Return Period for Environmental Loads – Combination of Wind and Wave Loads for Offshore Wind Turbines Claus F. Christensen and Torben Arnbjerg-Nielsen RAMBØLL, Bredevej 2, DK-2830 Virum Abstract: In order to reduce the CO 2 emissions the focus on renewable energy from wind turbines has increased in the last years. Due to the size of the wind turbines and the large area a wind turbine park requires it is reasonable to place the parks at sea. Building offshore wind farms generates needs for new knowledge about the environmental conditions and how the different loads should be combined. The present paper describes an approach for obtaining the environmental condition that corresponds to the maximal response for given return period. The environmental conditions are here the mean wind velocity and the significant wave height, but the described procedure is general and can easily be expanded. Moreover the corresponding partial safety factor is obtained for the operation design case and the extreme design case. 1. Introduction Design of offshore wind turbines is in general based on simulations of the response corresponding to predefined time series. The present paper describes an approach for the determination of these time series of the external environmental loads to be applied in the calculation of the offshore wind turbine response. The approach is a very general approach and it is illustrated by examples with two correlated environmental parameters, i.e. mean wind velocity and significant wave height for two different directions which corresponds to two different correlation levels. The approach is based on inverse FORM. By means of inverse FORM environmental contours can be determined independent of the structural response. Contours representing extreme environmental conditions, e.g. 50-year return period can be examined and the corresponding maximum structural response can be obtained. The scope of the present paper is to establish the return period for the different environmental loads that corresponds to an e.g. 50-year return period for the response and the corresponding partial safety factor. 2. Code format The proposed code format for the determination of the extreme response is illustrated in Figure 1. The external loads are given in terms of combinations of time series for a number of individual loads, e.g. wind, wave, current, etc. For each of these combined time series of environmental loads the maximum response is determined.
Transcript
Return Period for Environmental Loads – Combination of Wind andWave Loads for Offshore Wind Turbines
Claus F. Christensen and Torben Arnbjerg-NielsenRAMBØLL, Bredevej 2, DK-2830 Virum
Abstract: In order to reduce the CO2 emissions the focus on renewable energy fromwind turbines has increased in the last years. Due to the size of the wind turbines andthe large area a wind turbine park requires it is reasonable to place the parks at sea.Building offshore wind farms generates needs for new knowledge about theenvironmental conditions and how the different loads should be combined.
The present paper describes an approach for obtaining the environmental condition thatcorresponds to the maximal response for given return period. The environmentalconditions are here the mean wind velocity and the significant wave height, but thedescribed procedure is general and can easily be expanded. Moreover the correspondingpartial safety factor is obtained for the operation design case and the extreme designcase.
1. Introduction
Design of offshore wind turbines is in general based on simulations of the responsecorresponding to predefined time series. The present paper describes an approach forthe determination of these time series of the external environmental loads to be appliedin the calculation of the offshore wind turbine response.
The approach is a very general approach and it is illustrated by examples with twocorrelated environmental parameters, i.e. mean wind velocity and significant waveheight for two different directions which corresponds to two different correlation levels.
The approach is based on inverse FORM. By means of inverse FORM environmentalcontours can be determined independent of the structural response. Contoursrepresenting extreme environmental conditions, e.g. 50-year return period can beexamined and the corresponding maximum structural response can be obtained.
The scope of the present paper is to establish the return period for the differentenvironmental loads that corresponds to an e.g. 50-year return period for the responseand the corresponding partial safety factor.
2. Code format
The proposed code format for the determination of the extreme response is illustrated inFigure 1. The external loads are given in terms of combinations of time series for anumber of individual loads, e.g. wind, wave, current, etc. For each of these combinedtime series of environmental loads the maximum response is determined.
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The simulations are carried out for a number of time series, and the extreme response isdefined as the average value of the obtained extreme values for the various timesimulations.
Static and dynamic loadsF(t) = Σ Fi(t)
ResponseMax{R(t)}
Design extremeRd = γf E[Max{R(t)}]
Design ExtremeMc/γm > Rd
ResistanceMc/γm
Figure 1: Illustration of design process – time simulation.
The time series of the external loads are to be defined so that the average value of theextreme response found by the simulation is an estimate of the characteristic value ofthe response (50-year return period). The design value is found by multiplying thecharacteristic response with the partial safety factor and it is required to be larger thanthe design value of the carrying capacity.
In the following sections an approach is outlined for the determination of theenvironmental condition which leads to the 50-years return period of the response.Further the corresponding partial safety factor γf is estimated.
3. Contours of environmental parameters
Contours of environmental parameters are contours along which specified extremefractiles lie, ref. /1/. The contours are independent of the structure under consideration,making the contours a general and practical way of illustration extreme combinations ofenvironmental parameters.
The approach is based on first-order reliability method (FORM), or in fact inverseFORM in the sense that the environmental contours are identified corresponding tohyperspheres with a given radius β in the normalised space, ref. /1/ and /2/.
The extreme response of a given return period is then identified as the maximumresponse along the contour for the β corresponding to the required return period. Inaddition the point on the contour corresponding to the maximum response, identifies thecombination of the environmental parameter, which yields the maximum response forthe wanted return period.
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The basis for the evaluation of the environmental contour is the instantaneousdistributions for the stochastic environmental parameters.
In the present case two parameters are considered, wind and waves, but the approach isapplicable for higher dimensions as well . The instantaneous distributions are given asthe distribution of the mean wind velocity V and the significant wave height Hs
conditioned on the mean wind velocity
)(and)( vhFvF VHsV (1)
The mean wind velocity and wave height may also depend on the direction and thedistributions could therefore also be conditioned on direction. Especially the significantwave height is sensitive to the fetch length and water depth and may therefore vary a lotwith the direction.
Utili sing ” inverse FORM”, ref. /1/, the basis is the reliabili ty index β, corresponding tothe required return period. The following relationship exists between the reliabili tyindex β , the probabili ty pf, and the required return period Tr
)24365
1()1( 11
r
SSf T
Tp
⋅−Φ=−Φ= −−β (2)
where TSS in hours is the duration of the environmental conditions, e.g. mean windperiods or seastates and Tr is the return period in years.
In the standard normal space the interesting combinations are thus located on ahypersphere of radius β corresponding to the required return period Tr, described by
β=+ 22
21 UU (3)
where U1 and U2 are the coordinates in the standard normal space, from which thephysical environmental parameters are found from transformation, see ref. /3/,
))((
))((
21
11
UFHs
UFV
VHs
V
Φ=
Φ=−
−
(4)
3.1 Example: TSS for a 10-minute environmental condition
In case an n-years return period is required for a 10-minute environmental condition,e.g. mean wind velocity, the corresponding effective period TSS must be obtained. Dueto the large correlation between two subsequent mean wind velocities this period is not10 minutes.
4
Based on a time series of 17 year containing the 10 minutes mean wind velocitymeasured 45 m above ground, ref. /9/, the correlation function is estimated to
)/exp()( Ttt −=ρ
where T = 20.16 hours.
Based on the given correlation function the effective number of observations nef in atime series containing n, successive 10 minutes wind velocities can be found as, ref. /8/
11
12
)(21
−−
=
−+= ∑ j
n
jef jn
nnn ρ (5)
where ρj is the correlation between to mean wind periods with the distance j times 10minutes.
The value of Tss is then obtained as 10 minutes times n divided by nef, which yields a Tss
of about 40 hours or 241 periods of 10 minutes.
In case a 50-year return period is required for the environmental condition thecorresponding reliability index reads
74.3)2436550
401()1( 11 =
⋅⋅−Φ=−Φ= −−
fpβ (6)
For other return periods the corresponding reliability index is shown in Table 1 for theconsidered environmental condition.
Return period(year)
Reliability index (β)
Probability(pf)
5 3.12 9.13⋅10-4
10 3.32 4.57⋅10-4
50 3.74 9.13⋅10-5
100 3.91 4.57⋅10-5
200 4,08 2.28⋅10-5
500 4,28 9.13⋅10-6
1000 4,44 4.57⋅10-6
10000 4,91 4.57⋅10-7
Table 1: Return period and corresponding reliability index and probability for theconsidered environmental condition.
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3.2 Example: Contours at Horns Rev
The distribution at Horns Rev is based on 3 month of measurements covering alldirections. The significant wave height is measured every hour and the 10 minutes meanwind velocity is measured once each hour.
The mean wind velocity V in a height of 60 meters is assumed to follow a two-parameter Weibull distribution given as
))(exp(1)( kV a
vvF −−= (7)
where the parameters a is 11 m/s and k is 1.8. The distribution is used independent ofdirection and is in general found to fit well to the Danish wind climate.
The used distribution for the significant wave height conditioned on the mean windvelocity is based on approximately two months data. The 10 minutes average windvelocity is measured once each hour together with the significant wave height measuredevery hour. The distribution is obtained from two directions. The first direction – Case 1– covers the angle space 240° to 320°, where north corresponds to 0°. The otherdirection – Case 2 – corresponds to the angle space 40° to 110°. Due to the very limiteddata only the obtained distribution for case 1 is reasonable, whereas the distribution forcase 2 is very uncertain and serves only for ill ustrative purpose.
The significant wave height Hs, conditioned on the mean wind velocity, V, is assumedto follow a Gaussian distribution with the parameters given in Table 2 below
Hs conditioned on V Mean Value Standard DeviationCase 1 (240° to 320°) 0.13V 0.24 mCase 2 (40° to 110°) 0.07V 0.50 m
Table 2: Mean and standard deviation for the Gaussian distributed significant waveheight HS conditioned on the mean wind velocity in meter per second.
Based on the assumed distributions the correlation between the mean wind velocity andthe significant wave height can be calculated theoretically to 0.95 for case 1 and 0.62for case 2, respectively.
It is noted that the Gaussian distribution for the significant wave height includesnegative values for small mean wind velocities. However as the present analysisaddresses extreme values this is of no importance.
In the standard normal space the environmental condition along the contoursrepresented by
β=+ 22
21 UU (8)
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can be transformed into contours in the physical space utilising the above equations andthe following transformations
VUUFHs
ULnaUFV
VHs
kV
ασ +=Φ=
Φ−−=Φ=−
−
221
/111
1
))((
))(1(())(((9)
where α and σ are (0.13; 0.24) for case 1 and (0.07; 0.50) for case 2, and a is 11 m/sand k is 1.8.
The obtained contours for the two cases are shown in Figure 2 and the correlationbetween the environmental loads is clearly reflected in the shape of the contour.
Return period 5 yearReturn period 10 yearReturn period 50 yearReturn period 200 yearReturn period 1000 year
Figure 2: Environmental contours Horns Rev. Left: Case 1: direction WNW with highcorrelation. Right: Case 2: direction E with low correlation.
3.3 Example: Contours at Rødsand
Studies of joint distributions for significant wave height and wind velocity has beenreported in ref. /4/, based on an analysis of the environmental conditions at Rødsand.
In ref. /4/ the significant wave height is taken as the unconditioned parameter and themean wind velocity is then conditioned on the wave height. The significant waveheight, Hs, in an arbitrary sea state is assumed to follow a two-parameter Weibulldistribution
))(exp(1)(0
h
S h
hhFH
β−−= (10)
where h0 = 0.863 m and βh= 1.817. The 10-minute mean wind velocity V conditioned onthe significant wave height is assumed to be log-normal
where Hs is the significant wave height in meters and z denotes the height in metersabove sea level and a0 and a1 is given as
7582.1ln368.00 += za and 771.5ln0667.11 += za
In ref. /4/ it is stated that the auto-correlation function for the significant wave heightcan be adequately represented by a two-parameter exponential decay model as
))sinh()(cosh()exp()( btb
abtatt +−=ρ
where the parameters a and b are estimated to 0.837 and 0.793, respectively.
Based on the estimated correlation function and the formula given in equation (5) theeffective number of 1 hour sea-states in a time series with n observation can beobtained. The duration between two independent 1 hour sea-states is then obtained to 46hours.
)24365
461()1( 11
⋅⋅−Φ=−Φ= −−
rf T
pβ (14)
where Tr is the return period. For a 50-year return period the target β is 3.71.
Using the transformation given in equation (3) and (4) the environmental condition forRødsand can be obtained. The contours are given in Figure 3 for z equal to 70 m. It isseen from the figure that the correlation between the mean wind velocity and thesignificant wave height at Rødsand is high. Moreover it is seen that the environmentalparameters in general are somewhat smaller at Rødsand than at Horns Rev.
8
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
0 5 10 15 20 25 30 35 40Mean wind velocity [m/S]
Return period 5 yearReturn period 10 yearReturn period 50 yearReturn period 200 yearReturn period 1000 year
Figure 3: Environmental contours for mean wind velocity and significant wave heightat Rødsand
4. Extreme response – envir onmental parameters
In the previous section the relevant combinations of environmental parameterscorresponding to a given return period are identified. These combinations are to becombined with the response of the structure under consideration in order to determinewhere on the contour the extreme value lays for the given return period. This point willfurther more define the combination of external environmental parameters to be appliedin the deterministic design approach.
The used response model is described in ref. /5/. The model calculates the mean value,µr, standard deviation, σr, and the standard deviation on the response velocity, r
�σ ,based on given wave and wind spectra. The spactra depend on the mean wind velocityand significant waveheight.
The extreme value of the response is modelled by a filtered Poisson process, i.e.
))(1(exp(),(max rFttrF −⋅−= λ (15)
where λ is the intensity of the Poisson process, t the time period over which the extremeis considered and F(r) is the distribution of the pulses in the response process.
For a normal distributed response r as in ref. /5/ with the mean value and standarddeviation (µr, σr) the expected number of up-crossings of the level ε is given by Rice’sformula as
−−=
2
0 2
1exp)(
r
r
σµενεν ε (16)
9
where ν0 denotes the expected number of up crossings of the mean level µr per unit ofthe time t given by
r
r
σσ
πν
�
2
10 = (17)
Having the response given as a Gaussian process described by the normal distributionfunction as stated above and by assuming that each up crossing of the level ε isindependent, the distribution for the extreme in the period t can be approximated by
−−⋅−= ))(2
1exp(exp)( 2
0maxr
rtFσ
µενε (18)
The median value of the maximum response, which is slightly lower than the averagevalue, in the period t is thus given as
rr tµ
νσε +
−=
0
)2ln(ln2 (19)
4.1 Example: Response applied for illustration
The considered wind turbine used together with the environmental contours for HornsRev is an active stall-regulated turbine with a hub height of 63.5 m, placed on a waterdepth of 9 m. The lowest natural frequency of the structure is 0.401 Hz and the rotordisc are is around 3160 m2.
The sea roughness is put to 0.004 m and the turbulence intensity is assumed constantwith a value of 10.34 %. The waves are assumed to follow a Pierson-Moskowitzspectrum where the peak period is a function of the significant wave height given as
gHT sp /190= (20)
where g is the gravity. The response model is described in details in ref. /5/.
The design response for a wind turbine in operation is typically in the same range as thedesign response for a parked turbine under extreme conditions. The established modelfor the wind turbine response takes this automatically into account by changing thewind load when the mean wind velocity becomes larger than the so-called cut-out meanwind velocity, which in this case is put to 25 m/s. For larger mean wind velocities thewind turbine will be parked and the wind response will hereby reduced. The consideredresponse is the overturning moment and the shear force at the seabed and the calculatedresponse is seen in Figure 4 where the change in response at V=25 m/s also is verydistinct.
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Figure 4: Response for maximum expected shear force (left) and maximum expectedoverturning moment (right).
From the figures it is seen that the mean wind velocity governs the overturning moment,whereas the influence of the significant wave height is very limited. The shear force ismost sensitive to the significant wave height, but both environmental parameters areimportant when the shear force is considered.
The maximal response for a given return period is then obtained by searching on thecontours shown in Figure 2. For the operation design case the mean wind velocity islimited at 25 m/s and only the significant wave height increases when the return periodincreases. The maximal shear force and overturning moment are in all cases obtainedfor the same combination of wind and wave load. The results are given in Table 3 andTable 4.
Table 3: Characteristic shear force response and return periods for the individualenvironmental loads for the different response return periods for Horns Revcase 1 (large correlation).
Table 4: Characteristic overturning moment and return periods for the individualenvironmental loads for the different response return periods for Horns Revcase 1 (large correlation).
From Table 3 and Table 4 it is seen that the characteristic overturning moment is largestin the operation situation for return periods up to 50 years, whereas the characteristicshear force in the operation situation is largest up to a return period of 10 years.Moreover it is seen that when the correlation between the loads is high, the return periodfor the loads in the extreme situation is close to the return period for the response. In theoperation situation the wave height is limited due to the high correlation and becomesalmost constant for any return period. This emphasises that two design situation are tobe considered – operation and extreme environmental conditions.
Results for case 2 with low correlation are given in Table 5 and Table 6.
Table 5: Characteristic shear force response and return periods for the individualenvironmental loads for the different response return periods for Horns Revcase 2 (low correlation).
Table 6: Characteristic overturning moment and return periods for the individualenvironmental loads for the different response return periods for Horns Revcase 2 (low correlation).
In the second case where the correlation between the loads is more limited, it is seenthat the operation situation is governing the design for return periods up to around 50 to100 years. Moreover it is seen that for the shear force response, which is slightly wavedominated the return periods for the environmental loads are only about half of thereturn period for the response. For the overturning moment, which is dominated by thewind load due to the long internal arm, the reduction in return period is not thatsignificant. It is also seen that when the correlation between the loads is limited thesignificant wave height increases in the operation situation for increased return periods.
Return period 5 yearReturn period 10 yearReturn period 50 yearReturn period 200 yearReturn period 1000 year
�
Max shear force�
Max overturning moment
Operation Extreme
Figure 5: Location of the maximum response shown on the environmental contoursfrom Figure 3. Left: Horns Rev case 1: direction WNW with high correlation.Right: Horns Rev case 2: direction E with low correlation.
From Figure 5 it is seen that if the correlation between the loads is low, the loadcombination causing the maximum response is not obvious and the combination maydepend on the type of response. Figure 5 right, shows that the maximum expected shearforce (the full black circles) will occur for a larger significant wave height than theoverturning moment (the stars), which is dominated by the wind load.
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In order to evaluate the benefit of the given procedure, the response is calculated for the50-year return period for both environmental loads for the extreme situation, and a 50-year return period for the significant wave height together with a mean wind velocity of25 m/s for the operation situation. The 50-year return period corresponds to a meanwind velocity of 38.29 m/s and significant wave height of 5.09 m for the first case withlarge correlation and 3.36 m for the case with low correlation.
Operation situationCorrelation Hs [m] V [m/s] Shear force
Table 8: Operation responses for a 50 year return period for the significant wave heightand a mean wind velocity of 25 m/s.
From Table 7 and Table 8 it appears that if the correlation is large in the operationsituation a 50-years significant wave height is extremely conservative. The 25 m/scorresponds to a very low return period (approximately 0.37) and due to the strongcorrelation the significant wave height will be in the range of return period. In theextreme situation and when the correlation is low the benefit is more limited, but thoughstill considerable.
It should be noted that the given procedure assumes that the maximal response cannotoccur for a lower return period than the considered, which is a non-conservativeassumption. There is a minor probability of that the largest response can occur for a loadcombination that corresponds to a lower return period, but this probability is minor andwill decrease with the length of the considered period.
5. Par tial safety factor – response
In most codes it is the individual environmental loads that are multiplied by a partialsafety factor and not the response as suggested in this case. For an offshore wind turbinethe relation between the environmental loads and the response is non linear in somecases and the suggested procedure is therefore be more suitable.
According to the code format, see Section 2, the maximal expected response should bemultiplied by the partial safety factor, and the safety factor does therefore depend on thecoefficient of variation of the extreme response.
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The total coefficient of variation for the structural response contains the followingcontributions. A contribution due to the statistical uncertainty caused by the randomnature of the load process, a contribution covering the physical uncertainty in how theflow converts into load on the structure (for the wind load this term is around 25 %according to ref. /7/) and finally a contribution covering the model uncertainty. Thecoefficient of variation for the model uncertainty for the wind is according to ref. /7/around 14 %.
The variation of the extreme response obtained by the procedure described in Section 4can be established by determining the maximal response for different return periods, i.e.different fractiles in the upper tail of the response distribution.
Using the obtained response values for the chosen fractiles an extreme value distributioncan be fitted to these values. In this case a Gumbel distribution is fitted by use of a leastsquare fit, and the Gumbel distribution seems to fit very well to the obtained values. TheGumble distribution fits very well because the dependence between the response and theWeibull distributed mean wind is almost linear, especially for the case with largecorrelation. Knowing the parameters in the distribution fitted to the upper tail thecoefficient of variation of the responds can be calculated.
In Figure 6 the fitted Gumble distribution is shown together with the calculated valuesfor the extreme situation and large correlation between the environmental loads.
0,78
0,82
0,86
0,90
0,94
0,98
1,2 1,3 1,4 1,5 1,6Max Response: Shear force [MN]
Emperical
F-Gumbel
0,78
0,82
0,86
0,90
0,94
0,98
24,0 28,0 32,0 36,0 40,0 44,0Max Response: Overturning moment [MNm]
Emperical
F-Gumbel
Figure 6: Empirical and fitted extreme distribution for the extreme situation withlarge correlation between the environmental loads.
The corresponding figures for the operation situation for the case with large correlationis given in Figure 7.
15
0,78
0,82
0,86
0,90
0,94
0,98
1,20 1,22 1,24 1,26 1,28 1,30Max Response: Shear force [MN]
Figure 7: Empirical and fitted extreme distribution for the operation situation withlarge correlation between the environmental loads.
For the operation situation the extreme distribution fit is not unique, but the coefficientof variation on the operation response is very low because the mean wind velocity isconstant (25 m/s) and only the significant wave height increases when the return periodincreases. The obtained coefficient of variation on the response in the differentsituations is given in Table 9.
Operation situation Extreme situationCorrelation C.o.V. Shear C.o.V. Moment C.o.V. Shear C.o.V. Moment
For an offshore wind turbine the physical uncertainty may be lower than stated in ref./7/ which covers normal land structures, because the external pressure coefficient, theterrain topography and roughness is well determined. Moreover the uncertainty in theload transformation from the waves may be lower than the wind and a contributionaround 18 to 20 % instead of the 25 % may be more realistic. (The 25 % reduce to 18 %if the uncertainty contribution from the terrain topography and roughness is neglected).The total uncertainty used to determine the safety factor is then calculated as shown inthe following example taken from ref. /7/.
Considering a structure only exposed to wind load the total coefficient of variation canbe calculated as
)1)(1)(1)(1()1( 22222Jccqtot VVVVV
pe++++=+ (21)
where pe ccq VVV ,, and VJ are the coefficients of variation of the extreme wind, exposure
coefficient, external pressure coefficient and the model uncertainty.
The partial safety factor is then a function of the obtained total coefficient of variationVtot for the wind load.
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The safety factors in the Danish code DS 409 ref. /6/ for environmental loads areobtained by calibration at two values of the coefficient of variation i.e. 20 % and 40 %where the corresponding safety factors are found to be 1.3 and 1.5. Assuming a linearvariation around and between these to values the connection between the totalcoefficient of variation and the partial safety factor is obtained and shown in Figure 8.
γ = C.o.V. + 1,1
1,1
1,2
1,3
1,4
1,5
1,6
10% 20% 30% 40% 50%
Total coefficient of variation
Figure 8: Safety factor as a function of the coefficient of variation.
In order to use the relationship shown in Figure 8 the coefficient of variation for theresponse must be obtained and the contributions form the uncertainty in theenvironmental parameters, transformation from flow (wind and wave) to pressure andthe model uncertainty must be included.
In the purposed code format the total coefficient of variation is obtained as
)1)(1)(1()1( 2222Jcqtot VVVV +++=+ (22)
where Vc is the total uncertainty for the transformation of the loads to responseapproximately around 18 to 20 %.
The obtained partial safety factors for the operation and extreme situation are given inTable 10 for the two environmental cases obtained for Horns Rev.
From Table 10 it is seen that the partial safety factor for the operation situation shouldbe lower than in the extreme situation. Moreover the variation in the extreme situation islarger than in the operation situation where the governing uncertainty is the modeluncertainty and the physical uncertainty. These two uncertainty contributions can bereduced when a precise and accurate load model is used and when the knowledge aboutthe load process is increased.
Applying the safety factors in Table 10 together with the obtained characteristicresponse given in Table 3 to Table 6 the design loads shown in Table 11 can beobtained.
Response variable DesignSituation
Correlation Safetyfactor
Characteristicresponse
Designresponse
Shear force Extreme Large 1.36 1.38 MN 1.88 MNOverturning moment Extreme Large 1.41 33.0 MNm 46.7 MNmShear force Extreme Low 1.37 1.07 MN 1.47 MNOverturning moment Extreme Low 1.45 32.0 MNm 46.5 MNmShear force Operation Large 1.35 1.26 MN 1.69 MNOverturning moment Operation Large 1.35 34.3 MNm 46.1 MNmShear force Operation Low 1.35 1.14 MN 1.54 MNOverturning moment Operation Low 1.35 34.0 MNm 45.7 MNm
Table 11: Design loads for the operation and extreme situation for the case with largecorrelation and low correlation between the environmental loads.
From Table 11 it is seen that for the case with large correlation the largest design load isobtained for the extreme situation, where as for the case with low correlation theoperation situation is governing the design shear force and the overturning moment isgoverning by the extreme situation. The variation in the design loads is though limited.
6. Conclusions
The environmental contours for the mean wind velocity and significant wave height areestablished and the maximal structural response is obtained for the operation situationand the extreme situation. Moreover it is found that the auto-correlation is important inorder to estimate the effective number of environmental conditions for the consideredreturn period.
Furthermore the correlation between the environmental loads are important. It is foundthat in case of large correlation the benefit of the described procedure is very large forthe operation situation and limited for the extreme situation. For a low correlationbetween the loads the benefit is in general more limited, but still considerable.
Based on the calculated maximal response for different return periods an extremedistribution is estimated and the partial safety factor can be obtained. The obtainedsafety factors for the extreme design situations are in general in the same range as thepartial safety factors given in the Eurocode and the Danish code, ref. /6/ and /10/. Thepartial safety factors obtained for the operation situation are a bit lower due to the
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limited uncertainty, and it seams reasonably to use smaller partial safety factors for thedesign operation situation.
7. Acknowledgements
The paper form part of EFP J.nr. 1363/99-0007 “Designgrundlag for vindmølleparkerpå havet” (Design Regulations For Offshore Windfarms) which is financial supportedby the Danish Ministry of Environment and Energy and the power supply companiesELSAM and SEAS.
/3/ Ditlevsen, Madsen: Structural Reliabili ty Methods, Wiley, 1996.
/4/ Ronold, Knut: “Probabili stic Stability Analysis of Wind Turbine Foundation onClay in Cyclic Loading” , EFP’99, December 2000.
/5/ Tarp-Johansen, N. J., Frandsen, S.: “A Simple Offshore Wind Turbine Model forFoundation Design” , EFP’99, December 2000.
/6/ DS 409, Danish code of Practice for the Safety of Structures, 1998.
/7/ NKB Committee and Work Reports 1999:01 E, “BASIS OF DESIGN OFSTRUCTURES Proposals for Modification of Partial Safety Factors inEurocodes” .
/8/ Conradsen, K., Nielsen, L. B. and Prahm, I. P.: ”Review of Weibull Statistics forEstimation of Wind Speed Distributions” , Journal of Climate and appliedMeteorology, Vol. 23, No., 8, August 1984.
/9/ Kristensen, L., Jensen, G., Hansen, A. and Kirkegaard, P.: ”Field Calibration ofCup Anemometers” , Risø National Laboratory, January 2001.
/10/ Draft prEN 1990, Basis of Design, European Standard, September 2000.
![Load Design Chart[1]](https://static.documents.pub/doc/80x56/577d252c1a28ab4e1e9e332e/load-design-chart1.jpg)
