8/10/2019 1808-7660-1-PB.pdf

1/31

CHAPTER

2

5

EXPERIMENTAL

STUDIES

OF

ORCES

ON

ILES

by

J .R .Morison,J.W.

Johnson

and

M.P.

O'Brien

Department

of

Engineering,

University

of

California

Berkeley,Calif.

INTRODUCTION

In

thedesign

of

apilestruoture

exposed

to

surface

waves

of

a

given

height

and

period,

some of

thefaotors

involved

in

the

problem

and

studiedherein

arethesise,shapeandspacingofthe pilesandthemo-

mentdistribution on

uniform and

non-uniform

piles. Theoretical

and ex-

perimental

investigations

have

shown

thatthe

force

exerted

by

surface

waves

on

a

pile

consists

of

two components

a

drag

foroe

and

anin-

ertia

foroe.

he

drag

foroe

is

proportional

to

the

fluid

density,

the

projected

area and

the

square

of

the fluid particlevelocity.

he

in-

ertia

force,

inoludingthevirtualmass,is

proportional

to

thefluid

density,the volumeoftheobject and the

fluid

particle acceleration.

The

virtualmass

is

the apparent increaseof

the

displaced

mass of

fluid

necessary to

account

for the

increasein

foroe

resulting

fromthe

ac-

celeration

of

the

fluid

relative

to

the

object.

This

factor

i s

included

in

the

coefficient

of

massterminthe foroecalculations.

Theexperimental and

analytical

approachesto thepile problem

presentedin

this

paper

have

been

basedonthe

total

moment about

the

bottom

of

the pile

and

the

moment distribution overthe

length

of

the

pile.

n

order

to

calculate

a

theoretical

moment

it

is

necessary

to

obtain

from

the

experimental

results

two

empirioal

coefficients

a

drag

coefficient

and

a

mass

coefficient

(Morison,

O'Brien,Johnson

and

Schaaf,1950).he

theoretical equations

o ftotal

moment

corresponding

to

the

o r e s t , trough,andstill-waterlevelpositionsalongthe

surface

waveareusedtocomputethesecoefficientsfrom themeasured total

moments

at

the

same

positions.

sing these

coefficients

and

thetheory,

a

comparisonto

experimental

results

is

made

by

comparing

themaximum

moments,

thephase

relationships

of

maximum moments

to

thesurface

wave

orest,

and

oomparing

thecalculatedand

measured

totalmoment time

histories.

comparison

of

the

coefficients

obtained bytheseexperi-

ments

to

other

published

coefficients

obtained

in

different

manners,

somebeingsteady-flow values,showsthatthe resultshereinareof

therightorderofmagnitudebut

have

considerablevariability.'"

Furtherinvestigation

of

the

problemswouldclarify

the

reasons

for

thescatter

oftheooeffioients.

Using

the

experimentallydetermined ooeffioients,

themoment

distributions

on

uniform

diameter andvariable

diameter

round

piles

were

computed

and compared

to

the

measured

distributions. Thecom-

putedresultsare

shown

to

predict

the

moment

distribution with rea-

sonable

accuracy

fordesignpurposes.

x

Errors

occurred

in

Chapter

2 8 ,

"Design

of

Piling"

in

the

Proceedings,

FirstConferenceon Coastal Engineeringandare

oorreoted

int heAp-

pendix

of

this

Chapter.

340

8/10/2019 1808-7660-1-PB.pdf

2/31

EXPERIMENTALSTUDIESOFORCESONILES

Theeffects

of

site,

shape

and

spacing

of

piles

were

obtainedex-

perimentally*heltering and

mutual

interferenceeffects

werefound for

piles

arranged

inrows oroolumns.esults are

presented

incomparative

formasmomentratios

with

respeot toasinglecylindrical pile.

enter

piles

in

rows ofpiles

aligned

parallel

tothe

wave

crests

showedmaximum

moments

that

were

higher

than

those

fora

single

isolated

pile.

h e

mo-

ment

depended

upon

the relative

clearances.

oments

onpilesarranged

in

oolumns

parallel

to

thedirection

ofthe

wave

travel

showed

a

sheltering

effect

on

the

oenterpilesin

the oolumnswithmomentsless

than

those for

a

single

isolated

pile.

Moments

on

pilessuch asa n H

-

section

and a

flat

platesection

were

larger

than

those

for

cylindrical

piles

of

thesame

projected

area.

THEORETICAL

CONSIDERATIONS

The

dynamic

force

on

an

object

in

fluid

moving

with

a

steady-

statevelocity relativeto theobjectisgivenby theexpression

Fri

C

D/3

Au

2

1 )

where

Cp

s

coefficientof

drag*

p

fluiddensity.

A

projeoted area of objectperpendiculartothe

velooity.

u

undisturbed

fluid

velooity

relative

tothe

object.

The

coefficient

of

drag

mustbe

determined experimentally.tinoludes

thedynamiceffectsof

friotional

drag

and

of

form

dragresultingfrom

thedisturbanceof thefluidin thevioinity of thebody.

In steady state fluid

flow

the

drag

coefficient

is

related

to

the

flowby the

Reynolds

number

given

by

the

expression

where

Re

i-

2)

D

sharacteristicength

fhe

bject*

y

a

inematio

viscosity

ofheluid.

Ifhenhe

luid

s

n

on-steady

motion

pastn

bject,

the

c-

celerationoreceleration

fhe

luid

nhe

vicinity

f

he

bject

produces

oree

omponent.

Adding

his

oroe

ue

o

he

luid

nertia

tohe

riotional

orce,

theotalorce

s

given

by

he

xpression

(O'Brien

nd

Morison,

1950),

F C

Dy

oAu

2

+C

M/

oV

m

^ 3)

where

C

M

scoefficientof mass.

V

m

* volume

of

the

displaced

fluid

~

acceleration ofthe

fluidrelative

to

the

object.

Thecoefficient

of

mass

must

be

determined experimentally.

Thistotal

forcedoes

not

include

any

hydrostatic

forces.

T h e

system

under

con-

sideration

is

essentially

in abalanced

hydrostaticfield.

3 4 1

8/10/2019 1808-7660-1-PB.pdf

3/31

COASTAL

ENGINEERING

A

p i l e ,

extending

vertically

i n

a fluid

in

motiondue t o o s -

oillatory

w a v e s ,

i s

in a non-uniform

flow

field

with

respeot

t o

t i m e

and

t o

t h e submergedpile l e n g t h .onsiderap i l e atany

instant of

t i m e .

qua-

tion

( 3 ) mustb e

writtenin

t h e

differentialform and integrated

over t h e

pile lengthinorder t o

obtain

t h e totalresultant f o r o e on

t h e

p i l e .n

Equation

( 3 )

t h e

area

A

i s

D d S

and

t h e

displaced

volume

V

m

i s

(wD^/i)

d S .

T h u s ,

t h e

differential

foroe

on

t h e pile i s given b y

t h e

expression

dF^ D^ +

C^iSf ^ ds

4

)

where

D

=

pile

d i a m e t e r .

S

*

distanceabove

t h e

bottom

into

f l u i d .

Equation

( 4 )

may b e integratedi f CD,C y ,and

u ,

nddu/dta r e

known

a sf u n o t i o n s o f

t i m e

( t ) ,

or

t h e phase

a n g l e ,

and of

t h e

position S .

T a k i n g

S

( d +

y

+77)

where

d

s

depth

o f

s t i l l

w a t e r ,

a

d e p t h

below

t h e

mean water

surfaceto

t h e mean

particleposition

( m e a s u r e d negatively

d o w n w a r d ) ,

and

7 7 *

vertical

particle

displacement

aboutt h e mean p o s i t i o n ,

a n d assuming that

t h e

horizontalparticlevelooity

i s

s e r o

when7

0 ,

then

t h e horizontal

velooity

and

accelerationo f

t h e

fluid

in wave

action

a r e

given

b y t h e expressions( S t o k e s ,

1 9 0 1 ) ,

C o s 6

5 )

and

Sin

86 )

u

t

T

-

Slnn

- , , -

L

where

H

s

wave h e i g h t .

T

s

wave

p e r i o d .

L

*

wave length

8 Zirt/T,angularposition o f

partiole

in

i t s

orbit measured

counter-clockwisefrom

t h e

crest

position at

t i m e t

* 0 .

T h e coefficients C

D

a n d C

M

depend

upon

t h e

s t a t e

o f

t h e fluid

motion

with

respect

t o

t h e

object

motion*

ittle

i s

known about

either

of

t h e

coefficients

in

aooelerated

s y s t e m s .

s

a firs t approximation

they

a r e considered as constant

with respect totimeand position to

enable

integration o f

Equation

( 4 ) .h u s ,C

D

and

C J J become

overall

c o -

e f f i c i e n t s .

T h i s study

i s

based

o n

t h e

total

momentabout

t h e

bottom

of

t h e p i l e ,o r t h e t o t a l moment

contributed

byt h e wavemotiona b o v e

any

l e v e l ,

S i ,

above t h e

b o t t o m .

h i s

moment

i sgiven by t h e expression

u

-_,. 27TS

7 T

H

Co8h

-TT"

T

Sinh^Jl-

du

.

m

j >

Cosh

2

7TT[

L

dt

$

2

Sinn

2,rd

L

M i

S

s

( S - S i )

dP

7 )

3 4 2

8/10/2019 1808-7660-1-PB.pdf

4/31

(8)

EXPERIMENTAL

STUDIES

OF

FORCESONPILES

I n o r d e r t o simplify t h e calculationso f t h e first fewexperiments m a d e ,

i t

was

assumedthat

t h e wave

elevation

a b o v e

o r

below

mean

water

l e v e l

contributed l i t t l e

to

t h e

t o t a l

moment

about

t h e

b o t t o m ;hat

i s ,

7 7

at

t h e

s u r f a c e

was

s m a l l

comparedtod .

ence in Equation

( 7 )

t h e

wave

s u r f a c e

S

g

i s

reduced

t o d

andS

d

+ y .y making t h e neoessary

substi-

tutions

into

Equations

( 4 )

and

( 7 )

and

integrating,

w e

h a v e

P i

= - r r p

JUi

|C

D

kl

C o s

2

9 + C j f c , Si n

9\

M i

=

P 5

{

C

D

k

3

C o s

2

0+

C 2J L

S i n

9

- ci|cos8

Sin*]}

9)

H i e l i n e o f aotion o f t h e resultant t o t a l t h r u s t ,F j ,above t h e

l e v e l ,S i

i s

given

by

t h e

expression

M i

7

* ~

1 0 )

where

d.

477

+

glnh

jrd

.

inh

4

ki

7Td

\i

16

\Sinhrj

Sinh

TTd_

.

iQh

Si

2

, u

27r

d

Sinh

-r

(12)

(lZf-

i *mi+

47rd

Sinh

2_*Hi

Sinh

fjrSi

.

Coshi +Coshi

(13)

q&L

Sinh

ZL-

o s h

3p*

2Sinhifi

Equation

( 9 )

f o r

t h e

total

moment

contains

s i n e

and

c o s i n e

terms

which

a r e

functions

o f t h e

angular

position,

9

T h u s ,

a phase

a n g l e

i s

indicated which

d e p e n d s

upon t h e

relative

magnitude

of

t h e

s i n e and

o o s i n e

t e r m s ,

hewaveequations( 5 ) and ( 6 ) are referenced ata wave cresta t

t i m e t

s

0 .h e phase a n g l e ,/ 3 o f

t h e maximum

momentin

relationship

t o

t h e

wave crest i s determined

by

differentiating Equation

( 9 )

with

respectt o9

andsetting

t h e

resultsequal

to

s e r o j t h u s ,

27TSi k 2 v

$.

s i n

1

{Zl3dLZL2L)

16)

TTS1

k

v J

16

>

8HC

D

U--TT^ -r

343

8/10/2019 1808-7660-1-PB.pdf

5/31

COASTAL

ENGINEERING

T h e phase

a n g l e

of

Equation

( 1 5 )

s h o w s that t h e

maximum moment

usually d o e s n o t occur

when

a wave

c r e s t

passesa p i l e .hent h e p i l e

i s i n waterwhich

i s

shallow

compared

t o

t h e

wavelength ( d / L s m a l l ) ,

t h e

p h a s e

angleapproaches

z e r o .

hent h e pile d i a m e t e r i s s m a l l compared

to

t h e wave

height

( D / H

s m a l l ) t h e phaseangle

alsoapproaches z e r o .

T h e phase

angle

approaches

9 0

f o r

p i l e sin d e e p

water

( d / L

l a r g e )o r

for

l a r g e

p i l e si n

s m a l l

waves( D / n l a r g e ) .

Measured moment-timehistorieson t h e

p i l e

and wave surfaoe-time

historiesatt h e pile

a r e

used t o

d e t e r m i n e

CQ

and

Cg

from Equation

( 9 ) .

T w o variables a r e

involved

which

necessitate

seleotion

of two

timeswith

t h e corresponding

two

moments.

h e

solution

i s

simplified

i f t h e

s e -

l e c t e d t i m e s are

z e r o

( c r e s t

o r

trough

a t

t h e

p i l e )

and

t h e

one-quarter

o r three-quarter wave lengtht i m e( s u r f a o e profile a t t h e mean water

l e v e l ) .h e s e

t i m e s

result inSin 9

0 ,

andC o s

Q

s

0 ,r e s p e c t i v e l y .

T h u s ,t h e selectedpoints

r e d u o e

Equation

( 9 )

t o

t w o

e q u a t i o n s ,

eaoh

with

b u t

o n e

u n k n o w n ,

C * .

nd

C j .

respectively.

T h e

moment

distributionon a non-uniform p i l e ,that

i s

a pile

whioh

consistsof various

l e n g t h s

ofdifferentdiameters( F i g .1 ) re-

s u l t s

from

a

summation

of

the

moments

contributed

by

eaoh

s e c t i o n . T h e

solution

o f

Equation ( 9 )

f o r t h i s

system

i sgiven

by

t h e e x p r e s s i o n ,

SinQ- L .

( 1 6 )

t h e elevation at whioh t h e

t o t a l

moment

D _ Z

_

0.4

0.8

1.2

1.6

1.8

'/L

Fig.3.

Total

momen t

bouthe

ottom

of

aingle

circular

pile.

348

8/10/2019 1808-7660-1-PB.pdf

10/31

EXPERIMENTAL

STUDIES

OF

ORCES

ON

ILES

InFig.4 certain

features

should

benoted*hecoefficients

Cu

and C j were

evaluated

fromthe

momenthistory

atvalues

of

0 ,

7 7 " / 2 ,

IT

(3/2)

ir of the

angular

partiole position with

respect

to

the

wave crest.

hus,

the

computed

maximum

moment

may

be

different

from

the

measured

maximum

moment

for

these

conditions

where

the

phase

angle

betweenthewave crestandmaximum moment i sdifferentfrom zero.h e

oomputedcurves,Pig.

3 ,

showthis

difference.

Thati s ,aty/d 1.00

(bottom),

the

maximum measured

moment

and

the

maximum

oomputedmoment

do

notcoincide.

owever,

the

shape

of

the

moment

distribution as

a

func-

tion

of

depth,

using

t he average

values

of

Cp

and C J J

from themeasured

moment atthebottom

to

compute

themomentat any

depth,

follows

the

trend of

the

measured

moment

distribution.

Afurthercomparison

maybemadeof the effectof

pile

diameter

on

the

moment distribution

byreducing

the

moment

distribution toa

ratio

interms

of

the

maximum

moments.esults

areshown

in

Fig.

5

for

one

wave

condition*

The

oomputed

moment

ratio

and

the

experimental

mo-

ment

ratio

are

in

agreement

within

the

limits

of

experimental

error*

The

pile

diameter

does

not

have

any influence

on

themoment

distribution*

Hence,attention

can

beconcentrated

on

obtaining

moments

aboutonehinge

pointto

establish

the

necessary

criteria

to

enable

prediction

o f

the

momentsonapileduetowaveaction.

/athin

theaccuracy ofvaluesofC

D

and

C J J ,

the

resultant

foroe

asa function of

time

orwave

position

relativeto

the

pile

may

beob-

tained

from

Equation (8).

T h eaction

line

of

the

total

resultant foroe

i s

obtained from

where S i sthelocationoftheaction

line

above

the

bottom andUd is

themoment about a

hinge

pointa tthebottom. Theresultant foroeon

a

pile above

a hinge point at

any

position in

the

pile

may

be

obtained

in

a

similar

manner

except

for

the

seotion

of

the

pile near

the

water

surface.

Inthesetests

forces

werenotoomputed,sinceattention was

concentrated on

obtaining

reliable

values

of

C

D

and

Cwfrom

moment

histories.

Testson

a

variable

diameter

pile

he

total

moments

exerted

by

waves

onapilewhich hadvaried stepsof

diameters

wasdeterminedbyamodel

study.

The

dimensions

of

themodel

are

shown in

Fig.

6 .o

attempt

was

made

todeterminet h ecoefficients,CD

and

C

M

from the

resultson

the

stepped

pile.

Three

conditions

ofthe

stepped

pile

wereinvestigatedwith

respeot

to

the

coefficientsCD

and

C

M

as

determined

in

the

discussions

above

for

singlecylindrical piles. %emomentcontributed

for

each

seotion

of

the

pile

was

oomputed

from

Equation

(16)

using C

D

s

1.63,

C j |

1.51,

andthe experimentally measuredphaseangle, pj,of

the

total

moment

about

the

bottom.

omparison

of

the

moment

distribution

in the

form

of

the

ratio

of

the

moment

resulting

fromthewaveaction

349

8/10/2019 1808-7660-1-PB.pdf

11/31

COASTAL

ENGINEERING

2.

d

-.^f^Ss^

MML

AVERAGE VALUES

FO R

3 PILES

H

0183

T

L4

5

FT

T

6

SE C

d

96

FT

H/L

0

0370

d/L>0 3S6

/9

d

> PHASE ANGLE F O ROTALMOMENT

A T

EPTH d

OMPUTED

VALUE

FO R

ARIOUS PILES

AT

y/dIO

A MEASURED VALUES

FO R

PILE C

H

'

S

Co

69

ON,|,e3 >

2

54

D.

2 ,.

.1.79

."4.41

COMPUTED

CURVES

USING

o FROMMEASURED

RESULTS

Ty/d>l.00

I

00

00

O . O S

0

25

030

10

1 3

20

M

d

(FT-LBS)

Pig. .omentdistributionon uniformpile

Laboratoryresults.

0 . 0

0.20

0 . 40

d

0.60

0.80

1 . 0 0

00

-

1 "

D IA

PILE

THEORETICAL

A

Vt

EXPERIMENTAL

V A L U E S

(4-5-50)

AVERA6E

ALUES

F O R

3 PILES

$ 4

t

D

"

H0.163

L

5

FT

T

096

SEC

d 96 FT

H/L

O .OSTO

d/L>

0396

^ " O "

^

>s

^5

, ,

*v

&

N

^

*fr

A

0 . 1 02 0 3

0.6 0 . 7

0.84 0 . S

M/

MMAX

Fig.

.

imensionless

moment

distribution

of

uniform

pile.

09 10

350

8/10/2019 1808-7660-1-PB.pdf

12/31

EXPERIMENTALSTUDIESOFORCESONILES

(A

o .

z

o

o

z

o

o

1

UJ

o

8/10/2019 1808-7660-1-PB.pdf

13/31

COASTALENGINEERING

aboveany seleoted

point

to the

maximum

moment

about

the hinge

point

at

thebottom i sshownin

Fig.

7 .

Testaonpilesofvariousoross-seotional

shapes*

h e moment historyof

piles

with

variouscross-seotional

shapes wasdetermined

in

the

lab-

oratory

with

the

equipment

shown

in

Fig.

1 .

The

pile

oross-seotions

were

oiroular,flat plates andH

-seotions

with one-inoh projected width

in the

normal

dimension

as

detailed in

Fig.

8 .esultswere

interpreted

as

ratios

of

the maximum

moment

for

anygiven

shape

to

the

maximum

moment

forthe

oiroular

shape

(Table

4).

heH

-

section

was

oriented

in

three

different

directions

as

shown

in

the

table.

ll

piles

weresubjected

to

the

same

wave

conditions

as

indicated

in

Table

3 .

Table

3

Wave conditionsin testson oiroularpiles,

flat

plates

and

H

-

seotions.

Parameter

Wave

1

Wave2

#ave3

H ,

t .

0.681

0.342

0.4 54

L ,t .

7.54

3.87 5.39

T ,

s e c . 1.27

0.88

1.09

d ,

f t .

1.55

1.50

0.83

H/L

0.0903

0.0884

0.0843

d / L

0.206

0.388

0.154

Table

4

Effectof

pileshape

on

maximum

moment.

Pile

type

andsize

Orientation

Ratio

ajcimum

M o n t e a t forgiven

pile

type

Maximum moment for

oiroular pile

1

inoh

round

1 inch

H-seotion

1inoh

H-seotion

1inoh

H-seotion

1 inoh

flat

plate

-o

-H

as

0

-X

a=

90

a*45

1.00

8/10/2019 1808-7660-1-PB.pdf

14/31

EXPERIMENTAL

STUDIES

OFFORCESON

ILES

r

c

L =

'/I6-

1/16

1/16

__

k-,--J

DIMENSIONS O F MODEL

PILES

WAVE

m

DIRECTION

I

-r

EQUIVALENT

CYLINDER

SHOWN

BY

ASHED

IRCLE

Fig. .

ross

sections

of piles.

2

5

2.0

I

0.8

0.6

04

L E GE ND

o

R

e

=43l28

A

R

e

=

0288

projected

widthf l

F

a

FORCE

ATANGLE

F q,

0

FORCE

AT

ANGLE EQUAL

TO

0

60

75

B

0

5

ORIENTATION

N G L E ,a,

E GRE E S

Fig.

9.

Measured

H-section

rag

foroe

in

teady,

uniformlows

unction

forientation.

90

353

8/10/2019 1808-7660-1-PB.pdf

15/31

COASTAL

ENGINEERING

The

forceon theH

-

section

wasdetermined

in

a

wind

tunnel

under

steady-state

oondition

as a

function of

orientation

of

the

see-

tion.1 ' h e

maximum

foroeresultedatapproximatelythe45orientation

as

isshownin

Fig.

9 .

Thusthe

pile

results

for

that

orientation

wereconsideredasgiving

the

maximum moment

(primarily

beoause

this

orientation

gavethegreatest

projected

area)}onsequently,

under

wave

action

the

orientation

ofthe

H-seotion

was

not

varied

over angles

otherthan

the

45withrespecttothedirectionofwavetravel*

One

comparison oan

be

made

using

theH-sectio n

results

of

the

steady-state

foroe

ratio

andt he

maximum

moment

ratio

inthewave

aotion.atios

o f

the maximum moment

of

theH-seotion oriented

with

values

of

c

other

than zero

to

themaximum

momentwitha

s

0 may

becomparedtothe

corresponding

steady-stateforoeratios.

(Note

that

the

moment

arm

isconstant

in

the

comparison,

hence

momentsshould

be

in

thesame

ratio

as

foroes

assuming

the

foroe

distribution

is

similar

and

not

a

function

of

orientation.)

This

comparisonisshown inTable

5 .

Table

5

Effect

of

orientation

on

foroes

onH-seotion

in

steady

flow

andinoscillatory . f l o w .

Wave

Steepness

Orientation of

pile

-H

as

0

O

90

a4 6 '

Ratio

t

oroa

(

or

Moment)

at orientation

shown

Foroe( o r Moment)

at *

0

0.0903

0.0884

0.0843

(Breaker)

Steady

Flow

1.00

1.00

1.00

1.00

0.93

0.85

1.17

1.00

1.61

1.42

1.02

1.26

Differences

between

force

ratios

in

steady

state

and

in osoillatory

flow

are

notedinsome

oases

which

are

greater

thanany

experimental error.

Thus,the

steady-state

drag foroes(hencesteady-state

dragcoefficients)

are

notthecompletecriteriaby whioh

to

evaluatemoments

of

seotions

which

differ

from

the

circular

section. T h i scomparison

wouldindicate

the

presence

of

the

inertia

force

component,

afact

which

i s

confirmed

by

the

differencesin

phase

angles

listed

inBible

4 .

3 5 4

8/10/2019 1808-7660-1-PB.pdf

16/31

EXPERIMENTAL

STUDIESOFORCESONILES

Theplotsshown inFig.10arecomputed,and measuredmoment-

timehistoriesof

a

oiroular,

an

H-seotion and

a

flat

plate

pile

in

shal-

lowwaterwheretheeffeetofthevariable

lever

arm hasbeen considered

byusing

S

s

instead of

d

inEquations

1 1 ,

1 2 ,

1 3

and

1 4 *

he

coeffi-

cients

of

drag

and

mass

computed

from

the

measured

curve

are

given

in

Table

6

alongwiththewavecharacteristics.

Table 6

Coefficientsof

drag

and massforshallow waterwaves

Variable

Pile

ype

1

nch

1

nch

1

noh

oiroular

H-seotion

flat

plate

-

-

H ,eet 0.613 0.600

0.705

L ,eet

7.76 7.36 8.00

T,

sec.

1.25

1.27

1.27

d,eet

1.50

1.46

1.45

B/L

0.079

0.082

0.088

d/L

0.193 0.198 0.181

/3,degrees

6

14

0

Re

15,000

15,000

15,000

D

1.78

2.44

1.20

C

M

0.44

1.92 0.42

Onefeature

of

the

interpretation

of

the

equationsfrom whioh

the coefficients

of

massanddrag werecomputed isevidentinthere-

sults

shown

inTable

6 .

henthe

phase

angle

i s

small,

the

massooef-

fioientisevaluated from

momentswhioh

arenearthe

point

ofzeromo-

ment*mallexperimental errorsbecomesignificantandreduoe there-

liability

of

the

value

ofthe

mass

coefficient.

he

mass

coefficients

for

the

oiroularpileand

the

flat

plate

pile

are

smallas

compared

to

those reportedin

Table

2 .heselowooeffioients

are

not

representative*

3 5 5

8/10/2019 1808-7660-1-PB.pdf

17/31

COASTAL

ENGINEERING

08

07

06

-*

r

*

*M*iirtd-

L,"

_ H*0I3F

L*7759F

dl500F

T

-

Computed

1 ,

r

X

r

E C

M

09

04

03

02

x

H

0

~MuredWaterSurfaceral

It'

11

J

J

J-.0I93

i

0

079

IT*

OTA L

LITUD

/

t

^

MEASURE )

AMP-

EF

HEM O M ENT

'

//

^

/

/

V

^ J

/ j

M

M

T

0

01

02

SW L

{

H'O)

/

\

\

\

V

>

/

/

W A V

E

IRECT

O N

03

04

N

N

v

a

03

o

e

o7

o

8/10/2019 1808-7660-1-PB.pdf

18/31

EXPERIMENTAL

STUDIESOFORCESONILES

Effeot of mutual

interference

of

pilest

he

one-inoh oiroular

and

flat

plate piles

were

arranged

inrowsparallel

tothewavedirection and in

columnsperpendioulartothewavedirection(seeFig.

1 1 ) .hreepiles

were

used

ineaoh case

with moment

measurements

made

ont hecenterpile

(Fig.12).paoings

between

t he pileswere^D,D

and

ijD,where

D

is

thepilediameter.

esults

are

shown

in

Table

7 .

%e

ratio

of

the

max-

imum

moment

on the

oenter

pile

ofthe

oolumn

or

row

to

the

maximum

mo-

ment on a

single

pileshowstheresultsofinterference effects*h e

wave

conditions used

werethesame

as

listed

in

Table

3 .

Table7

Effectof

mutual

interference

ofpiling

Wave

Steepness,H/ L

(SeeTable3 )

Ratios

Moment

onoenter pile

Moment

on

single

pile

TF

PileGap*'

ML

owofcircular

pile

perpendicular

to

wave

travel

0.0903

0.0884

0.0845(Breaker)

2.43

1.69

1.42

0.90

1.14

1.04

0.94

1.23

Row

of

f l u t eplates perpendioular to

wave

travel

0.0903

0.0884

0.0843

(Breaker)

1.49

1.93

2.22

1.46

1.40

1.72

1.64

1.17

1.31

Column ofoiroular

pileparallel

to

wave

travel

0.0903

0.0884

0.0843

(Breaker)

0.39

0. 60

0.96

0.7 1

0.71

0.7 6

0.72

0 . 7 4

0.87

*

s

1

inch

for

all

piles.

Theresultsshowthat,at

spaoings

oflessthan

l

D

in

the row

arrangement,

interference

effeots

are

noticeable.

ighermoments

areex-

perienced by

theoenter

pile

as

contrasted

to

a

single

pile. T h e

block-

ingeffeot

of

adjacent

piles

increasestheforoeand resultingmomenton

a n

individual

pile.heblocking

effect

deoreasesasthespacing

between

piles

increases.orthelimitedrange ofthetests,

the

blocking

effeot

is

oonoluded

to

be

negligibleforspaoingsof

l

Dor greater.

Results

from

the

piling arranged

incolumnsshow asheltering

effeot,(Table

7 ^in

that

moments

were

less

than

those

represented

by

a

3 5 7

8/10/2019 1808-7660-1-PB.pdf

19/31

COASTAL

ENGINEERING

single

pile* Themaximumspacingatwhichthe

shelteringeffecti s

negligible

wasnotreachedin

these

tests.

Forcesonorose members

;

he

measurementof

the

horizontalforceon

oross-menberswasmadeon

a foroebalance apparatus.

he

cross-member

was

mounted

on

a

rod

which

was

pivoted

near

its

center

and

restrained

by

calibrated

springs

at

one

end

(Fig.

13).

h e

submergedpart

ofthe

rod

wasshielded

from

the

waveactionso

that

a

taretest,withoutthe

oross-member

attached)showed only

about

one-peroent

deflection. T h e

foroe

and

the

wavecharacteristics

were

recorded

inthe

same

manner

as

inthecase ofthesingle piles.

Three

lengths

( 2 - ,5 and10 inches)

of

cross-members

were

used

so

that

theendeffectscould

bedetermined.

The

measurement

of

the

vertical

foroe

oncross-members

was

made

directly

by

a

oalibrated spring

system.h e

oross-member

was

placed

at

the

end ofa

vertical

rod

that

was

attached

t osprings

(Fig.

14).

he

submerged

part

of

the

rod

was

shielded

and

held

in

guides

near

the

oross-

member.

tare

test

showed

lessthan

one-peroent

deflection.he

wave

characteristicsweremeasured i j -

feetin

front

andl

feet behind the

oross-member

with

a

reference

measurement

of

the

wave

orest

being

made

directlyabovethecross-member*h eforoe and

wavecharacteristics

were

recorded

simultaneously

on

the

same

oscillograph

reoord.

hesame

wave

conditions

were

reproduoed

as

those

used

forthe

measurement

of

the

horizontalforces

on

the

cross-members.

n

both

thetests

of

the

horizontal andoftheverticalforoes,thesamewaveconditionswere

usedforthe horizontal and inclined

members

at

the

1/3

and 2/ 8posi-

tions

ofwater

depth.

The

horizontal

foroe

per

unit

length on

a

cross-member

(Tables

8

and

9)

indicated

thatthe

orientation

of

the

oross-member

is

not

criticalfor

model

studies.h etestshowedalso thattheendeffectsare

not

appreciable.

hevertical

foroe

per

unit

length

on a cross-member

(Table10)

indicated

someeffeotsdue toorientation.

hemagnitudes

of

the

forces

wereabout

halfthosefor

thehorizontal

direction.

FIELDPILETESTS

Themodel tests,as

desoribed

above,

yielded

aconsiderable

amount of

information

on

the

momentsand

foroes

on

piles

subjected

to

a

wide range

of wave

conditionsand

depths

of

immersion. T h e

limited

sizeof

the

model

system

introduces

a

possible

soaleeffectin

the

direct

application

ofthe

model

results

to

predict

prototype behavior.

Thus,prototypetests

were

made

inan

attempt to correlatemodel and

prototypebehavior

to

substantiate

the analysis

and

results

from the

model

tests(Snodgrass,Rice,andHall,

1951).

T h e field

tests

were

conductednear

shoreat

Monterey,

Califor-

nia,

with

acylindricalpileof

3 &

inoh outsidediameter*he pile was

hinged at

the

bottom

at

approximately

sand

level.estraining

bars

at

the

top

of

thepilewerearranged with straingageelementsoonneotedto

recording equipment.hestrain

recordsyielded

the

force-timehistory

of

the

pile

under

the

action

ofthe

incident

waves.

alibrationsof

the

strainrecording

equipment

were

madeboth

in

thelaboratory

and

inthe

field.

3 5 8

8/10/2019 1808-7660-1-PB.pdf

20/31

EXPERIMENTAL

STUDIES

OFFORCESONPILES

(0 VARIEDRO M V

TO

l-j")

(0=

I")

DIRECTION O F

WAVE

TRA VE L

O

*

a

l_L

I

q

*

a

-

o

o

a .

O W O F

R O U N D

PILING

b.

RO W

F

FLAT

PLATES

( P E R P E N D I C U L A R

O

WAVE

RAVEL)

Fig.

11.

Arrangement

fpiling,for

tests

on

mutualnterference.

c .

OLUMN

F

R O U N D

PILING

(PARALLELO WAVERAVEL)

W W

E

/RIGC

PILE

,

AV E

[DIRECTION

H I N G E

B O T T O M

X*vV- K

*

n1 0

n

w 1 0

o

n o

**

l

gg88RB:(;(ilR&8S.?S83S

>

o

oo

o

oo

O S

0 > t(t'

K888ioia82888Soicno>S8s

10000

s

s

3 8

i

361

8/10/2019 1808-7660-1-PB.pdf

23/31

o

EH

D

COASTAL

ENGINEERING

o

Q

8

0>

s

3

ooooooooo HOOOO

ooooooooo ooooo

Noicacnei

ooooooooo

ooooo

8

< o

33t-

r

S8SS883S

o

o

oooooooo

BIB

IO

0

(DIO

loqioSSSat-

oooooooo

a

O aStOCOOCOCOOCOCO

8

HHHNririNHH

ssssseg

S8n *

m

(0o

0

S

O

o

OOO

U>OO

o

o

o

o

SSSSSSSSSS

3 3 3 3 3

*?'?

*

}

*

1 i

. i*

ooooooooooooooo

nH4rinNN SS

S

o o- i

43

IO

*

O

OOO S

O

O

*

**

O

4

H

H

-l

H-t

*

-l

-l-4H

o

u

O "

HHrirtHriHHH

OOOO

N

tMl>4

s i

*j

4

98Hn9

c o t ?

< S

t o

3

58 S

O

&

~

tot-tototototocotoHwnn

+5

1, OHQIflQQU)0>ID

>K

pO

lOIOIOIOIOiOIOIOlO

W M

OOOOOOOOOoooo

HHHHOOOOHO

n

oo

t-

#

o

UIO \

rfSSS

?88

??????I?

trt-

t

t-

362

8/10/2019 1808-7660-1-PB.pdf

24/31

EXPERIMENTAL

STUDIES

OF

ORCES

ON

ILES

Thewaveheight historywasobtained froma recordingpressure

actuated

diaphragm type

wave meter

which

was

located

approximately

two

feetabovethesand

bottom

and

adjacentt othepile* Twoauxiliarygra-

duatedpileswere

placedseaward

o f

the

measuringpile, 3 h e measuring

pileandbracing

structure

also

were

painted

with alternate

black

and

white

bands,

each

onefoothigh.

otion

picturestaken

from

the

beach

reoorded the

surface profile

of

the

waves

as

theypassed

the

pile.

clock

was

suspended

in

the

field

ofview

ofthecamera

to

provide

timing

intervals

between

successive

framesof

the

film,

he

wavevelooity at

the pile

was

obtained

fromthe

distancebetween

the

seawardauxiliary

pile

and

themeasuring pile

(19.8

feet),andt he

time interval of the

wave

crest

travelbetween

these

points.

he

motion

picturesalso

re-

oordedwave heightsatthemeasuring pile.roughand

orest

elevations

of

eachwave

were

obtained

from

the

intersection

of

the

water

profile

with thegraduated

vertioal

piles.herecordfrom

the

wave

meter also

gave

waveheights and

periods*

Analysis

of data*

D i e

analysis

as presented

previously

in this

paper

includesthetworesistance terms

that

containCp

and

C J J ,and

also

the

phase angle

relationship,/ 3 ,between

the

two

resistance

terms.

n

theanalysisofthefield pileresults,the

timing

accuracy wasnot pre-

cise

enough

to

determine

the

time

comparison

betweenthe

water

surface

profileand

the

momenthistory.

The

data

and resultswereobtainedforwavesinvariouscondi-

tions depending

on

t he

stage

ofthe tide,ome

data were

obtained

with

the

pile

in

a

f o a m

line

shoreward

ofthe

breaker.

ther

datawere

obtain-

ed

with

the

pile

inthesmoothunbroken swellseaward of

the

breaker. T h e

data

have

been

segregated

with

respect

to

the

waveoondition

at

the

pile

into

the

following

groupst

1 )

foam line}

2 )

f o a m lineimmediately

shoreward ofthebreakerpoint}3 )reaker}4 )sharp

peaked

swell

at

incipient

breaks

5 )

sharppeaked

swell immediately

seaward

of the

breaker

point;

nd( 6 )wellsomedistance

seaward

ofthe

breaker

point.

The

data

are

summarized

in

Table

1 1 .

The

waveforce,whichis

actually

a

distributed

force

extending

from

the

ocean

bottom

to

the

watersurface,wasreoorded asan

equivalent

force atthecalibrationpoint.y multiplyingthe reoorded forcebythe

calibration-point lever-arm ( 9

feet

8

inches)

the

total

moment

of

the

wave

force

about

the

bottom

hinge

was

determined.

hen

the

maximum

foroe

exists

(approximatelyat the time

the

wave

orest

passes

thepile),the

oentroid

ofthe

wave

foroe

was assumed

to

be

looated

near

the

mean

height

ofthe

wave.

hislocationof the

oentroid

was

estimated

by

considering

the

horizontaloomponentofthepartiolemotion asobserved in

modelstudies.

By

computingthe waveforoeat themean

wave

height,

as

definedabove,

the

data

werefound tobereasonably

consistent.

he

values

obtained

from

the

computation

indicate

thatwaves

of

a given

site

andhhape

will

exert thesame force at the oentroidindependentofwater-levelchanges

over

the

rangeencountered inthetests,althoughthemoment aboutthe

hinge

point

varied

considerably

due

to

variation of the

effeotive

lever

a rm

asthewaterdepth

changed.

graph

of thewaveforoe atmean wave

height

is

shown

in

Fig.

1 5 .

3 6 3

8/10/2019 1808-7660-1-PB.pdf

25/31

COASTAL

ENGINEERING

Table

11

Testdata

on

fieldpile

WAVE

WAVE

WAVE

HAV E

H A

LL iVAlICh

ELbVATItr

bTILL

u&rSkjtiED

TOTAL

COEFFICIENT

H O . TtTf

HEIGHT

PERIOD

VELOCITY

UEASUKED)

OF

CREST

N

OF

TPCUGhN

WATER

LEVEL

FORCE

lOVKt.'T

OF

D R A G

B

FILE

FILE

Ft.

E

Ft.

I

See. Ft

./Sec.

So

Ft.

St

Ft.

Lbs. Ft-Lbs.

1

FL

4.6

10.7

8.0

3.4

5.20

67

662

2

PL

4.6

12.1

18.8

8.0

3.5

5.00

67

662

1.06

3

FL

4.2

11.7

17.6

6.0

3.8

4.93

84

626

1.71

4 FL

4.2

9.3

17.6

7.6 3.4 4 .CO 64 629

1.34

5

FL

4,0 8.3

IS.6

7.4 3.4

4.73

34

330

0.63

6

FL 3.6

12.0

17.6

7.0

3.4

4.93

51

496

1.69

7

FL

S.6

7.7

16.8

6.8

2.2

3.40

53

516

1.52

e FL

3.6

10.3

15.7

6.9

3.4

4.67

33

320

1.46

5

FL-B

4.1

12.1

lb .7

7.4

3.3

4.67

46 475 1.91

10

B-FL

4.6

t.J

20.1

6.5 3.7

5.10 51 496

59

11

B 6.0

10.1

21

.U

6.2 3.2

4.87

56

536

0.49

12

B

4.6

12.2

23.5

8.3

3.5

4.60

67

662

0.63

13

B

3.9

11.2

14.9

6.7

2.8

4.20

32

310

1,06

14

B

3.9

10.6

16.7

7.0

3.1

4.40

27 266 0.73

16

B

3.6 8.4

17.9

6.4 2.8 4.00 34

330

0.91

16

B 3.3

11.0

14.4

5.2

1.9

3.00

28

279

1.31

17

B

3.3

10.3

14.2

6.7

3.4

4.50

23

226

1,28

18

B

3.0

6.5

3.5

4.60

23

226

-

IS SP-B

3.4

11.0

14.b

5.6 2.4

S.SS

17

165

0.85

20

SP-B

3.3 10.6

16.6

7.0

3.7

4.80

IS

186 0.86

21 SP-B

3.3

9.0

14.4

6.0

2.7

3.80

13

124

0.64

22

SP-B

2.3 13.1

14.3

6.0 2.7 3.47 3

33 0.39

23

SP-B 2.0 8.6

16.9

4.8 2.8

3.47

4

43

0.67

24

SP

4.5

_

7.6 3.3

4.60

6

46

.

23

SP

3.7

-

6.2 2.6

3.73

12

113

..

26

SP 3.6 12.1

18.8 7.4

3.8

4.80

17

165

0.44

27

SP

3.6

12.1

20.1

6.9

3.4

4.67

11

109

0.26

28

SP

3.3

10.8

14.8 6.0

2.7

3.70

14 134

0.64

29

SP

3.3 9.1

14.8

5.9

3.3

3.70

6

62

0,26

SO

SP

3.1 13.0 17.7

6.3

S.7

4.73 IB 176

0.78

31

SP

3.1 10.0

14.2

6.9

2.6

3.63 10 93 0.49

32

SP

3.0 11.0 16.6 6.5 3.6

4.67 9 88 0.46

33

SP

2.9 10.9

13.0

6.4

2.5

3.47

8

76

0.60

34

SP

2.6

11.7

14.8

6.1

3.3

4.23

9

93

0.69

36

SP

2.7

_

6.0

3.3

4.20

5

53

-

36

SP

2.6

_

5.9

3.3

4.50

6 51

-

37

8

3.4

9.3

16.7

6.7

3.3

4.43

9

85

0.32

38

s

3.3

9.4

12.6

6.2

2.9

4.00

16

156 0.98

39

s

3.0

8.4

16.6

6.4

3.4

4.40

12

130

0.69

40

8

2.9

4.6

16.7

6.5 3.6 4.57

6

56

0.27

41

s

2.7

9.3

14.1

6.4

3.7

6.00

6

57

0.55

42

s

2.7

7.5

16.1

6.9 3.2

4.10

7

70

0.54

43

8

2.6

9.4 13.6

6.9

3.3

4.17 7

72

0.80

44

8

2.6

>

6.9

3.4

4.23 7

70

-

43

s

2.4 11.8

16.6

6.7

3.3

4.10 3

33

0.29

46

s

2.4

10.7

16.8

6.0 2.6

3.40

8

76

0.67

47

s

2.4

9.6

18.6

6.0

3.6

4.40 6

62

0.67

48

8

tA

9.2

16.9 5.6

3.2

4.00 6

46

0.43

48

8

2.3

11.9

19.4

6.7

4.4

5.07

11

109

0.86

60

3

2.3

6.9

r

6.7

3.4

4.17

3

29

.

61

8 2.2

9.4

-

5.9

3.7

4.43

4 41

m

62

8

2.2 8.5

13.7 5.2 3.0 3.73 5

60

0.74

63

8

2.1 13.1

5.6

3.4

4.10

1 36

m

64

8 2.1

7.7 13.6

4.9

2.8

3.6C

2

16

0.26

66

S

2.1

7.6 14.1 6.2

4.1

4.67

4 35

0.63

66

S

2.1

7.0

21.4

5.3

3.2

3.90

4

39 C.29

67

s

2.1

-

-

6.5

4.4

6.10

6 74

-

68

8

2.0 11.4 12.6 4.8 2.8 3.53

3

29

0.68

69

8

2.0

7.6

19.1

6.2

3.2

3.87

6

64

0.66

60

S 2.0

6.0

14.4

5.6

3.5 4.17

47

0.86

61

8

2.0 4.4 16 .6

6.2

4.2 4.87

f

62

0.69

G 2

8

2.0

_

6.2 3.2 3.87

4 35

-

63

8

1.9

10.0

14.8

5.8 3.9 4.43

2

21

0.45

64

S

i.9

6.4

4.6

6.13

+

41

-

66

S

1.6

12.4

21.4

5.2

3.4

4.00

23

0.24

66

s

1.8

10.0

11.0

4.5

i l 3.30 6

26

0.94

67

s

1.6

9.6

21.7

6.0

4.2 4.80

C

79

0.88

68

s

1.8

9.1

20.2

6.7 8.9 4.60

4 35 C.43

69

s

1.7

11.6

22.4

6.2

4.5

6.07

7 68

0.89

70

s 1.7

10.3

6.4

4.7

6.27

5

47

71

8

1.7

_ _

4.4

2.7

3.27

2

17

72

8

1.7

6.4

3.7

4.27

33

. .

73

6

1.6

11.1

4.2 2.6

3.13

T

4

.

74

8

1.6

10.9

14.4

4.S

3.2

3.73

2

17

0,54

FL

(Foam

line);

B

(Breaker);

SP-B

(Sharp

peak

swell

start-

ing to

break):

L- B

(Breaker

with

somefoam)SP

(Sharp

peak

swell);S

(Swell)

364

8/10/2019 1808-7660-1-PB.pdf

26/31

EXPERIMENTALSTUDIES

OF

FORCES

ON

PILES

Table11cont'd.

Testdataonfieldpile

HAVE

WAVE HAVE HAVE HAVE S.LEVATI01I

ELEVATIOr

ST;LL > J E A S

ED

TOTAL

CCEFFICBJT

NO .

TYPE

HEIGHT

PERIOD VELOCITY

(LIAISED)

OF

CHEST

ll

TRCLCT

H

H

.IT

LEVEL

FORCE CT OF

D R A G

D

P ILE

PILE

H

T

H

S

0

S

r

d

3

F

r

11

Ft.

So.

Pt./Seo.

Ft.

Ft.

Lbs.

Ft-Lba.

Ft.

76

S

1.6

6.6

_.

6.2 3.6

4.13

3

30

76

S

1.6

7.8

14.9

E.3

3.7

..23

3

33

0.96

77

S

1.6

4.2

6.6

3.9 4.13

3

27

78

8

1.6 -

f.4

3.6

4.33

3

33

.-

79

8

1.6 10.6

16.7

S.3

3.8

4.30

2

19

0.52

80

1.6

9.0

....

6.0 3.5

4.00

1

5

81

3

1.6 8.3

17 J

4.4

2.9

3.40

1 14

0.37

82

s

1.6

.... .._

5.1

3.6

4.10

3

33

83

s

1.4

12.2

19.2

4.2

2.8

3.27 3

29

C.63

84

8

1.4

10.0

_..

s.e

4.4

4.60

2

21

86

8

1.4

- ....

C.4

*.o

4.47

4

37

.

86

s

1.4

_ _

....

E.9 4.5

4.97

34

87

s

1.3

10.2

_

4.7

3.4

3.83

29

....

88

s

1.3

6.8

_ _ *

6.5

4.2

4.63

Z

17

89

s

1.3

.

._

6.0

4.7

5.13

3

29

.

90

s

1.3

_...

....

6.0

4.7

6.13

b

48

.

91

s

1.3

....

....

E.6

4.3 4.73

4

37

._.

92

8

1.3

.

....

6.0 3.7

4.13

29

96

8

1.2 13.3

.._

4.6 3.4

3.80

2

21

....

94

3

1.2

12.4 12.3

5.3 4.6

5.CO 1

29

2.72

96

8

1.2

11.4

16.1

4.9

3.7

4.10

2

19

1.14

96

3

1.2

10.6

10.4

6.0

4.8 6.17

3

34

97

S

1.2

_..

.-

4.7

3.5

3.96

2 22

. -

98

3

1.1

11.8

12.6

3.9 2.8

3.17

1

12

1.06

99

8

1.0

12.7 ....

4.7

3.7

4.03 1

10

100

3

1.0

12.2

13.7

3.7

2.7

3.03

2

17

1.60

101

8

1.0

-

....

4.6

3.5 3.63

1

10

102

S

0.9

9.6

12.6

3.6 2.7

3.00

1

8

1.23

10 3

s

0.8

S4

i

5.2

4.4

4.63

1

13

.

104

s

0.8

-

5.4

4.6

4.67

1

12

..

106

s

0.7

_ ._

4.9 4.2 4.43 1

10

....

106

1

0.7

....

4.6

3.9

4.13

1 8

....

10 7

s

0.6

7.1 19.6 5.0

4.4

4.60

2

16

2.66

* (Swell).

365

8/10/2019 1808-7660-1-PB.pdf

27/31

COASTAL

NGINEERING

OU0

featurebecomesapparent in

reviewing the

data

that

permits

a

comparisonbetween

the

model

results

and

the

fieldtest

results.

x

he

majorityofthe fieldtestconditionswereobtainedwith

samll

ratiosof

the

pile

diameter

to

the

wave height,

and

with

small

ratios

of

the

water

depthatthe piletothewavelength.

ndertheseconditions,the phase

angle

as

given

by

Equation

( 1 5 )

approacheszero

and

the

maximum

moment

of

Equation

( 9 )

occurs

when

the

time

angle,

8

,is

zero.

Equation ( 9 )

for

a

pile

hinged

at

the

bottom

then

reduces

to

2

^3*isintroduoed asarefinement of

k j j

to includean approximation of

velocity

distributions

ina

wave

o f

finite

heightin

shallow

waterj

thati s ,

itAafrf+iffttBlnhlffft-

0 o h

Jffil

+

1

(19)

k

4 (Sinnill

where

d

St+V

s

assum ed

till-water

evel)

S

0

wave

rest

levation

bove

he

ottom

S - f cwave

rough

levationboveheottom

H

wave

height

For

mallvalues

f /L ,

Sinh

7TS

0

L

spproxim ated

y

7rS

0

/L,

and inh

7Td/Ls

pproxim ated

y2Td/L.

These

pproxim at ionsesult

in

D

-T 75H

2

L

2

S

0

)

Asthewave

velocity i s

related

to

the

length

and periodby

CL/T,

we

find

that

C

D

2 *W

d

2 2 )

5

pD

2

S

All variables

on

the

right

side

of

Equation

(22)

weremeasured

and ODthen

oomputed.

Qis a

drag

coefficient

whioh

depends

upon the

state

ofthe

disturbance

of

thewave

motion

due

to themovement

of

the

wave

past

the

pile.

or

shallow-water

waves,

the

velooity

distribution

fromtheorestof

the

wavet o the

bottom

is afunction oftheratio of

wave

heightto

water

depth,

and

is

essentially independent

of

the

wave

lengthor

period.

he

resulting moment

on

the pile,and

henoe

C

D

,are

functions

of

thisratio,

H/d.

h e results are

shown

in

Fig.

16

on

thisbasis,withsegregation

oftheresults

aooording

to

wave

type*he

field pile resultswereobtained forwaveconditionsofd/ L lessthan

0.06,

with the

majority

of the

waves

characterized

by

d/ L

less

than

0.03.

3 6 6

8/10/2019 1808-7660-1-PB.pdf

28/31

EXPERIMENTAL

STUDIESOFFORCESON

PILES

X

1

n

o

m

n

b

e

p

e

a

a

M

X

u

o

p

-<

a ,

a,

e

o

o

O

Si

I-l

W)

N

S

a s o

X

U

it

T3

-H

c e

O

IS

m

8/10/2019 1808-7660-1-PB.pdf

29/31

COASTAL

ENGINEERING

T h esoatter of the

resultsreflectstheaccuracyoft hedataand

theaoouraoy oftheassumptionsof

Equation

( 2 2 ) ,

D

i

a

computedfrom

Equation

(22)

which

containsthesquare

of

thewavevelocityandthe

square

of

the

wave

height.

mall

discrepancies

ofthese

variables

may

produoe

appreciable

differences

in C

D

he maximum

momentwas

obtained

from

theforoe,whiohw as

measured

to

withinone

pound.

any

of

the

measured

forceswerefrom oneto f i - r opounds.

ome

soatter

of

results

is

necessarily

expected.

Enoughdata

were

taken

to

permitthe following

general

obser-

vations.

1 )

oam

lines

and

breakers

produoe

highervalues

of C

D

than

unbrokenswells.

2 )

orvaluesof

H/ d

greater

than

0*4,

an

average

value

of C

D

equal

to 0.50

bestrepresents

the results.

S)

or

values

of

H/ d

lessthan

0.4,

C

D

becomes

largerthan0.50,

The

assumptions

of

Equation

(22)

become

invalid in

this

range

of

H/d.

A

direct

comparison of

the

model

test

results

withthe

field test

resultscannot

be

made.hesamerange

of

thegoverningparameterswas

not

covered

in

the

two

series

of

tests,

particularly

the

ranges

of

d/ L

and H/d.n Fig.

16

dragcoefficientsof 1.0to2. 5areshownforvalues

H/ dbetween 0.4

and

0.1.hesemagnitudes

of

thedrag

coefficients

are

in

the

same

rangeas

those

obtainedfrom

the

model studies.

owever,

thevaluesofd/ Lof thefieldtestswere notthesame

as

themodel

tests.

s

mentioned

in

the

model

test

summary,

complete

correlations

including

alldefining

parameters

havenotyetbeen

attained.oat-

tempts

have

been

made

tooarry

the

field resultsbeyond Fig.

1 6 .

CONCLUSIONS

The analysisofforoesand momentsonpilesassummarizedherein

contains

two

coefficients

whioh must

be

determined

experimentally

he

coefficient

of

mass

and

the

coefficient

of

drag.heresultssofarob-

tained indicate

that

the

theoretical value

of

2. 0

for

t h e

coefficient

of

massis adequatefor computing

the

foroesoncircularpiling.or the

coefficient

of

drag,

however,

additional results

are

needed

with

a

large

rangeof

the

variables

ofpilediameter,wave height,wavelength,and

water

depth*

The resultsshow

that momentsmeasured about

a

single

hinge point

will

suffice

in establishing

the

magnitudesof

the

coefficients.

he

moment

distribution

fromcoefficients

obtainedfrom momentsabout a

bottomhinge

pointagree

with

measured

moment

distributions.

Measured momentsonpilesof cross-sectionalshapeother than

circularshow coefficients

whioh

area functionof

the

shape

of

the

pile*

Steady-state

dragcoefficients

cannotbe

used

as

drag

ooeffioients

in

the

analysis

of

periodic

motion*

3 6 8

8/10/2019 1808-7660-1-PB.pdf

30/31

EXPERIMENTAL

STUDIES

OF

FORCESON

PILES

Resultsoft i i einterference

effects

of rowsofoiroular piling,

whilelimitedinsoope,indicatedthatforclearancesgreaterthan

li

pile

diameters

he

interference effects arenegligible.oments

on

oenter

pilesofa row are

inoreased

as

compared

to momentsonan iso-

lated

pile

forspaoingsless

than

1 J S

ilediameters*

Momentson oiroularpiles arranged

in

columns

are

decreased

as

comparedto momentsonanisolatedpile*olimitsweredeterminedat

which

the

moment

became

independent

of

the

spacing.

RECOMMENDATIONS

The

following

experiments

on

model

piles

arereoommended

f or

comparison

purposeswith theoreticalwork

and prototype

tests.

1 .

easurement

of waveforoedistribution onsinglepilesof

various

diameters

are

needed

in

order

to

compare

with

Equations

( 4 )

and

( 8 ) .

2 .

xperiments

with a

greater

numberof waveconditionsonoir-

oularpiles,H-sections,flat plates

and

various

other

objects

are

needed

in

order

to

establish

the relationship

of

the

co-

efficientsofdragand

massto the

wave

characteristics.

3 .nvestigationshouldbe madeof

the

mathematical

theories

per-

taining

to

piles

and

other

objects

subject

to

waveaction

with

respect

to

foroe,

wave

reflection,

wave

diffraction

and

flow

conditionsin thevicinityofthe

object*

4 .

nvestigation

should

bemade

of

breaking

waves

on

model

structures

inoludingthedevelopment

of

foroe

reoording

equipment.

ACKNOWLEDGMENTS

The

aboveinvestigationsweresponsored by the

Office

ofNaval

Research,

Bureau

of

Yardsand Dooks,

T h eCaliforniaCompany,and

InternationalMarine

Platforms,

Ino.

Morison,J.R,

(1950a)omentdistribution onsteppedoaissonjeries

3 5 ,ssue1 ,IER,Universityo f Calif.,Berkeley,Calif.

Morison,J.R.

1950b)oment

distribution

exerted

bywaveson

piling}

Series

3 5 ,ssue 2 ,IER,UniversityofCalif.,Berkeley,Calif.

Morison,

J.R.,

( 1 9 5 0 c )

The

foroes

exertedby

waves

on

marine

structuresj

Series

35,

Issue

3 ,

E R ,

University

of Calif.,

Berkeley,

Calif*

Morison,

J.R.,

O'Brien,

M.P.,Johnson,

J.W.

and

Sohaaf,S.A.

(1960)

Theforoes

exerted

by

surface

waves

on

piles;

etroleum

Trans.

AIMS,

vol.

189,

p.149-154.

3 6 9

8/10/2019 1808-7660-1-PB.pdf

31/31

COASTAL NGINEERING

O'Brien,

M.P.,

and

Morison,

J.R.

(1950)T h e

forces

exert*d

by

waves

on

objects;

eries3 ,

Issue

310,

I J B R ,

niversityof

Calif,

Berkeley,

Calif.

Snodgrass,

F.E.,

Rice,E.R.,andHall,M .

(1961)ave foroeeonpiling

(Montereyfield

test))

eries

3 5 ,

Issue

4 ,

SR,University

of

Calif.,

Berkeley,

Calif.

Stokes,Sir G.G.

(1901)

n thetheoryo f

oscillatory

waves/ath,

and

PhysicalPapers,vol.V ,CambridgeUniversity Press

APPEHDIX

Corrections to

"Design

ofPiling".hapter

2 8 ,Proceedings

of the

First

Conference

on

Coastal

Engineering

Page

257,

line

13

C

M *

*

(

use

heoreticalvalueof

2.0)

Page

57 ,

line

4

M

z

s

P

S

~^

I

D

2

os

2

6+

J-j

K i

M

Sin

6

J

. (2.0)

(10)2

)2

{ 0