-
Ocean Engng, Vol. 17, No 3, pp. 235-261, 1990. 0029-8018/90
$3.00 + .00 Printed in Great Britain. Pergamon Press plc
MODEL STUDIES OF THE MOTION RESPONSE OF A DAMAGED FOUR COLUMN
SEMISUBMERSIBLE IN
REGULAR AND IRREGULAR WAVES
B. M. STONE, M. A. SULLIVAN, V. M. ARUNACHALAM and D. B.
MUGGERIDGE Ocean Engineering Research Centre, Memorial University
of Newfoundland, St John's, Newfoundland
A1B 3X5, Canada
Abstract--A brief review of the stability requirements of
semisubmersibles is presented. Results of the dynamic response of a
damaged, twin pontoon, four column semisubmersible at a scale of
1:100 are discussed. The tests involved both regular and irregular
waves with the model oriented in head, beam and quartering
directions for both intact as well as damage conditions. Four
damage conditions representing partial damage to one column were
simulated: two in windward (positive) direction and two in leeward
(negative). The "light damage" condition represented about 9%
flooding of the damaged column, while for the "moderate damage" the
flooding was equivalent to about 18%. For moderate damage
conditions, regular wave studies showed that the motions are
essentially nonlinear, although for light damage conditions this
cannot be said with certainty. Model tests showed certain asymmetry
in the motions of the damaged semisuhmersible with respect to the
position of the damaged column. Moderate damage conditions seemed
to produce significant subharmonic response of the vessel in a
frequency range which is twice the natural frequency of the vessel
in heave. These observations were confirmed from the results of
irregular wave studies. Irregular wave studies showed that the
quartering sea pitch and roll motions in windward damage conditions
are as significant as those in the leeward conditions which was not
the case for regular wave studies. The energy due to the motion of
the semisubmersible was concentrated in the frequency of 0.7-1.3
Hz, which corresponds to the energetic range of the normal sea
state. The natural frequencies of the vessel in damaged condition
in pitch, roll and heave are higher than the corresponding
frequencies in the intact condition of the vessel. The natural
frequency in heave, for both intact and damage conditions, is
higher than either those of pitch and roll in similar conditions.
These natural frequencies in pitch and roll begin to approach that
of the natural frequency in heave as the damage condition
increases. This is true irrespective of the position of the damaged
column or the sea state. The value of the natural frequency in
heave itself increased much more slowly with increase in damage
condition. It was inferred that the nonlinear wave pressure term
played only a minor role in the asymmetry of motions of the vessel,
while the mooring characteristics had a more dominant
influence.
1. INTRODUCTION
SEMISUB~ERSIaLES are becoming attractive as production units for
developing marginal and deep water oil fields. The functions and
requirements of these production units are more demanding than the
drilling units. Hence, it is recognized that consistent with risk
criteria associated with fixed production systems, a more rigorous
design criterion needs to be applied to floating production systems
than is presently being applied to mobile offshore drilling units
(MODUs). An important design criterion for floating units is the
stability criterion. One of the fundamental stability criteria for
MODUs has been the intact area ratio which has been applied by
regulatory bodies since its formal introduction two decades ago by
the American Bureau of Shipping (ABS). This original rule was
derived on an empirical basis from experiences gained over many
years in real world stability situations and accidents encountered
by ships. The International
235
-
236 B.M. ST~)N~ et ~/.
Maritime Organization (IMO) has adopted an extension of ABS
rules for world-wide service of MODUs. It has since been recognized
that the IMO code is inadequate for harsh environments such as the
North Sea and Eastern Canada (Praught et al., 1985: Springett and
Praught, 1986). A critical review of the existing and proposed
requirements on the stability conditions for semisubmersibles is
presented by Kuo et al., (1983), Havig (1983), Hammett (1983),
Dahle (1985), Mowatt and Allen (1986), Martinovich and Praught
(1986), Springett and Praught (1986) and Pawlowski (1987). Most of
the above propose that there is a need to incorporate as much
dynamic information as possible for dealing with the stability
requirements of semisubmersibles. At the same time, industry is
concerned that many changes, both proposed and enacted, are not
based on any demonstrated weaknesses in the present rules.
Stability criteria developed for ships are based on the
hydrostatic restoring capabilities of the floating vessel subjected
to a mean wind force. The principle behind the intact ratio
criterion is that the structure must be able to absorb the energy
from the heeling moment when inclined. It may be noted that the
assumption involved in this principle, namely the heeling moment
determined by the horizontal wind force and the horizontal
hydrostatic reaction force acting through the centre of lateral
resistance of the underwater part, is not always true for a moored
structure. Semisubmersibles are also different compared to ships in
their shape of displacement volume. In spite of these facts, the
stability criteria for semisubmersibles, as mentioned earlier, have
their origins in traditional naval architecture. The problem of
stability of MODUs is even more complex when other environmental
forces are simultaneously acting along with the wind. In fact, Kuo
et al. (1983) and Takarada el al. (1986) go so far as to report
that the existing stability criteria considering only unmoored
vessels subject only to wind moments is not sufficient to prevent
dangerous situations in violent seas.
In the early part of the last decade there were two major marine
disasters involving semisubmersibles. In the first case, the
Alexander L. Kielland, in 1980, capsized due to structural damage
resulting in the loss of a vital buoyancy element. In the later
case, in 1982, the Ocean Ranger capsized as an intact unit
(Mogridge et al., 1986). These incidences were perceived to
indicate an apparent deficiency in both intact as well as damaged
stability criteria for semisubmersibles. As a response to the above
marine disasters, attempts have been made to improve the
understanding of the physical processes involved in stability. The
Norwegian Maritime Directorate (NMD) and the U.K. Department of
Energy commissioned Mobile Platform Stability (MOPS) projects and
the results have been made public in recent years. ABS has
developed a ,loint Industry Project (,liP) to address similar
topics. MOPS and ,liP programs were developed to study the effect
of wind, wave and current acting either alone or in combination on
the stability of a semisubmersible. The effect of wind alone on the
static stability of a semisubmersible was studied by Macha and Reid
(1984) as a part of SNAME panel program.
Early experiments to assess intact stability criteria of
semisubmersibles were started by Numata et al. (1976) and Kuo et
al. (1977) even before these marine disasters as part of SNAME
panel program. After extensive testing of typical semisubmersible
models under wind and wave conditions, they concluded that no
capsizing tendency is possible for semisubmersibles in a condition
of normal intact stability under regular
-
Motion response of a damaged four column semisubmersible 237
wave conditions. However, they questioned any such possibility
for a combined wave and wind condition due to the influence of
steepness of waves and steady tilting of the vessel. They have also
emphasized the inappropriateness of the area ratio criterion for
semisubmersible design.
The study of the dynamic behaviour of semisubmersibles in a
condition of normal intact stability is well documented (Numata et
al., 1976; Kuo et al., 1977), but the study of the behaviour of a
damaged unit is very limited. In fact, outside of the programs such
as MOPS (Naess and Hoff, 1984; Herfjord, 1984) and JIP (Collins and
Grove, 1988; Stiansen et al., 1988), there are few published works
on this topic. The relevant passage (section 3.17.5) of ABS (1988)
on this topic reads: "Based on authoritative wind tunnel tests as
in section 3.17.4 and behaviour tests of a representative model in
waves, or by proven calculation methods, alternative stability
criteria may be considered for approval."
In this paper we present the outcome of model studies of an
intact as well as a damaged, four column, twin pontoon
semisubmersible unit subjected to both regular (Stone, 1986) and
irregular waves. The simulated damage conditions represent partial
loss of buoyancy to one column.
2. EXPERIMENTAL PROGRAM
Experiments were conducted in a wave-tow tank (length 58.3 m;
width 4.6 m; depth 3.0 m) at the Memorial University of
Newfoundland. The tank is equipped with an MTS servohydraulic
piston-type wave generator at one end of the tank which can be
programmed to generate regular and irregular waves of desired
characteristics. A detailed description of the tank has been given
by Muggeridge and Murray (1981) and Little (1985).
2.1. Model construction and its properties
The model semisubmersible is a twin pontoon four column unit
constructed to a scale of 1:100, and is considered similar in
geometry and mass properties to the GVA 4000 design. Details of
model construction and the measurement of physical and experimental
characteristics of the model are given by Stone (1986). Only a
brief mention of the various aspects of the model is given
here.
The model was constructed entirely of polyvinyl chloride (pvc).
For the deck structure and pontoons, pvc sheets of 0.318 mm
thickness were used, while machined thickwail pvc tubing and
machined pvc rods were used for columns and bracings, respectively.
Pontoons were equipped with two ballast tubes running parallel
through the length of the pontoons with provisions for ballast
weights. Each column was equipped with a threaded rod which allowed
for adjustment of ballast. Underwater joints were hot air welded
while glue joints were employed for the box deck structure. The
profile and general configuration of the model with all major
dimensions is shown in Fig. 1. The constructed model in the final
stages of completion is shown in Fig. 2. These arrangements
provided control of the position of horizontal and vertical centres
of gravity, draft and metacentric height of the model, all of which
were adjusted to correspond to the simulated values of the
prototype.
-
238 B .M. STONY. et al.
,U - - 1290
1292 ! 54 72 - - 80.56
PROFILE
J 3300
1
750
~ - 0.00 1292
I I
16.00 ~J~
-- 33 O0
20 50
I 1 20 - - 750
- . .72 - - -~ . - , . .oo -~- - . . . . 70.72
FRONT VIEW
54,72
SECTION A-A - PONTOONS
1 I o
MAIN DECK
FIG. 1. General arrangement of the semisubmersible model.
2.2. Measurement of static stability and natural periods The
natural periods of the model in pitch and roll for both
free-floating and moored
conditions were measured using a level sensor. The heave natural
period for the free- floating condition was obtained by an
acccelerometer while a linear rotary potentiometer was used to
obtain the corresponding period in the moored condition. In all
instances, a digital signal analyzer with an accuracy of 0.01 sec
was used to process the transducer signal. The physical properties
and measured experimental characteristics of the model are given in
Table 1 and show good agreement with the prototype values except
pitch and roll which are slightly lower for the moored condition. A
simple inclining experiment was carried out to obtain the static
stability characteristics of the model at the operating draft. To
this end, an external heeling moment was applied to the model using
equal weights attached to the eye bolts installed at equal distance
from the axis of rotation. The angle of inclination was measured
using a two axis electrolytic level sensor. The resulting static
stability curve agreed well with the computed values (Stone,
1986).
2.3. Modelling the mooring system The spread mooring system used
in earlier model tests (Lundgren and Berg, 1982;
Mathisen et al., 1982) of the same semisubmersible unit (GVA
4000) along with the
-
FI~. 2. Model semisubmersible (1:100 scale) in the final phase
of construction.
239
-
FIG. 6. Model undergoing tests under simulated moderate damage
condition in regular waves.
240
-
Motion response of a damaged four column semisubmersible 241
information collected on the prototype mooring from Naval
Architect (1981), Price and Wu (1983) and Grtaverken Arendal (1984)
formed a basis for our model (Table 2). The model mooring system
consisted of an 8-point system deployed in a 45 symmetrical
pattern. Due to limited width of the wave tank (4.6 m) it was not
possible to model the mooring system on the basis of weight per
unit length. Hence, the mooring system was simulated by compound
springs. To obtain the geometric configuration (segmental length,
angle of inclination) and stiffness characteristics (horizontal and
vertical tension and their rate of change) of the prototype mooring
system a static analysis following the traditional catenary
equation (Korkut and Hebert, 1970; Rothwell, 1979) was performed
for slack and taut modes of the mooring line. Figure 3 shows the
mooring line tension for the horizontal excursion while Fig. 4
shows the same for vertical excursion. Using these data the
stiffness of the springs, permissible stretch and initial
attachment angle of the mooring system were selected to correctly
model horizontal and vertical stiffnesses as a function of the
horizontal displacements over the whole range. Given the dominant
influence of the mooring system in providing horizontal restoring
force relative to that in the vertical direction (which is mostly
determined by hydrostatic characteristics) the model mooring system
stiffness was largely based on the horizontal stiffness. The
resulting system provided close agreement for horizontal excursions
while it approximated the less important vertical excursions (Figs
3 and 4).
2.4. Simulated damage condition Damage conditions were simulated
by adding weights to a column at the height of
its vertical centre of gravity, which inclined the model with
approximately equal amounts of heel and trim. This method of damage
simulation may be representative of the flooding of the vessel. In
the first case, referred to in this paper as the "light damage"
condition, the inclination of the damaged column was 12 - 0.4 and
the deck was entirely above the water surface while the pontoons
were completely immersed in the water. In the other case, referred
to as the "moderate damage" condition, a larger angle of
inclination of 20 --- 0.5 of the column was simulated. In this
case, the pontoons and the deck both pierced the water surface. The
weights had an equivalent displacement volume of 487.8 and 975.6 cm
3 which correspond to column lengths of 3.73 and 7.46 cm. In terms
of the percentage of buoyancy, the simulated damage conditions were
equivalent to 9.1 and 18.2% of total flooding of the damaged column
from its keel to main deck.
2.5. Instrumenting the model Initially, the relative positions
of the model, mooring touch-down (at the tank wall)
and mooring termination points were established for all three
orientations (head, beam and quartering directions) of the model
with respect to the direction of wave advance. The model was
rigidly held at these pre-established positions, the compound
spring mooring assembly connected into the mooring line just below
the fairleader, and the required pretension (127.5 g) applied. The
top end of the spring assembly was connected to a 0.6 mm nylon
coated stainless steel cable run via the fairleader to a rigid
attachment under the main deck. Similarly, the lower end of the
spring assembly ran through a pulley (located at the touch-down
point on the tank wall) to a cantilever beam load cell mounted on
the tank wall (Fig. 5).
-
242 B. M, SroNiet ~tl.
TABI,E 1. PtIYSICAL DIMENSIONS AND EXPERIMIN1AI. PROPERI'IES OF
MODFA. AND PROIOFYPE
Designation
1. Pontoons Length (m) Beam (m) Height (m) Bilge radius (m)
2. Columns Diameter (m)
Spacing (center-center) Longitudinal (m) Beam (m)
3. Braces Diameter (m) Height of center (above keel) (m)
4. Deck Lower deck
Length (m) Beam (m)
Tween deck Length (m) Beam (m)
Main deck Length (m) Beam (m)
5. Height Keel to lower deck (m) Keel to main deck (m)
6. Center of gravity Vertical (above keel) (m) Longitudinal
(from midship) (m) Transverse (from center line) (m)
7. Radius of gyration Pitch Roll
8. Natural period (frequency)
Heave, sec (Hz) Pitch, sec (Hz) Roll, sec (Hz) Surge, sec (Hz)
Sway, sec (Hz) Yaw, sec (Hz)
9. Displacement Operational (m s)
Model (1:100) Prototype
0.806 80.56 0.16t) 16.00 0.075 7.5/) 11.013 1.35
0.130 12 .9(1
0.547 54.72 0.547 54.72
0.021 2.06 0.112 11.20
t).547 54.72 1t.547 54.72
0.623 62.32 0.547 54.72
0.670 67.00 0.575 57.50
I).33 33.00 0.41 41.00
0.210 20.97 0.0 0.0 0.0 1/.0
11.273 27.80 0.296 29.20
Free Moored Free Moored 2.1 (0.480) 21. (0.480) 21 (0.0480) 21
(0.0480) 4.1 (0.245) 3.6 (0.286) 41 (0.0245) 37 (0.0285) 5.0
(0.200) 4.3 (0.235) 52 (0.0195) 46 (0.0224) - - (--) 7.3 (0.140) -
- (--) - - (--) - - (--) 8.9 (0.119) - - ( - - ) - - (--) - - ( - -
) - - ( - - ) - - ( - - )
0.024 24,368
-
Motion response of a damaged four column semisubmersible 243
TABLE 2. PROTOTYPE MOORING SPECIFICATIONS FORMING THE BASIS OF
MODEL MOORING SYSTEM
Designation Prototype values
1. Linear weight 1.323 kN/m 2. Proof load 4730 kN 3. Breaking
load 6010 kN 4. Total chain length 900 m 5. Pretension 1275 kN 6.
Water depth 195 m 7. Fairleader depth 5.33 m 8. Anchor chain 76 mm
(grade K4)
HODEL Tx --X"- HODEL TM
PROTOTYPE Tx --X"-- PROTOTYPE TU
o t - /
i
o. g - - - - L ~ * . . . . ~0 ~$ ~0 - IS -10 ~ 5 10 15 20
HORIZONTRL OISPLRCEMENT (a)
FIG. 3. Moof ing l inetens ion as a ~nct ion ofhor izontalexcurs
ion o f the vessel(comparison of mode land prototype data).
Four light emitting diodes (LEDs) were mounted noncolinearly at
the four corners on the deck of the vessel along with a control
unit. An electrolytic two axis level sensor was mounted on the
longitudinal centreline at the stern of the vessel. Two electronic
cameras with photo-sensitive detectors were mounted 90 apart on
custom mounts at the tank wall along with an administration unit.
These cameras provided the angular displacements of LEDs from the
origin of its focal planes. The initial x, y and z coordinates of
the LEDs and the inclination of the cameras were determined in the
tank coordinate system using precision survey instruments. Using
these data as input, the system software calculates two
transformation matrices (one for each camera). This
-
244 B .M. SIoN~ et al.
z
==.*
t/J o I--O =
.
o- -25 -20 -15 -10 -S
MODEL Tx - -X - - HODEL T u
PROTOTTPE Tx
--~c-- PROTOTYPE TW
10 15 20 25 VERTICRL DISPLFICEMENT (m)
FtG. 4. Mooring line tension as a function of vertical excursion
of the vessel (comparison of model and prototype data).
enables measurements made by the cameras to be transformed to
the tank coordinate system enabling the six degrees-of-freedom
motion response of any vessel to be monitored in real time. Laurich
(1984) provides an in-depth description of the selective spot
(SELSPOT) recognition system and associated software being used at
this facility.
A strain gauge conditioner and amplifier system connected to a
digital multimeter was used to establish and measure the mooring
line tension. All mooring line load cells were calibrated in situ
prior to each series of tests. Wave profiles were measured at two
locations in the tank using twin wire linear resistance wave
probes. The wave probes were calibrated before and after each
series of experiments. A schematic representation showing relative
positions of the vessel, SELSPOT system, load cells, wave probes
and mooring system used in the experimental arrangement is given in
Fig. 5.
3. TEST PROGRAM
Model tests were carried out with three different orientations
of the vessel (head, beam and quartering) with respect to wave
direction for even keel and simulated damage conditions at
operating draft. These tests were carried out for both regular and
irregular waves. A summary of the test conditions is provided in
Table 3. The model undergoing test in regular waves under moderate
damage conditions is shown in Fig. 6.
-
Motion response of a damaged four column semisubmersible 245
SELSPOT CAMERA
oWAVE PROBE
:O ~7 ~LED
WAVE PROBE
o
LEVEL SENSOR'~
-
246 B. M. Stoxt: et al.
TABI.E 3. SUMMAR't O1" MOI)I-I I I{SI (ONDI I IONS
Orientat ion of vessel
(A) Head
(B) Beam
(C) Quarter ing
Column with loss Loss of buoyancy Angle of inclination of
buoyancy volume, cm ~ of column in
degrees-:-
Heel tangle in degrees*
3-4 0.0 0.6 + 0.4 7-8 487.8 + 1 /.6 8.2 7-8 975.6 + 19.5 13.5
5-6 487.8 - 12.3 - 8.3 5-6 975.6 - 19.5 - 13.11
34 11.0 + 0.4 + 0.1 1-2 487.8 + 12.4 + 0.89 1-2 975.6 +20.5 +
14,5 7-8 487.8 12.11 - 8.6 7-8 975.6 - 19.9 -- 14.2
3-4 0.0 -+ 11.4 + tl.2 1-2 487.8 +12.2 + 9./1 1-2 975.6 +20.2 +
14.6 5-6 487.8 -13 .1 - 8.5 5-6 975.6 -21/.2 - 13.5
Tr im angle in degrees ~
- 0.5 - 8.2 -13 .8 + 9.11 --14.3
+ 11.5 8.6
-13 .9 - 8.3 -13 .6
+ 0.3 - - 8.2
13.6 +9.9
+14.7
*Positive angles correspond to windward damage tSign convention
follows right-hand rule.
Draft Water depth Vessel orientation Wave conditions:
Regular waves Wave periods Wave height
Irregular waves Spectrum used Significant height Significant
period
and negative angles correspond
211.5 cm (operating draft). 1.95 m. Head, beam and quartering
seas.
From 11.711 to 2.50 sec in steps of 0.10 sec. 6.0 -+ 1.0 cm.
ISSC spcctrum. 3.0 cm 5.0 cm 7.5 cm 9.5 cm. I).81 sec 0.92 see
1.03 sec 1.19 scc.
to leeward damage.
3.1. Regular waves
For each vessel orientation and damaged condition, the vessel
was subjected to 19 wave periods ranging from 0.7 to 2.5 sec in
steps of 0.1 sec. The wave heights were approximately 6 -+ 1.0 cm
(Table 3).
3.2. Irregular waves In order to understand the behaviour of the
vessel in irregular waves and to see
what, if any, difference there would be from that of the regular
wave field the tests were repeated using an International Ship
Structures Congress (ISSC) spectrum. For each vessel orientation
and simulated damaged conditions, four spectra were run with
significant wave periods of 0.81, 0.92, 1.03 and 1.19 sec. The
corresponding significant wave heights were 3.0, 5.0, 7.5 and 9.5
cm. In all, the vessel was subjected to 60 spectra in this study
(Table 3).
3.3. Data recording and analysis Time histories of wave profiles
measured by both the probes were recorded on an
instrumentation tape recorder. SELSPOT data for the
corresponding time interval were
-
Motion response of a damaged four column semisubmersible 247
digitized and transferred to computer compatible magnetic tapes.
From SELSPOT data recordings, amplitudes of motions of the
semisubmersible in surge, heave, sway, pitch, roll and yaw were
obtained.
4. RESULTS AND DISCUSSIONS
4.1. Regular waves
Comparison of even keel results. The motions of the vessel under
even keel conditions were compared with those of Lundgren and Berg
(1982) for all available data. The work of Lundgren and Berg was
carried out at a scale of 1:65 with even keel conditions for both
regular and irregular sea states. Such a comparison for the regular
sea even keel response amplitude operator (RAO) for heave showed a
good agreement throughout the entire frequency range, except near
the resonant frequency of the vessel (0.50 Hz) where there was some
marginal discrepancy. Such variations are to be expected, given the
effect of damping near the resonant condition, for any small shifts
in the experimental wave conditions and model natural frequency.
Comparison of surge motion under even keel conditions showed
acceptable levels of agreement. Pitch motion RAO also showed a good
agreement for wave frequencies higher than 0.50 Hz. However, for
wave frequencies less than 0.50 Hz, it was found that our results
were consistently lower than those of Lundgren and Berg (1982). To
ensure that the present studies did provide the correct motions,
tests were repeated for wave frequencies between 0.25 and 0.50 Hz.
In these extended studies it was observed that the pitch motion
attained a sharp peak at about 0.27 Hz, which closely agreed with
the measured natural frequency of the vessel in pitch. Hence, it
could be inferred that the large pitch RAO observed in the work of
Lundgren and Berg (1982) for wave frequencies less than 0.50 Hz is
possible due to a slow receding part of the RAO after attaining the
peak value at or about 0.27 Hz, instead of exhibiting a sharp peak
as observed in the present study.
Comparison of the heave RAO in beam seas showed good agreement
as in the case of head seas. The roll motion agreement in beam sea
was quite good throughout the entire frequency range except near
0.45 Hz where the results of Lundgren and Berg (1982) showed a peak
value. However, the actual value of peak was much less than that
exhibited for pitch motion RAO in head seas. The sway motion, in
our studies, was slightly larger than that of Lundgren and Berg
(1982). This change might be due to the sensitivity of horizontal
motions to changes in the pretensions as shown by Price and Wu
(1983). However, it is believed that our compound mooring system
provided the correct restoring forces over the entire range of
excursion as shown in Figs 3 and 4.
4.1.1. Damaged condition: head seas
Heave motion. Heave motion RAO for the light damage condition
showed a similar trend as in the case of even keel. This
observation was applicable for both windward and leeward positions
of the damaged column. The RAO for the light damage condition was
almost the same as for the even keel case except near the resonant
frequency and near 0.90 Hz. The resonant condition for moderate
damage seemed to occur at a
-
248 B .M. STOYI: et al,
frequency slightly higher than the natural frequency. The
moderate damage produced a slightly larger peak value of RAO near
its resonant frequency. Near 0.90 Hz, under the moderate damage
condition, there was found to be another peak of reduced value for
both windward and leeward positions. Symmetry of the RAO with
respect to windward and leeward direction as reported by Huang et
al. (1982) and Huang and Naess (1983) was observed only to a
certain extent in our studies.
Surge motion. A comparison of the surge RAO for windward light
damage conditions showed that it was almost the same as for even
keel condition. For windward moderate damage, there was only a
marginal reduction. For the leeward orientation of the damaged
column for both light and moderate damage conditions there was an
equally marginal reduction in the surge RAO compared with even keel
values. For all conditions, there is a progressive reduction in
surge RAO with increase in the incident wave frequency from 1.0 at
0.4 Hz to 0.1 at 1.2 Hz.
Sway motion. No significant sway motion was observed either in
windward or leeward position under any damage conditions, with the
RAO typically being less than 0.05 except near 0.85 Hz. Near 0.85
Hz, the windward sway RAO was about 0.10 while for the leeward
damage it was 0.20. The even keel values were even more reduced in
magnitude throughout the whole frequency domain.
Yaw motion. It was observed that for the light damage condition,
yaw was almost zero for all wave frequencies as in the case of even
keel. For the moderate damage condition, there appeared to be some
yaw motion, near 0.80 Hz. These observations were true for both
windward and leeward positions of the damaged column, but as the
values were typically 0.05, there was no measurable yaw motion.
Pitch motion. The pitch motions for damage conditions, shown in
Fig. 7, indicated that for both windward and leeward positions,
light damage produced almost the same motion as for the even keel
situation throughout the entire range of frequency. For moderate
damage, the pitch motion is quite different for both windward and
leeward positions of the damaged column, which exhibits
well-defined peak values near 0.85 Hz and 0.45 Hz. Leeward moderate
damage condition produced a peak RAO of 2.5 while the corresponding
windward value was about 1.5 at about 0.85 Hz, The other peak at
0.45 Hz in both windward and leeward damage conditions were about
40% less than their corresponding larger peak value.
Huang et al. (1982) and Chen et al. (1986) reported the
existence of significant subharmonic motion in heave at wave
frequencies near twice the natural frequency of the vessel in
heave. In our studies, this phenomenon occurred in the moderate
damage condition for both windward as well as leeward conditions
when the pontoons and the deck pierced the water surface. In the
studies of the above authors, this phenomenon occurred only in the
leeward damage condition.
Roll motion. Roll motions shown in However, the corresponding
peaks are windward and leeward) produced an
Fig. 8 exhibit similar trends as the pitch motion. much reduced.
Light damage conditions (both almost uniform RAO throughout the
whole
-
Motion response of a damaged four column semisubmersible 249
0
OJ
o~ qrt
E u
o o
o
0 .4 .< nr
r" U
O. 113
0
,/ \\ / \ /
\ /
(8) leve l
. . . . . . . . +iO" (Windwlrd)
/ \ ,2o" (**naw=rd)
/ \ / \
/ \ \ \
\
I I I
E u
tO O . -
2 0
n - O
=3 -
0
0
0
r \ (.) I I \ l ,v ,1
\ - l o " (Leewaral
/ \ -20" (Lee*I l l 'd) --
/ \ / \ I /\ \ \ / \
\ / \ \ I \
j , \ ~ \ \
I ! I 0.3 0 .6 0 .9 t .2 i .5
Frequency (Hz]
FZG. 7. Pitch RAO for head sea regular wave condition.
frequency range and its magnitude was not significant, the value
being about 0.10. For moderate damage two peaks were produced for
both windward and leeward damage conditions, as in the case of
pitch motion. The largest peak RAO was attained in leeward moderate
damage near 0.85 Hz and the magnitude was about 1.2. The windward
moderate damage condition peak RAO near 0.90 Hz was about 0.50.
The foregoing discussions on heave, pitch and roll motions for
damage conditions (Figs 7 and 8) show that moderate damage at the
leeward column produced larger peak motions than for other
conditions. These peak values are observed not only near the region
of natural frequency of the vessel in heave (0.49 Hz) but also near
the frequency
-
250 B.M. StuNt: el al.
g]
o
o
nr LO
'-' o - o
E o
~
0
~r kO
0 ~r
0
o
(a) +iO" (Windward)
. . . . . . . . . +20" (windward)
h / / ' \
I I I
(b)
- iO ' (Leeward}
. . . . . . . . . . @O' (Leeward)
/ \ I \ / \
/ \ / \ . .
i 01 # 0 .3 0 .6 .9 i .2 ~.5
Frequency (Hz)
FIG. 8. Roll RAO for head sea regular wave condition.
range 0.90 Hz where subharmonic motions have been observed.
Again, leeward moderate damage produced well-defined peak RAOs in
yaw and sway near 0.45 Hz. For windward moderate damage, these
observations were valid but the magnitude of the peaks were
reduced. This shows the effect of coupling as discussed by Mathisen
et al. (1982). This coupling effect is particularly understandable
for vessels with symmetry in the xz and yz planes. It may be
pointed out that the results of the time domain simulation of large
amplitude wave effects on four, six and eight column
semisubmersibles by Naess et al. (1985), Chen et al. (1986) and
Matsuura and lkegami (1986) showed a similar large nonlinear roll
motion considered to be subharmonic in nature with a frequency near
one-half the wave exciting frequency. This motion is caused
predominantly by nonlinear time dependent restoring characteristics
of the vessel when the draft is shallow. The wave exciting
frequency at which this subharmonic motion of the vessel can be
induced was, as discussed before, about twice the natural frequency
of the vessel in heave.
4.1.2. Damaged condit ion: beam seas
The translational (surge, sway and heave) motion RAOs and the
rotational (pitch, roll and yaw) motion RAOs, for beam orientation
of the rig, indicated that the
-
Motion response of a damaged four column semisubmersible 251
discussions brought out for head sea conditions could be
directly applied to beam sea results as well since similar trends
were maintained for corresponding damage conditions. It may be
recalled that the motions are referred with respect to the fixed
tank coordinate system.
4.1.3. Damaged condition: quartering seas
The RAO for surge and sway in quartering seas were almost
identical. This is to be expected for a semisubmersible of this
type, having an almost square column configuration. However, the
pitch (Fig. 9) and roll (Fig. 10) do not exhibit such a response.
Except for this difference, the behaviour of the semisubmersible in
quartering
If)" ,~ (a)
leve l .
u -. o ,, /\ o . - +20" (Windward) i / / \ / \ - \ / o \ . , \ /
" - - \ / -J u o \ ~- .~ /
~ / \
I I I
0
0
U
Ot
0- 0
r r
e- U
n 0 .~
t13
0
0
O ,
0.3
(D)
,tO* (Leeward)
20" (Leeward)
/ /
f ^ I 1
/ \ / \ / \ I \
\ I \ \ N I \
\.._J \ \
\
I I 0.6 0 .9 ~ .2 1 .5
Frequency (Hz)
FIG. 9. Pitch RAO for quartering sea regular wave condition.
-
252 B .M. STONE el tl/.
E .~o
O
-
Motion response of a damaged four column semisubmersible 253
0 0
a I "0 0
0 D . -
a I
0 O_
U ~ .io
0 O
O
0 0
I 13 0
0 . - "0 GI
g 10
0
u ,M ,IJ
n
o o
0
(e) t . t8 Windward |6 .4
. . . . . . . . 2 .08 Windward (6 .6
2 .5e Htndwerd (6.
( ) ind icate wave he ight in ca
I !
/ I I
0.3
(n)
( l
t . t s Leeward (5.61
2 .0e Leeword (6 .9)
2 .51 Leewerd (6 .2 ) -
ind icate wove he ight in cm
0 .6 0 .9 t .2 F requency (Hz.)
1.5
FIG. 11. FFT of time series from pitch motion response (head
sea--moderate damage--regular wave data).
2. Second-order effects, due to incident conditions, motion and
mooring characteristics of the vessel;
3. The asymmetry of the motion of the vessel with respect to the
wave direction, particularly when the damage is moderate;
4. The asymmetry is independent of the direction of sea state
with respect to the vessel orientation.
The coupled motions of the vessel and the factors influencing it
were discussed earlier. The second-order effects and the influence
on the motion asymmetry will be discussed now. Figure 11 showed
that the asymmetry was noticeable both in the first- order as well
as the second-order motions. It should be noted that the incident
wave height at 0.90 Hz used for the tests with leeward side damage
of the vessel was lower than those with windward side damage of the
vessel (5.60 cm and 6.40 cm). In spite of this reduced wave height
for the leeward damage condition, the first- and second-order
motions were higher. The first-order motion at 0.40 Hz was at least
60% more for the leeward condition than for the windward damage
condition in spite of the wave height being almost equal. At 0.50
Hz, although the wave height for leeward direction was small, the
reduction in first-order motion was not proportional to the
reduction in wave height. The motion was much more reduced for
windward direction. Naess and Hoff
-
254 B .M. SmN~ e/ a/.
(1984) and Huse and Nedrelid (1985) computed the effect of the
increased wave height (from 2 cm to 4 cm) in understanding the
asymmetry of the motions with respect t~ wave direction for a twin
pontoon (eight column) vessel listed at about 12.5 . Their results
showed that the asymmetry at this angle of list (equivalent to the
light damage condition in this study) was not influenced by the
wave steepness. This showed that the second-order effect due to
nonlinear pressure terms on the asymmetry of the motions is
negligible. In addition, if one looked at the graphs of Naess and
Hoff (1984) and Huse and Nedrelid (1985) on the influence of draft
on the motion of the vessel at a list angle of 15 the asymmetry in
motion with respect to wave direction was found to be reduced when
the draft was increased beyond 24 m (in full scale) where both the
pontoons were well below the water surface. That is, when the
effect of the waves were not directly felt by the inclined pontoons
near the free surface. As observed by other workers, and confirmed
in our present study, when the pontoons come closer to the water
surface either partly or wholly, the hydrodynamic phenomenon is
quite different than when they are well below the water surface
since there will be additional diffraction as well as wave
generation effects. However, these effects should be independent of
the position of the damaged column. The only difference that might
be contributing to forces when the damaged column is on the
opposite side of the weather will be the interference effects due
to the columns being at varying lengths below the water surface.
However, they cannot be so much different as to explain the
observed asymmetry of motions, when the damaged column is on the
windward side or on the leeward side.
Thus, it implies that the motion in the leeward direction is
influenced by additional phenomena other than the wave effect
alone. This leaves us to at least explore whether this asymmetry
could be possibly due to any drastically changed mooring
characteristics of the vessel. If one takes into account the fact
that the natural frequency of the vessel is shifted towards higher
frequency particularly in pitch and roll (this is clearly
demonstrated for irregular waves), then this seems a possibility. A
moored body under the action of waves oscillates about the mean
position it attains after the drifting. Since the net horizontal
drifting force is in the direction of wave advance, the windward
mooring lines are held taut in comparison to the leeward mooring
lines irrespective of the position of the damaged column. Hence,
the leeward side mooring line has sufficient freedom to oscillate
about its equilibrium position, as compared to the windward
line.
4.2. Irregular waves
Although the experiments were carried out using four different
spectra, complete analysis will be given only to one spectrum (0.81
sec) in head sea condition. To conserve the length of the paper,
the results from other spectra will be restricted to bringing out
only the very salient features.
4.2.1. Damaged condition: head seas
Heave motion. The heave magnitude spectrum showed that most of
the energy due to motion is concentrated within the frequency range
of 0.60 Hz and 1.10 Hz for even keel and all conditions of damage.
The resonance phenomenon under even keel condition occurred, as in
the case of regular waves, near 0.50 Hz which corresponded to the
natural frequency of the vessel in heave. As the damage condition
increased from light to moderate, the resonant condition seemed to
occur at a higher frequency
-
Motion response of a damaged four column semisubmersible 255
than the natural frequency of the unit. This was quite evident
for moderate leeward damage while for other damage conditions it
was slightly discernable. The resonant peak value in windward
damage was less than the corresponding peak in the high energy
frequency range (0.6-1.10 Hz). However, it was not true for leeward
damage. As in the case of regular waves, resonant heave motion was
higher for leeward damage, the peak value increasing with severity
of damage. Moderate windward damage produced at resonance an amount
only equal to the even keel values.
Surge motion. From the surge magnitude spectrum for windward and
leeward positions of the damaged column it was observed that most
of the energy due to the motion, as in heave, is concentrated in
the frequency range of 0.60--1.10 Hz. The maximum peak value of
surge RAO for windward light and moderate damage was less than the
corresponding even keel value. In other frequency ranges, the
magnitude for even keel and damage conditions was almost the same.
The leeward damage produced larger peak values in surge motion
which was slightly larger than for windward or even keel positions
at the frequency of about 0.9 Hz. In both windward and leeward
damage conditions, the peak value increased with increase in the
severity of damage. One interesting phenomenon in surge motion was
the presence of an additional higher frequency secondary component
of considerable surge motion in the frequency range of 1.3-1.5 Hz
for even keel. The maximum value in this range remained almost the
same for all the damage conditions as for the even keel
position.
Sway motion. The magnitude spectrum for sway motion showed that
throughout the entire frequency range, the sway motion at light and
moderate damage for both leeward and windward positions was
slightly more than the corresponding even keel values. However, the
sway motion under even keel was insignificant when compared with
the corresponding surge and heave motions.
Pitch motion. The pitch motion of the vessel in head sea
orientation is presented in Fig. 12 for even keel values and for
both windward and leeward position of the damaged column. As in
surge and heave motions, most of the energy is concentrated around
the frequency range of 0.70-1.20 Hz. The peak value for windward
damage in this frequency range for both light and moderate damages
is slightly less than even keel values, while the corresponding
values for leeward damages are slightly larger. Apart from this,
there is a well-recognizable peak value of about 0.12 for leeward
moderate damage near the frequency of 0.45 Hz. For windward
moderate damage this peak is not well-pronounced at this frequency.
For light damage in both windward and leeward condition, looking at
the shape of the graph, it could be said that there appears to be a
recognizable peak near the frequency of 0.2 Hz.
Roll motion. The magnitude spectrum for roll motion is given in
Fig. 13. The discussions presented above for the pitch motion is
applicable for the roll motion as well, although the magnitude of
the peaks in the roll motion is much reduced when compared with the
pitch motion. The peak value in leeward moderate damage was about
0.06.
-
256 B .M. STONE et al.
;t (a)
: l eve l
. . . . . . . . . +$0" (Windward)
- - - - +20" (Windward)
4J
I I 1
~O
o OI m
4.1
O= lid
O_
4.)
n 0 0
/ \ / \
/ \
(Io) l eve l
~O'(LeewaPd)
-20"(Leeward)
; \
I I 0.3 0 .6 0.9 ~..2 t .~
Frequency (Hz.)
FiG. 12. Pitch response for head sea in irregular wave
condition. (ISSC spectrum--significant period = 0.81 sec.)
Yaw motion. The yaw magnitude spectrum showed insignificant
motion for the entire frequency range and all damage conditions.
There appeared to be a peak value near 0.45 Hz for the leeward
damage condition, the magnitude of which was about 0.10. In other
frequency ranges for all damage and even keel conditions, the
magnitude was less than 0.05.
4.2.2. Damaged condition: beam seas
The magnitude spectra for all six degrees-of-freedom in beam
seas showed similar trends for all damaged conditions and the
values were almost nearly equal to the corresponding head sea
values. The motion energy was again concentrated in the frequency
range of 0.70-1.10 Hz.
4.2.3. Damaged condition: quartering seas
The heave magnitude spectrum for quartering seas showed that the
response was similar to the head sea and beam sea conditions. The
motion energy was again concentrated in the frequency range of
0.60-1.20 Hz. The peak values were slightly lower than the
corresponding values for head sea. However, the shift in the
resonant
-
Motion response of a damaged four column semisubmersible 257
frequency position as the damage was increased was more
well-defined than in the head sea.
The pitch motion magnitude spectrum shown in Fig. 14 indicated
that the values are significantly higher than the head sea values
(Fig. 12). Leeward damage again produced increased motion compared
with the windward damage. A careful look at the graphs in Fig. 14
also shows a shift in the resonant frequency for both light and
moderate damage conditions.
The roll motion magnitude spectrum for quartering sea showed a
similar trend as that of the head and beam sea conditions. The
magnitudes were almost equal to that of the corresponding head sea
conditions.
4.3. Effect of higher sea states The effect of increased sea
states on the motion of the vessel with moderate damage
is shown in Fig. 15 for head sea orientation and windward
position of the damaged column. As expected, the magnitude spectrum
shows higher values of motion with an increase in the sea state.
The energy due to motion in higher sea states seems to be
0
0
01
ill
i o ~ - o o o
o
Ill) 2eve2
+tO" (Ntndwor'd)
+20" (Ntndward)
I I I
Ill
O_ 0 'O 0 ;3 .kin
/ i (D) lllve'i I I 1 io" t,ee~,arci) I \ 20" ILeew, rcll I
\
\1~-I \ /~ \ /\ I \/~'-/\ --, x~. f ~ M.
0.3 0i,6 01.9 11.2 1.5 Frequency (Hz . )
FIG. 13. Roll response for head sea in irregular wave condition.
(ISSC spectrum---significant period = 0.81 sec.)
-
258 B.M. S]oN[ et al.
O~ o o (a} l eve l
\\ . . . . . . . . . +iO" (Wlndwerd]
o_ ~ / ~ - - +20" (Windward) "~ o ~ ~'~
i ! \
oo. (I0) l eve l
s // . . . . . . . . . iO" (Leeward) "o ,~ ] / -20"
(Leeward)
\,,~/ \\ / ? X o '~.\,._ -. \\
O. . / "X o ~. .~
o ! I I
g .3,,. 0 .6 0 .9 i .2 t .5 Frequency (Hz . )
Fie,. 14. Pitch response for quartering sea in irregular wave
condition. (ISSC spectrum--significant period = 0.81 sec.)
concentrated at a lower frequency range than for the lower sea
states as seen in the heave and surge spectrum.
5. CONCLUSION
Model results of the dynamic response of a partially damaged,
twin pontoon, four column semisubmersible showed that moderate (and
higher) damage conditions seemed to produced significant
subharmonic motion response of the vessel. These subharmonic
motions occur at a frequency that is twice the natural frequency of
the vessel in heave (intact condition), which lies within the
normal range of wave excitation frequencies. Model tests also
showed asymmetry in the motions of the damaged semisubmersible with
respect to the position of the damaged column. These observations
were confirmed from the results of both regular and irregular wave
studies. Additionally, irregular wave studies showed that the
energy due to the motion of the wave was concentrated in the
frequency domain of 0.7-1.3 Hz, which corresponds to the energetic
range of the normal sea state. It appears from both regular and
irregular wave studies that the natural frequency of the vessel in
pitch and roll tends to increase faster from its intact value, and
approaches the value of the natural frequency in heave as the
damage
-
Motion response of a damaged four column semisubmersible 259
0
o
Q Q
o 0
o
o
0 r~ m 13 0
m . - "O 0
4J 4.0 m g i
o 4-)
0 o
0
(s) t . 03 seconds
O. 92 seconds
~ o. . I seconds -
I I I
(a| t .03 seconds
0.92 seconds
, 0 .8 t seconde
! !
0.3 0 .6 0 .9 1!.2 t .5
Frequency (Hz . )
FIG. 15. Effect of higher-order sea states on pitch and roll
response for head sea in irregular wave condition (leeward moderate
damage condition).
condition is increased. This is true irrespective of the
position of the damaged column or the orientation of the vessel
with respect to the wave direction. The value of the natural
frequency in heave itself slowly increases with increase in damage
condition. The asymmetry in the motion of the damaged vessel with
respect to the wave direction was equally true whether the vessel
was in head, beam or quartering orientation. It appeared that
nonlinear wave effects have only a minor role when compared to the
influence of mooring characteristics in predicting the motions of
the damaged vessel.
Acknowledgements--This research was supported financially by the
National Sciences and Engineering Research Council of Canada to Dr
D. B. Muggeridge through grant A4885.
REFERENCES AMERICAN BUREAU OF SNIPPING (ABS) 1988. Rules for
Building and Classing Mobile Offshore Drilling Units
(MODU). American Bureau of Shipping, Paramus, New Jersey. CnE~,
H.H., StuN, Y.S. and WILSON, J.L. 1986. Towards rational stability
criteria for semisubmersihles--
a pilot study. Proceedings of the 3rd International Conference
on Stability of Ships and Ocean Vehicles, 22-26 September, Gdansk,
Poland, Vol. 2, pp. 61-68. Politechniqie Gdanskie.
-
26(I B.M. SIONE et al.
COLLINS, J.l. and GROVE, T.W. 1988. Model tests of a generic
semisubmersible related to a study assessing stability criteria.
OTC Paper No. 5801, Proceedings of the 20th Offshore Technology
Conference, 2-5 May, Houston, Texas, Vol. 3, pp. 497-504.
DAm.E, L.A. 1985. Mobile platform stability--project synthesis
with recommendations for new philosophies for stability
regulations. OTC Paper No. 4988, Proceedings of the 17th Offs'hore
Technology Conference, 6-9 May, Houston, Texas, Vol. 3, pp.
269-278.
GOTAVERKEN ARENDAI, A.B. 1984. Outline specification for a
scmisubmersible drilling unit. GVA 4000. GVA, Sweden.
HAMMErr, D.S. 1983. Future semisubmersible drilling units.
Proceedings of the RINA International Symposium on
Semisubmersibles--the New Generation, 17-18 March, London, U.K.
(Paper No. 9). Royal Institution of Naval Architects.
HAVIG, K.M. 1983. New Norwegian regulations for semisubmersible
unit. Proceedings of the RINA International Symposium on
Semisubmersibles--the New Generation, 17-18 March, London, UK,
(Paper No. 3). Royal Institution of Naval Architects.
HERFJORD, K. 1984. MOPS Report No. 16: Mobile platforms
stability model tests. Norwegian Hydrodynamics Laboratory Report
No. 183357, Trondheim, Norway, 76 pp.
HUANG, X., HOFF, J. and NAESS, A. 1982. On the behavior of
semisubmersible platforms at large angles. OTC Paper No. 4246,
Proceedings of the 14th Offshore Technology Conference, 3-6 May.
Houston. Texas, Vol. 2, pp. 193-203.
HUANG, X. and NAESS, A. 1983. Dynamic response of a heavily
listed semisubmersible platform. Proceedings of the 2nd
International Symposium on Ocean Engineering and Ship Handling, 1-3
March, Gothenburg, Sweden, pp. 575-587. Swedish Maritime Research
Centre.
HusE, E. and NEDRELID, T. 1985. Hydrodynamic stability of
semisubmersibles under extreme weather conditions. OTC Paper No.
4987, Proceedings of the 17th Offshore Technology Conference, 6-9
May, Houston, Texas, Vol. 3, pp. 263-268.
KORKUT, M.D. and HEBERI, E.J. 1970. Some notes on static anchor
chain curve. OTC Paper No. 1161), Proceedings of the 2nd Offshore
Technology Conference, 22-24 April, Houston, Texas, pp.
147-160.
Kuo, C., LEE, A., WELYA, Y. and MARTIN, J. 1977. Semisubmersible
intact stability--static and dynamic assessment and steady tilt in
waves. OTC Paper No. 2976, Proceedings of the 9th Offshore
Technology Conference, 2-5 May, Houston, Texas, Vol. 4, pp.
145-154.
KUO, C., VASSALOS, D. and LEE, B.S. 1983. Methods of dealing
with the stability of semisubmersibles. University of Strathclyde,
Department of Ship and Marine Technology, 20 pp.
LAURICft, P.H. 1984. The SELSPOT system: technical report.
National Research Council of Canada, Mechanical Engineering
Division, Report No. 23187.
LIVrLE, L. 1985. Hardware and software modifications to
equipment at MUN wave tank. Ocean Engineering Research Group
Report, Memorial University of Newfoundland, Canada.
LUNDGREN, J. and BERG, A. 1982. Wave induced motions of a
four-column semisubmersible obtained from model tests. OTC Paper
No. 4230, Proceedings of the 14th Offshore Technology Conference,
3-6 May. Houston, Texas, Vol. 1, Offshore Technology
Conference.
MACHA, J.M. and REID, D.F. 1984. Semisubmersible wind loads and
wind effects. SNAME Transactions, 92, 85-124.
MARTINOVICH, W.M. and PRAUGHT, M.W. 1986. Stability requirements
for semisubmersibles: a designers view point. Proceedings of the
Conference on Stationing and Stability, 16-18 June, University of
Strathclyde, U.K., pp. 3-40. Graham and Trotman, U.K.
MATHISEN, J., BORRESEN, R. and LINDBERG, K. 1982. Improved strip
theory for wave-induced loads on twin hull semisubmersibles.
Proceedings of the 1st Offshore Mechanics~Arctic Engineering~Deep
Sea Systems, 17-18 September, Gothenburg, Sweden, pp. 7.1-7.23.
MATSUURA, M. and IKEGAMI, K. 1986. Time domain simulation of
semisubmersible platform in severe sea condition. Proceedings of
the 5th Symposium on Offshore Mechanics and Arctic Engineering
(OMAE), Tokyo, Japan, 13-18 April, Vol. 3, pp. 15-22. ASME.
MOGRIDGE, G.R.. PRATI, B.D. and JAMIESON, W.W. 1986.
Hydrodynamic model study of the semisubmersible "'Ocean Ranger".
Proceedings of the 5th International Symposium on Offshore
Mechanics and Arctic Engineering (OMAE), 13-18 April, Tokyo, Vol.
3, pp. 1-8. ASME.
MOWA'FI', G.A. and ALLEN, A.P. 1986. Floating production
facility conversion: compliance with current regulations.
Proceedings of the Conference on The Way Forward for Floating
Production Systems, 15-18 December, London, U.K. (Paper No. 6). IBC
Technical Services Ltd.
MUGGERIDGE, D.B. and MURRAY, J.J. 1981. Calibration of a 58 m
wave flume. Can. J. Civil Engng 8, 449-455. NAESS, A. and How, J.R.
1984. MOPS Report No. 17: Time simulation of the dynamic response
of heavily
listed semisubmersible platforms in waves. Norwegian
Hydrodynamic Laboratory Report No. 183347, Trondheim, Norway, 25
pp.
NAESS, A., HOFF, J.R. and HERFJORD, K. 1985. Modelling of the
dynamic behaviour of damaged platforms
-
Motion response of a damaged four column semisubmersible 261
by time domain simulation methods and model tests. Proceedings
of the 4th International Conference on Behaviour of Offshore
Structures (BOSS 85), Delft, The Netherlands, 1-5 July, pp.
195-204. Elsevier, Amsterdam.
NAVAL ARChITECt, 1981. GVA 4000 and the new 2000. Naval
Architect, September 1981, E211-E213. NtJMAXA, E., MICHEL, W.H. and
McCLURE, A.C. 1976. Assessment of stability requirements for
semisubmersible units. SNAME Transactions, 84, 56--76.
PAWLOWSgl, M. 1987. Some inadequacies of the stability rules for
floating platforms. University of Glasgow,
Department of Naval Architecture and Ocean Engineering, Report
No. NAOE-87-30, 20 pp. PaAUGHT, M.W., HAUUErr, D.D., HAU~rON, J.E.
and SI'RINGErr, C.N. 1985. Industry action on stability of
mobile offshore drilling units: a status report. OTC Paper No.
4986, Proceedings of the 17th Offshore Technology Conference, 6-9
May, Houston, Vol. 3, pp. 251-262.
PRICE, W.G. and Wu, Y. 1983. Hydrodynamic coefficients and
responses of semisubmersibles in waves. Proceedings of the 2nd
International Symposium on Ocean Engineering and Ship Handling, 1-3
March, Gothenburg, Sweden, pp. 393-414. Swedish Maritime Research
Centre.
ROTHWELL, A. 1979. A graphical procedure for the stiffness of a
catenary mooring. J. appl. Ocean Res. 1, 217-219.
SPRINGE'TI', C.N. and PRAUGHT, M.W. 1986. Semisubmersible design
considerations--some new developments. Mar. Technol. 23, 12-22.
STIANSEN, S.G., STANLEY, G., SHIN, Y.S. and SHARK, G. 1988.
Developments of a new stability criteria for mobile offshore
drilling units. OTC Paper No. 5802, Proceedings of the 20th
Offshore Technology Conference, 2-5 May, Houston, Vol. 3, pp.
505-514.
STONE, B.M. 1986. An experimental study of the motion response
in regular waves of a semisubmersible under damage conditions, M.
Eng. thesis, Memorial University of Newfoundland, Canada, 115
pp.
TAKARADA, N., NAKAJIMA, T. and INOUE, R. 1986. A phenomenon of
large steady tilt of a semisubmersible platform in combined
environmental conditions. Proceedings of the 3rd International
Conference on Stability of Ships and Ocean Vehicles, 22-26
September, Gdansk, Poland, pp. 225-238. Politechniqie Gdanskie.