5. LOADS 100 - DNVresearch.dnv.com/skj/OffGuide/CH5.pdf · Report No. 95-2018 Chapter 5 JANUARY 4,...

Guideline for Offshore Structural Reliability Analysis - General Page No._____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Report No. 95-2018 Chapter 5

JANUARY 4, 1995

5. LOADS 100

5.1 Environmental Loads 1005.1.1 General 1005.1.2 Environmental Data 100

5.1.2.1 Wind 1005.1.2.2 Waves 1025.1.2.3 Current 1065.1.2.4 Sea Water Level 109

5.1.3 Environmental Models 1095.1.3.1 Short Term Description 1095.1.3.2 Long Term Joint Environmental Description 1145.1.3.3 Long Term Marginal Distributions of Environmental Parameters 1165.1.3.4 Uncertainty of Long Term Distributions and Extremes 1175.1.3.5 Environmental Description for Operational Purposes 119

5.1.4 Load Calculations 1195.1.4.1 General 1195.1.4.2 Wind Loads 1215.1.4.3 Hydrodynamic Loads 1215.1.4.4 Loads due to Sea Water Level Variations 1235.1.4.5 Ice Loads and Loads due to Earthquake 123

5.2 Permanent Loads 123

5.3 Live Loads 124

5.4 Accidental Loads 124

REFERENCES 125


DNV Report No. 95-2018 Chapter 5

Skjong,R, E.B.Gregersen, E.Cramer, A.Croker, Ø.Hagen, G.Korneliussen, S.Lacasse, I.Lotsberg, F.Nadim,K.O.Ronold (1995)“Guideline for Offshore Structural Reliability Analysis-General”, DNV:95-2018

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5. Loads

5.1 Environmental Loads

5.1.1 General

Environmental processes are random in nature and represent a necessary input for evaluation ofenvironmental loads. The guideline is mainly focused on meteorological and oceanographicconditions, i.e., on wind, waves, current and sea water level.

5.1.2 Environmental Data

5.1.2.1 Wind

The common wind observations include mean wind speed, mean wind direction and maximumwind speed within the observation interval. Measurements are typically carried out atlighthouses, ships, at fixed positions at sea, or from satellite. The wind observations are takensimultaneously all over the world, at: 00:00, 03:00, 06:00, 09:00, 12:00, 15:00, 18:00, 21:00GMT; or 0-30 minutes before this time, Andresen (1985). The standard wind data representmeasured or calibrated 10-minute average speed, 10 m above ground or mean sea level. Windinstruments on buoys are usually mounted approximately 4 m above sea level.

If calibration of the wind data is performed, then a model uncertainty will be involved additionalto a measurement uncertainty. Wind data are recorded visually or with the aid of instruments.Visual observations are performed with reference to either movement of vegetation or the size ofocean waves, and is meant to describe 10-minute average wind speed 10 m above ground ormean sea level. The observations also give information about wind direction.

There exist two atlases including global visual wind data: a Global Wave Statistics atlas, BritishMaritime Technology (1986), and a recently published Japanese atlas for the North Pacific,Watanabe et al. (1992), the latter containing both visual and instrumental data. For the NorthPacific, the accuracy of the Japanese visual wind data is probably higher than that of the GlobalWave Statistics data, because the Global Wave Statistics data were collected from ships whosedensity of traffic in the North Pacific area was rather low.

Instrumental wind data are collected by anemometers (the wind direction may be also measuredby a wind vane). Except for hand-held anemometers, the anemometers usually average windspeed over 10-minute periods, and the result is usually registered on a graph. The instantaneouswind direction may also be recorded on a graph. Concerning the wind hindcast data it is morereasonable to assume 1 hour average wind speed. Wind observations (visual, instrumental)belong to the standard meteorological observations and should therefore fulfill the WorldMeteorological Organization, WMO, accuracy requirements, WMO (1983), which for thesynoptic meteorology wind parameters are as follows:

Wind speed : ± −1 0 1. ms for U ms1015≤ − and ±20% for U ms10

15> −

Wind direction: ±10 degrees




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where U10 denotes standard wind speed at 10 m above the ground. The quoted accuracy valuesare the 95% confidence limits.

In general, instruments are encumbered with internal instrument precision limitations. In the caseof visual observations, it is the observer's responsibility to evaluate these errors. The visualobservations collected from ships of opportunity are of varying quality and should be used withcare. Most of the anemometers have higher accuracy than required by WMO, see Table 5. 1.Tentative accuracy of wind data is given in Table 5. 2 (Θw wind direction, U10 =wind speed).

Table 5. 1 Accuracy of anemometers presented as the 95% confidence intervals,WMO (1983)

Instrument Accuracy Wind speed

Accuracy Wind direction

Vaisala ±2% up to 20 1ms−

±4% over 20 1ms− ±100

Fuess 90z ± −1 0 1. ms up to 25 1ms− ±100

MI 48/250 ± −max( . , %)1 0 101ms ±100

Propeller ± −1 0 1. ms up to 9 1ms−

±10% over 9 1ms− ±100

Propeller mounted on buoy ± −max( . , %)1 6 201ms

Table 5. 2 Instrumental accuracy of wind data, Bitner-Gregersen and Hagen(1990)

Data type Parameter Systematicerror

Random errorDistribut. Distribution parameters x σ x

Visualat Z m= 10

DirectionWind speed

negligiblenegligible

Normal θW 50

Normal u10 max( . , . )0 5 0 10110ms U−

Instrumentalat Z m= 10

DirectionWind speed

negligiblenegligible

Normal θW 50

Normal u10 0 5. × accuracy interval

of instrument, see Table 5.1

The sampling variability standard deviation for the synoptic 10-minute average wind speed canbe assumed to be as follows, Pierson (1983)

σ = 0.8 m/s for u10 < 20 m/s

(5. 1)

σ = 1.0 m/s for u10 ≥ 20 m/s

and is recommended to be modelled as a normally distributed variable, N ( , )0 2σ .




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5.1.2.2 Waves

The amount of information about the wave climate represented by a set of measured data isclosely related to the observation mode. Wave data are normally collected during approximately20 minutes each 3rd or 6th hour, and are assumed to represent stationary sea states between themeasurements. The sea state statistics is usually characterized by:

• significant wave height, Hs , or HMO (Hs=significant wave height evaluated from the waverecord, HMO=significant wave height evaluated from the wave spectrum)

• average zero-upcrossing (or zero-downcrossing) wave period, Tz or TMO2 (Tz =average zero-

up/zero-down crossing wave period evaluated from a wave record, TMO2=average zero-crossing period evaluated from the wave spectrum)

• spectral peak period, Tp , • the main wave direction, Θ .

Wave field data can be obtained visually or by means of an instrument. Visual observations arecarried out at lighthouses, weather ships, merchant ships, and describe average wave conditionsfor periods of 20 minutes. They include information about main wave direction, wave height,wave period, and sometimes also information about swell.

Instrumental observations may be collected by wave buoys, shipborne wave recorders (SBWR),surface-piercing instruments, radars, lasers and satellites. Measurements are carried out at buoystations, weather ships, fixed and mobile platforms, or by means of a satellite, and representapproximately 20-minute time series of sea surface elevations.

There are three types of wave buoys; heave, heave-pitch-roll, and cloverleaf buoys. All wavebuoys record sea surfaces elevations in situ. In addition, heave-pitch-roll buoys measure seasurface slopes, and cloverleaf buoys measure sea surface slope and curvatures. A Waveriderbuoy, WRB, is a heave buoy, and has for a long time accounted for most of the wave datarecorded on a world-wide basis. WRB data are generally accepted as the standard wavemeasurements for the design work at sea.

The World Meteorological Organization, WMO (1983), accuracy requirements for wave dataare:

± 20% for significant wave height and ± 1.0s for the average wave period.

The numbers should be interpreted as 95% confidence interval limits. However, the accuracy ofthe actual wave data collected from ships of opportunity are widely varying and generallysuspect.

There is no generally valid one-to-one relationship between the visual wave height and thesignificant wave height (instrumentally measured), or between the visual wave period and zero-crossing wave period (instrumentally measured). Thus, usually correction factors should beapplied to the visual observations, Bitner-Gregersen and Hagen (1990).




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The Global Wave Statistics (GWS) visual observations of wave climate, see British MaritimeTechnology (1986), represent the only truly global set of wave data with a sufficiently longobservation history to give reliable global climatic statistics. British Maritime Technology (1986)states that it should not be necessary to apply any correction factors, usually used for estimatingwave height and wave period from visual observations. However, the accuracy of the data is stillquestioned in the literature. As indicated by Soares and Moan (1991), Chen and Thayamballi(1991), Bitner-Gregersen et al. (1993) and Bitner-Gregersen and Cramer (1994), the GWS datashould be used with care, and if possible they should be checked against available instrumentalor hindcast data for considered areas. For the North Pacific, the visual wave observations owingto Watanabe et al. (1992) are probably of higher accuracy than the Global Wave Statistics data.The Global Wave Statistics data were collected from ships whose density of traffic in the NorthPacific area was rather low.

The instrumental accuracy depends on the type of instrument used. A study by Hasselman et al.(1973) shows that properly calibrated instruments are in general equally accurate. Wave buoysare regarded as being highly accurate instruments, and error in the estimated significant waveheight due to imperfections of the wave buoys may be considered as negligible for most seastates, Steel and Earle (1979), Monaldo (1988). During the severe sea conditions, the buoy maybe drawn through the crest of wave, causing a smoothing effect in the recorded data. In thepresence of a strong surface current, the buoy will most likely underestimate high wave heights.External forces on the buoy (e.g., breaking waves, mooring) may cause violent accelerations, thatwill lead to overestimation of the waves. These uncertainties are difficult to quantify. In steepwaves, the differences between sea surface oscillations recorded by a fixed (Eulerian) probe orlaser, and those obtained by a free-floating (Lagrangian) buoy can be very marked. Reference ismade to Longuet-Higgins (1986), Vartdal et al. (1989), Marthinsen and Winterstein (1992). Thusthe wave buoy data should not be used for estimation of wave profiles in steep waves, or wavesinducing the ringing phenomenon.

Studies by Bitner-Gregersen and Hagen (1990) show that measurement errors of WRB data, HFradar data, and SBWR data are completely masked by the natural randomness. However, SBWRtends to overestimate HS by about 8%.

Modelled wave data are produced operationally by major national meteorological services andare filed by the data centers. The accuracy of these data may vary and depends strongly on thehindcast models applied to generate the data as well as the adopted wind field. To allow hindcastdata to be used, the underlying hindcast models must be calibrated with measured data.

Table 5. 3 and Table 5. 4 include sampling variability standard deviations (uncertainty due to alimited data set) of the significant wave height and zero-crossing wave period, respectively, forvarious observed sea states for the JONSWAP spectrum. The sampling variability standarddeviations of the significant wave height and zero-crossing wave period for the Pierson-Moskowitz spectrum are shown in Figure 5. 1 and Figure 5. 2. Figure 5. 1 shows that an unbiasednoise in the measurement system will increase the measured HS . This sampling variability leadsto extrapolations of extreme wave heights and periods that are biased, as illustrated qualitativelyfor wave height by Bitner-Gregersen and Hagen (1990). A review of data from 17 storms atForties carried out by Earle and Baer (1982) indicates that the storm-peak significant waveheights determined from a single 17-minute record every three hours are biased by about 6%,relative to three-hour-average values, see Figure 5. 3.




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Figure 5. 1 The sampling variability standard deviation of Hmo for the Pierson-Moskowitzspectrum. An independent error source of 1% has been added to the sampling variability; Bitner-

Gregersen and Hagen (1990). The sampling variability is recommended to be modelled as arandom normally distributed variable.

Table 5. 3 The sampling variability standard deviation σHMO (in %) of HMO for the JONSWAP

spectrum; Bitner-Gregersen and Hagen (1990).

The sampling variability is recommended to be modelled as a normally distributed variable.

HM 0 TM 02 (sec)(m) 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 Average0-1 3.3 3.8 4.1 4.4 4.8 5.1 5.5 5.6 5.9 6.2 6.5 6.7 5.21-2 4.5 3.7 4.1 4.4 4.8 5.1 5.5 5.6 5.9 6.2 6.5 6.7 5.32-3 5.1 4.5 4.4 4.8 5.1 5.5 5.6 5.9 6.2 6.5 6.7 5.53-4 5.3 4.7 4.8 5.1 5.5 5.6 5.9 6.2 6.5 6.7 5.64-5 5.5 5.7 5.0 5.1 5.5 5.6 5.9 6.2 6.4 5.75-6 6.1 5.6 5.2 5.5 5.6 5.9 6.2 6.4 5.86-7 6.3 6.4 5.6 5.5 5.6 5.9 6.2 6.4 6.07-8 6.7 6.3 5.6 5.6 5.9 6.2 6.4 6.18-9 6.8 6.0 5.7 5.9 6.2 6.4 6.29-10 6.8 6.1 5.9 6.2 6.4 6.310-11 7.0 6.5 6.0 6.2 6.4 6.411-12 7.0 6.3 6.2 6.4 6.512-13 7.4 6.8 6.3 6.4 6.713-14 7.8 7.2 6.6 6.4 7.014-15 7.9 7.5 6.9 6.5 7.2Ave-rage

3.9 4.2 4.7 5.1 5.4 5.5 5.8 6.2 6.2 6.2 6.4 6.7




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Table 5. 4 The sampling variability standard deviation σTM02 (in %) of TM02 for the JONSWAP

spectrum, Bitner-Gregersen and Hagen (1990).

The sampling variability is recommended to be modelled as a normally distributed variable.

HM 0 TM 02 (sec)(m) 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 Average0-1 1.5 1.7 1.9 2.0 2.2 2.4 2.5 2.6 2.7 2.9 3.0 3.1 2.41-2 1.5 1.7 1.9 2.0 2.2 2.4 2.5 2.6 2.7 2.9 3.0 3.1 2.42-3 1.7 1.9 2.0 2.2 2.4 2.5 2.6 2.7 2.9 3.0 3.1 2.53-4 1.9 2.1 2.2 2.4 2.5 2.6 2.7 2.9 3.0 3.1 2.54-5 1.9 2.1 2.2 2.4 2.5 2.6 2.7 2.9 3.0 2.55-6 2.1 2.3 2.4 2.5 2.6 2.7 2.9 3.0 2.66-7 2.2 2.3 2.4 2.5 2.6 2.7 2.9 3.0 2.67-8 2.3 2.5 2.5 2.6 2.7 2.9 3.0 2.68-9 2.5 2.6 2.6 2.7 2.9 3.0 2.79-10 2.6 2.7 2.7 2.9 3.0 2.810-11 2.7 2.8 2.8 2.9 3.0 2.811-12 2.8 2.8 2.9 3.0 2.912-13 2.8 2.9 2.9 3.0 2.913-14 2.8 2.9 2.9 3.0 2.914-15 2.8 2.9 3.0 3.0 2.9Ave-rage

1.5 1.7 1.9 2.1 2.2 2.4 2.5 2.7 2.8 2.9 3.0 3.1

Figure 5. 2 The sampling variability standard deviation of Tmo2 for the Pierson-Moskowitzspectrum. An independent error source of 1% has been added to the sampling variability; Bitner-

Gregersen and Hagen (1990). The sampling variablility is recommended to be modelled as arandom normally distributed variable.




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Figure 5. 3 Illustration of the effect of sampling variability on the variance in the distribution ofsignificant wave height, Heideman et al. (1994).

5.1.2.3 Current

In most cases, the horizontal current velocity component is much higher than the vertical one.Also, it is more difficult to measure vertical than horizontal current velocities. The main bulk ofdata available are horizontal ocean current vectors, which are uniquely given in terms of speedand direction. In the guideline, attention is made to this type of data.

The main bulk of current data from Norwegian waters have been collected by the AanderaaCurrent meter Model 4 (RCM4). Other current meters in use are, e.g., the modified AanderaaCurrent Meters RCM4S, electromagnetic current meters (ECM), acoustic travel time (ATT)current meters (such as SIMRAD UMC), vector measuring current meters (VMCM), andrecently designed acoustic doppler current profilers.

For assessment of current data, it is important to have information both on the dynamic behaviourof the mooring of the current meter and of the current meter itself. Various types of moorings arepossible; the current rig may, for example, be fastened to a ship or a fixed platform, or to surfaceor subsurface buoys.

The apparent advantage of having the instrument attached to a fixed platform is that the motionof the platform itself is negligible; the disadvantage is that the platform may disturb the flow. Incase the current rig is fastened to a ship, the recordings have to be corrected for the ship's ownmovements, which may be substantial in rough weather. Owing to high expenses involved withinstrumenting a ship for current measurements, only few and short time series of current areobtained from measurements from ships.

Both for practical and economical reasons, time series at various depths through the watercolumn are normally acquired by mooring the instruments to a surface or subsurface buoy. Asubsurface buoy is typically deployed at 30-40 m below the sea surface; a surface buoy isrequired for measurements higher up in the water column.




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A data set may be erroneous due to instrument failure, such as loss of rotor or marine growth.Before application of a data set in design, it is important to make sure that a data quality checkhas been carried out. An intercomparison study between Aanderaa RCM4, RCM4S, VMCM andUCM current meters was performed in the Oceanographic Data Acquisition Project, ODAP(1986). The UCM instruments were taken as standard, and calibration formulas were establishedfor the other instruments. It was found that in general the bias was negligible for the RCM4S andVMCM from 50 m and deeper, and for the RCM4 from about 200 m and deeper. Above 200 m,the following RCM4 correction formula was suggested

[ ]τ = −��

��

max , max( , )/1

20 2 2 1 2

U U ameas meas (5. 2)

where τ is the true velocity and Umeas is the measured RCM4 value, and

[ ]a h ms= +1111 2 30 2 1 2. ( / . )

/ cm s/ at a depth of 25 m

[ ]a h m cm ss= +584 1 2 38 2 1 2. ( / . ) /

/ at a depth of 50 m (5. 3)

[ ]a h m cm ss= +812 1 4 79 2 1 2. ( / . ) /

/ at a depth of 100 m

It appears that the RCM4 measurements tend to overpredict the current velocity, and that this"overspeeding" by the RCM4 decreases with increasing current velocity.

Finally, it is suggested that, due to data uncertainty, measured current values are taken asnormally distributed estimates with mean values equal to the observed values and with standarddeviations of about 5-10 cm/s. If results of a calibration are available, the mean values should becorrected for possible bias. For Aanderaa RCM4 data, it is recommended that the correctionformulas presented above are used.

Figure 5. 4 and Figure 5. 5 show a distribution of the Morison drag force within a given sea statefor depths of 15 and 75 m, respectively. The distribution is calculated for significant wave height,zero-crossing wave period and current speed first fixed to their respective mean values;

h ms = 7 0. , t sz = 9 0. , u m sc = 0 7. / at 15 m water depth, and u m sc = 0 5. / at 75 water depth,

and then assumed to have a variation, owing to data uncertainty, about these mean values;( , )H Ts z modelled by a bivariate normal distribution with mean values 7.0 m and 9.0 s, standarddeviations 0.420 m and 0.243 s, and correlation coefficient 0.70, and the current velocity Uc

modelled by a normal distribution with mean value 0.7 m/s at 15 m water depth and 0.5 m/s at 75m water depth, and 10% coefficient of variation.




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Figure 5. 4 The distribution of the Morison drag force within a given sea state at depthd m=15 0. ; Bitner-Gregersen and Hagen (1990).

Figure 5. 5 The distribution of the Morison drag force within a given sea state at depthd m= 75 ; Bitner-Gregersen and Hagen (1990).

It is observed that by ignoring data uncertainties non-conservative values for the force at 15mdepth are obtained. At 75 m however, conservative values are obtained for a probability ofexceedance higher than 2 10 5× − .




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5.1.2.4 Sea Water Level

Variations in the sea water level are caused by• astronomical tides• metorologically induced surges

Water level data are collected either by using mechanical instruments or by using pressuregauges, wave buoys, wave radars, and lasers. Mechanical instruments have been used mainly forthe data collection along the Norwegian coast and at Svalbard, while pressure gauges, wavebuoys, and lasers have been used for recording the data from the Norwegian Continental Shelf.The mechanical instrument data are available in analogue form. Some of these data, however,have been digitized. The accuracy of these recordings is 2-3 cm. The sea water level datacollected by other instruments represent usually 10-minute average sea water levels logged every5-10 minutes and sometimes also every one hour. It is important to check whether substantialshifts in reference level takes place over time, in particular when instruments are put into serviceafter a period without recording. In recent years, several numerical models have been developedfor calculations of sea water level. For use of the computed water level data it is necessary toknow the assumptions and limitations of the models. The sea water level data are usually givenas residual sea water levels, i.e., the total sea water level reduced by the tide.

5.1.3 Environmental Models

5.1.3.1 Short Term Description

Environmental conditions are given through a set of sea states. A sea state is represented by anumber of environmental characteristics, i.e., statistical and deterministic properties of waves,wind, currents, and sea water level. Within each sea state, which has a certain duration, theseproperties are assumed to be constant. The environmental processes that constitute the loadconditions on the structure are therefore modelled as stationary stochastic processes within eachsea state. The following epistemic uncertainties are associated with such a short-termenvironmental description: measurement uncertainty, statistical uncertainty (due to a limitedsample, a fitting technique applied), and modelling uncertainty.

Wind

Wind has a stochastic nature and varies strongly in time and space. It is characterised by theaverage velocity U , the direction ϕ, and the gustiness U T . (The transverse, ′V , and vertical,

′W , wind components are usually neglected.)

Within a short term situation, the turbulent component U T is reasonably well modelled as astationary and homogeneous zero-mean Gaussian process with marginal probability density

f u uU T

T

T

UT

T

( ) exp ( )= −�

��

�

��

12

12

2

πσ σ(5. 4)




12

The variance is given by:

σ κUTc U2 2= (5. 5)

where U is the 1-hour mean wind speed 10 m above mean sea level, MSL, κ is the surfaceroughness parameter, and c is a proper constant depending on the actual gust definition and towhich extent the wind force is affected by the volume of the exposed structure. The latter effectis more accurately accounted for by introducing an aerodynamic admittance function into thewind spectrum, Davenport (1977). However, for some applications it can be reasonably wellaccounted for by a proper choice of c . κ will to some extent vary with the underlying seaconditions.

Wind velocity changes both with averaging time and height over the sea surface. For this reasonthe averaging time and the height must always be specified. It is common practice in design touse average wind velocity over 1 minute, 10 minutes or 1 hour.

The average wind speed and the wind profile may be estimated by the formula

[ ]U z t U z t zz

ttr r

r r

( , ) ( , ) . ln . ln= + −1 0137 0 04 (5. 6)

where

z = height above the still water sea surfacezr = reference height (often 10 m)t = averaging timetr = reference value for the averaging time (often 60 s, or 3600 s)U z t( , ) = average wind speed by specified z and t

U z tr r( , ) = reference wind speed.

Gust wind cycles with period shorter than about 1 minute, may be described by the gust spectrumdue to Harris, see Ochi and Shin (1988)

S f U z t ff

( ) ( , )( ) /= ′

+ ′4

22

2 5 6κ (5. 7)

where

′f = non-dimensional frequency, ′ = ⋅f f L u z t/ ( , )S = power spectral density ( / )m Hz2

f = frequency ( )HzL = length scale dimension ( )m ; may be chosen equal to 1800 mκ = surface roughness parameter; may be chosen equal to 0.0020 for rough sea and 0.0015 for moderate seaU z t( , ) = average wind velocity.

Experience indicates that the Harris model should not be used for the low frequency range( f < −10 2 Hz).




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Waves

Most offshore structures are designed to sustain gravity waves. We distinguish between gravitywaves in two states; namely wind sea, when the waves are in consistence with the local windwhich generates them, and swell, when they have escaped the influence of the generating wind.For low and moderate seas, a sea state will often be of a combined nature, i.e., it will consist ofboth wind sea and swell, Haver (1980), Soares (1984), Torsethaugen (1987, 1993). The wind seaand the swell will usually correspond to rather different frequency ranges and most often also tosomewhat different directions.

In design practice the following short term wave characteristics are used: (1) The significantwave height, HS , is defined as the average over the 1/3 highest waves in the wave record, oralternatively as H Hs mo= = 4ση , i.e., four times the standard deviation of the wave elevationprocess. For narrow-banded Gaussian waves, the two definitions become nearly identical. (2)The average zero-crossing wave period, Tz , derived from spectral moments, or alternatively thespectral peak period Tp ,. (3) The main wave direction, Θ, is most conveniently associated withthe wind direction. (4) For more detailed description, the analytical wave spectrum, S f( ), and thedirectional wave spectrum are used.

The distribution of the sea surface elevation η in deep water is usually well approximated by aGaussian model

fη

ηπσ

η µση

η

η( ) exp ( )= −

−�

��

�

��

12

12

2 (5. 8)

where µη and ση denote mean value and standard deviation, respectively. When the sea surfaceelevation is non-Gaussian, especially in intermediate and shallow water depths, the Hermitemodel, see Winterstein (1988), including skewness and kurtosis characteristics of the sea surfaceelevation is recommended.

The crest heights are well modelled by the Rayleigh distribution in deep water when non-linearities can be neglected and by 3-parameter Weibull distribution in the case of non-linear seasurface. The distribution of the individual wave heights in deep water is well described by theRayleigh curve only when the root-mean-square (rms) amplitude parameter a is used instead ofthe standard deviation ση , Longuet-Higgins (1980), Bitner-Gregersen (1983).

Thus the normalized wave height distribution is given by

f ( ) expη η η1

1 12

2 4= −�

��

�

�� (5. 9)

where

η1 = H a/H a= =2 wave heighta = root-mean-square (rms) amplitudea B= 2ση

B=parameter, typical values of B lie in a range 0.91-0.98.




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For intermediate and shallow water the Glukovskij distribution, Glukovskij (1966), Massel(1989), is recommended for representation of wave heights. A joint distribution of wave heightsand periods by means of the Longuet-Higgins distribution is recommended for approximation inreliability analyses, see Longuet-Higgins (1983).

For fully developed seas the Pierson-Moskowitz spectrum, Pierson and Moskowitz (1964), canbe used, otherwise the JONSWAP spectrum, Hasselman et al. (1973), applies. This is defined as

S f g f ffm

f ffm

m( ) ( ) exp( ( ) )exp ( )

= −− − −− −

α π γ σ2 4 5 4 22 54

2

2 2

(5. 10)

in which

fm = frequency at the spectrum maximum

α= generalized Phillips constant

γ= ratio of maximum spectral energy to maximum of the corresponding Pierson-Moskowitz spectrum

σ σ= a for f fm≤ , i.e., left-sided width

σ σ= b for f fm> , i.e., right-sided width

The JONSWAP spectrum is recommended for use in the reliability analysis.

The spectrum parameters may be assumed to be fixed or random variables. A lognormaldistribution with COV = 0 10. is commonly applied to model the uncertainty in the power of 4applied to the frequency term f in the Pierson-Moskowitz spectrum, see Kirkemo et al. (1988).

For fixed structures influenced by dynamics, e.g., deep water jackets and jackups in intermediatewater depths, a double-peaked spectrum for wind sea and swell should be considered if thecombined seas are important. The Torsethaugen spectrum (1987, 1993) is then recommended.

A possible non-conservatism is related to the choice of spectral model, as the Pierson-Moskowitzand JONSWAP spectra may lead to underestimation of the dynamic response by up to 25%,Bitner-Gregersen and Haver (1992), Karunakaran et al. (1992), see Figure 5. 6. This is due to thedifference in the frequency exponent between these models and the Torsethaugen model, seeTorsethaugen (1987). The frequency exponent is used to define the equilibrium range of thespectrum, i.e., how far out in the high-frequency range the model gives a good fit to the observedor empirical spectrum. The JONSWAP and Pierson-Moskowitz spectra adopt f −5 , while theTorset-haugen model uses f −4 . This implies that the Torsethaugen spectrum contains moreenergy around the natural period of the structures considered than the other models do, and thedynamic component of the response may become increased when using this model spectrum.Measurements indicate that the true high-frequency behaviour calls for a power term somewherebetween f −5 and f −4 .

Wind sea waves are not infinitely long-crested, and directional spectra are required for acomplete statistical description of a wind sea. A wave energy spreading function is introduced to




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account for the energy spreading among directions for a short crested sea. A common choice ofspreading function is a cosine power, e.g.,

w nne

nn( ) ( )

( )cos ( ),θ θ

πθ θ

1

2 1 22 12 1

2 1 2− = ⋅ +

+−− Γ

Γ | |θ θ π1 − < (5. 11)

where Γ (.) is the gamma function, θ is the main wave direction, and n is the exponent in thecosine function. For details reference is made to Kirkemo et al. (1988).

Figure 5. 6 A reliability analysis of a specific North Sea jacket. Axial stress versus reliabilityindex for different wave spectra, Bitner-Gregersen and Haver (1992).

Wave conditions which are to be described for design purposes, may be described also by thedeterministic design wave methods. The deterministic wave parameters may, however, bepredicted by statistical methods. There are analytical and numerical wave theories. Among thesethe following may be mentioned:

• linear wave theory, by which the wave profile is described as a sine function• solitary wave theories for particular shallow water• cnoidal wave theories which cover the waves above as special cases• Stokes wave theories for particularly high waves• stream-function waves which are based on numerical methods and accurately describe the wave kinematics over a broad range of water depths.

For recommendations of the wave theories application reference is made to DNV ClassificationNote 30.5 (1991).

Various types of design wave profiles have been suggested in the literature, typically for fixedoffshore platforms that respond quasi-statically to wave loads. These include, for example, the"NEWWAVE" profile used by Shell, based on the correlation function of the wave elevationprocess, Tromans et al. (1991). This uses conventional methods from random process theory,imposing the expected extreme wave crest in the storm duration, together with the average wave




16

profile around this crest. Extensive simulation studies have suggested that this profile, andsimilar results based on the extreme wave crest, provide rather accurate results for quasi-static,drag-dominated structures, e.g., Winterstein et al. (1994). Results are found to be rather morecomplex, however, for dynamic structures.

Ocean Current

The total ocean current is the resulting effect of several processes, whose relative importance arechanging with time. However, the current field can be divided into two subfields: a current fielddependent on the actual weather conditions and a residual current independent of the actualweather conditions.

Sea Water Level

Sea water level, SWL, D is defined commonly as the observed water level at the site when waveshave been averaged out. It contains contributions due to astronomical tides W , meteorologicallyinduced surges S (generated by wind and atmospheric pressure variations), and mean waterdepth dw

d d s ww= + + (5. 12)

The contribution owing to tide-surge interaction, which may be important in regions of veryshallow water, is herein neglected.

5.1.3.2 Long Term Joint Environmental Description

Long term variations of sea state characteristics may be approximated by joint environmentalmodels or by marginal distributions. For establishing a joint environmental description reliablesimultaneous measurements have to be available.

Joint models provide a complete description of the environmental parameters for use in areliability analysis. Additionally, such models may also be used for addressing the relativeimportance of the various environmental variables concerning their respective contribution to thefailure probability.

Joint models for various pairs of environmental parameters can be found in the literature, e.g.,E&P Forum (1985), Heideman et al. (1987), Labeyrie and Olagnon (1993). A jointenvironmental model developed by Bitner-Gegersen and Haver (1988, 1989, 1990) is morecomplete and includes the following environmental parameters:

• 1-hour mean wind speed, Uw

• wind and main wave direction, Θ (assumed to be the same)• current speed (collinear with wind and waves), Vc

• significant wave height; Hmo (wind sea and swell)• spectral peak period, Tp (wind sea or swell)• sea water level D (astronomical tides, W , meteorologically induced surges, S ).




17

The wave energy is divided between swell and sea according to a Torsethaugen model (1987).The model assumes that the surges and tides, S and W , are independent. Furthermore, it isassumed that the tidal level, W , is independent of all other environmental parameters. The longterm description of the environmental conditions is thus given by the joint probability densityfunction

f h t v u s w f h t v u s f f wH T V U SW H T V U S Wmo p c w mo p c wΘ Θ Θ( , , , , , , ) ( , , , , | ) ( ) ( )|θ θ θ= ⋅ (5. 13)

A uniform density function applies to the tidal water level W

f wwW ( ) ,= 1

2 0

− ≤ ≤w w w0 0 (5. 14)

if a sawtooth model is assumed for the time variation of this water level, or an arc sine densityfunction

f ww w

W ( ) =−

1

02 2π

, − ≤ ≤w w w0 0 (5. 15)

if a sinusoidal time variation is assumed. Here, w0 =HAT (Highest Astronomical Tide), and−w0 =LAT (Lowest Astronomical Tide). The uniform density function represents a rather crudeapproximation. The arc sine density function is usually a better approach, since the tidal waterlevel process is often reasonably well represented by a slowly varying sinusoidal wave. One maythen consider to let w0 be a random variable, representing the inherent variability in theastronomical tide amplitude, rather than just fixing it to the highest astronomical tide.

The direction variable, Θ , is conveniently discretized into a certain number of sectors and isdescribed by the corresponding probability mass function p i iiΘ( ), ,... maxθ = 1 . Furthermore, thedescription for each sector is established by factorizing the joint distribution as follows;

f h t v u w

f v h f u h f s h f t h f hH T V U

V H U H S H T H H

mo p c w

c mo w mo mo p mo mo

|

| | | | , |

( , , , , | )

( | , ) ( | , ) ( | , ) ( | , ) ( | ), , ,

Θ

Θ Θ Θ ΘΘ

θ

θ θ θ θ θ= ⋅ ⋅(5. 16)

i.e., given Hmo and Θ , the random variables V U Sc w, , , and Tp are assumed to be mutuallyindependent.

The current speed is characterized by the conditional probability mass function,p v hV H j jc mo| , )( | , );Θ θ j j= 1 2,, ..., .max

There is no theoretical preference when it comes to deciding on probabilistic models for thevarious conditional density functions. The respective choices have therefore been made on anempirical basis and are as follows;

• wind - f u hU Hw mo| ( | , )Θ θ ; a two parameter Weibull distribution given sea state severity Hmo .




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• waves - f t h f h pT H Hp mo mo| ( | , ) ( | ) ( )|Θ Θ Θθ θ θ ; a 3-parameter Weibull distribution for the wave

height, a conditional lognormal distribution for the wave period

• current - p v hV Hc mo| , ( | , )Θ θ

The total current is divided into two subfields; a wind and wave generated current, Vcw( ) , and a

residual current, Vcr( ) , including all other current components. Both these fields are discretized

into some few possible occurrences. The first field is assumed to be fully correlated to thesignificant wave height, i.e., for a given significant wave height, h , the wind and wave-inducedcurrent reads;

V hcw( ) ' '= +α α0 1 0 ≥ ≥ −z Dwc

Vcw( ) ;= 0 z Dwc< − (5. 17)

D hwc = +α α2 3' '

where z is the vertical coordinate measured as positive from the sea level and upwards, such that−z is the depth below sea level, and Dwc is the vertical extent of the wind/wave generated

current field. α α α α0 1 2 3′ ′ ′ ′, , , are empirical parameters.

The residual current component, Vcr( ) , is assumed to be completely independent of the remaining

environmental characteristics, and is described by a marginal probability mass function. The totalresulting current is finally obtained by adding the two components.

The joint environmental model approximates the current field by a very simple discrete model. Ifthe current proves to be very important in the reliability analysis, then the model should berevised.

• sea water level - f s hS Hmo| ,( | , )Θ θ a normal distribution given the significant wave height.

The distributions of the wind speed, current speed and sea water level in the joint model areconditional on the significant wave height representing the total sea (wind sea and swell). Themodel has been fitted to the data at Haltenbanken off the coast of Mid-Norway.

The joint model described above has recently been extended, see Bitner-Gregersen (1993), inorder to include the possibility of environmental effects arriving simultaneously from differentdirections. This is of importance for several engineering applications, including design ofmooring systems. The extended model has been calibrated for Haltenbanken conditions. Thewave direction relative to the wind direction is modelled using a beta distribution, withparameters specified as functions of the significant wave height. Similarly, the current directionrelative to the wind direction is also modelled using a beta distribution, but with constantparameters for a specific site.

5.1.3.3 Long Term Marginal Distributions of Environmental Parameters




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When simultaneous time series are not available environmental parameters may be approximatedby marginal distributions. Below, some recommendations on choice of the long termdistributions are given. However, each data set should be considered carefully as the same modelmay introduce conservative errors in one application and nonconservative errors in otherapplications.

Wind

The long term probability distribution of the average wind velocity at a fixed height level is wellapproximated by the Weibull type.

The mean of the gust wind velocity, defined for instance as the average wind velocity during aninterval of 3 seconds, has a long-term probability function, frequently of the Weibull type.

The variability of the extreme value can be calculated from the long term distribution or byadopting the Gumbel distribution.

Waves

The long term distribution of the significant wave height and individual wave height are usuallywell approximated by a 3-parameter Weibull distribution. The zero-upcrossing wave period andthe spectral peak period are well described by the log-normal distribution.

Variability of the extremes can be calculated from the long term distribution or by applying theGumbel model.

Current

The long term distribution of the total current velocity may be described by a 3-parameterWeibull distribution. The variability of the extremes can be modelled by the Gumbel distributionor by raising the Weibull distribution to a certain power.

5.1.3.4 Uncertainty of Long Term Distributions and Extremes

The following epistemic uncertainties are related to the long term environmental description:measurement uncertainty, statistical uncertainty (due to a limited sample, a fitting techniqueapplied) and model uncertainty (due to choice of the statistical model, the effects of clustering,and climate uncertainty). Various studies quantifying different types of uncertainty have beencarried out (e.g., Soares and Moan (1983), Carter and Challenor (1983), Bitner-Gregersen andMathisen (1988), Olufsen and Bea (1990), Winterstein and Haver (1991), Hagen (1992),Winterstein and Kleiven (1994)).

Long-term variability in the climate may be present. Model uncertainty of the climate uncertaintytype therefore appears when the observed data are obtained from a time interval that is not fullyrepresentative for the long-term variation of the environmental conditions (e.g., a design wave,calculated from a data set including moderated years only, will be underestimated). The databaseneeds to cover at least 20 years or preferably 30 years or more in order to account for climaticuncertainty. In regions where the predominating storm type is a hurricane, and the frequency ofoccurrence of extreme hurricanes at side is low (such as in the Gulf of Mexico), the uncertainty




20

in the 100-year wave height might not reach a "comfortable" level until the data base coverageactually approaches 100 years. Therefore, a long term data base with no bias and moderateuncertainty, such as hindcasts, can provide a more reliable extrapolation to extreme conditionsthan a short term data base of measurements, even if the uncertainty is small. Prediction ofextreme wave heights in regions where the extratropical and tropical storms are present isdiscussed by Heideman et al. (1994).

A fundamental problem in reliability analysis is to estimate quantiles of the extreme sea statecharacteristics from limited data sets. In general, there is a trade-off between global models basedon all data, and extreme event models based on the largest observations only. The globalapproach utilizes data from long series of regular observations. This can obscure critical tailbehavior and introduce correlation among observations (e.g., clustering). However, it is lesssensitive to uncertainties in the few largest data points. If the duration associated with each datapoint is HR hours, then the Y-year value is that which is exceeded once in Y*365*24/HR datapoints, which may be read from a curve fitted to the cumulative distribution function andextrapolated beyond the data.

The alternative method is the event approach, also known as the "peak-over-threshold" method,POT. Extreme observations in the event approach may be nearly independent, but theirscarceness increases the statistical uncertainty relative to the global approach. The method is alsosensitive to errors in the few highest data points. If the average frequency of events considered isF per year, then for a long return period Y, the Y-year event is that which is exceeded once inY*F events, which may be read from a curve fitted to the cumulative distribution of the events.

There is no general agreement on whether the global approach or the event method should beused. A choice between the methods should depend on the data set at hand as well as theapplication considered. However, for fatigue calculations for steel or steel welds all data shouldgenerally be preferred.

Table 5. 5 Statistics of estimates of Gumbel location parameter ( A=10), from sample sizesN=10, 20, 40; Carter and Challenor (1983)

(M.S.E. denotes the mean square error)

N MLE Jack- Moments Linear regression Geometric mean slopeknife /N /(N-1) Gumbel Grin. Exp. Barn. Gumbel Grin. Exp.

Bias10 0.04 0.00 0.06 0.03 -0.00 0.04 -0.00 -0.00 -0.03 0.02 -0.0320 0.01 -0.01 0.02 0.01 -0.01 0.01 -0.02 -0.01 -0.03 -0.01 -0.0340 0.02 0.01 0.03 0.03 0.01 0.03 0.01 0.01 0.01 0.02 -0.01Variance10 0.12 0.11 0.12 0.12 0.11 0.12 0.12 0.12 0.11 0.12 0.1220 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.06 0.05 0.0540 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03M.S.E.10 0.12 0.12 0.12 0.12 0.11 0.12 0.12 0.12 0.12 0.12 0.1220 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05 0.06 0.05 0.0540 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03Table 5. 5 and Table 5. 6 include statistics of estimates of Gumbel location parameter A andscale parameter B




21

F x x A B( ) exp( exp( ( ) / ))= − − − (5. 18)

for different plotting positions (Gumbel, Gringorten, expected probability, and Barnett plottingposition) and fitting techniques (maximum likelihood method, jackknife, methods of moments,linear regression, and geometric mean slope).

Winterstein and Kleiven (1994) present analytical methods to quantify the effects of clusteringand statistical uncertainty due to a limited sample. They also demonstrate that a 100-year waveheight estimated from a parametric model fit to all wave heights observed over 18 years at aNorth Sea location is 10% higher than the one estimated from an extreme event model thatconsiders only the 18 annual maxima. It does not appear that this difference can be explained bywave height dependence, or by statistical uncertainty due to the limited sample of 18 annualmaxima.

Table 5. 6 Statistics of estimates of Gumbel scale parameter ( B=1.0), from sample sizes N=10,20, 40; Carter and Challenor (1983)

(M.S.E. denotes the mean square error)

N MLE Jack- Moments Linear regression Geometric mean slopeknife /N /(N-1) Gumbel Grin. Exp. Barn. Gumbel Grin. Exp.

Bias10 -0.07 0.01 -0.08 -0.03 0.19 0.01 0.02 0.02 0.24 0.05 0.0620 -0.04 -0.00 -0.04 -0.01 0.13 0.01 0.00 0.01 0.16 0.04 0.0340 -0.02 -0.00 -0.02 -0.01 0.08 0.01 0.01 -0.00 0.10 0.03 0.03Variance10 0.06 0.08 0.08 0.09 0.13 0.10 0.10 0.09 0.15 0.11 0.1120 0.03 0.03 0.05 0.05 0.06 0.06 0.06 0.05 0.08 0.06 0.0640 0.01 0.02 0.03 0.03 0.03 0.03 0.03 0.02 0.03 0.03 0.03M.S.E.10 0.07 0.08 0.09 0.09 0.17 0.10 0.10 0.09 0.21 0.12 0.1220 0.03 0.03 0.05 0.05 0.08 0.06 0.06 0.05 0.10 0.07 0.0640 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.02 0.04 0.03 0.03

5.1.3.5 Environmental Description for Operational Purposes

In operational design and planning the time history or duration of events is the key parameter.For further information about persistence/duration statistics for operational purposes reference ismade to Bjerke et al. (1990).

5.1.4 Load Calculations

5.1.4.1 General

The reliability analysis of marine structures is dependent on the environmental loads acting onthe structures. Loads induced by wind, wave, current, sea water level, ice, snow, and earthquakeare all of random nature and should be described by probability theory. In this report, loads dueto wind, waves, current, and sea water level are mainly discussed. For ice and earthquakesreference is made to ISSC (1991).




22

Load models are affected by measurement uncertainty (through environmental parametersincluded in load models), statistical uncertainty (due to estimation of the environmentalparameters from a limited data set, and due to estimation technique applied), and modeluncertainty (due to choice of an environmental description and a load model adopted).

A common procedure is to treat wind, waves, currents, and sea water level separately and thencombine the independent extremes as if these extremes were to occur simultaneously. This is onthe conservative side and may result in an unnecessary overestimation of the design loads.However, for the structures for which only one of the environmental loads dominates, e.g., thewave load, the assumption of simultaneity of the extremes is still satisfactory. For otherstructures the design loads should rather be calculated by using a consistent joint description ofwind, waves, current, and sea water level. Unfortunately, very few data bases of reliablemeasurements are available for such purposes. Concerning wind and waves, reliable hindcastdata represent an adequate data source for establishing a proper joint description of thesequantities, especially if some simultaneous measurements are available for calibration purposes.There is still a limited number of simultaneous current data. For many areas it is therefore notpossible to fully utilize a joint description. Further investigations are still required before thejoint environmental description can be fully utilized in design.

The metocean criteria in API RP2A, API RP2A (1993a), Moses and Larrabee (1988), permit thedesigner of a new platform to take full advantage of joint probability. The guideline criteria inthe UK, UK Department of Energy (1990), recognize the fact that extreme waves, wind, currentand sea water level do not necessarily occur at the same time or in the same direction, but do notallow the designer to take advantage of this. As compensation, the UK criteria allows thedesigner to use an unrealistically low drag coefficient. The Norwegian Petroleum Directorate(NPD) guidelines, NPD (1992), allow a small reduction in metocean criteria due to jointprobability considerations. The NPD allows use of 10-year current with 100-year waves and 100-year wind, but still requires the waves and current to be applied simultaneously and collinearly.Like the UK guidelines, the NPD guidelines allow the use of low drag coefficients, partly ascompensation for the conservatism in the guideline metocean criteria.

When choosing a joint probabilistic description of the environmental processes, it is convenient,first of all, to identify the class/classes of structures it is meant to be applied to. The methodadopted for the calculation of design load effects, and the level of sophistication of anenvironmental model will depend very much on the properties of structures under consideration.

Classification of Structures and Load Mechanisms

It is suggested to classify marine structures into three classes according to the nature of motions:

Floating structures: This class includes all ships and semi-submersibles, either anchored to thebottom by catenary mooring, or freely floating. It is characteristic for these systems that they maybe exposed to large vertical as well as horizontal motions. The resulting motions are typicallygenerated by the simultaneous action of quasistatic and dynamic wind loads, first and secondorder (drift) wave loads, where the effect of a possible current is properly accounted for.

Articulated (compliant) structures: These structures are fixed to the bottom such that theyessentially attain no (or very small) direct vertical motion. However, they are typically exposedto large horizontal motions, and since they are fixed to the bottom this will inevitably introduce acertain offset-induced vertical motion. The load mechanisms are similar to those given for thefloating structures. This class includes tension leg platforms and articulated columns.




23

Fixed structures: These structures are rather rigidly fixed to the bottom and are thus exposed torather small motions. The load mechanisms are much simpler for these structures. They are notexposed to any drift force and the wind load is very well modelled as a quasi-static load process.The wave-induced response, if necessary including effects of a possible current, may be of aquasi-static or dynamic nature depending on the natural periods of the structural system.

5.1.4.2 Wind Loads

Static Wind Loads

Static wind loads have to be taken into considerations for all types of structures. Wind load isused as a part of the design criteria when designing anchor lines, mooring equipment, structuralmembers etc. In case of floating structures, righting levers must be adequate to withstand theoverturning moments from the wind. For these purposes, time averaging of extreme values of thewind speed U is given by codes. The wind load may be calculated as

F U c ADw= 1

22ρ (5. 19)

where cDW is the drag coefficient given by several codes for a number of structural members, A is

some measure of the exposed area, ρ is the air mass density (ρ is taken equal 1 2 3. /kg m for dryair). This practice, however, usually leads to overestimation of the wind load, depending on thevalue of cDW

.

The accuracy can be improved by testing a scale model of the structure in a wind tunnel which,preferably, should model the velocity and turbulence profile of the actual site as well.

Dynamic Wind Loads

For compliant and floating structures, for which wind-induced response is important, the varyingwind component should be included and expressed by a wind load spectrum. Besides mooredsemisubmersibles, tension leg platforms (TLPs) are especially sensitive to dynamic wind loads.In gusty winds, TLPs experience horizontal motions depending largely on the wind spectra andon hydrodynamical damping, which is one of the major uncertain parameters in the calculation ofmotion amplitudes.

5.1.4.3 Hydrodynamic Loads

Even though the same basic principles prevail for hydrodynamic loads on ships and otheroffshore structures, actual problems and methods for assessing these loads in the design stage arequite different between ship structures on the one hand and other offshore structures on the other.The overview of the available methods applied at present for calculation of the hydrodynamicalloads on ships is given in ISSC (1991). Herein, the discussion is limited to offshore structuresother than ships.

Morison Type of Loads




24

For a number of offshore structures, the diameters of the most important load collecting elementsare small compared to a characteristic wave length. The loads on tubular structural elements arecalculated by the well-known Morison formula

[ ]F D C v C v DC v vM w M z D= + − +ρ π ρ4

12� ( ) � (5. 20)

where

F = force per cylinder length in flow and motion directionD = cylinder diametervz = cylinder velocityvw = water velocity perpendicular to structural memberv = v vw z− = relative velocity�v = acceleration, time derivative of velocityCM = inertia coefficientCD. = drag coefficientρ = water mass density

The formula is restricted to vertical structural elements.

The values of the coefficients CM and CD are held to be of particular significance for design, butthey are still subject to discussion. They are therefore both a source of model uncertainty. Forcommon structural cross sections, typical values of CD are found in the range between 1.0 and2.0, however a value as low as 0.8 are also used from time to time. Similarly, typical values ofCM are found in the range between 1.6 to 2.5.

The drag coefficient CD is a function of Reynolds number. The inertia coefficient CM can in manycases be evaluated theoretically, as the inertia force is essentially the same force as that evaluatedby integrating the pressure over the cylinder surface in a velocity potential representation.Different values of the drag coefficient CD and the inertia coefficient CM below and above seawater level should be considered because of marine growth.

The drag term is non-linear in the velocity v . The relative importance of the drag term isgoverned by the wave steepness and the characteristic diameter.

In the reliability analysis it is recommended to adopt CM as a lognormally distributed variablewith COV = 0 10. , and CD as a lognormally distributed variable with COV = 0 20. −0 30. ,Haring and Spencer (1979), Dean et al. (1979) .

Diffraction Theory

For large-volume structures (i.e., structures for which a characteristic diameter is comparable tothe wave length), the hydrodynamic loads have to be determined by means of diffraction theory.An overview of the existing diffraction methods is given in ISSC (1991). The diffraction theoryis based on potential theory and viscous effects are neglected. Usually, a linear diffractionanalysis will have a sufficient accuracy, such that the load process becomes a linear function ofthe wave process.




25

Non-linear diffraction theory should be used for shallow water structures, for structures situatedin arctic areas with the presence of ice, for structures for which slow drift effects are important,and for calculation of springing response of a TLP.

Forces in the splash zone are not adequately described by linear waves. This effect may,however, be accounted for by various stretching techniques without adhering to the full non-linear theory.

5.1.4.4 Loads due to Sea Water Level Variations

For some offshore structures, sea water level variations should be included in calculation of thedesign loads, e.g., for a TLP a variation in water level will directly affect air gap and thereby thetether stress.

Conservative design levels will be obtained if the extreme surge and tide parameters are simplyadded together. Alternatively a joint probability model for combination of the tides and surgesmay be applied.

5.1.4.5 Ice Loads and Loads due to Earthquake

In some cases loads due to ice and earthquake have to be considered. For review of the existingmodels for ice and earthquake loads reference is made to ISSC (1991).

5.2 Permanent Loads

The uncertainty in self weight of offshore structures is normally considered to be small due tocontrol of weights during design and fabrication. At an early design stage, it is common toinclude a contingency factor of 10% on weight to account for uncertainty. This contingencyfactor is reduced as the fabrication proceeds, and it is finally removed when weighing of thestructure has been performed.

Fjeld (1978) has referred to data from Ravindra et al. (1974), Lind (1976), and Allen (1975) forpermanent load data. It is stated by Fjeld that there is agreement on a coefficient of variation inthe range of 0.07 to 0.11 and an insignificant bias factor up to 1.05. (The bias factor is defined asthe ratio of the true mean value to the nominal calculated value). Fjeld (1978) has used a biasfactor of 1.05, and a normal distribution with a coefficient of variation of 0.13 in derivation ofload effect data. As this distribution is related to that of the load effect, it includes uncertaintiesresulting from the structural analysis in addition to the uncertainty of the load.

Moses and Larabee (1988) have given some background for calibration of the API RP2A-LRFDfor fixed platforms. Herein, reference is made to studies on building loads by Ellingwood et al.(1980) with respect to dead weights. The bias factor is considered to be in the range 1.0 to 1.05and coefficient of variation from 0.05 to 0.10. Including the uncertainties that result from theanalysis, the coefficient of variation used for calibration of API RP2A-LRFD is 0.08 and the biasfactor is set equal to 1.0. The distribution is assumed to be a normal distribution.

For design of conventional offshore structures a normal distribution with coefficient of variationof 0.13 and a bias factor of 1.05 is recommended.




26

5.3 Live Loads

Extensive studies of variability of live loads have been published; however, these mainly relatesto offices, housing and bridges. Investigations clearly demonstrate that variability decreases withincreasing loading area. For the design of local parts, the possibility of concentrated heavy loadsobviously has to be considered. Fjeld (1978) therefore included the following considerations:1. Main structural elements of offshore structures are considered and not secondary structures

where the design may be governed by odd concentrated loads.2. It is the responsibility of the platform supervisor to assure that the design loads specified by

the owner are not exceeded. This is a real difference compared with structures left free forpublic use.

3. Live loads are defined as those loads exceeding the minimum dead load of the structure. Thislive load often is composed of huge modules to be lifted on board the platform by crane. Theelements of this live load are not much different from those of the dead load of the structure.Fjeld therefore based his analysis on similar statistical properties for dead loads and liveloads.

However, special attention should be given to structural support of heavy live loads, for examplethe mounting of a crane pedestal to a deck.

Moses and Larabee (1988) claims that the variability for live load is larger than for dead loadssince load placement and analysis should be more uncertain. They assume an overall coefficientof variation of 0.14 for the load effect and a bias factor equal to 1.0.

A normal distribution for live loads may be assumed for traditional design of offshore structureswith a coefficient of variation of 0.14 and bias factor equal to 1.0.

5.4 Accidental Loads

The probability of failures due to accidental loads is significantly governed by the risk of anaccidental event. The risk is normally derived or extrapolated from available statistics. It istherefore obvious that it is important to have a sound relation between the statistical basis for therisk evaluation and the structure in question. Such a sound relation is not always easy toestablish, for example if the available statistics for accidental loads pertain to jacket structures,while the structure in question is a tension leg platform, for which the jacket statistics may notnecessarily be representative. For further guidance on design with respect to accidental loads,reference is made to Veritec (1988).




27

REFERENCES

Allen, D.E. (1975), "Limit State Design - A Probabilistic Study", Canadian Journal of CivilEngineering, March 1975.

American Petroleum Institute (1993a), "Recommended Practice for Planning, Designing andConstructing Fixed Offshore Platforms - Load and Resistance Factor Design", RP2A-LRFD,First Edition, July 1, 1993.

Andresen, L. (1985), "Vindmålinger", Report (in Norwegian), DNMI (The NorwegianMeteorological Institute), Oslo, Norway.

Bitner-Gregersen, E.M. (1983), "Nonlinear Effects of Statistical Distribution of Deep WaterWaves", in North Sea Dynamics, ed. by Sundermann/Lenz, Springer-Verlag, Berlin/Heidelberg,Germany.

Bitner-Gregersen, E.M. (1993), “Distribution of Multidirectional Environmental Effects”, DetNorske Veritas Research Report No. 93-2066, to be published.

Bitner-Gregersen, E.M., and E. Cramer (1994), "Accuracy of the Global Wave Statistics Data",Proceedings, ISOPE-94 conference, Osaka, Japan.

Bitner-Gregersen, E.M., E. Cramer, and R. Løseth (1993), "Uncertainties of Load Characteristicsand Fatigue Damage of Ship Structures", Proceedings, OMAE-93 conference, Glasgow,Scotland.

Bitner-Gregersen, E.M. and Ø. Hagen (1990), "Uncertainties in Data for the OffshoreEnvironment", Structural Safety, Vol. 7., pp. 11-34.

Bitner-Gregersen, E.M. and S. Haver (1989), "Joint Long Term Term Description of theEnvironmental Parameters for Structural Response Calculations", Proceedings, 2nd InternationalWorkshop on Hindcasting and Forcasting", Vancouver, B.C., Canada.

Bitner-Gregersen, E.M., and S. Haver (1991), "Joint Environmental Model for ReliabilityCalculations", Proceedings, ISOPE-91 conference, Edinburgh, Scotland.

Bitner-Gregersen, E.M., S. Haver, and R. Løseth (1992), "Ultimate Limit State with CombinedLoad Processes", Proceedings, ISOPE-92 conference, San Fransisco, Cal.

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31

—A—Accidental load, 124Aerodynamic admittance, 110Astronomical tide

highest, 115lowest, 115

—B—Bias, 107, 123, 124

—C—Clustering, 117, 118, 119Confidence

interval, 101, 102limits, 101

Cumulative distribution function, 118Current, 100, 103, 106, 107, 114, 115, 116, 117, 119,

120, 121

—D—Damping, 121Dead load, 124Diffraction theory, 122Drag coefficient, 120, 121, 122

—E—Earthquake load, 123Event

extreme, 118, 119Excitation process

earthquake, 123

—F—Fatigue, 118

—G—Gaussian process, 109Gravity wave, 111

linear theory, 113Gust wind, 117

—I—Inertia coefficient, 122Inertia force, 122Inherent variability, 115Instrumental accuracy, 103

—J—Jackknife, 119

—L—Linear regression, 119Live load, 124Load, 109, 113, 120, 121, 122, 123, 124, 127

dead, 123, 124earthquake, 123live, 124permanent, 123wave, 113, 120, 127wind, 120, 121

Load process (Excitation process), 121, 122Lognormal distribution, 112, 116LRFD (Load and Resistance Factor Design), 123, 125,

127

—M—Model, 100, 110, 111, 112, 114, 115, 116, 117, 119,

120, 121, 123uncertainty, 100, 117, 120

—O—Observations, 100, 101, 102, 103, 112, 118

—P—Potential, 122Potential theory, 122Power spectral density, 110Probability of failure, 124

—R—Rayleigh distribution, 111Reliability index, 113Resampling

jackknife, 119Response, 112, 121, 123Return period, 118Ringing, 103

—S—Safety index (reliability index), 113Sea elevation (surface elevation), 113Sea state, 102, 103, 107, 108, 109, 111, 114, 115, 118Significant wave height, 102, 103, 106, 107, 111, 114,

116, 117Simulation, 114Skewness, 111Spectral density, 110Spectrum

JONSWAP, 103, 105, 112Torsethaugen, 112

Springing, 123State, 102, 103, 107, 108, 109, 111, 114, 115, 118Statistical uncertainty, 109, 117, 118, 119, 120Stochastic process, 109




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normal, 109Surface elevation, 102, 111, 113Swell, 102, 111, 114

—T—Tail behavior, 118Turbulence, 121Turbulence intensity, 121

—W—Wave climate, 102Wave crest, 113Wave direction, 102, 111, 113, 114Wave force

drag, 107, 108inertia, 122

Wave height, 102, 103, 106, 107, 111, 112, 114, 116,117, 118, 119distribution, 111significant, 102, 103, 106, 107, 111, 114, 116, 117

Wave period, 102, 103, 107, 111, 116, 117Wave spectrum, 102, 111

JONSWAP, 103, 105, 112Torsethaugen, 112

Wave theory, 113linearized, 113

Weibull distribution, 115, 116, 117Wind, 100, 101, 103, 109, 110, 111, 112, 114, 115,

116, 117, 119, 120, 121gustiness, 117

Wind sea, 111, 112, 114Wind spectrum, 110Wind speed

mean, 100, 110, 114

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