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Reprinted: 24-03-2001Website: www.shipmotions.nl

Report 0809-P, November 1988,Delft University of Technology,Ship Hydromechanics Laboratory,Mekelweg 2, 2628 CD Delft,The Netherlands.

Model Experiments on Jack-Up Platform Hydrodynamics

J.M.J. Journée, W.W. Massie, B. Boon and R. Onnink

1. INTRODUCTION

This report describes the experimentscarried out with two simplified modelsshowing the principals of elevated jack-up platforms. The purpose of theseexperiments is to investigatehydrodynamic as well as structural non-linearities in the interaction between thestructure and water.As such, this model design and testingprogram forms a first step in an intendedseries of hydrodynamic model andpossibly prototype measurements ofhydrodynamic forces and dynamicstructural response of jack-up platformsin both regular and irregular waves. Thewhole series of these hydrodynamicmeasurements is in turn, only a part ofthe entire project to investigate thedynamic behaviour and fatigue life ofjack-up platforms in order to developmore appropriate design criteria andevaluation methods for such platforms.This involves also diverse topics such as

fatigue testing of joints, computersimulations and reliability analysis usingalso non-linear effects.Since the design of any structure todayinvolves computer simulations, thecomputer simulation of the non-lineardynamic behaviour of an elevated jack-up platform will play an important rolein the total project. Proper representationof the hydrodynamic interaction of thestructure with the sea is essential for thesuccess of a dynamic simulation. This istherefore one of the first items to beinvestigated, at least in a preliminaryway.The model tests described here areintended to provide significant insightinto the non- linearities involving theconversion from hydrodynamics toforces acting on jack-ups and theinfluence of the structural response onthose loads. Also they will provide a firstset of data against which a non-linearcomputer simulation can be checked.

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2. MODEL DEFINITION

Purpose of the Experiments

The traditional quasi-static calculation ofthe response of a jack-up to waves isbased upon the following assumptions:• A description of hydrodynamic

forces, determined for an (assumed)fixed structure from the local flowconditions, using a linearisedMorison equation.

• A design wave (one wave with acertain height and period) approachis used, while a possible current istaken into account by adding thecurrent velocity to the wave particlevelocities.

• A rigid deck, with rigid deck-legconnections and legs hinged (orfixed) at the seabed.

• A geometric non-linearity, whichoccurs with jack-ups as a result ofsecondary moments generated whenthe deck load becomes eccentric tothe reaction forces during dynamichorizontal displacements.

The response to irregular rather thanregular waves is often determined byadding the wave particle velocities of theindividual waves and the current, andusing this combined velocity in theMorison formula.A dynamic calculation of the responsecan be performed in two different ways.The first method is a time domainsimulation of the structural responseusing the absolute water particlevelocities as input into the Morisonformula. The other method is asimulation in the frequency domainusing a linearised Morison approach anda dynamic amplification for eachindividual wave.

A more correct dynamic simulation mayhave to take into account relative ratherthan absolute water particle velocities, inother words take into account theinteraction between hydrodynamic loadsand structural responses.To gain some information to make thislatter approach possible modelexperiments are necessary. In particularthese are required when wavefrequencies are approaching the naturalfrequency of the jack-up and responsemotion amplitudes do have anappreciable influence on the relativewater particle velocity.

Model Particulars

As explained above, the purpose of themodel tests is to gain insight in asituation where structural motionresponse will have significant impact onthe relative water particle velocities.Also it is important to investigate theplatform behaviour for wave frequenciesin the vicinity of the resonant frequencyof the platform. These requirements to alarge degree dictate the dimensioning ofthe model. It is deemed advisable to usemaximum possible model dimensions,which are dependent on the available testfacilities.For these experiments use has beenmade of Towing Tank I of the ShipHydromechanics Laboratory during aperiod that a new one replaced thetowing carriage. Because of theseactivities the maximum available waterdepth in the basin was restricted to about2 meters.This 2.0 meters depth dictated a leglength slightly more than that. Wavespossible in the basin had a frequencyranging from about 0.7 until 1.3 Hz anda wave amplitude up to about 0.040meter. The full range possible was used

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in the tests. In order to avoidcomplications in this stage of theresearch program it was decided toprovide no rotation restraint at the legfooting.With the diameter as a variable thehydrodynamic loads were determined,neglecting the role of roughness. In fullscale it is common in a quasi-staticcalculation to allow maximumdeflections of a jack-up platform in theorder of 2 percent of the free leg lengthfor maximum design conditions. It wasdecided to aim for similar deflections inthe maximum model test conditions.This, together with an average waveperiod of 1.0 seconds and a maximumwave amplitude of 0.040 meter, dictatedthe IE ⋅ value for the legs for variousleg diameters. Given a leg diameter and

IE ⋅ value, the leg wall thickness onlydepends upon the elasticity modulus ofthe leg material chosen. Realistic valueswere found for relatively large diameterPVC legs and small diameter copperlegs.As the model should be tested around itsresonance a platform natural period ofaround 1.0 seconds, being the averagewave period, was considered to benecessary. With the leg dimensions andmaterials given this dictated the mass ofthe deck structures for the two models.Two different deck masses for theslender leg jack-up model were decidedupon, in order to check the influence onthe response of a shift in platformnatural frequency and the impact of thesecond order leg bending. It waschecked that buckling risk would benon-existent. The leg spacing wasdetermined by the whish to studypossible total load cancellation as aresult of spatial phase differences in thehydrodynamic loading of the variouslegs. Based upon a mean wave period of

about 1.0 seconds the leg spacing wastaken as 0.700 meter.

Table 1 Dimensions of the 3 Models

Figure 1 Model Dimensions

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The dimensions of the jack-up modelsare shown in Table 1 and Figure 1.

Figure 2 Pictures of Model No. 1 inExperimental Set-UP

Figure 2 shows two pictures taken frommodel number 1 in the towing tank,before filling the tank with water.

Model Scale

It is important to note that these modelsare not intended to represent actual full-scale jack-ups. Rather they should beconsidered as very small jack-ups atscale 1:1. Thus scale effects are non-existent. Nevertheless these small jack-ups possess characteristics that arecomparable to those of normal sizedjack-ups. They allow studying thespecial features that are subject of thepresent research, i.e. the effect of non-linearities in wave loading and responsesin the area near platform resonance

where interaction between those isimportant.

Dimensions of the Three Models

Model Dimensions

Pictures of Model No 1 in ExperimentalSet-Up

3. EXPERIMENTAL SET-UP

The time and budget limitations for thistest series prevented the design orpurchase of specialised instrumentation.The project was set up for "off the shelf"instrumentation. Such equipment wasavailable at the Ship HydromechanicsLaboratory for the measurement offorces, accelerations and displacements.However, none of these was designedfor submerged operation.

Forces

Nine dynamometers, based on strain-gauge measurement of bending resultingfrom shear forces, were coated with aflexible water proofing material so thatthey could be used while submerged.Experience had already been gained withthis in other tests. These newly coatedunits were first tested and calibratedbefore installation in the present set-up.The results of the calibrations are iven inAppendix I.Force measurements were limited to theregistration of the force componentsalong each of the three axes with theorigin at the base of each leg A, B or C:• x along the tank, positive toward the

wave maker• z vertical, positive upwards• y perpendicular to these according to

a right-handed axis system.

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The flexibility of the legs precluded thatthe static indeterminance of the systemcaused problems. Careful attention todimensions as well as installationprocedures made it possible to keep suchresulting residual loads within a rangewhich could be discounted via thecalibration and balancing.The leg hinges and dynamometers areshown in the figures below.

Figure 3 Picture of Leg Hinges andDynamometers

Figure 4 Close-Up Picture of LegHinges and Dynamometers

These nine dynamometers were labeledAx, Ay, Az, Bx, By, Bz, Cx, Cy and Cz

respectively. The correspondingmeasured forces were denoted XA, YA,ZA, XB, YB, ZB, XC, YC and ZC,respectively.A tenth dynamometer Dx was used tomeasure the forces due to waves on thelegs with the platform held motionless.The dynamometer was fixed in spaceand connected with the platform atlocation D of the deck by means of adouble cardanic coupling mechanism.This force was indicated by XD and theresults of the calibration ofdynamometer Dx are given in AppendixI.

Accelerations and Displacements

An 5-g accelerometer was mounted onthe deck in such a way that it measured xand y components of the acceleration atthe location D at the deck of theplatform. These accelerations wereindicated by Dx&& and Dy&& .Additionally a bit redundantly, thehorizontal x and y displacements of thedeck were measured at locations A andC, so as to detect any possible rotations.These displacements, indicated by xA, yA,xC and yC., respectively, also provide fora direct check of the accelerationmeasurements.

Waves

A two-wire conductance wave probe, asnormally used in this towing tank,measured the waves. The wave meterwas mounted adjacent to the platform sothat its record is in phase with that of the"windward" leg A. This wave elevationwas indicated by Aζ .

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Calibrations

The various measuring elements, such asforce meters, displacement meters andaccelerometers were individuallycalibrated before installation. The resultsof these calibrations are summarised inAppendix I. Later calibrations were onlycarried out in a more direct way.The natural frequency of the platformhas been determined. Since model 1 hasfirst been installed in a dry tank, it waspossible to determine its naturalfrequency both in air and in still water.For models 2 and 2-M only a naturalfrequency determination in still waterwas possible.

4. TESTING PROGRAM

General Purpose

The general purpose of the testingprogram was to determine the influenceof the platform motion response on thehydrodynamic non-linearity asmanifested via quadratic drag and theensuing impact on the superpositionprinciple as often used in navalarchitecture. The results of this work areessential for the description of thehydrodynamics of jack-up platforms, tobe used in computer simulations.Data from the various test runs wererecorded in an analog form, so that itmay be worked out in a variety of waysin the future. Additionally, significantdata were simultaneously displayedvisually on an UV paper-tape recorder asa check.

The "traditional naval architectsapproach" of examining only the firstharmonics of responses was notfollowed in these tests. One standard

processing step will be the determinationof spectra for the various signalsrecorded. In some cases both peak andRMS values of the recorded (irregular)signals will be of interest.Data from a number of the runs will beused to check the computer simulations.This can be done both with regular andirregular waves.

Regular Waves

Results of experiments carried out inregular waves, using at least threedifferent wave heights and a range ofwave periods which includes the naturalperiod of the structure in water, will beused to determine the basic response ofeach structure.If the behaviour is completely linear,then a plot of deck displacementamplitude divided by the waveamplitude versus wave frequency willyield a family of identical curves,showing the well-known resonancepeak. The degree to which these curvesare individual, thus wave amplitudedependent, is a indication of the non-linearity of the situation.

Non-linearities such as quadratic draglead to the phenomena that a wave(input) at one frequency yields forcecomponents (output) at this samefrequency as well as at higher harmoniesof this. Conversely, the presence of extraenergy at high frequencies in output ascompared to input can be an indicationof non-linear behaviour. Forcecomponents in the y-direction can implythe presence of lift forces. However,these are only expected to be of smallamplitude, in particular for the modelwith the large diameter legs.

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Paired Regular Waves

A first check of the superpositionprinciple, which makes the study of alinear(ised) system so attractive, is toexpose the models to a wave consistingof a superposition of two regular wavesof different frequency as used above.Such paired waves, themselves, show awell-known beat pattern with alternatingsegments of large and small amplitude.The wave frequencies were chosen suchthat they "embrace" the naturalfrequency of the model; one frequency isbelow the natural frequency and oneabove it. If linearity and superposition ispreserved, then the result of this testshould be predictable from the resultswith regular waves.

Wave Spectra Response

The response of the model to waveshaving a known, so measured, energyspectrum was also determined. It is notdeemed necessary to generate a wavespectrum in the model, which exactlysatisfies a theoretical model such as thatdetermined by the mean JONSWAPspectrum. The linearised responsefunction, determined by dividing theoutput spectrum by the input wavespectrum can be compared to thatdetermined using regular waves.

5. SELECTED EXPERIMENTALRESULTS

As a check a few selected experimentalresults, derived from the UV recordings,were examined during the experiments.The data, used for this purpose, aretabulated in the summary of theexperiments in Appendix I. These resultsare given below in graphs withoutdetailed discussion.

Before starting the experiments inwaves, the platform deck of modelnumber 1 was loaded by static forces inthe x-direction. The resulting verticalforces at the hinged connection of thethree legs to the bottom, ZA, ZB and ZC

were measured. The results are given inFigure 5. It is clear that the sum of thesemeasured vertical forces, ZA+ZB+ZC, hasto be zero. However the figure showsthat a force of about 5 N remains.

Figure 6 shows the displacements in thex-direction, due to these static loads inthe x-direction.

Figure 7 shows the amplitudes of thehorizontal displacement in the x-direction of the platform deck of modelnumber 1 in simple regular waves withthree different nominal amplitudes.

Figure 8 shows the amplitudes of a waveforce component measured at the decklevel of the fixed model number 2 insimple regular waves with one nominalamplitude.

Figure 9 shows the amplitudes of thehorizontal displacement in the x-direction of the platform deck of thismodel in simple regular waves with fivenominal amplitudes. These force anddisplacement amplitudes are also shownfor model number 2-M in the Figure 10and Figure 11 for three nominal waveamplitudes.

Figure 12 shows the horizontaldeflections of the platform deck ofmodel number 2, due to a statichorizontal load on the platform deck inthe x-direction. These horizontaldeflections are also shown for modelnumber 2-M in Figure 13.

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Figure 5 Vertical Reaction Forcesdue to a Static Horizontal Load in thex-Direction on the Platform Deck of

Model No 1

Figure 6 Horizontal Deflection of thePlatform Deck of Model No 1, due to a

Static Horizontal Load in the x-Direction on the Platform Deck

Figure 7 Amplitude of the HorizontalDisplacement in the x-Direction of the

Platform Deck of Model No 1 inSimple Regular Waves

Figure 8 Amplitude of a Wave ForceComponent of Model No 2 in Simple

Regular Waves

Figure 9 Amplitude of the HorizontalDisplacement in the x-Direction of the

Platform Deck of Model No 2 inSimple Regular Waves

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Figure 10 Amplitude of a WaveForce Component of Model No 2-M in

Simple Regular Waves

Figure 11 Amplitude of theHorizontal Displacement in the x-Direction of the Platform Deck ofModel No 2-M in Simple Regular

Waves

Figure 12 Horizontal Deflections ofthe Platform Deck of Model No 2, dueto a Static Horizontal Load in the x-

Direction on the Platform Deck

Figure 13 Horizontal Deflections ofthe Platform Deck of Model No 2-M,due to a Static Horizontal Load in the

x-Direction on the Platform Deck

6. ACKNOWLEDGEMENT

The authors are indebted to Dr. Sv.Spassov (Research Fellow from theBulgarian Ship Hydrodynamics Centrein Varna) and Mr. P.J. Spaargaren(student-assistant of the Faculty of CivilEngineering) for their contributions tothis project; especially for thedimensioning of the jack-up models.Their work has been reported in anInternal Technical Report of the ShipHydromechanics Laboratory:

Spassov Sv. and P.J. SpaargarenOn Jack-Up Platforms andMarine Riser Dynamics,Delft University of Technology,Ship HydromechanicsLaboratory, Report No. 0793-M,May 1988.

APPENDIX I:SUMMARY OF EXPERIMENTS

The experiments were carried out inTowing Tank Number I of the ShipHydromechanics Laboratory during themonths July and August 1988.

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The width of this tank is 4.200 meter.The water depth was 2.004 meter duringall experiments and the constanttemperature of the fresh water was about17.0 0C.The experiments were carried out withthree jack-up models, in order numberedby 1, 2 and 2-M. Jack-up number 2-M isidentical to jack-up number 2, butmasses of 1.05 kg are added at the decklevel on the centerline of each leg.The axis system and the location aregiven in the figure below.

Figure 14 Axis System and Locationin Towing Tank I

The calibration factors of the 9dynamometers at the lower leg-ends arelisted below:Ax: 1 Volt = 46.2 NAy: 1 Volt = 42.7 NAz: 1 Volt = 41.5 NBx: 1 Volt = 47.8 NBy: 1 Volt = 43.6 NBz: 1 Volt = 46.6 NCx: 1 Volt = 44.7 NCy: 1 Volt = 43.0 NCz: 1 Volt = 44.8 NThe calibration factor of thedynamometer used to measure the forcein the space-fixed top-side of theplatform, caused by the wave forces, isgiven by:Dx: 1 Volt = 20.0 NAn instrumentation recorder was usedfor registration of the various signals aslisted below:Channel 01: force signal XA

Channel 02: force signal ZA

Channel 03: force signal XBChannel 04: force signal ZB

Channel 05: force signal XCChannel 06: force signal ZCChannel 07: displacement signal xA

Channel 08: displacement signal xCChannel 09: displacement signal yA

Channel 10: displacement signal yCChannel 11: not availableChannel 12: acceleration signal Dx&&Channel 13: wave elevation signal ζ

The tape speed was 17/8 inch per second.The signals on channels 12 and 13 wererecorded directly, via a modulator-demodulator. A reference voltage of

2± Volt or 1± Volt was given on thetapes regularly too. All requiredinformation for data processing, such ascalibration data, amplification factors,etc., was stored on the voice channel ofthe recorder.An UV paper-tape recorder was used forregistration of the various signals aslisted below:Channel 01: acceleration signal Dy&&Channel 02: acceleration signal Dx&&

(also on IR)Channel 03: displacement signal Cx

(also on IR)Channel 04: displacement signal Ax

(also on IR)Channel 05: displacement signal Cy

(also on IR)Channel 06: displacement signal Ay

(also on IR)Channel 07: force signal AY

or force signal DXChannel 08: force signal CYChannel 09: force signal BYChannel 10: not available

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Channel 11: wave elevation signal ζ(also on IR)

Channel 12: not used

The standard calibration factors of thesesignals are as follows:ζ : 1.0 cm = 1.0 cm on UV

Ax : 1.0 cm = 2.0 cm on UV

Ay : 1.0 cm = 2.0 cm on UV

Cx : 1.0 cm = 2.0 cm on UV

Cy : 1.0 cm = 2.0 cm on UV

Dx&& : 1.0 g = 14.14 cm on UV

Dy&& : 1.0 g = 14.14 cm on UV

AY : 1.0 V = 42.7 N = 5.0 cm on UV

BY : 1.0 V = 43.6 N = 5.0 cm on UV

CY : 1.0 V = 43.0 N = 5.0 cm on UV

DX of jack-up number 1:1.0 V = 20.0 N = 1.0 cm on UV

DX of jack-up number 2 and 2-M:1.0 V = 20.0 N = 4.5 cm on UV

For a few runs an enlarged scale wasused for the wave elevation signal on thepaper-tape. This is marked in the tableswith a comment.When looking in the direction oppositethe paper transport, (standing in front ofthe recorder) the positive direction of thesignals is a movement from left to righton the UV recorder. Left is also definedby the numbered side of the paper-tape.

During the experiments in irregularwaves the transient time after starting thegeneration of the waves and beforestarting the registration of the signalswas about three minutes. This was doneto get a proper registration of thebehaviour of the platform. For each runin irregular waves the measuring timewas about 20 minutes.

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APPENDIX II: TABLES WITH EXPERIMENTAL DATA

In the following tables all experiments are listed in the order as they have been carriedout. In these tables some runs are marked with "free oscillation". These experimentswere carried out in still water. If no counter reading is given, then the signals wererecorded on the UV paper-tape recorder only.The mark "reference signal" means that a reference voltage of 2± Volt or 1± Volt wasgiven on the instrumentation recorder.

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