Methodology for evaluating suitability of wave and wave force data for determining drag and inertia coefficients

40 INTRODUCTION r

'I

urn voor

ScheepahydromecJij,iJ

Maketweg 2. 2021 CD

_!ft

IGLI

O1-Although a number o laboratory and field programs have been conducted to investigate the general problem of interaction of waves and structures.

there is still a wide range of scatter in the reported force coefficients. leaving the platfoud designer with either the necessity of applying a safety factor that is larger than desirable or using coefficients lower than the general range of reported values. Clearly oneof the reasons for this scatter is that in most studies reported, the velocities and accelerations were not measured but were determined from the measured sea surface using some wave theory. With the development of the electromagnetic current meter. the next two decades will undoubtedly result in a number of programs in which simultaneous measurements of velocities and forces are conducted; hence, this source of scatter will be reduced. Other sources of scatter include the use of an inexact interaction relationship, different roughness characteristicsof the test cylinders. experimental error and the characteristics of the data; this paper Concerns

the latter source. lt is shown that depending on the wave and cylinder characteristics, data can be well- orpoorlyconditioned for resolving drag or inertia coefficients and it isbelieved that much of the scatter in the reported coefficients may be from data that were poorly conditioned for resolving them. Methods are pre9nted for evaluating the 8uitability of data for determining either the drag or inertia coefficients. The methods are des-cribed for analysis in the time and frequency domain and it is found that there is a general loss of resolution when coefficients are determined from force spectra (frequency domain) due to loss of the phase information. The methods are illustrated by application to three sets of field data and one set of

laboratory data.

SOURC 0? ERRORS Consi4O! a wave forcemea5urflt program

as ahOwo.inyigUre .

peasured forces coild be on a short 'ength

of test pilingor on a pilinS

sxtend1'R over aconsiderable portion of the depth.

To obtain drag and

inettia coeff16tet5 the measured

forces areusuallY cottC1ated with the wave

kinCZ0t5 in accorde with the I4orisCU

(8) eq031100written beloWfor a

unit iength of a verticalpilins of

diametur. D:

2

f(t)

_C0*l

+C'U

where C0 and C are the drag and inertia

force coeffict ta, 5peCttly5e the mass densitl of the

fluid and U and are the

botiZOmt8l cOmPOoontsof watet

parttClC velocitY andacceleratton resPeCtmiu

According to the ich of the naly5ia

procedure. the drag and

inertia OCfft0nts

can be em mined as a

functtofl of any

para-meter censud ed to beof signi

canoe. e.g the geynoldS

number or the RsuIeSAB

CarPent number. idtallY the wave

force iett

omtatiofl programwould includO

measurement of thewater

0ticle

b.inemmuae

en, the

instrl0mt0ti0D to

reliablY measurewater particle

baa only become available in the

last

decadO. More generallY the

particle veloCit5

are inferred from the

measurementsobtained fromOUC

or more sieve ataffe according

to eons wave theory.

The following parasravha revioW

some of themore obvious

poesibke sourcesof

error8.

prctotati0n5hi

The 5ocaLledMorisom equatiofl

Lpreaentnd as Eq. (i) has beenquestiomnd

am providiRSa suitable

relationship fatrepteeentiRS wave

forces oncylindraSi

members. jhough thiS

equation was first presented to j9O,and

considerable

LntCrCst baa beenshown in developiRR en

improved relati°"''

s morereliab equation has not yet been deVeloP1"

SarpkeY5 (9) has employnd the Moris°" equation to detelmita dragand inertia

coefficients fromhis oscillating water tunnel xperimetausing.

parameters. tOeReynOldS number end the

Keu1eRa

Carpenter parameter. SarpkaYa found

that. emeeptover a limited range of the

Keulegan..Cpetet parametet. for

which the wake 0f facts erarather erratic.

the Itorison equati0fl representS

the 05i1lattng forces on the

cylindet vith

aurprisinS good accuracy. SarpkeYa'e results

are of special interest to a diacussion of the suitabilitY of the

MoriSon equationbecause his kinematics

are known rather preciselY. rjfl1. Sarpkaya

found that the root mean square error between she force as

determiand from theMotison equaticfl and the

measured

force normalized by the rout mean equare of the

measured force snged from 2 to 10 percent end arepreseflt5ti value i.e on

the odet of 10 to 12 percent.

2

(1)

is

.5 4

TRODOLOGY FOR EVALUATING SUITABILITY OF WAVE AND

WAVE FORCE DATA FOR DETERNIN INC DRAC AND INERTIA COEFFICIENTS

Robert C. Dean Deparoment of Civil Engineering U.S.A.

Professor of Civil Engineering University of Delaware and College of Marine Studies Newark. DE 19711

Boss '76

.REHAVIOUR OF OFF'

SHORE STRUCTURES

The Ne.wsgIsfl ,t1tutO

42

,//V/

-,_,-,

Figure 1 DefinitiOn Sketch 1Wave and Wave Force Measurement System

Direction of

Wave Propagation

Teat Secti u,u

Pure a horizontaL wlt pirticic velocityund the ned, Cisc 8

Average Agreement With StreamFumctio Wave Theory

3

Wave Staff

3jtics

Until the development of the electrOmaSetc

flow mater in the past decade. t baa notbeen poesible to

adequately measure thekinematics in afield program.

eia shortcomingbaa required that

the kinematics usedin the correlation of isasured forces with the Hanson equation be established

through the use cf some .uitable wave theory. The problem is 0ttCularl)' complicatod.

because in general., the sea surface is nonlinear end irregular end

the waves mayoriginate

from a range of directiOnS. An a4ditiOO1

computation is that the wave tkOny simply cannot establish the presence of a steadycurrent if one should exist

at the aits.

it can be demonstrated easily that if a current exists

in the samedirection as that of wave propagation, then this can result in an

large dvag coefficient in the vicinityof the peak forces,especially if the data are

drag

dominant. As an example of the problems

associated wl cb the use of shallow water theories. Le Mehaute. ., have measured water particle

kinematics in a

wave tank andcompared the results with a number of

theories. Figure a presents an example of these results in which it is seen that

tIe maximum Water particle

velocity as predicted bya number of wave theories exhibits a Wide range of values. Furthermore, it is clear that if the wave force

measurements were

con-ducted and the drag coefficient waredetenminod using the two

theories exhibiting the widest range, the associated dragcoeffiCientS would differ

by a factor of

apprOximateiY nina. Dean and La Meheute (1) have compared the

stream functiOfl wave theory with these data and found it to provide better

agreement than the others tested.

ErrOr5

There are a number of possible featureswhich could result in experfmetal errors that'ould effect the drag and inertia coefficient5.

Errors could result from measurement of the seasurface, calibretiom of the force transduCers,

errors In measuring the waterparticle kinematiCs. etc. One

0satbilitY of experimental error is simply instrumentation 5ensitivity and the low magnitudes

of forces and other variables during periods of small waves.

Chanaint SurfaceCharacteristics of the

It precauti ens are not taken through theapplication of suitable surface coatings, biological growth Will soon populate surfaces placed in a

marina environment. The form and rates of growth of these

encrustatioma is not well krOwa at the present, however, it has been established byMiller (7) that a relatively small ratio of surface roughneaa height to piling diameter can result

1 large increases in the drag coefficient.

Miller imeersed cylinde5 of 0.05, 13 Cr4 .15 m In diameter in sea water for a1moat a year. After drying, the

I ' growths were removed leaving the barniclencr0stsd, corroded - _{ware then tested in a Wind tunnel.} It was found that thedrag

43

coefficients associated with the cylinders were on the order of unity. The relative roughnesses were on the order of .02 and the range of testing extended beyond the usual Reynolds number transition range. In his oscillating water tunnel teats. Sarpkaya found that for a roughened cylinder the drag and inertia coefficients depend on the Reynolds number, the Keulegan-Csrpentar parameter and also the relative roughness of the cylinder. For a relative roughness of one-fiftieth, the drag coefficient as determined by Sarpkaya is nearly uniform with Reynolds number at a value of approximately 1.7 and with a minimum value of approximately 1.5. The corresponding results for steady flow are a drag coeffi-cient of 1.2 at the lower Reynolds numbers and decreasing to a minimum value of approximately .8.

Data Poorly-Conditioned for Determination of Drag and Inertia Coefficients Given that there are features on the data which are not repreaented by the Morison equation, which might be due to tha inapplicability of this equation, or due to experimental errors, then it is possible that some of the errors would

tend to correlate with the various terms in the Morison equation and carry through to errors in the drag and inertia coefficients. Generally, it will be shown in the following sections that data are usually well-conditioned for the determination of one or the other of the hydrodyonmic coefficients. In particular, if the drag forces tend to dominate, than the data are better conditioned for determining the drag coefficient and the inertia coefficient would tend to be contaminated .by the errors of various sources noted earlier. ConverBely, if the inertia force

consider waves of height, H, and period, T, propagating past a section of vertical cylinder of diameter, 0. At a distance, 8, from the bottom in a water depth, h, the maximum drag and inertia force components (f0)mjnd (fi)mer unit length are, according to linear wave theory

112 _{2 cosh kS 2}

Dmex - -r r 0

sinh kh

(f)

C3O1TD211 2coshkS

max

4 sinhkh

- wave angular frequency. k - wave number, h - waterdepth and S -vertical distance above the bottom. The ratio of the drag toinertia components is

_______ - eoah R(S)

_(f)

C., en sinh kb

(4)

for purposes of evaluating this ratio, CD/C4 nay be selected as 0.5. The ratio, R, can also. be related to Keulegan parameter, UnT

D

UT C.

I(S)

0 CD

and, of course, can also be related to the Sarpkaya-Garrison parameter,i /D in which 4 is the total relative displacement of the cylinder with respect to the

water

1(8) (6)

Figures 3, 4 and 5 present values of for S/h values of 0, 0.5 and 1.0, respec-tively. Each graph has ratios 1 of 0.25, 0.5, 3.0, 2 end 4. The use of these graphs readily provides a basil for evaluating the relative importance of drag and inertia force components.

The maximum total drag and inertia force components obtained by integrating Eqs. (2) and (3) up to the meanfree surface (n - 0) are

and if again the ratio CD/C is taken as 0.5; the R/D values for total force Components are presented in Figure 6 for I values of 0.25, 0.4, 1, 2 and 4.

In the following sections, methodology will be developed f or a morecomplete

5'seaamtot of the suitability of data for determining drag and inertia coefficienta.

(5)

component tends to dominate, them reasonable resolution in the inertia coefficient C.,D_H 2kb

can be expected along with contamination of the calculated drag coefficient.

If

the maximum dreg and inertia force coefficients are of the same order of magnitude, then reasonable resolution in both of these coefficients can be expected if the general quality of the data is good.

Dmax (7) (B) g

2 r

(1 + sinh kh tanh kh - pg METHODOLOGY The ratio I is

Consider measured wave and/or kinematics and wave force data.

It is intuitive

2kb

that if the drag forces are large, the data are batter conditioned for determining

R drag coefficients and vice versa. To establish which force component ia dominant,

(F)

_Dnax

CH

+_{einh 2kb} II ₍₉₎ tnnh kb 2s C.D 6 ₄₅ 44 ₅

4 300 200 150 100 50 .46 0 ç lU j _{LL -} - I ..U.US..UUU..IUIU1U1UI1h1

i..su

LCJ us u.i.I...UI.s...11U1a1U5

P

iU .uIr..UIUU UI.

I T11

:i

:fl;

U .: UU ..SPUUUUIVUUIUUUPU

.U. U

_{I.UUUIUUUUUNUUUU}

_U

-!

.

U U U

I...:

:1Jii!III!!I!ijlli!i

IiiiiiII

i:.-.Dh..i

h..u1:..:r'I

U

I

U -.u...UUUUUUUUUIU IUU IUUUUU -

-...UUUUUUUIUUUUUUU U1 .U..U.UIUUU WA

IIJU.pilK.0 1.ilIO.iPjMhiI

U

U

'

UUIUIUIUUUI

1151 UI US PIUUUUUUUIUUuUuuuP

U U

U..UI.UU.Ul.IUUUUU1AUU1

ISUUUU U...I.UUUUIUUSUIU UIUIIIUU UUSUU ...UUSUUUUUSUUUU5US .1 UNsU

...II.UIuIUIUUU

1.111.1.

'SI

U. IUSIUIUUUIUIIUUPII US U

...UU1UUUUU U U I

I

U

i

hhhi'idll L

11111114

I -

.u.0

hi

::

lISP

U.!P.P

. 0 0.1. 0.2 0.3 0.4 h/I.0

FIGURE 3 Required Values of HID to Result in VariousRatios of

Haxinun Drag to Inertia Force Conponents,at S - 0

7 U D

-...-0 FIGURE 4 0.1 0.2 0.3 0.4 0.5

Required Values of H/fl to Result In Various RatioB of Maxfmun Drag to Inertia ForceConponenta at S - 0.5 h

8

47

-...

rn'.

:

30 25 20 35 10 0 0 0.1 0.2 0.3 TilL0

FURE 5 Required Values of H/D to Result in Various )Isxixsum Drag to Inertia Force Component Ratios, S - Ti

04

0.5 (CD) sin es of Equal Error, C (CM)

(ii) Data We11-Cond.tioned for Deter-mining Drag Coeffieients

I

CD _(CD)Ojfl

figure 7 Interpretation 0f Error Surfaces

FIGURE 6 Required Values of HID to Result in Various

Ratios of MaxisuS Drag to Inertia Force

Components

' CD

(Ti) Data VeU-Conditiofled for Deter-mining Inertia Coefficients

!.

T

Ii

TT

I

Iii

IfflI

i

[L4

L

t

'4. 'i4-

-E

h

1:

±L IL

j

hr

Eli

4:t

ii

E' 111111

1NI:!ii:h GP

hILI

.i4

Time Domain Analysis

First consider analysis Y the time domain. The measured force per unit length data will be denoted by fm(ti) and the associated wave spectraldensity

by S(). The analysis is

considered to be the determination of the drag (CD) and inertia (CM) coefficients byfitting the measured data by the following equation

f(ti) -

a.

uj +

p (10)

in which the subscript "p" denotes a predicted value. For purposes here. we will consider a least squares solution asfoUowS

50 an2 0: CD

U+CM

(U) 2

-0:

CD

£ UU

+ CM

-

ff3

(12)

veroTE4t(CDUjiujI

CMl

Os-f

)2 (13)

and the overbars indicate averaging over all i values. e.s..

In general, simultaneous solution of Eqs. (U) and (12) leads to the following definitions of the least squares"best fit"CD CM

f

tJIJ!

mi i

i

ff3

_i

m

_i

i

(14) (16) where

For purposes here, it willsimplify the following discuseism greatly end not detract from the interpretation if we coutder the waves to be linear and the use of data over the full wave cycle. In this case, it can be shown rigorously that

ujul

a o (18)

The beat fit least squares CD and C are simplified to 2

i

(CM)IsIn

-4

i

4

-f U

i

4

Next consider the mean square error c12 as defined by Eq. (13)

-

(CpD\2

22_

-ci

-

i

+

(

2i_)

IC pD f 01rD2\

+2(P)\CMTi UjIUil

-2

(CD2) f U U

i

i

(17)

Eq. (21) def thee a quadratic "error surfacyhicb is aminimum at

(Cx)mi. The lines of constant error values, ci2 (Cm,Cn). are ellipses. Figure 7 Provides a qualitative interpretation for the cases of drag end inertia dominant

isa.

It ii clear from this figure that the steeper the slope of the error surface

12

with., for example, the drag coefficient, then the better the data are suited for evaluating the drag coefficient. To evaluate further the suitability of the data to resolve drag and inertia coefficiente, consider the change in drag and inertia coefficients from their minimum values associated with a given error in the value of the error surface.

1_

_(cacD+*cM

22

a

_5.

_{a22 (ACM2} + _ac ac (Ac.)(AcM) (22) acM acD

and, because the elope of the error surface at the minimum is zero (Eqs. ) and (12)1, Eq. (22) reduces to a

22

_a1

(g)2

C C +

''

ac

+ ;;;;r

2 a2 + ac0 acM

Prom Eqs. (21') and (14). we find

22

I 2(2i-_ 2_{) U1}

7

22

a acDacH. 0

The suitability of the data for determining drag (or Inertia) coefficients can be expressed from Eqs. (24) and (25) as the change in drag (or inertia) coefficient associated with a change in error surface, keeping

CM (or C.,) constant and vice versa. 13 52 11(1:

-c

c.

- _a

j mn D pD Jf (27) (28) i2

where if _{is snail, the data are veil-conditioned for determining CD (i.e.,} the minimum is sharply defined with repect to this cocfficiet) and a similar

comment applies to CM. _{A nenaure of the relative suitability of data for}

detetmining drag or inertia coefficients is provided by the ratio of the axes of the error ellipse. _{Defining this valus as}

CM

21/u14

Ui

and if the U end data were simple harmonic

U - U cos at 41nax a sin at

__i

4

8

- 4

(U,)2 2

and the ratio becomes

2 irD/4 a

which can be expressed in terms of the '-.4".' drag and inertia forces as

CM Dmsz

-

inax (33)

14

(29)

The error surface characteristics for a simple harmonic motion can be investi-gored by utilizing Eqs. (23) and (30) - (33). The error surface above the

niAizaum value can be expressed in dimensionless form as

-

-

-

j mm 13 LCD 2

1 /tmax'2

M ₂₁

Dmax

-

+

c-Figure 8 presents the error surface for the case of simple harmonic motion and

-Daax' inax - 2.0 for dimensionless moan square error contoursas presented on the left hand side of Eq. (36). It is seen that if the moan square error is on the order of 10 percent, then for this example the drag coefficient can range

between 4 50 percent of the calculated value and the inertia coefficient can range

between ± 85 percent of the calculated value. The question arises as to what value is dppropriate as a measure of the error. Although there is no clear basis

for estimating this value, it appears that some fraction of the minimum error would be reasonable. The basis is that this is a measure of the error in forces as

represented by the Horison equation. Some of this or a related error will correlate with the components of the !4orison equation, thereby contaminating the associated

coefficient. Another way of stating this is that if the error is of the same order of magnitude as one of the force components, than considerable caution should be exercised in accepting the value of the associated force coefficient which is similar to the ratio developed previously on an intuitive basis.

In interpreting Eq. (35) for application to data, as discussed previously any data set will always contain information not consistent with the predictor equat.lon

(in our case Morison's equation). Denoting this component of information as "noise," it is reaaonable that some of this noise will correlate spuriously such that the more poorly defined coefficient will contain errors. Table I provides an

intuitive basis for evaluating the suitability of data f or determining drag and inertia coefficients.

TABLE I

SUITABILITY OF DATA FOR DETERMINING DRAG AND INERTIA COEFFICIENTS

(36)

Range of R Data Ralatively

Well-Conditioned for Determining

0-1/4

C

1/44

C0aedC,

'4

CD

15 55

Frequency Domain nalyais

A second possible approach for determining the drag and inertia coefficients is by fitting measured pressure spectra to predicted, see Figure 9. Borsan Q) has presented a method in which, for the simplest case, the drag force is ltnssriz5 to yie1d

and for this case

56

S(a) -

( D)2 _{U2 5(a) +(C}

in which S(a) and S(a) are the spectra of the horizontal velocities and accelers-tions respectively, and is the mean square of the velocity for the level and time series under consideration. Before examining in detail the suitability of a set of data for determining CD and CM. it is instructive to compare analysis in the tine and frequency domain for a very Idealized case. Consider a force result-ing from simple harmonic motion which is exactly described by

f(t) -/

(38)

In the tine domain, there would be no difficulty in extracting a drag end inertia coefficient from these data using the equations developed in the earlier section. If the spectrum of the force is taken; however, according to the method described by Eq. (37), the phase information is lost and In easenco we have one

equation and two unknowns.

2 u2 _{S (a) +}

_S(a)

Sf(o) -

(j--)

and for the considered case of a single frequency 2 u2 Umax Su 2 Umax 2 17 (37) (39)

Sea Surface Spectrum

1

Transfer Punctions S (a) S (a) n

s(a)

S,(a) 1 1 correlation _

D)2su

+

t

Force Spectrum

Figure 9 Schematic for Determining Drag and Inartia Coefficients

from Measured Wave and Force Spectra

18 -I (CD21LL)25) (CD)ainl (CM)mjfl 57

j.

c-I A1 CD2 + A (-43)

where

4

Umax

lIT

'2

4

Az E (2!L)2₄ 2 u2_max5,(c)

The possible pairs of and c2 that satisfy Eq. (43) describe an ellipse with the actual pair just being one possible pair. Note this effect is a result of the loss of phase information when utilizing the energy spectrum of forces and

that the indeterminacy in CD and C.1 results even if the data are described

exactly by the predictor equation. Although this example represents an extrema idealization of the actual case, it does illustrate that if the wave spectrum

is very narrow, analysis in the frequency domain may not be wall-suited for

determining drag and inertia coefficients. Moreover, eve though the sea surface

spectrum any be broad, the resulting velocity and acceleration spectra atdepth

may be quite narrow from hydrodynamic filtering. This point is further illustrated

in Figure 10. where the transfer functions from sea surface to velocity and

acceleration spectra are presented versus angular frequency for approximately

mid-depth in a total water depth of 100 ft. Qualitatively, if the sea surface spectrum is so narrow that there are not substantial differences in the transfer functions over the width of the spectrum, then good results can not beexpected

from the spectral analysis approach.

0 1

Angular Frequency, .2 _(red/sac)

2

Figure 10 Example of Velocity ned Acceleration Transfer

Functions

19

to examinethe suitability of the spectral

method tO obtain drag sad inertia

in more detail, consider a east_5quas

procedure in which the

errors areminimized between themeasured and predicted

spectra. where fl

-

+ ( C002 2 + (CM

23_)2 S(a)

-(48)

and (Sf denotes the measured

force spectrum and the sum is now taken over the

frequencY domain. Eqs. (46) and (47) lead to definition

of the minimum dragand

inertia coefficiante

-i-0;

_aC

-0

83

s 151?oi

S4 s 55 2

S(a1) SfJ

if the error surface Cj2 CD2CM2 ± expanded

20 (47) (49) (SO) 59 a k

I

₀

-0.

u I I S Velocity Transfer ° 0 4.- function U 0.l0 C o I. S. I h - 100 ft

,'

'

Acceleration S.S e S 55 ft .&'-' Transfer C 01 Function

0.05

a 0 5' o

-

F 1% 0 ls U o

-

-I S S 0 I I U U 2015

Wave Period (eec)

10 8 6 5 4 4 1%/I._5

CMmi_n;;i . SlS4

S2S3

(22J

-

(8)2 (YD)4 + (cM2.!4 S,a2(Ci) Co

+ S2(a) + 2!

(__)2 u2

(CM !J_)2

S(oj) S(a )

IT

ui

.2 (C0 )2 u2

_{s(oj) S(o1)}

2 (CMO ₄ S'(o )

ui

end it is seen that rha ellipse axes are no longer parallel to theC0.C., we. The principal disadvantage of the spectral method for determining drag and inertia coefficients appears to be for very narrow band spectra for which in the limit it has been demonstrated that loss of phase results in inadequate information for determining drag and inertia coefficients.

Eq. (56) provides a basis for determining the changes in errors due to a change in one of the coefficients; however, the result is omewbat more complicated than

presented in Eqs. (27) and (28).

EVALUATION OF AVAILAELE )4SUREMENT RESULTS

In this section, several data bases will be evaluated with regard to their suitability for determining drag end inertia coefficients. Table II presents the field data sources and characteristics.

Field Data

The field data and analysis efforts have been described in References 2, 4, 5, 11, and 12. The data characteristics were utilized to calculate the ratio of

drag force for the maximum wave height and for one-quarter the maximum wave height. For Wave Projects I and II, the ratio was computed at three levels because measurements were made at a number of levels spanning the full depth. The results are presented in Tables III and IV.

It is seen that for Wave Project I, the ratio varied ,fron 0.26 to 2.69, whereas for Wave Project II, the range is from 0.28 to 2.06. The conclusion from thcae calculations is that these measurement programs included a sufficient range of piling diameters, wave heights, dynamometer levels, etc.; however, the sane weight should not be attached go drag coefficients obtained from all elevations and all wave heights.

The Bass Strait results are presented in Table IV. The ratio varies from 0.5 to 2.1 and the conclusions are similar to those for Wave Projects I and II.

(56) 22 Ii 0

z

C

s-.

iT I. 5.

Us-es

s.cs. -a. 514 we ITI r4 0.a U 5.0 44<14 C 4.T 0 OMan 0 C Sm

-.4 a, o lT UflIT4 a,

.

-,..

.a

r

_.a,e

O.1 In-I_.a,.

. .a,

11 I. 1 I%l OS .44 5 .1 II 45.1 4405 .0 S.44 C 14 sU M o n.n >151S1 0 U

'

P. U 044 o .4 .4 -4 a. P1 a, .4 .0 0. a 0 Ta Ins. a.-' In ., In Cl a 5 U I. 44 '4. 41 u 54

;,

Ia 5. U 5 . '4 '4 Sb U 5

.,

Ia 5. II 5 an 543 5 5 61 60 21

TABLE III

RATIOS OF MAXIMUM DRAG TO INERTIA FORCE COMPONENTS FOR WAVE PROJRCT I AND II DATA

4

aDat5

Sarpkaya'° teat conditions (9) were chosen tO illustrate the method to laboratory results. Based on the previouslY noted dimensionless error

of 0.1 4eteriflhnd by SarphaYa, it can be shown thathis data 5hould not contain 5puriOUS effects of the type noted here for KeulegaD_CarPentec numbers, K,

component of greatest consequence.

REFERENCES

Boraaa. L.E., "The Spectral Density for OceanWave Forces," y43ihltc

______________ Rapt. No. H. 9-8. Berkeley, Calif., Dec., 1965.

Dean. K. C. and 0. N. Asgaard, "Wave Forces: Data Analysis and Engineering Calculation Method," .7. Pet. Tech., pp. 368-375, March, 1970.

Dean, N. C. and La Mehauto. "Experimental Validity of Water Wave Theories," Paper presented at the 1970ASCE Structural Engrg. Coal., Portland. Oregon, April 8, 1970.

Evans, D. .7., "Analysis of Way; Force Data," Preprinta. 1969 hare Technology Conf., Vol. I, Paper No. 1005. pp. 1-51 to 1-70.

5, K.tm, Y. K. and H. C. Iiibbard, "Analysis of Simultaneous Wave Force and Water Particle Velocity Measurements, Proc. 1975 Offshore Tech. Cent., Vol. £ Paper 10. 2192, pp. 461-470.

6. Le Mehaute. II.. D. Divoky and A. tin, "ShallowW.itcr Waves: A Comparison

of Theory and Experiment." Proc.. 11th. Coat. cia Coastal F.ngr., Chip. 7,

1968.

24 63

F

Data Source Pile Ratia: Dax1tITlax in the range

Diameter Relative Distance Above Bottom, S/b

I (ft) 1 a K a 100

S/b - 0 s/h - 0.5 S/h - 1.0 a_ma'/4 hhiss' Hma'/4 8mar/4 Baa'

which is approximatelythe range investigatedbe Sarpkayl. The conclustoD is_{to maintain}

2 0.51 2.05 0.55 2.21 0.67 2.69 therefore, that, by IcnoLng

his kinematicS wail Sarpkala was able

Wave Proj act I .34 1.37 .37 1.47 45 1.80

a good accuracy ever the entire range of his test conditions.

4 .26 1.03 .28 1.10 .34 1.35 SUMMARY AND CONCLUSIONS

Wave ProjeCt 1113.71 0.28 1.13 .34 1.34 .52 2.06 A method baa beenpresented to investigate the error surfaces resulting from frequencY domain. For

the least squares analysis procedure inthe time domain end

a given set of data and analysis results. a procedure baa been suggested for providing an upper limit on the errors in the drag and inertia coefficients._{force maasure'}

The procedure should also prove useful in the design of wave_is in

TABLE IV meat installations to ensure that the desired relative

accuracy obtained

the coefficients of interest.

-relative Finally. Figures 3 - 6 should be of assistance in assessing the RATIOS OF MAXIMUM DRAG TO INERTIA FORCE C0MPONTS

FOE BASS STRAIT

suitability of a wave forcemeasurement program f or determininS drag and inertia_{the force}

Wave Height _Du.ax' I>niax coefficients and also In design applications, In quickly atermifling 0.5

2,1

23 62

7. Miller. B. L., "The Hydrodynamic Drag of Roughened Circular Cylinders," Meeting. The Royal Institution of Naval Architects, Paper No. 9,

1976.

B. Nerison. 3. R., O'Brien, H. P., Johnson, 3. V. and Schaaf, S. A., "The

Force Exerted by Surface Waves on Piles," Trans., LIME (1950), 189,149-154.

9,Sarpkaya, T. "Vortex Shedding and Resistance in Harmonic Plow About Snooth and Rough Circular Cylinders at High Reynolds Numbers," Kept. No. NPS-59SL76021. U.S. Naval Post Graduate School, Monterey, Calif., 1976.

j0,Sarpkaya. P., "Periodic Flow About Cylinders tn Critical Regina." Abstract 15th International Cont. on Coastal Engrp., Hawaii, 1976, pp. 434-437. 11.Thrasher, L. W. and P. N. Aagaard, "Measured Wave Force Data on Offshore

Platforms," Preprints, 1969 Offshore Tech. Conf., Vol. 1, Paper No. OTC1006, pp. 1-71 to 1-82.

l2JJheeler. .1. D., "Method for Calculating Forces Produced by Irregular Waves," Preprint, 1969 Offshore Tech. Cant., Vol. I, Paper No. 1007, pp. 1-83 to 1-94. 64 23

Boss

'76

.BEPIAVtOUR OF OFF- -SHORE STRUOflJREC. The Nsrwoglsfl ?flsUhdS d ToehflsIOGy

LARGE SCALE LIQUEFACT1( TESTS

g.H. do Leeuw

Delft Soil NechafliCn Leboratoly

The Nethollaflds

Abstract

A IS x 27.7 square metres caisson with a height of 10 metres. weighing 1785 tons, was placed in 7 metres deep water gnd tent loaded with a prograemo ofhorizontal cyclic loads up to 9000 kN with frequencies up to iRz. The measurements of mere than 120 sensors were stored on magnetic tape to be processed by computer at a

later date, while the moat relevant results., wererecorded on analogue recordore to enable a visual control of thebehaviour of' the caisson and the subsoil dur-ing the test. Total stresses in variotsdirections, pore water pressures and deformations of the subsoil were msured. Thecaisson displacements were de-termined with the aid of lasers and optical methods.

Tests were run first on a 3oae1y packed sandy seabottom and later on a denai-tied aubsoil to study liqiofaction phenomena, generation and dissipation of pore pressures and in generbl to check the results of various methods used to predict

,0

ft

Four predictiOaTethOd5 used the finite element approach. Furthermore predict-ions were mad1 using plastic analysis. Two predictpredict-ions were made using model-test tee es.

Test -'-up, instrumentation end execution of the tests are described. Some re-1ev- results are shown.

performance.