thrust restraint design for ductile iron pipe reports/design-thrust... · published in 1984, the...

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THRUST RESTRAINT DESIGN

FOR DUCTILE IRON PIPE

Sixth Edition

2006

Foreword

PUBLISHED IN 1984, the first edition of Thrust Restraint Design for Ductile Iron Pipe pre-sented suggested design procedures for the restraint of thrust forces in pressurized, buriedDuctile Iron piping systems.

DIPRA’s Technical Committee reviewed the 1984 edition and approved revisions to the sug-gested design procedures, which were incorporated in the second edition issued in 1986.

The second edition was reviewed by DIPRA’s Technical Committee in 1988, resulting in onlyeditorial revisions that were incorporated in the 1989 edition.

In 1991 DIPRA’s Technical Committee reviewed the 1989 edition. This review incorporatedpressure classes and 60- and 64-inch-diameter pipe. In addition, the following topics wereaddressed in the third edition issued in 1992:1. Encroaching restrained lengths2. Combining thrust blocks and restrained joints3. Pipe in casings4. Future excavations

The third edition was reviewed in 1996. This review resulted in a clarification to the equa-tion used for determining restrained length of a tee branch, as well as the addition of a sectionthat addressed combined vertical offsets. A clarification in the unit frictional force for standardasphaltic coated pipe vs. polyethylene encased pipe, with the addition of the “unit frictionalresistance” term (Ff), was also included. The fourth edition was issued in 1997.

The fifth edition was issued in 2002. It included: 1) the addition of a cautionary note forthe design of gravity thrust blocks when one leg is not horizontal; 2) the addition of well-grad-ed gravels and gravel-sand mixtures to the table of soil parameters; 3) cautionary notes wereadded regarding how to analyze encroaching restrained joints whose bend angles approached90º and; 4) the elimination of Appendix A (values for Fs, (Fs)b, and Rs), and Appendix B(restrained joint design tables for horizontal bends). Appendices A and B were eliminated dueto the extensive use of DIPRA’s thrust restraint design program which is capable of generat-ing all the data contained therein. This program can be downloaded from DIPRA’s website athttp://www.dipra.org.

The fifth ediotion was reviewed in 2006, resulting in only editorial revisions and change offormat that were incorporated in the 2006 edition.

Conservative assumptions, along with an explicit safety factor, have been employed toassure a conservative design with an adequate overall safety factor. In order to facilitatethe use of these suggested design procedures, soil types have been divided into broadcategories with significantly different characteristics. Because actual soil conditions varywidely, however, anyone using this paper as a guide should conduct soil tests to ensurethat the proper design parameters are chosen for the soil type present at the site of thepipeline project. For any given project, the ultimate responsibility for the proper use ofthe equations and other data provided in this paper rests with the design engineer. Whenusing restrained joint pipe, consult the DIPRA member companies regarding properinstallation procedures.

THRUST RESTRAINT DESIGNFOR DUCTILE IRON PIPE

Fifth EditionTable of ContentsThrust Restraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Thrust Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Design Pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Pipe-soil Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Thrust Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Restrained Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Horizontal Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Unit Frictional Force, Fs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Polyethylene Encasement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Unit Bearing Resistance, Rs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Vertical Down Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Vertical Up Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Tees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Reducers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Dead Ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Encroaching Restrained Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Equal Angle Vertical Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Combined Horizontal Equal Angle Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Combined Vertical Equal Angle Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Restrained Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Select Backfill Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Combining Thrust Blocks and Restrained Joints. . . . . . . . . . . . . . . . . . . . . . . . . . . 19Pipe in a Casing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Future Excavations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Deflected Unrestrained Ductile Iron Pipe Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Computer Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Restrained Length Calculation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Tables11. Horizontal Bearing Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1612. Dimensions and Unit Weights of Pipe and Water . . . . . . . . . . . . . . . . . . . . . . . 1113. Suggested Values for Soil Parameters and Reduction Constant, Kn. . . . . . . . . 1214. Soil Classification Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Figures11. Push-on Joint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1212. Internally Balanced Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1313. Thrust Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314. Thrust Force for Various Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1415. Bearing Block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1516. Gravity Thrust Block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717. Horizontal Bend /Vertical Up Bend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818. Unit Normal Forces on Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1919. Standard ANSI /AWWA C150/A21.50 Laying Conditions . . . . . . . . . . . . . . . . . 1110. Vertical Down Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1311. Tees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1412. Reducers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1513. Dead Ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1514. Equal Angle Vertical Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1615. Combined Horizontal Equal Angle Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1716. Combined Vertical Equal Angle Offsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2

Thrust RestraintDuctile Iron pipe and fittings are mostoften joined with push-on (Figure 1) ormechanical joints. Neither of these jointsprovides significant restraint against lon-gitudinal separation other than the fric-tion between the gasket and the plain endof the pipe or fitting. Tests have shownthat this frictional resistance in the joint isunpredictable, varying widely with instal-lation conditions and other factors that areinsignificant in other respects. Thus,these joints should be considered as offer-ing no longitudinal restraint for designpurposes.At many locations in an underground

or aboveground pipeline, the configura-

tion of the pipeline results in unbalancedforces of hydrostatic or hydrodynamic ori-gin that, unless restrained, can result injoint separation.Generically, these unbalanced hydro-

static and hydrodynamic forces are calledTHRUST FORCES. In the range of pres-sures and fluid velocities found in water-works or wastewater piping, the hydro-dynamic thrust forces are generallyinsignificant in relation to the hydrostaticthrust forces and are usually ignored.Simply stated, thrust forces occur at anypoint in the piping system where thedirection or cross-sectional area of thewaterway changes. Thus, there will be

thrust forces at bends, reducers, offsets,tees, wyes, dead ends, and valves.Balancing thrust forces in under-

ground pipelines is usually accomplishedwith bearing or gravity thrust blocks,restrained joint systems, or combinationsof these methods. Presented herein is ageneral discussion of the nature of thrustforces as well as suggested approaches tothe design of both thrust block andrestrained joint systems for balancingthese forces. The suggested designapproaches are conservatively based onaccepted principles of soil mechanics.

Figure 1Push-on Joint

3

Thrust ForceThe internal hydrostatic pressure actsperpendicularly on any plane with a forceequal to the pressure (P) times the area(A) of the plane. All components of theseforces acting radially within a pipe arebalanced by circumferential tension inthe wall of the pipe. Axial components

acting on a plane perpendicular to thepipe through a straight section of the pipeare balanced internally by the force actingon each side of the plane (Figure 2).Consider, however, the case of a bend

as shown in Figure 3. The forces PA act-ing axially along each leg of the bend

are not balanced. The vector sum ofthese forces is shown as T. This is thethrust force. In order to prevent separa-tion of the joints a reaction equal to and inthe opposite direction of T must be established.

Figure 2Internally Balanced Force

Figure 3Thrust Force

PA

PA PA

θ

T = 2 PA sin (θ /2)

PA

4

Figure 4 depicts the net thrust force atvarious other configurations. In each casethe expression for T can be derived bythe vector addition of the axial forces.

Figure 4Thrust Force for Various Configurations

PA r

PA r

PA r

PA r

Tee

PA b

PA b

PA 1

P1A P2 A

PA

Dead End

Closed Valve

Wye

T = PA

T = P ( A 1- A 2 )

Reducer

PA 2

T = PA b

T = PA b

T = (P1- P2 ) A

5

Design PressureThe design pressure, P, is the maximumpressure to which the pipeline will besubjected, with consideration given tothe vulnerability of the pipe-soil systemwhen the pressure is expected to beapplied. In most cases this will be the testpressure of the pipe, applied shortly afterinstallation when the pipe-soil system isnormally most vulnerable.

Pipe-soil StructureFor buried pipelines, thrust restraint isachieved by transferring the thrust force

to the soil structure outside the pipe. Theobjective of the design is to distribute thethrust forces to the soil structure in such a manner that damage does notoccur to the restrained pipe system andjoint separation does not occur in unre-strained joints.

Thrust BlocksOne of the most common methods of pro-viding resistance to thrust forces is theuse of thrust blocks. Figure 5 depicts atypical bearing thrust block on a horizon-

tal bend. Resistance is provided by trans-ferring the thrust force to the soilthrough the larger bearing area of theblock such that the resultant pressureagainst the soil does not exceed the hor-izontal bearing strength of the soil.Design of thrust blocks consists of deter-mining the appropriate bearing area ofthe block for a particular set of condi-tions. The parameters involved in thedesign include pipe size, design pressure,angle of the bend (or configuration of thefitting involved), and the horizontal bear-ing strength of the soil.

Figure 5Bearing Block

Undisturbed Soil

Bearing Pressure

θ

Sb

45°

45°

bSb

Sb

Ht

h

Sb

T

6

The following are general criteria forbearing block design.—Bearing surface should, where pos-sible, be placed against undisturbedsoil. Where it is not possible, the fillbetween the bearing surface andundisturbed soil must be compact-ed to at least 90% Standard Proctordensity.

—Block height (h) should be equal toor less than one-half the total depthto the bottom of the block, (Ht ), butnot less than the pipe diameter(D ′ ).

—Block height (h) should be chosensuch that the calculated block width(b) varies between one and twotimes the height.

The required bearing block area is

Then, for a horizontal bend,

where Sf is a safety factor (usually 1.5 forthrust block design). A similar approachmay be used to design bearing blocks toresist the thrust forces at tees, deadends, etc. Typical values for conservativehorizontal bearing strengths of varioussoil types are listed in Table 1.In lieu of the values for soil bearing

strength shown in Table 1, a designermight choose to use calculated Rankinepassive pressure (Pp) or other determi-nation of soil bearing strength based onactual soil properties.Gravity thrust blocks may be used to

resist thrust at vertical down bends. In agravity block, the weight of the block isthe force providing equilibrium with thethrust force. The design problem is thento calculate the required volume of the

thrust block of a known density. The ver-tical component of the thrust force inFigure 6 on page 7 is balanced by theweight of the block.It can easily be shown that Ty=PA

sin θ. Then the required volume of theblock is

where Wm=density of the block material.Here, the horizontal component of thethrust force

Tx=PA (1-cos θ)

must be resisted by the bearing of theright side of the block against the soil.Analysis of this aspect will follow like theabove section on bearing blocks. Calculations of Vg and Tx for orienta-

tions other than when one leg is horizon-tal should reflect that specific geometry.Ab=hb=

SfTSb

b = Sf 2 PA sin (θ/2)h Sb

(1)

Vg=Sf PA sin θ

Wm(2)

Table 1Horizontal Bearing Strengths

Soil

MuckSoft ClaySiltSandy SiltSandSandy ClayHard Clay

*Bearing StrengthSb (lb/ft2)

1,0001,0001,5003,0004,0006,0009,000

*Although the above bearing strength values have been used suc-cessfully in the design of thrust blocks and are considered to be con-servative, their accuracy is totally dependent on accurate soil identification and evaluation. The ultimate responsibility for select-ing the proper bearing strength of a particular soil type must restwith the design engineer.

7

Restrained JointsAn alternative method of providingthrust restraint is the use of restrainedjoints. A restrained joint is a special typeof push-on or mechanical joint that isdesigned to provide longitudinal re -straint. Restrained joint systems functionin a manner similar to thrust blocks, inso-far as the reaction of the entire restrainedunit of piping with the soil balances thethrust forces.The objective in designing a

restrained joint thrust restraint system isto determine the length of pipe that mustbe restrained on each side of the focus ofa thrust force. This will be a function ofthe pipe size, the internal pressure, depthof cover, the characteristics of the soilsurrounding the pipe, and whether thepipe is polyethylene encased. The

following is a method of accomplishingthe design objective. As with most engi-neering problems, the exact nature of theinteraction of the restrained pipe unit andthe soil is extremely complex. Limi ta -tions of the ability to measure the actualparameters involved and limitations onavailable knowledge of the precise natureof the interaction require that a practicaldesign procedure be based on variousassumptions. The assumptions employedin the following design procedure are, ineach case, conservative. This fact,together with the explicit safety factoremployed in the procedure, results in aconservative design with an adequateoverall safety factor.The proposed design equation for hori-

zontal bends (Equation 3, page 8) and the

suggested soil parameters (Table 3, page12) are the outgrowth of a design proce-dure originally proposed by Carlsen.1Carlsen’s design procedure was basedsolely on theoretical considerations andwas conservatively limited to well-com-pacted trench conditions. The modifica-tion of Carlsen’s design procedureembodied herein is the result of full scaletests of 12-inch Ductile Iron pipe with 45°and 90° bends buried in clay.2 The datagenerated by these tests and data avail-able from model studies with 2-inch pipein sand3 confirm the conservatism of the present design procedure. Futurework in this field should be devoted tolarge-diameter piping systems, with the objective of further confirming thisconservatism.

Figure 6Gravity Thrust Block

θ

TTy

Sb

Sb

Horizontal Plane

Tx

8

The thrust force must be restrained or balanced by the reaction of therestrained pipe unit with the surroundingsoil. The source of the restraining forcesis twofold: first, the static frictionbetween the pipe unit and the soil, andsecond, the restraint provided by the pipeas it bears against the sidefill soil alongeach leg of the bend. Both of these forcesare presumed to be functions of therestrained length L on each side of thebend and they are presumed to act in thedirection opposing the thrust force (i.e.,directly opposing impending movementof the bend).

Horizontal Bends (Figure 7)Figure 7 is a free body diagram of arestrained pipe unit where L is the lengthof the restrained pipe on each side of the

bend. The unit frictional resistance is shown as a distributed force of unit value Ff . The total frictional resistance on each side of the bend isthen FfL cos (θ/2).It is not purported that Figure 7 repre-

sents the actual pipe-soil behavior withall trench types and the variousrestrained joint designs available.Variations in the way different restrainedjoints respond to loadings, along with soiland installation variables, make this a sit-uation which defies precise theoreticalrepresentation. The approach presented,which includes safety factors, is a practi-cal and conservative general thrustrestraint design that has been verified byavailable test data and numerousinstalled systems.The bearing resistance is shown as a

distributed force with a maximum unit

value of Rs at the bend, diminishing lin-early to 0 at L. This assumption is basedon the fact that the bearing resistance(passive resistance in the soil) is propor-tional to deformation or movement. Asthe restrained joints take load, maximummovement will occur at the bend. Thetotal assumed bearing resistance on eachside of the bend is 1/2RsL cos (θ/2).The equilibrium equation for the free

body is then

PA sin (θ/2) = FfL cos (θ/2)+1/2RsL cos (θ/2)

Employing a safety factor and solving for L,

Sf = Safety factor (Usually 1.5)

L=Sf PA tan (θ/2)Ff + 1/2Rs

(3)

Figure 7*Horizontal Bend

θ

PA

L

Ff

Rs

PA sin (θ/2)

[Ff+1/2Rs]L cos (θ/2)

Ff = Fs; For standard asphaltic coated pipeFf = 0.7 Fs; For polyethylene encased pipe

*Free body diagram also applies to vertical up bend.

9

Unit Frictional Force, FsA static frictional force acting on a body isequal in magnitude to the applied force upto a maximum value. In the conventionalanalysis, the maximum static friction isproportional to the normal force betweenthe surfaces which provide the friction.The constant of proportionality, in thiscase called the coefficient of friction,depends upon the nature of the surfaces.Potyondy’s empirical work indicates thatfor friction between pipe and soils, theforce is also dependent upon the cohe-sion of the soil.4

Thus

Fs=A pC + W tan δ

where

C = fcCsAp= surface area of the pipe bearing

on the soilδ = f φφ

Ap=πD′ (for bends, assume 1/2 the2 pipe circumference bears

against the soil)= πD′ (for tee branches, dead end

conditions, and reducers,assume the full pipe circum-ference bears against thesoil)

Values of soil cohesion (Cs ) and inter-nal friction angle of the soil (φ) must beknown or conservatively estimated forthe soil at a particular installation. fc andfφ are related to soil types and pipematerial. Table 3 presents conservativevalues of these parameters for DuctileIron pipe in seven general classificationsof saturated soils.

The unit normal force W is given by

W = 2 We + Wp + Ww

where the earth load (We ) is taken as theprism load on the pipe in pounds. Theearth load is doubled to account for theforces acting on both the top and the bot-tom of the pipe (see Figure 8). The unitweight of the pipe and water (Wp + Ww)is given in Table 2 on page 11.

Then

for bends:

Fs = πD ′

C + (2We + Wp + Ww) tan δ2 (4a)

Figure 8Unit Normal Forces On Pipe

We

We+Wp+Ww

W=2We+Wp+Ww

for tee branches, dead end conditions andreducers:

(Fs)b = πD ′C + (2We + Wp + Ww) tan

δ (4b)

Extraordinary installations mightresult in lesser loads and frictional resis-tance on the pipes than that calculated bythese equations and as shown in Figure 7.When such conditions exist, this must beprovided for in the design.

PolyethyleneEncasement Limited experimental data suggest thatthe frictional resistance terms (Fs) and(Fs)b should be multiplied by a factor of0.70 for pipe encased in polyethylene filmto determine the appropriate value of Ffto use in the equations.

10

The maximum unit lateral resistance, Rs,at the bend is limited so as not to exceeda rectangular distribution of the Rankinepassive soil pressure, Pp , which is gener-ally less than the ultimate capacity of thesoil to resist pipe movement. Passive soilpressure is a term generally defined asthe maximum horizontal pressure thatwill be resisted by the soil structure with-out shearing failure of the soil. Horizontalsubgrade pressure will result in a defor-mation of the soil structure. The resis-tance offered by the subgrade soil increas-es with this deformation or strain forpressures less than the passive soil pres-sure. In soils having a density thatexceeds the critical void ratio (this condi-tion is usually obtained in stable, undis-turbed soil and in backfill compacted toapproximately 80% or more of theStandard Proctor density), the movementor deformation that occurs in developingthe full passive soil pressure is very smallin relation to the allowable, or available,movement at the bend in restrained push-on or mechanical joint systems used withDuctile Iron pipe.

The passive soil pressure for a particu-lar soil is given by the Rankine formula:

where: Pp = passive soil pressure (lbs/ft2)γ = backfill soil density (lbs/ft3)Hc= mean depth from surface to

the plane of resistance infeet (centerline of a pipe orcenter of bearing area of athrust block) (ft)

Cs= soil cohesion (lbs/ft2)Nφ= tan2 (45° + φ /2)φ = internal friction angle of the

soil (deg.)

As discussed above, the full Rankinepassive soil pressure, Pp, can be devel-oped with insignificant movement in well-compacted soils. For some of the standard Laying Conditions (see Figure 9)for Ductile Iron, the design value of pas-sive soil pressure should be modified by afactor Kn to assure that excessive move-ment will not occur. Therefore,

Rs = K n Pp D′

Empirically determined values for Kn canbe found in Table 3. In this context, thevalue chosen for Kn depends on the com-paction achieved in the trench, the back-fill materials, and the undisturbed earth.For the convenience of the designer,

DIPRA has developed a computer program – Thrust Restraint Design forDuctile Iron Pipe – to assist with calculations for most restrained jointconfigurations. It is based on the sevensoil types and suggested parameters inTable 3. The suggested values of theparameters listed in Table 3 are believedto be very conservative; however,DIPRA cannot assume responsibilitythat these values correspond to actualconditions at any particular job site.

Unit Bearing Resistance,Rs

Pp = γ HcNφ+ 2 Cs √Nφ (5)

(6)

11

Table 2Dimensions and Unit Weights of Pipe and Water

NominalPipe Size (in)

PressureClass

Pipe OutsideDiameter, D′ (ft)

Cross-sectionalArea of

Pipe, A (in2) Wp (lbs/ft) Ww (lbs/ft)Wp + Ww*(lbs/ft)

3468

10121416

18202430

36424854

6064

350350350350

350350250250

250250200150

150150150150

150150

0.330.400.580.75

0.931.101.281.45

1.631.802.152.67

3.193.714.234.80

5.135.47

12.318.137.364.3

96.7136.8183.8237.7

298.6366.4522.7804.2

1152.01555.22026.82602.1

2981.23387.0

10121824

30394757

667893123

163206261325

371410

461324

37537294

119147212329

4736428381078

12371407

14183148

6792119151

185225305452

63684810991403

16081817

Figure 9Standard ANSI/AWWA C150/A21.50 Laying Conditions for Ductile Iron Pipe

* For 14-inch and larger pipe, consideration should be given to the use of laying conditions other than Type 1.

† “Flat-bottom” is defined as “undisturbed earth.”

‡ “Loose soil” or “select material” is defined as “native soil excavated from the trench,free of rocks, foreign material, and frozen earth.”

†† AASHTO T-99 “Standard Method of Test for the Moisture-Density Relations of SoilsUsing a 5.5 lb (2.5 kg) Rammer and a 12 in. (305 mm) Drop.” Available from theAmerican Association of State Highway and Transportation Officials.

** Granular materials are defined per the AASHTO Soil Classification System (ASTMD3282) or the Unified Soil Classification System (ASTM D2487), with the exception thatgravel bedding/backfill adjacent to the pipe is limited to 2” maximum particle size perANSI/AWWA C600.

*Based on minimum pressure class pipe with standard cement-mortar lining. The difference in Wp + Ww for other pipe pressureclasses is not normally significant in relation to these calculations and these values may be used conservatively regardless of pipepressure class. However, the designer may use actual pipe weights for optimum design if desired.

TYPE 1*Flat-bottom trench.† Loose backfill.

TYPE 4Pipe bedded in sand, gravel, orcrushed stone to depth of 1/8 pipediameter, 4-inch minimum. Backfillcompacted to top of pipe. (Approxi -mately 80% Standard Proctor, AASH-TO T-99.)††

TYPE 2Flat-bottom trench.† Backfill lightlyconsolidated to centerline of pipe.

TYPE 5Pipe bedded to its centerline in com-pacted granular material, 4-inchminimum under pipe. Compactedgranular** or select material‡ to top of pipe. (Approximately 90%Standard Proctor, AASHTO T-99.)††

TYPE 3Pipe bedded in 4-inch minimum loosesoil.‡ Backfill lightly consolidated totop of pipe.

Table 3Suggested Values for Soil Parameters and Reduction Constant, Kn

Table 4Soil Classification Chart (Adaptation of ASTM D2487† )

Kn

A21.50 Laying Condition

2γ**(pcf)

fcfφ Cs(psf)

φ(deg)

SoilDescription*

SoilDesignation* 3 4 5

Clay 10 .80† 300

.50†

.80† 90 .20 .40 .60 .85Clay of Medium to Low Plasticity, LL‡<50, <25% Coarse Particles § [CL & CL-ML]***

Silt 129

.50†

.75† 0 .80† 90 .20 .40 .60 .85Silt of Medium to Low Plasticity, LL‡<50, <25% Coarse Particles § [ML & ML-CL]***

Clay 20 .80† 300

.50†

.80† 90 .40 .60 .85 1.0Clay of Medium to Low Plasticity w/Sand or Gravel,

LL‡<50, 25-50% Coarse Particles § [CL]***

Silt 229

.50†

.75† 0 .80† 90 .40 .60 .85 1.0Silt of Medium to Low Plasticity w/Sand or Gravel,

LL‡<50, 25-50% Coarse Particles § [ML]***

Coh-gran20

.40†

.65† 200 .40† 90 .40 .60 .85 1.0Cohesive Granular Soils, >50% Coarse Particles §

[GC & SC]***

SandSilt 30

.50†

.75† 0 .80† 90 .40 .60 .85 1.0Sand or Gravel w/Silt, >50% Coarse Particles §

[GM & SM]***

Good Sandor Gravel 36

.75†

.80† 0 .80† 100 .40 .60 .85 1.0Clean Sand or Gravel, >95% Coarse Particles §

[SW, SP, & GW]***

* See “Select Backfill Considerations” on page 19.** For conservatism, values for γ shown in Table 3 and used in this procedure are lower than the soil weight values used to calculate earth loads in ANSI/AWWA C150/A21.50. All other values in Table 3

assume saturated soil conditions and were also selected as such for conservatism.‡ Liquid Limit.§ “Coarse Particles” are those particles held on a No. 200 Sieve.

*** See Table 4 for more detailed soil descriptions.† These values to be used for Laying Condition Type 2.

Typical NamesMajor Divisions Group Symbols

Well-graded gravels and gravel-sand mixtures, little or no finesGW

GP Poorly graded gravels and gravel-sand mixtures, little or no fines

Coarse-grained Soils More than 50%

retained on No. 200 sieve*

Fine-grained Soils 50% or

more passes No. 200 sieve*

Sands

More than 50%

of coarse fraction

passes No. 4 sieve

Silts And

Clays

Liquid limit

greater than

50%

Silts And

Clays

Liquid limit

50% or less

Gravels 50%

or

more of coarse

fraction retained

on No. 4 sieve

Sands

With

Fines

Clean

Gravels

Gravels

With

Fines

Clean

Sands

Silty gravels, gravel-sand-silt mixturesGM

Clayey gravels, gravel-sand-clay mixturesGC

Well-graded sands and gravelly sands, little or no finesSW

Poorly graded sands and gravelly sands, little or no finesSP

Silty sands, sand-silt mixturesSM

Clayey sands, sand-clay mixtures

Inorganic silts, very fine sands, rock flour, silty or clayey fine sands

Inorganic clays of low to medium plasticity, gravelly clays, sandy clays, silty clays, lean clays

Organic silts and organic silty clays of low plasticity

Inorganic silts, micaceous or diatomaceous fine sands or silts, elastic silts

Inorganic clays of high plasticity, fat clays

Organic clays of medium to high plasticity

Peat, muck and other highly organic soils

SC

ML

CL

OL

MH

CH

OH

PTHighly Organic Soils

12

† For more detailed information about classification criteria, please consult ASTM D2487.* Based on the material passing the 3-in. (75-mm) sieve.

13

The following design equations for verti-cal bends, tees, reducers, and dead endswere derived with assumptions similar tothose used in the derivation of the hori-zontal bend equation (Equation 3). Spacedoes not permit full discussion of the deri -vations, nor does it allow discussion of allpossible fittings and thrust configurations.

Vertical Down Bends(Figure 10)Note: For conservatism, the weight of theearth, pipe, and water directly opposingthe thrust force is ignored; however, theweight of the earth, pipe, and water is usedin calculating the Unit Frictional Force, Fs.

Summation of forces in the “Y” direction:

Σ FY = 0 Gives

2PA sin (θ/2)-2 FfL cos (θ/2)=0

Employing a safety factor and solving for L,

L = [Sf PA tan (θ/2)]FfSf = Safety factor (Usually 1.5)

Vertical Up Bends (Figure 7)

Notes: 1. Force diagram is identical to that for horizontal bends (see Figure 7).

2. As the bend system in this case will attempt to move in the direction of thrust, and against the bottom of the trench, the values of Kn in this case should be chosen to reflect the conditions of the trench bottom on which the pipe rests, assuming adequate bell holes are provided. In most cases, values represent-ing those of Type 4 or 5 trench conditions may be used, as the trench bottom is normally relatively undisturbed.

Figure 10Vertical Down Bends

θ /2

Y2 PA sin (θ /2)

L

L

Ff

Ff


L = [Sf PA tan (θ/2)]Ff + 1/2 Rs


(7)

(8)

Tees (Figure 11)PAb = L b Ff + 1/2 RsLr

Employing a safety factor and solving for Lb ,

14

Figure 11Tees

PAb

Lr

Rs=KnPpDr′

LbFf

LbNote: Restrained length of tee branch is

not proportional to pressure and must be calculated for each internal pressure situation.

Lb = [Sf PAb - 1/2 RsLr]FfRs = KnPpD′r

(9)

Ab = Cross sectional area of branch (in2)Lb = Length of branch (ft) to be

restrainedLr = Total length between first joints

on either side of tee on the run(ft)

D ′r = Diameter of run (ft)Ff = (Fs)b ; For standard asphaltic

coated pipe

Ff = 0.7 (Fs)b ; For polyethylene encased pipe

(Fs)b = Unit frictional force (lbs/ft) onbranch

= πD ′C + (2We + Wp + Ww ) tan δ(used for tee branches, dead endconditions and reducers)


Ff = (Fs )b ; For standard asphaltic coated pipeFf = 0.7 (Fs )b ; For polyethylene encased pipe

15

Figure 12Reducers

Ff 2

Ff

L

PA

PA2

L2 L1

PA1Ff 1

Figure 13Dead Ends

Ff = (Fs)b; For standard asphaltic coated pipeFf = 0.7 (Fs)b; For polyethylene encased pipe

Ff 2 = (Fs)b2; For standard asphaltic coated pipeFf 2 = 0.7 (Fs)b2; For polyethylene encased pipe

Ff 1 = (Fs)b1; For standard asphaltic coated pipeFf 1 = 0.7 (Fs)b1; For polyethylene encased pipe

Reducers (Figure 12)A1= Cross sectional area of larger pipeA2= Cross sectional area of smaller pipe

L1 = [Sf P(A1 - A2)]Ff1

S f = Safety factor (Usually 1.5)

(10)

Dead Ends (Figure 13)

L = [Sf PA]Ff

S f = Safety factor (Usually 1.5)

(12)

(11)

Note: If straight run of pipe on small sideof reducer exceeds

L2 = [Sf P(A1 - A2)]Ff 2

then no restrained joints arenecessary.

Encroaching RestrainedLengthsBoth horizontal and vertical offsets arecommonly encountered in restrained sec-tions of a line. These offsets should bemade with as small a degree bend as pos-sible in order to minimize the thrust loadsand restrained length required. Also, inthese configurations an increase in linesegment length could be detrimental tothe pipeline or surrounding structures dueto over-deflection of the joints; therefore,the restrained joints should be fullyextended (if applicable) during installation.In certain configurations, fittings may be

close enough to one another that adjacentcalculated restrained lengths overlap. Insituations of this type, one approach is to:

Employing a safety factor and solving for L1,

16

Figure 14Equal Angle Vertical Offset (θ°)*

Ff

Ff

Rs

L2

L1

L

L

2PA sin (θ /2)

2PA sin (θ /2)


1) Restrain all pipe between the two fittings;

2) Assume 1/2 of the restrained pipe length between the two fittings acts to resist the thrust force of each fit-ting; and

3) Using the appropriate equations, calculate the additional restrained length required on the outer legs of the fittings.Following are two such examples:

Equal Angle Vertical Offset(θ°)* (Figure 14)For L1:ΣF = 0[2PA sin (θ/2)] = [FfL cos (θ/2)]+

[FfL1 cos (θ/2)]

L1 =Sf 2PA tan (θ/2) – L

Ff(13)

L2 =Sf 2PA tan (θ/2) – LFf + 1/2 Rs

(14)

For L2:ΣF = 0[2PA sin (θ/2)]= [FfL cos (θ/2)]+

[1/2 RsL cos (θ/2)]+[FfL2 cos (θ/2)]+[1/2 RsL2 cos (θ/2)]



* As the bend angle approaches 90º, lateral movement of the outer legs approaches zero. For this condition, restrain all pipe between the fittings and restrain the outer legs as dead ends.

17

Combined Horizontal Equal Angle Bends (θ°)* (Figure 15)For L1:ΣF = 0[2PA sin (θ/2)] = [Ff L cos (θ/2)] + [1/2 Rs L cos (θ/2)] + [Ff L1 cos (θ/2)] + [1/2 Rs L1 cos (θ/2)]


Figure 15Combined Horizontal Equal Angle Bends (θ°)*

F fFf

RsRs

L 1L1

L L

2PA sin (θ /2)2PA sin (θ /2)



(15)



18

Figure 16Combined Vertical Equal Angle Offsets (θ°)*

Ff Ff

L1 L1

PA PA

PAPA

PA PA

PA PA

LL

L L

2PA sin (θ /2)2PA sin (θ /2)


Combined Vertical EqualAngle Offsets (θ°)* – UnderObstruction (Figure 16)Vertical offsets are often combined toroute a pipeline under an obstruction orexisting utility. If the required restrainedlengths of the vertical up bends do notoverlap, the system may be treated as twoindividual vertical offsets (Figure 14). Ifthe required restrained lengths do over-lap, one approach is to:

1) Restrain all pipe between the outer-most two fittings;

2) Due to opposing forces, the thrust

forces of the middle two fittings (ver-tical up bends) are counteracted;

3) Assume 1/2 of the restrained pipe length between the vertical down and vertical up bends acts to resist the thrust force of the vertical down bends; and

4) Using the appropriate equations, cal-culate the additional restrained length required on the outermost legs of the offset system (vertical down bends). The resulting equation

is the same as for the vertical down bend in the single vertical offset (Equation 13):

L1 =Sf 2PA tan (θ/2) – L

Ff(16)


Combined Vertical EqualAngle Offsets (θ°)* – OverObstructionThis can be analyzed in the same man-ner as Figure 16 with the followingequation:


(17)


Note: This equation also applies to combined horizontal equal angle offsets(θ°) – around an obstruction.


19

Restrained LengthIn practice, the actual restrained lengthattained will generally be in multiples oflength of an individual piece of pipe (normally 18 or 20 feet). The length cal-culated indicates the minimum requiredrestrained length for each side of thebend. Thus, calculated lengths of 0 to 18or 20 feet normally call for one restrainedjoint at the fitting, 18 to 36 or 20 to 40feet normally require two restrainedjoints, etc.

Select BackfillConsiderationsIf restrained joint pipe is laid in trenchbackfill with markedly different supportcharacteristics than the native soil, specialconsiderations may be required. As thepipe is pressurized, it will transmit passivepressure to the backfill that will in turntransmit this pressure to the native soil.Therefore, the material that results in thesmaller unit bearing resistance (Rs) shouldbe used for the passive resistance and theunit friction force (Fs) should be based onthe backfill material surrounding the pipe.If restrained joints are used in swamps

or marshes where the soil is unstable, orin other situations where the bearingstrength of the soil is extremely poor, theentire pipeline should be restrained toprovide adequate thrust restraint.

Combining Thrust Blocksand Restrained JointsCombining restrained joints and thrustblocks by designing each system indepen-dently of the other and then incorporatingboth to the piping system normally yieldsthe greatest degree of security.It is often poor practice to mix systems

based on each system being designed toresist a percentage of the resultant thrustforce. Both thrust blocks and restrainedjoint pipe systems require slight movementbefore their respective thrust restraintcapability can be developed. Those move-ments must be compatible for the combina-tion to be successful. Because of the uncer-tainties of the degree of these movementsbeing compatible, this design approachmust be given special consideration.

Pipe in a CasingIt is often necessary to install restrainedjoint pipe through a casing pipe. The func-tion of restrained joint pipe is basically totransfer thrust forces to the soil structure.Therefore, if the annular space between thetwo pipes is not grouted in, the length ofrestrained pipe inside the casing should notbe considered as part of the restrainedlength to balance the thrust force. Whenrestrained joint pipe is installed through acasing pipe, the restrained joints shouldnormally be fully extended.

Future ExcavationsOne particular concern of those with respon-sibility for infrastructure pipeline design,installation, and maintenance is the possibili-ty of substantial excavation in the close vicin-ity of previously installed restrained pipe andfittings including parallel excavations.Remembering the usual function ofrestrained pipes in transmitting thrust forcesto the soil structure, it is obvious that if thisstructure is removed or significantly dis-turbed with the pipeline under pressure, thesafety and stability of the system may becompromised. In this regard, it would seemreasonable to temporarily shut down closeexisting restrained lines to do such work, orto conduct such operations during lowestpressure service conditions. Where this isnot practical or possible, alternate provisionsmight be safely employed. These precau-tions might include supplementary thrustblocking, restraint with laterally loaded pilesor batter piles at the thrust focus, special pipeanchors, or other careful, sequential, andinnovative engineering and construction pro-cedures. Proper engineering and construc-tion judgment must be exercised in theseconditions.2

Deflected UnrestrainedDuctile Iron Pipe JointsUnrestrained push-on and mechanical jointDuctile Iron pipe are capable of deflectionsup to 8° (depending on joint type and pipesize). These joints are well-suited fordiverting pipelines from obstructions orwhen following the curvature of streetsand roads. In an effort to keep thrust forcesto a minimum, joint deflections should beutilized whenever possible rather than fit-

tings. In pressurized systems, thrustforces develop at these joint deflections. Inthe vast majority of installations the soil-pipe interaction will result in reasonablesecurity and stability of the joints. Only inextraordinary circumstances, e.g., unstablesoils, high internal pressure in combinationwith very shallow cover, etc., is the securi-ty threatened. In these situations, soil-pipethrust resisting principles, not unlike thosepresented in this manual, may be applied tothese unrestrained joint situations.

Computer ProgramFor the convenience of the designer, acomputer program has been developedbased upon the procedures and equationsof this manual. It can be used to assist withcalculations of both Unit Frictional Forceand Unit Bearing Resistance. Additionally,the computer program may be used tofacilitate calculations in determining therequired length of restrained piping. Thisprogram can be downloaded from DIPRA’swebsite at http://www.dipra.org.

Restrained LengthCalculation ProcedureEXAMPLE: 30-inch Ductile Iron pipelineto be buried under 6 feet of cover in a cohe-sive granular backfill that will be compactedto 80% Standard Proctor density to the topof the pipe (Laying Condition 4). The thrustrestraint design pressure is 150 psi.Determine the length of restrained pipingrequired at a 90° horizontal bend.

STEP 1: Establish known values for:

L =SfPA tan (θ/2) Ff + 1/2 Rs

Where:Rs = KnPpD′Sf = 1.5P = 150 psiD′ = 32/12 = 2.67 ftA = 36π(D′)2 = 806.3 in2

θ = 90°Kn = 0.85 (From Table 3)Ff = Fs

(Eq. 3)

20

STEP 2: Determine Unit FrictionalResistance, Fs

Fs = πD′�C + (2We+ Wp+ Ww) tan δ2

Where:C = fcCs= (0.40) (200) = 80 psf

fc = 0.40Cs = 200 psf

We=HγD′= 6× 90× 2.67=1442lbs/ft

H= 6 ft of cover (given)γ = 90 pcf (From Table 3)

Wp + Ww = 452 lbs/ft (From Table 2)δ = fφφ = (0.65) (20) = 13°

fφ = 0.65φ = 20°

Then:

Fs=π(2.67)(80)

+[2(1442)+452]tan13°2

Fs=335.5+770.2=1105.7 lbs/ft

STEP 3: Determine Passive Soil Resis-tance, Pp

Pp = γHcNφ+ 2 Cs√Nφ (Eq. 5)

Where:Hc = H+1/2D′ = 6 + 2.67 = 7.33 ft

2

Nφ = tan2(45+φ/2)=tan2(45+20)=2.042

Then:Pp = (90)(7.33)(2.04)+

(2)(200) √2.04Pp = 1345.8+ 571.3= 1917.1 lbs/ft2

STEP 4: Substitute known and deter-mined values into Equation 3 listed in STEP 1 to determine required restrained length.

L =(1.5)(150)(806.3)tan (90/2)

1105.7+ [1/2 (0.85)(1917.1)(2.67)]

L =181,417.5

1105.7+2175.4

L = 55.3 ft.

NOTE: The DIPRA Computer Program,Thrust Restraint Design forDuctile Iron Pipe, may be used to facilitate calculations in determining the required lengthof restrained piping.

γ = Backfill soil density (lbs/ft3) (See Table 3)

W = Unit normal force on pipe= 2 We + Wp + Ww (lbs/ft)

We = Earth prism load (lbs/ft)= γHD′

Wm = Density of thrust block material(lbs/ft3)

Wp = Unit weight of pipe (lbs/ft) (SeeTable 2)

Ww = Unit weight of water (lbs/ft) (See Table 2)

θ = Bend angle (degrees)

δ = Pipe friction angle (degrees)

φ = Soil internal friction angle(degrees) (See Table 3)

Sf = Safety factor (usually 1. 5)

Vg = Volume of thrust block (ft3)

References1. Carlsen, R.J., “Thrust Restraint forUnderground Piping Systems.” CastIron Pipe News, Fall 1975.

2. Conner, R.C. “Thrust Restraint ofBuried Ductile Iron Pipe,” Proceed -ings of Pipeline Infrastructure Con -fer ence, Boston, Massachusetts,June 6-7, 1988. Published by ASCE,New York, NY, 1988, p. 218.

3. Reference U.S. Pipe & FoundryCompany research (Unpublished).

4. Potyondy, J.G., M. Eng., Skin FrictionBetween Various Soils andConstruction Materials.

5. ASTM D 2487—Classification ofSoils for Engineering Purposes.

NomenclatureA = Cross-sectional area of pipe

(inch2) = 36π D′ 2 (See Table 2)

Ap = Surface area of pipe exterior(ft2/ft)

b = Thrust block width (ft)

C = Pipe cohesion (lbs/ft2)

Cs = Soil cohesion (lbs/ft2) (See Table 3)

D′ = Outside diameter of pipe (ft) (See Table 2)

fc = Ratio of pipe cohesion to soilcohesion (See Table 3)

Ff = Unit frictional resistance (lbs/ft)

Fs = Unit frictional force assuming 1/2 the pipe circumference bearsagainst the soil (lbs/ft)

(Fs)b = Unit frictional force assuming the entire pipe circumference contacts the soil (lbs/ft)

fφ = Ratio of pipe friction angle to soil friction angle (See Table 3)

h = Thrust block height (ft)

H = Depth of cover to top of pipe (ft)

Hc = Depth of cover to pipe center-line (ft)

Ht = Depth to bottom of thrust block(ft)

Kn = Trench condition modifier (SeeTable 3)

L = Minimum required restrainedpipe length (ft)

Nφ = tan2 (45° + φ/2)

P = Design pressure (psi)

Pp = Passive soil pressure (lbs/ft2)

Rs = Unit bearing resistance (lbs/ft)

Sb = Horizontal bearing strength of soil (lbs/ft2 (See Table 1)

T = Resultant thrust force (lbs)

(Eq. 4a)

} (From Table 3)

} (From Table 3)

Manufactured from recycled materials.

American Cast Iron Pipe CompanyP.O. Box 2727Birmingham, Alabama 35202-2727

Atlantic States Cast Iron Pipe Company183 Sitgreaves StreetPhillipsburg, New Jersey 08865-3000

Canada Pipe Company, Ltd.1757 Burlington Street EastHamilton, Ontario L8N 3R5 Canada

Clow Water Systems CompanyP.O. Box 6001Coshocton, Ohio 43812-6001

Griffin Pipe Products Co.1011 Warrenville Road Lisle, Illinois 60532

McWane Cast Iron Pipe Company1201 Vanderbilt RoadBirmingham, Alabama 35234

Pacific States Cast Iron Pipe CompanyP.O. Box 1219Provo, Utah 84603-1219

United States Pipe and Foundry CompanyP.O. Box 10406Birmingham, Alabama 35202-0406

An association of quality producers dedicated to highest pipestandards through a program of continuing research.245 Riverchase Parkway East, Suite OBirmingham, Alabama 35244-1856Telephone 205 402-8700 FAX 205 402-8730http://www.dipra.org

Copyright © 2006 by Ductile Iron Pipe Research Association.This publication, or parts thereof, may not be reproduced in any form without permission of the publishers.

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TRD/11-06/4MPublished 11-06Revised 2-12

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