossings, providesan understanding of earth loading pressures and subsequentpipe deflection for thermoplastics such as HDPE wheninstalled by HDD.Soil loading on pipe installed by HDD is dependent on manyof the same parameters as pipes installed by open-trenchmethod, such as depth of bury, ill-situ soil properties, pipediameter, etc. , but additionally, other factors such as the mud-slurry properties and diameter of boreholes play critical rolesalso.Since HDD boreholes are typically 50 percent larger thanthe outside diameter of the pipe, it is the deformation of thesoi l around the borehole that transfers earth loads (and liveloads i f applicable) to the pipe itself.According toASTM F1962,"As the deformation occurs, a cavity of loosened soil formsabove the borehole.This cavity is filled by soil sloughing fromabove it.The process causes the soil to bulk, that is, the densityof the sloughed soil is less than the density of the lmdisturbedsoil.The sloughing process continues lmtil an equilibrilun isreached where the stiffness of the sloughed soil is sufficient toresist further sloughing from the soil above. This bulkillg stateresults in archillg of load around the pipe (that is , the earthload applied to the pipe is less than the geostatic stress orprism load) ." Figure 5 illustrates this.

Figure 5: Soil Arching in HOD, applies tonon-viscous soilsOnly when a pipe is drilled into a depth that is at least fivetimes the outside diameter of the pipe should credit for archillg be considered. While the doclUnent acknowledges a lack

of published equations for calculating earth loads on pipesinstalled by HDD,it makes references to some recent publications on soil archillg in other trenchless constmction methodsthat may be utilized to arrive at a realistic loading on the pipe.An equation is provided to calculate the possible deflection ofthe pipe.ConclusionIn addition to the importance of accounting for the soilload on buried pipe (dead load), it is also important toaccOlmt for live loads,whenever applicable, such as movingvehicles (live load) when a pipe is buried lUlder a highway

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or railroad embankment . One way in which this is doneis by u e of modified Boussinesq equations , details ofwhich were no t discussed in this article.

It is important to remember that the concern for soilpressure on a pipe is limited to empty pipe or gravityflow pipelines where the conduit never flows fuU . Inmunicipal pressure piping systems, where the internalpressure is typically much greater than external soilpressure , the former supports the latter when the line isplaced into service. For larger diameter flexible pressure pipelines however, it is always appropriate to run acheck that the soil conditions are appropriate to limitthe pipe 's allowable vertical de flection as permitted byspecification and to prevent any damage to rig id liningsand/or coatings due to excessive deflection.

The value of soil load analysis is to arrive at therequired pipe strength necessary to build a municipalpipeline of sufficient structural integrity to serve itsdesign life. The design process varies from rigid to flexible pipe , and usually by pipe material also. The secondpart of this series in the next issue will review currentdesign practices for rigid and flexible pipes with regardsto earth loading.Shoh Rahman is the wes tern regional engineer fo rNorthwest Pipe Co ., based in Southern Cal if. He is anAssociate Editor (Pipe Materials) for the ASCE Journal ofPipeline Systems Engineering and Practice.

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ReferencesASTM (2005), "Standard Guide fo r Use ofMaxi-Horizontal

Directional Drilling fo r Placement of Polyethylene Pipe orConduit under Obstacles, Including River Crossings,"P1962-05,ASTM International, West Conshohocken, PA

Marston,M. G. , andA. o.Anderson (1913), "The Theory ofLoads on Pipes in Ditches and Tests o f Cement and ClayDrainTile and Sewer Pipe,"Iowa State Universi ty EngineeringExperiment Station, Bulletin 31 ,Ames, Iowa

Marston, M. G. (1930), "The Theory of Externa l Loads onClosed Conduits in the Ligllt of the Latest Experiments,"Iowa State University Engineering Experiment Station,Bulletin 96,Ames, Iowa

Spangler, M. G. (1941), "The Structww Design of FlexiblePipe Culverts,"Iowa State University Engil leeringExperimentStation, Bulletin 153,Ames, Iowa

Spangler, M. G. , and R. L. Handy (1982), Soil Engineering,4dJ ed. , ew York: Harper & Ro wWatkins, R. K. and M. G. Spangler (1958), "SomeCharacteristics of dJe Modulus o f Passive Resistance of Soil- A study in SinJilitude," Proceedings Highway Research

Board 39: 389-397

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The Trenchless Technology magazine article Rigid and Flexible Pipes: An objective

Understanding of Pipe-Soil Interaction, Design and Installation, published in the

November 2010 issue (Vol. 19, No. 11), has several missing figures that were originally

submitted to the Editor by the Author, but could not be published due to lack of space. In

particular, Figures 3a and 3b, mentioned in the article but not included, are critical to

understanding some of the equations that are discussed. These two figures appear below:

Figure 3a, 3b: Embankment Condition Soil Loading in Rigid Pipe, in Flexible Pipe

Furthermore, the two additional figures shown below, will be helpful in obtaining a better

understanding of the Marston Load Theory, as well as the differences between Rigid and

Flexible pipes, as discussed in the article.

Response to Soil Loading in Trench of Rigid Pipe, of Flexible Pipe