LOAD AND SAFETY LEVEL ON
JACKET STRUCTURES IN NORSOK N003
By
Arne Kvitrud, Sondre Nordheimsgate
9, 4021 Stavanger.
Made
5.2.2001, but put on Internet 3.8.2004.
The purpose
of this note is to review the load and safety levels inherent in the NORSOK
N003 standard. I will:
1. Review
the NORSOK procedure versus a previous "North Sea Design Practice"
(NSDP), API RP2ALRFD and the draft ISOstandard. To do this I have to find the
major differences between the standards.
2. Review
the NORSOK N003 procedure versus measurements on North Sea structures. Again
the comparison must to some extent be made using comparisons with API and NSDP.
3. Evaluate
the results of the procedure and implementation in Norway.
The NORSOK
N003 give the following requirements:
“6.2.4.2
Slender tubular structural elements
For
structures with small motions, the wave actions can be calculated as follows:
a.
If the KeuleganCarpenter number (KC) is less than 2 for a structural
element, the actions may be found by means of potential theory:
aa) If the ratio between the wave
length L and the tubular diameter D is greater than 5, the inertia term in the
Morison formula can be used with C_{M} = 2.0.
ab) If the ratio
between L and D is smaller than 5, the diffraction theory should be used.
b.
If KC is greater than 2, the wave action can be calculated by means of
the Morison formula, with C_{D }and C_{M} given as functions of
the Reynold number Re, the KeuleganCarpenter number KC and relative roughness.
It should be noted
that Morison’s equation ignores lift forces, slam forces and axial
FroudeKrylov forces.
c.
For surface piercing framed structures consisting of tubular slender
members (e.g. conventional jackets) extreme hydrodynamic actions on unshielded
circular cylinders are calculated by Morison’s formula on the basis of
·
Stokes 5^{th} order or Stream function wave kinematics and a
kinematics factor on the wave particle velocity, which is 0.95 for North Sea
conditions. This kinematics factor is introduced in the regular wave approach
to account for wave spreading and irregularity in real sea states.
·
drag and inertia coefficients equal to
C_{D} = 0.65 and C_{M} = 1.6 for smooth members.
C_{D} = 1.05 and C_{M} = 1.2 for rough members.
These values are applicable for u_{max
}T_{i}/D > 30, where u_{max} is the maximum horizontal
particle velocity at storm mean water level under the wave crest, T_{i}
is the intrinsic wave period and D is the leg diameter at the storm mean water
level.
d.
Flow conditions with u_{max }T_{i}/D < 30  in
regular waves may arise with slender members in moderate seastates which are
relevant for fatigue analysis.
Fatigue analysis can normally be
conducted with no current. The wave kinematics factor and conductorshielding
factor should be taken to be 1.0. C_{D} and C_{M} depend on the
sea state level, as parameterised by KC. For small waves with KC referred to
the mean water level in the range 1.0 < KC < 6, the hydrodynamic
coefficients can be taken to be:
C_{D} = 0.65 and C_{M} = 2.0 (smooth member)
C_{D} = 0.8 and C_{M} = 2.0 (rough members)
Members are considered smooth at
the installation stage. During operation members 2 m above MWL are considered
smooth. See Section 6.6.1.
e.
For (dynamic) spectral or timedomain analysis of surface piercing
framed structures in random Gaussian waves and use of modified Airy (Wheeler)
kinematics with no account of kinematics factor, the hydrodynamic coefficients
should in absence of more detailed documentation be taken to be:
C_{D} = 1.0
and C_{M} = 2.0
These values apply
both in stochastic analysis of extreme and fatigue action effects.
If the time domain
analysis is carried out with the nonsymmetry of wave surface elevation
properly accounted for, the hydrodynamic coefficients in item c) could be
applied
f.
Wave actions on conductors/risers may contribute to the global actions
on structures. If conductors/risers are closely spaced the actions on them may
be modified as compared to actions on individual components, due to
hydrodynamic shielding. Guidance on the shielding factor for drag actions when
the fluid flows in parallel with the main axes of a rectangular array of
cylinders may be found in ISO 131892. When the angle between the wave or current
direction and the direction of the rows of cylinders is between 22.5^{o}
and 67.5^{o}, the shielding factor in ISO 138192 can be used when the
spacing is determined as the average for the two directions. A possible
increase in the added mass (and inertia actions) for closely spaced cylinders
should be accounted for.
Shielding reduction factors
should not be applied for platforms without documentation.”
Torgeir
Moan initiated in 199495 several Norwegian companies to do analysis of jacket
structures and compare the load levels in the API RP2ALRFD standard with a
"North Sea Design Practice" (NSDP). The main element in the
"North Sea Design Practice" was the use of at dragfactor of 0.7 and
an inertia coefficient of 2. The following results are to a large extent based
on this evaluation exercise:
The
analysis was performed by Jan Inge Dalane (1995) and he found for API / NSDP:
Comments 
Base
shear 
Overturning
moment 

NSDP 
100% 
100% 

+API
hydro coeff. 
1.05 vs
0.75 on CD 
120% 
118% 
+API
water depth 
175.6 vs
172.2m 
116% 
114% 
+API
period 
15.8 vs
13.517.5 sec 
117% 
106% 
+API
current 
0.29 vs
1.0 m/s 
79% 
76% 
+
kinematics factor 
1.0 vs
1.0 
79% 
76% 
Dalane
(1995) did not say anything about if shielding was included. The API formulae
should include kinematics reduction. A current blockage of 0.85 was used,
probably is shielding included in "Hydro coeff".
The
analysis was performed by Jan Inge Dalane (1995) and is later presented in
Gudmestad and Moe (1996). He found for
API / NSDP:
Comments 
Base
shear 
Overturning
moment 

NSDP 
100% 
100% 

+API
hydro coeff. 
1.05 vs
0.75 on CD 
123% 
118% 
+API water
depth 
83.1 vs
81.7m 
120% 
117% 
+API
period 
14.8 vs
12.516.5 sec 
113% 
116% 
+API
current 
0.36 vs
1.0 m/s 
92% 
96% 
+
kinematics factor 
0.95 vs
1.0 
83% 
87% 
Dalane (1995)
did not say anything about if shielding was included. A current blockage of
0.85 was used, probably is shielding included in "Hydro coeff".
The
analysis was performed by Ingar Scherf and Jørund Osnes (1995). They used in
their API analysis :
a)
kinematics reduction factor of 0.95,
b) current
blockage factors of 0.74 to 0.88, based on "actuator disk" model
given in the API commentary. The numbers varied by direction.
c)
conductor shielding factor of 0.862 is used both for NSDP and API, based on
platform specific numerical simulations by Lick Engineering
d) no
change neither in current nor in the wave period
They found :
Base
shear 
API/NSDP 
End on 
109% 
Diagonal 
113% 
Broadside 
115% 
Mudline
moment 

End on 
106% 
Diagonal 
109% 
Broadside 
110% 
Comment :
conductor shielding factor is not a part of a NSDP.
Hansen
(1995) analysed the two jacket structures at Oseberg. He used for the API
analysis:
a) kinematics
reduction factor of 0.95,
b) current
blockage factors of 0.7, 0.8 and 0.85 dependent on direction,
c)
conductor shielding of 1.0 both for API and NSDP,
d) drag
coefficient for NSDP of 0.77 vs 1.05 for API,
e) no
change in current nor in the wave period.
He got for
Oseberg B and C :
Base
shear 
OSEBERG B
API/NSDP 
OSEBERG C
API/NSDP 
End on 
101% 
103% 
Diagonal 
105% 
107% 
Broadside 
102% 
102% 
Mudline
moment 

End on 
100% 
110% 
Diagonal 
104% 
105% 
Broadside 
101% 
102% 
By
introducing a constant current of 0.5 m/s instead of a 10 year value profile of
0.571.12 m/s he reduced the load level in the API calculations with 1520%.
The maximum
overturning moments and base shear forces are first calculated (Wang, 2000).
Jacket joints are then used as an example to check the maximum usage factors
for inplace condition by applying SESAM code check. Comparison is made based
on different design basis, i.e., NPD 1998 and NORSOK N003. To comply with
NORSOK N003, the following modifications was made:
1) Cd =
0.65 Cm= 1.6 for smooth members and Cd = 1.05 Cm = 1.2 for rough members are
applied instead of Cd = 0.7 and Cm = 2.0 according to NPD 1998. In addition, a factor
of 10% due to anodes are applied in both cases.
2) A
blockage factor of 0.85 is introduced for current.
3) A wave
kinematics factor of 0.95 is implemented.
The
definition of smooth members is according to NORSOK N003 1999, i.e., members 2
m above MWL. The maximum base shear forces and overturning moments are then
calculated and compared. It is found a maximum increment of 7% by applying
NORSOK N003. Within this 7%, the major contribution comes from point 1) above.
It is also observed that the larger C_{D} for rough members leads to
larger forces and moments for as much as 19%. On the other hand, the
introduction of blockage factor and wave kinematics, gives maximum 4% and 9%
reduction on moments, respectively.
Jacket structures
with no marine growth on it will when using NORSOK N003 get a significant load reduction compared
with previous NSDP. This will be relevant for unpiled or partly unpiled
situations.
Jacket
structures with marine growth will get about the same level of loading
using both NORSOK N003 and NSDP.
For fatigue
analysis the loading will be significantly
reduced because of the low inertia coefficients.
API and
NORSOK N003 have about the same load description. One major difference is
connected to the combination of environmental parameters. NORSOK N003
describes the combination of 10^{ 2}, 10^{ 2} and 10^{1}
for wave, wind and currents. The API combination of waves and current typically
give a 20% load reduction compared with NORSOK N003. The API does not have
stochastic lad description as NORSOK N003.
The draft
ISO standard has about the same environmental load description as API. The main
difference from API to the present draft ISO standard (ISO/TC67/SC7/WG3) is a
further reduction in the kinematics reduction factor from 0.95 to about 0.89.
The reduction in the wave load part will be about (0.95 / 0.89)^{2} =
1.14. The total load will not have this reduction if current is present, but a
value of about 10% is probably reasonable.
The Ekofisk
2/4A platform (Kanter, 1995a) was instrumented and measured during the winter
season 199394. The platform is an eight leg jacket production, drilling and
quarter platform installed in 1971. The water depth in 1993/94 was about 72.5m.
The data
was analysed in three different manners : the single wave analysis approach
based on wave time records ("level 1"), the short term statistical
analysis ("level 2") and the long term statistical approach
("level 3"). The instrumentation consisted of two EMI lasers, two
current meters, one deck accelerometer and 7 stations with four strain sensors
around the member circumference. The analysis is mainly based on a storm at
28.1.1994 having a significant wave height of about 9.2m. The largest
individual wave was 14.8m with a wave period of 11.4s. The current velocities
at the storm maximum were 0.05  0.16 m/s, and are neglected in the analysis.
The loads
were calculated using API RP 2A 20.th edition. Stoke V order theory has been
used and the velocities at both wave crest and wave trough positions have been
investigated.
The
kinematics reduction factors are calculated individually for each storm, based
on sea surface wave measurements, giving an average value of 0.92 in the wave
direction. The kinematics reduction factor reduced the predicted response by
average factors of 0.85 and 0.91 for level 1 and 2 respectively. The shielding
in the conductor group reduced the load by 13.8%.
18
individual waves were calculated having wave heights between 8.0 and 14.8m. For
each of the five structural members the COV was 0.32  0.26  0.18  0.33
0.38, with an average of 0.29. This is for the maximum base shear situation.
For the minimum base shear situations the COV were 0.36 0,35  0.28  0.47 
0.53, with an average of 0.40. These values are calculated for a load procedure
deviating slightly from API, but I assume they will be reasonable correct also
for API.
Viewing
the maximum shear case, the average bias of all (level 1) was 1.28. For the four largest (H above 13m) the
average ratio bias was 1.18. The COV is also reduced, to about 10%. My
interpretation is that when the drag contribution increases, the predictions
improves.
For the
minimum shear situation the same type of calculations are not performed, but in
my interpretation it seams to give a bias of about 1.0 for all storms and
members and 0.9 for the largest waves. The COV is also reduced to about 1020%
for the minimum base shear case.
For the
level 2 (stochastic) analysis the COV for six members were 0.20  0.16  0.13 
0.15  0.17  0.09, with an average of 0.15. The average bias for all six
storms was 1.32, but for the two largest it was 1.21.
Introducing
a reduced kinematics reduction factor, compared with API RP 2A, my
interpretation is that the loads in severe storms are predicted about correct.
There is an overprediction for the wave crest and an underprediction for the
wave trough. The standard deviation for individual members is in the order of
magnitude 20%.
The
accuracy of the predictions seems to be reduced when the sea states is reduced.
Both the bias and the COV increase when reducing the wave height.
To
compare with ISO the bias should be reduced with (0.89/0.92)^{2} =
0.94. To compare with NORSOK N003 and API the bias should be increased with
(0.95/0.92)^{2} = 1.07.
The
Ekofisk 2/4W platform was instrumented and measured during the winter season
199192 (Kanter, 1995b). The platform is a three leg jacket installed in 1972.
The water depth in 1991/92 was about 76.8m. The wave loading on the platform is
influenced by the Ekofisk Barrier. The effect in the predictions is taken into
account using McCamy&Fuchs theory.
The data
was analysed in three different manners : the single wave analysis approach
based on wave time records ("level 1"), the short term statistical
analysis ("level 2") and the long term statistical approach
("level 3"). The instrumentation consisted of one EMI lasers, one
deck accelerometer and 3 stations (one leg and two braces) with four strain
sensors around the member circumference. The largest individual wave was 17.8 m
and the wave period was 10.1s. The current velocities at the storm maximum were
typically 0.1m/s, and are neglected in the analysis.
The loads
were calculated using API RP 2A 20.th edition. Stoke V order theory has been
used and the velocities at both wave crest and wave trough positions have been
investigated.
The
kinematics reduction factor was not used in the load predictions. The predicted
responses would have been reduced with about 10% if the kinematics reduction
factor had been taken into account (Kanter, 1995b).
14
individual waves were calculated having wave heights between 4.9m and 17.8m.
For axial tension of the three structural members the bias ( for waves
above 8m) was 1.27, 1.12 and 1.15, with
an average of 1.18 (predicted/measured).
The corresponding COV ( for waves above 8m) were 0.17, 0.14 and 0.39, with an average of 0.23 (predicted/measured). For axial compression
of the three structural members the bias ( for waves above 8m) was 0.97, 0.99
and 0.98, with an average of 0.98. The corresponding COV ( for waves above 8m)
were 0.42, 0.38 and 0.21, with an
average of 0.34. These values are
calculated for a load procedure deviating slightly from API, but in general
they will be reasonable correct also for API. For the comparison with the ISO
draft, the bias should be reduced with about 10% because the kinematics
reduction factor had been taken into account (Kanter, 1995b).
For the
level 2 (stochastic) three sea states were analyses having significant wave
heights from 6.7m to 7.4m. For axial tension of the three structural members
the bias was 1.26, 1.09 and 0.50, with an average of 0.95 (predicted/measured). The corresponding COV ( for waves above 8m)
were 0.19, 0.13 and 0.17, with an
average of 0.16 (predicted/measured).
For axial compression of the three structural members the bias ( for waves above
8m) was 0.74, 0.82 and 0.39, with an
average of 0.65. The corresponding COV (
for waves above 8m) were 0.06, 0.09 and
0.15, with an average of 0.10. These
values are calculated for a load procedure deviating slightly from API, but in
general they will be reasonable correct also for API. For the comparison with
the ISO draft, the bias should be reduced with about 10% because the kinematics
reduction factor had been taken into account (Kanter, 1995b).
In a
verbal presentation done by Jan Inge Dalane in Statoil 29.11.1995 he said that
for one member (A3) of the Draupner platform an average between calculated
according to API and measured of 1.32 and a COV of 0.37. These numbers varied
from member to member. The predictions were done using API and a kinematics
reduction factor of 0.95.
The
platform is a four legs hotel platform. It had 12 accelerometers, 45 strain
gauges and 24 pile strain gauges. The waves were measured by a wave rider 2 km
away. The measurements were performed in the winter season 198182. Current
were measured at three levels. The current velocities were neglectable during
all the storms. Data were analysed for seven storm periods. The wave spreading
was calculated based on the covariance matrix of the total response of the
platform. The highest sea states had almost no spreading.
Bruce et
al (1984) demonstrate that for lower sea states (H_{S} = 2.5m  6.5m),
which is inertia dominated,  a good fit was obtained between predictions and
measurements. Only one large storm (H_{S} = 11.3m) is analysed. Here a
large non conservative discrepancy (factor of 1.27) was found. A stochastic
approach was used. The predictions were made with CD=1 and CM=2. No additional
account was taken for marine growth or anodes. The large discrepancy between
the measurements and the predictions is surprising!
Bruce et
al (1984) demonstrate that the stochastic approach gave 35% lower loads than
the design wave approach used in the design on 2/4H.
Lick
Engineering (1986) conclude that DS 449 is conservative in predicting forces,
when the wave height and period are known. DS 449 has C_{D} = 0.7 (page
23 + 31) as a minimum, the C_{M} was 2.0 and Stoke V kinematics was
used. The analysed storms have H_{s} between 2m and 7m.
According
to fig 2.5 in the report, the fit between the measurements and calculations
seems to be reasonable good. The COV seems to be high. Based on the figure and
the storm N27 having the highest responses, I have calculated a bias
(measured/calculated) of +19% and a COV of 25%. For storm N37 (number two
highest), seven of eight measurements give the measured forces to be higher
than the calculated.
Webb and
Corr (1989) conclude that that at C_{M }= 1.6 give a conservative value
for the loading and drag coefficients of 0.8 / 0.65 are conservative when considering
the overall forces on the platform. No further details are given on the load
calculation procedure. My interpretation of their figure 21 is that also C_{M
}= 1.2 would have given a conservative result. The platform had no
conductors.
Heideman
and Weaver (1992) also present results from Magnus. They describe it as an
inertia dominated structure. On total moment on the platform they report a bias
(measured  calculated) of 14 % and a COV of 32% compared with the API load
procedure. They also apply a "variable" type of coefficients as
described in the API commentary and get a bias of +18% and a COV of 32%.
Because
of the kinematics reduction factor, the ISO bias will be less favourable.
Webb and
Corr (1989) stated that tests of Forties gave C_{M} – values ranging
from 0.4 to 1.7, but no details are given.
The
platform is a four legs jacket structure. It is bridgeconnected to the
neighbour platform and it is used for quarter. It has no conductors or risers.
It had two measuring devises. The platform was instrumented with 12
accelerometers and 16 strain gauges. Data were analysed for the period
19821984. The analysed sea states varied from 5.5m to 10.8m significant wave
height.
Heavner
et al (1984) used C_{m} = 2.0 and C_{D} = 0.7 to do predictions
of the behaviour of the structure. They used a stochastic approach for the
analysis of the measurements. For H_{s}=9m the ratio of drag and
inertia forces are about 0.8. The platform was much stiffer than assumed in the
design. This is most probably caused by very conservative soil data. The comparison between predictions and
measurements were done using the observed stiffness.
For a H_{s}
= 5.7m storm the measured and the calculated data fit well at mudline. At
cellar deck the measured horizontal displacements are 3060% lower than the
calculated. Most of the difference is probably caused by the present of the
bridge, which were not in the design model. One calculation taking into account
the bridge showed a good agreement between the measured displacement and the
prediction. At mudline their table 6 give an average bias of the displacements
(measured  calculated) of +8% and a COV
of 15%.
Heideman
and Weaver (1992) present results from Tern. 165 individual waves in three
storms were analysed. They demonstrate a significant scatter and also a large
difference between different storms. Nearly all the data from the January 1992
storm fall below the curve fitted through the first two storms. All data have H
above 8m. It is a mixed draginertia dominated structure.
On
overturning moment they report a bias (measured  calculated) of +7 % and a COV
of 25% compared with the API load procedure. They also apply a
"variable" type of coefficients as described in the commentary of API
and get a bias of 7% and a COV of 25%.
On total
shear on the platform they report a bias (measured  calculated) of +11 % and a COV of 24% compared with the API
load procedure. They also apply a "variable" type of coefficients as
described in the commentary of API and get a bias of 6% and a COV of 24%.
Because
of the kinematics reduction factor, the ISO bias will be less favourable.
I assume that the ISO load procedure give a 10% load
reduction compared with API,  and API give almost the same as SNDP. I further
assume that the ISO load procedure for inertia dominated structures ( C_{M }=
1.2) give an order of magnitude of 50% load reduction compared with SNDP. I
have also assumed the COV to be about the same using SNDP or ISO.
To make a
clear summary from the investigations is not easy, because each investigator
has done it his way, but an attempt might be as follows. The results are mainly
based on response parameters and will also be very dependent on the modelling
of the structure and the loading.
Platform 
Bias 
ISO (calculated
 measured) 
COV 
Comments 
Ekofisk
2/4A 
+23% to
14% 
3040% 
drag
dominated 
Ekofisk
2/4W 
0 
36% 
Individual
waves 
Valhall
QP 
20% 
15% 
mixed
inertia + drag + stochastic 
Draupner 
+30% 
37% 
sea
states undefined 
Gorm 
40% 
25% 
low sea
states assumption mainly inertia 
Tern 
3% to
16% 
2425% 
mixed
inertia + drag 
Magnus 
+8% to
24% 
32% 
inertia
dominated 
There is
no clear tendency in the results, but my interpretation is that in average the
loads are slightly under predicted using
the ISO procedure. The COV is high for a given sea state or wave, an average
will be 2530%.
I have
not found any examples of analysis of jackets without marine growth.
Bruce et
al (1984) demonstrate that a stochastic approach give 35% lower loads than the
design wave approach used in the design on 2/4H.
Platform 
Bias 
ISO (calculated
 measured) 
COV 
Comments 
Ekofisk
2/4A 
+23% to
14% 
3040% 
drag dominated 
Ekofisk 2/4W 
0 
36% 
Individual
waves 
Ekofisk
2/4H 
40% 
 
mixed
drag + inertia + stochastic 
Valhall
QP 
20% 
15% 
mixed inertia
+ drag + stochastic 
Draupner 
+30% 
37% 
sea
states undefined 
Gorm 
40% 
25% 
low sea
states assumption mainly inertia 
Tern 
3% to
16% 
2425% 
mixed
inertia + drag 
Magnus 
+8% to
24% 
32% 
inertia
dominated 
An increase
in the environmental action (load) coefficient in the NORSOK can probably
compensate for the reduction in loading caused by the ISO procedure. An assumption which has to be made is
that the current loads is not reduced from the combination of 10^{ 2},
10 ^{ 2} and 10 ^{1} for wave, wind and currents.
The NORSOK
N001 give at present a load factor of 1.3 for a high consequence platform and
a possibility of 1.15 on a low consequence platform. To use very low load
factor is not appropriate. A minimum safety level should be left for systematic
errors and "gross" human errors. They are not handled by the
reliability model (Kvitrud et al, 2001).
Introducing
the ISO standard in Norway, will have the following consequences on the load
level of fixed steel structures:
a)
significantly reduce loading on drag dominated structures without marine
fouling. The change will mostly influence loading during installation and might
also increase the use of anti fouling systems.
b) significantly
reduce the loading on inertia dominated structures. This will mostly influence
the fatigue loading, but also some inertia dominated structures
c) minor
reduction in loading in ULS for drag dominated structures
The
reductions have to be justified by a more correct load calculation procedure,
than the present NSDP. However, the ISO load calculation procedure seams to
give loads which are lower than measured on offshore platforms.
If the ISO procedure is to be used, an increase
of the action factor from 1.3 seems reasonable. An assumption which has to be made is that the
current loads is not reduced from the combination of 10 ^{ 2}, 10 ^{
2} and 10 ^{1} for wave, wind and currents, as given in the
NORSOK N001.
Dalane Jan Inge
: A comparison of the New API Load Procedure with NPD, Statoil report no
95/327, rev 0, Stavanger, 23.3.1995
Gudmestad
Ove T and Geir Moe : Hydrodynamic Coefficients for Calculation of Hydrodynamic
Loads on Offshore Truss Structures, Marine Structures, no 9, pp 745758, 1996
Hansen Tor
: Wave Force Benchmarking, Oseberg B and C Jackets, Norsk Hydro, Bergen, 2.1.1995.
Heavner
J, I Langen and K Syvertsen : Valhall QP, EMP project, final report, Otter
report STF88 F 84037, Trondheim 26.7.1984.
Heideman J.
C. and Weaver T. O. : Static Wave Force Procedure for Platform Design, Civil
engineering in the oceans no 5, Collage station, Texas, pp 496517, 1992.
Kanter P
A : "Installation of instrumentations for platform 2/4A, summary from the
2/4A instrumentation project", Offshore Design, Billingstad, 29.9.1995.
Kanter P
A : "Installation of instrumentations for platform 2/4W, summary from the
2/4W instrumentation project", Offshore Design, Billingstad, 11.10.1995.
Langen I, N
Spidsøe, J W Heavner and T Thuestad : Valhall QP EMP project, structural system
identification, progress report 1.1, Trondheim 18.2.1983
Lick
Engineering : Evaluation of platform monitoring results (Gorm), volume II,
detailed report, Copenhagen, June 1986.
Scherf Ingar and Jørund Osnes : Wave force
benchmarking  North Sea Platforms, letter from Offshore Design to Torgeir
Moan, Asker, 15.2.1995
Wang Xiaozhi: Heimdal HMP1 
Comparison between NPD 1998 and NORSOK N003 1999, Norsk Hydro, Oslo,
20000128.
Webb R M
and R B Corr : Full scale measurements at Magnus. Proceedings of E&P Forum
Workshop on Wave and Current kinematics and Loading, Paris, 2526 October,
1989.