External Loads

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AWWAMANUAL

hapter

External Loads

LOAD DETERMIN TIONExtemalloads on buried pipe are generally comprised of the weight of the backfill com-bined with live and impact loads. The Marston theory (1929) is generally used to deter-mine the loads imposed on buried pipe by the soil surround ing it . This theory isapplicable to both flexible and rigid pipes installed in a variety of conditions, includingditch and projecting conduit installations. Ditch conduits are structures installed andcompletely buried in narrow ditches in relatively passive or undisturbed soil. Projectingconduits are structures installed in shallow bedding with the top of the conduit project-ing above the surface of the natural ground and then covered with the embankment . Forpurposes of calculating the extemal vertical loads on projecting conduits, the field condi-tions affecting the loads are conveniently grouped into four subclassifications. They arebased on the magnitude of settlement of the interior prism of soil relative to that of theexterior prismt and the height of the embankment in relation to the height at which set-tlemen ts of the interior and exterior prisms of soil are equal (Spangler 1947).Steel pipe is considered to be flexible, and th e Marston th eory provides a simple procedure for calculating extemal soil loads on flexible pipe. f he flexible pipe is buried ina ditch less than two times the width of the pipe, the load is computed as follows:

Where: We = dead load on th e conduit , in lbllin t (kgm) of pipeCd = load coefficien t based on HeBd where He is the h eight of fillabove conduit, and Bd is defined below.w = unit weight of fill , in lb/ft3 (kg/m3Bd = width of trench at top of pipe in ft m)e = diameter of pipe in ft (m)

'TI-le backfill prism directly above the pipe.tTI le bacldill prism between the trench walls and vertical lines drawn at the OD of the pipe.

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(6-1 )


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60 STEEL PIPEIf the pipe is buried in an embankment or wide trench, the load is computed as

follows:(6-2)

Where:Cc = coefficient for embankment conditions, a function of soil properties.

For flexible pipe, the settlement ratio Spangler 1947) is assumed to be zero, inwhich case

6-3)

Where:He =height of fill above top of pipe in ft (m)

Then:

(6-4)

The dead load calculation in Eq 6-4 is the weight of a prism of soil with a widthequal to that of the pipe and a height equal to the depth of fill over the pipe. Thisprism load is convenient to calculate and is usually used for all installation conditionsfor both trench and embankment conditions. For use in the Iowa deflection formula,divide Eq 6-4 by 12 for US Customary units and by 1,000 for metric units.

In addition to supporting dead loads created by earth cover, buried pipelines canalso be exposed to superimposed , concentrated, or distributed live loads. Concentratedlive loads are generally caused by truck-wheel loads and railway-car loads. Distributed live loads are caused by surcharges, such as piles of material and temporarystructures. The effect oflive loads on a pipeline depends on the depth of cover over thepipe. A method for determining the live load us ing modified Boussinesq equations ispresented by Handy (1982).

DEFLECTION DETERMIN TIONThe Iowa deflection formula was first proposed by M.G. Spangler (1941) . It was latermodified by Watkins and Spangler (1958) and has frequently been rearranged . In oneof its most common forms, deflection is calculated as follows:

Where:( 3 )_ D KWru - 1 EI 0.061 E r3

t x = horizontal deflection of pipe, in in. mm)Dt =deflection lag factor 1.0-1.5)

(6-5)

'Deflection lag factor, D accounts for long-term deflection as a result of consolidation or settlement of backfillmaterial at the sides of the pipe. For pressure pipe, D is 1.0, because long-term deflections are largely preventedby the supporting action of the internal hydrostatic pressure.

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Where:

K =bedding constant (0.1)W = load per unit of pipe length, in lbllin in.r = radius, in in. (mm)EI =pipe wall stiffness

EXTERNAL LOADS 61

E = modulus of elasticity (30,000,000 psi [206,842,710 kPa] for steel and4,000,000 psi [27,579,028 kPa] for cement mortar)I transverse moment of inertia per unit length of individual pipe wallcomponents* = t3/12, where t is in in. (mm)E =modulus of soil reaction in lbf/in2 (kPa) (Tables 6-1 and 6-2).

Allowable pipe deflection for various lining and coating systems that are oftenaccepted are

Mortar-lined and coated= 2 percent of pipe diametertMortar-lined and flexible coated= 3 percent of pipe diameterFlexible lined and coated= 5 percent of pipe diameterIn addition to other considerations, the allowable pipe deflection is also dependenton the type of jointing system being utilized.Live-load effect, added to dead load when applicable, is generally based onAASHTO HS-20 truck loads or Cooper E-80 railroad loads as indicated in Table 6-3.,These values are given in pounds per square foot and include a 50 percent impact factor. There is no live-load effect for HS-20 loads when the earth cover exceeds 8 t(2.44 m) or for E-80 loads when the earth cover exceeds 30ft (9.14 m).Modulus of soil reaction E is a measure of stiffness of the embedment material ,which surrounds the pipe. This modulus is required for the calculation of deflection

and critical buckling stress. E is actually a hybrid modulus that has been introducedto eliminate the spring constant used in the original Iowa formula. t is the product ofthe modulus of passive resistance of the soil used in Spangler s early derivation andthe radius of the pipe. It is not a pure material property.Values ofE were originally determined by measuring deflections of actual installations of metal pipe and then back-calculating the effective soil reacti on. Because E isnot a material property, it cannot be uniquely measured from a soil sample, thereforedetermining E values for a given soil has historically presented a serious problem fordesigners.

'Under load, the individual elements-i.e., mortar lining, steel shell, and mortar coating-work together as laminated rings E8l 8 E1h Eclc-shell, lining, and coating.) Structurally, the combined action of these elementsincreases the moment of inertia of the pipe section, above that of the shell alone, thus increasing its ability toresist loads. The pipe wall stiffness of these individual elements is additive.

tMortar-lined and coated AWWA C205) pipe deflection is based on a maximum mortar coating thickness ofIl /4 in. (32 mm). Flexible pipe coatings include AWWA C209, C210, C213, C214, C215, and C222. Flexible pipelinings and coatings include AWWA C210, C213, C222, C224, and C225.

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62 STEEL PIPETable 6-1 Values* of modulus of soil reaction, (psi) based on depth of cover, type of soil, andrelative compaction

Standard AASHTO relative compaction*Depth of Cover 85% 95% 100%

Type of Soilt t m) psi (kPa) psi (kPa) psi (kPa) psi (kPa)Fine-grained soils 2-5 (0.06-1.5) 500 (3,450) 700 (4,830) 1,000 (6,895) 1,500 (10,340)with less than 25% 5-10 (1.5-3.1) 600 (4,140) 1,000 (6,895) 1,400 (9,655) 2,000 (13,790)sand content (CL, 10-15 (3.1-4.6) 700 (4,830) 1,200 (8,275) 1,600 (11,030) 2,300 (15,860)ML, CL-ML) 15-20 (4.6-6.1) 800 (5,520) 1,300 (8,965) 1,800 (12,410) 2,600 (17,930)Coarse-grained soils 2-5 (0.06-1.5) 600 (4,140) 1,000 (6,895) 1,200 (8,275) 1,900 (13,100)with fines (SM, SC) 5-10 (1.5-3.1) 900 (6,205) 1,400 (9,655) 1,800 (12,410) 2,700 (18,615)

10-15 (3.1- 4.6) 1,000 (6,895) 1,500 (10,340) 2,100 (14,480) 3,200 (22,065)15-20 (4.6-6.1 1,100 (7,585) 1,600 (11,030) 2,400 (16,545) 3,700 (25,510)

Coarse-grained soils 2-5 (0.06-1.5 700 (4,830) 1,000 (6,895) 1,600 (11,030) 2,500 (17,235)with little or no fines 5-10 (1.5-3.1) 1,000 (6,895) 1,500 (10,340) 2,200 (15,170) 3,300 (22,750)(SP, SM, GP, GW 10-15 (3.1-4.6 1,050 (7,240) 1,600 (11,030) 2,400 (16,545) 3,600 (24,820)

15-20 (4.6-6.1) 1,100 (7,585) 1,700 (11,720) 2,500 (17,235) 3,800 (26,200)* Hartley, James D. and Duncan, James M., E' and its Variation with Depth. Journal ofTransportation, Division ofASCE,

Sept. 1987.t Soil type symbols are from the Unified Classifica tion System.* Soil compaction. When specifying the amount of compaction required, it is very important to consider the degree of soil com

paction that is economically obtainable in the field for a particular installa tion. The density and supporting strength of thenative soil should be taken into account. The densification of the backfill envelope must include the haunches under the pipeto control both the horizontal and vertical pipe deflections. Specifying an unobtainab le soil compaction value can result ininadequate support and injurious deflection. Therefore, a conservative assumption of the supporting capability of a soil isrecommended, and good field inspection should be provided to verify th at design assumptions arc met.

Table 6 2 Unified soil classificationSymbol Description

GW Well-graded gravels, gravel-sand mixtures, little or no finesGP Poorly graded gravels, gravel-sand mixtures, little or no finesGM Silty gravels, poorly graded gravel-sand-silt mixturesGC Clayey gravels, poorly graded gravel-sand-clay mixturesSW Well-graded sands, gravelly sands, little or no finesSP Poorly graded sands, gravelly sands, little or no finesSM Silty sands, poorly graded sand-silt mixturesSC Clayey sands, poorly graded sand-clay mixturesML Inorganic silts and very fine sand, silty or clayey fine sandsCL Inorganic clays of low to medium plasticityMH Inorganic silts, micaceous or diatomaceous fine sandy or silty soils, clastic siltsCH Inorganic clays of high plasticity, fat claysOL Organic silts and organic silt-clays of low plasticityOH Organic clays of medium to high plasticityPt Peat and other highly organic soils

Source: Clnssificntion of Soils for Engineering Purposes. ASTM Stnndnrd 02487-69, ASTM Philadelphia, Pa (1969).

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EXTERNAL LOADS 63Table 6 3 Live load effect

Highway HS-20 Loading* Railroad E-80 LoadingHeight of Cover Load Height of Cover Loadft (m) psf (kg1m 2 ft (m) psf (kg1m21 (0.30) 1,800 (8,788) 2 (0.61) 3,800 (18,553)2 (0.61) 800 (3,906) 5 (1.52) 2,400 (11,718)3 (0.91) 600 (2,929) 8 (2.44) 1,600 (7,812)4 (1.22) 400 (1,953) 10 (3.05) 1,100 (5,371)5 (1.52) 250 (1,221) 12 (3.66) 800 (3,906)6 (1.83) 200 (976) 15 (4.57) 600 (2,929)7 (2.13) 176 (859) 20 (6.10) 300 (1,465)8 (2.44) 100 (488) 30 (9.14) 100 (488)

Neglect live load when less than 100 psf; use dead load only.

To circumvent the problems inherent in working with the hybrid modulus E , theconstrained soil modulus Ms Krizek et al. 1971) has been used more frequently.The constrained modulus is a constitutive material property, which is measured asthe slope ofthe secant of the stress-strain diagram obtained from a confined compressiontest of soil. t may also be calculated from Young's modulus Es, and Poisson's ratio uof the soil by

M = E 5 1-u)s 1+u) 1 - 2u)

6-6)The soil modulus can be determined from common consolidation tests, triaxial labo

ratory tests, or from field plate-bearing tests of the actual soil in which the pipe will beembedded.Because Ms is taken as the secant modulus, it accounts in part for nonlinearities in

stress-strain response of soil around the pipe. Determination of Ms is based on theactual load applied to a pipe. Decreasing the load results in a decreased value for M5 Many researchers have studied the relationship between E and Ms with recommendations varying widely (E = 0.7 to 1.5 M 5 . This is understandable, because s is apure soil property, whereas E is empirical. t appears justified to assume the two tobe the same, E = Ms.

UCKLINGPipe embedded in soil may collapse or buckle from elastic instability resulting fromloads and deformations. The summation of external loads should be equal to or lessthan the allowable buckling pressure. The allowable buckling pressure Qa may bedetermined by the following:

( 1 ) , ,EJ)l/2qa = FS 32RwB E D3 6-7)

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64 STEEL PIPEWhere:

qa =allowable buckling pressure*, in psi kPa)S =2.0D = diameter of pipe, in in . mm)Rw = water buoyancy factor

= 0.33 hwlh), 0 s; hw s; hhw = height of water surface above top of pipe, in in . mm)h = height of ground surface above top of pipe, in in. mm)B = empirical coefficient of elastic support dimensionless)

1= .. .. :::1 4e -0.065H)Equivalent metric equation:

1

Where:1 4e -0 .213H)

H = height of fill above pipe, in ft m)E = modulus of soil reaction see Table 6-1)EI = pipe wall stiffness see Eq 6-5)

Normal Pipe nstallationsFor determination of external loads in normal pipe installations , use the followingequation:

Where:6-8)

hw = height of water above conduit in in. mm)w = specific weight of water = 0.0361 lb/cu in . 0.0098 kPalmm3)Pu=internal vacuum pressure in psi kPa) =atmospheric pressure lessabsolute pressure inside pipe, in psi kPa)

We = vertical soil load on pipe per unit length, in lb/in. kPalmm)In some sit uations, live loads should be considered as well. However, simultaneousapplication oflive-load and internal-vacuum transients need not normally be considered.Therefore, iflive loads are also considered, the buckling requirement is satisfied by

6-9)Where:

WL =live load on the pipe per unit length, in lb/in. kPa/mm)

'NOTE: Where internal vacu urn occurs with cover depth less than 4 ft 1.2 m), but not less than 2ft 0.6 m), cureshould be exercised. This is particularly important for large-diameter pipe. In no case shall cover depth be lessthan 2 ft 0.6 m) for pipe diameters less than 24 in. 600 mm), 3 ft 0.9 m) for pipe diameters 24 in. 600 mm)through 96 in. 2,400 mm), und 4 ft 1.2 m) for pipe over 96 in. 2,400 mm) in diameter.

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66 STEEL PIPETable 6 4 Influence coefficients for rectangular areas

m AIH n = BJH or m AIHor

n BIH0 10 20 30 40 50 60 70 80 91 01 21 52 0253 05 0

10 0

010 20 30 40 50 60 70 80 91 01 21 52 02 53 05 0

10 0

0 10 0050 0090 0130 0170 0200 0220 0240 0260 0270 0280 0290 0300 03100310 0320 03200320 032

1 00 0280 0550 0790 1010 1200 1360 1490 1600 1680 1750 1850 1930 2000 2020 2030 2040 2050 205

0 20 0090 0180 0260 0330 0390 0430 0470 0500 0530 05500570 0590 06100620 0620 0620 0620 062

1 20 0290 05700830 1060 12601430 1570 1680 17801850 1960 2050 2120 2150 2160 2170 2180 218

0 30 01300260 0370 0470 0560 0630 0690 0730 0770 0790 0830 0860 0890 0900 0900 09000900 090

1 50 0300 05900860 1100 1310 14901640 1760 1860 1930 2050 21502230 2260 2280 2290 2300 230

0 400170 0330 0470 0600 0710 0800 0870 0930 0980 1010 1060 1100 11301150 1150 1150 1150115

2 00 0310 06100890 1130 1350 1530 1690 1810 1920 2000 2120 2230 2320 2360 23802390 2400 240

0 50 0200 0390 0560 0710 0840 09501030 1100 1160 12001260 1310 13501370 1370 1370 1370 137

2 50 0310 0620 0900 1150 1370 1550 1700 1830 1940 2020 215022 60 2360 2400 2420 2440 2440 244

0 60 0220 0430 0630 0800 0950 1070 1170 1250 1310 1360 14301490 15301550 1560 1560 1560156

3 00 0320 0620 0900 1150 13701560 1710 1840 1950 2030 2160 22802380 2420 2440 2460 2470 247

0 70 0240 0470 0690 0870 1030 1170 12801370 1440 14901570 1640 1690 1700 1710 1720 1720172

5 00 0320 06200900 1150 13701560 1720 1850 19602040 2170 2290 2390 2440 2460 2490 2490 249

0 80 0260 0500 0730 0930 1100 1250 13701460 1540 1600 1680 1760 181018301840 1850 1850185

1000 0320 0620 09001150 1370 1560 1720 1850 19602050 218023 00 2400 2440 2470 2490 2500 250

0 900270 0530 07700980 1160 13101440 1540 1620 1680 17801860 1920 1940 1950 1960 1960 196

0 0320 0620 09001150 1370 1560 1720 1850 19602050 2180 2300 2400 2440 2470 2490 2500 250

Source: Newmark, N.M. Simplified Computation of Vertical Pressures in Elastic Foundations Circ. 24. Engrg. Exp. tn . Uniu.of Illinois 1935).

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X'

y

UniformlyDistributed

Load, P I8I X

Source: Spangle ; M.G. Handy, R.L. Soil Engineering. Harper and Row, New Yorh 4th ed., 1982).Figure 6-1 Position o area

If height of cover is 3.0 ft (0.914 m), thenm =0.610 n =0.333

Coefficient = 0.07P = 1,615 psf

(P =0.7 (4)(28,152) =7,883 kg/m2)

EXTERNAL LOADS 67

Using th e Iowa formula (Eq 6-5) to calculate deflection fo r 54-in. (1,372 mm) pipeand 60-in. (1,524 mm) pipe, wall thickness 1 4 in. (6.35 mm) for each size, E = 1,250 psi(8.618 MPa), Dt = 1.0, and soil weight of 120 pcf (1,922 kg/m3) , the results ar e

Total load (dead and live load):2ft (0.61 m) cover :

we [ 120)(2) + 2,700 ] 12; 4 = 40.8rW c = 1, 922 (2) + 13, 180) 20r 0 = 34. r1, 0

3 ft (0.914 m) cover:

we [< 120)(3) + 1,615 ]12;4 = 27 .4rwe= ( 1, 922 (0.914 ) + 7,883 ) ~ ; 0 = 19.279r

Using Spangler s formula, deflection =60 in. (1,524 mm), 2ft (0.61 m) cover: = 1.58 in. (40.1 mm) = 2.6

3 ft (0.914 mm) cover: = 1.06 in. (26.9 mm) =1.854 in. (1,372 mm), 2ft (0.61 m) cover: = 1.41 in. (35.8 mm) =2.6

3ft (0.914 m) cover:= 0.95 in. (24.1 mm) =1.8Copyright D 2004 American Water Worles Association, All Rights Reserued.


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68 STEEL PIPE

COMPUTER PROGR MS __Traditional procedures depending on weight and the elastic modulus of soil to determine pipe deflections and stress have been discussed. However, computer programsthat permit a more rational determination in the design of pipe are now availablefrom universities consulting engineers and manufacturers.

REFERENCESHandy, R.L. 1982. Soil Engineering 4th ed.New York: Harper Row Publishers.Howard, A. 1977. Modules of Soil ReactionValues for Buried Flexible Pipe. Jour.Geotechnical Engr. Div.-ASLE.Krizek, R.J., R.A. Parmelee, J.N. Kay, and

H.A. El Naggar. 1971. StructuralAnalysis and Design of Pipe. Report 116.HCHRP.Marston, A. 1929. The Theory of ExternalLoads on Closed Conduits in the Light ofthe Latest Experiments. In Proc. of theNinth Annual Meeting Highway Res.Board.Spangler, M.G. 1947. UndergroundConduits-An Appraisal of ModernResearch. Proc. ASCE. June.

. The Structural Design of FlexiblePipe Culverts. 1941. Bull. 153. Ames,Iowa: Iowa State College.Watkins, R.K., and M.G. Spangler. 1958.Some Characteristics of the Modulus ofPassive Resistance of Soil: A Study inSimilitude. Highway Research BoardProc. 37:576.

The follow ing references are not cited in thetext.Barnard R.E. 1948. Design Standards forSteel Water Pipe. Jour. AWWA 40:24.. 955. Behavior of Flexible Steel PipeUnder Embankm ents and in Trenches.Bull. Middletown, Ohio: Armco DrainageMetal Products, Inc.

. 1957. Design and Deflection Controlof Buried Steel Pipe Supporting EarthLoads and Live Loads. Proc. ASTM57:1233.

Braune Cain, and Janda. 1929. EarthPressure Experiments on Culvert Pipe.Public Roads 10:9.Burmister, D.M. 1951. The Importance ofNatural Controlling Conditions UponTriaxial Compression Test Conditions.Special Tech. Pub. 106. Philadelphia, Pa.:American Society for Testing andMaterials.

Housel, W.S . 1951. Interpretation of TriaxialCompression Tests on Granular Soils.Special Tech. Pub. 106. Philadelphia, Pa.:American Society for Testing andMaterials .

Luscher U. 1966 . Buckling of SoilSurrounded Tubes. Jour. Soil Mechanicsand Foundations Div.-ASCE November.Proctor, R.R. 1933. Design and Constructionof Rolled-Earth Dams. Engineering NewsRecord 111:245.

. 1948. An Approximate Method forPredicting the Settlement of Foundationsand Footings . In Second InternationalConference on Soil MechanicsFoundation Engr. The HagueNetherlands.Proudfit, D.P. 1963. Performance of LargeDiameter Steel Pipe at St. Paul. Jour.AWWA 55(3):303.Reitz, H.M. 1956 . Soil Mechanics andBackfilling Practices . Jour. AWWA48(12):1497.Report on Steel Pipelines for UndergroundWater Service. 1936. Special Investigation888. Chicago: Underwriters Labs., Inc.Sowers, G.F. 1956. Trench Excavation andBackfilling. Jou r. AWWA 48(7):854.Span gler M.G. 1948 . UndergroundConduits-An Appraisal of ModernResearch. Trans. ASCE 113:316.

. 1951-1952. Protective Casings forPipelines. Engineering Reports 11. Ames,Iowa: Iowa State College.Spangler, M.G., and D.L. Phillips. 1955.Deflections of Timber-Strutted CorrugatedMetal Pipe Culverts Under Earth Fills.Bull. 102. Highway Research Board; Pub.350. Washington, D.C.: National Academyof Sciences-National Research Council.Terzaghi, K 1943. Theoretical Soil Mechanics.New York: John Wiley Sons.Wagner, A.A. 1951. Shear Characteristics ofRemolded Earth Materials. Special Tech.Pub. 106. Philadelphia, Pa.: AmericanSociety for Testing and Materials.Wiggin, T.I-I. M.L. Enger, and W.J. Schlick.1939. A Proposed New Method forDetermining Barrel Thicknesses of CastIron Pipe, Jour. AWWA 31:811.

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