Pipeline Design for Water Engineers

PIPELINE DESl6N fOR WATER EN6IMEERS THIRD REVISED AND UPDATED EDITION

DEVELOPMENTSIN WATER SCIENCE, 40

OTHER TITLES IN THIS SERIES VOLUMES 7-3 ARE OUT OIF PRINT 4 J.J. FRIED GROUNDWATER POLLUTION 5 N. RAJARATNAM TURBULENT JETS 6 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS 7 v. HANK AND J. SVEC GROUNDWATER HYDRAULICS 8 J. BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL AFRICA 9 T.A. McMAHON AND R.G. MElN RESERVOIR CAPACITY AND YIELD 10 G. KOVACS SEEPAGE HYDRAULICS 1i w.n. GRAF AND C.H. MORTIMER (EDITORS) HYDRODYNAMICSOF LAKES: PROCEEDINGS OF A SYMPOSIUM 12-13 OCTOBER 1978. LAUSANNE, SWITZERLAND 12 W. BACK AND D.A. STEPHENSON (EDITORS) CONTEMPORARY HYDROGEOLOGY: THE GEORGE BURKE MAXEY MEMORIAL VOLUME 13 M.A. MARlfJO AND J.N. LUTHIN SEEPAGE AND GROUNDWATER 14 D. STEPHENSON STORMWATER HYDROLOGY AND DRAINAGE 15 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS (completely revised edition of Vol. 6 in the series) 16 W. BACK AND R. LETOLLE (EDITORS) SYMPOSlClM ON GEOCHEMISTRY OF GROUNDWATER 17 A.H. EL-SHAARAWI (EDITOR) IN COLLABORATION WITH S.R. ESTERBY TIME SERIES METHODS IN HYDROSCIENCES 18 J.BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL REGIONS 19 D. STEPHENSON PIPEFLOW ANALYSIS 20 I.ZAVOIANU MORPHOMETRY OF DRAINAGE BASINS 21 M.M.A. SHAHIN HYDROLOGY OF THE NILE BASIN 22 H.C.RIGGS STREAMFLOW CHARACTERISTICS 23 M. NEGULESCU MUNICIPAL WASTEWATER TREATMENT 24 L.G.EVERETT GROUNDWATER MONITORING HANDBOOK FOR COAL AND OIL SHALE DEVELOPMENT 25 W. KINZELBACH GROUNDWATER MODELLING: AN INTRODUCTION WITH SAMPLE PROGRAMS IN BASIC 26 D. STEPHENSONAND M.E. MEADOWS KINEMATIC HYDROLOGY AND MODELLING 27 A.M. EL-SHAARAWI AND R.E. KWIATKOWSKI (EDITORS) STATISTICAL ASPECTS OF WATER CIUALITY MONITORING - PROCEEDINGS OF THE WORKSHOP HELD AT THE CANADIAN CENTRE FOR INLAND WATERS, OCTOBER 1985 28 M.JERMAR WATER RESOURCES AND WATER MANAGEMENT 29 G.W. ANNANDALE RESERVOIR SEDIMENTATION 30 D.CLARKE MICROCOMPUTER PROGRAMS IN GROUNDWATER 31 R.H. FRENCH HYDRAULIC PROCESSES IN ALLUVIAL FANS 32 L. VOTRUBA, 2. KOS. K. NACHAZEL, A. PATERA ANDV. ZEMAN ANALYSIS OF WATER RESOURC_ESYSTEMS 33 L. VOTRUBA AND V. BROZA WATER MANAGEMENT IN RESERVOIRS 34 D. STEPHENSON WATER AND WASTEWATER SYSTEMS ANALYSIS 35 M.A. CELlA ET AL. COMPUTATIONAL METHODS IN WATER RESOURCES, VOLUME 1 MODELING SURFACE AND SUB-SURFACE FLOWS. PROCEEDINGS OF THE VII INTERNATIONAL CONFERENCE, MIT. USA, JUNE 1988 36 M.A. CELIA ET AL. COMPUTATIONAL METHODS IN WATER RESOURCES, VOLUME 2 NUMERICAL METHODS FOR TRANSPORT AND HYDROLOGICAL PROCESSES. PROCEEDINGS OF THE V11 INTERNATIONAL CONFERENCE, MIT, USA, JUNE 1988 37 D.CLARKE GROUNDWATER DISCHARGE TESTS: SIMULATION AND ANALYSIS

THIRD REVISED AND UPDATED EDITION

DAVID STEPHENSON Department of Civil Engineering University of the Witwatersrand Johannesburg, South Africa

ELSEVlER Amsterdam - Oxford - N e w York - Tokyo 1989

ELSEYIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 2 1 1, 1000 A€ Amsterdam, The Netherlands Distributors for the United States and Canada:

ELSEVIER SCIENCE PUBLISHINGCOMPANY INC. 655, Avenue of the Americas New York, NY 10017, U.S.A.

ISBN 0-444-87373-2

0 Elsevier Science Publishers B.V., 1989 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./ Physical Sciences & EngineeringDivision, P.O. Box 330, 1000 AH Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred t o the publisher. No responsibility is assumed by the Publisher for any injury and/or damage t o persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Printed in The Netherlands

V

PREFACE TO FIRST EDITION

Pipelines lengths

are

and

being

working

are

essential

for

years

has

recently

to

constructed

pressures.

achieve economic

resorted

to

been

in

and

in

an

and

safe

semi-empirical

done

ever-increasing

Accurate

rational

designs.

design

bases

Engineers

formulae.

to r a t i o n a l i z e

effort

diameters,

design

have

Much

the

work

design

of

pipelines. This as

book

well

as

retaining

presenting

oook

or

hydraulic

subject

is

to

but

field.

a l so of

be

bring

useful

infancy

and

of

the

graphs

in

planning

of

features

manufacture, practice

design

of

which

large

at

the water

in

the It

are

should

stressed

of

may

suitable the

as

and

were of

In

are

and

the

is

techniques

to

the

Pipelines covered

as

and

many

half, book

t h i s book other

be

noted

that

covered pipes,

and v a r i o u s coatings.

opposed

by

will

fluids some

of

not

desk. to

of

The the the

computers.

design

deal

in

and and

detail

i t replace design

Emphasis

industrial

pub1 ications.

on

is

the

and

domestic

Although

directed

be of use to engineers i n v o l v e d as of

patents.

methods

structural

nor should

mind

hydraulics

with

does

Many

research.

the assistance of

in will

in t h e i r

calculators

The

other

students.

are s t i l l

in

engineer's

in

the book

further

concerned

the

to

techniques

background

of

the c i v i l

introduction

advanced

for

aim

bear

l a y i n g a n d operation, from

Although

the

problems

second

discussed.

many

concrete

leads

many

book

data.

post-graduate

prepared with

this

of

be

for

design methods

instances,

an

most

and

provide

computers

engineer,

piping

described

may

pipelines.

piping

is

proposed

book half

ancillary

of

many

the sound theoretical

book

acceptance

with

techniques in

d a t a on

under-graduate

modern

the

rational

such as mathematical optimization,

solution

first

It

contains

to

new

on

the most modern design

i3ecause of

methods

codes

some

material

approaches

engineer. also

the s u b j e c t s ,

The

pub1 ished

conventional

the

the

col lates

well the

as

solids

designs

These

stiffening

and

include pipes

and

techniques

types and

gases.

of

pre-

branches

VI

The S . I .

system of

metric u n i t s i s preferred i n

imperial u n i t s a re g i ve n a n d equations examples work in

text.

summarized general chapter.

at

these The the

for as

many they

The

end

appendix data.

problems a n d

instances.

of

the reader

often elaborate on

algebraic

references a r r a n g e d

other useful

in many

Most g r a p h s

a r e represented i n uni versa1 dimensionless form.

are given

through the

i n brackets

the book although

symbols

that in

gives

used

chapter

together

the order of further

i s advised

ideas not in

the

references

Worked to

highlighted

each

chapter

are

with

specific

and

subject matter i n the and

standards

and

PREFACE TO SECOND EDITION

The

gratifying

in small ations

response

amendments to

to

the f i r s t

the second

e d i t i o n of

impression,

t h i s book

resulted

a n d some major a l t e r -

i n t h i s new edition.

The

chapters

replaced

by

on

data

transport

more

of

relevant

solids

to

and

water

sewers

Thus

chapter on the effects of a i r i n water pipes i s included, chapter

on

pumping

systems

for

water

have

engineers.

new

as well as a

The

pipelines.

been

a

latter

was

reviewed by B i l l Glass who added many of h i s own ideas. There

are

additions and

u p d a t i n g throughout.

There

is additional

information on p i p e l i n e economics and optimum diameters i n Chapter 1 . A

comparison

Chapter and

2.

The

sewer

drainage

of

currently sections

flow

are

engineer

used

on non-circular

omitted.

and

‘Stormwater

Hydrology

introduction

to

water

friction

as

These

such

are

and

Drainage’

hammer

theory

sections

together.

An

on

structural

largely

covered

enlarged

design

section

on

is

now

pipe and p a r t l y

are

of

in

preceeds

the

the

made

full

in

pipes

interest

to

author’s

the book

1981).

A

basic

design

of

water

(Elsevier,

l i n e s i n Chapter 4 .

hammer protection of pumping a n d g r a v i t y

The

formulae

of

flexible

soil-pipe

pipes

are

interaction

brought

and

limit

states of f l e x i b l e pipes preceeds the design of s t i f f e n e d pipes. Although recognised needs

some

that

of

this

refreshing

the

new

edition

is

now

fairly

basic,

it

is

i s d e s i r a b l e for both the p r a c t i c i n g engineer who

and

the

student

p i p e l i n e design f o r the f i r s t time.

who

comes

across

the

problem

of

VIII

PREFACE

TO THIRD E D I T I O N

Recent research i n c a v i t a t i o n a n d flow control h a s prompted a d d i t i o n a l sections on pipes a n d make up

this.

There

secondary this

a r e also new

stress.

edition.

Some

sections on

Additional sections

supports

references

appearing

and

in

a

to

exposed

new

layout

p r e v i o u s editions,

noteably on p i p e network systems a n a l y s i s a n d o p t i m i z a t i o n have been ommitted

as

p a r a l l e l book

they

were

considered

‘Pipeflow A n a l y s i s ’

more

appropriate

in

b y the same p u b l i s h e r .

the

alJthOr’S

IX

ACKNOWLEDGEMENTS

The b a s i s for course of

Engineers although I the

my

01 i v e r ,

and

in

t h i s book was d e r i v e d from my experience a n d i n the

duties

the Hand Water

these

Engineers.

organizations

Board a n d Stewart, S v i r i d o v

The

may

extensive

therefore

be

knowledge reflected

of

herein

I am solely to blame f o r any inaccuracies o r misconceptions.

am g r a t e f u l twins

with

Consulting

during

to my wife Lesley,

many

a

lost

who,

weekend,

i n a d d i t i o n to looking a f t e r assiduously

typed

the

first

d r a f t of t h i s book.

David Stephenson

X

CONTENTS

CHAPTER 1

ECONOMIC PLANNING

.

.

.

lntroduct ion P i p e l i n e Economics B a s i c s of E c o n o m i c s M e t h o d s of Ana I y s i s Uncertainty in Forecasts Balancing Storage

CHA?TER 2

. . . . . .

.

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.

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.

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HYDRAULICS

The F u n d a m e n t a l E q u a t i o n s of F l u i d F l o w F l o w H e a d Loss R e l a t i o n s h i p s . . Empirical Flow Formulae 2 a t i o n a l Flow Formulae C o m p a r i s o n of F r i c t i o n F o r m u l a e M i n o r Losses . . P r e s s u r e and F l o w C o n t r o l i n P i p e s lntroduct ion T y p e s of V a l v e s I so l a t i n g V a Iv e s Control Valves C a v i t a t i o n in C o n t r o l V a l v e s . . I n t e r a c t i o n b e t w e e n C a v i t a t i o n a n d W a t e r Hammer P r e s s u r e s

. . . . . . . . . . . . . . . . . .

CHAPTER 3

1 2 9 10 11 14

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. .

16 18 18 19 24 26 28 28 28 29 29 32 34

P I P E L I N E SYSTEM ANALYSIS AND DESIGN

. . . . . . . . . . . . . . .

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.

Network A n a l y s i s E q u i v a l e n t P i p e s for P i p e s in S e r i e s o r P a r a l l e l Loop Flow Correction Method The Node H e a d C o r r e c t i o n M e t h o d A l t e r n a t i v e M e t h o d s of A n a l y s i s iqetwork A n a l y s i s b y L i n e a r T h e o r y O p t i m i z a t i o n of P i p e l i n e Systems D y n a m i c P r o g r a m m i n g f o r O p t i m i z i n g Compound P i p e s T r a n s p o r t a t i o n P r o g r a m m i n g for L e a s t - c o s t A1 l o c a t i o n o f Resources L i n e a r P r o g r a m m i n g f o r D e s i g n of l e a s t - c o s t Open N e t w o r k s

. . . . . . . . .

37 37 38 40 41 43 44 45

.

.

48

. . . . . . . . . . . .

52

.

.

.

.

XI

CHAPTER 4

WATER HAMMER AND SURGE

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R i g i d Water Column Surge Theory M e c h a n i c s o f W a t e r Hammer E l a s t i c W a t e r Hammer T h e o r y Method o f A n a l y s i s Effect of F r i c t i o n Protection of Pumping Lines Pump I n e r t i a Pump B y p a s s R e f l u x V a l v e Surge Tanks Discharge Tanks A i r Vessels In-Line Reflux Valves Release V a l v e s Choice o f P r o t e c t i v e D e v i c e

.

. . . . . .

CHAPTER 5

AI3

. . . . . . .

. . . . . . . .

IN P I P E L I N E S

Introduction Problems of A i r Entrainment A i r I n t a k e a t Pump Sumps A i r Absorption a t Free Surfaces H y d r a u l i c Removal of A i r H y d r a u l i c Jumps Free F a l l s A i r Valves Head Losses in P i p e l i n e s W a t e r Hammer

. . . . . . . . . . . . . . . . .

CHAPTER 6

58 60 64 64 68 69 73 76 77 79 85 89 91 93

. . . . . . . . . .

97 97 99 101 102 102 104 105 108 109

EXTERNAL LOADS

. . . . . .

. . . .

. . . . .

. . . . . . .

Soil Loads Trench conditions Embankment Conditions Superimposed Loads T r a f f i c Loads Stress Caused b y Point Loads Uniformly Loaded Areas . Effect o f R i g i d Pavements

. . . . . . . . . . . . . . . . .

. . . . . . .

.

113 113 116 120 121 121 122 123

XI1 CHAPTER 7

CONCRETE PIPES

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Effect of B e d d i n g Prestressed Concrete Pipes Circumferential Prestressing C i r c u m f e r e n t i a l P r e s t r e s s a f t e r Losses Circumferential Stress u n d e r F i e l d Pressure L o n g i t u d i n a l Prestressing L o n g i t u d i n a l Stresses A f t e r L o s s e s P r o p e r t i e s o f Steel and C o n c r e t e

CHAPTER 8

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160 162 165 172 173 173 174 175 176

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. . . . . .

. . . . . .

179 179 179 180 180 180

STEEL AND F L E X I B L E P I P E

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

I n t e r n a l Pressures Tension R i n g s to Resist I n t e r n a l Pressures D e f o r m a t i o n of C i r c u l a r P i p e s u n d e r E x t e r n a l L o a d Effect of L a t e r a l Support S t r e s s d u e to C i r c u m f e r e n t i a l B e n d i n g More General Deflection Equations S t i f f e n i n g R i n g s to R e s i s t B u c k l i n g w i t h no side support Tension R i n g s Stiffening Rings

CHAPTER 9

. . . . . . . . . . . . . . . . . . . . . . . . . .

10

. .

142 143 146 149 151 152 156 156 156

SECONDARY STRESSES

Stresses a t Branches Crotch Plates Internal Bracing Stresses a t Bends T h e P i p e a s a Beam Longitudinal Bending Pipe Stress a t Saddles . . Ring Girders Temperature Stresses

CHA?TER

127 129 131 131 133 134 136 136

P I PES.

. . . . . . . . .

. . . . . . . . .

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. . . . . . . . .

. . . . . . . . .

F I TT I NGS AND APPURTENANCES

. . . . . . . . . . . . . .

?ipe M a t e r i a l s Steel P i p e Cast I r o n P i p e Asbestos Cement P i p e Concrete P i p e Plastic Pipe

. . . . . .

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.. .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.. . . . . . . . . . . . . . . . . . . .

.. . . . . . . . . . . . . . . . . . . . .

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

L i n e Val ves Sluice Valves B u t t e r f l y Valves Globe Valves Needle a n d Control Valves Spherical Valves Reflux Valves A i r Valves A i r Vent Valves A i r Release Valves Thrust Blocks Forces Induced by Supports . L o n g i t u d i n a l Stress Temperature Stresses Forces at Bends L a t e r a l Movement Forces on Supports Unbalanced Forces Flow Measurement Venturi Meters Nozz I es Orifices Bend Meters Mechanical Meters Electromagnetic I n d u c t i o n Mass a n d Volume Measurement Te I erne t ry

CHAPTER 1 1

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182 182 183 184 184 185 186 186 186 188 190 194 195 195 196 196 197 197 198 198 199 1 99 200 200 201 201 201

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205 206 208 208 210 212 21 6 21 7 218 21a 222 223

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.

.

.

.

.

L A Y I NG AND PROTECTION

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. . . . . . . . . . . . . . . .

Selecting a Route L a y i n g a n d Trenching Thrust Sores Pipe Bridges Underwater Pipelines Joints a n d Flanges Coatings Linings Cat hod i c Prot ec t ion Galvanic Corrosion Stray Current E l e c t r o l y s i s Thermal I n s u l a t i o n

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.

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XIV

CHAPTER 12

PUMP I NG I NSTALLAT I ON5

I n f l u e n c e of Pumps in P i p e l i n e Design T y p e s of P u m p s P o s i t i v e Displacement Types C e n t r i f u g a l Pumps T e r m s and D e f i n i t i o n s Head Total Head Net P o s i t i v e S u c t i o n Head S p e c i f i c Speed Impeller Dynamics Pump C h a r a c t e r i s t i c C u r v e s ivto t o r s Pumpstat ions

. . . . . . . . . . .

. .

. . . . . . . . . . .

228 228 228 229 231 23 1 231 232 233 234 236 239 240

GENERAL REFE2ENCES AND STANDARDS

. . . . . .

242

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250

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252 253 254 255 256

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258 260

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BOOKS FOR FURTHER READING

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APPEND I X

. . . . . . . .

Symbols for p i p e f i t t i n g s Properties of p i p e shapes P r o p e r t i e s of w a t e r P r o p e r t i e s of p i p e m a t e r i a l s Conv ers i o n f a c t o r s

AUTHdR SUBJECT

INDEX INDEX

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. . . . .

. . . . .

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1

CHAPTER 1

ECONOMIC PLANNING

I NTRODUCT ION

Pipes

have

been

used

for

many c e n t u r i e s

for

transporting fluids.

The Chinese f i r s t u s e d bamboo p i p e s t h o u s a n d s o f y e a r s ago, p i p e s were

unearthed a t

were

in

England.

that

pressure

used

however, used

extensively

were f i r s t

grade

diameters square

spiral

small

and

3

to

welded

became

available

is

still

and

working

The

Welding

and

for

the

Cast

design

of

pipelines

with

10 Newtons have

Reliable

per been

welded

or

a l s o made

asbestos cement,

this

was pipes

facilitating

techniques

pipelines

iron,

i n c r e a s i n g use o f

P i p e l i n e s a r e now

conditions.

pipes

iron

Steel

circumferentially

p r e - s t r e s s e d concrete, varying

cast

used.

pressure over

manufactured.

suit

of

t h e e n d of t h e l a s t c e n t u r y ,

longitudinally

to

advent

manufactured. and

p i p e s to b e m a n u f a c t u r e d .

claywares,

the

large r o l l i n g m i l l s has enabled

be

enabling

were

Century

c e n t u r i e s wood-stave

with

large bore pipelines.

metres

in r e i n f o r c e d concrete,

and

19th

later

only

pipelines

steels a n d

over

millimetre

perfected

was

introduced towards

c o n s t r u c t i o n of high

It

the

in

In

Pompeii.

and lead

flow

plastics formulae

century,

thereby

a l s o p r o m o t i n g t h e use of p i p e s . Prior fluids

to

this

century

transported

common

means

for

Liquid chemicals

being

pumped

now o v e r world.

by

water

a n d sewage

pipeline.

transporting

and

solids

gases

in slurry

The g l o b a l

kilometres

of

e x p e n d i t u r e on

pipelines

and

oils

form or

t h r o u g h p i p e l i n e s on ever

two m i l l i o n

were p r a c t i c a l l y

Nowadays

over

the o n l y

are long

the

distances.

in containers

i n c r e a s i n g scales.

most

are

also

There a r e

pipelines i n service throughout

the

p i p e l i n e s i n 1974 was p r o b a b l y o v e r

5 5 000 m i l l i o n . There

are

many

advantages

of

pipeline

o t h e r methods s u c h a s r o a d ,

rail,

waterway

(1)

the

most

Pipelines

are

often

( c o n s i d e r i n g e i t h e r c a p i t a l costs,

(2)

Pipelining

costs

are

not

very

transport

compared

with

and air:-

economic

form

of

transport

r u n n i n g costs o r o v e r a l l c o s t s ) . susceptible

to

fluctuations

in

2 prices,

since

the major cost

i s the c a p i t a l o u t l a y and subsequent

o p e r a t i n g costs are r e l a t i v e l y small. Operations

are

not

to

susceptible

attendance i s r e q u i r e d .

labour

disputes

as

little

Many modern systems operate automatical-

lY. Being

hidden

beneath

the

ground

a

pipeline

will

not

mar

the

n a t u r a l environment.

A b u r i e d p i p e l i n e i s reasonably secure against sabotage. A

pipeline

is

independent of

external

influences

such

as

traffic

congestion and the weather. There

is

normally

no

problem of

r e t u r n i n g empty

containers

to

the source.

It

is

relatively

easy

to

increase the c a p a c i t y of

a pipeline by

i n s t a l l i n g a booster pump.

A b u r i e d p i p e l i n e w i l l not d i s t u r b surface t r a f f i c a n d services. ( 1 0 ) Wayleaves

for

pipelines

are

usually

easier

to

obtain

than

for

than

for

roads and r a i l w a y s .

(11)

The

accident

rate

per

- km

ton

is

considerably

lower

other forms of t r a n s p o r t .

(12) A

pipeline

can

cross

rugged

terrain

difficult

for

vehicles

to

cross. There are of course disadvantages associated w i t h p i p e l i n e systems:The

initial

capital

uncertainty

in

expenditure

the

demand

i s often

some

large,

degree

of

involved

in

so i f there i s any

speculation

may

be

necessary. There

is

often

a

high

cost

( e s p e c i a l l y long fuel

lines).

Pipelines

used

(although

cannot

be

there

are

for

more

multi-product

than

filling

a

one m a t e r i a l

pipelines

operating

pipeline

at on

a

time batch

bases).

There solids,

are

operating

problems

associated

with

the

pumping

of

such as blockages on stoppage.

I t i s often d i f f i c u l t

to locate leaks o r blockages.

P I PEL I NE ECONOM I CS

The main cost

of

a p i p e l i n e system i s u s u a l l y that of the p i p e l i n e

3 itself.

The

gravity

pipeline

systems b u t

cost

is

fact

in

practically

as the adverse head

cost

for

increases so the power

the

only

and

pumping s t a t i o n costs increase.

1.1

Table

indicates

some

relative

costs

for

typical

installed

p i p e l i nes. With the

the

time

year,

economic

of

writing

and

particular increase

instability pipeline

relative the

faster

costs

cost

of

than

those

and rates of

costs for

may

different

petro-chemical of

inflation prevailing at

increase

by

materials

materials

concrete

20% o r more per

for

will

such

instance,

vary.

as

PVC

In may

so these f i g u r e s

should be inspected w i t h caution. TABLE 1 . 1

Relative P i p e l i n e Costs Bore mm

Pipe M a t e r i a l

150

6 7

PVC Asbestos cement Reinforced concrete Prestressed concrete M i l d steel High tensile steel Cast i r o n

i

i

a,

3

C

D

m L a,

m

c

[r

C .a, C

U

m

m In L a,

m

I

a .-C LL

D

m

a .-C L

145

m

a L

.-C

C

m

.-0 a,

C

-

5

r.-

U

E

D .-

m

m m

.-Um m

a, m

QJ

m

c

5

-

3 -

LL

.-a

m

-

m

i a,

vi

- .-5

C

L a, a, c

5 .-i V

m

146 (8.13) The

stresses

shown A)

that

are

indicated

by

Fig.

a s s i s d e c r e a s e d t h e r i n g s t r e s s Fr

w h i c h c o u l d h a v e been anticipated.

to equal

for

8.1,

the circumferential

f o r s m a l l s,

wall

v

0.3.

=

tends to

It

f

pds/

a p l a i n pipe,

the circumferential p i p e wall stress F

pd/2t.

tends to

W

+ A ) , w h i c h w o u l d b e e x p e c t e d , and t h e l o n g i t u d i n a l

be

(ts +

Fr tends

N o t e t h a t f o r s m a l l A,

stress of

may

Also,

4 pds/(ts

beding stress

Fb

tends to zero. For l a r g e r i n g spacing ( > approx.

pd

1

F tends to

1

+ 0.9lA/t&

pd

+ 0.91

tJtd/A

(8.14)

2t

1.65

Fb tends to

2-1,

(8.15)

2t

t e n d s to @ i.e. t h a t f o r a p i p e w i t h o u t r i n g s . 2t I t may be observed b y comparing F F r and Fb f r o m F i g s .

and F

W

8.la,

W’

8.lb in

and 8 . l c

fact

Fw,

reduced

if

t h a t t h e m a x i m u m s t r e s s f o r most p r a c t i c a l r i n g s i z e s i s the

circumferential

r i n g spacing should be area

A

pipe

wall

stress.

s / J y z i s l e s s t h a n a p p r o x i m a t e l y 2.0.

should

longitudinal

be of

cross

l e s s than

the

same

sectional

2 J l d

order

area

of

Also,

is

only the

the r i n g cross sectional

and

magnitude

between

Fw

I n other words,

rings,

as the p i p e w a l l to

ts,

enable

the

r i n g s t o b e o f use.

DEFORMATION O F CIRCULAR P I P E S UNDER EXTERNAL L O A D

large

For

diameter

sures,

the external

under

external

bending,

Spangler

critical occur

at

pipes

load is frequently

load

by

buckling,

under

low

t h e c r i t i c a l one.

overstressing

due

internal

pres-

Pipes may f a i l to

arching

or

excessive deflect ion. elastic

For

only,

flexible

and

rings

under

plane

stress

subjected

to

vertical

loads

(1956) e v a l u a t e d t h e b e n d i n g moments and d e f l e c t i o n a t

points around the crown,

the

the

circumference.

The

i n v e r t or t h e s i d e s .

worst

b e n d i n g moments

T h e b e n d i n g moments p e r

147

Angle of bottom

suwor? p degrees

Angle of tmttom support

Fig.

8.3

p

D e f l e c t i o n c o e f f i c i e n t s for

degrees

loaded pipe.

148 u n i t length a r e g i v e n b y a n equation of the form

M

R

where and

(8.16)

NWR

=

is

N

is

the a

pipe

respectively).

The

W

radius,

coefficient.

(Nt,

vertical

i s the v e r t i c a l

Nb

and

and

NS f o r

horizontal

load per top,

changes

unit

length

bottom and in

sides

diameter

are

p r a c t i c a l l y equal a n d opposite a n d a r e of the form A

NnWR3/EI

=

where N

(8.17)

i s a coefficient.

A

The moment of i n e r t i a I per u n i t length of p l a i n p i p e w a l l I

t3/12

=

Figs.

(8.18)

8.2

and

at

vertical

deflections

unit

the

8.3

moments

line

load or

a

length),

Collapse of

to

been

and

of

the

and

pipe

for

Nt,

sides

Nb a n d Ns f o r the

respectively,

diameter.

The

coefficients

across the w i d t h of

different

angles

of

and

N

bending

A

are

the p i p e

bottom

for

support 6

the

for a

( W per

,

as

8.4.

a steel p i p e w i l l p r o b a b l y not occur u n t i l the diameter

distorted

normally

linings,

bottom

load d i s t r i b u t i o n

5 percent of

should

g i v e values of

top,

indicated i n Fig.

has

is

the be

some 10 o r 20 percent. diameter limited

are

to

I n p r a c t i c e deflections

sometimes

about

2

tolerated.

up

The deflection

percent to prevent damage to

a n d for pipes w i t h mechanical j o i n t s .

The h y d r a u l i c properties,

i.e.

the cross sectional area a n d wetted

perimeter a r e not affected noticeably f o r normal d i s t o r t i o n s . LOAD W /UNIT LENGTH OF PIPE

UPTHRUST

F i g . 8.4

Pipe l o a d i n g and deflections

149 Effect of L a t e r a l Support The of

lateral

flexible

lateral

support

pipes

support

of

sidefill

in a

considerably

and

trench

increases the s t r e n g t h

reduces

deformations.

to a p i p e the r i n g bending stresses a t

Without

the s o f f i t a n d

haunches o r deflections would l i m i t the v e r t i c a l e x t e r n a l load the p i p e could

carry.

But

l a t e r a l l y as the

it

sidefill

be

may

a

is

in

the

established

compacted

sides

with

the

of

the

will

fill

deflect

outwards

i n c r e a s i n g the pressure of

pipe.

vertical

a r c h action as well

load

An

equilibrium

being

condition

transferred

as b y r i n g action.

The

to

the

stress due

i s compressive so that the load which the p i p e can

to the a r c h action

i s considerably h i g h e r than i f the p i p e were a c t i n g in bending.

carry the

extreme case,

the

lateral

stress a n d the p i p e wal I w i l l equal

a

loaded v e r t i c a l l y thereby

against

haunches b y

In

pipe

stress

will

equal

the v e r t i c a l

be i n p u r e compression,

load

w i t h the stress

to wd/2t

where If could

w

W/d

=

the

p i p e underwent

support

whatever

(8.19)

arch

would

no noticeable

be

strength

the sides of the pipe,

determined

i s given i.e.

by

lateral

distortion bending

the

to the p i p e b y

the

load

strength

it

plus

the s o i l pressure on

the permissible v e r t i c a l

load per u n i t area

on the p i p e i s

w

w

=

+ w

b

(8.20)

a

i s the permissible b bending stress or more l i k e l y

where

equal

w

to

lateral

servatively, greater

load

(limited

this

pressure on

as

lateral

indicated

dead

by

ring

i s the a r c h i n g load, a the sides of the p i p e , which, con-

in

subsequent

pressure i s approximately

pressure due to soil

either

by deflection). w

may be taken as the a c t i v e soil pressure,

than

the a c t i v e

soil

bending

load o n l y

one

but i s usually

equations.

For

sand,

t h i r d of the v e r t i c a l

and for clay

i t i s approximately

h a l f the v e r t i c a l pressure. I f the v e r t i c a l active and away

lateral

increase the from

load i s g r e a t e r than the sum of the r i n g load p l u s

soil

the

pressure,

lateral pipe

the

pressure.

and

pipe wall

will

deflect out

laterally

The h o r i z o n t a l stress w i I I decrease

Barnard

(19571,

using

elastic

theory,

150 suggests assuming a pressure equal wall

triangular

to total

stress d i s t r i b u t i o n w i t h the horizontal

vertical

pressure minus r i n g load a t the p i p e

decreasing l i n e a r l y to zero at 2.5d away from the p i p e w a l l .

corresponding AX/2

1.25

=

where E 1.25

i s the effective modulus of

pressure

factor

becomes 1.4

time,

a

e l a s t i c i t y of the s o i l .

The factor

increased as the l a t e r a l deflection increases, since the

radial

for

(8.21 )

d/ES

(w-w,)

should be

1.7

The

l a t e r a l deflection of each side of the p i p e i s

increases for

deflection

as

the

r a d i u s of

2 percent of

a deflection of

of

5 percent.

and an a d d i t i o n a l

c u r v a t u r e decreases.

The deflection

The

the diameter

also

and

increases w i t h

25 to 50 percent of the i n i t i a l deflection can

be expected e v e n t u a l l y . If

the

creep

decrease. e.g.

On

deflection

the

plastics,

other

of

the

hand

soil

pipe

can compensate f o r

large,

is

materials

this,

lateral

which

support

exhibit

can

creep,

a n d could even shed v e r t i c a l

load. The

relationship

determined modulus

from

of

degree of of

between stress and s t r a i n f o r

laboratory

elasticity

of

triaxial

soil

varies

for

N/mmz

for

fill

widely

compaction o r n a t u r a l density,

l o a d i n g and moisture content.

modulus

consol i d a t i o n

loose c l a y

is

or

approximately

as

it

loosely

density

Values h i g h e r than

be

The effective on

soil

c o n f i n i n g pressure, may be as

as 20 N/mm2 f o r

3 N/mmzfor

compacted to 90% Proctor

Proctor density.

depending

F o r example

high

the s o i l should tests.

type,

duration as 2

low

dense sands.

compacted f i l l ,

The

5 N/mrn2

a n d 7 N/mmz f o r f i l l

to 95%

100 have been recorded for moist

compacted sands. The r i n g

load on

indicated

by

as

ponds

to

bottom

the p i p e

Equ.

8.17.

support

i s p r o p o r t i o n a l to t h e e l a s t i c deflection

T a k i n g N,

over

30'

and

equal the

t o 0.108,

load over

which corresthe entire

pipe

width and p u t t i n g AY A -

d

AX

--

0. 108wd3 8E I +0.043ESd3

=

For p l a i n

a

A , then s o l v i n g f o r A/d

=

function

of

pipe

and 8.21, (8.22)

I = t3/12,

diameter,

from 8.17

so one has an equation f o r deflection

loading,

soil

modulus

and

the

ratio

as

wall

th i ckness/di ameter. A -

d

--

0.108~ 0.67E(t/d)'

+ 0.043Es

(8.23)

151 The r e l a t i o n s h i p between deflection a n d wal I thickness f o r p l a i n p i p e i s p l o t t e d i n F i g . 8.5. I t w i l l be observed that a steel p i p e wall

thickness

restrain

5MPa a n d soil Pipes trench

are

to

diameter.

as

low

distortion

as

to

4%

of

the

2% p r o v i d e d

diameter

the

soil

will

be

sufficient

modulus

is

greater

to

than

load i s less than 50 kPa. sometimes

increase The

the

lateral

strutted

internally

vertical

diameter

support

increases

during and

when

backfilling

reduce

the

of

the

horizontal

the s t r u t s a r e removed

a n d the p i p e tends to r e t u r n to the r o u n d shape.

The v e r t i c a l deflec-

tion a n d tendency to b u c k l e a r e consequently reduced considerably.

STRESS DUE TO C I RCUMFERENT I A L BEND I NG

It

i s possible to compute w a l l stresses due to bending a n d a r c h i n g

(Stephenson, the f u l l

1979).

w i d t h of

If

i t can be assumed that the load i s spread over

the p i p e

( a =

180')

and the bottom support i s over

( 6 = 60") f o r f l e x i b l e p i p e , then from (8.17) a n d F i g . 8.3,

60'

AY

=

0.103wbd

4

/8E1

(8.17b)

Now from (8.21), A X = 2.5(w-wb)d/ES Equating

AY a n d A X ,

the total

load,

w The

=

b

w I /d3 I/d3

bending

+

(8.21b)

a n d s o l v i n g for w b

the r i n g load i n terms of w

(8.24)

0.006ES/E

moment

in

the

wall,

M,

is

due

to

ring

load a n d

is a

maximum a t the base a n d from (8.16)

M

=

where

r

the

W

is

the

distance from

extreme f i b r e

i s taken

a

-

(8.25)

0 . 1 9 ~ d 2 / 2 hence b e n d i n g stress f = Mr/l b b the centre of

(t/2 for p l a i n wall

g r a v i t y of

pipe).

the section

The balance of

the

to

load

in a r c h action of the p i p e according to (8.20) so

0. 006wES/E

I /d'

(8.26)

+ 0. 006ES/E

The bottom w a l l hoop stress i s fa

=

wad/2a

where

a

is

the

plain wall pipe).

(8.27) cross

sectional

area

of

wall

per

unit

length

( t

for

152 The =

total

+

fb

lateral

fa,

permissible stress f

+

(l/d3 w

=

permissible

ES to steel

+

i n terms of

(8.28)

load w

The r e l a t i o n s h i p

i s a f u n c t i o n of

moduli of soi

a n d the r a t i o o

i s plotted

i n Fig.

the permis

f o r p l a i n wal

8.5

w i t h E = 210 000 N/rnmz, a n d f = 210 N/mrn2.

pipe,

For t h i c k as

the base i s f

0.003 dE /Ea

the r e l a t i v e thickness t / d

E.

at

is

Thus the permissible v e r t i c a l s i b l e stress,

i n the w a l l

l o a d i n g p e r u n i t area

0.006ES/E)f

r/d

0.1

compressive stress

therefore

more

load

can

deflection

becomes

the

is

pipe

the permissible load increases w i t h wal I thickness

pipes,

be

taken

large

i n r i n g bending. that

so

the

i n p u r e compression,

hoop stress.

Actually

side w a l l

so (8.27) p l u s (8.25)

soil

and

For t h i n n e r

side-thrust

the

limit

pipes,

increases

i s due

the

to

the

until wall

hoop stress exceeds that a t the base,

i s not the l i m i t i n g stress f o r h i g h a r c h i n g .

On the same c h a r t i s p l o t t e d b u c k l i n g load

The

(8.29a)

/32ESEl/d3

=

W

b u c k l i n g equation,

support. gated

This

by

proposed b y

ClRlA

(1978)

allows

for

lateral

may be compared w i t h an a l t e r n a t i v e equation

the

Transport

and

Road

Research

Laboratory

investi-

(which

is

found to o v e r p r e d i c t w ) : W

The

=

( 1 6 E s 2 E l / d 3 )1 / 3 g i v i n g a deflection of

load w d

on the c h a r t for

any

is

selected

(8.29b)

from

2% i n the diameter

The c h a r t

(8.23).

p a r t i c u l a r w a l l thickness r a t i o . in

each

case

from

the

The lowest permissible load w

chart

by

comparing

overstressing and b u c k l i n g lines f o r the r e l e v a n t t / d Similar

charts

should

be

i s also p l o t t e d

thus y i e l d s the l i m i t i n g c r i t e r i o n

p l o t t e d where

and E

stiffening

deflection,

.

rings

a r e used

a n d where a l t e r n a t i v e m a t e r i a l moduli and permissible stresses a p p l y . By

careful

design

it

is

c r i t e r i a a t the same load.

possible

to

reach

the

limit

in

two

or

more

T h i s i s c a l l e d balanced design.

More General Deflection Equations Spangler the

backfill

(1956) in

a

allowed more

for

lateral

theoretical

he d e r i v e d f o r v e r t i c a l deflection i s :

way

support than

to

the

Barnard.

pipe The

due

to

equation

153 UZWd3 8 E l + 0.06Esd”

A =

(8.30)

T h i s corresponds to ( 8 . 2 2 )

i s substituted for N

i f UZ

A

and a v a l u e of

0.15 i s assumed f o r N A i n the denominator ( i n s t e a d of 0.108 i n 8.22) s o i l consolidation time l a g factor

Here U = Z =

bedding

constant

(varies

from

( v a r i e s from 1.0

0.11

for

point

to 1.5). support

to

0.083 f o r b e d d i n g the f u l l w i d t h of p i p e ) , n o r m a l l y taken as 0.1. 1

moment of i n e r t i a of p i p e w a l l per u n i t length.

=

passive resistance modulus of s i d e f i l l .

E = The Due

to

pressure

inside a

pipe

the

that

vertical

fact

the

may

also

contribute

diameter

to

its

stiffness.

i s compressed to s l i g h t l y

less t h a n the h o r i z o n t a l diameter,

the v e r t i c a l u p t h r u s t due t o i n t e r n -

al

the s i d e t h r u s t b y an amount of

pressure becomes g r e a t e r

which

tends

to

return

the

than

p i p e t o a c i r c u l a r shape.

2@

A more general

expression f o r v e r t i c a l deflection thus becomes A

=

UZWd3

8 E I + 0.05ESd’

(8.31)

+ 2 UZpd3

W

Q

0.002

0.005

0.01

0.02

Relative thickness t / d

F i g . 8.5

Permissible load on p l a i n p i p e

0.03

154 ST

FFENING RINGS TO Morley

pipes

BUCKLING W I T H NO SIDE

RESIST

(1919) developed a

under

uniform

stiffening

ring

tice.

theory

The

external

bined internal

for

of

stiffened

often

indicates

i s considered necessary

in p r a c -

pressure.

spacings wider also

theory

than

neglects

the

the

SUPPORT

The

buckling theory

possibility

of

failure

a n d e x t e r n a l pressures and bending.

under

com-

The equations do,

however, y i e l d an i n d i c a t i o n of s t i f f e n i n g r i n g spacing. Using which

an

indicates

axial

the

she1 I

cylindrical no

analogy

a

take

without

and

assumes

comparison w i t h the diameter. w

2E

=

1

-

developed

external

b u c k l ing. the

wall

an

equation

w,

which a

pressure,

The equation a l lows f o r thickness

is

small

in

v i s Poisson's r a t i o , (8.32)

d7 I = t3/12, so

For p l a i n p i p e ,

w

Morley

El

24 1 - v 2

=

strut,

maximum v e r t i c a l

can

expansion,

with

t

(3)

v2

(8.33)

Experiments i n d i c a t e d a p e r m i s s i b l e stress 25% less than the theoretic a l , so f o r steel,

1.65 E

t

w

=

For

thick-wal led

stresses the w a l l

(8.34) tubes,

the

material

to

intermediate wal I thickness, and

elastic

yield.

An

col lapse i t s elastic

pressure limit

wi II

be

( w = 2ft/d)

that

which

whereas f o r

f a i l u r e w i I I be a combination of b u c k l i n g

empirical

formula

indicating

the

maximum

permissible pressure on a p i p e of intermediate thickness i s (8.35) where f

i s the y i e l d stress.

The e x t e r n a l resist w, s,

buckling.

load may be increased i f s t i f f e n i n g r i n g s a r e used to It

was

found

i s i n v e r s e l y p r o p o r t i o n a l to if s

by

experiment t h a t

the collapse

load,

the distance between s t i f f e n i n g r i n g s ,

i s less than a c e r t a i n c r i t i c a l length,

L.

155 From experiment L = 1 . 7 3 E

(8.36)

so i f w

=

2E ( t / d ) 3 for s t i f f e n i n g pipe, then f o r s t i f f e n e d p i p e ,

w

=

L2E ( t / d j 3 = 3.46

The

actual

permissible

(8.37)

stress

is

less

than

the theoretical

due to

imperfections i n the m a t e r i a l a n d shape of p i p e , so the p r a c t i c a l r i n g spacing i s g i v e n by

(8.38) If

the

full

vertical

elastic

external

r e n g t h of pressures

i.e.

he p i p e i s to be developed w

=

'Jt,

then

the

ring

o resist spacing

shou I d be

(8.39) t be of use i f w >1.65E ( - ) 3 . I t should also be ascerd 2f t tained that w z - , which i s the e l a s t i c y i e l d p o i n t . d = Pft/d, then r i n g s w i l l o n l y be of use i f If w

Rings w i l l o n l y

t/d