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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
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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
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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
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(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
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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
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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
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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)
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W A V
E
IRECT
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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
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H I N G E
B O T T O M
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ENGINEERING
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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
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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
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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
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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*
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