LOAD AND SAFETY LEVEL ON JACKET STRUCTURES IN NORSOK N-003

By Arne Kvitrud, Sondre Nordheimsgate 9, 4021 Stavanger.

Made 5.2.2001, but put on Internet 3.8.2004.

Retur

 

INTRODUCTION

Purpose

 

The purpose of this note is to review the load and safety levels inherent in the NORSOK N-003 standard. I will:

 

1. Review the NORSOK procedure versus a previous "North Sea Design Practice" (NSDP), API RP2A-LRFD and the draft ISO-standard. To do this I have to find the major differences between the standards.

2. Review the NORSOK N-003 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.

 

NORSOK N-003

 

The NORSOK N-003 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 Keulegan-Carpenter 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 CM = 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 CD and CM given as functions of the Reynold number Re, the Keulegan-Carpenter number KC and relative roughness.

It should be noted that Morison’s equation ignores lift forces, slam forces and axial Froude-Krylov 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 5th 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
CD = 0.65 and CM = 1.6 for smooth members.
CD = 1.05 and CM = 1.2 for rough members.

These values are applicable for umax Ti/D > 30, where umax is the maximum horizontal particle velocity at storm mean water level under the wave crest, Ti is the intrinsic wave period and D is the leg diameter at the storm mean water level.

d.                  Flow conditions with umax Ti/D < 30 - in regular waves may arise with slender members in moderate sea-states which are relevant for fatigue analysis.

Fatigue analysis can normally be conducted with no current. The wave kinematics factor and conductor-shielding factor should be taken to be 1.0. CD and CM 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:
CD = 0.65 and CM = 2.0 (smooth member)
CD = 0.8 and CM = 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 time-domain 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:

CD = 1.0 and CM = 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 non-symmetry 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 13189-2. When the angle between the wave or current direction and the direction of the rows of cylinders is between 22.5o and 67.5o, the shielding factor in ISO 13819-2 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.”

 


COMPARISONS OF LOAD DESCRIPTIONS

 

Torgeir Moan initiated in 1994-95 several Norwegian companies to do analysis of jacket structures and compare the load levels in the API RP2A-LRFD 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:

 

Veslefrikk jacket

 

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 13.5-17.5 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".

 

Sleipner SLR jacket

 

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 12.5-16.5 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".

 

 

Ekofisk 2/4-A

 

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.

 

Oseberg B and C

 

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 0.57-1.12 m/s he reduced the load level in the API calculations with 15-20%.

 

Heimdal HMP1

 

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 in-place condition by applying SESAM code check. Comparison is made based on different design basis, i.e., NPD 1998 and NORSOK N-003. To comply with NORSOK N-003, 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 N-003 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 N-003. Within this 7%, the major contribution comes from point 1) above. It is also observed that the larger CD 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.

 

Conclusion API-LRFD vs NSDP

 

Jacket structures with no marine growth on it will when using NORSOK N-003 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 N-003 and NSDP.

 

For fatigue analysis the loading will be significantly reduced because of the low inertia coefficients.

 

Conlusion NORSOK N-003 vs API-LRFD

 

API and NORSOK N-003 have about the same load description. One major difference is connected to the combination of environmental parameters. NORSOK N-003 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 N-003. The API does not have stochastic lad description as NORSOK N-003.

 

Conlusion NORSOK N-003 vs the ISO draft

 

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.

 

 


Comparison between the ISO procedure and full scale measurements

 

Ekofisk 2/4-A

 

The Ekofisk 2/4-A platform (Kanter, 1995a) was instrumented and measured during the winter season 1993-94. 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 10-20% 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 N-003 and API the bias should be increased with (0.95/0.92)2 = 1.07.

 

Ekofisk 2/4-W

 

The Ekofisk 2/4-W platform was instrumented and measured during the winter season 1991-92 (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).

 

 

Draupner

 

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.

 

 

Ekofisk 2/4-H

 

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 1981-82. 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 (HS = 2.5m - 6.5m), which is inertia dominated, - a good fit was obtained between predictions and measurements. Only one large storm (HS = 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 2/4-H.

 

Gorm

 

Lick Engineering (1986) conclude that DS 449 is conservative in predicting forces, when the wave height and period are known. DS 449 has CD = 0.7 (page 23 + 31) as a minimum, the CM was 2.0 and Stoke V kinematics was used. The analysed storms have Hs 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.

 

Magnus

 

Webb and Corr (1989) conclude that that at CM = 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 CM = 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.

 

Forties

 

Webb and Corr (1989) stated that tests of Forties gave CM – values ranging from 0.4 to 1.7, but no details are given.

 

Valhall QP

 

The platform is a four legs jacket structure. It is bridge-connected 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 1982-1984. The analysed sea states varied from 5.5m to 10.8m significant wave height.

 

Heavner et al (1984) used Cm = 2.0 and CD = 0.7 to do predictions of the behaviour of the structure. They used a stochastic approach for the analysis of the measurements. For Hs=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 Hs = 5.7m storm the measured and the calculated data fit well at mudline. At cellar deck the measured horizontal displacements are 30-60% 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%.

Tern

 

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 drag-inertia 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.

 

Conclusions on deterministic analysis

 

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 ( CM = 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 2/4-A

+23% to -14%

30-40%

drag dominated

Ekofisk 2/4-W

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%

24-25%

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 25-30%.

 

I have not found any examples of analysis of jackets without marine growth.

 

Conclusions on stochastic analysis

 

Bruce et al (1984) demonstrate that a stochastic approach give 35% lower loads than the design wave approach used in the design on 2/4-H.

 

 

Platform

Bias - ISO

(calculated - measured)

COV

Comments

Ekofisk 2/4-A

+23% to -14%

30-40%

drag dominated

Ekofisk 2/4-W

0

36%

Individual waves

Ekofisk 2/4-H

-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%

24-25%

mixed inertia + drag

Magnus

+8% to -24%

32%

inertia dominated

 

 

SAFETY LEVEL AND PRECAUTIONS

 

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 N-001 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).

 

CONCLUSIONS

 

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 N-001.

 

REFERENCES

 

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 745-758, 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 496-517, 1992.

 

Kanter P A : "Installation of instrumentations for platform 2/4-A, summary from the 2/4-A instrumentation project", Offshore Design, Billingstad, 29.9.1995.

 

Kanter P A : "Installation of instrumentations for platform 2/4-W, summary from the 2/4-W 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 N-003 1999, Norsk Hydro, Oslo, 2000-01-28.

 

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, 25-26 October, 1989.