OTC 16180

Rogue wave impact on offshore structures

Gunther Clauss, Katja Stutz, Christian Schmittner, Technical University Berlin, Germany

Copyright 2004, Offshore Technology Conference

This paper was prepared for presentation at the Offshore Technology Conference held in Hous-ton, Texas, U.S.A., 3-6 May 2004.

This paper was selected for presentation by an OTC Program Committee following review ofinformation contained in an abstract submitted by the authors(s). Contents of the paper, aspresented, have not been reviewed by the Offshore Technology Conference and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect any posi-tion of the Offshore Technology Conference , its officers, or members. Electronic reproduction,distribution, or storage of any part of this paper for commercial purposes without the writtenconsent of the Offshore Technology Conference is prohibited. Permission to reproduce in printis restricted to an abstract of not more than 300 words; illustrations may not be copied. Theabstract must contain conspicuous acknowledgement of where and by whom the paper waspresented.

AbstractFor the design and operation of offshore structures, heave mo-tion, airgap, splitting forces as well as bending moments arekey parameters to reduce down time and ensure safe opera-tions. The increasing number of reported rogue waves withunexpected large wave height (Hmax

�Hs � 2 � 0), crest height

(ηc�Hmax � 0 � 6), wave steepness and group pattern (e.g. Three

Sisters) suggests a reconsideration of design codes by imple-menting an Accidental Limit State with a return period of 10000years. For investigating the consequences of specific extremesea conditions numerical simulations of the seakeeping behav-ior, including motions and structural forces, as well as modeltests have been carried out with FPSOs and semisubmersibles ina reported rogue wave, the Draupner New Year Wave. Both, fre-quency and time-domain results are presented. With frequency-domain analysis the profound data for the standard assessmentof structures, concerning seakeeping behavior, operational limi-tations and fatigue are obtained. In addition, time-domain anal-ysis in real rogue waves gives indispensable data on extremes,i.e. motions and structural forces. As the wave/structure inter-action is analyzed in deterministic (freak) wave sequences themost critical position is evaluated by systematic simulations,and the causes of (nonlinear) structure response are revealed.

IntroductionSurviving a freak wave - what an experience. However, onlyscarce observations are available of such mystic disasters.

Reports on individual extreme waves in deep water men-tion either single high waves or several successive high waves.

Fig. 1—Rogue wave observations - Bay of Biscay (top) and AtlanticOcean South (bottom) 1

Fig. 1 shows two exceptional and frightening events 1. Breath-taking waves have also been presented by Faulkner 2 who pro-poses the definition Hmax � 2 � 4Hs for abnormal wave height.From a probability analysis of rogue wave data recorded from1994 to 1998 at North Alwyn Wolfram et al. 3 conclude thatthese waves are generally 50% steeper than the significantsteepness, with wave heights Hmax � 2 � 3Hs. The preceding and

2 OTC 16180

succeeding waves have steepness values around half the signifi-cant values while their heights are around the significant height.Registrations of rogue waves are shown in Fig. 2 and 3:

� a giant wave (Hmax� 25 � 63m) with the crest height ηc

�18 � 5m hit the Draupner jacket platform on January 1,19954

� off Yura harbor in the Japanese Sea a 13.6m wave withηc� 8 � 2m has been recorded in a sea state of Hs

� 5 � 09m5

Exceptional waves have also been reported from the Norwe-gian Frigg field6 - Hs

� 8 � 49m, Hmax� 19 � 98m, ηc

� 12 � 24m,water depth d � 99 � 4m, as well as from the Danish Gormfield7 - Hs

� 6 � 9m, Hmax� 17 � 8m, ηc

� 13m, water depthd � 40m. All these wave data, with Hmax

�Hs � 2 � 15 and

ηc�Hmax � 0 � 6, prove that rogue waves are serious events which

should be considered in the design process. Although theirprobability is very low they are physically possible. It is a chal-lenging question which maximum wave and crest heights candevelop in a certain sea-state characterized by Hs and Tp.

In addition to the global parameters Hs and Tp the individualwave height and shape as well as its effects on a structure de-pend on superpositions and the interaction of wave components,i.e. on local wave characteristics. Phase relations and nonlinearinteractions are key parameters to specify the relevant surfaceprofile at the structure as well as the associated wave kinematicsand dynamics.

Fig. 2—North Sea, Draupner jacket platform 4 - New Year wave onJanuary 1, 1995, Hs � 11 � 92m, Hmax � 25 � 63m � 2 � 15Hs; ηc � 18 � 5m �0 � 72Hmax , d � 70m)

Fig. 3—Japanese Sea, off Yura harbour, Japanese National Mar-itime Institute 5, Hs � 5 � 09m, Hmax � 13 � 6m � 2 � 67Hs; ηc � 8 � 2m �0 � 6Hmax, d � 43m

As a consequence, for the assessment of offshore structuresit is recommended to combine the advantages of frequency andtime-domain analysis.� Frequency-domain analysis serves as basis for conven-

tional stochastic evaluation of significant forces, motionsand loads in a given seaway, and the resulting operationallimitations8

� Time-domain analysis yields the response of an off-shore structure to individual wave sequences includingfreak waves. The procedure allows the analysis ofwave/structure interaction and the determination of ex-treme motions and structural forces in sea states with in-tegrated freak waves. If deterministic wave sequences oreven real registrations like the New Year Wave (Fig. 2) orthe Yura Wave (Fig. 3) are selected as input data, the gen-esis of the propagating wave train up to the culminationpoint can be analyzed. Depending on the position of thewave/structure interaction the maximum impact is deter-mined.

This paper presents the evaluation of rogue wave impacts onFPSOs and semisubmersibles comparing frequency and time-domain results. The numerical investigations are backed up byexperimental validation. The seakeeping tests allow the precise(deterministic) generation of design wave groups or even theDraupner New Year Wave sequence at a selected target position.Consequently, it is suited for investigating the mechanism of ar-bitrary wave/structure interactions, including slamming, greenwater and capsizing as well as other survivability design aspectsbecause cause-reaction chains can be traced. In conclusion, youcan observe your structure in a real freak wave - and survive.

Wave generation and experimental setupTo simulate rogue wave sequences experimentally a fast andprecise method is required which can be adopted to the test pur-pose easily.

As a first step, the design spectrum and a target positionxtarget is selected. At this location, the target wave train is eitherdesigned or given as an existing wave registration like the NewYear Wave.

This wave train is transformed upstream to the position ofthe wave maker which requires an adequate wave propagationmodel. On the basis of linear wave theory the specified am-plitude distribution of the target wave train is given as Fouriertransform F

�ω � xtarget � with circular frequency ω as a function

of wave number k. Adaptation of the phase spectrum to thewave maker location x0 gives the Fourier transform in x0:

F�ω � x0 � ��F � ω � xtarget � � ei ωt � k xtarget � x0 � � � . . . . . . . . . . . . . (1)

As the process is strictly linear and deterministic, wavegroups as well as arbitrary wave sequences can be analyzedback and forth in time and space.

For a given design variance spectrum of an unidirectionalwave train, the phase spectrum is responsible for all local char-acteristics, e.g. the wave height and period distribution as wellas the location of the highest wave crest in time and space. Forthis reason, an initially random phase spectrum argF

�w � is op-

timized to generate the desired design wave train with specifiedlocal properties9.

The set-up of the optimization problem is illustrated for atransient design wave within a tailored group of three succes-sive waves in random sea. The target zero-upcrossing wave

OTC 16180 3

heights of the leading, the design and the trailing wave are de-fined by Hl � Hd and Ht . The target locations in space and timeof the design wave crest height ζd are xtarget and ttarget . Thesedata define equality constraints. The maximum values of stroke,velocity and acceleration of the wave board motion define in-equality constraints to be taken into account 10.

Fig. 4—Optimized phase spectra and associated wave trains result-ing from different initial phase distributions

The heights of the leading and the trailing waves adjoiningthe design wave are set to be Hl

� Ht� Hs. Note that this

wave sequence is quite representative for rogue wave groupsas has been proved by Wolfram et al. 3 who classified 114extremely high waves with their immediate neighbors out of345245 waves collected between 1994 and 1998 at North Al-wyn.

The surface elevation is described by N � 512 data pointswith time step of dt � 0 � 2s resulting in a time window of102.2 s. The design variance spectrum remains unchangedand 70 components in the frequency range of ω

�ωp

� 0 � 5 toω

�ωp

� 3 � 5 are considered.

As illustrated in Fig. 4, the optimization process finds localminima, i.e. a number of different wave trains which dependon the initial phase values. Hence the random character of theoptimized sea state is not completely lost.

Fig. 5—New Year Wave as registered at Draupner Field and mea-sured (at scale 1:81) in the wave tank

For generating higher waves, i.e. the extremely high Draup-ner New Year Wave train, the linear approach is expanded by asemi-empirical nonlinear procedure which is based on the factthat short and high wave groups with strong nonlinear char-acteristics evolve from long and low wave groups which arecharacterized by linear principles. As the total energy of thewave is invariant during its metamorphosis, the initial Fouriertransform of the linear wave train is introduced as ”wave infor-mation” and selected as the backbone of wave propagation 11.This wave information along with the adequate celerity at eachtime step give the nonlinear phase characteristics of the wavetrain12. The detailed shape of the resulting wave train is devel-oped at each time step considering the temporary steepness ofthe wave. This iteration principle can be used either for back-ward transformation (wave generation) as well as for forwardtransformation (calculation of the moving reference frame wavetrain at cruising ships13).

From the wave train at the position of the wave maker thecorresponding control signals are calculated using the hydrody-namic transfer function (relating wave board motion to wave el-evation), the geometrical RAO (which considers the flap type),and the electric-hydraulic RAO. This control signal is used togenerate the specified wave train which is measured at the targetposition in the tank. Model test results are presented in Fig. 5.As compared to the target wave sequence of the New Year Wave(in full scale data), wave heights and phase relations are satis-factorily modeled.

Fig. 6—Seakeeping test in wave tank

The seakeeping tests with semisubmersibles and FPSOs arecarried out in a 80m long wave flume, see Fig. 6. Water depthis 1.5m. A computer controlled piston-type wave paddle gen-

4 OTC 16180

erates the selected wave sequences within a given band of fre-quencies, including regular and irregular waves as well as wavepackets and deterministic wave trains.

Motions are registered by a video camera, observing LEDsfixed on the deck of the models. For measuring splitting forcesthe cross bracing of the semisubmersible is equipped with straingauges. Vertical bending moments are registered similarly byconnecting the two elements of the model by steel profilesequipped with strain gauges.

Numerical simulationThe evaluation of motions, splitting forces and bending mo-ments is carried out with the program systems WAMIT (WaveAnalysis, developed at Massachusetts Institute of Technology)for wave/structure interaction at zero-speed 14,15 and TiMIT(Time-domain investigations, developed at MassachusettsInstitute of Technology), a program for transient wave/bodyinteractions at arbitrary speed 16,17. Three-dimensional panelmethods using potential theory are implemented in both pro-grams. WAMIT solves the equation of motion in frequency-domain, and is therefore applicable only for zero-speed prob-lems. Results of motions and forces are given uniquely as re-sponse amplitude operators (RAO) by amplitude and phase. Re-sponse spectra are calculated by multiplying the selected wavespectrum by the squared magnitude of the RAO 18. From thearea under this response spectrum the significant and maximumresponse is determined. Based on these results operational lim-its are deduced, and - combined with wave scatter diagrams -the down-time of the structure can be evaluated 8,19.

With TiMIT a further development for zero- and non-zero-speed problems has been achieved, solving the equations com-pletely in time-domain. The time-dependent potentials result-ing from the impulsive forcing are calculated in a first step.Then the impulse-response functions are determined by inte-grating the pressure over the mean wetted body surface. Theyprovide the complete hydrodynamic characteristics of the bodyand serve as basis for subsequent time-domain simulation orfrequency-domain analysis.

Hydrodynamic analysis This section presents a short intro-duction to mathematical background. For details see 16,20–22.

The analysis of a compact rigid body with six degrees of free-dom is described by a boundary value problem. The total ve-locity potential φ

�x � t � for an inviscid, incompressible fluid and

irrotational flow follows from Laplace equation

∆φ�x � t � � 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

Assuming linear theory the total velocity potential φ is givenas superposition of the individual potentials due to incomingplane waves and the wave systems arising from the motions ofthe body

φ�x � t � � φ0 � φ7 � 6

∑k � 1

φk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

with φ0 incident wave potentialφ7 potential of scatter wave fieldφk potential of the radiation wave field

evoked by a motion in mode k

These potentials describe the initial wave field φ0 and its reflec-tion on the body surface resulting in the scatter wave field φ7.The last term in Eq. (3) describes the radiation wave fields φk

which follow from body motions in 6 degrees of freedom.On the wetted body surface normal velocity is zero. For a

moving body this condition results into:

∂φi

∂n� s � n � � on Sb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

The linearized kinematic and dynamic boundary condition onthe free surface are merged into the generalized free surfacecondition:

∂φi

∂z� ω2

gφi� 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)

On the ocean bottom normal velocities are zero:

∂φi

∂n� 0 � for z � � d � . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)

φi�i � 0 � 1 � � � � � 7 � holds for any potential, which are superim-

posed to form the complete solution. Finally in the farfieldthe Sommerfeld radiation condition for the scatter and radiationwave field must be satisfied:

limR � ∞

�R

�∂φ j

∂R� ikφi � � 0 � j � 1 � � � � � 7 . . . . . . . . . . . . . . (7)

The initial boundary value problem, defined by Laplaceequation (2) and the above boundary conditions, is transformedinto an integral equation by applying Green’s second theorem 20

and, after some manipulation, we obtain:

2πφ�x � t � ��

Sb � � φ�x � t � G 0 �n

�x � ξ � � G 0 � � x � ξ � φn

�x � t ��� dS

� t� ∞

� Sb � � φ

�x � t � Gtn

�x � ξ � t � � Gt

�x � ξ � t � φn

�x � t � � dSdτ � 0

(8)

This equation allows to solve for the unknown scatter and ra-diation potentials on the mean position of the body surface Sb.The wetted body surface has to be discretized into N panels (seee.g. Fig. 7 or 13) where the boundary conditions are satisfied onthe collocation point. Based on this potential the instationaryBernoulli equation gives the (linearized) dynamic pressure:

pdyn� � ρ

∂φ∂t

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (9)

which defines the forces and moments acting on the body:

F � � Sb �

pdynn � dS � � ρ � Sb �

∂φ∂t

n � dS . . . . . . . . . . . . . . . . . (10)

OTC 16180 5

With Newtons second law and assuming the body and its forc-ing comprise a stable linear system, the equation of motion isobtained23:

�M � a � s � Bs � Cs � t

� ∞

K�t � τ � s � τ � dτ � F

�t � . . . . . . . . (11)

From equation (11) the unknown motions in 6 degrees of free-dom are calculated in time-domain. Note that the resulting mo-tions are given as impulse-response function which are the re-action of the body on an impulsive forcing (see right side of theequation). The motions of the body in arbitrary wave trains arecalculated in a subsequent step by convolution of the impulseresponse functions with the wave train.

In the following applications the wave trains measured dur-ing experiments are used to carry out the simulations and al-low therefore direct comparison between simulation and exper-iment.

In frequency-domain, Eq. (11) is solved for harmonic excita-tion. Divided by the wave amplitude ζa the equation is reducedto: � � ω2 � M � a � � iωB � C � H

�ω � � Fa

ζaeiγ . . . . . . . . . . . . . . (12)

with the unknown response amplitude operator H�ω � � sa

ζaeiε,

representing amplitude sa and phase shift ε of the motion infrequency-domain. γ is the phase of forcing.

Hydroelastic analysis The program WAMIT allows the anal-ysis of generalized modes of body motions, in addition to theusual six degrees of rigid-body motions. By defining the shipbending modes the associated structural deformations can becalculated. Legendre polynomials 24 Pi

�x � � i � 2 � 3 � � � � are found

to approximate very well the bending modes of a ship 25. Thedeflection line for each bending mode is given by the product ofthe calculated amplitude and the corresponding Legendre poly-nomial.

wi�x � � sia � Pi � 5

�x � � i � 7 � 8 � � � � . . . . . . . . . . . . . . . . . . . . (13)

The indexing takes into account, that the first 6 indices are re-served for the conventional rigid body motions. For severalbending modes, the total deflection results from complex addi-tion of the individual deflection lines. Twice differentiation ofthe deflection line, multiplied with the flexural stiffness resultsin the bending moment of the ship:

Mb�x � � � w � � � x � � EIy

�x � . . . . . . . . . . . . . . . . . . . . . . . . . . . . (14)

ApplicationsFor the investigation of the impact of freak waves on offshorestructures two typical types of offshore structures are selected:� Drilling semisubmersible of type GVA 4000 especially de-

signed for operations in harsh environment, Fig. 7. Pon-toon length is 80.56m, pontoon beam 16m, column spac-ing (longitudinal and transverse) 54.72m, column diameter12.9m, and operation draught 20.5m. The wetted surfaceof the body is discretized into 760 panels.

� FPSO (Floating Production Storage Offloading) with alength of Lpp

� 194 � 4m, beam 37.8m, draught 10.09m,and a displacement of 65250t. The wetted surface is dis-cretized with 336 panels for the numerical simulations, seeFig. 13.

Model tests have been carried out for both structures at a scaleof 1:81.

Numerical simulations of the seakeeping behavior includesix (coupled) rigid body motions, however the presentation isrestricted to heave as critical parameter during operation. In ad-dition, the airgap and the splitting forces of the semisubmersibleare determined.

Vertical bending moments are measured by strain gaugesat the intersection of the fore and aft body of the model (seeFig. 13). The amplitudes of the bending modes calculatedwith WAMIT are transformed into the vertical bending moment(Eqn. (13) and (14)).

Semisubmersible - Heave, Airgap and Splitting forces Foroperation of semisubmersibles heave motion, airgap and split-ting forces are key parameters.

Fig. 7—Main dimensions and discretization with 760 panels on themean position of the semisubmersible GVA 4000

The semisubmersible GVA 4000 is modelled from plexiglasand cut into halves. The parts are connected by two aluminiumprofiles equipped with strain gauges from which the splittingforces are derived directly. On the deck of the model, lightemitting diodes are attached and their motions are registeredwith a video camera to determine heave and pitch motion.

Fig. 8 shows the wave as modeled in the wave tank (all mea-surements are converted to full scale) and the associated heavemotion as well as airgap. For comparison the results of theTiMIT simulation are presented - with slightly higher valuesdue to neglected viscous damping. This fact is responsible forthe higher airgap as compared to the simulation. Fig. 9 (mid-dle) presents the RAO of splitting forces showing measured andcalculated data. To analyze local extreme phenomena of thesplitting forces in time-domain an inverse Fourier transforma-tion (IFFT) is applied to the calculated RAO in a postprocess-ing step, considering the corresponding phases from the New

6 OTC 16180

Fig. 8—Semisubmersible GVA 4000 in (modelled) New Year Wave(Hmax � 23m) - Results of numerical simulation (TiMIT) and modeltests of semisubmersible GVA 4000: Heave and airgap (measuredat a scale 1:81, presented as full scale data)

Year Wave. Fig. 10 presents the splitting forces of the semisub-mersible GVA 4000 in the (modelled) New Year Wave compar-ing numerical and experimental results.

Table 1—Maximum motions and structural forces of GVA 4000 com-paring time- and frequency-domain results

Semisubmersible GVA 4000

Time-domain Frequency-domainmaximum New Year Wave Hs

� 11 � 92mdouble amp- Hmax

� 23 � 13m T0� 10 � 8s

litudes of Exp. Sim. PM JONSWAPheave 7.0m 8.6m 10.5m 9.88mairgap 7.62m 9.87m - -

split force 71.5MN 63.6MN 76.7MN 76.1MN

In frequency-domain the 20-min New Year Wave registrationgives the sea spectrum in Fig. 9 (top) with Hs

� 11 � 92m andT0� 10 � 8s. The corresponding JONSWAP spectrum (γ � 3 � 3)

and the Pierson-Moskowitz spectrum are shown for compari-son. Note that the New Year Wave registration coincides wellwith the PM spectrum. Thus, the New Year Wave sequencerepresents a quite exotic sample of a conventional PM spec-trum. Consequently, the significant and maximum motions andforces can also be determined by spectral analysis. From thearea under the response spectrum mi the significant double am-plitude�2sia � s � 4

�mi � . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (15)

and the maximum double amplitude�2sia � max

� 1 � 86 � � 2sia � s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (16)

Fig. 9—Frequency domain analysis of splitting forces of GVA 4000in beam seas (β � 90 � ): Sea spectra - response amplitude operator- response spectra

is derived.

Results are presented in Table 1. Evidently, the maximumvalues of motions and forces (double amplitudes) as predictedfrom frequency-domain evaluations are quite higher as com-pared to measured data and time-domain numerical results ina freak wave. Consequently, the prognosis based on the stan-dard frequency-domain procedure proves to be reliable and issufficient to cover even freak wave effects. Note that maximumdouble amplitudes based on JONSWAP-spectra give compara-ble results (see Fig. 9 and Table 1).

So far, the hydrodynamic analysis of the semisubmersibleGVA 4000 is related to the (modelled) New Year Wave witha maximum height of 23.1m only. Comparison of WAMIT,TiMIT and wave tank results proof that TiMIT is a reliabletool for predicting time-domain impacts, even in extremely high

OTC 16180 7

250 300 350 400 450 500−10

0

10

20

time [s]

ζ [m

]

New Year Wave generated in wave tank

250 300 350 400 450 500−50

0

50

time [s]

split

ting

forc

e [1

06 N]

calculatedmeasured

Fig. 10—Comparison of experimental and calculated splittingforces for semisubmersible GVA 4000 (measured at a scale 1:81,presented as full scale data)

Fig. 11—Focused TiMIT results of motion behavior in freak wavesequences with varied peak wave height (Wave sequence - Timeregistration of heave motion)

waves. On this basis a sensitivity study has been launched to in-vestigate the effect of increase of freak wave height (and steep-ness), integrated in the New Year Wave sequence.

Fig. 11 presents illustrative (focused) results. With increas-ing freak wave height we observe higher direct response anda slight deviation of the subsequent motions. The semisub-mersible is following the exciting wave elevation with littlephase shift. Concerning the maximum values, Fig. 12 illustratesthat the heave motion is non-linearly increasing with freak waveheight.

FPSO - Heave, Pitch and Bending Moment FPSOs arewidely used in deep and harsh offshore areas. Therefore, aship-type structure has also been selected for our rogue wave

Fig. 12—Relation of maximum double amplitude of heave motionand peak wave height in freak wave sequences

Fig. 13—Model of the FPSO with the two hull halfs connected bystrain gauges and discretization of the FPSO with 336 panels

investigation. Regarding structural loads bending moments areprobably one of the most critical values. In Fig. 13 the model(scale 1:81) as well as the dicretized wetted hull of the FPSOare presented.

Again, the (modelled) New Year Wave has been used forcomparative studies. Fig. 15 presents the associated heave andpitch motion as well as the bending moment. Note that thetime series of the bending moment is calculated from the RAOobtained by WAMIT, see Fig. 14, in the same manner as thesplitting forces of the semisubmersible. As has been stated inequations (13) and (14): Legendre polynomials describe the ge-ometry of the deflection line and their second derivatives thecurvature of the deflection line. The product with the curva-ture and the calculated amplitudes is proportional to the bend-ing moment. The total curvature derived from the three bending

8 OTC 16180

Fig. 14—RAO of bending moment, comparison of experimental andnumerical results

Wave registration ζ�t �

Heave motion s3�t �

Pitch motion s5�t �

Bending moment Mb�t �

Simulation Experiment

Simulation Experiment

Simulation Experiment

Fig. 15—FPSO: Heave, pitch motion and bending moment from ex-periment and TiMIT (with Hmax � 23 � 1m)

modes, and thus the bending moment, is obtained by complexaddition, and the resulting RAO is presented in Fig. 14. Thenumerical results, calculated by TiMIT, are again satisfactorilyvalidated by model test data.

To achieve detailed information of the freak wave impactwe started a sensitivity study to investigate the worst positionof the FPSO. Nine locations have been selected varying from� 3

�2Lpp to � 3

�2Lpp. Registrations at 3 positions are pre-

sented in Fig. 16. In addition Table 2 gives all calculated andmeasured data. Before the seakeeping tests, the wave propa-gations at all 9 locations have been recorded separately without

the ship to obtain undisturbed wave registrations as input for thenumerical simulation. Comparing numerical and experimentalresults the excellency of TiMIT (based on linear theory) is con-firmed again.

This is quite surprising, as nonlinear effects of wave/structureinteractions seem to be insignificant in this case. It should benoted, however, that the highest waves in the wave train arevery steep and thus the analysis considers (nonlinear) real seaconditions. The second surprise follows from the detailed studyof the wave propagation: Our reference freak wave sequence,see Fig. 16 (middle column), is not the highest wave. Just oneship length before (at x1

� Lpp) the maximum wave height is25m, due to a very deep trough (Table 2).

A stochastic analysis based on Pierson-Moskowitz and JON-SWAP spectra with significant wave height of 11 � 92m and zero-upcrossing period of 10 � 8s results in values for the maximumdouble amplitudes of heave and pitch, which are quite compa-rable:

PM spectrum JONSWAP spectrum�2s3a � max 10.4m 9.1m�2s5a � max 13.7

�14.5

��2Mb � a � max 4128.5MNm 4457.5MNm

Table 2—Maximum motions and structural forces of the FPSO lo-cated at different positions in the New Year Wave

FPSOHmax

�2s3a � max

�2s5a � max

�2Mba � max

[m] [m] [ � ] [106 kNm]Exp. 10.56 14.38 4.54x1 � 3

2 Lpp Sim.23.9

9.07 13.86 3.95Exp. 10.99 14.87 4.64x1 � Lpp Sim.

25.010.54 14.5 4.14

Exp. 11.40 15.08 4.79x1 � 12 Lpp Sim.

23.710.33 14.23 4.14

Exp. 10.87 14.40 4.60x1 � 14 Lpp Sim.

24.59.67 14.61 3.98

Exp. 11.57 15.61 4.42x1 � xorig Sim.23.1

8.94 12.81 3.50Exp. 11.22 15.37 4.46x1 � 1

4 Lpp Sim.21.5

9.07 13.17 3.34Exp. 10.60 15.00 4.94x1 � 1

2 Lpp Sim.20.3

9.55 14.38 3.70Exp. 11.02 14.30 4.26x1 � Lpp Sim.

19.810.18 15.34 3.93

Exp. 10.51 13.88 4.38x1 � 32 Lpp Sim.

20.110.05 14.42 3.84

ConclusionsWhat happens to a FPSO or a semisubmersible in a freakwave? Are motions and loads higher than predicted by stan-dard stochastic evaluations? This paper presents a comprehen-sive study comparing time-domain and frequency-domain in-vestigations of offshore structures in rogue waves, validatedby seakeeping tests in irregular sea states with integrated

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x1� xorig x3

� xorig � Lppx2� xorig

� Lpp

Wave registration ζ�t � at x2 Wave registration ζ

�t � at x1 Wave registration ζ

�t � at x3

Heave motion s3�t � at x2 Heave motion s3

�t � at x1 Heave motion s3

�t � at x3

Pitch motion s5�t � at x2 Pitch motion s5

�t � at x1 Pitch motion s5

�t � at x3

Bending moment s5�t � at x2 Bending moment s5

�t � at x1 Bending moment s5

�t � at x3

SimulationExperiment

SimulationExperiment

SimulationExperiment

Fig. 16—Heave, pitch motions and bending moment of FPSO at varied positions of the midship section in the New Year Wave - TiMIT simulationand experiment

deterministic freak wave sequences. This model test tech-nique allows the accurate simulation of the selected Draup-ner New Year Wave (with a slightly lower wave height ofHmax

� 23 � 1m). Consequently, numerical time-domain resultsare directly compared to experimental data, and cause-reactionchains of wave/structure interactions can be detected and vali-dated. As a result, the time-domain program TiMIT proves tobe an excellent tool for the analysis of the selected structures i.e.a FPSO with a high block coefficient and a semisubmersible infreak waves. Motions, airgap, splitting forces and bending mo-ments are predicted satisfactorily.

Systematic variation of the wave height of the rogue wavehidden in a normal storm sea reveals the sensitivity of structuralresponse of the semisubmersible due to changed wave condi-tions. The results show a nonlinear increase of responses, for-tunately significantly less than proportional.

A second systematic analysis tackles the question, what hap-pens if the structure is exposed to the incoming freak wave fur-ther downstream or upstream. Surprisingly, the New Year Waveis even more severe at the position of one ship length upstream

confirming the importance of time and phase information andthe need for precise simulations and model test.

In conclusion, as numerical and experimental simulationscan model impacts of extreme waves on offshore structures pre-cisely, these tools are ideally suited to investigate cause-reactionchains of wave-structure interactions. Fortunately, the com-parison of time and frequency-domain results point out thatthe frequency-domain standard approach for investigating seakeeping characteristics and operational limitations as well aswave scatter depending down-time evaluations are still suffi-cient even if rogue waves are hidden in the sea.

Acknowledgements

The authors want to express their gratitude to the EuropeanCommunity for funding the research project MAXWAVE (con-tract number EVK-CT-2000-00026). Thanks also to JanouHennig for her support in generating the wave board signal forthe New Year Wave.

10 OTC 16180

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