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  1. 1. Reprinted: 24-03-2001 Report 0809-P, November 1988,Website: 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. Onnink1. INTRODUCTION fatigue testing of joints, computer simulations and reliability analysis usingThis report describes the experiments also non-linear effects.carried out with two simplified models Since the design of any structure todayshowing the principals of elevated jack- involves computer simulations, theup platforms. The purpose of these computer simulation of the non-linearexperiments is to investigate dynamic behaviour of an elevated jack-hydrodynamic as well as structural non- up platform will play an important rolelinearities in the interaction between the in the total project. Proper representationstructure and water. of the hydrodynamic interaction of theAs such, this model design and testing structure with the sea is essential for theprogram forms a first step in an intended success of a dynamic simulation. This isseries of hydrodynamic model and therefore one of the first items to bepossibly prototype measurements of investigated, at least in a preliminaryhydrodynamic forces and dynamic way.structural response of jack-up platforms The model tests described here arein both regular and irregular waves. The intended to provide significant insightwhole series of these hydrodynamic into the non- linearities involving themeasurements is in turn, only a part of conversion from hydrodynamics tothe entire project to investigate the forces acting on jack-ups and thedynamic behaviour and fatigue life of influence of the structural response onjack-up platforms in order to develop those loads. Also they will provide a firstmore appropriate design criteria and set of data against which a non-linearevaluation methods for such platforms. computer simulation can be checked.This involves also diverse topics such as 1
  2. 2. 2. MODEL DEFINITION A more correct dynamic simulation may have to take into account relative ratherPurpose of the Experiments than absolute water particle velocities, in other words take into account theThe traditional quasi-static calculation of interaction between hydrodynamic loadsthe response of a jack-up to waves is and structural responses.based upon the following assumptions: To gain some information to make this• A description of hydrodynamic latter approach possible model forces, determined for an (assumed) experiments are necessary. In particular fixed structure from the local flow these are required when wave conditions, using a linearised frequencies are approaching the natural Morison equation. frequency of the jack-up and response• A design wave (one wave with a motion amplitudes do have an certain height and period) approach appreciable influence on the relative is used, while a possible current is water particle velocity. taken into account by adding the current velocity to the wave particle Model Particulars velocities.• A rigid deck, with rigid deck-leg As explained above, the purpose of the connections and legs hinged (or model tests is to gain insight in a fixed) at the seabed. situation where structural motion• A geometric non-linearity, which response will have significant impact on occurs with jack-ups as a result of the relative water particle velocities. secondary moments generated when Also it is important to investigate the the deck load becomes eccentric to platform behaviour for wave frequencies the reaction forces during dynamic in the vicinity of the resonant frequency horizontal displacements. of the platform. These requirements to a large degree dictate the dimensioning ofThe response to irregular rather than the model. It is deemed advisable to useregular waves is often determined by maximum possible model dimensions,adding the wave particle velocities of the which are dependent on the available testindividual waves and the current, and facilities.using this combined velocity in the For these experiments use has beenMorison formula. made of Towing Tank I of the ShipA dynamic calculation of the response Hydromechanics Laboratory during acan be performed in two different ways. period that a new one replaced theThe first method is a time domain towing carriage. Because of thesesimulation of the structural response activities the maximum available waterusing the absolute water particle depth in the basin was restricted to aboutvelocities as input into the Morison 2 meters.formula. The other method is a This 2.0 meters depth dictated a legsimulation in the frequency domain length slightly more than that. Wavesusing a linearised Morison approach and possible in the basin had a frequencya dynamic amplification for each ranging from about 0.7 until 1.3 Hz andindividual wave. a wave amplitude up to about 0.040 meter. The full range possible was used 2
  3. 3. in the tests. In order to avoid about 1.0 seconds the leg spacing wascomplications in this stage of the taken as 0.700 meter.research 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 E ⋅ I value for the legs for variousleg diameters. Given a leg diameter and E ⋅ I value, the leg wall thickness onlydepends upon the elasticity modulus ofthe leg material chosen. Realistic values Table 1 Dimensions of the 3 Modelswere 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 Figure 1 Model Dimensions 3
  4. 4. where interaction between those isThe dimensions of the jack-up models important.are shown in Table 1 and Figure 1. Dimensions of the Three Models Model Dimensions Pictures of Model No 1 in Experimental Set-Up 3. EXPERIMENTAL SET-UP The time and budget limitations for this test series prevented the design or purchase of specialised instrumentation. The project was set up for "off the shelf" instrumentation. Such equipment was available at the Ship Hydromechanics Laboratory for the measurement of forces, accelerations and displacements. However, none of these was designed for submerged operation. Figure 2 Pictures of Model No. 1 in Forces Experimental Set-UP Nine dynamometers, based on strain-Figure 2 shows two pictures taken from gauge measurement of bending resultingmodel number 1 in the towing tank, from shear forces, were coated with abefore filling the tank with water. flexible water proofing material so that they could be used while submerged.Model Scale Experience had already been gained with this in other tests. These newly coatedIt is important to note that these models units were first tested and calibratedare not intended to represent actual full- before installation in the present set-up.scale jack-ups. Rather they should be The results of the calibrations are iven inconsidered as very small jack-ups at Appendix I.scale 1:1. Thus scale effects are non- Force measurements were limited to theexistent. Nevertheless these small jack- registration of the force componentsups possess characteristics that are along each of the three axes with thecomparable to those of normal sized origin at the base of each leg A, B or C:jack-ups. They allow studying the • x along the tank, positive toward thespecial features that are subject of the wave makerpresent research, i.e. the effect of non- • z vertical, positive upwardslinearities in wave loading and responses • y perpendicular to these according toin the area near platform resonance a right-handed axis system. 4
  5. 5. The flexibility of the legs precluded thatthe static indeterminance of the system These nine dynamometers were labeledcaused problems. Careful attention to Ax, Ay, Az, Bx, By, Bz, Cx, Cy and Czdimensions as well as installation respectively. The correspondingprocedures made it possible to keep such measured forces were denoted XA, YA,resulting residual loads within a range ZA, XB, YB, ZB, XC, YC and ZC,which could be discounted via the respectively.calibration and balancing. A tenth dynamometer Dx was used toThe leg hinges and dynamometers are measure the forces due to waves on theshown in the figures below. legs with the platform held motionless. The dynamometer was fixed in space and connected with the platform at location D of the deck by means of a double cardanic coupling mechanism. This force was indicated by XD and the results of the calibration of dynamometer Dx are given in Appendix I. Accelerations and Displacements Figure 3 Picture of Leg Hinges and An 5-g accelerometer was mounted on Dynamometers the deck in such a way that it measured x and y components of the acceleration at the location D at the deck of the platform. These accelerations were indicated by x D and &&D . && y Additionally a bit redundantly, the horizontal x and y displacements of the deck were measured at locations A and C, so as to detect any possible rotations. These displacements, indicated by x A, yA, x C and yC., respectively, also provide for a direct check of the acceleration measurements. Waves A two-wire conductance wave probe, as normally used in this towing tank, measured the waves. The wave meter was mounted adjacent to the platform so that its record is in phase with that of the "windward" leg A. This wave elevation Figure 4 Close-Up Picture of Leg was indicated by ζ A . Hinges and Dynamometers 5
  6. 6. Calibrations processing step will be the determination of spectra for the various signalsThe various measuring elements, such as recorded. In some cases both peak andforce meters, displacement meters and RMS values of the recorded (irregular)accelerometers were individually signals will be of interest.calibrated before installation. The results Data from a number of the runs will beof these calibrations are summarised in used to check the computer simulations.Appendix I. Later calibrations were only This can be done both with regular andcarried out in a more direct way. irregular waves.The natural frequency of the platformhas been determined. Since model 1 has Regular Wavesfirst been installed in a dry tank, it waspossible to determine its natural Results of experiments carried out infrequency both in air and in still water. regular waves, using at least threeFor models 2 and 2-M only a natural different wave heights and a range offrequency determination in still water wave periods which includes the naturalwas possible. period of the structure in water, will be used to determine the basic response of each structure.4. TESTING PROGRAM If the behaviour is completely linear, then a plot of deck displacementGeneral Purpose amplitude divided by the wave amplitude versus wave frequency willThe general purpose of the testing yield a family of identical curves,program was to determine the influence showing the well-known resonanceof the platform motion response on the peak. The degree to which these curveshydrodynamic non-linearity as are individual, thus wave amplitudemanifested via quadratic drag and the dependent, is a indication of the non-ensuing impact on the superposition linearity of the situation.principle as often used in navalarchitecture. The results of this work are Non-linearities such as quadratic dragessential for the description of the lead to the phenomena that a wavehydrodynamics of jack-up platforms, to (input) at one frequency yields forcebe used in computer simulations. components (output) at this sameData from the various test runs were frequency as well as at higher harmoniesrecorded in an analog form, so that it of this. Conversely, the presence of extramay be worked out in a variety of ways energy at high frequencies in output asin the future. Additionally, significant compared to input can be an indicationdata were simultaneously displayed of non-linear behaviour. Forcevisually on an UV paper-tape recorder as components in the y-direction can implya check. the presence of lift forces. However, these are only expected to be of smallThe "traditional naval architects amplitude, in particular for the modelapproach" of examining only the first with the large diameter legs.harmonics of responses was notfollowed in these tests. One standard 6
  7. 7. Paired Regular Waves Before starting the experiments in waves, the platform deck of modelA first check of the superposition number 1 was loaded by static forces inprinciple, which makes the study of a the x-direction. The resulting verticallinear(ised) system so attractive, is to forces at the hinged connection of theexpose the models to a wave consisting three legs to the bottom, ZA, ZB and ZCof a superposition of two regular waves were measured. The results are given inof different frequency as used above. Figure 5. It is clear that the sum of theseSuch paired waves, themselves, show a measured vertical forces, ZA+ZB+ZC, haswell-known beat pattern with alternating to be zero. However the figure showssegments of large and small amplitude. that a force of about 5 N remains.The wave frequencies were chosen suchthat they "embrace" the natural Figure 6 shows the displacements in thefrequency of the model; one frequency is x-direction, due to these static loads inbelow the natural frequency and one the x-direction.above it. If linearity and superposition ispreserved, then the result of this test Figure 7 shows the amplitudes of theshould be predictable from the results horizontal displacement in the x-with regular waves. direction of the platform deck of model number 1 in simple regular waves withWave Spectra Response three different nominal amplitudes.The response of the model to waves Figure 8 shows the amplitudes of a wavehaving a known, so measured, energy force component measured at the deckspectrum was also determined. It is not level of the fixed model number 2 indeemed necessary to generate a wave simple regular waves with one nominalspectrum in the model, which exactly amplitude.satisfies a theoretical model such as thatdetermined by the mean JONSWAP Figure 9 shows the amplitudes of thespectrum. The linearised response horizontal displacement in the x-function, determined by dividing the direction of the platform deck of thisoutput spectrum by the input wave model in simple regular waves with fivespectrum can be compared to that nominal amplitudes. These force anddetermined using regular waves. displacement amplitudes are also shown for model number 2-M in the Figure 105. SELECTED EXPERIMENTAL and Figure 11 for three nominal waveRESULTS amplitudes.As a check a few selected experimental Figure 12 shows the horizontalresults, derived from the UV recordings, deflections of the platform deck ofwere examined during the experiments. model number 2, due to a staticThe data, used for this purpose, are horizontal load on the platform deck intabulated in the summary of the the x-direction. These horizontalexperiments in Appendix I. These results deflections are also shown for modelare given below in graphs without number 2-M in Figure 13.detailed discussion. 7
  8. 8. Figure 7 Amplitude of the Horizontal Displacement in the x-Direction of the Platform Deck of Model No 1 in Simple Regular Waves Figure 5 Vertical Reaction Forcesdue to a Static Horizontal Load in the x-Direction on the Platform Deck of Model No 1 Figure 8 Amplitude of a Wave Force Component of Model No 2 in Simple Regular WavesFigure 6 Horizontal Deflection of the Figure 9 Amplitude of the HorizontalPlatform Deck of Model No 1, due to a Displacement in the x-Direction of the Static Horizontal Load in the x- Platform Deck of Model No 2 in Direction on the Platform Deck Simple Regular Waves 8
  9. 9. Figure 13 Horizontal Deflections of Figure 10 Amplitude of a Wave the Platform Deck of Model No 2-M,Force Component of Model No 2-M in due to a Static Horizontal Load in the Simple Regular Waves x-Direction on the Platform Deck 6. ACKNOWLEDGEMENT The authors are indebted to Dr. Sv. Spassov (Research Fellow from the Bulgarian Ship Hydrodynamics Centre in Varna) and Mr. P.J. Spaargaren (student-assistant of the Faculty of Civil Engineering) for their contributions to Figure 11 Amplitude of the this project; especially for the Horizontal Displacement in the x- dimensioning of the jack-up models. Direction of the Platform Deck of Their work has been reported in an Model No 2-M in Simple Regular Internal Technical Report of the Ship Waves Hydromechanics Laboratory: Spassov Sv. and P.J. Spaargaren On Jack-Up Platforms and Marine Riser Dynamics, Delft University of Technology, Ship Hydromechanics Laboratory, Report No. 0793-M, May 1988. APPENDIX I: SUMMARY OF EXPERIMENTS Figure 12 Horizontal Deflections ofthe Platform Deck of Model No 2, due The experiments were carried out in to a Static Horizontal Load in the x- Towing Tank Number I of the Ship Direction on the Platform Deck Hydromechanics Laboratory during the months July and August 1988. 9
  10. 10. The width of this tank is 4.200 meter. Channel 02: force signal ZAThe water depth was 2.004 meter during Channel 03: force signal XBall experiments and the constant Channel 04: force signal ZBtemperature of the fresh water was about Channel 05: force signal XC17.0 0 C. Channel 06: force signal ZCThe experiments were carried out with Channel 07: displacement signal x Athree jack-up models, in order numbered Channel 08: displacement signal x Cby 1, 2 and 2-M. Jack-up number 2-M is Channel 09: displacement signal yAidentical to jack-up number 2, but Channel 10: displacement signal yCmasses of 1.05 kg are added at the deck Channel 11: not availablelevel on the centerline of each leg. Channel 12: && acceleration signal x DThe axis system and the location are Channel 13: wave elevation signal ζgiven in the figure below. The tape speed was 17/8 inch per second. The signals on channels 12 and 13 were recorded directly, via a modulator- demodulator. A reference voltage of ± 2 Volt or ± 1 Volt was given on the tapes regularly too. All required information for data processing, such as calibration data, amplification factors,Figure 14 Axis System and Location etc., was stored on the voice channel of in Towing Tank I the recorder. An UV paper-tape recorder was used forThe calibration factors of the 9 registration of the various signals asdynamometers at the lower leg-ends are listed below:listed below:A x: 1 Volt = 46.2 N Channel 01: acceleration signal &&DyA y: 1 Volt = 42.7 N Channel 02: acceleration signal x D&&Az: 1 Volt = 41.5 N (also on IR)Bx : 1 Volt = 47.8 N Channel 03: displacement signal x CBy : 1 Volt = 43.6 N (also on IR)Bz : 1 Volt = 46.6 N Channel 04: displacement signal x AC x: 1 Volt = 44.7 N (also on IR)C y: 1 Volt = 43.0 N Channel 05: displacement signal yCCz: 1 Volt = 44.8 NThe calibration factor of the (also on IR)dynamometer used to measure the force Channel 06: displacement signal y Ain the space-fixed top-side of the (also on IR)platform, caused by the wave forces, is Channel 07: force signal Y Agiven by: or force signal X DDx : 1 Volt = 20.0 NAn instrumentation recorder was used Channel 08: force signal YCfor registration of the various signals as Channel 09: force signal Y Blisted below: Channel 10: not availableChannel 01: force signal XA 10
  11. 11. Channel 11: wave elevation signal ζ (also on IR) For a few runs an enlarged scale wasChannel 12: not used used for the wave elevation signal on the paper-tape. This is marked in the tablesThe standard calibration factors of these with a comment.signals are as follows: When looking in the direction oppositeζ: 1.0 cm = 1.0 cm on UV the paper transport, (standing in front of the recorder) the positive direction of thex A : 1.0 cm = 2.0 cm on UV signals is a movement from left to right y A : 1.0 cm = 2.0 cm on UV on the UV recorder. Left is also definedx C : 1.0 cm = 2.0 cm on UV by the numbered side of the paper-tape. yC : 1.0 cm = 2.0 cm on UV During the experiments in irregular&&x D : 1.0 g = 14.14 cm on UV waves the transient time after starting the&&D : 1.0 g = 14.14 cm on UV y generation of the waves and beforeYA : 1.0 V = 42.7 N = 5.0 cm on UV starting the registration of the signalsYB : 1.0 V = 43.6 N = 5.0 cm on UV was about three minutes. This was done to get a proper registration of theYC : 1.0 V = 43.0 N = 5.0 cm on UV behaviour of the platform. For each run X D of jack-up number 1: in irregular waves the measuring time 1.0 V = 20.0 N = 1.0 cm on UV was about 20 minutes. X D of jack-up number 2 and 2-M: 1.0 V = 20.0 N = 4.5 cm on UV 11
  12. 12. APPENDIX II: TABLES WITH EXPERIMENTAL DATAIn 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. 12
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