1. Reprinted: 24-03-2001 Report 0809-P, November 1988,
Website: www.shipmotions.nl 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 fatigue testing of joints, computer
simulations and reliability analysis using
This report describes the experiments also non-linear effects.
carried out with two simplified models Since the design of any structure today
showing the principals of elevated jack- involves computer simulations, the
up platforms. The purpose of these computer simulation of the non-linear
experiments is to investigate dynamic behaviour of an elevated jack-
hydrodynamic as well as structural non- up platform will play an important role
linearities in the interaction between the in the total project. Proper representation
structure and water. of the hydrodynamic interaction of the
As such, this model design and testing structure with the sea is essential for the
program forms a first step in an intended success of a dynamic simulation. This is
series of hydrodynamic model and therefore one of the first items to be
possibly prototype measurements of investigated, at least in a preliminary
hydrodynamic forces and dynamic way.
structural response of jack-up platforms The model tests described here are
in both regular and irregular waves. The intended to provide significant insight
whole series of these hydrodynamic into the non- linearities involving the
measurements is in turn, only a part of conversion from hydrodynamics to
the entire project to investigate the forces acting on jack-ups and the
dynamic behaviour and fatigue life of influence of the structural response on
jack-up platforms in order to develop those loads. Also they will provide a first
more appropriate design criteria and set of data against which a non-linear
evaluation methods for such platforms. computer simulation can be checked.
This involves also diverse topics such as
1

2. 2. MODEL DEFINITION A more correct dynamic simulation may
have to take into account relative rather
Purpose of the Experiments than absolute water particle velocities, in
other words take into account the
The traditional quasi-static calculation of interaction between hydrodynamic loads
the 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 of
The response to irregular rather than the model. It is deemed advisable to use
regular waves is often determined by maximum possible model dimensions,
adding the wave particle velocities of the which are dependent on the available test
individual waves and the current, and facilities.
using this combined velocity in the For these experiments use has been
Morison formula. made of Towing Tank I of the Ship
A dynamic calculation of the response Hydromechanics Laboratory during a
can be performed in two different ways. period that a new one replaced the
The first method is a time domain towing carriage. Because of these
simulation of the structural response activities the maximum available water
using the absolute water particle depth in the basin was restricted to about
velocities as input into the Morison 2 meters.
formula. The other method is a This 2.0 meters depth dictated a leg
simulation in the frequency domain length slightly more than that. Waves
using a linearised Morison approach and possible in the basin had a frequency
a dynamic amplification for each ranging from about 0.7 until 1.3 Hz and
individual wave. a wave amplitude up to about 0.040
meter. The full range possible was used
2

3. in the tests. In order to avoid about 1.0 seconds the leg spacing was
complications in this stage of the taken as 0.700 meter.
research program it was decided to
provide no rotation restraint at the leg
footing.
With the diameter as a variable the
hydrodynamic loads were determined,
neglecting the role of roughness. In full
scale it is common in a quasi-static
calculation to allow maximum
deflections of a jack-up platform in the
order of 2 percent of the free leg length
for maximum design conditions. It was
decided to aim for similar deflections in
the maximum model test conditions.
This, together with an average wave
period of 1.0 seconds and a maximum
wave amplitude of 0.040 meter, dictated
the E ⋅ I value for the legs for various
leg diameters. Given a leg diameter and
E ⋅ I value, the leg wall thickness only
depends upon the elasticity modulus of
the leg material chosen. Realistic values
Table 1 Dimensions of the 3 Models
were found for relatively large diameter
PVC legs and small diameter copper
legs.
As the model should be tested around its
resonance a platform natural period of
around 1.0 seconds, being the average
wave period, was considered to be
necessary. With the leg dimensions and
materials given this dictated the mass of
the deck structures for the two models.
Two different deck masses for the
slender leg jack-up model were decided
upon, in order to check the influence on
the response of a shift in platform
natural frequency and the impact of the
second order leg bending. It was
checked that buckling risk would be
non-existent. The leg spacing was
determined by the whish to study
possible total load cancellation as a
result of spatial phase differences in the
hydrodynamic loading of the various
legs. Based upon a mean wave period of Figure 1 Model Dimensions
3

4. where interaction between those is
The 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 resulting
model number 1 in the towing tank, from shear forces, were coated with a
before 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 coated
It is important to note that these models units were first tested and calibrated
are 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 in
considered as very small jack-ups at Appendix I.
scale 1:1. Thus scale effects are non- Force measurements were limited to the
existent. Nevertheless these small jack- registration of the force components
ups possess characteristics that are along each of the three axes with the
comparable 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 the
special features that are subject of the wave maker
present research, i.e. the effect of non- • z vertical, positive upwards
linearities in wave loading and responses • y perpendicular to these according to
in the area near platform resonance a right-handed axis system.
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5. The flexibility of the legs precluded that
the static indeterminance of the system These nine dynamometers were labeled
caused problems. Careful attention to Ax, Ay, Az, Bx, By, Bz, Cx, Cy and Cz
dimensions as well as installation respectively. The corresponding
procedures 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 to
The leg hinges and dynamometers are measure the forces due to waves on the
shown 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. Calibrations processing step will be the determination
of spectra for the various signals
The various measuring elements, such as recorded. In some cases both peak and
force 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 be
of these calibrations are summarised in used to check the computer simulations.
Appendix I. Later calibrations were only This can be done both with regular and
carried out in a more direct way. irregular waves.
The natural frequency of the platform
has been determined. Since model 1 has Regular Waves
first been installed in a dry tank, it was
possible to determine its natural Results of experiments carried out in
frequency both in air and in still water. regular waves, using at least three
For models 2 and 2-M only a natural different wave heights and a range of
frequency determination in still water wave periods which includes the natural
was 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 displacement
General Purpose amplitude divided by the wave
amplitude versus wave frequency will
The general purpose of the testing yield a family of identical curves,
program was to determine the influence showing the well-known resonance
of the platform motion response on the peak. The degree to which these curves
hydrodynamic non-linearity as are individual, thus wave amplitude
manifested 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 naval
architecture. The results of this work are Non-linearities such as quadratic drag
essential for the description of the lead to the phenomena that a wave
hydrodynamics of jack-up platforms, to (input) at one frequency yields force
be used in computer simulations. components (output) at this same
Data from the various test runs were frequency as well as at higher harmonies
recorded in an analog form, so that it of this. Conversely, the presence of extra
may be worked out in a variety of ways energy at high frequencies in output as
in the future. Additionally, significant compared to input can be an indication
data were simultaneously displayed of non-linear behaviour. Force
visually on an UV paper-tape recorder as components in the y-direction can imply
a check. the presence of lift forces. However,
these are only expected to be of small
The "traditional naval architects amplitude, in particular for the model
approach" of examining only the first with the large diameter legs.
harmonics of responses was not
followed in these tests. One standard
6

7. Paired Regular Waves Before starting the experiments in
waves, the platform deck of model
A first check of the superposition number 1 was loaded by static forces in
principle, which makes the study of a the x-direction. The resulting vertical
linear(ised) system so attractive, is to forces at the hinged connection of the
expose the models to a wave consisting three legs to the bottom, ZA, ZB and ZC
of a superposition of two regular waves were measured. The results are given in
of different frequency as used above. Figure 5. It is clear that the sum of these
Such paired waves, themselves, show a measured vertical forces, ZA+ZB+ZC, has
well-known beat pattern with alternating to be zero. However the figure shows
segments of large and small amplitude. that a force of about 5 N remains.
The wave frequencies were chosen such
that they "embrace" the natural Figure 6 shows the displacements in the
frequency of the model; one frequency is x-direction, due to these static loads in
below the natural frequency and one the x-direction.
above it. If linearity and superposition is
preserved, then the result of this test Figure 7 shows the amplitudes of the
should 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 with
Wave Spectra Response three different nominal amplitudes.
The response of the model to waves Figure 8 shows the amplitudes of a wave
having a known, so measured, energy force component measured at the deck
spectrum was also determined. It is not level of the fixed model number 2 in
deemed necessary to generate a wave simple regular waves with one nominal
spectrum in the model, which exactly amplitude.
satisfies a theoretical model such as that
determined by the mean JONSWAP Figure 9 shows the amplitudes of the
spectrum. The linearised response horizontal displacement in the x-
function, determined by dividing the direction of the platform deck of this
output spectrum by the input wave model in simple regular waves with five
spectrum can be compared to that nominal amplitudes. These force and
determined using regular waves. displacement amplitudes are also shown
for model number 2-M in the Figure 10
5. SELECTED EXPERIMENTAL and Figure 11 for three nominal wave
RESULTS amplitudes.
As a check a few selected experimental Figure 12 shows the horizontal
results, derived from the UV recordings, deflections of the platform deck of
were examined during the experiments. model number 2, due to a static
The data, used for this purpose, are horizontal load on the platform deck in
tabulated in the summary of the the x-direction. These horizontal
experiments in Appendix I. These results deflections are also shown for model
are given below in graphs without number 2-M in Figure 13.
detailed discussion.
7

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 Forces
due 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 Waves
Figure 6 Horizontal Deflection of the Figure 9 Amplitude of the Horizontal
Platform 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. 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 of
the 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. The width of this tank is 4.200 meter. Channel 02: force signal ZA
The water depth was 2.004 meter during Channel 03: force signal XB
all experiments and the constant Channel 04: force signal ZB
temperature of the fresh water was about Channel 05: force signal XC
17.0 0 C. Channel 06: force signal ZC
The experiments were carried out with Channel 07: displacement signal x A
three jack-up models, in order numbered Channel 08: displacement signal x C
by 1, 2 and 2-M. Jack-up number 2-M is Channel 09: displacement signal yA
identical to jack-up number 2, but Channel 10: displacement signal yC
masses of 1.05 kg are added at the deck Channel 11: not available
level on the centerline of each leg. Channel 12: &&
acceleration signal x D
The axis system and the location are Channel 13: wave elevation signal ζ
given 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 for
The calibration factors of the 9
registration of the various signals as
dynamometers at the lower leg-ends are
listed below:
listed below:
A x: 1 Volt = 46.2 N Channel 01: acceleration signal &&Dy
A 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 C
By : 1 Volt = 43.6 N (also on IR)
Bz : 1 Volt = 46.6 N Channel 04: displacement signal x A
C x: 1 Volt = 44.7 N
(also on IR)
C y: 1 Volt = 43.0 N
Channel 05: displacement signal yC
Cz: 1 Volt = 44.8 N
The calibration factor of the (also on IR)
dynamometer used to measure the force Channel 06: displacement signal y A
in the space-fixed top-side of the (also on IR)
platform, caused by the wave forces, is Channel 07: force signal Y A
given by: or force signal X D
Dx : 1 Volt = 20.0 N
An instrumentation recorder was used Channel 08: force signal YC
for registration of the various signals as Channel 09: force signal Y B
listed below: Channel 10: not available
Channel 01: force signal XA
10

11. Channel 11: wave elevation signal ζ
(also on IR) For a few runs an enlarged scale was
Channel 12: not used used for the wave elevation signal on the
paper-tape. This is marked in the tables
The standard calibration factors of these with a comment.
signals are as follows: When looking in the direction opposite
ζ: 1.0 cm = 1.0 cm on UV the paper transport, (standing in front of
the recorder) the positive direction of the
x 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 defined
x 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 before
YA : 1.0 V = 42.7 N = 5.0 cm on UV starting the registration of the signals
YB : 1.0 V = 43.6 N = 5.0 cm on UV was about three minutes. This was done
to get a proper registration of the
YC : 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. APPENDIX II: TABLES WITH EXPERIMENTAL DATA
In the following tables all experiments are listed in the order as they have been carried
out. In these tables some runs are marked with "free oscillation". These experiments
were carried out in still water. If no counter reading is given, then the signals were
recorded on the UV paper-tape recorder only.
The mark "reference signal" means that a reference voltage of ± 2 Volt or ± 1 Volt was
given on the instrumentation recorder.
12

13. 13

14. 14

15. 15

16. 16

17. 17

18. 18

19. 19

20. 20

21. 21

22. 22