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1 Iteratioal Wid Egieerig Coferece IWEC 014 WAVE INDUCED FATIGUE LOADS ON MONOPILES - NEW APPROACHES FOR LUMPING OF SCATTER TABLES AND SITE SPECIFIC INTERPOLATION OF FATIGUE LOADS M. SEIDEL Sevio SE Fraz-Lez-Str. 1, Osabrück, Germay marc.seidel@sevio.com, Keywords: Frequecy domai, wave loadig, moopile, lumpig, site iterpolatio Summary: Offshore wid turbies are subject to dyamic excitatio from wave loads. Especially whe moopile substructures are used, sigificat fatigue loads ca be iduced by waves, which are the goverig the desig. Calculatios i the frequecy domai are very efficiet to compute such wave iduced loads ad by applyig some simplificatios, very compact equatios ca be derived for the determiatio of fatigue loads. Based o such simplified formulas further methods for lumpig of scatter diagrams ad for iterpolatios of fatigue loads for differet positios withi a wid farm are preseted i this paper. 1 INTRODUCTION As moopile substructures for offshore wid turbies gai market share i ever deeper waters [1], wave excitatio becomes more ad more importat. It is therefore crucial to gai good uderstadig of the relevat parameters ad to develop tools for rapid calculatio of fatigue loads, which are typically goverig for the structural dimesios. Calculatios i the frequecy domai are a helpful method i this respect ad with some simplificatios, which ca be applied to offshore wid turbies supported by moopiles, very compact equatios ca be derived to compute wave iduced fatigue loads. Based o a method developed by the author i [] some practical applicatios of the method are discussed i this paper. FREQUENCY DOMAIN ANALYSIS Calculatios i the frequecy domai are used frequetly i the Oil&Gas idustry to compute wave iduced respose of offshore structures. Geeral iformatio about this method ca be foud i Hapel [3] ad Barltrop [4]. The geeral theory of frequecy domai calculatios is ot repeated here for brevity. Symbols i geeral follow the otatio used by Hapel [3], uless oted otherwise.

2 3 A SIMPLIFIED METHOD TO DETERMINE WAVE INDUCED FATIGUE LOADS The method developed i [] is briefly summarized i the followig. As this paper does ot iclude all otatios ad relevat backgroud iformatio, it should ideally be read together with []. 3.1 Assumptios for the proposed simplified method The followig simplificatios are made, which are acceptable for offshore wid turbies mouted o moopile substructures: 1. Oly the first mode is cosidered for respose calculatios, as higher modes are outside of the frequecy cotet from wave excitatio.. Low structural dampig is assumed, typically a modal dampig ratio of =1.0% is used for offshore wid turbies fouded o moopiles. 3. As structural dampig is low, the respose ca be assumed to be arrow-baded ad oly the regio close to the first atural frequecy 0 is relevat for all terms which are a fuctio of. 4. Drag loadig is eglected as this is small for fatigue waves. 5. Hydrodyamic dampig is eglected as the velocity of the structure is small. 3. Summarized formula With the assumptios listed above, a simplified expressio ca be derived to compute wave iduced fatigue loads. The detailed derivatio ad defiitios ca be foud i []. Fatigue loads are calculated as damage equivalet loads (DEL). See [] regardig the coversio to other umber of referece cylces. z 0 ac 3/ 4 M eq, Nref 1Hz S 0 0 H a, 0 HTB (1) K0 0 With: H H TB a,0 zzac 0 0z zz 0 z 1 z dz Trasfer fuctio tower bottom () TB d D z 0 CM z 0 z 0 z dz Hydrodyamic trasfer fuctio (3) 0 4 These formulas ca be easily evaluated aalytically, oly modal aalysis eeds to be performed umerically.

3 3.3 Coclusios Some importat coclusios ca be draw from this expressio: 1. DELs are proportioal to (1/ 0 ) 0.5 i.e. if dampig is e.g. doubled, the fatigue loads decrease by 30%! This illustrates that dampig is oe of the major factors to assess reliably. Furthermore, dampig assumptios should ot be overly coservative to eable a ecoomic desig.. Damage is proportioal to the square root of spectral wave eergy at the first atural frequecy. This is importat whe lumpig of the scatter diagram shall be performed, as will be show later. 3. Mode shape ad hydrodyamic properties aroud the still water level are of particular importace. The hydrodyamic trasfer fuctio is liearly proportioal to mode shape amplitudes i the wave loaded zoe, as ca be see from Eq. (3). Reducig modal amplitude below still water level is therefore particularly helpful to reduce fatigue loads. 4. I total, fatigue loads are proportioal to 0 3, whe all other parameters are uchaged. This is a idicatio that a large head mass (from the turbie) is ot ecessarily disadvatageous, as this decreases the atural frequecy. 4 LUMPING OF THE SCATTER DIAGRAM I order to decrease the required umber of calculatios, the scatter diagrams (wid speed vs. wave height ad wave height vs. wave period) are ofte codesed (or lumped ). Ideally, lumpig of the H S -T P -diagram is doe i a way that both the quasi-static cotributio ad the dyamic (resoat) cotributio is captured. Figure 1: Quasi-static ad dyamic momet lies for a wave-loaded moopile 3

4 This is schematically show i Figure 1. The quasi-static momet lie does oly show iteral member forces below the highest poit of wave load attack. The dyamic momet lie shows load all over the structure, this momet lie is domiated by the structural respose i the first mode. 4.1 Weightig Damage icurred by a certai sea state is proportioal to (DEL) m, where m is the egative iverse slope of the S-N curve. Codified S-N-curves for welded details have values of m=3 ad m=5. I order to calculate DELs, a S-N-curve with oly oe slope must be used, ad m=4 is the used as the represetative value. This must be cosidered whe lumpig sea states. 4. Quasi-static lumpig: Equivalet sigificat wave height Wave loads o idividual members do have a quasi-static effect, i.e. the wave loads cause iteral member forces i the members where they apply. Wave loads are described by the well-kow Moriso s equatio (4), see e.g. Hapel [3] for details. F 4 t C D u t C D ut ut M 1 D (4) Wave iduced forces are therefore proportioal to the water particle acceleratio (Eq. (5)) for the iertia term ad the square of water particle velocity (Eq. (6)) for the drag term. Water particle acceleratio ad velocity are liearly depedat o wave amplitude for liear waves: Water particle velocities (horiz.): k k z cosh h ut a cos( k x t) (5) sih h Water particle acceleratios (horiz.): k k z cosh h u t a si( k x t) (6) sih h It follows that quasi-static fatigue loads ca be assumed to be proportioal to H S, where is 1 if the wave loadig is iertia domiated ad if the wave loadig is drag domiated. A equivalet wave height ca therefore be computed for each wid speed as: H s _ eq H m s, p p 1 m As wave loads o moopiles are iertia domiated, = 1 applies. 4

5 4.3 Resoat (dyamic) lumpig: Equivalet peak period Additioal to the (local) quasi-static cotributio, global dyamic excitatio does occur. For sleder structures, like moopiles, this is ofte the domiat effect. For stiff structures, like jackets, this effect may be egligible. Dyamic fatigue loads are proportioal to S (see Eq. (1)), where S is the spectral eergy of the wave spectrum at first atural frequecy. This has bee derived for a arrow bad respose, which is a good approximatio i case dyamic excitatio is sigificat. Weightig o basis of the spectral value at the atural frequecy is the idea of followig approach, as dyamic fatigue loads are proportioal to S. The followig relatioship does the apply: m S H S, TP, 0 p S 0 (7) eq p with p(): Probability for sea state with H S, ad T P, The spectral values S H S T, P, 0 1/ m 0 0, depedig o wave height, peak period ad first atural frequecy, have to be determied for each etry i the scatter matrix. As the gradiet of the wave spectra is high adjacet to the peak period, a peak period bi size of oe secod (which is typically the case) will ot lead to accurate results. Hece, a refiemet of the peak period by a factor of 10 is recommeded by meas of a splie iterpolatio. The spectral values are computed based o the refied scatter matrix. After the applicatio of the weightig formula show above, a equivalet spectral value is determied for the respective wave height row of the matrix. Based o the equivalet spectral value ad the sigificat wave height the equivalet peak period ca be recalculated. This is a backcalculatio (iterative procedure) which esures that the target value for the spectral eergy at atural frequecy is achieved. Two solutios exist for this back-calculatio, oe T P value o the ascedig part of the spectrum ad oe T P o the descedig part (see Figure for a example). For moopile cofiguratios with Multi-MW turbies the higher T P i geeral is the represetative oe as the atural frequecy of the turbie is low. This must be idetified for each specific case. 5

6 Figure : Idetificatio of the correct equivalet peak period (JONSWAP) T P =8.0s is most represetative for a wave height of H S =3.15m ad is selected; atural frequecy marked by dashed lie 5 SITE PARAMETER Whe fatigue loads for a complete wid farm eed to be calculated, it is ofte ot practical (or eve impossible) to perform load iteratios for every positio. A few positios (with varyig structural properties, soil coditios ad water depths) are the calculated ad these loads must be applied to all structures. This ca be doe coservatively or some sort of iterpolatio must be adopted. Oe possible parameter to choose for iterpolatio is atural frequecy. The results from five differet complete load simulatios for a North Sea wid farm are show i Figure 3. The data sets cover differet water depths, but also differet load iteratios with differeces i structural dimesios. The geeral tred shows what ca be expected: The fatigue loads decrease with a higher atural frequecy, which ca be attributed to smaller wave excitatio. But although the geeral tred is captured, large differeces ca be see for the regressio lie vs. actual results. Such a iterpolatio quality is ot suitable for desig purposes. Water depth as a parameter provides eve poorer correlatio, as the impact of soil stiffess is ot captured i this case. 6

7 Figure 3: Fatigue loads (at uspecified elevatio) plotted vs. first atural frequecy of the combied structure A better parameter ca be foud based o the method derived before. If Eq. (1) is simplified, it ca be stated that fatigue loads are proportioal to the followig parameter S: S K , orm 0 HTB Ha, 0 S (8) eq 0 This expressio is valid if the fatigue loads are govered by dyamic wave excitatio, which is ofte the case for moopiles. If wid loads are goverig (i.e. for a very stiff system) the this site parameter would ot be a good choice. This site parameter ca be used to evaluate fatigue loads for all positios withi a wid farm. Load simulatio ca be performed for the sites havig miimum ad maximum site parameter ad iterpolatio ca be used i betwee. Iterpolatio ca be performed with much simpler tools (e.g. Excel) as all steps ca be doe i a spreadsheet, except for the modal aalysis for each site. The latter ca be performed i a structural aalysis program (or eve that ca be doe i Excel, but this requires a bit more work). Results are show i Figure 4 for the same data set as used for Figure 3. It ca be see that the correlatio is ow very good, which makes the site parameter a suitable parameter to perform iterpolatio, esp. durig the stage where desig iteratios are performed ad quick respose cycles from structural desiger to load calculatios egieer are required. 7

8 Figure 4: Fatigue loads (at uspecified elevatio) plotted vs. site parameter 6 SUMMARY I this paper, ew approaches for lumpig of a scatter diagram (scatter matrix) ad iterpolatio of site specific fatigue loads have bee demostrated based o o frequecy domai cosideratios. Simplificatios relevat for moopile substructures have bee used to determie a compact formula which allows rapid calculatio of wave iduced fatigue loads. These approaches allow for more accurate ad fast calculatios of wave iduced fatigue loads for offshore wid turbies with moopile support structures. 7 REFERENCES [1] Seidel, M.: 6MW Turbies with 150m+ Rotor Diameter - What is the Impact o Substructures? Coferece proceedigs DEWEK: Breme 01. [] Seidel, M.: Wave iduced fatigue loads - Isights from frequecy domai calculatios. Stahlbau 83 (014), p DOI: /stab [3] Hapel, K.-H.: Festigkeitsaalyse dyamisch beaspruchter Offshore-Kostruktioe. Brauschweig: Vieweg, [4] Barltrop, N.; Adams, A.: Dyamics of fixed marie structures. Oxford: Butterworth- Heiema