Floating BW

Karen Merlevede

breakwaterStudy of the functional design of a floating offshore

Academiejaar 2011-2012Faculteit Ingenieurswetenschappen en ArchitectuurVoorzitter: prof. dr. ir. Julien De RouckVakgroep Civiele Techniek

Master in de ingenieurswetenschappen: bouwkundeMasterproef ingediend tot het behalen van de academische graad van

Begeleiders: ir. Vicky Stratigaki, Piet Haerens (IMDC)Promotor: prof. dr. ir. Peter Troch

A good traveler has no fixed plans,

and is not intent on arriving.

- Lao Tzu

i

Dankwoord

Als eerste wil ik graag mijn begeleider, Piet Haerens, bedanken voor het aanreiken van dit

onderwerp. Natuurlijk heb ik van tijd tot tijd zitten vloeken op het concept ’thesissen’, maar

ik mag mij gelukkig prijzen dat ik het steeds een boeiend thema ben blijven vinden! Verder

wil ik ook mijn promotor, Peter Troch, bedanken voor de begeleiding aan de start van het

academiejaar. Dankzij hen kon ik een vlotte start maken, wat ervoor gezorgd heeft dat die

typische laatste thesis stress mij bespaard gebleven is, OEF! Peter Mercelis wil ik graag be-

danken voor zijn begeleiding tijdens de dagen die ik op IMDC doorbracht en het nalezen van de

hele boel, Joris Rooseleer voor de input in verband met het verankeringssysteem en Phillipe

de Schoesitter voor de aangename babbels op IMDC en de info over moonpools ed. Evert

Lataire wil ik bedanken om mij als bouwkundig studentje in te leiden in een stukje van de

maritieme wereld. Verder wil de belangrijkste mensen in mijn leven bedanken, mijn familie. In

het bijzonder mijn ouders, voor hun onvoorwaardelijke steun en omdat ze mij de kans hebben

gegeven om burgerlijk te gaan studeren. Mijn zus, Anne, voor het tussen-thesis-door-tripje

en de vele tips over maritieme toepassingen, Torretje, voor de uitleg over verankeringen, mijn

broer Stijn, voor de fietstelefoontjes! Ook bedankt aan de BWC, het waren aangename mid-

dagen op de magnel. Ann sorry als ik je gefrustreerd heb door teveel snipperdagen te nemen!

Verder wil ik ook een zot leuk mannetje bedanken, Wally! Danku om altijd te luisteren naar

mijn ’zottigheid’, ik ben blij dat je onder mij woont! Djanxke, bedankt om zo geduldig te zijn.

Dat kan niet altijd even gemakkelijk zijn, maar voor familie heb je natuurlijk wel iets over!

And last but not least, wil ik mijn partner in crime, Bo, bedanken omdat we samen altijd

zulke goede mopjes en plannen maken. Ooit gaan we de nacho’s terugvinden!

Copyright

The author gives permission to make this master dissertation available for consultation and

to copy parts of this master dissertation for personal use. In the case of any other use, the

limitations of the copyright have to be respected, in particular with regard to the obligation

to state expressly the source when quoting results from this master dissertation.

ii

Study of the functional design

of a floating offshore breakwater

by

Karen Merlevede

Master dissertation submitted in order to obtain the academic degree of

Master of Civil Engineering (major Water and Transportation)

Head supervisor: Prof. Dr. Ir. P. Troch

Supervisor: Ir. P. Haerens

Department of Civil Engineering

Head of department: Prof. Dr. Ir. J. De Rouck

Faculty of Engineering

Ghent University

Academic year: 2011–2012

Summary

These days, green energy is getting more and more attention in our society, and with this, theconstruction of offshore wind farms is gaining interest. With the development of these farms,a need for constant maintenance is created. This means a constant presence of maintenancevessels, crew boats, and equipment in the wind farm area will be necessary. In view of this,it is interesting to investigate the concept of an offshore shelter location. This location wouldhave two main functionalities: a sheltering location for the vessels, and a logistic function.One solution to this problem could be the creation of an offshore harbour based on floatingbreakwaters (FB). This option is investigated in this dissertation.The starting point of this report is the determination of the hydraulic and structural boundaryconditions. Hydraulic boundary conditions were obtained by analyzing time series of measuredwave heights and directions, provided by IMDC. Structural boundary conditions were deter-mined based on the new offshore support vessel presented by Offshore Wind Assistance N.V.(OWA).After these boundary conditions are defined, a preliminary design, based on previous research,is made. This preliminary design is then modeled in MILDwave software, which lead to anoptimization of the FB length, and a study of different FB layouts.Since the motions of the FB need to be limited to assure safe working conditions, a motionanalysis is performed using AQUA+ software. From this it will become clear that there willbe a problem regarding the limitations of these motions. In view of these findings, the designof a heave FB is proposed.

Keywords: floating breakwater, offshore wind farms, offshore harbour, heave floating break-water

iii

Study of the functional design of a floating offshorebreakwater

Karen Merlevede

Supervisor(s): Peter Troch, Piet Haerens

Abstract— This article discusses a theoretical approach in the design ofan offshore floating breakwater (FB). The choice of hydraulic and struc-tural boundary conditions is discussed, after which a preliminary design ismade. This design is then optimized using MILDwave software. A motionanalysis is performed with AQUA+ software. Finally, a design for a heavefloating breakwater is proposed.

Keywords—floating breakwater, offshore wind farms, offshore harbour,heave floating breakwater

I INTRODUCTION

NOWADAYS , green energy is getting more and more atten-tion in our society. The European directive 2009/28/EC [1]

states that Belgium needs to obtain 13% of the electricity con-sumption from renewable energy sources by 2020. To accom-plish this, the installation of offshore wind farms (OWF) is gain-ing interest. With the development of these offshore wind farms,a need for constant maintenance is created. This means a con-stant presence of maintenance vessels, crew boats, and equip-ment in the wind farm area will be necessary. In view of this,it is interesting to investigate the concept of an offshore shelterlocation. This location would have two main functionalities: asheltering location for the vessels, and a logistic function. Onesolution to this problem could be the creation of an offshore har-bour based on floating breakwaters (FB).

II HYDRAULIC BOUNDARY CONDITIONS

Time series of registered wave heights and directions over aperiod of 20 years have been provided by IMDC. By construct-ing several JAVA tools, this data was analyzed using ACES soft-ware, and afterwards presented graphically in excel. The bound-ary conditions will be determined for two cases.• Case 1: working conditions, for which 95% workability innormal weather conditions is intended in this design. Theseboundary conditions will be used for the preliminary design andthe motion analysis. It is noted that case 1 circumstances also as-sume that waves incident perpendicular to the longitudinal axisof the FB. The design wave height and period are different foreach direction. However, it is seen that most waves are comingfrom the SW direction, which is why the FB will be oriented per-pendicular to this direction. The design wave height and periodfor case 1 circumstances will be those of the SW direction. Inthe analysis of possible FB layouts, the individual wave heightsand periods per direction will be taken into account.• Case 2: a storm with a return period of 50 years, used for thedesign of the mooring system.

Table I summarizs the applied hydraulic boundaries both case1 and 2. Water level, wind and current speed are only important

K. Merlevede is with the Civil Engineering Department, Ghent University(UGent), Gent, Belgium. E-mail: [email protected] .

in the the design of the mooring system and are therefore onlydetermined for case 2 conditions.

TABLE I: Hydraulic boundaries

Case 1 Case 2Hdes 2,5 m 5,0 mTdes 9 s 10 s

Waterlevel - 6,25 m TAWWind speed - 25 m/s

Current speeds - 1 m/sReturn period - 50 y

III STRUCTURAL BOUNDARY CONDITIONS

III-A Design vessel

In [2], a new Offshore Wind Assistance (OWA) support vesselis presented. This vessel will not only be used for crew transfer,but also for seabed survey, scour monitoring and cable inspec-tion, etc. It has a beam over all of 10,04 m, a length over allof 25,75 m, and a draught of 1,75 m. The preliminary designwill be influenced by the design vessel in length. It will be as-sumed that only one OWA vessel will be mooring at the floatingbreakwater, and that this requires a minimum length of 50 m.

III-B Safe working criteria

The criteria to ensure safe working conditions are listed here.• The waves on the lee side of the structure need to be attenu-ated to 1 m to ensure a sheltering environment [3]. The direc-tional maximum value of C can be determined by dividing 1 mby the directional design wave height.• The heave motion needs to be limited to 1m, the roll motionto 5° and the pitch motion to 1° [4].• The wave overtopping needs to be limited to 0,01m3/m/s[5].

IV PRELIMINARY DESIGN

The preliminary design will be based on case 1 boundaryconditions. Two processes of energy transportation are impor-tant for the preliminary design: diffraction and transmission.Diffraction considerations will lead to an optimal length, whiletransmission will lead to an optimal width/draught ratio.

IV-A Diffraction

Diffraction can be quantified using Wiegel diagrams [6].However, these are developed for semi-infinite breakwaters. Inthis case of an offshore floating breakwater, the gap methodas described in the Shore Protection Manual [7] is applicable.

Using this method, it can be determined that the minimum FBlength will be 225mm.

IV-B Transmission

[8], [9], [10], and [11] developed approaches to quantify thetransmssion process. These approaches are applied to testcasesby [12], [13], and [14]. From this it is found that the equationby [11] provides the most accurate results. The transmissionaccording to [11] is given by

Ct =gT 2 sinh(k(d−D))

2π2(W + d tanh(3, 5Dd )) cosh(kd)

(1)

Using this equation, and assuming an initial width of 40 m,leads to a minimum draught of 8 m.

IV-C Overtopping

The mechanism of overtopping will determine the necessaryfreeboard of the structure. Using equations proposed by [15] andthe limitations for overtopping discharge leads to a minimumfreeboard of 4 m.

V MILDWAVE MODEL

MILDwave [16] is a wave propagation model based on thedepth-integrated mild-slope equations of [17].To model an object in the wave field, the cells are assigned acertain absorption coefficient (S). This coefficient ranges fromzero to one; zero meaning the cell consists out of water, andone meaning the cell is fully reflective and does not absorb anyenergy. The difficulty is that MILDwave does not offer a specificinput for floating objects. [18] studied the layout of a farm offloating wave energy converters (WEC) using MILDwave, andfound that the best way to model a floating object is to assign alinearly varying S over the width of the structure. This approachis verified by applying this technique to the same testcases thatwere used to determine the best applicable equation.

VI STUDY OF THE LAYOUT USING MILDWAVE

Three types of FB layout will be modeled in MILDwave. Abeam shape, an L shape, and a U shape.

VI-A Beam shaped FB

The beam shaped structure is oriented perpendicular to theSW direction, where most waves are coming from. The resultsshow that the length of the FB can be reduced to 150 m.

VI-B L-shaped FB

Since the fourth quadrant on the wind rose also produces rel-atively high waves, an L-shape is the subject of this section.Three types in particular are studied: L/150/150, L/150/100, andL/100/100. The first number stands for the length of the sideperpendicular to the SW, while the second number is the lengthof the leg perpendicular to the NW. The L/150/150 layout atten-uates waves coming from the SSE-N segment sufficiently. It isnoticed that the attenuation coefficient, C, is often only half ofthe maximum allowable value for the SW-N segment. This is

why L/150/100 is studied. This layout suffices for the same di-rections as the L/150/150, except for the north. Again, it is seenthat C is well beneath the maximum allowable value for SSE-Wdirections. This is why the last L-shape modeled is L/100/100.In this case, the FB is efficient for waves coming from the SSW-NWN segment. However, waves coming from the first quadrantare not attenuated sufficiently. This is why the U-shaped FB willbe studied in the next section.In every L-shaped layout, problems with reflecting waves arepresent. This is the case when waves are attacking the leewardside of the structure. The reflection decreases when reducing thelength of the legs. The asymmetrical layout showed the mostnegative reflection properties. Generally, the L/100/100 layoutwas found to be the most satisfying.

VI-C U-shaped FB

The final layout modeled, is a U-shaped FB of which the par-allel sides measure 100 m, and the connecting side 155 m. Thislayout offers sufficient attenuation for waves coming from theSW to the NE. However, for waves coming from the south, theattenuation is significantly lower that in the case of an L-shape.This is because the waves are reflected inside the U-shape, am-plifying the resulting wave heights. For waves coming from theSSE, SE, and ESE, the resulting wave heights are even higherthan the incoming wave heights. A comparison between thebeam shaped FB, the U-shaped FB and the L/100/100 config-uration is shown in figure 1.

Fig. 1: Comparison between the beam shaped FB, L/100/100, and U-shaped FB

This figure shows that the directions of sufficient attenuationand the directions for which C exceeds one are different for eachlayout. It is found that the wave amplifying directions in the caseof L/100/100 are more harmful than in the case of the U-shapedFB, because the incoming waves are smaller in the latter case.Nonetheless, this reflection is to be damped as much as possible,for example by adding wave absorbing structures on the leewardside of the structures. Extensive theoretical and experimentalresearch on this topic is recommended.

VII MOTION ANALYSIS

The motions of the FB need to be limited. [4] states that threemotions in particular have to be studied: heave, roll, and pitch.The period of resonance of floating bodies for these motions isusually found somewhere between 5 s and 20 s, an interval thatalso contains the design wave periods.The motion analysis is performed using AQUA+ software, andresults in Response Amplitude Operators, or RAO’s. They aredefined by [19]

Response(t) = (RAO)η(t) (2)

where η(t) is the wave profile as a function of time, t. Thecalculations were performed for different wave incidences: 0°;22,5°; 45°; 67,5°; and 90°. The results of this analysis are listedhere.• The maximum heave RAO amplitude equals 1,61 m/m for awave period of 10 s; case 1 conditions will result in a heavemotion of 4 m,• the maximum pitch RAO amplitude equals 1,18 °/m for awave period of 10 s; case 1 conditions will result in a pitch mo-tion of 2,95°,• the maximum roll RAO amplitude equals 2,2 °/m for a waveperiod of 9 s; case 1 conditions will result in a roll motion of5,5°.None of these motions fall within the limits proposed by [4].A mooring line anchoring system will not be able to restrainthese motions sufficiently. Reducing the motions is possible bychanging the FB layout, adding a moonpool, or adding a skirt.Furthermore, the mooring system can be designed in such a waythat the motions can be restrained. Two possible alternatives areproposed: a tension leg mooring system, and a heave FB. Thelatter will be researched extensively in the next section.

VIII HEAVE FLOATING BREAKWATER

[12] performed research on this type of FB, and compared itto a regular fixed breakwater. According to his research a heaveFB will always be more efficient than the fixed type because ofthe extra damping by the heave motion itself, causing additionalloss of wave energy. In this section, the piles will be designed tomake sure their dimensions are realistic. First the forces actingon the FB and the piles need to be determined. In both casesthese are forces due to wind, current and waves.

VIII-A Forces acting on the floating breakwater

VIII-A.1 Wind and current

Wind and current forces are calculated using the approach de-scribed in [20]. This leads to a wind force of 485 kN and a cur-rent force of 1 231 kN. The approximating points of applicationare 38,25 m and 32,25 m above the sea bed, respectively.

VIII-A.2 Wave forces

Wave forces are calculated by the Froude-Krylov theory asdescribed in [19]. However these equations are only validfor fully submerged objects, which leads to an overestimation.The approach by Goda [21] delivers a more realistic result,93 949 kN, with a point of application of 34,16 m above the seabed.

VIII-B Forces acting on the piles

The pile diameter is assumed to be 4,5m.

VIII-B.1 Wind and current

Wind and current forces are again calculated using the ap-proach in [20]. This leads to a wind force of 91 kN and a currentforce of 263 kN.

VIII-B.2 Wave forces

According to [22], wave forces on piles can be calculated us-ing the Morison equation. This leads to a total wave force of1 323 kN, with a point of application of 19,70 m above the seabed.

VIII-C Pile design

Assuming 6 piles are present in the design of the heave FB,means each pile will take on 1/6 of the total force acting on theFB itself. The total bending moment for one pile at the sea bedequals 573 839 kNm.

VIII-C.1 Wall thickness

Using the approach described in [23] a wall thickness of0,08 m can be determined.

VIII-C.2 Penetration depth

In [23] methods of Vandepitte [24] are described to determinethe penetration depth. Following this approach leads to a mini-mum depth of 28 m below the sea bed.

VIII-C.3 Pile length

The total pile length consist out of the penetration depth, thewater depth, and the extreme water level. This leads to a totallength of 68,25 m.

VIII-C.4 Results

The design for the heave floating breakwater is shown in fig-ure 2.

IX CONCLUSIONS AND RECOMMENDATIONS

In this text, a design is proposed for a heave FB. Althoughroll and pitch motions are restrained in this concept, the heavemotion is not. A system will need to be designed to allow safemooring at the FB, despite these up- and downward motions.Alternatively research can be done on how to restrain the heavemotion completely.Wave basin experiments are strongly advised, since the ap-proach in this text is purely theoretical. Only experimental ob-servations can map the behaviour of different layouts, wave in-cidences, etc.

REFERENCES

[1] European Parliament and Council, “Directive 2009/28/ec of the europeanparliamant and of the council,” Official Journal of the European Union,pp. 16 – 61, April 2009.

[2] the GeoSea Newsflash, “Owa fast crew transfer vessel,” Stan Messemaek-ers, p. 11, 2011.

[3] J. De Rouck, Zee- en Havenbouw, Universiteit Gent, 2011.[4] Pianc, “Criteria for movements of moored ships in harbours,” Supplement

to bulletin n° 88, 1995.

Fig. 2: Heave Floating Breakwater

[5] T Pullen, NWH Allsop, T Bruce, A Kortenhaus, H Schuttrumpf, andJW van der Meer, “Wave overtopping of sea defences and related struc-tures: Assessment manual,” Die Kuste: Archive for research and technol-ogy on the north sea and baltic coast, 2007.

[6] R.L. Wiegel, “Diffraction of waves by semi-infinite breakwaters,” Journalof Hydraulic Div., 1962.

[7] Corps of Engineers US Army, Shore Protection Manual, Coastal Engi-neering Research Center, 1984.

[8] E.O. Macagno, “Experimental study of the effects of the passage of a wavebeneath an obstacle,” Proceedings of Academie des Sciences, Paris, 1953.

[9] D.B. Jones, “Transportable breakwater - a survey of concepts,” NavalCivil Engineering Laboratory, 1971.

[10] J.J. Stoker, Water waves. The mathetmatical theory with applications, In-terscience Publishers New York, 1957.

[11] H Wagner, A Gotz, R Reinsch, and HJ Kaiser, “Schwimmende wellen-brecher im einsatz in einem tagenbaurestsee mitteldeutschlands,” Binnen-schifffahrt ZfB, 2011.

[12] E Tolba, Behaviour of Floating Breakwaters under Wave Action, Ph.D.thesis, Bergische Unversitat, 1999.

[13] E K Koutandos and C Koutitas, “Floating breakwater response to wave ac-tion using a boussinesq model coupled with a 2dv elliptic solver,” Journalof Waterway, Port, Coastal and Ocean Engineering, pp. 243–255, 2004.

[14] T Nakamura, N Mizutani, N Hur, and D S Kim, “A study of the layout offloating breakwater units,” in proceedings of The International Offshoreand Polar Engineers Conference, 2003.

[15] C Franco and L Franco, “Overtopping formulas for caisson breakwaterswith nonbreaking 3d waves,” Journal of waterway, port, coastal and oceanengineering, pp. 98–108, march/april 1999.

[16] P Troch, V Stratigaky, and L Baelus, “Reference manual of mildwave,”2011.

[17] AC Radder and MW Dingemans, “Canonical equations for almost peri-odic, weakly nonlinear gravity waves.,” Wave motion, pp. 473–485, 1985.

[18] Charlotte Beels, Optimization of the Lay-Out of a Farm of Wave EnergyConverters in the North Sea, Ph.D. thesis, Ghent University, 2010.

[19] S.K. Chakrabarti, Hydrodynamics of Offshore Structures, WIT Press,1987.

[20] Pianc, “Floating breakwaters, a practical guide for design and construc-tion,” Supplement to bulletin n° 85, 1994.

[21] Y Goda, Random Seas and the Design of Maritime Structures, WorldScientific Publishing Company, 2000.

[22] J. De Rouck, Offshore constructions, Universiteit Gent, 2011.

[23] L. De Vos, Optimalisation of scour protection design for monopiles andquantification of wave run-up, Ph.D. thesis, Universiteit Gent, 2008.

[24] D. Vandepitte, Berekeningen van constructies, Universiteit Gent, 1979.=2

Studie van het functioneel ontwerp van eendrijvende offshore golfbreker

Karen Merlevede

Supervisor(s): Peter Troch, Piet Haerens

Abstract—Dit artikel bespreekt het theoretisch ontwerp van een offshoredrijvende golfbreker (ENG: floating breakwater (FB)). De keuze voor hy-draulische en structurele randvoorwaarden wordt besproken, waarna eenvoorontwerp gemaakt wordt. Dit ontwerp wordt dan geoptimaliseerd metbehulp van MILDwave software. Een bewegingsanalyse wordt uitgevoerdmet behulp van AQUA+ software. Uiteindelijk wordt een finaal ontwerpvoor een heave floating breakwater voorgesteld.

Keywords— drijvende golfbreker, offshore windmolenparken, offshorehaven, heave floating breakwater

I INLEIDING

DEZER dagen is groene energie niet meer weg te denkenuit onze maatschappij. De Europese richtlijn 2009/28/EC

stelt dat Belgie 13% van zijn energieconsumptie uit hernieuw-bare bronnen moet halen tegen 2020 [1]. Het is niet verwon-derlijk dat offshore windmolenparken meer en meer interesseopwekken. De ontwikkeling van deze parken, brengt een con-stante nood aan onderhoud met zich mee. In dit opzicht kan hetinteressant zijn om offshore een schuilhaven te voorzien. Dezekan meteen ook een logistieke functie hebben. Een mogelijkeoplossing voor dit vraagstuk is de aanleg van een offshore drij-vende golfbreker waaraan de schepen kunnen afmeren.

II HYDRAULISCHE RANDVOORWAARDEN

Tijdreeksen van geregistreerde golfhoogtes en -richtingenover een periode van 20 jaar werden aangereikt door IMDC.Deze data werd geordend door middel van verschillende tools,geprogrammeerd in JAVA, waarna ze geanalyseerd werd inACES. De randvoorwaarden worden bepaald voor twee speci-fieke gevallen.• Case 1: werkomstandigheden, waarbij 95% werkbaarheidwordt beoogd in normale weersomstandigheden. Deze rand-voorwaarden zullen gebruikt worden bij het voorontwerp vande FB, en de bewegingsanalyse. Hierbij wordt opgemerkt datcase 1 omstandigheden overeenkomen met het geval waarbijgolven loodrecht op de langse as van de FB invallen. De on-twerpgolfhoogte en -periode zijn verschillend voor elke richting,maar omdat in de golfanalyse opgemerkt werd dat de meestegolven uit de ZW richting komen, wordt de golfbreker lood-recht op deze richting georienteerd. Daarom zijn voor case 1 deontwerpgolfhoogte en -periode voor deze richting aangenomen.In de analyse van de FB layout (zie verder), wordt echter reken-ing gehouden met de ontwerpgolfhoogte en -periode voor elkerichting afzonderlijk.• Case 2: extreme weersomstandigheden, een storm met re-tourperiode 50 jaar, gebruikt voor het ontwerp van de ver-ankeringen

K. Merlevede, Civil Engineering Department, Ghent University (UGent),Gent, Belgium. E-mail: [email protected] .

Tabel I vat de randvoorwaarden voor case 1 en 2 samen. Wa-ter niveau, wind- en stroomsnelheid zijn enkel belangrijk in hetontwerp van de verankering en worden dan ook niet bepaaldvoor case 1.

TABLE I: Hydraulische randvoorwaarden

Case 1 Case 2Hdes 2,5 m 5,0 mTdes 9 s 10 s

Waterniveau - 6,25 m TAWWindsnelheid - 25 m/s

Stroomsnelheid - 1 m/sRetourperiode - 50 j

III STRUCTURELE RANDVOORWAARDEN

III-A Ontwerpschip

In [2], wordt een nieuw onderhoudsschip voorgesteld, on-twikkeld door OWA (Offshore Wind Assistance). Dit schip zalinstaan voor crew transfers, zeebodem inspectie, erosie inspec-tie, kabel inspectie, enz. Het heeft een LOA van 25,75 m, BOAvan 10,04 m, en een diepgang van 1,75 m. Het voorontwerpwordt beınvloed door het ontwerpschip in die zin dat er een min-imale lengte zal vereist zijn om het schip veilig te laten afmeren.Deze minimale lengte wordt hier vastgelegd op 50 m.

III-B Veiligheidscriteria

De criteria die veilige werkomstandigheden waarborgen wor-den hieronder weergegeven.• De golven aan de leizijde van de constructie moeten gedemptworden tot 1 m om een veilig golfklimaat te creeren [3],afhankelijk van de ontwerpgolfhoogte per richting zal zo dedempingscoefficient C kunnen bepaald worden als de verhoud-ing tussen 1 m en deze directionele ontwerpgolfhoogte,• het dompen moet beperkt worden tot 1 m, rollen tot 5° enstampen tot 1° [4],• golfovertopping moet beperkt worden tot 0,01m3/m/s [5].

IV VOORONTWERP

Het voorontwerp wordt gemaakt op basis van case 1 rand-voorwaarden. Twee processen van energieoverdracht zijn hiervan belang; diffractie en transmissie. De diffractie zal een opti-male lengte van de FB bepalen, terwijl transmissie resulteert ineen optimale breedte/diepgang verhouding.

IV-A Diffractie

Het diffractiefenomeen kan in kaart gebracht worden aan dehand van Wiegel diagrammen [6]. Omdat deze ontwikkeldzijn voor half oneindige golfbrekers, wordt de ’gap methode’toegepast voor offshore golfbrekers die beschreven wordt in deShore Protection Manual [7]. Hiermee kan een minimale lengtebepaald worden van 225 m.

IV-B Transmissie

[8], [9], [10] en [11] ontwikkelden methodes voor hetfenomeen van transmissie. Door deze aanpakken toe te passenop een aantal testcases ([12], [13] en [14]), gekozen omwille vanhun gelijkaardige hydraulische randvoorwaarden, kan bepaaldworden welke formule het meest van toepassing is in dit geval.Er wordt besloten dat de formule door [11] het meest vantoepassing zal zijn. De transmissie wordt dan beschreven door


2π2(W + d tanh(3, 5Dd )) cosh(kd)

(1)

Aan de hand van deze formule, en een breedte van 40 mvooropstellend, wordt een minimum diepgang berekend van8 m.

IV-C Overtopping

Overtopping bepaalt de vrijboord van de constructie. Gebruikmakend van de vergelijkingen opgesteld door [15] en de limi-eten opgesteld door [5], wordt een minimum vrijboord gevon-den van 4 m.

V MILDWAVE MODEL

MILDwave [16] is een golfvoortplantingsmodel gebaseerdop de diepte-geıntegreerde mild-slope vergelijkingen van [17].Om een object in het golfveld te modelleren wordt er aan decellen een bepaalde absorptiecoefficient (S) toegekend. Dezekan gaan van 0 tot 1, waarbij 0 staat voor een watercel en 1voor een volledig reflectieve cel. Er bestaat echter geen een-duidige manier om drijvende objecten te modelleren in MILD-wave. [18] bestudeerde hoe een wave energy convertor (WEC)gemodelleerd kan worden door experimentele testen te vergeli-jken met MILDwave output. Haar bevindingen tonen dat hetlineair laten varieren van S de beste methode is in het gevalvan WEC. Deze aanpak wordt gestaafd door het modelleren vandezelfde testcases die gebruikt werken om de ontwerpformulevoor tranmissie te bepalen.

VI STUDIE VAN DE LAYOUT AAN DE HAND VANMILDWAVE

Drie mogelijkheden voor de FB layout zullen gemodelleerdworden in MILDwave: een balkvorm, een L-vorm en een U-vorm.

VI-A Balkvorm

Het voorontwerp wordt loodrecht op het ZW gemodelleerd,gezien de meeste golven uit deze richting komen. De resultatentonen aan dat de lengte van de balkvorm gereduceerd kan wor-den tot 150 m.

VI-B L-vorm

Gezien het vierde kwadrant van de windroos ook relatief hogegolven voortbrengt, wordt een L-vorm bestudeerd. In het bij-zonder worden drie types onderzocht: L/150/150, L/150/100 enL/100/100. Hierbij staat het eerste getal steeds voor de lengtevan de zijde loodrecht op het ZW, en het tweede voor de zij-de loodrecht op het NW. De L/150/150 configuratie dempt gol-ven uit het segment ZZO-N voldoende. Er wordt ook opge-merkt dat de dempingscoefficient voor het segment ZW-N vaakslechts de helft bedraagt van de maximaal toeglaten waarden.Daarom wordt L/150/100 gemodelleerd. Deze layout volstaatvoor dezelfde richtingen als de L/150/150, met uitzondering vanhet noorden. Het is opnieuw duidelijk dat C zich onder de max-imaal toegelaten waarde bevindt voor de richtingen ZZO-W.Daarom wordt als laatste L-vorm gekozen voor L/100/100. Indit geval is de FB efficient voor golven uit het ZZO-NWN seg-ment. Golven uit de noord-oostelijke richtingen worden echterniet voldoende gedempt, waardoor een U-vorm gemodelleerdzal worden in een latere fase.In elke vorm zijn problemen met reflectie zichtbaar als golveninvallen op de lijzijde van de structuur. Er wordt wel opgemerktdat de reflectie afneemt als de lengte van de benen daalt in desymmetrische configuraties. De asymmetrische layout zal demeest negatieve reflectie opleveren. Algemeen gezien wordt deL/100/100 layout het meest bevredigend bevonden. De richtin-gen waarvoor de golven voldoende gedempt worden komen minof meer overeen met L/150/150, en de reflectie is ook lager.

VI-C U-vorm

Als laatste layout wordt een U-vorm bestudeerd waarvande evenwijdige benen 100 m meten, en de verbindende zijde155 m. Deze structuur biedt voldoende bescherming tegen gol-ven komend uit het ZW tot het NO. Echter, voor golven uit hetzuiden zal de demping aanzienlijk lager zijn dan in het gevalvan een L-vorm. Dit komt doordat de golven binnen in de U-vorm gereflecteerd worden, waardoor een onrustig golfklimaatontstaat. Voor golven komend uit het ZZO, ZO en OZO zijn deresulterende golfhoogtes groter dan de invallende. Een vergeli-jking tussen deze U-vorm en de L/100/100 vorm wordt getoontin figuur 1.

Fig. 1: Vergelijking tussen L/100/100 en de U-vorm

Deze figuur toont dat de richtingen waarvoor de golven vol-

doende gedempt worden en de richtingen waarvoor C groteris dan een verschillen voor de drie configuraties. Er wordtbesloten dat de invalsrichtingen waarvoor de golven versterktworden meer nefast zijn in het geval van L/100/100 dan voorde U-vorm. Dit is zo omdat de invallende golfhoogtes in hetlaatste geval kleiner zijn. Niettemin moet deze reflectie zoveelmogelijk gedempt worden, bijvoorbeeld door het toevoegen vanabsorberende inrichtingen aan de lijzijde van de structuren. Erwordt aangeraden om dit probleem van reflectie theoretisch enexperimenteel te onderzoeken.

VII BEWEGINGSANALYSE

De bewegingen van de FB moeten beperkt worden om de vei-ligheid te waarborgen. [4] stelt dat drie van de zes mogelijke be-wegingen bestudeerd moeten worden; dompen, rollen en stam-pen. De reden hiervoor ligt in het feit dat de natuurlijke periodevoor deze drie bewegingen tussen 5 en 20 s te vinden is, m.a.w.een interval dat ook de ontwerpperiodes omvat. De bewegingvan de FB wordt bestudeerd met AQUA+ software; wat resul-teert in Response Amplitude Operators of RAO’s. Deze wordengedefineerd door [19]

Response(t) = (RAO)η(t) (2)

met η(t) het golfprofiel in functie van de tijd, t. De resultatenworden hieronder opgesomd.• De maximale RAO voor dompen bedraagt 1,61 m/m voor eenperiode van 10 s; toegepast op case 1 randvoorwaarden resul-teert dit in een dompbeweging van 4 m,• de maximale RAO voor stampen bedraagt 1,18 °/m voor eenperiode van 10 s; toegepast op case 1 randvoorwaarden resul-teert dit in een stampbeweging van 2,95 °,• de maximale RAO voor rollen bedraagt 2,2 °/m voor een peri-ode van 9 s; toegepast op case 1 randvoorwaarden resulteert ditin een rolbeweging van 5,5 °.

Geen enkele van deze bewegingen valt binnen de limietenvoorgesteld door [4]. Een traditioneel verankeringssysteem metankerlijnen zal niet in staat zijn deze bewegingen voldoendetegen te houden. De bewegingen kunnen eventueel beperkt wor-den door de layout van de golfbreker aan te passen, door het to-evoegen van een moonpool, of door toevoegen van een skirt. Ditzijn aanpassingen aan het ontwerp van de golfbreker zelf. De be-wegingen kunnen ook tegengehouden worden door het ontwerpvan het verankeringssysteem. Twee opties worden hier vermeld:een tension leg mooring systeem, en een heave floating break-water. De laatste van deze twee wordt hierna meer in detailbesproken.

VIII HEAVE FLOATING BREAKWATER

In het onderzoek van [12] werd duidelijk dat een heave float-ing breakwater beter presteert dan een vaste drijvende golf-breker. Dit fenomeen wordt toegeschreven aan het feit dat hetinduceren en onderhouden van de heave beweging energie vergt,waardoor er dus extra verlies aan golfenergie is. Het voordeelvan een flexibele constructie gaat hier natuurlijk wel verloren. Indeze paragraaf worden de palen voor dit systeem ontworpen omte verifieren of hun afmetingen realistisch zouden zijn. Hierbij

is het noodzakelijk om te weten welke krachten er zullen aan-grijpen op zowel de golfbreker als de palen zelf. Deze krachtenzijn het gevolg van wind, stroming en golven.

VIII-A Krachten op de drijvende golfbreker

VIII-A.1 Wind en stroming

Wind- en stromingskrachten worden berekend aan de handvan de methode beschreven in [20]. Dit leidt tot een windkrachtvan 485 kN en een stromingskrachtn van 1 231 kN. De aangri-jpingspunten van deze krachten bevinden zich op 38,25 m en32,25 m respectievelijk, boven de zeebodem.

VIII-A.2 Golfkrachten

Golfkrachten worden een eerste maal berekend aan de handvan de Froude-Krylov theorie, beschreven in [19]. Deze meth-ode is echter enkel geldig voor volledig ondergedompelde ob-jecten, wat leidt tot een overschatting. Daarom worden ze eentweede maal berekend, deze keer aan de hand van de meth-ode ontwikkeld door Goda [21] voor caisson golfbrekers, waareen meer realistisch drukverloop aangenomen wordt. Dit leidttot een golfkracht van 93 949 kN met een aangrijpingspunt van34,16 m boven de zeebodem.

VIII-B Krachten op de palen

Als paaldiameter wordt een waarde van 4,5 m aangenomen.

VIII-B.1 Wind en stroming

Wind- en stromingskrachten worden opnieuw berekend aande hand van de methode beschreven in [20]. Dit resulteert ineen windkracht van 91 kN en een stromingskracht van 263 kN.

VIII-B.2 Golfkrachten

Volgens [22] en [23] kunnen krachten op palen berekend wor-den aan de hand van de Morison vergelijking. Hiermee wordteen totale golfkracht van 1 323 kN berekend, met een aangri-jpingspunt van 19,70 m boven het zeebed.

VIII-C Ontwerp van de palen

Er worden 6 palen gebruikt in het ontwerp, waardoor elkepaal 1/6 van de krachten aangrijpend op de golfbreker zal opne-men. De totale kracht op een paal wordt dan 17 489 kN, en hetbuigmoment 573 839 kNm.

VIII-C.1 Wanddikte

Gebruik makend van de methode beschreven in [24] voor hetontwerp van monopiles, wordt een wanddikte van 0,08 m berek-end.

VIII-C.2 Insteekdiepte

In [24] wordt de methode van Vandepitte [25] gebruikt omde insteekdiepte van monopile funderingen te bepalen. Wan-neer dezelfde aanpak gevolgd wordt, wordt een minimale in-steekdiepte van 28 m gevonden.

VIII-C.3 Lengte

De totale lengte van de paal bestaat uit de som van de in-steekdiepte, de water diepte en het extreme waterniveau. Ditalles leidt tot een totale lengte van 68,25 m.

VIII-C.4 Resultaat

Het bekomen ontwerp wordt getoond in figuur 2.

Fig. 2: Heave Floating Breakwater

IX CONCLUSIE EN AANBEVELINGEN

In deze tekst werd een ontwerp voorgesteld voor een heavefloating breakwater. Hoewel rol- en stampbewegingen hierdoorvermeden worden, kan de structuur nog steeds dompen. Er zaleen systeem moeten ontworpen worden om schepen, ondanksdeze beweging, tot veilig te laten afmeren aan de golfbreker. Erkan eventueel ook onderzocht worden wat het effect zou zijn in-dien ook de dompbeweging tegengehouden wordt.Algemeen worden golfbak testen aangeraden gezien de aanpakin deze tekst zuiver theoretisch is. Enkel experimentele obser-vaties kunnen het gedrag van verschillende layouts e.d. in kaartbrengen.

REFERENCES

[1] European Parliament and Council, “Directive 2009/28/ec of the europeanparliamant and of the council,” Official Journal of the European Union,pp. 16 – 61, April 2009.

[2] the GeoSea Newsflash, “Owa fast crew transfer vessel,” Stan Messemaek-ers, p. 11, 2011.

[3] J. De Rouck, Zee- en Havenbouw, Universiteit Gent, 2011.[4] Pianc, “Criteria for movements of moored ships in harbours,” Supplement

to bulletin n° 88, 1995.

[5] T Pullen, NWH Allsop, T Bruce, A Kortenhaus, H Schuttrumpf, andJW van der Meer, “Wave overtopping of sea defences and related struc-tures: Assessment manual,” Die Kuste: Archive for research and technol-ogy on the north sea and baltic coast, 2007.

[6] R.L. Wiegel, “Diffraction of waves by semi-infinite breakwaters,” Journalof Hydraulic Div., 1962.

[7] Corps of Engineers US Army, Shore Protection Manual, Coastal Engi-neering Research Center, 1984.

[8] E.O. Macagno, “Experimental study of the effects of the passage of a wavebeneath an obstacle,” Proceedings of Academie des Sciences, Paris, 1953.

[9] D.B. Jones, “Transportable breakwater - a survey of concepts,” NavalCivil Engineering Laboratory, 1971.

[10] J.J. Stoker, Water waves. The mathetmatical theory with applications, In-terscience Publishers New York, 1957.

[11] H Wagner, A Gotz, R Reinsch, and HJ Kaiser, “Schwimmende wellen-brecher im einsatz in einem tagenbaurestsee mitteldeutschlands,” Binnen-schifffahrt ZfB, 2011.

[12] E Tolba, Behaviour of Floating Breakwaters under Wave Action, Ph.D.thesis, Bergische Unversitat, 1999.

[13] E K Koutandos and C Koutitas, “Floating breakwater response to wave ac-tion using a boussinesq model coupled with a 2dv elliptic solver,” Journalof Waterway, Port, Coastal and Ocean Engineering, pp. 243–255, 2004.

[14] T Nakamura, N Mizutani, N Hur, and D S Kim, “A study of the layout offloating breakwater units,” in proceedings of The International Offshoreand Polar Engineers Conference, 2003.

[15] C Franco and L Franco, “Overtopping formulas for caisson breakwaterswith nonbreaking 3d waves,” Journal of waterway, port, coastal and oceanengineering, pp. 98–108, march/april 1999.

[16] P Troch, V Stratigaky, and L Baelus, “Reference manual of mildwave,”2011.

[17] AC Radder and MW Dingemans, “Canonical equations for almost peri-odic, weakly nonlinear gravity waves.,” Wave motion, pp. 473–485, 1985.

[18] Charlotte Beels, Optimization of the Lay-Out of a Farm of Wave EnergyConverters in the North Sea, Ph.D. thesis, Ghent University, 2010.

[19] S.K. Chakrabarti, Hydrodynamics of Offshore Structures, WIT Press,1987.

[20] Pianc, “Floating breakwaters, a practical guide for design and construc-tion,” Supplement to bulletin n° 85, 1994.

[21] Y Goda, Random Seas and the Design of Maritime Structures, WorldScientific Publishing Company, 2000.

[22] J. De Rouck, Offshore constructions, Universiteit Gent, 2011.[23] M.C. Deo, Waves and structures, Indian Institute of Technology, 2007.[24] L. De Vos, Optimalisation of scour protection design for monopiles and

quantification of wave run-up, Ph.D. thesis, Universiteit Gent, 2008.[25] D. Vandepitte, Berekeningen van constructies, Universiteit Gent, 1979.=2

Contents

Preface ii

Overzicht iii

Extended abstract iv

Extended abstract (Nederlands) viii

List of symbols and acronyms xvii

1 Introduction 1

1.1 Framework of this master dissertation . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Objectives of this master dissertation . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Structure of this master dissertation . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Literature Study 6

2.1 History of floating structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Types of floating structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Floating Breakwaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Types of floating breakwaters . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.3 Behaviour under wave action . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.4 Experimental Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.5 Numerical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.6 Influence of different parameters . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

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3 Hydraulic boundary conditions 24

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Wave heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.2 Design wave height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Wave period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 Water level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.5 Wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.6 Current speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.7 Conclusions: boundary conditions for general design . . . . . . . . . . . . . . . 35

4 Structural boundary conditions 36

4.1 Design vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Safe working criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.1 Attenuated wave height . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.2 Motions of the FB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.3 Overtopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 Preliminary Design 39

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Wave diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2.1 Regular waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2.2 Random waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2.3 General approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3 Wave transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3.1 Previous research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.3.2 Verification of the proposed methods . . . . . . . . . . . . . . . . . . . . 46

5.4 Overtopping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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6 MILDwave Model 53

6.1 Introduction to MILDwave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.2 Modeling floating objects in MILDwave . . . . . . . . . . . . . . . . . . . . . . 55

6.2.1 Previous research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.2.2 Testcase 1: Tolba (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.2.3 Testcase 2: Koutandos et al. (2005) . . . . . . . . . . . . . . . . . . . . 57

6.2.4 Testcase 3: Nakamura et al. (2003) . . . . . . . . . . . . . . . . . . . . . 57

6.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

7 Optimizing the preliminary design 60

7.1 Modeling the preliminary design . . . . . . . . . . . . . . . . . . . . . . . . . . 60

7.2 Study on the FB layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

7.2.1 Beam shaped layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

7.2.2 L shaped layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.2.3 U-shaped layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

7.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

8 Motion analysis 76

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

8.2 Aqua+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

8.3 Response Amplitude Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

8.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

8.4.1 Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

8.4.2 Roll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

8.4.3 Heave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

8.5 Discussion and solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

9 Heave Floating Breakwater 83

9.1 General concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

9.2 Forces acting on the floating breakwater . . . . . . . . . . . . . . . . . . . . . . 84

9.2.1 Wind and current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

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9.2.2 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

9.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

9.3 Forces acting on the piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

9.3.1 Wind and current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

9.3.2 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

9.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

9.4 Pile design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

9.4.1 Wall thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

9.4.2 Penetration depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

9.4.3 Final pile design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

9.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

10 Discussion and recommendations 101

10.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

10.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

A Offshore Wind Farm concessions 108

B ACES output file 110

C Cumulative wave heights per direction 117

D Extreme wave heights per direction 126

E Diffraction diagrams 131

E.1 Regular waves: Wiegel (1962) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

E.2 Irregular waves: Goda (2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

F MILDwave testcases 134

F.1 Testcase 1: Tolba (1999) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

F.2 Testcase 2: Koutandos et al. (2005) . . . . . . . . . . . . . . . . . . . . . . . . . 139

F.3 Testcase 3: Nakamura et al. (2003) . . . . . . . . . . . . . . . . . . . . . . . . . 143

G MILDwave optimization 147

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G.1 Influence of the FB length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

G.2 Beam shaped FB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

G.3 L/150/150 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

G.4 L/150/100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

G.5 L/100/100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

G.6 U shaped FB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Bibliography 173

List of Figures 177

List of Tables 184

xvi

List of symbols and acronyms

C coefficient of wave attenuation Hres/Hi (-)

Cd coefficient of wave diffraction Hd/Hi (-)

Cmax maximum coefficient of wave attenuation to obtain a safe environment

Cr coefficient of wave reflection Hr/Hi (-)

Ct coefficient of wave transmission Ht/Hi (-)

d water depth (m)

D draught of the FB (m)

FB floating breakwater

g gravitational acceleration (m/s2)

H95% wave height with 95% probablity of occurence

H1/3 significant wave height calculated from the time domain

Hd wave height after diffraction

Hi incoming wave height

Hr wave height after reflection

Ht wave height after transmission

Hm0 significant wave height calculated from the frequency domain

k dimensionless wave number (2πL ) (-)

l length of the FB (m)

L wave length according to Airy wave theory (m)

L0 deep water wave length gT 2

2π (m)

OWA offshore wind assistance N.V.

OWF offshore wind farm

q average overtopping discharge (m3/m/s)

RAO response amplitude operator

Rc freeboard of the FB

ρwater mass density of sea water (1026kg/m3)

xvii

Chapter 0. List of symbols and acronyms

ρair mass density of air (1,029kg/m3)

S absorption coefficient in MILDwave (-)

T wave period (s)

TLP tension leg platform

VLFS very large floating structure

W width of the FB (m)

xviii

Chapter 1

Introduction

1.1 Framework of this master dissertation

Nowadays, green energy is getting more and more attention in our society. The European

directive 2009/28/EC (Parliament and Council, 2009) states that Belgium needs to generate

13% of its provision of electricity from renewable energy sources by 2020. To accomplish this,

the installation of offshore wind farms (OWF) is gaining interest. Actually three projects

for the construction of OWF in the Belgian part of the North Sea are ongoing: C-Power on

Thorntonbank, Belwind on Bligh Bank , and Northwind on ’Bank zonder Naam’. Four others

are already planned.

Thorntonbank Offshore Windfarm (C-Power) will have 55 wind turbines, located roughly 30

kilometers off Zeebrugge. The project started in 2007 with the construction of the first 6

foundations, built using gravity base foundations. These were installed in 2008. Phase 2 and

3 of the project consists of installing the remaining windmills using jacket foundations. The

first 6 windmills have a capacity of 5 megawatt each, and are currently active. The other 55

windmills are under construction, and will each have a capacity of 6,15 megawatt. Thornton

bank offshore wind farm will have an annual energy generation of 1 000 000 000 kWh, which

is the equivalent of the annual consumption of 600 000 inhabitants (http://www.c power.be/,

2012).

The Belwind OWF has a capacity of 165 MW, and delivers energy to 330000 households/year.

Located at 42 kilometers off the coast of Zeebrugge, it is the world’s most offshore located

wind farm. Its annual energy generation is estimated to be in the order of the equivalent of

the annual energy consumption of 175 000 households.

Northwind will be located on the sand bank ’Bank zonder Naam’, at 38 kilometers off the

coast, and aims to install 72 windmills with a capacity of 3 MW each.

Three new projects already gained concessions: Rentel, NORTHER, and SEASTAR, while one

concession area is still to be denoted. The location of these wind farms are shown in Appendix

A .

1

Chapter 1. Introduction

With the development of these offshore wind farms, a need for constant maintenance is cre-

ated. Survey needs to be done in order to detect scour around the foundations. If scour is

present the resulting scour pits will need filling. The transport cables will also need regular

survey. These surveys can be done using ROV’s or by diving inspections. The foundation

structures will need to be inspected regularly as well. On top of this, there will be a need, dur-

ing these maintenance operations, for the supply of spare parts and containerized items (the

GeoSea Newsflash, 2011), and crew transfers. This means a constant presence of maintenance

ships, crew boats, and equipment in the wind farm area will be necessary.

However, when supplies are needed, the maintenance ships have to sail to the harbour (Zee-

brugge or Oostende). A trip that takes at least 2 hours depending on the weather conditions,

and the type of vessel. In view of this it is interesting to investigate other solutions, and

assess if an offshore shelter location is a valuable alternative. This location would have two

main functionalities: a sheltering location for the ships, and a logistic function. This way the

maintenance ships can stay in position, and maintenance operations are not interrupted, while

other ships take care of the transportation of goods.

Creating an artificial island, that combines shelter for vessels doing maintenance, with other

functionalities, like a rescue harbour of logistic center, is one solution to answer the needs.

This solution, however, is very expensive, and needs the involvement of different stake hold-

ers. An alternative could be the creation of a shelter harbour based on floating breakwaters.

Since floating breakwaters are a common solution when working in deep water conditions, this

thesis will focus on a preliminary design for such a breakwater by performing a feasibility study.

1.2 Objectives of this master dissertation

The main objective of this master dissertation is to perform a feasibility study of such a floating

structure and propose a preliminary design, with two main focus points:

� obtain sufficient wave attenuation to create safe mooring conditions

� limit the motions of the structure itself to allow safe mooring of ships, and safe storage

of goods

Several parameters will be studied, such as the dimensions of the floating breakwater, the

layout, and the mooring system.

This dissertation does not aim to be complete regarding the structural design of the FB. It

is a starting point for further research, which, as will become clear in this report, is highly

recommended.

2


1.3 Structure of this master dissertation

Chapter 2 summarizes the results of the performed literature study. A brief overview will

be given on the history of floating bodies in general, after which the focus will be put on

floating breakwaters (FB). After providing some general information about the advantages,

disadvantages, types, etc. the results of experimental, and numerical studies performed in the

past will be summed up. From these studies it will be determined which parameters will be

investigated further with respect to the performance of the FB.

In chapter 3 and 4 the boundary conditions are determined. There are two types that can

be distinguished. Firstly there are the hydraulic boundaries such as design wave heights, de-

sign wave periods, design water levels, etc. Secondly there are structural boundary conditions

depending on the design vessel, the expected wave attenuation, the motion restraints, and the

overtopping limit.

Chapter 5 concerns the preliminary design. In this chapter the processes of diffraction,

and transmission are treated separately. Diffraction properties are viewed using diffraction

diagrams by Wiegel (1962) for regular waves, and diffraction diagrams by Goda (2000) for

irregular waves. Combining this with the so called gap method, as described in the Shore

Protection Manual (US Army, 1984) will give a first indication of this process. Secondly the

transmission will be regarded using design guidelines of four researchers: Macagno (1953),

Jones (1971), Stoker (1957), and Wagner et al. (2011). To see which equation or working

method is more suitable for the conditions in this master dissertation, three testcases with

similar conditions are chosen. The working methods of the different authors are applied to

each of these testcases, providing the most reliable method for the preliminary design. From

these considerations, a preliminary design is proposed which will be the starting point for the

rest of the studies in this report.

The design will now be optimized using MILDwave. In chapter 6 it is investigated how a

floating object should be modeled in MILDwave software. This is done by modeling the same

testcases used in chapter 5 in various ways, to see which approach provides the most consistent

results.

In chapter 7 the preliminary design is optimized. First the length of the FB is adjusted,

after which the effect of different breakwater layouts is studied. From the hydraulic bound-

aries design wave heights for every direction are determined, and thus the maximum value of

C, the overall attenuation coefficient. C is defined by the ratio of the resulting wave height

on the leeward side of the structure, to the incoming wave height. Three layouts will be the

3


subject of this chapter. A simple beam shaped FB, an L-shaped FB, and finally a U-shaped FB.

A very important property of the FB is of course the motion of the structure itself. This is

why in chapter 8 a motion analysis is performed using Aqua+ software that provides the

response amplitude operators (RAO) of a simple beam shaped structure. This will bring to

light that the motions of the FB are too large for safe mooring, let alone storage of goods.

At the end of this chapter, possible solutions to this problem are proposed, one of which is

discussed in detail in chapter 9

The difficulties disclosed in chapter 8 are addressed in chapter 9 by proposing a heave float-

ing breakwater. This type of structure is moored using vertical piles, making sure the only

possible motion the structure can undergo is the up- and downward motion or heave. In this

chapter the feasibility of such a structure is investigated with regard to the pile dimensions,

penetration depth, etc.

To conclude this master dissertation, the results and concerns are summarized in chapter 10,

followed by recommendations for further research.

The general approach of this master dissertation is presented in figure 1.1.

4


Figure 1.1: General approach

5

Chapter 2

Literature Study

2.1 History of floating structures

VLFS, or Very Large Floating Structures, were first introduced in the 1920s, when Edward R.

Armstrong proposed a floating airport called ’Seadrome’ (figure 2.1) for transatlantic flights.

His idea was to ground the airplanes in the middle of their long flight to refuel. However,

in 1927 the first non-stop flight from New York to Paris took place, rendering the idea of

seadromes unnecessary (Wang and Tay, 2011).

Figure 2.1: Seadrome (Armstrong, 1929)

Further development of floating structures took place during World War II, when the US

Navy Civil Engineering Corps used Armstrongs concept to build a pontoon flight deck, to be

6

Chapter 2. Literature Study

positioned near Great Britain. Secondly, at the end of World War II, there was a need for

instant harbours for the invasion forces on the Normandy beaches. These temporary ports were

constructed using two types of breakwaters. The first type, Phoenix breakwaters, consisted

out of concrete caissons that were positioned offshore and sunken down in order to create

a bottom founded breakwater. The second option were the so called Bombardon floating

breakwaters, which are presented in figure 2.2. These were floating steel structures with a

cruciform cross section that were anchored between the Phoenix breakwaters (Farmer, 1999).

However, in 1944 a great storm caused these Bombardon FB to break loose, which lead to

massively damaged harbour infrastructure.

Figure 2.2: Bombardon Floating Breakwater (Martin, 2004)

The flexibility of these floating structures lead to several studies after WO II regarding con-

cepts, theories, and experiments with different configurations. The benefits were clear: the

constructions could be built on dry land, then towed to their position where they could be

either anchored or sunk into place. On top of this, it was also possible to relocate these struc-

ture relatively easily.

In 1975 the idea of VLFS was revived by Kiyonori Kikutake, a Japanese architect. He designed

Aquapolis, a floating city, as centerpiece for the world fair in Okinawa. Aquapolis stayed open

until 1993 and was eventually towed away and dismantled in 2000 (Wang and Tay, 2011).

As the big cities grew denser and denser, there was a need for expansion of the airfields, prefer-

ably outside the city. In 1995 the Japanese performed a test in Tokyo bay, building a floating

runway of 1 km length, in order to test the soundness of VLFS for use as an airport (Wang and

Tay, 2011). The results showed that the hydro-elastic response of the floating runway did not

affect aircraft operations, and that a floating airport could in fact be a sustainable solution.

All around the world, the use of VLFS is growing in different fields. From floating oil storage

bases, offshore military bases and floating nuclear plants to floating stages and tennis courts.

The possibilities are endless.

7


2.2 Types of floating structures

In general, floating bodies can be divided into two types, semi-submersible structures and

pontoon structures. A third option, the tension leg platform, is also discussed here because of

the properties of the mooring system.

Semi-submersible structures

A semi-sub is a platform raised above sea level, which obtains its buoyancy from ballasted,

watertight pontoons located below the ocean surface, and wave action. An example is shown

in figure 2.3. They are used in deep water conditions where the influence of wave energy is

not present at half a wavelength below the water surface. A semi-sub can change its draught

by deballasting. When moving the platform, the ballast tanks are emptied, which decreases

the draught. This way there will be minimal resistance and maximum manoeuverability when

transporting the platform from one place to another. The concept often finds application as

a heavy lift vessel because of its capability to increase the draught, and thus getting quite

close to the object that needs to be lifted (Gerwick, 2000). They’re held on location by

mooring systems and dynamic positioning. Semi-subs do not offer sufficient wave attenuation

to create a sheltering environment. This means that if semi-sub structures are used to build

an offshore harbour, additional floating breakwaters would be required to create favourable

wave conditions inside the harbour.

Figure 2.3: Semi-submersible structure (Minnes, 2003)

8


Pontoon type structures

Pontoon type structures are generally used in calm waters where low wave energy is present.

The structure, a rectangular hull, simply rests on the water surface, and is kept in place

by mooring systems, and/or dynamic positioning systems. The main advantages of pontoon

structures are the high stability, low manufacturing costs, and easy maintenance and repair.

However, they have not yet been used in open seas, where the waves are relatively high (Ali,

2005). Different kind of pontoon type structures have been built. Dual pontoon structures

proved to be very promising, as well as twin pontoon structures. These pontoon structures are

discussed extensively in the next section. A special type of floating structures are mega floats,

as shown in figure 2.4. These are large pontoon type floating structures, with at least one

dimension greater than 60 m. They are often protected by a breakwater. Mega floats are cost

effective in large water depths, environmentally friendly, and easy to construct and remove

(Wang and Tay, 2011).

Figure 2.4: Mega float structure (Watanabe et al., 2004)

Tension leg structures

Tension leg platforms (TLP) are used in extremely large depths (>300 m). The mooring system

is connected to a template on the sea bed, after which the platform is partially deballasted.

This results in a vertical tensile force in the wires or piles because of the buoyancy of the

hull, which restricts movements in the vertical directions (heave). Horizontal movement is still

allowed, but minimal due to the restoring forces of the pretension. As stated above, they are

mostly used in very deep waters. Which also means the TLP system is most often combined

with semi-submersible structures (Ali, 2005). An example of a TLP structure is shown in

figure 2.5.

9


Figure 2.5: Tension leg platform (Siddiqui and Ahmad, 2001)

2.3 Floating Breakwaters

2.3.1 Introduction

Most of the above mentioned floating structures do not offer shelter against extreme weather

conditions. In this report, a floating breakwater, where the ships can moor directly onto, will

be designed. The advantages of such a structure are listed here (http://www.marbef.org/

wiki.Floating_Breakwaters, 2011):

� In case of poor foundation possibilities, when the soil prohibits bottom supported

breakwaters, they are an excellent alternative,

� in deep water conditions, when the water depth becomes larger than 6 m, they become

less expensive than bottom founded breakwaters,

� the water quality is ensured which is important for marine biodiversity and ecology,

� in case of ice formation they can be removed and towed to protected areas,

� visual impact is minimal,

� they can be rearranged into a new layout with minimum efforts.

10

http://www.marbef.org/wiki.Floating_Breakwaters



The main function of a floating breakwater is to attenuate waves. The difficult part of de-

signing floating breakwaters are often the connections between different modules. They are

subjected to corrosion, wear, and fatigue. The objective will often be to construct solid hulls

as long as possible, causing the number of connections to decrease (Pianc, 1994).

Floating breakwaters can be classified by configuration or by wave attenuation mechanism.

When classifying by configuration, pontoon breakwaters, mat breakwaters, A-frames, and

tethered breakwaters can be distinguished (Pianc, 1994). They each have their own field of

application, advantages, and disadvantages that will be discussed in section 2.3.2 .

The classification by wave attenuation mechanism yields a distinction between reflective and

dissipative structures (Pianc, 1994). In reality both processes will contribute to the attenua-

tion mechanism, but one can be dominant. Reflective systems ideally reflect all of the incident

wave energy. An example of such a system would be the pontoon breakwater. A dissipa-

tive system destroys the wave energy through viscous or turbulent effects. To amplify this

effect turbulence generators have been developed, which force the wave induced flow to break

through slots or perforations (e.g. perforated walls). The problem with these generators is the

fact that their behaviour cannot yet be predicted theoretically, which means test results have

to be interpreted with care. Another example of turbulence generators are open tube floating

breakwater systems. These consist out of horizontal open tubes, with randomly distributed

lengths, placed under water. The axis is parallel to the mean wave propagation direction. Be-

cause of the head losses within the tubes, and the turbulence at the shore side of the structure

due to randomness of the flow, energy is dissipated (Pianc, 1994).

Station keeping of floating breakwaters can be achieved in two ways. Either by mooring lines

or by piles. The use of piles eliminates sway motions, and reduces roll motions to a minimum,

which leads to lower coefficients of transmission. A problem with using piles are the connec-

tions of the piles to the breakwater, which wear down quickly. Mooring lines will always be

more suitable in deeper water. However, there will also be difficulties connecting the mooring

lines to the breakwaters, and, even more importantly in this case, they might allow too much

motion of the breakwater to ensure safe working conditions (Pianc, 1994).

2.3.2 Types of floating breakwaters

Different types of floating breakwaters are discussed in this section.

11


Pontoon floating breakwaters

Pontoon breakwaters are the most effective type, since the overall width can be in the order

of half the wavelength, which, according to Pianc (1994), means they will attenuate the waves

sufficiently. They offer the best prospects for multiple use (use as a walkway, storage, etc.).

Several subtypes have been developed.

Twin pontoons or ’Catamaran-shaped pontoons’ (Pianc, 1994), as shown in figure 2.6 dis-

tribute the given mass to achieve a longer roll period. This results in a more stable platform

than would be achieved with the same mass in a simple pontoon shaped floating breakwater.

The corners provide additional energy loss by dissipation, and the water mass between the

hulls will add damping zones, especially to the sway motion.

Figure 2.6: Catamaran floating breakwater

A second alternative is called the dual-pontoon type floating breakwater, and is represented

in figure 2.7, where two pontoons are connected sideways by a rigid deck. Research on this

type of floating breakwater has been performed by Williams and Abdul-Azm (1997). A dual

pontoon floating breakwater attenuates waves similar to a single pontoon but will also destroy

energy by turbulence between the two floating bodies.

Figure 2.7: Dual pontoon floating breakwater

Mat floating breakwaters

Mat breakwater types can, for example, be built out of old tires. Obviously they are a low cost

solution, and easy to construct. They are much less effective for use in long wave lengths than

pontoon type floating breakwaters and have a smaller design life (Farmer, 1999). A simple

12


representation of a mat floating breakwater is shown in figure 2.8 .

Figure 2.8: Mat floating breakwater

A-frame floating breakwaters

An A-frame is a combination of vertical walls that reflect the wave energy and outriggers for

stability that will also develop a large roll period. This configuration is shown in figure 2.9.

Figure 2.9: Aframe floating breakwater

Tethered floating breakwaters

The last type that will be discussed is the tethered floating breakwater. Wave attenuation

is obtained through drag, produced during the oscillations of a field of spheres tethered to

remain just below the surface (Pianc, 1994). This concept is clearified in figure 2.10.

Figure 2.10: Tethered floating breakwater

13


2.3.3 Behaviour under wave action

There are three main processes that determine the behaviour of a FB: transmission, reflection

and diffraction.

Wave diffraction is the process where wave energy is transferred along the crest, perpendicular

to the direction of the wave propagation, from points of greater wave height to points of

lesser wave height. This causes wave crests to spread into the shadow zone in the lee of the

breakwater (CEM, 2008). A graphical representation of this process is shown in figure 5.1.

Figure 2.11: Diffraction process (US Army, 1984)

The transport of energy underneath, and on the sides of the structure is called transmission.

Reflection is the process where energy is reflected by the structure. A graphical representation

of these processes is shown in figure 2.12.

Figure 2.12: Transmission process

These three processes are characterized by their respective coefficients; Ct, Cr and Cd.

Ct =Ht

Hi(2.1)

Cr =Hr

Hi(2.2)

Cr =Hd

Hi(2.3)

14


where Ht is the transmitted wave height, Hr the reflected wave height, Hd the diffracted wave

height, and Hi the incident wave height.

These coefficients can be combined in one overall attenuation coefficient ’C’, which is described

by

C =Hres

Hi(2.4)

where Hres equals the resulting wave height due to the presence of the structure.

Every freely floating structure has six independent degrees of motion; heave, sway, surge, yaw,

pitch, and roll. These motions are defined in figure 2.13.

Figure 2.13: Six independent motions of a freely floating structures (Ardakani and Bridges, 2009)

For these motions, the natural frequency, which is a property inherent to the structure, can

be calculated. If the wave frequency approximates the natural frequency for a certain motion,

the motions of the FB will be amplified, which will render the FB to be less efficient. One

of the main challenges in the design of floating breakwaters is to avoid this phenomenon of

resonance as much as possible. According to Pianc (1995) the natural frequencies for sway,

surge, and yaw lie in the range of 20 s to several minutes, while the frequencies of heave, pitch,

and roll can be found in the range of 5 to 20 s. The designer needs to have knowledge of

the expected wave conditions in order to know which motions might cause problems. He also

needs to understand the response of the floating body to the wave profile. This behaviour

becomes even more complicated if the influence of the mooring system, and the connection

between modules are taken into account. This is why accurate design can only be achieved by

numerical or physical modeling.

15


2.3.4 Experimental Studies

Over the years, a lot of studies were preformed to investigate the influence of several pa-

rameters on the behaviour of floating breakwaters. A few of these studies are discussed here

according to the researched parameters.

Shape and dimensions

Several shapes of floating breakwaters are possible. In this paragraph, the influence of these

shapes on the attenuation capacity will be discussed.

Koutandos and Koutitas (2004) performed experiments in a wave flume on several models: sin-

gle fixed floating breakwaters, heave motion floating breakwaters, single fixed floating break-

waters with an attached front plate (permeable and impermeable) and double fixed floating

breakwaters. They found that a single fixed floating breakwater acts more as a reflective struc-

ture, while the heave motion floating breakwater was more dissipative. The attached plates

did enhance the efficiency significantly, but no real difference was found between permeable

and impermeable plates. They concluded that a double fixed floating breakwater would be the

most effective solution, but in terms of cost-effectiveness the floating breakwater with attached

plate is advised (Koutandos et al., 2005).

Gesraha (2006) studied the effect of two sideboards that are very thin compared to the length

of the incident waves, and the beam of the breakwater. His model is presented in figure 2.14.

He made a numerical model, as well as an experimental verification, and investigated several

variables: the exciting forces, breakwater responses, and the coefficient of transmission. He

found that adding side boards leads to larger heave motions, but other motions were lower, re-

sulting in a lower coefficient of transmission. He concluded that this configuration could result

in a more economical design, if the design is tuned to the incident wave frequency (Gesraha,

2006). Again, the positive effect of sideboards on the attenuation capacity is shown.

Dong et al. (2008) examined the wave transmission coefficients of pontoon floating breakwa-

ters, and double pontoon floating breakwaters. The results showed that the double pontoon

breakwater reduces wave energy better than the single type. However, both types needed to

have a sufficiently high width in order to get a small Ct (Dong et al., 2008). The difference in

attenuation capacity was not significant.

Pena et al. (2011) started their experiments from a reference model (model A in figure 2.15)

with two side-boards (fins), and tested the influence of several variations to this basic design.

The different models are presented in figure 2.15. Model B was used to determine the influence

of the width, model C for the influence of the fins and model D for the influence of the design.

16


Figure 2.14: Model Gesraha (2006)

Figure 2.15: Models Pena et al. (2011)

When comparing model A to model B, they found that a reduction of the width by 10% has

no significant influence on the coefficient of transmission. Comparing model A and C showed

an improvement of energy dissipation which obviously leads to a decrease of Ct. However,

they noted that the increase in dissipation is small in comparison to the potential cost of pro-

longing the fins. Model D showed that even with no spacing between two modules, meaning

there would be an increase of width by 50%, the energy dissipation would increase by 35%.

However, increasing the spacing between two modules only leads to 5% dissipation increase,

leading to a non cost-effective solution (Pena et al., 2011). In conclusion, the width of the

floating breakwater needs to increase significantly to improve the attenuation performance. In

addition, it is shown once again that sideboards are an important factor regarding the wave

17


attenuation.

Material of the Floating Breakwater

Wang and Sun (2010) first tested the influence of a porous side wall by comparing a structure

with an impermeable wall to a structure with a porous wall (porosity n 0,63). It was found

that the transmitted wave height is higher for structures with an impermeable side wall, be-

cause there is an energy accumulation in an enclosed domain. In porous structures energy

dissipation will take place.

Wang and Tay (2011) compared a porous floating breakwater to an impermeable floating

breakwater. Porous floating breakwaters are found to have a lower Cr. Energy dissipation will

play a more important role for porous floating breakwater than wave reflection (Wang and

Tay, 2011).

Layout of the different modules

Nakamura et al. (2003) investigated the effect of an inclined layout (see figure 2.16) using wave

flume and wave basin experiments. The layout where the units are positioned obliquely to the

centerline of the floating breakwater reduced the transmitted waves behind the breakwater

more than the conventional setting. This can be seen on figure 2.16 where C, the ratio of the

attenuated wave height to the incoming wave height, is shown (Nakamura et al., 2003).

Figure 2.16: Breakwater Layout Nakamura et al. (2003)

Martinelli et al. (2008a) also investigated the influence of different layouts with wave basin

experiments. They used four different layouts, as presented in figure 2.17.

18


Figure 2.17: Martinelli Layout: I-shapes and J-shape (Martinelli et al., 2008a)

The 0° I-shape and the J-shape showed a similar coefficient of transmission. When increasing

wave obliquities, Ct decreased.

The layout of the floating breakwater will clearly be an important factor. As shown by Naka-

mura et al. (2003) the position of the structure with respect to the incoming waves will influence

the behaviour. The research by Martinelli et al. (2008b) indicates that an L-shaped floating

breakwater does not give better results than an I-shaped structure.

2.3.5 Numerical Studies

Numerical models have been developed, and can be divided into two main approaches. The

first approach that will be discussed here comes from wave theory, and discusses the effect

of the presence of a structure in the waves. The second model simplifies the problem to a

mass-spring dynamic system, for which equations of motion can be derived. Both systems are

explained more in this section.

Linear Potential Theory

A first approach to study the influence of a FB is derived from wave theory. If the fluid is

assumed to be inviscid, incompressible, and irrotational, the fluid velocity can be described

by the velocity potential (Chakrabarti, 1987). This potential can be subdivided into different

contributing components, and has to satisfy the Laplace equation:

∆2Φ = 0 (2.5)

Williams and Abdul-Azm (1997) used this theory to study the response of dual pontoon floating

breakwaters to surge, heave, and pitch motions. They divided the total velocity potential into

incident, scattered, and radiated wave components.

19


Φ = Φi + Φs +3∑

m=1

ηmΦRm (2.6)

where Φl is the component of incident waves, Φs scattered waves, and ηm is the displacement

amplitude in the mth mode of oscillation where 1,2 and 3 stand for the surge, heave, and pitch

motions (Williams and Abdul-Azm, 1997). Furthermore, the velocity potential was simplified

using Boussinesq approximations, and then solved with the appropriate boundary conditions.

Using this model, the effects of several parameters on the performance of the floating break-

water were studied. They are summarized here.

� width: A wider structure leads to a higher Cr, and a lower Ct.

� draught: A deeper draught leads to a more efficient barrier, leading to a higher Cr, and

a lower Ct.

� pontoon spacing: For low frequencies, Ct will be minimal for the smallest spacing. For

high frequencies it will be minimal for large spacing. The reason for this behaviour lies

in the fact that in long waves, and a small spacing, the two pontoons will act as one

continuous barrier, while in short waves, and larger spacing they will act independently,

as if they were two breakwaters in series.

� mooring line stiffness: The location of the resonant peak can be adjusted by varying

the mooring line stiffness. A lower stiffness causes the structure to be more dynamically

sensitive. This leads to sharp maximum and minimum values of Ct over the frequency

range of interest. A mooring system with higher stiffness will cause a more uniform

coefficient of reflection, but only over a narrow frequency range.

� The natural frequency of a dual pontoon floating breakwater will be higher than in the

case of a single pontoon floating breakwater.

Later on Williams et al. (2000) performed a similar numerical study, but this time for two

conventional floating pontoon breakwaters (Williams et al., 2000). They found that transmis-

sion properties strongly depend on the draught, width, and spacing of the pontoons, and the

mooring line stiffness.

Hydrodynamic mass-spring system

A second approach to describe the performance of a FB comes from the maritime point of

view. The interaction between the FB, and the water can be viewed as a mass-spring system,

for which equations of motion can be derived. Hydrodynamic coefficients of the structure can

be determined, which can be substituted in the motion equations of the dynamic mass-spring

system. From these equations wave amplitudes can be determined.

20


Fousert (2006) wrote his thesis on the study of floating breakwaters as a dynamic wave at-

tenuating system (Fousert, 2006). He developed the ReFBreak model (Rectangular Floating

Breakwater Design Model), to determine the dimensions of his floating breakwater. His hy-

drodynamic mass-spring model is shown in figure 2.18.

Figure 2.18: Hydrodynamic mass-spring system (Fousert, 2006)

Describing this two-dimensional linear system by a set of coupled equations of motion for

heave, sway and roll, lead him to expressions for heave, sway, and roll wave amplitudes. He

defined the total amplitude of the wave transmitted to the leeward side of the structure by the

sum of these contributions, plus a contribution due to underflow underneath the structure.

Variables in this model are width, draught, mass, mooring line damping, and stiffness; and

the possibility of placing a rigid screen underneath the structure. With this ReFBreak model

he performed an analysis to determine the importance of each parameter. His final conclusion

was that an optimal design for small wave periods (<10 s) has a large width/draught; while the

design for long wave periods (>10 s) should have a ratio close to one. He also concluded that

a screen is only valuable when small wave periods (<10 s) are considered. Other conclusions

on width, draught, mass, screen, and mooring line stiffness are included in section 2.3.6.

2.3.6 Influence of different parameters

Several parameters play an important role in the behaviour of a floating breakwater. The most

important ones, and their effect on the performance of the structure are summed up here.

Shape of the cross section

� In case of a double pontoon floating breakwater, the influence of increasing the spac-

ing between two pontoon modules only leads to a 5% increase in energy dissipation

(Pena et al., 2011).

21


� The natural frequency of a dual pontoon floating breakwater will be higher than

the natural frequency of a single pontoon floating breakwater (Pena et al., 2011).

Draught

� A deeper draught will require a longer wave to put the structure into vertical oscil-

lation (Fousert, 2006).

� A deeper draught will make a more efficient barrier, causing the coefficient of trans-

mission to decrease (Pianc, 1994).

Width

� A structure with width greater than half a wavelength will be effective (Pianc, 1994).

A structure with variable width, to perform in a larger range of wave periods, is an

option (Fousert, 2006).

� A wider structure leads to a lower Ct (Fousert, 2006).

Mass

� A heavier structure will cause the resonance peak to grow (Fousert, 2006).

Screen

� A screen will cause an increase of sway motion, a decrease of transmission under-

neath the structure, and a decrease of roll motion. As long as the increase of sway

is less than the decrease of underflow, a screen is recommendable (Gesraha, 2006).

� For small wave periods, a larger screen draught will cause a larger range of wave

periods in which the screen has a positive effect on the wave transmission (Fousert,

2006).

Mooring line stiffness

� An increase of stiffness results in a decrease of the sway motion amplitude (Fousert,

2006).

� An initial increase of stiffness results in a decrease of heave motion, but as the

stiffness becomes larger the natural frequency of the system is changed, turning it

into an under-damped hydrodynamic system. This means it will go into resonance

on relatively high frequency waves.

Layout

� An inclined layout is found to be more effective (Nakamura et al., 2003).

22


2.4 Conclusions

The starting point of this thesis will be a simple pontoon shaped FB. This chapter shows that

several parameters, such as width, draught, etc., are important in the design of the FB, and

are thus worth investigating.

The first step in the design process will be a simple preliminary design of the pontoon shaped

FB, using the guidelines by Pianc (1994). After this, the FB will be modeled in MILDwave

to investigate the influence of different layouts. Finally, a motion analysis will be performed,

which will lead to a definitive design proposal.

23

Chapter 3

Hydraulic boundary conditions

3.1 Introduction

This chapter concerns the determination of the hydraulic boundaries, valid in the North Sea.

There are several parameters that will be discussed in this section: wave height and period,

water level, wind speed, and current speed. Three parameters in particular will be important

for the preliminary design of the floating breakwater: water level, wave height, and wave

period. Firstly, water level will influence the anchoring characteristics and the transmission of

waves by the floating breakwater. Secondly, wave heights need to be attenuated sufficiently by

the floating breakwater to create a sheltered environment. Finally, wave periods will determine

the interaction between waves and structure, which is explained in section 2.3.3.

Wind speed and current speed will be of importance in the design of the mooring system and

will be used in the calculation of the forces acting on the FB.

Time series of registered wave heights and directions over a period of 20 years have been

temporary provided by IMDC. This data was acquired from the Hydrometeo service of the

Coastal Division of the Flemish Region. By constructing several JAVA tools, this data was

analyzed using ACES software and afterwards presented graphically in excel. Methodologies

for preparing the sample etc. are explained in this chapter.

The boundary conditions will be determined for two cases:

� Case 1 is the situation where the floating breakwater acts as a sheltered environment, and

a logistic center. This is the case of normal weather circumstances, when maintenance

is ongoing. In this report, 95% workability is intended.

� Case 2 is the situation of storm with a return period of 50 years. This case will be used

for the design of the mooring system and the determination of the solicitations due to

wind, waves, and current.

24

Chapter 3. Hydraulic boundary conditions

3.2 Wave heights

3.2.1 Data processing

Preparation of the sample

The first step in the preparation of the sample is to divide the wave data into a set of directions,

each with a segment of 22,5°. A JAVA tool was constructed to generate 16 output files; one

for each direction. The next step is to distinguish storms from one another in the data. Each

storm is then represented by one characterizing wave height in the analysis. In this thesis,

the peak-over-threshold method is applied, which only takes the peak heights over a certain

threshold value into account. Choosing the threshold value is a delicate process, which is why

the influence of the threshold is also investigated in this section. If the threshold is set too

high, there will not be enough data to perform a meaningful analysis. If it is set too low,

too much data will be part of the analysis which would lead to a distorted picture of the

actual situation. According to Goda (2000), a statistical sample requires independency of the

individual data. Applying this to storm data, it’s important to make a distinction between

independent storms to make sure data of one storm is not used twice or more in the analysis.

A storm has three main characteristics.

1. A storm has wave heights that exceed the threshold value,

2. the time difference between two wave peaks has to be smaller than 48 hours,

3. the difference in height between the lowest peak and the smallest wave height in the

storm has to be smaller than 66% of the smallest wave height.

These demands are shown graphically in figure 3.1. Only when these three demands are all

met at the same time, two wave peaks will be considered part of the same storm. The highest

of those peaks will then be retained for further analysis. Again, a JAVA tool was developed

to sort the data according to the above stated demands. It is noted that the significant wave

heights calculated in this section will represent H1/3.

ACES

The Automated Coastal Engineering System offers the option to perform ’Extremal Significant

Wave Height Analysis’ on a set of storm data. The data files generated by the JAVA tool can

be loaded into ACES automatically. Other input parameters are the observation length (in

years), and confidence interval, which is set to 90% in this case. ACES calculates the significant

wave height according to five different extreme value distributions: the Fisher-Tippett type I

(or Gumbel) distribution, and the Weibull distribution in which k is set as 0,75; 1 (exponential

distribution); 1,4; and 2. The results are then extrapolated for different return periods. For

25


Figure 3.1: Storm demands

each distribution, the coefficient of correlation is also calculated by ACES. In this thesis, wave

heights corresponding to the distribution with the highest correlation are retained. An example

of ACES output is given in appendix B.

3.2.2 Design wave height

The design wave height will vary throughout this master dissertation. Different situations can

be imagined, where different wave heights will be of importance.

The first case concerns situations where ships will moor at the FB. In this report, 95% work-

ability in normal weather conditions is assumed. This means that the design wave height for

the structural design will be the wave height that has a probability of non exceedance of 95%

(H95%).

The second case is the design of the mooring system. Ships will not moor at the FB in storm

conditions, however, this does not mean the FB won’t be present in the wave field. This is

why the mooring system will be designed for a significant wave height with a return period of

50 years.

3.2.3 Results

Normal weather conditions

Table 3.1 summarizes the directional significant wave height with a probability of occurrence

of 95%.

26


Table 3.1: Directional H95%

Direction H95% Direction H95%

N 2,50 m S 1,80 m

NNE 2,00 m SWS 2,50 m

NE 2,00 m SW 2,50 m

ENE 2,00 m WSW 2,50 m

E 1,50 m W 2,50 m

ESE 1,25 m WNW 2,50 m

SE 1,25 m NW 2,70 m

SSE 1,50 m NWN 2,50 m

Detailed cumulative plots of wave heights per direction can be found in appendix C.

Another important factor is the relative number of waves coming from each direction. This

way the orientation of the breakwater can be determined.

Figure 3.2: Wave rose (probablity of non exceedance)

The specific probabilities of occurrence for each direction are presented in table 3.2.

Figure 3.2 shows that most waves will be coming from the segment between SWS and WSW.

However, a relatively large percentage of waves will also be coming from the segment between

WSW and NWN, with relatively large wave heights. The same remark is valid for the segment

between NNE and ENE. These considerations should be taken into account in the study on

27


Table 3.2: Directional probability of occurrence (m)

Direction Probability of occurrence Direction Probability of occurrence

N 3,4% S 8,2%

NNE 6,3% SWS 10,1%

NE 6,3% SW 11,8%

ENE 6,0% WSW 10,9%

E 4,8% W 6,7%

ESE 3,7% WNW 5,2%

SE 3,7% NW 4,3%

SSE 4,7% NWN 3,8%

the layout of the FB. Each wave direction will have a different H95%, which means the FB

demands will be different for each direction of wave attack. This will become more clear in

chapter 7.

It is noted that the preliminary design will assume a FB position perpendicular to the SW

direction. This means that for case 1 boundary conditions, the design wave height is 2,5 m.

Significant wave heights

The significant wave heights calculated by ACES software are summarized in table 3.3 and

represented graphically in figure 3.3.

Table 3.3: Directional significant wave height (m)

Return Period (y) N NNE NE ENE E ESE SE SSE

2 3,7 3,5 3,4 2,9 2,7 2,4 2,5 2,6

5 4,1 3,9 3,7 3,3 3,0 2,9 2,9 2,8

10 4,4 4,1 3,9 3,6 3,2 3,1 3,1 3,0

25 4,8 4,4 4,1 4,0 3,5 3,4 3,4 3,2

50 5,1 4,5 4,3 4,3 3,6 3,6 3,6 3,3

100 5,3 4,7 4,4 4,7 3,7 3,8 3,7 3,4

Return Period (y) S SWS SW WSW W WNW NW NWN

2 3,1 3,7 3,8 3,8 3,5 3,7 3,7 3,7

5 3,5 4,0 4,2 4,1 4,0 4,0 4,1 4,1

10 3,8 4,2 4,4 4,3 4,4 4,2 4,4 4,4

25 4,2 4,4 4,8 4,6 4,8 4,5 4,7 4,8

50 4,6 4,6 5,0 4,8 5,1 4,7 5,0 5,1

100 4,9 4,8 5,3 4,9 5,5 4,9 5,3 5,4

28


Figure 3.3: Directional significant wave height (m)

The influence of the threshold is investigated here for waves coming from the north. It is

found that when the threshold changes from 2 m to 3 m, the significant wave height for a

return period of 2 years increases by 9 cm, which is negligible in view of the uncertainties of

the entire analysis. Figure 3.4 shows the comparison between POT values of 2; 2,5 and 3 m.

Case 2 boundary conditions will be used for the design of the mooring system. Assuming the

structure is oriented perpendicular to the SW direction, this leads to an incoming significant

wave height of 5,0 m, with a return period of 50 y.

3.3 Wave period

The design wave period will be an important parameter. It will become clear in chapter 5

that a higher wave period will lead to a higher wave transmission, causing the need for a wider

structure to provide sufficient wave attenuation. Again, a distinction is made between case 1

and case 2 design conditions.

A table of occurrence has been given by IMDC, and is shown in figure 3.5. This table links

certain significant wave heights to the accompanying wave periods, thus describing what the

probability of a certain wave period is, given a certain significant wave height.

In case 1, a wave height of 2,5 m will be assumed for the structural design, and the wave period

with 95% probability of occurrence will be 9 s. This is a conservative approach since the 95%

probablity of non exceedance is combined with a 95% probablity of occurence of a certain wave

29


Figure 3.4: Influence threshold value - northern direction

Figure 3.5: Table of occurrence

period.

In case 2, the design wave height will be 5,0 m. Since figure 3.5 does not offer information

for this wave height, a different approach for the determination of the design wave period is

needed. To determine the wave periods, IMDC proposes a value of the peak wave period in

function of the significant wave height (IMDC, 2005), valid for extreme conditions.

Tp = 4, 4√Hmo (3.1)

Hmo represents the significant wave height calculated as a function of the wave spectrum. The

significant wave height calculated, however, is H1/3, obtained by analysis in the time domain.

An approximating relation between these two has been determined by Goda (2000), and was

verified for measurements at the Belgian coast.

30


HmO = 1, 06H1/3 (3.2)

From these equations the approximated wave periods can be determined. They are summarized

in table 3.4.

Table 3.4: Summary peak wave periods (IMDC)

Return period (y) N NNE NE ENE E ESE SE SSE

2 8,7 8,5 8,3 7,7 7,5 7,0 7,19 7,3

5 9,2 8,9 8,7 8,2 7,9 7,7 7,7 7,6

10 9,5 9,2 8,9 8,6 8,1 8,0 8,0 7,8

25 9,9 9,4 9,2 9,1 8,4 8,4 8,4 8,0

50 10,2 9,7 9,3 9,4 8,6 8,6 8,6 8,2

100 10,4 9,8 9,5 9,8 8,8 8,8 8,8 8,3

Return period (y) S SWS SW WSW S WNW NW NWN

2 8,0 8,7 8,8 8,8 8,5 8,7 8,7 8,7

5 8,5 9,0 9,3 9,2 9,1 9,1 9,1 9,1

10 8,9 9,2 9,6 9,4 9,5 9,3 9,5 9,5

25 9,3 9,5 9,9 9,7 10,0 9,6 9,9 9,9

50 9,7 9,7 10,2 9,9 10,3 9,8 10,2 10,2

100 10,0 9,9 10,5 10,1 10,6 10,00 10,5 10,5

Case 2 in the design of the floating breakwater will adopt a design wave height of 10 s, which

is the resulting value for the SW direction with a return period of 50 years.

3.4 Water level

The extreme water levels will be of importance when determining the properties of the mooring

system. They are provided by IMDC via the ’Hydraulisch Randvoorwaardenboek’ for the

Flemish coast (IMDC, 2005), and can be seen in figure 3.6.

31

Chapter

3.

Hyd

rau

licbo

un

dary

con

ditio

ns

Figure 3.6: Extreme water levels (IMDC, 2005)

32


Again, return periods of 50 years will be assumed for the design of the FB.

3.5 Wind speed

In the ’Hydraulisch Randvoorwaardenboek’ for the Flemish coast, IMDC developed an extreme

value distribution for wind speeds as a function of the return period. This graph is shown in

figure 3.8. The wind speed will only be used in calculations of the forces acting on the floating

breakwater, which will be performed for case 2 boundary conditions. This means the wind

speed with a return period of 50 years will be used. Figure 3.8 shows that a wind speed of

25 m/s is a good approximation for the mean value of the different directions.

3.6 Current speed

IMDC (2005) does not propose a limiting value for the current speed in offshore design. How-

ever, the ’Management Unit of the North Sea Mathematical Models’, or MUMM, provides real

time information on hydraulic predictions for several stations in the North Sea. Various data

can be accessed, such as wind speeds, water levels, current speeds, etc. A prediction for the

current speed is shown in figure 3.7. Judging by this data, a current speed of 1 m/s can safely

be assumed.

Figure 3.7: Thorntonbank North current forecast MUMM

33

Chapter

3.

Hyd

rau

licbo

un

dary

con

ditio

ns

Figure 3.8: Extreme value distribution for the wind speed (IMDC, 2005)

34


3.7 Conclusions: boundary conditions for general design

Throughout this report, a uniform water depth of 30 m will be assumed. Table 3.5 shows the

results of this chapter for both case 1 and 2. These are the hydraulic boundary conditions

that will be used in the remainder of this report.

Table 3.5: Hydraulic boundaries

Case Hdes Tdes Waterlevel Wind speed Current speed Return period

Case 1 2,5 m 9 s - - - -

Case 2 5,0 m 10 s 6,25 m TAW 25 m/s 1 m/s 50 y

These boundary conditions are somewhat conservative, but will lead to a safe design of the

FB.

35

Chapter 4

Structural boundary conditions

4.1 Design vessel

In the GeoSea Newsflash (2011), a new Offshore Wind Assistance (OWA) support vessel is

presented (see figure 4.1). This vessel will not only be used for crew transfer, but also for

seabed survey, scour monitoring, cable inspection, etc. A few technical details are presented

in table 4.1.

Figure 4.1: OWA support vessel

The preliminary design of the FB will be influenced by the design vessel, especially in length.

It will be assumed that only one OWA vessel will be mooring at the floating breakwater, which

requires a minimum length of 50m.

36

Chapter 4. Structural boundary conditions

Table 4.1: OWA support vessel

Breadth over all 10,04 m

Length over all 25,75 m

Draught 1,75 m

Passenger number 24

Maximum speed 25 kts

4.2 Safe working criteria

4.2.1 Attenuated wave height

The waves need to be attenuated sufficiently to allow the ships to moor safely at the FB.

De Rouck (2011a) included guidelines for the maximum allowable wave height in harbours

as a function of the DWT. From these guidelines it can be concluded that attenuating the

incoming waves to a wave height of 1 m will be a safe approach.

4.2.2 Motions of the FB

To allow safe working conditions on, and in the vicinity of the FB, motion criteria need to be

defined. Any floating structure will have six independent degrees of motion: heave, roll, pitch,

sway, surge, and yaw. The definition of these movements is depicted in figure 4.2.

According to Pianc (1995) only heave, roll, and pitch motions will be of importance in the

design of a FB. This will be explained more in detail in chapter 8. Pianc (1995) also prescribes

guidelines for the maximum allowable motions for various types of ships to assure safe working

conditions. These guidelines are listed in table 4.2.

Table 4.2: Motion Criteria (Pianc, 1995)

Ship Type Cargo Handling Equipment Heave (m) Pitch (°) Roll (°)

Fishing vessels Lift-on-lift-off 0,4 3 3

Freighters, Coasters Ship’s gear 0,6 1 2

Ferries, Ro-Ro Side ramp 0,6 1 2

General cargo - 1,0 2 5

Container vessels 50% effeciency 1,2 2 6

Bulk carriers Cranes 1,0 2 6

These conditions will be investigated more closely in chapter 8.

37

Chapter 4. Structural boundary conditions

Figure 4.2: Six degrees of motion

4.2.3 Overtopping

The overtopping criterium will play an important role in the determination of the freeboard of

the structure. It imposes the need to limit the overtopping rate q, expressed in m3/m/s. The

overtopping manual (Pullen et al., 2007) proposes several limits depending on the use of the

structure. The strictest recommendations are made for the case of human access. A tolerable

limit of 10 l/m/s or 0,01m3/m/s, when trained staff is present, is advised.

4.3 Conclusion

The structural boundary conditions are summarized here.

� The design vessel imposes a minimum FB length of 50 m.

� The waves need to be attenuated to a wave height of 1 m on the lee side of the structure

(De Rouck, 2011a).

� The motions need to be limited according to Pianc (1995) guidelines. The maximum

values for heave, roll and pitch in table 4.2 are 1,0 m; 2 °; and 6 ° respectively.

� The average overtopping discharge needs to be limited to 0,01m3/m/s (Pullen et al.,

2007).

38

Chapter 5

Preliminary Design

5.1 Introduction

In this chapter, preliminary dimensions will be determined for a simple pontoon shaped float-

ing breakwater. This geometry will later on be the starting point for the FB model input in

MILDwave, the motion analysis in Aqua+, and a first approximation of the mooring character-

istics. In view of wave attenuation, only the effects of wave diffraction and wave transmission

will be taken into account.

Height, length, and width of the FB will be determined. Length will mainly be determined

by the necessary number of berths, and the wave diffraction process. Width and draught of

the structure will depend on wave transmission. Freeboard will be defined by the overtopping

criterium.

The preliminary design of the FB falls under case 1 circumstances, as defined in chapter 3.

The design conditions are repeated in table 5.1.

Table 5.1: Hydraulic boundaries: case 1

Hdes Tdes

2,5 m 9 s

In section 5.2 it is explained how the diffraction process will determine the length of the

structure. Section 5.3 concerns the transmission process. It is investigated what the most ap-

plicable design approach will be, by comparing the work of several researchers, using testcases

with circumstances similar to the ones used in this report. In section 5.4 it is demonstrated

how limiting the mean overtopping discharge determines the necessary height of the structure.

Finally, in section 5.5 the dimensions of the preliminary design are set.

39

Chapter 5. Preliminary Design

5.2 Wave diffraction

Wave diffraction is the process in which energy is transferred along a wave crest. It partly

determines the wave climate behind a natural or man-made barrier (Goda, 2000). A graphical

representation of this process is shown in figure 5.1.

Figure 5.1: Diffraction process (US Army, 1984)

The wave diffraction problem is mostly treated for a semi-infite breakwater or a gap between

two breakwater arms. However, in this case, the complementary case of the gap situation

needs to be studied. A method for offshore breakwaters is proposed in the Shore Protection

Manual (US Army, 1984).

CD =√C ′r

2 + C ′l2 + 2C ′lC

′rcos(θ) (5.1)

in which

� CD equals the final coefficient of diffraction

� C ′l equals the coefficient of diffraction for incoming waves at the left tip of the breakwater

� C ′r equals the coefficient of diffraction for incoming waves at the right tip of the break-

water

� θ equals the relative phase angle between the two waves coming around the two ends

In the preliminary design, only incoming waves perpendicular to the structure will be consid-

ered. This means θ will become zero, equation 5.1 is now simplified.

CD =√C ′l

2 + C ′r2 (5.2)

Using this expression, the coefficient of diffraction can be determined from different diagrams

showing the distribution of the ratio of diffracted wave height to incoming wave height. These

40


diffraction diagrams have been prepared for both regular and random waves. Both approaches

will be explained in the following paragraphs.

5.2.1 Regular waves

Diffraction diagrams for regular wave conditions have been prepared by Wiegel (1962) for a

single semi-infinite breakwater. Assumptions made in the development of these diagrams are

listed here.

� Water is an ideal fluid (inviscid and incompressible),

� the waves are of small amplitude, and can be described by linear wave theory,

� the flow is irrotational, and conforms to a potential function which satisfies the Laplace

equation,

� the water depth shoreward of the breakwater is constant.

In the preliminary design, only head waves will be of concern. The Wiegel diagram for this

situation is included in appendix E.1.

5.2.2 Random waves

Goda (2000) states that application of diagrams based on regular waves is not recommended.

He proposes diffraction diagrams based on equations for random waves, where calculations of

wave heights are performed using the directional wave spectrum.

S(f, θ) = S(f)G(θ|f) (5.3)

where

� S(f): the absolute value of the wave energy

� G(θ|f): the directional spreading function

In his work, Goda states that the coefficient of diffraction for random waves is determined by

the following expression.

CD = [1

m0

∞∫0

θmax∫θmin

S(f, θ)K2d(f, θ)dθdf ]

12 (5.4)

where K2d(f, θ) denotes the diffraction coefficient of regular waves with frequency f, and direc-

tion θ, and m0 is the integral of the directional spectrum (Goda, 2000). The calculation of

41


the diagrams proposed by Goda are based on the Bretschneider-Mituyasu spectrum in com-

bination with the Mitsuyasu-type spreading function. The spreading function of Mitsuyasu

is strongly dependent on the parameter s, which represents the degree of directional energy

concentration. The diffraction diagrams for random waves, as proposed by Goda, are devel-

oped for two values of smax: 10 and 75. Goda also proposes simple guidelines to determine

the maximum spreading parameter for a certain case.

� Wind waves: smax = 10,

� swell with short decay distance (with relatively large wave steepness): smax = 25,

� swell with long decay distance (with relatively small wave steepness): smax = 75.

In this case, wind waves will be of importance, and smax will be 10. The diffraction diagram

for irregular, head waves is included in appendix E.1.

5.2.3 General approach

The length of the FB will depend on three factors: the design vessel, the required number of

berths, and the diffraction of the waves. In chapter 4 it was found that the minimum length

to berth one OWA vessel would be 50m. Combining this with the demand of minimum wave

height, the total length of the FB can then be determined. In appendix E it is shown that the

difference in results between the approach using diffraction diagrams for irregular vs. regular

waves is negligibly small, which is why only regular waves will be taken into account for the

preliminary design.

5.3 Wave transmission

The effect of transmission will determine the width and the draught of the structure, and

depends on several properties of the FB, as described in Pianc (1994).

CT = f(d

L,H

L︸︷︷︸Wave

,W

L,h

d︸︷︷︸Geometry

,M

ρWh,

I

MW 2︸︷︷︸Mass

,hG

h,kW

Mg︸︷︷︸Mooring

, θ,W√gd

γ︸︷︷︸V iscosity

) (5.5)

The parameters in this equation are explained in figure 5.2.

As indicated in equation 5.5, the most important parameters are the properties of the incoming

wave, the geometry of the structure, the mass of the structure, the properties of the mooring

system, and the viscosity of the water. Research has been done by Macagno (1953), Jones

(1971), Stoker (1957), and Wagner et al. (2011). Applicable equations for the coefficient of

transmission will be studied in this section to get a clear view of the influencing parameters

42


Figure 5.2: Definition of the parameters in equatino 5.5

on the process of wave transmission. After this, case studies will be performed, comparing

the results of each equation to the results of experimental research done by Tolba (1999),

Koutandos et al. (2005) and Nakamura et al. (2003). These three testcases have been selected

because of the similar hydraulic boundary conditions compared to the ones defined in chapter

3.

5.3.1 Previous research

As said in the previous paragraph, several authors studied the behaviour of floating breakwa-

ters in light of the transmission process. Their resulting approaches are listed below.

Macagno (1953)

As described by Pianc (1994) an analytical model has been proposed by Macagno (1953). It’s

based on a rigid floating body of finite width which is fixed relative to the sea bottom. It’s

noted in Pianc (1994) that this formula is not valid for large relative draught values. In his

calculations, Macagno proposes the following expression for the coefficient of transmission.

CT =1√

1 + [ πWsinh(kd)Lcosh(k(d−D)) ]

2(5.6)

where

� W: width of the floating breakwater

� L: wave length

� k: dimensionless wave number

43


� d: depth of the water

� D: draught of the structure

Jones (1971)

Jones (1971) prepared several graphs to determine the coefficient of transmission depending

on the structure width (W), wave length (L), draught (D) and water depth (d). These are

shown in figures 5.3 to 5.5. His research is based on the theory by Macagno (1953), which

means similar results are expected from these two approaches.

Figure 5.3: Transmission coefficient for rigid, rectangular surface barrier, L/d = 1.25 (Jones, 1971)


Looking at the graphs, it’s clear that the relative draught (D/d) is of great influence for low

values, but around the value of 0,6 there is almost no significant decrease in Ct with increasing

relative draught.

Stoker (1957)

Stoker treated the case of a rigid board, fixed in shallow water at the still water surface, using

linear wave theory (Tolba, 1999). He also assumed that no energy was lost due to dissipation,

which means the following equation is valid.

44



√C2t + C2

r = 1 (5.7)

He found following analytical expressions for Ct and Cr.

Ct =1√

1 + (πWL )2(5.8)

Cr =πWL√

1 + (πWL )2(5.9)

In his research, Stoker also mentions that the above described equations are not to be used

without caution for deep and transitional water conditions. Higher order theories should be

applied for small values of h/L, especially when (W/2)/L has a value smaller than 1.

Wagner et al. (2011)

The last method discussed in this section to determine Ct is provided by Wagner et al. (2011).

Based on deep water conditions, equation 5.10 is proposed. Furthermore, Wagner assumes a

value for Cr defined by equation 5.7.


2π2(W + d tanh(3, 5Dd )) cosh(kd)(5.10)

Conclusion

A comparison between the aforementioned equations for the approximation of Ct is shown in

figure 5.6.

The lowest coefficients of transmission are found when using the formula proposed by Wagner,

while the highest results are obtained by using Macagno (1953). To know which method is

45


Figure 5.6: Comparison equation 5.6, 5.8, 5.10. T = 9 s, h = 12 m, d = 30 m

more close to the reality of this particular case study, the following section of this report will

concern case studies on experiments by Tolba (1999), Koutandos et al. (2005) and Nakamura

et al. (2003).

5.3.2 Verification of the proposed methods

To verify the correctness of the previous listed methods, a couple of test cases, based on

existing research, will be discussed.

Testcase 1: Tolba (1999)

In his research, Tolba (1999) investigated the influence of different variables on Ct for restrained

floating breakwaters, floating breakwaters allowing limited roll motions, and heave floating

breakwaters (which only allow heave motion). He found that allowing limited roll movements

(up to a maximum of 6°) has little to no effect on the amount of transmitted energy. Also,

Cr and Ct in case of the heave FB are always smaller than the values obtained for the fixed

FB. His explanation for this behaviour lies in the fact that the heave FB will need energy to

induce the heave motion, thus leading to extra loss of energy.

The results of Tolba are presented in graphs, one of which is shown in figure 5.7.

The conditions under which this graph can be used, combined with a couple of basic assump-

46


Figure 5.7: Tolba (1999). Restrained body. D/d = 1/6, Hi/L = 0,014-0,048, B/d = 1/2

tions about the wave climate leads to input parameters, are shown in table 5.2.

Table 5.2: Dimensions experiments Tolba (1999)

Width (W) 25 m

Draught (D) 8,3 m

Wave period (T) 7 s

Incoming wave height (Hi) 3,67 m

Water depth (d) 50 m

Since W/L equals 0,33 it can be seen from figure 5.7 that the value for Ct should lie around

0,21. Table 5.3 shows the analytical results for every equation.

Table 5.3: Analytical results testcase Tolba

Equation Ct

Macagno (1953) 0,44

Jones (1971) 0,49

Stoker (1957) 0,70

Wagner et al. (2011) 0,24

In this case study, it’s clear that the Wagner method will deliver the most accurate results.

It’s also clear that the equation by Stoker delivers much different results than the experiments.

This was expected, since the case study here takes place in transitional waters, whereas Stoker

47


developed theories for shallow waters. The methods by Macagno and Jones are much alike, as

expected. They overestimate the transmission with a factor two. Further research is needed

to make valid conclusions.

Testcase 2: Koutandos et al. (2005)

Experiments were conducted by Koutandos et al. (2005) in the CIEM flume of the Catalonia

University of Technology, Barcelona. In particular, a single fixed FB was investigated. The

dimensions used in the experiment are listed below.

Table 5.4: Dimensions experiments Koutandos et al. (2005)

Width (W) 2 m

Length (l) 2,8 m

Draught (dr) 0,4 m

Wave period (T) 2,04 s


Water depth (d) 2 m

The results of their experiments are summarized in the following graph (where B stands for

the width (W) in this case).

Figure 5.8: Koutandos et al. (2005) Ct

In the case of table 5.4, B/L equals 0,32 and dr/d equals 1/5. The resulting Ct for a single

fixed FB in regular waves, is 0,39. When using these dimensions and hydraulic boundaries in

the different equations, the results summarized in table 5.5 are obtained.

Wagner will provide the best results, while Stoker overestimates the amount of transmitted

energy. Tranmission for Macagno and Jones is also a little high, but more acceptable in

48


Table 5.5: Analytical results testcase Koutandos et al. (2005)

Equation Ct

Macagno (1953) 0,57

Jones (1971) 0,55

Stoker (1957) 0,71


comparison to Stoker. It’s becoming clear that this last method will not be applicable here.

A last test is performed.

Testcase 3: Nakamura et al. (2003)

In their research, Nakamura et al. (2003) study the effect of the layout of a series of FB on Ct.

To do this, they first determine the general characteristics of one FB by means of experiments

in a two-dimensional wave tank at Nagoya University. The following dimensions were tested.

Table 5.6: Dimensions experiments Koutandos et al. (2005)

Width (W) 0,304 m

Draught (dr) 0,136 m



Water depth (d) 0,95 m

This means that B/L equals 0,32. According to Nakamura et al. (2003) the obtained Ct has a

value of 0,16. The results of equations 5.6, 5.8, and 5.10, and the graphs by Jones (1971) are

listed below.

Table 5.7: Analytical results testcase Nakamura et al. (2003)

Equation Ct

Macagno (1953) 0,38

Jones (1971) 0,37

Stoker (1957) 0,71


For the third time, Wagner et al. (2011) provides the best results.

49


Conclusion

The fact that the equations proposed by Stoker (1957) persistently overestimate the effect of

transmission was to be expected. Stoker indicated in his work that these equations can not

be used in non shallow water conditions. This report clearly ranges in the transitional area,

which makes the Stoker equations inapplicable here. The approaches according to Macagno

(1953) and Jones (1971) provide similar results, but overestimate the transmission. The three

case studies show that Wagner et al. (2011) provide the best approach in these conditions.

The preliminary design will be based on equation 5.10, as far as transmission is concerned.

5.4 Overtopping

The height of the structure will mainly be determined by the overtopping of the waves, which

can be expressed as q (m3/m/s), the average discharge per unit length of the structure.

Overtopping equations for caisson breakwaters have been developed by Franco and Franco

(1999), and will be used here to approximate q.

Q = exp (−3.0hc

Hmoγsγβ) (5.11)

where hc equals the freeboard, Hmo the significant wave height as defined in chapter 3, γβ

an angular coefficient equal to unity for long crested perpendicular incoming waves and γs a

coefficient of porosity equal to unity for a plain impermeable wall. Furthermore, Q equals the

dimensionless discharge defined by

Q =q√gHmo

(5.12)

where q equals the average discharge per unit length of the structure, which of course needs

to be limited.

The limit in this case depends on the activities on, and behind, the structure. The overtopping

manual (Pullen et al., 2007) proposes several limits depending on the use of the structure.

The most strict recommendations are made for the case of human access. A tolerable limit of

10 l/m/s or 0,01m3/m/s, when trained staff is present, is advised.

5.5 Conclusion

The preliminary design will be the result of the boundary conditions shown in table 5.8.

Combining the effects of transmission and diffraction is somewhat ambiguous. Research on

this topic has been done by Garceau (1997). It was found that superposition of both effects

50


Table 5.8: Boundary conditions preliminary design

Hi 2,5 m

T 9 s

d 30 m

H’ 1,0 m

Design vessel 1 OWA vessel

minimum length around 50 m

usually overestimates the attenuation coefficient C which is defined as the ratio of the result-

ing wave height to the incoming wave height. This is especially the case when dealing with

long wave lengths. In light of these results, it’s opted to view transmission and diffraction

independently in the preliminary design. The FB length will be optimized in chapter 7, using

MILDwave software. Waves of 2,5 m need to be attenuated to 1 m, meaning the coefficient of

diffraction and the coefficient of transmission both have a maximum value of 0,4.

The transmission process will determine the width of the FB. As said before, Ct needs to

be limited to 0,4. Equation 5.10 for a draught of 8 m and a width of 40 m leads to a Ct of

0,36. Of course, other combinations of width/draught are possible. In case of equation 5.10,

the required breakwater width increases quasi linearly with decreasing draught, and no real

optimum can be found here. However, nowadays supertankers, post-panamax ships, etc. with

beam larger than 40 m are quite common. If the width of the FB is set to 40m, which could

be the beam for a large oil tanker, the draught of 8 m follows from equation 5.10.

The length of the floating breakwater will be determined by the length of the design vessel

on the one hand, but also by the diffraction process. The design vessel imposes a minimum

length of around 50 m, as mentioned in table 5.8. Following the approach explained in section

5.2 for offshore breakwaters, leads to a maximum Cd value of 0,28. Using Wiegel diagrams

for regular waves results in a minimum length on both sides of 0,75 times the incoming wave

length, which in this case equals 0,75 x 116,82 m or 87,61 m. This results in a total breakwater

length of 87,61 m + 50 m + 87,61 m or 225 m, rounded off.

The total height of the structure will be determined by the overtopping criterium as described

in section 5.4. A freeboard Rc of 4 m leads to an average discharge of 0,01 m3/m/s.

Combining all these conditions results in the following dimensions for the preliminary design.

These dimensions are shown in figure 5.9.

51


Table 5.9: Dimensions preliminary design

W (width) 40 m

l (length) 225 m

D (draught) 8 m

Rc (freeboard) 4 m

Figure 5.9: Sketch of the preliminary design

52

Chapter 6

MILDwave Model

6.1 Introduction to MILDwave

MILDwave is a wave propagation model developed within the research unit Coastal Engineer-

ing of the Department of Civil Engineering at Ghent University, under the supervision of prof.

dr. ir. Peter Troch (Troch et al., 2011). It’s based on the depth-integrated mild-slope equa-

tions of Radder and Dingemans (1985). For more information about the underlying theories

and equations in MILDwave, reference is made to Troch et al. (2011).

MILDwave consists of two executables: a preprocessor and a postprocessor. Using the pre-

processor, which is presented in figure 6.1, several parameters can be adjusted. The first tab

in the preprocessor concerns the grid dimensions. The wave field is divided into cells, and a

length dimension in both x and y direction can be assigned to those cells. The size of these

grid cells will determine the accuracy of the calculation, as well as the time needed to perform

it. In this tab it’s also possible to implement sponge layers that will absorb the wave energy,

reducing boundary effects in the calculations of the wave field.

The second tab concerns the wave itself. Parameters such as wave height, wave period, regular

or irregular waves, and wave direction can be adjusted here.

The tab bathymetry makes it possible to input any kind of bathymetry the user wants to

apply. Since a constant water depth will be assumed in this work, this option will not be used.

The cell type tab will be of great importance here. This makes it possible to model any ob-

ject in the wave field by the simple input of a bitmap figure. Assigning different absorption

coefficients to different colours in this bitmap drawing, makes it possible to influence the inter-

action of waves and object. Section 6.2 concerns the study on how to model floating objects

in MILDwave by adjusting these absorption coefficients.

The input files can then be imported in the calculator, as presented in figure 6.2. This calcu-

lator then produces several output files, the most important one being the VARdata file. This

file contains the values of the ratio of resulting wave height to incoming wave height, or in

other words the value of the coefficient of attenuation (C). Using a script in Matlab this file

53

Chapter 6. MILDwave Model

Figure 6.1: Preprocessor MILDwave

is analyzed, resulting in a contour plot of these C values, rendering a more detailed insight in

the effect of the modeled object on the wave field.

Figure 6.2: Calculator MILDwave

54


6.2 Modeling floating objects in MILDwave

6.2.1 Previous research

To model an object in the wave field, the cells are assigned a certain absorption coefficient (S).

This coefficient ranges from zero to one, zero meaning the cell consists out of water and one

meaning the cell is fully reflective and does not absorb any energy. The difficulty here is that

MILDwave does not offer a specific input possibility for floating objects. Beels (2010) studied

the layout of a farm of floating wave energy converters (WEC) using MILDwave. Comparing

the results of physical tests to a model in MILDwave, she found that a WEC is best modeled

by assigning a linearly varying absorption coefficient over the length of the WEC, ranging

from 0,9 to 0,99. To study if this approach is also applicable in the case of a FB, the same

three testcases that were studied in section 5.3.2 are reviewed here as well. They will each be

modeled in different ways, and comparing the results will point out the best way to model a

FB.

Two main approaches of modeling the FB in MILDwave will be tested in this section. The

first approach will be to model the FB as a homogeneous object with a constant absorption

coefficient. The input for this model will be a simple unicolour rectangle, to which a certain

absorption coefficient will be assigned. An example of the input .bmp file is shown in figure 6.3.

Figure 6.3: Homogeneous model

The second approach will be a model with an absorption coefficient varying linearly over the

width of the FB.. An input model of this heterogeneous approach is presented in figure 6.4.

Each layer is assigned a different S ranging from 0,90 to 0,99; the lowest value is assigned to

the side of the incoming waves.

It’s noted that the FB in the three testcases will be modeled long enough to exclude effects

of diffraction as much as possible. This way only the coefficient of transmission is obtained,

which is the value provided by the experimental results in the concerning studies. Sponge

layers will be implemented on the lower and upper side of the wave field. Along the sides

of the wave field no sponge layers will be modeled, since this may result in situations where

too much energy is absorbed sideways by these layers. By comparing the results of the three

55


Figure 6.4: Non homogeneous model

testcases, it will be made clear what the best approach of modeling a FB in MILDwave will

be.

6.2.2 Testcase 1: Tolba (1999)

First of all, for more background information on the study performed by Tolba (1999), the

reader is referred to section 5.3.2. A short overview of the properties of the model is shown in

table 5.2. An example of output generated by analysis in Matlab is presented in figure 6.5.

Figure 6.5: Contour plot MILDwave model, Tolba testcase, model with heterogeneous S

The leeward side of the FB is located at the topside. Figure 6.5 shows a Kd value around 0,14

which is very close to the experimental result found by Tolba (0,15).

Output files of all models are included in appendix F. A general overview of the results of the

Tolba testcase are presented in figure 6.6, where the ’value’ on the abscissa stands for

the results of the heterogeneous model.

56


Figure 6.6: Results MILDwave model, Tolba testcase

These results show that two models will provide the correct value for Ct. The model with

varying S, and the model with a constant S of 0,96. Other cases need to be reviewed before

making any conclusions about the correct model.

6.2.3 Testcase 2: Koutandos et al. (2005)

For more background information on the study performed by Koutandos et al. (2005), the

reader is referred to section 5.3.2. A short overview of the properties of the model is shown in

table 5.4. The output files of this case can also be found in appendix F. A general overview of

the results of the Koutandos testcase are presented in figure 6.7.

Figure 6.7 shows a good approximation for Ct when the FB is modeled homogeneously with

S equal to 0,97. The heterogeneous model underestimates the transmission with a Ct value of

0,20 instead of the expected 0,25.

6.2.4 Testcase 3: Nakamura et al. (2003)

For more background information on the study performed by Nakamura et al. (2003), the

reader is referred to section 5.3.2. A short overview of the properties of the model are sum-

marised in table 5.6. The output files of this case can also be found in appendix F. A general

overview of the results of the Nakamura et al. (2003) testcase are presented in figure 6.8.

57


Figure 6.7: Results MILDwave model, Koutandos testcase

Figure 6.8: Results MILDwave model, Nakamura testcase

These results show that there is an excellent agreement between the heterogeneous model

and the experimental results. Contrary to the Tolba testcase, a homogeneous model with

58


constant S equal to 0,96 is not a good approach for this case study. The best homogeneneous

approximation is found for the model where S equals 0,95.

6.2.5 Conclusion

For every testcase, a good approximation of the expected Ct values can be made by homo-

geneous modeling of the FB. However, the value of the absorption coefficient that provides

the most reliable results, is different for every testcase. The heterogeneous model results in

two very good approximations, and one underestimation of the amount of transmitted energy.

Taking these remarks into account, the heterogeneous approach will be used to model the FB.

Knowing this, the preliminary design can now be modeled in MILDwave, which should provide

a C value of around 0,4. Chapter 7 concerns the modeling of the preliminary design as well

as the optimisation of breakwater length and layout.

59

Chapter 7

Optimizing the preliminary design

The preliminary design consists out of a simple pontoon-shaped structure of width 40 m,

draught 8 m, and length 225 m. The object of this chapter is to model this design in MILD-

wave, and study the effect of different breakwater layouts. In chapter 6, the heterogeneous

model proved to provide good results in MILDwave, which is why this approach will be used

throughout this chapter as well.

7.1 Modeling the preliminary design

The first step in this process is to model the preliminary design in MILDwave. Looking at

figure 3.2, it becomes clear that most waves will come from the SW direction (11,8 %). This

leads to a FB orientation that is perpendicular to this direction. The design wave height for

this case equals 2,5 m. If it is expected that the waves on the leeward side of the breakwater

should be no higher than 1 m, the overall attenuation coeffient, C, should have a maximum

value of 0,4. The properties of the preliminary design are summarized again in table 7.1.


W (width) 40 m

l (length) 225 m

D (draught) 8 m

Rc (freeboard) 4 m

Modeling this preliminary design in MILDwave leads to an input drawing as pictured in figure

7.1. On the right side of the drawing the applied coefficients of absorption are clearified.

The structure will be modeled in a domain of 3000 m x 3000 m, making sure unwanted effects of

reflection on the side of the wave field etc. do not influence on the results. Furthermore, a wave

height of 2,5 m; a wave period of 9 s; and a water depth of 30 m will be applied. Simulations

will each run for 500 s with a time interval of 0,07 s.

60

Chapter 7. Optimizing the preliminary design

Figure 7.1: Input MILDwave preliminary design

The resulting contour plot is presented in figure 7.2.

Figure 7.2: MILDwave: contour plot of the preliminary design

The attenuation coefficient on the leeward side of the structure lies between 0,3 and 0,4. Since

the preliminary design was based on a maximum C of 0,4; it’s clear that the model will suffice.

The length of the floating breakwater was determined using diffraction diagrams for regular

waves, and the approximate gap-method for the design of offshore breakwaters as described

in the Shore Protection Manual (US Army, 1984). Since both of these methods have certain

inital assumptions, the combination of both obviously leads to an approximate length. Figure

7.2 indicated that there is still room to reduce the FB length. Breakwater lengths of 200 m,

150 m, and 100 m were studied in MILDwave. The results are summarized in table E.1.

The breakwater length can be reduced to 150 m. Detailed contour plots of the above mentioned

simulations are included in appendix G.

61


Table 7.2: Influence of the floating breakwater length

Length C

100 m 0,50

150 m 0,35

200 m 0,30

7.2 Study on the FB layout

In chapter 3, the probability of occurrence and design wave heights for each direction were de-

termined. These H95% values lead to the maximum value of C per direction. This information,

along with the probability of occurrence for each direction, is summarized in table 7.3.

Table 7.3: H95% per direction

Direction occ H95% Cmax Direction occ H95%

N 3,4 % 2,50 m 0,40 S 8,2 % 1,80 m 0,56

NNE 6,3 % 2,00 m 0,50 SWS 10,1 % 2,50 m 0,40

NE 6,3 % 2,00 m 0,50 SW 11,8 % 2,50 m 0,40

ENE 6,0 % 2,00 m 0,50 WSW 10,9 % 2,50 m 0,40

E 4,8 % 1,50 m 0,68 W 6,7 % 2,50 m 0,40

ESE 3,7 % 1,25 m 0,80 WNW 5,2 % 2,50 m 0,40

SE 3,7 % 1,25 m 0,80 NW 4,3 % 2,70 m 0,37

SSE 4,7 % 1,50 m 0,68 NWN 3,8 % 2,50 m 0,40

From table 7.3 it can be seen that most waves will be coming from the segment SWS-WSW,

and that they also have relatively large wave heights. A first approach will be to orient the FB

perpendicular to the SW, therefore blocking this segment. However, large wave heights will

also be coming from the segment W-NWN. For this reason an L shaped FB will be investigated.

Finally, it is seen from table 7.3 that the segment NNE-ENE also provides a relatively large

percentage of waves, with relatively large wave heights. Because of this, the last breakwater

layout that will be investigated is a U shape. Waves coming from E to SSE have a small wave

height, which indicates attenuation might not be necessary. However, if they collide with the

structure, they are reflected. This may cause a resulting wave height that is higher than the

incoming wave height. Which is also something that will be studied in this section.

There are two ways to model oblique incident waves in MILDwave. This first one is to im-

plement a certain angle of incidence. This approach will not be used here, since this causes

unwanted boundary effects. The second method, which will be applied here, is to draw the

FB itself oblique, while maintaining the original angle of incidence in MILDwave. In light

62


of this it’s important to keep in mind that the heterogeneous method of modeling the FB as

defined in chapter 6 requires an absorption coefficient that increases in the direction of the

wave propagation. It has to be mentioned that the MILDwave results will not coincide with

reality, as this software was not developed to model floating objects. The model is used here

to quantify effects of oblique incident waves, and changes to the layout of the structure. But

when it comes to studying the actual wave attenuation, wave basin experiments are advised

to verify the MILDwave model.

7.2.1 Beam shaped layout

Considering the symmetry of the structure, only SW, WSW, W, WNW, and N directions

were modeled here. Contour plots of the beam shaped simulations can be found in appendix

G section G.2. These results are summarized in table 7.4, and presented graphically in figure

7.3.

Table 7.4: Influence of different wave incidence angles for the beam shaped FB

Direction CMILDwave(m) Cmax Direction CMILDwave(m) Cmax

N 1,30 0,40 S 0,40 0,56

NNE 1,20 0,50 SWS 0,40 0,40

NE 1,20 0,50 SW 0,35 0,40

ENE 1,20 0,50 WSW 0,40 0,40

E 1,30 0,68 W 0,40 0,40

ESE 1,20 0,80 WNW 0,45 0,40

SE 0,90 0,80 NW 0,90 0,37

SSE 0,45 0,68 NWN 1,20 0,40

The gray area in figure 7.3 represents the attenuation capacity of the FB for waves coming from

the individual directions. The dashed line stands for the maximum value of C per direction.

As long as the gray hatched area lies under the dashed line, the attenuation capacity of the

FB will suffice. Wave attenuation will suffice for the SSE-W segment. However, waves coming

from the directions from NWN to SE will not be attenuated sufficiently. Waves coming from

the NWN to the ESE will even be amplified, due to reflection. This phenomenon of reflection

is shown for incoming waves from the NE on figure 7.4.

On this figure it can be seen that the resulting wave height on the NE side of the structure is

higher than the incoming wave height. This means the incoming wave heights of 2,00 m in the

NE case, will be amplified to 2,4 m. Waves coming from the ESE direction have a design wave

height of 1,25 m, which is very close to the intended resulting wave height of 1 m. However,

due to the reflection effect, these wave heights are amplified to 1,5 m. It’s obvious that this

reflection needs to be reduced as much as possible, for example by wave absorbing structures.

63


Figure 7.3: Results for the beam shaped floating breakwater. —: CMILDwave, - - -: Cmax

Figure 7.4: Reflection in the case of the beam shaped FB

64


7.2.2 L shaped layout

The previous section showed that a beam shaped FB will not suffice for the directions WNW

to SE. Since large wave heights are coming from the WNW-NE segment, it seems logical to

construct an L-shaped FB. It was found that the minimum length for sufficient attenuation

in the case of perpendicular wave incidence is 150 m. The starting point in this section is

an L-shaped structure, where both legs have a length of 150 m, which will be referred to as

L/150/150. After this, an asymmetrical L-shape will be simulated where one leg is 150 m,

and the other one 100 m. The reason the shortest leg will measure 100 m is because of the

free space that is required to berth the design vessel. Subtracting the width of the FB, 40 m,

from this length, leaves a length 60 m to moor the vessel. This configuration will be referred

to as L/150/100. The final L configuration will consist out of two equally long legs of 100 m,

referred to as L/100/100.

L/150/150

This section covers the results of a symmetrical L-shaped layout, with both legs measuring

150 m in length. Detailed results are presented in table 7.5. The configuration, and the re-

sulting C values are presented in figure 7.5. Contour plots resulting from the MILDwave

simulations are included in appendix G.3.

Table 7.5: Inlfuence of different wave incident angles for the symmetric L shaped FB 150x150

Direction C Cmax Direction C Cmax

N 0,40 0,40 S 0,40 0,56

NNE 0,50 0,50 SWS 0,30 0,40

NE 1,30 0,50 SW 0,25 0,40

ENE 1,50 0,50 WSW 0,15 0,40

E 1,70 0,68 W 0,15 0,40

ESE 1,50 0,80 WNW 0,15 0,40

SE 1,30 0,80 NW 0,25 0,37

SSE 0,50 0,68 NWN 0,30 0,40

This layout was designed for waves coming from the SE direction to the NE direction. From

figure 7.5 it can be seen that this configuration will suffice for waves coming from the segment

SSE-NNE. Waves coming from the directions NE and SE, however, will not be attenuated

enough. They will even be amplified due to the reflection process, with a C value of 1,30.

65


Figure 7.5: Results for L/150/150. —: CMILDwave, - - -: Cmax

This is the case for all directions from NE to SE. Comparing the resulting wave heights after

reflection in the case of the beam shaped FB and the L/150/150 layout shows that the reflection

will be higher in the latter case. This is because the waves will reflect on both legs.

L/150/100

This section covers the results of an asymmetrical L-shaped layout, with one leg measuring

150 m in length, and the other one 100 m. The results are summarized in table 7.6. This

configuration, and the MILDwave results, are presented in figure 7.6. Contour plots resulting

from the MILDwave simulations are included in appendix G.4.

Figure 7.6 shows an increase in the attenuation coefficient, C, for the W to NE directions. The

comparison between the different L-shapes can be found in section 7.2.2. This configuration no

longer suffices for waves coming from the N direction, contrary to the L/150/150 layout. The

study of a U-shaped FB is imposed. The value of C is significantly lower than the maximum

value for the directions SSE to W. This means the leg length of 150 m may be reduced as well.

In the next section, a symmetrical L shape with both legs measuring 100 m is studied.

Comparing the situations for L/150/150 and L/150/100 for waves attacking on the leeward

side of the structure, shows that the reflection will be higher in the case of L/150/150. This

66


Table 7.6: Inlfuence of different wave incident angles for the asymmetric L shaped FB


N 0,50 0,40 S 0,40 0,56

NNE 1,00 0,50 SWS 0,30 0,40

NE 1,30 0,50 SW 0,25 0,40

ENE 1,30 0,50 WSW 0,15 0,40

E 1,40 0,68 W 0,20 0,40

ESE 1,50 0,80 WNW 0,30 0,40

SE 1,00 0,80 NW 0,35 0,37

SSE 0,50 0,68 NWN 0,35 0,40


shows that the reflection will decrease if the length of the legs decreases. This will be verified

by simulating the L/100/100 layout.

67


L/100/100

This section covers the results of a symmetrical L-shaped layout, with both legs measur-

ing 100 m in length. The results are summarized in table 7.7. This configuration, and the

MILDwave results, are presented in figure 7.7. Contour plots resulting from the MILDwave

simulations are included in G.5.

Table 7.7: Inlfuence of different wave incident angles for the symmetric shaped FB 100x100


N 0,45 0,40 S 0,45 0,56

NNE 0,60 0,50 SWS 0,35 0,40

NE 1,20 0,50 SW 0,35 0,40

ENE 1,40 0,50 WSW 0,20 0,40

E 1,50 0,68 W 0,20 0,40

ESE 1,40 0,80 WNW 0,20 0,40

SE 1,20 0,80 NW 0,35 0,37

SSE 0,60 0,68 NWN 0,35 0,40

These results indicate a better approximation of the maximum C values than the L/150/150,

and the L/150/100 shapes. A remaining problem is the fact that the attenuation is not suf-

ficient for waves coming from the N to E directions. As said before, this will be handled in

section 7.2.3 by modeling a U-shaped FB.

Figure 7.7 also shows that the reflection has decreased significantly compared to the L/150/150

configuration. A detailed comparison between L/150/150, L/150/100, and L/100/100 is dis-

cussed in the next section.

Conclusion L-shaped layout

Figure 7.8 shows the attenuation capacity of the three studied L-shaped, together with the

maximum value for C.

This figure shows that the attenuation capacity for the directions SSE to NE will be largest

in the case of L/150/150. However, the reflection will be higher for this case as well. Starting

from the NE direction, to the SE direction, the value of C will be lower for L/100/100 than

for L/150/150, rendering this last configuration less interesting when waves are attacking the

leeward side of the structure.

Another interesting remark here is the fact that in the case of an asymetrical configuration,

the NNE direction will also be a reflecting direction. Which is not the case for L/150/150 and

L/100/100. This effect is shown in figure 7.9.

68



Generally all L-shaped configurations suffice for the third and fourth quadrants on the wind

rose. The difference in behaviour lies mainly in the first and second quadrants. Here, the

L/100/100 layout is found to be the most satisfying, since this configuration offers the least

problems with reflection. However, reflection problems are still present, and research on how

to decrease this problem is recommended.

7.2.3 U-shaped layout

The last layout that will be studied is a U-shaped FB. The parallel legs each measure 100 m in

length, while the connecting leg measures 155 m. This last dimension has been chosen to allow

sufficient spacing between both parallel legs. The dimensions for this layout are indicated in

figure 7.10. Detailed results are presented in table 7.8, and shown graphically on figure 7.10.

Contour plots resulting from the MILDwave simulations are included in appendix G.6.

This layout is found to be effective for waves coming from the SWS-NE direction. However,

comparing this layout to the L/100/100 shape shows that the U-shaped FB is sufficient and

insufficient in different areas than the L/100/100 layout. This can be seen in figure 7.11. Waves

coming from the SWS now cause problems, where in the case of L/100/100 these waves were

69


Figure 7.8: Comparison L/150/150, L/150/100, and L/100/100

Figure 7.9: Comparison L/150/150, L/150/100, and L/100/100 for the NNE direction

attenuated sufficiently. This is because these waves reflect inside the U structure, increasing

the resulting wave height inside the structure.

70


Table 7.8: Inlfuence of different wave incident angles for the U shaped FB


N 0,15 0,40 S 1,00 0,56

NNE 0,20 0,50 SWS 0,50 0,40

NE 0,35 0,50 SW 0,35 0,40

ENE 0,50 0,50 WSW 0,20 0,40

E 1,00 0,68 W 0,15 0,40

ESE 1,10 0,80 WNW 0,15 0,40

SE 1,30 0,80 NW 0,10 0,37

SSE 1,10 0,68 NWN 0,15 0,40

Figure 7.10: Results for the U shaped FB. —: CMILDwave, - - -: Cmax

Figure 7.11 and figure 7.10 show that the only directions experiencing a value of C that is

larger than one, are the ESE, SE, and SSE directions. The C values in these cases are 1,10;

1,30; and 1,10 respectively. This results in wave heights inside of the structure of 1,4 m; 1,6 m;

and 1,6 m. The L/100/100 shape, however, has C values larger than one for the NE, ENE,

E, ESE, and SE directions. The incoming wave heights for the NE and ENE directions in

71


Figure 7.11: Comparison between L/100/100 and the U-shaped FB layout

particular, are larger than those coming from the second quadrant on the wind rose. The

largest wave height in this range is found for the NE/ENE directions and is 2,0 m. In case of

the L/100/100 layout and the NE direction, this wave height is amplified 1,5 times; resulting in

a wave height of 3 m. It’s clear that the range over which waves are amplified in the case of the

U-shaped FB, is less harmful than the range of amplification in the L/100/100 configuration.

On top of this, the amplification due to reflection in case of the U-shaped FB is only noticeable

at the entrance of the FB. The C-value indicated in table 7.8 is the mean value inside the U-

shape. A detailed coloured plot of the wave basin is shown in figure 7.12.

The climate inside the U-shape will have a C-value that lies around 1, while the C-value at the

entrance can go as high as 1,5. The problem of amplified wave heights is thus mostly present

at the entrance of the U-shaped FB.

7.3 Conclusions

In this chapter, the preliminary design was modeled in MILDwave. This lead to an optimiza-

tion of the breakwater length, reducing it from 225 m to 150 m. After this, several FB layouts

were studied: a beam shape, L-shapes, and a U-shape. This was done for different wave inci-

dence angles.

The beam shaped structure was oriented perpendicular to the SW direction, where most waves

72


Figure 7.12: Reflection in the case of the U shaped FB, direction SE

are coming from. The results in MILDwave showed that this configuration would suffice for

waves coming from the SSE-WNW segment. In this layout, problems with reflecting waves

when waves are attacking the leeward side of the structure, are present.

Since relatively high waves are coming from the fourth quadrant of the wind rose as well,

an L-shape was modeled. Three types of L structures were studied: L/150/150, L/150/100

and L/100/100. A symmetrical L-shape with both legs measuring 150 m proved to attenuate

waves for the segment SSE-N sufficiently. It was also seen that the attenuation coefficient

for the SW-N segment was often in the order of half the maximum value. This is why the

second layout studied here was an asymmetrical L shape of which the leg perpendicular to

the NW direction measured 100 m. This layout was found to suffice for the same directions

as the L/150/150, except for waves coming from the north. It was noticed that for the direc-

tions SSE-W, the value of C was significantly lower than the maximum value. This lead to

a symmetrical L-shape, with both legs measuring 100 m. In this case, the FB was found to

be efficient for waves coming from the SSE-NWN segment. However, waves coming from the

N, NNE and NE were not attenuated enough. Since waves coming from these directions have

relatively large values for H95%, a U shape was the subject of the next simulations. In light

of reflecting waves, it was found that an asymtrical configuration has a negative influence for

the NNE direction, which was indicated in figure 7.8 and 7.9. This is because less waves are

retained by the leg perpendicular to the NW direction. It was also concluded that a shorter leg

73


length would decrease the amount of reflected energy. Generally, all L-shaped configurations

suffice for the third and fourth quadrants on the wind rose. The difference in behaviour lies

mainly in the first and second quadrants. Here, the L/100/100 layout is found to be most

satisfying, since this configuration offers the least problems with reflection. However, reflection

problems are still there, and research on how to decrease this phenomenon is recommended.

The final design was a U shaped FB of which the parallel legs measured 100 m, and the long

side 155 m. This structure provided sufficient wave attenuation for waves coming from the SW

to the NE. However, for waves coming from the south, the wave attenuation was significantly

lower than in the case of an L shaped FB. This is because the waves are reflected inside the U

shape, amplifying the waves inside. For the directions SSE, SE, and ESE the resulting wave

heights are even larger than the incoming wave heights. A comparison between this U-shape

and L/100/100 was shown in figure 7.11. This indicated that the directions where C is larger

than unity are different for both layouts. It is concluded that the directions of wave amplifica-

tion in the case of L/100/100 are more harmful than in the case of the U-shaped FB. However,

this amplification due to reflection needs to be decreased as much as possible. For example, by

adding wave absorbing structure on the leeward side of the structures. This type of solution,

however, still needs extensive theoretical and experimental research.

To conclude this chapter, a comparison between the beam shaped FB, L/100/100, and U-

shaped FB is presented in figure 7.13. This figure shows that each configuration has its own

range of sufficient attenuation capacity, and problems with reflection amplifying the incoming

wave heights.

74


Figure 7.13: Comparison between the beam shaped FB, L/100/100, and U-shaped FB

None of the above solutions will provide sheltering for every wave direction. However, the

L/100/100 and the U-shape are found to be the most satisfying solutions to the problem. The

L/100/100 does attenuate sufficiently for seven wave directions, while the U-shape fails for six

directions. The maximum reflection in both cases is 1,5; this is not clear from figure 7.13 since

there the average C value is depicted. It has already been mentioned that the wave amplifying

directions for the L/100/100 shape are more harmful than for the U-shape. However, for both

layouts this reflection will need to be attenuated. Reflecting wave directions for the U-shaped

FB are E to S, and for the L/100/100 NE to SE. The relative probability of occurrence for both

of these segments is more or less the same. Finally, it is noted that the L/100/100 configuration

is much more economical than the U-shaped layout. From this it can be concluded that the

L/100/100 shape is preferred here over the other studied layouts.

75

Chapter 8

Motion analysis

8.1 Introduction

One of the FB’s main goals is to offer the possibility of berthing maintenance vessels. To safely

do so, the motions of the FB itself of course need to be limited. There are several factors that

will induce FB motion: wind, current, waves, tidal movements, etc. In this report, the first

three will be considered as main environmental parameters. As mentioned before, a floating

body has six independent degrees of motion: heave, roll, pitch, sway, yaw, and surge. The

Pianc report concerning movements of moored ships in harbours (Pianc, 1995) states that

three motions in particular need to be studied: heave, roll, and pitch. The period of resonance

of floating bodies for these motions is usually found somewhere between 5 s, and 20 s and; the

range of wave periods for which the FB is designed in this case lies within this interval. The

period of resonance for sway, yaw, and surge motions are mostly found in the range of 20 s to

several minutes. Pianc (1995) makes recommendations for the motion criteria for safe working

conditions. These are summarized in table 8.1.

Table 8.1: Motion Criteria (Pianc, 1995)

Ship Type Heave (m) Pitch (°) Roll (°)

Fishing vessels 0,4 3 3

Freighters, Coasters 0,6 1 2

Ferries, Ro-Ro 0,6 1 2

General cargo 1 2 5

Container vessels 1,2 2 6

Bulk carriers 1 2 6

These criteria are indications for vessels, and not for a floating breakwater. However, they

give an insight into the acceptable motions of the FB, in order to safely moor vessels.

The motion analysis will be performed using Aqua+ software. More information is included

76

Chapter 8. Motion analysis

in section 8.2. The analysis will be performed for case 1 boundary conditions, since the

mooring of vessels means the 95% workability limit needs to be respected. The results of this

motion analysis are response amplitude operators (RAO’s) for the FB. The meaning of these

parameters, that are an inherent property of the FB itself, is explained in section 8.3.

8.2 Aqua+

Aqua+ provides information on the seakeeping behaviour of ships or marine structures (Carrico

and Maisonneuve, 1995). An input data file, containing information on the geometry of the

structure, is analyzed by solving the radiation-diffraction problem resulting in the relative

motions of the structure itself. The water depth and wave incidence angle can be adjusted, as

well as the range of wave periods over which the calculations should be performed. For more

information about the software, the reader is referred to the Aqua+ user’s guide (Carrico and

Maisonneuve, 1995).

The analysis of the FB motions are performed for the preliminary design with an adjusted

length of 150 m as determined in chapter 7. Considering the symmetry of the FB, the only

wave incidences that will be regarded here are 0°; 22,5°; 45°; 67,5°; and 90°. Using an excel

spreadsheet (provided by ir. Evert Lataire), the Aqua+ output can then be translated into

RAO amplitudes and phase shifts.

8.3 Response Amplitude Operators

The response of a floating structure to regular wave excitation can be represented by the

’Response Amplitude Operator’ or RAO, which are transfer functions. An input of the exciting

wave force results in an output of the structure response. In other words, they are the response

of the structure per unit wave amplitude (Chakrabarti, 1987). Chakrabarti (1987) describes

RAO’s by equation 8.1.

Response(t) = (RAO)η(t) (8.1)

where η(t) is the wave profile as a function of time, t (Chakrabarti, 1987). They can be derived

for different parameters: motions of the structure, accelerations of the structure, applying

forces on the structure, etc. In this case, the motion RAO’s will be studied.

Using RAO’s, the FB motions are easy to find. As mentioned in section 8.2, Aqua+ output

can be translated into RAO amplitudes, and phase shifts for the heave, pitch, and roll motions.

The phase shifts occur, because the response of the structure does not coincide with the impact

of the exciting wave force. These shifts are different for every one of the three motions, and

combining them, results in the overall movement of the structure. However, in the scope of this

77


work, it’s only necessary to know the individual maximum motions, which is why the phase

shifts will be disregarded here. The amplitudes are of great importance. The heave motion

amplitude is expressed in m/m. This means that the heave response to a certain incoming

wave height - with a certain wave period - can be obtained by multiplying this wave height by

the RAO, for that particular wave period. The same remark is valid for roll and pitch, which

are both expressed in °/m.

8.4 Results

The calculations were performed for different wave incidences: 0°; 22,5°; 45°: 67,5° and 90°.

Because of the symmetry of the FB, there is no need to consider angles over 90°. The angle of

incidence β is defined in figure 8.1.

Figure 8.1: Definition angle of incidence

The RAO values were determined over a range of wave periods from 3 to 33 seconds. The

results for pitch, roll and heave are discussed in the following paragraphs.

8.4.1 Pitch

RAO values for pitch are presented in figure 8.2. The pitch motion reaches a maximum RAO

value of 1,18 for a wave incidence angle of 90°, and a wave period of 10 s. This means the

the FB will undergo an up- and downward rotation around its transversal axis of 1,18° for an

incoming significant wave height of 1m. However, the design wave height in this report for

case 1 boundary conditions is 2,5 m. This means an up- and downward movement of 2,95° is

expected. This does not meet any of the requirements for safe mooring according to Pianc

(1995)(see section 8.1).

8.4.2 Roll

Roll RAO values are presented in figure 8.3. A wave incidence angle of 0° (meaning wave

direction is aligned to the structure) causes no roll movement. Increasing wave obliquity

causes an increasing roll motion. A maximum RAO is obtained for the perpendicular waves

with a wave period of approximately 9 seconds. A maximum RAO of 2,2 means that the

structure will rotate over an angle of 2,2° left and right around it’s longitudinal axis, for an

78


Figure 8.2: RAO modulus - Pitch

incident wave height of 1m. Applied to the design wave height, a maximum roll movement

of 5,5° is expected for perpendicular waves. This exceeds the requirements according to the

Pianc guidelines.

8.4.3 Heave

The modulus for the heave movement is shown in figure 8.4. Similar to the roll motion,

heave will also be reinforced with increasing wave obliquity, reaching a maximum RAO for

an incidence of 90°. Wave periods of 10 seconds cause a RAO value of 1,61 for perpendicular

waves, meaning the structure will undergo a vertical up- and downward motion of 4,03 m for

an incident wave height of 2,5 m. This also exceeds the advised criteria by Pianc.

8.5 Discussion and solutions

The floating breakwater design is sufficient in light of wave attenuation. However, the influence

of waves, current, and wind causes the structure to move too much, making it impossible to

safely moor vessels alongside the FB. Anchoring the FB with mooring lines or chains will not

restrain the motions sufficiently to make them fall within the limits proposed by Pianc (1995).

There are various solutions worth investigating to solve this problem. Firstly, it is noted that

79


Figure 8.3: RAO modulus - Roll

Figure 8.4: RAO modulus - Heave

the motion analysis was performed for the beam shaped FB. Other layouts will have different

roll, pitch, and heave motions. For example, Martinelli et al. (2008b) showed in their experi-

80


mental research that an L-shaped FB will have smaller roll motions than a beam shaped FB.

The same effect is expected for a U-shaped FB.

A second recommendation that is made here, is the effect of a moonpool (a ’hole’ in the hull of

the floating structure) on the motions of the FB. A simple representation of such a structure

is shown in figure 8.5.

Figure 8.5: Definition sketch of a moonpool

Moonpools are often used in barges and platforms to lower equipment, such as ROV’s, into

the water. Inside the moonpool, two types of water motions will occur: sloshing and piston

motion. Sloshing is the movement of water from the front- to the backplates of the moon-

pool. Piston is the up- and downward motion of the water column. The moonpool acts as a

mass-spring system, which means both effects have their own eigenfrequency, which should be

taken into account when designing the moonpool, to avoid resonance (Aalbers). The water

motions inside the moonpool will influence the motions of the structure (Det Norske Veritas,

2010). Jakobsen (2008) shows in his master dissertation that the motions of a barge are in

fact damped in case a moonpool is present, especially the heave motion.

In chapter 2, a catamaran FB was described. Because of the distribution of the mass, this

structure has a larger roll period than a regular beam shaped FB. The air that is enclosed

under the hull also provides extra damping for the heave motion. Furthermore it is mentioned

that the water mass between the hull provides additional damping, especially for the sway

motion (Pianc, 1994). In light of this, it is recommended to study the effect of adding a skirt

below the structure. They are known to increase the damping of floating structures, and thus

to reduce the motions. Cozijn et al. (2005) show that adding a skirt to a buoy increases damp-

81


ing of heave, roll, and pitch motions. This alternative to reduce the FB motions is certainly

worth researching. A definition sketch of such a skirt is shown in figure 8.6.

The previous mentioned solutions to the motion problem of the FB require adjustments to

Figure 8.6: Definition sketch of a skirt

the structure itself. However, it is also possible to restrain the motions by using a special

type of mooring system. The first one that will be discussed here is tension leg mooring. As

mentioned in chapter 2, a tension leg mooring system excludes heave motion, and limits roll,

and pitch motions. This is considered to be a viable solution in this case, and is recommended

for further studying. Kim et al. (207) show that, while roll motions will be restrained, sway

motions might become relatively important in this design. Obviously sway motions that are

too large will also cause problems when mooring ships at the FB.

A second mooring alternative is the so called heave floating breakwater. This type of FB has

been researched by Tolba (1999). The structure is restrained by mooring piles, which elimi-

nates roll, pitch, sway, surge, and yaw motions. Heave motions, however, are still allowed as

they have a positive effect on the wave attenuation. This subject is discussed extensively in

chapter 9.

82

Chapter 9

Heave Floating Breakwater

In chapter 8 it was found that the floating breakwater motions are relatively large, meaning

no vessels would be able to moor alongside the FB. These motions can not be restrained

sufficiently by means of mooring lines or chains. To eliminate the motions of sway and roll,

a heave floating breakwater is proposed. Instead of using traditional mooring lines to anchor

the structure, the FB will be restrained by piles. The only motion allowed in this system is

heave. Tolba (1999) performed research on this type of FB, and compared it to a regular fixed

breakwater. According to his research a heave FB will always be more efficient than the fixed

type because of the fact that energy is needed to induce and maintain the heave motion. The

advantages of a heave FB are clear. It will function better as a pier because of the elimination

of sway and roll motions, and it will attenuate the waves better than a fixed structure because

of the heave motion. However, the advantage of designing a flexible construction is no longer

valid for this type of structure.

Important parameters in the design of a heave FB are the number of piles, as well as the

diameter and wall thickness of those piles. Tolba (1999) distinguishes two types of forces

acting on the FB. This first type are the vertical forces (water pressure, weight of the body,

etc.) of which the net vertical force causes the heave motion itself. Only a very small percentage

of these forces is transmitted to the piles due to friction, which is why they will be disregarded

in the pile design. The second type are horizontal wave forces. Tolba (1999) states these are

transmitted completely to the pile system.

The first part of this chapter will explain the general concept of a heave floating breakwater.

After this, the forces due to wind, current and waves on the floating breakwater itself and on

the piles will be calculated. From these forces the necessary pile diameter and wall thickness

can be determined, as well as the penetration depth in the sea bottom.

83

Chapter 9. Heave Floating Breakwater

9.1 General concept

The heave only concept will be applied here to the beam shaped FB. The general idea, as

explained before, is to moor the FB with vertical piles, to eliminate roll and sway movement.

However, because of the advantageous effect of the heave motion, the structure will not be

restrained in the vertical direction. Consequently a solution will need to be designed to allow

vessels to moor alongside the FB, that takes the excessive heave motion into account. To

design this heave FB, the mooring piles need to be dimensioned for the acting forces. These

forces can be divided into two main types, forces acting directly on the piles and forces acting

on the FB. The causes of these forces are wind, waves and current. An assumption will be

made for the number of piles on each side. The total force acting on one pile can then be

calculated, and from this, the necessary section modulus.

The mooring system of the heave floating breakwater will be determined for case 2 boundary

conditions. They are summarized in table 9.1.

Table 9.1: Parameters for wind and current force calculation

Hdes 5,0 m

Tdes 10 s

Waterlevel 6,25 m TAW

uwind 25 m/s

ucurrent 1 m/s

9.2 Forces acting on the floating breakwater

The forces acting on the FB will be determined for the preliminary design, with an adjusted

length of 150 m. The dimensions for the heave FB calculations are summarized in table 9.2.

Table 9.2: Dimensions Heave FB

Width (W) 40 m

Length (l) 150 m

Draught (D) 8 m

Freeboard (hc) 4 m

In this section the forces due to wind, current, and waves acting on the floating breakwater

will be calculated. It will be assumed that all forces act in the same direction, perpendicular

to the longitudinal side of the FB.

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9.2.1 Wind and current

Wind and current forces will be calculated using the approach advised by Pianc (1994).

Fd = CdAρu2

2(9.1)

Where Cd equals the drag coefficient which has a recommended value of 2 (Pianc, 1994). ’A’

equals the cross-sectional area in the plane normal to the force, u equals the component of

velocity in the direction of the force and ρ equals the mass density of air or sea water. In the

case of wind force u equals the velocity of wind, while in case of current u equals the velocity

of the current. The values for the different parameters are presented in table 9.3. In this table,

Awl stands for the longitudinal cross-sectional area in the plane normal to the wind force and

Acl for the longitudinal cross-sectional area in the plan normal to the current force.

Table 9.3: Parameters for wind and current force calculation

Cd 2

Awl 600 m2

Acl 1 200m2

ρair 1,293 kg/m3

ρseawater 1026 kg/m3

uwind 25 m/s

ucurrent 1 m/s

The choice for the boundary conditions for wind and current speed is substantiated in chapter

3. Substituting these values into equation 9.1 results in values shown in table 9.4. In this table,

the point of application is also shown. These are approximating values since it was assumed

the force would apply in the center of the plane, perpendicular to the direction of the force. In

section 9.2.2 it will become clear that wind and current forces are negligibly small compared

to the wave forces, which makes the error caused by this approximation very small.

Table 9.4: Wind and current load calculation

Force Point of application

Wind load 485 kN 38,25 m

Current load 1 231 kN 32,25 m

9.2.2 Waves

Calculating wave forces on offshore structures has been researched by many authors. It’s a

difficult thing to do, because of the complexity of the interaction of the structure with the

85


waves (Chakrabarti, 1987). This is why in this section, two different approaches by Goda and

Chakrabarti will be used, and compared to determine the wave forces.

Design wave height

The design wave height (Hmax) used to determine the wave forces, is the maximum wave height

that can occur in the sea state. Goda (2000) advises that Hmax = 1, 8H1/3 for non breaking

waves. The assumption of non breaking waves is validated using the approach described by

De Rouck (2011a). The wavelength can be calculated iteratively using Airy wave theory.

L0 =gT 2

2π(9.2)

ki = 2π/Li (9.3)

Li+1 = L0 tanh(ki+1d) (9.4)

The water depth d equals 36,25 m and the wave period T is 10 s. This leads to a wave length

of 144 m. Since d/L equals 0,21; this means this report treats the case of transitional waters.

According to De Rouck (2011a), this means waves won’t break in case the following demand

is met.

s =H

L= 0, 142 tanh(kd) (9.5)

In this case, s equals 0,034; and the left hand side of equation 9.5 is 0,12. This means the

waves will not be breaking in this case, and the advised design wave height of 1,8H1/3 by Goda

is applicable. Goda adds that this recommendation is in consideration of the performance

of many prototype breakwaters. Vertical caisson breakwaters have to be designed for this

maximum wave height, because no damage is allowed. This is different, for example, for

rubble mound breakwaters, where a certain percentage of damage is acceptable. In the case

of floating breakwaters, no damage will be allowed. This means that the recommendation for

Hmax by Goda, is also valid here.

Chakrabarti (1987)

Chakrabarti (1987) states that wave forces can be determined in three different ways:

� using the Morison equation,

� using the Froude-Krylov theory,

� using the Diffraction theory.

86


Each of these methods has its limitations and boundary conditions. The wave force can

be divided into two components: a drag force, and an inertia force. If the flow separates

from the structure, forming a wake, the drag force will become significantly large and the

Morison equation is valid (Chakrabarti, 1987). This is the case when the structure dimensions

are relatively small compared to the incoming wave length. Deo (2007) states that if the

characteristic dimension, in line with the wave propagation, of the structure is smaller than

15% of the incoming wave length, the Morison equation is valid. This equation linearly adds

the inertia and drag component. On the other hand, when the structure dimensions are large

compared to the wave length, the wave will be scattered and diffracted, and the drag force

will become less important. Then the diffraction theory may be used to calculate the resulting

wave force, which is done using potential theory. For situations that lie in between these two

extremes, the Froude-Krylov theory is valid. This theory is explained later on. In his work,

Deo (2007) proposes limits for the use of each approach. They are presented in figure 9.1.

Figure 9.1: Regions of applicablity according to Deo (2007)

In this graph, the parameter D stands for the dimension of the structure in the direction of

the wave propagation which in this case equals the width of the FB, 40 m. The wavelength, L,

equals 144 m. D/L now equals 0,28 and H/D is 0,125. Figure 9.1 shows that both the Morison

equation and the diffraction theory are not applicable here. The wave forces on the FB, will

be calculated using Froude-Krylov theory.

To explain the basic assumptions of the Froude-Krylov theory, it’s necessary to first explain

what the Froude-Krylov force exactly is. There are several forces acting on a floating body,

87


caused by regular waves. These are generally classified into viscous and non-viscous forces.

Viscous forces are not important here, since the structure is lying still. Non-viscous forces

can again be subdivided into Froude-Krylov forces and diffraction forces. The latter ones are

due to the fact that the floating body will disturb, and thus diffract, the waves. The Froude-

Krylov force assumes an undisturbed pressure field due to the waves (Journee and Massie,

2001). Integrating this pressure field over the body surface, leads to the wave force. The

Froude-Krylov theory uses this force, with the necessary corrections in order to consider the

fact that the wave pressure field is in fact disturbed by the presence of the structure. However,

Chakrabarti (1987) claims that if the diffraction effect is considered to be small, the correction

simplifies to a single coefficient. He developed simple expressions for the horizontal wave force

for the case of a submerged rectangular block. His methods are described here.

The expression of dynamic wave pressure is given by

p = ρgH

2

cosh(ks)

cosh(kd)cos(kx− ωt) (9.6)

where k = 2π/L equals the dimensionless wave number, d the water depth, ρ the mass density

of seawater (1026 kg/m3), g the gravitational constant (9,81m/s2), H the design wave height

and x, s, and t variables for distance, height and time. Integrating this pressure over the body

surface results in the wave force acting on the structure.

Fx = CH

∫∫S

pnxdS (9.7)

where CH equals the horizontal force coefficient, nx the direction normal perpendicular to

the structure and S the surface area of the submerged structure. Chakrabarti applied these

equations to the situation of a rectangular submerged block with dimensions l1, l2 and l3 where

l1 is the width of the FB in this case, l2 the length, and l3 the height. He developed equation

9.7 as the difference of integrals on the front, and back faces of the block.

Fwave =CHρHl22 cosh kd

s0+l32∫

s0− l32

cosh ksds[cos (kl12− ωt)− cos (

kl12

+ ωt)] (9.8)

where s0 is the distance from the ocean bottom to the center axis of the structure.

Determining the force coefficient CH is a delicate process. Chakrabarti (1987) proposes a

classification of factors according to the diffraction parameter ’ka’, where ’a’ is a characteristic

dimension. In the case of a FB, ’a’ is taken to be the width of the structure which leads to a

diffraction parameter of 1,75. In a range of ka from 0 to 5, Chakrabarti advises a horizontal

force coefficient of 1,5.

The input for equation 9.8 is summarized in table 9.5.

88


Table 9.5: Parameters for wave load calculation

CH 1,5

l1 150 m

l2 40 m

l3 12 m

H 9 m

ρ 1026 kg/m3

k 0,05

d 36,25 m

s0 34,25 m

Evaluating equation 9.8 leads to a wave force of 161 855 kN.

An important remark to be made here, is that the approach used by Chakrabarti is only valid

for fully submerged structures. The wave pressure per meter, as it was calculated here, is

presented in figure 9.2.

Figure 9.2: Wave force per meter in depth

The light gray area in the figure represents the FB. The freeboard of the structure, which

measures 4 m, will not be submerged. In reality the wave pressure above the waterline reduces

89


to zero, causing the wave force to follow the dashed curve in figure 9.2. This means the total

force, as calculated by Chakrabarti, will be an overestimation of the real force. To check the

quantity of this error, a second method to calculate wave forces on structures is applied in

section 9.2.2.

Dividing the static moment of the darker grey area in 9.2 by the surface area, results in the

point of application, which lies 32,71 m above the sea bottom.

Goda (2000)

In his work, Random seas and design of maritime structures, Goda discusses the design of

vertical breakwaters. More specifically, he develops formulas for the wave pressure acting

on the upright sections. The wave pressure distribution, as assumed by Goda, for a vertical

breakwater, is shown in figure 9.3.

Figure 9.3: Wave pressure distribution on an upright section of a vertical breakwater (Goda, 2000)

Contrary to Chakrabarti, the wave pressure distribution assumed by Goda reduces above the

waterline. Figure 9.4 shows the horizontal wave pressure distribution acting on the floating

breakwater.

The values for p1, p2, p3 and p4 can be calculated using the following formulas.

p1 =1

2(1 + cosβ)(α1 + α2 cos2 β)ρgHmax, (9.9)

p2 =p1

cosh(2πh/L), (9.10)

p3 = α3p1, (9.11)

90


Figure 9.4: Wave pressure distribution on the FB

p4 =

p1(1−hcη∗ ) : η∗ > hc,

0 : η∗ ≤ hc.(9.12)

η∗ = 0, 75(1 + cosβ)Hmax, (9.13)

α1 = 0.6 +1

2

[4πh/L

sinh(4πh/L)

]2, (9.14)

α2 = min

[hb − d

3hb

(Hmax

d

)2

,2d

Hmax

], (9.15)

α3 = 1− h′

h

[1− 1

cosh(2πh/L)

]. (9.16)

In these equations β stands for the angle between the direction of wave approach and a line

normal to the breakwater, which is 0 in this case. The parameter h equals the water depth,

which is 36,25m. Equation 9.12 represents the water pressure at the top of the FB and η∗

the maximum elevation to which the wave pressure is exerted, calculated by equation 9.13.

Furthermore, the parameter hc stands for the freeboard of the structure. In equation 9.15,

hb represents the water depth at the location at a distance 5H1/3 seaward of the breakwater.

In this report a uniform water depth is assumed, which leads to hb = 36,25 m. In the same

equation d equals the draught of the structure. Referring to figure 9.3, h’ in equation 9.16 will

in this case also equal the draught.

91


Evaluating these equations for the case of the preliminary design with case 2 boundary condi-

tions leads to the results summarized in table 9.6.

Table 9.6: Wave pressures according to Goda

Hmax 9m

eta* 13,5 m

p1 57 604N/mm2

p2 22 729N/mm2

p3 49 907N/mm2

p4 40 536N/mm2

α1 0,64

α2 0

α3 0,87

From these results, the total wave pressure can now be calculated with the following equation:

P =1

2(p1 + p3)h

′ +1

2(p1 + p4)h

∗c , (9.17)

h∗c = min [η∗, hc] (9.18)

This results in a total wave force of 626,33 kN/m, or 93 949 kN for the structure as a whole.

The point of application of this force can easily be determined by dividing the static moment

by the total force, and equals 34,16 m.

Discussion of the results

Results of both calculations by Chakrabarti and Goda are shown in table 9.7.

Table 9.7: Results wave force calculation according to Chakrabarti and Goda

Chakrabarti Goda

Wave force 161 855 kN 93 949 kN

Point of application 32,71 m 34,16 m

It has been mentioned earlier that the wave pressure distribution as assumed by Chakrabarti

is too conservative, since his approach applies to a fully submerged structure. This is not the

case here, since the FB has a freeboard of 4 m. As expected, the wave force calculated using

Goda’s approach is much smaller than when the equations by Chakrabarti are used. Since the

wave pressure distribution assumed by Goda is more realistic, these results will be used in the

rest of the calculations.

92


9.2.3 Conclusion

The total force acting on the FB is composed out of forces due to current, wind and waves.

The results of the calculations are shown in table 9.8.

Table 9.8: Total force acting on the FB

Force (kN) Point of application (m)

Current 1 231 32,25

Wind 485 38,25

Waves 93 949 34,16

9.3 Forces acting on the piles

Wind and current loads on the piles are determined using the approach as described by Pianc

(1994). Wave loads are calculated using Morison equations as suggested by Chakrabarti (1987).

To determine the forces acting on the piles, an initial diameter needs to be assumed. A pile

diameter of 4,5 m will be adopted here, which will be used to determine the wall thickness.

The mooring system will consist out of six piles (three on each side) in total.

9.3.1 Wind and current

Referring to section 9.2.1, equation 9.1 is now applied to piles. This means the cross-sectional

area perpendicular to the concerning force (wind or current), is defined as the projected surface

in a vertical plane through the centerline of the pile. Applying the same parameters as in

section 9.2.1, leads to a wind load of 91kN, and current load of 263 kN for each pile.

9.3.2 Waves

As mentioned before, wave loads will be calculated using the Morison equation. This equation

becomes valid if the diameter of the pile is smaller than 15% of the wavelength (Deo, 2007),

which is the case here. The theory developed by Morison et al. (1950) divides the wave force

into two components: a drag component and an inertia component.

f = fi + fd (9.19)

fi = CMρπD2

4

du

dt(9.20)

93


fD = CDρD

2u|u| (9.21)

These are the forces per unit length of the vertical cylinder, with CM the mass coefficient, CD

the drag coefficient, D the pile diameter, ρ the mass density of sea water and u the horizontal

water particle kinematics, which can be described by:

u =gTH

2L

cosh k(z + d)

cosh kdcos(ωt) (9.22)

with ω = 2πT .

Recommendations for the values of the hydrodynamic coefficients (CM and CD) are given by

De Rouck (2011b). CD will be determined by the Reynolds number Re and the roughness of

the pile.

Re =uD

ν(9.23)

where u = umax, ν = 10−6m2/s the kinematic viscosity of sea water and

umax =πH

T

L0

LA(9.24)

with L0 = gT 2

2π the wave length in deep water and LA the Airy wave length. In this case

L0/LA equals 1,08. This leads to a value for umax of 3,07 m/s. Substituting this value into

equation 9.23 results in a Reynolds number of 13,8 x 106. Since this means the calculations are

performed in the supercritical range, Re > 5 x 105, CD will vary from 0,6 to 1 with increasing

roughness of the piles. Because of the expected marine growth, the most negative Cd value will

be assumed here, which is 1. Since Re > 5 x 105, CM equals 1,5 according to De Rouck (2011b).

Combining equation 9.22 with equations 9.20 and 9.21 leads to the following expressions for

fi and fD:

fi = CMρgπD2

4H

[π cosh k(z + d)

L sinh kd

]sin(−ωt) (9.25)

fD = CDρgD

2H2 gT

2

4L2

[cosh k(z + d)

cosh kd

]2cosωt| cosωt| (9.26)

The total wave force over the length of the pile and the bending moment at the level of the

sea bed can be determined by integrating equations 9.25 and 9.26 over the height of the pile.

F =

η∫−d

(fi + fD)dz (9.27)

94


M =

η∫−d

(fi + fD)(z + d)dz (9.28)

Plotting these equations in function of time, as shown in figure 9.5, gives an indication of the

time when the result of both force components reaches a maximum value. Via trial and error

it is found that the time of maximum wave force impact is 8,9 s; and that the wave force itself

at this time is 1 323kN. The maximum bending moment is 31 056 kNm. Dividing this moment

by the wave force results in the point of application of the wave force, which is 19,70 m.

Figure 9.5: Wave force on one pile in function of time

9.3.3 Conclusion

The forces acting on one pile due to waves, current, and wind are summarized in table 9.9.

Table 9.9: Total force acting on one pile

Force (kN) Point of application (m)

Current 263 18,13

Wind 91 38,25

Waves 1 323 19,70

95


9.4 Pile design

9.4.1 Wall thickness

The diameter of the pile is set to 4,5 m. Now the wall thickness has to be determined to make

sure the pile can resist the bending moment. This bending moment is assumed to reach a

maximum value at the sea bed. Table 9.10 lists all acting forces and their respective righting

arms, z.

Table 9.10: Forces on heave floating breakwater

Force z

Forces on piles Wind (F1) 91 kN 38,25 m

Current (F2) 263 kN 18,13 m

Waves (F3) 1 323 kN 19,70 m

Forces on FB Wind (F4) 485 kN 38,25 m

Current (F5) 1 231 kN 32,25 m

Waves (F6) 93 949 kN 34,16 m

The forces on the floating breakwater itself will be divided over the piles. If six piles are

present to moor the structure safely (three on each longitudinal side), each pile will carry one

sixth of the total force acting on the floating breakwater. The total force on one pile will then

be:

Fpile = Fpile,current + Fpile,wind + Fpile,waves+

1

6(FFB,current + FFB,wind + FFB,waves) = 17 489 kN (9.29)

The total bending moment at the bottom of the pile will be:

Mpile = Mpile,current +Mpile,wind +Mpile,waves+

1

6(MFB,current +MFB,wind +MFB,waves) = 573 839 kNm (9.30)

The forces acting on one pile are shown in figure 9.6.

The bending moment can be used to calculate the required section modulus (De Vos, 2008).

W =M

σ=π(D4

0 −D4i )

32D0(9.31)

where M stands for the total maximum bending moment, σ for the tensile strength for steel,

and, finally, D0 and Di for the outer and inner diameter of the pile. Assuming a tensile strength

96


Figure 9.6: Forces acting on one pile

of 500N/mm2 for steel, and an outer diameter of 4,5 m leads to a required wall thickness of

0,08 m.

9.4.2 Penetration depth

The lateral bearing capacity of the pile will determine the penetration depth. De Vos (2008)

calculates this capacity using the method described by Vandepitte (1979). The assumptions

he made, are presented in figure 9.7. The pile resistance consists out of three components.

� Active and passive soil pressure, on both sides of the pile,

� neutral soil pressure, on both sides of the pile,

� passive soil pressure acting on the sides of the soil wedge ABD, which is pushed upwards.

Vandepitte (1979) developed equations for the ultimate resistant force, HU and moment MU .

HU =1

6γt20

[3(δp − δa)ω2b− 3(δ′p − δa)(1− ω2)b+

6λn(2ω2 − 1)a tanψ + 2ω3t0 tanφ tan3

(π

4+φ

2

)](9.32)

97


Figure 9.7: Lateral bearing capacity (De Vos, 2008)

MU =1

6γt30

[−2(δp − δa)ω3b+ 2(δ′p − δa)(1− ω3)b+

4λn(1− 2ω3)a tanψ − ω4t0 tanφ tan3

(π

4+φ

2

)](9.33)

where γ is the density of the soil, in this case 10 kN/m3 for wet sand; t0 is the pile penetration

depth as shown in figure 9.7; δp, δ′p and δa the passive and active soil pressures, which are

explained later; λn the neutral soil pressure coefficient 0,5; ωt0 the depth of the rotating point

below the bed; a and b the pile width; φ the angle of internal friction and ψ the angle which

the active and passive forces make with the horizontal (De Vos, 2008).

Equations for passive and active soil pressures are listed below.

δp = λp cosψ (9.34a)

δ′p = λ′p cosψ′ (9.34b)

δa = λa cosψ (9.34c)

98


with

λp =cos2 φ

cosψ

(1−

√sin(φ+ψ) sin(φ+ε)

cosψ cos ε

)2 (9.35a)

λ′p =cos2 φ

cosψ′(

1−√

sin(φ+ψ′) sin(φ+ε)cosψ′ cos ε

)2 (9.35b)

λa =cos2 φ

cosψ

(1 +

√sin(φ+ψ) sin(φ−ε)

cosψ cos ε

)2 (9.35c)

where ε equals the angle of the sea bed with the horizontal, which is 0° in this case since a

uniform water depth is assumed. As shown in figure 9.7, ψ = 2φ/3 and ψ′ = −φ/3. The

angle of internal friction, φ, is set to 30°, which is the standard value for sandy soils. The

applying horizontal force is known from section 9.4.1, 17 489kN. The required penetration

depth to ensure sufficient lateral bearing capacity can now be determined via trial and error.

It is found that when the penetration depth is 28 m, the lateral bearing capacity of the pile

equals 18 039 kN, which is sufficient to resist the total force on the pile, which equals 17 489 kN.

9.4.3 Final pile design

The total length of one pile will consist out of the summation of the penetration depth, the

water depth, and the freeboard of the structure.

l = lpenetration + d+ hc = 28m+ 36, 25m+ 4m = 68, 25m (9.36)

The properties of the piles are summarized in table 9.11

Table 9.11: Pile properties

Diameter 4,5 m

Wall thickness 0,08 m

Total length 68,25 m

Penetration depth 28 m

9.5 Conclusion

The designed heave floating breakwater is presented in figure 9.8.

99

Chapter 10

Discussion and recommendations

10.1 Discussion

This master dissertation concerns a feasibility study for the design of an offshore floating

breakwater, applied to the North Sea wind farm area. The literature study indicated that

the most important parameters in this design would be width, and draught of the structure.

Furthermore, the length would be important in relation to diffraction characteristics.

In the first chapters, the boundary conditions were set. They were divided into two main

conditions, hydraulic and structural.

Hydraulic boundary conditions were subdivided into two cases. The first case, is the case of

95% workability. In this case ships can moor at the FB, supplies can be stocked, and so on.

The second case concerns a 50y storm. This is the case which was used to design the mooring

system of the structure. The resulting conditions can be found in table 3.5.

The structural boundary conditions are various. On the one hand there are the demands due

to the design vessel, which in this case is an OWA vessel designed for the maintenance of

offshore wind farms. On the other hand there are limitations to the motions of the structure

and the overtopping, to ensure safe working conditions on, and along the FB. These conditions

and demands were described in chapter 4.

After the boundary conditions were set, a preliminary design was made of the floating break-

waters’ dimensions. The different processes of wave energy transportation were simplified

to two main processes: diffraction and transmission. The diffraction process determined the

length of the FB, while the transmission process determined the width and draught. In light of

diffracting waves, diffraction diagrams by Wiegel (1962) and Goda (2000) were used. Insight

in the tranmission process was gained by comparing different approaches by Macagno (1953),

Jones (1971), Stoker (1957), and Wagner et al. (2011), and applying them to three testcases by

101

Chapter 10. Discussion and recommendations

Tolba (1999), Koutandos et al. (2005) and Nakamura et al. (2003). These cases were selected

because of the similarity between their boundary conditions and those defined in chapter 3.

Doing so, the approach applying best to the situation here, was selected, and a preliminary

design for transmission was made accordingly. Finally, the overtopping was handled using

equations developed by Franco and Franco (1999), from which the necessary freeboard of the

structure was determined. This resulted in the dimensions of the preliminary design, which

are shown in table 10.1.


W (width) 40m

l (length) 225m

D (draught) 8m

Rc (freeboard) 4m

In chapter 7, the effect of different layouts on the attenuation capacity was studied. To do this,

the FB was modeled in MILDwave, a wave propagation model developed within the research

unit Coastal Engineering of the Department of Civil Engineering at Ghent University, under

the supervision of prof. dr. ir. Peter Troch (Troch et al., 2011). However, MILDwave does

not offer a simple input for floating objects, which imposed the need to study how floating

objects should be modeled in this software. Beels (2010) studied the layout of a farm of

floating wave energy converters (WEC) using MILDwave. Comparing the results of physical

tests to a model in MILDwave, she found that a WEC is best modeled by assigning a linearly

varying absorption coefficient over the length of the WEC, ranging from 0,9 to 0,99. To verify

if this is the correct approach in the case of floating breakwaters, which have a much larger

length than width contrary to the square shaped WEC models, different approaches to model

objects in MILDwave were applied to the same testcases used in chapter 5. On the one hand

the FB were modeled by what was called ’a homogeneous approach’, where the structure was

assigned only one absorption coefficient S. This approach was performed for several values of

S. On the other hand, a heterogeneous approach was used, dividing the FB over it’s width in

several longitudinal layers, and assigning a different S to each layer ranging from 0,90 to 0,99.

The lowest value of S was assigned to the side of the incoming waves. A representation of this

approach is shown in figure 10.1.

The study showed that the heterogeneous approach is indeed the best way to model a floating

breakwater in MILDwave, which was expected.

Knowing how to model a floating object in MILDwave, it was possible to model the preliminary

design to see if it would suffice. The first thing noticed was that the floating breakwater

length could be reduced from 225 m to 150 m. After the design was optimized, the influence of

102


Figure 10.1: Non homogeneous model

different FB layouts was studied: more specifically a beam shaped structure, an L shape and

a U shape. It is pointed out that this study only quantifies the effect of different layouts and

wave incidences, since the MILDwave model can no longer be verified at this point.

The beam shaped structure was oriented perpendicular to the SW direction, where most waves

are coming from. The results in MILDwave showed that this configuration would suffice for

waves coming from the SSE-WNW segment. For the wave directions NWN-ESE, it was seen

that the incoming wave height would be amplified due to reflection.

Since relatively high waves are coming from the fourth quadrant of the wind rose as well, an

L-shape was modeled. Three types of L structures were studied: L/150/150, L/150/100, and

L/100/100. A symmetrical L-shape with both legs measuring 150 m proved to attenuate waves

for the segment SSE-N sufficiently. It was also seen that the attenuation coefficient for the SW-

N segment was often in the order of half the maximum value. This is why the second layout

studied here was an asymmetrical L shape of which the leg perpendicular to the NW direction

measured 100 m. This layout was found to suffice for the same directions as the L/150/150,

except for waves coming from the north. It was noticed that for the directions SSE-W, the

value of C was significantly lower than the maximum value. This lead to a symmetrical L-

shape, with both legs measuring 100 m. In this case, the FB was found to be efficient for waves

coming from the SSE-NWN segment. However, waves coming from the N, NNE and NE were

not attenuated enough. Since waves coming from these directions have relatively large values

for H95%, a U shape was the subject of the next simulations. In light of reflecting waves, it

was found that an asymmetrical configuration has a negative influence for the NNE direction,

which was indicated in figure 7.8 and 7.9. This is because less waves are retained by the leg

perpendicular to the NW direction. It was also concluded that a shorter leg length would

decrease the amount of reflected energy. Generally, all L-shaped configurations suffice for the

third and fourth quadrants on the wind rose. The difference in behaviour lies mainly in the

first and second quadrants. Here, the L/100/100 layout is found to be most satisfying, since

this configuration offers the least problems with reflection. However, reflection problems are

still there, and research on how to decrease this phenomenon is recommended.

The final design was a U shaped FB of which the parallel legs measured 100 m, and the

connecting side 155 m. This structure provided sufficient wave attenuation for waves coming

103


from the SW to the NE. However, for waves coming from the south, the wave attenuation was

significantly lower than in the case of an L shaped FB. This is because the waves are reflected

inside the U shape, amplifying the waves inside. For the directions SSE, SE, and ESE the

resulting wave heights are even larger than the incoming wave heights. A comparison between

this U-shape and L/100/100 was shown in figure 7.11. This indicated that the directions where

C is larger than unity are different for both layouts. It is concluded that the directions of wave

amplification in the case of L/100/100 are more harmful than in the case of the U-shaped FB,

because the incoming wave heights are smaller in the latter case. However, this amplification

due to reflection needs to be decreased as much as possible. For example, by adding wave

absorbing structures on the leeward side of the structures. This type of solution, however, still

needs extensive theoretical and experimental research.

To conclude a comparison between the beam shaped FB, L/100/100, and U-shaped FB is

presented in figure 10.2. This figure shows that each configuration has its own range of

sufficient attenuation capacity, and problems with reflection amplifying the incoming wave

heights.

Figure 10.2: Comparison between the beam shaped FB, L/100/100, and U-shaped FB

None of the above solutions will provide sheltering for every wave direction. However, the

L/100/100 and the U-shape are found to be the most satisfying solutions to the problem. The

L/100/100 does attenuate sufficiently for seven wave directions, while the U-shape fails for six

directions. The maximum reflection in both cases is 1,5; this is not clear from figure 7.13 since

there the average C value is depicted. It has already been mentioned that the wave amplifying

104


directions for the L/100/100 shape are more harmful than for the U-shape. However, for both

layouts this reflection will need to be attenuated. Reflecting wave directions for the U-shaped

FB are E to S, and for the L/100/100 NE to SE. The relative probability of occurrence for

both of these segments is more or less the same. Finally, it is noted that the L/100/100 con-

figuration is much more economical than the U-shaped layout. From this it can be concluded

that the L/100/100 shape is preferred here over the other studied layouts.

Modeling the floating breakwater in MILDwave showed that the wave attenuation capacity of

the structure is sufficient. However, this is not the only condition that needs to be fulfilled

for the breakwater to work accordingly. The motions of the structure need to be limited, to

allow safe mooring and working conditions. This is why in chapter 8 a motion analysis was

performed using Aqua+ software. This motion analysis results in ’Response amplitude opera-

tors’ or RAO’s, which indicate the response of the structure to a certain exciting wave. From

this analysis it was concluded that FB motions would be far too high to ensure safe mooring

and working conditions. A traditional mooring system is not able to restrain these motions

sufficiently, which is why the concept of a heave floating breakwater is proposed in chapter 9.

A heave floating breakwater is moored using vertical piles, which restrain roll and pitch mo-

tions, and only allow heave motions. This kind of structure was studied by Tolba (1999),

and he found that the attenuation capacities were better than fixed floating breakwaters. To

design these mooring piles, the forces acting on both floating breakwater and the piles needed

to be determined. In both cases this concerns forces due to wind, current and waves. The

first two were easy to determine using the approach as described in Pianc (1994). The latter

was more complicated. A distinction was made between wave forces acting on the floating

breakwater and wave forces acting on the piles. The floating breakwater dimensions are in

the order of the wave length. This is why they were calculated using Froude-Krylov theory

as proposed by Chakrabarti (1987). Pile dimensions are much smaller than the wave length,

which is why the Morison equation can be applied here (Deo, 2007). From these forces, using

the approach as proposed by Beels (2010), the required section modulus can be calculated.

This leads to a minimum pile diameter of 4,5 m and a wall thickness 0,08 m. After this, the

theory by Vandepitte (1979) was used to determine the necessary penetration depth of the

piles into the sea bed, 28 m. Eventually the final heave floating breakwater design was shown

in figure 9.8.

10.2 Recommendations

The design proposed in this thesis is just one out of many possible solutions to the problem.

However, research on this topic is still very much needed. Floating breakwaters have been

105


used in the past, but never in North Sea conditions and with dimensions in the order of the

ones determined here.

The subject has been treated numerically in this dissertation, which gives a good insight in

the influencing parameters etc. However, without experimental testing no valid conclusions

can be made. Most testing performed in the past took place in the wave flume. This does

not give insight in the process of diffraction, and only maps the processes of transmission and

reflection. Insight in the interaction between transmission and diffraction will lead to more

optimized design methods. Wave basin experiments are strongly advised. Stating that these

tests can be performed using MILDwave is correct to a certain level. The MILDwave model

for a simple beam has been verified, and is considered trustworthy. However, when the FB

layout becomes more complex, this model becomes more unsure. It can only be used to quan-

tify certain adjustments to the structure, but it can not be relied on to deliver veracious results.

In chapter 8 it was shown that the motions of the FB need to be limited. In this dissertation

the choice has been made to do so using a vertical pile mooring system. On the one hand this

solution eliminates the advantage of a flexible structure. On the other hand, it was shown by

Tolba (1999) that the heave motion has a positive influence on the attenuation capacity of

the structure. The system eliminated roll and pitch motions, but not heave. Further study

on how to eliminate, or at least reduce, this heave motion is recommended. An alternative

is to design a system for the vessels to moor at the FB without being inconvenienced by the

heave motion. However, as long as the heave motions are too high, the FB can not be used

as a logistic center. The heave motion could be eliminated by restraining the FB vertically as

well. This would eliminate the positive effect of the heave motion on the attenuation capacity

of the FB. Further research on this topic is advised.

The heave FB is only one alternative to solve the problem of motions. In chapter 8 several

propositions were made. Firstly, the effect of a different FB layout on the motions still needs

to be researched. Secondly adding a moonpool, and/or a skirt to the structure will have a pos-

itive effect on the motions. Thirdly a tension leg mooring system could be a viable alternative

to the heave FB. The structure is pulled down using tension legs, which causes the buoyancy of

the structure to exceed the weight. Therefore a new downward force is created, which results

in total restraint against the heave motion, and a partly restraint against pitch. Roll motions

will be counteracted by the restoring force resulting from the horizontal component of the

pre-tension (Journee and Massie, 2001).

Finally, it is pointed out that this report concerns a purely theoretical approach of the subject

of a floating breakwater. The practical design of such a structure will require a much more

106


detailed study of materials, connections, installation methods, etc.

107

Appendix A

Offshore Wind Farm concessions

Three projects for the construction of OWF in the Belgian part of the North Sea are ongoing:

C-Power on Thorntonbank, Belwind on Bligh Bank , and Northwind on ’Bank zonder Naam’.

Three new projects already gained concessions: Rentel, NORTHER and SEASTAR, while one

concession area is still to be denoted. The location of these projects is shown in figure A.1.

108

Appendix A. Offshore Wind Farm concessions

Figure A.1: Concessions Belgian coast

109

Appendix B

ACES output file

An ACES output file contains the significant wave heights for return periods of 2,5, 10, 25, 50

and 100y for four types of distributions. The Fischer-Tippett type 1 distribution, and Weibull

distributions with k = 0,75; 1,00; 1,50; and 2,00. For each of these results, the correlation

factor is included as well, from which it can be determined which distribution is most fitting

in that particular case. An example of an ACES output file is presented in this chapter.

110

Appendix B. ACES output file

EXTREMAL SIGNIFICANT WAVE HEIGHT ANALYSIS NOORDEN N = 28 STORMS NT = 28 STORMS NU = 1.00 K = 20.00 YEARS LAMBDA = 1.40 STORMS PER YEAR MEAN OF SAMPLE DATA = 3.592 M STANDARD DEVIATION OF SAMPLE = 0.495 M ---------------------------------------------------------------------- FISHER-TIPPETT TYPE I (FT-I) DISTRIBUTION F(Hs) = EXP(-EXP(-(Hs-B)/A)) - Equation 1 A = 0.396 M B = 3.370 M CORRELATION = 0.9874 SUM SQUARE OF RESIDUALS = 0.0568 M RANK Hsm F(Hs<=Hsm) Ym A*Ym+B Hsm-(A*Ym+B) (M) Equation 3 Equation 5 (M) (M) Equation 4 1 4.82 0.9801 3.906 4.9175 -0.0965 2 4.68 0.9445 2.863 4.5043 0.1767 3 4.39 0.9090 2.349 4.3005 0.0915 4 4.20 0.8734 2.000 4.1621 0.0379 5 4.11 0.8378 1.732 4.0560 0.0510 6 3.97 0.8023 1.513 3.9691 -0.0031 7 3.93 0.7667 1.326 3.8950 0.0330 8 3.87 0.7312 1.161 3.8298 0.0352 9 3.83 0.6956 1.013 3.7713 0.0627 10 3.68 0.6600 0.878 3.7178 -0.0368 11 3.62 0.6245 0.753 3.6682 -0.0442 12 3.55 0.5889 0.636 3.6217 -0.0697 13 3.50 0.5533 0.525 3.5776 -0.0736 14 3.48 0.5178 0.418 3.5355 -0.0545 15 3.40 0.4822 0.316 3.4948 -0.0898 16 3.37 0.4467 0.216 3.4552 -0.0902 17 3.34 0.4111 0.118 3.4164 -0.0804 18 3.29 0.3755 0.021 3.3780 -0.0860 19 3.27 0.3400 -0.076 3.3397 -0.0747 20 3.26 0.3044 -0.173 3.3010 -0.0410 21 3.22 0.2688 -0.273 3.2617 -0.0427 22 3.21 0.2333 -0.375 3.2210 -0.0080 23 3.21 0.1977 -0.483 3.1784 0.0296 24 3.13 0.1622 -0.598 3.1327 0.0013 25 3.12 0.1266 -0.726 3.0821 0.0349 26 3.07 0.0910 -0.874 3.0235 0.0465 27 3.05 0.0555 -1.062 2.9490 0.0990 28 3.02 0.0199 -1.365 2.8289 0.1921

111


RETURN PERIOD TABLE with 90% CONFIDENCE INTERVAL RETURN PERIOD Hs SIGR Hs-1.65*SIGR Hs+1.65*SIGR (Yr) (M) (M) (M) (M) Equation 6 Equation 10 2.00 3.69 0.11 3.51 3.88 5.00 4.11 0.18 3.82 4.40 10.00 4.40 0.23 4.03 4.77 25.00 4.77 0.30 4.28 5.26 50.00 5.05 0.35 4.47 5.63 100.00 5.33 0.40 4.66 5.99 ---------------------------------------------------------------------- WEIBULL DISTRIBUTION k = 0.75 F(Hs) = 1-EXP(-((Hs-B)/A)**k) - Equation 2 A = 0.318 M B = 3.216 M CORRELATION = 0.9547 SUM SQUARE OF RESIDUALS = 0.3193 M RANK Hsm F(Hs<=Hsm) Ym A*Ym+B Hsm-(A*Ym+B) (M) Equation 3 Equation 5 (M) (M) Equation 4 1 4.82 0.9828 6.489 5.2779 -0.4569 2 4.68 0.9477 4.233 4.5610 0.1200 3 4.39 0.9126 3.280 4.2581 0.1339 4 4.20 0.8775 2.688 4.0700 0.1300 5 4.11 0.8423 2.267 3.9361 0.1709 6 3.97 0.8072 1.944 3.8335 0.1325 7 3.93 0.7721 1.685 3.7512 0.1768 8 3.87 0.7369 1.471 3.6831 0.1819 9 3.83 0.7018 1.289 3.6256 0.2084 10 3.68 0.6667 1.134 3.5761 0.1049 11 3.62 0.6315 0.998 3.5330 0.0910 12 3.55 0.5964 0.878 3.4950 0.0570 13 3.50 0.5613 0.772 3.4613 0.0427 14 3.48 0.5262 0.678 3.4312 0.0498 15 3.40 0.4910 0.593 3.4041 0.0009 16 3.37 0.4559 0.516 3.3797 -0.0147 17 3.34 0.4208 0.446 3.3577 -0.0217 18 3.29 0.3856 0.383 3.3377 -0.0457 19 3.27 0.3505 0.326 3.3195 -0.0545 20 3.26 0.3154 0.274 3.3030 -0.0430 21 3.22 0.2802 0.227 3.2880 -0.0690 22 3.21 0.2451 0.184 3.2744 -0.0614 23 3.21 0.2100 0.146 3.2621 -0.0541 24 3.13 0.1749 0.111 3.2511 -0.1171 25 3.12 0.1397 0.080 3.2413 -0.1243 26 3.07 0.1046 0.053 3.2327 -0.1627 27 3.05 0.0695 0.030 3.2254 -0.1774 28 3.02 0.0343 0.011 3.2195 -0.1985

112


RETURN PERIOD TABLE with 90% CONFIDENCE INTERVAL RETURN PERIOD Hs SIGR Hs-1.65*SIGR Hs+1.65*SIGR (Yr) (M) (M) (M) (M) Equation 6 Equation 10 2.00 3.55 0.16 3.28 3.82 5.00 3.99 0.33 3.45 4.53 10.00 4.37 0.48 3.58 5.17 25.00 4.94 0.71 3.77 6.11 50.00 5.40 0.90 3.92 6.88 100.00 5.89 1.09 4.09 7.69 ---------------------------------------------------------------------- WEIBULL DISTRIBUTION k = 1.00 F(Hs) = 1-EXP(-((Hs-B)/A)**k) - Equation 2 A = 0.513 M B = 3.081 M CORRELATION = 0.9861 SUM SQUARE OF RESIDUALS = 0.0461 M RANK Hsm F(Hs<=Hsm) Ym A*Ym+B Hsm-(A*Ym+B) (M) Equation 3 Equation 5 (M) (M) Equation 4 1 4.82 0.9814 3.982 5.1246 -0.3036 2 4.68 0.9462 2.922 4.5805 0.1005 3 4.39 0.9110 2.419 4.3223 0.0697 4 4.20 0.8758 2.086 4.1513 0.0487 5 4.11 0.8407 1.837 4.0233 0.0837 6 3.97 0.8055 1.637 3.9209 0.0451 7 3.93 0.7703 1.471 3.8356 0.0924 8 3.87 0.7351 1.329 3.7625 0.1025 9 3.83 0.7000 1.204 3.6985 0.1355 10 3.68 0.6648 1.093 3.6416 0.0394 11 3.62 0.6296 0.993 3.5904 0.0336 12 3.55 0.5944 0.902 3.5438 0.0082 13 3.50 0.5593 0.819 3.5011 0.0029 14 3.48 0.5241 0.743 3.4617 0.0193 15 3.40 0.4889 0.671 3.4251 -0.0201 16 3.37 0.4537 0.605 3.3909 -0.0259 17 3.34 0.4186 0.542 3.3589 -0.0229 18 3.29 0.3834 0.484 3.3287 -0.0367 19 3.27 0.3482 0.428 3.3003 -0.0353 20 3.26 0.3130 0.375 3.2733 -0.0133 21 3.22 0.2779 0.326 3.2477 -0.0287 22 3.21 0.2427 0.278 3.2232 -0.0102 23 3.21 0.2075 0.233 3.1999 0.0081 24 3.13 0.1724 0.189 3.1777 -0.0437 25 3.12 0.1372 0.148 3.1563 -0.0393 26 3.07 0.1020 0.108 3.1358 -0.0658 27 3.05 0.0668 0.069 3.1161 -0.0681 28 3.02 0.0317 0.032 3.0971 -0.0761

113


RETURN PERIOD TABLE with 90% CONFIDENCE INTERVAL RETURN PERIOD Hs SIGR Hs-1.65*SIGR Hs+1.65*SIGR (Yr) (M) (M) (M) (M) Equation 6 Equation 10 2.00 3.61 0.14 3.38 3.84 5.00 4.08 0.25 3.67 4.49 10.00 4.44 0.34 3.87 5.00 25.00 4.91 0.46 4.14 5.67 50.00 5.26 0.56 4.34 6.18 100.00 5.62 0.65 4.54 6.70 ---------------------------------------------------------------------- WEIBULL DISTRIBUTION k = 1.40 F(Hs) = 1-EXP(-((Hs-B)/A)**k) - Equation 2 A = 0.771 M B = 2.890 M CORRELATION = 0.9940 SUM SQUARE OF RESIDUALS = 0.0273 M RANK Hsm F(Hs<=Hsm) Ym A*Ym+B Hsm-(A*Ym+B) (M) Equation 3 Equation 5 (M) (M) Equation 4 1 4.82 0.9799 2.646 4.9313 -0.1103 2 4.68 0.9446 2.136 4.5380 0.1430 3 4.39 0.9094 1.870 4.3325 0.0595 4 4.20 0.8742 1.683 4.1887 0.0113 5 4.11 0.8390 1.538 4.0763 0.0307 6 3.97 0.8038 1.417 3.9830 -0.0170 7 3.93 0.7686 1.313 3.9027 0.0253 8 3.87 0.7333 1.220 3.8317 0.0333 9 3.83 0.6981 1.138 3.7677 0.0663 10 3.68 0.6629 1.062 3.7092 -0.0282 11 3.62 0.6277 0.991 3.6550 -0.0310 12 3.55 0.5925 0.926 3.6043 -0.0523 13 3.50 0.5572 0.864 3.5566 -0.0526 14 3.48 0.5220 0.805 3.5112 -0.0302 15 3.40 0.4868 0.749 3.4679 -0.0629 16 3.37 0.4516 0.695 3.4262 -0.0612 17 3.34 0.4164 0.643 3.3860 -0.0500 18 3.29 0.3812 0.592 3.3468 -0.0548 19 3.27 0.3459 0.542 3.3085 -0.0435 20 3.26 0.3107 0.494 3.2709 -0.0109 21 3.22 0.2755 0.445 3.2338 -0.0148 22 3.21 0.2403 0.397 3.1968 0.0162 23 3.21 0.2051 0.349 3.1598 0.0482 24 3.13 0.1698 0.301 3.1223 0.0117 25 3.12 0.1346 0.251 3.0840 0.0330 26 3.07 0.0994 0.200 3.0441 0.0259 27 3.05 0.0642 0.144 3.0013 0.0467 28 3.02 0.0290 0.081 2.9523 0.0687

114


RETURN PERIOD TABLE with 90% CONFIDENCE INTERVAL RETURN PERIOD Hs SIGR Hs-1.65*SIGR Hs+1.65*SIGR (Yr) (M) (M) (M) (M) Equation 6 Equation 10 2.00 3.68 0.13 3.46 3.89 5.00 4.13 0.20 3.80 4.46 10.00 4.43 0.25 4.02 4.84 25.00 4.80 0.31 4.28 5.32 50.00 5.06 0.36 4.46 5.65 100.00 5.31 0.40 4.64 5.97 ---------------------------------------------------------------------- WEIBULL DISTRIBUTION k = 2.00 F(Hs) = 1-EXP(-((Hs-B)/A)**k) - Equation 2 A = 1.078 M B = 2.638 M CORRELATION = 0.9824 SUM SQUARE OF RESIDUALS = 0.0747 M RANK Hsm F(Hs<=Hsm) Ym A*Ym+B Hsm-(A*Ym+B) (M) Equation 3 Equation 5 (M) (M) Equation 4 1 4.82 0.9785 1.960 4.7501 0.0709 2 4.68 0.9433 1.694 4.4635 0.2175 3 4.39 0.9080 1.545 4.3026 0.0894 4 4.20 0.8728 1.436 4.1852 0.0148 5 4.11 0.8375 1.348 4.0905 0.0165 6 3.97 0.8022 1.273 4.0098 -0.0438 7 3.93 0.7670 1.207 3.9385 -0.0105 8 3.87 0.7317 1.147 3.8740 -0.0090 9 3.83 0.6965 1.092 3.8145 0.0195 10 3.68 0.6612 1.040 3.7590 -0.0780 11 3.62 0.6259 0.992 3.7064 -0.0824 12 3.55 0.5907 0.945 3.6563 -0.1043 13 3.50 0.5554 0.900 3.6080 -0.1040 14 3.48 0.5202 0.857 3.5612 -0.0802 15 3.40 0.4849 0.815 3.5155 -0.1105 16 3.37 0.4497 0.773 3.4705 -0.1055 17 3.34 0.4144 0.732 3.4260 -0.0900 18 3.29 0.3791 0.690 3.3817 -0.0897 19 3.27 0.3439 0.649 3.3373 -0.0723 20 3.26 0.3086 0.608 3.2924 -0.0324 21 3.22 0.2734 0.565 3.2466 -0.0276 22 3.21 0.2381 0.521 3.1996 0.0134 23 3.21 0.2029 0.476 3.1508 0.0572 24 3.13 0.1676 0.428 3.0992 0.0348 25 3.12 0.1323 0.377 3.0436 0.0734 26 3.07 0.0971 0.320 2.9820 0.0880 27 3.05 0.0618 0.253 2.9098 0.1382 28 3.02 0.0266 0.164 2.8144 0.2066

115


RETURN PERIOD TABLE with 90% CONFIDENCE INTERVAL RETURN PERIOD Hs SIGR Hs-1.65*SIGR Hs+1.65*SIGR (Yr) (M) (M) (M) (M) Equation 6 Equation 10 2.00 3.73 0.12 3.53 3.93 5.00 4.14 0.16 3.87 4.41 10.00 4.39 0.19 4.07 4.71 25.00 4.67 0.23 4.29 5.05 50.00 4.86 0.25 4.44 5.28 100.00 5.03 0.28 4.58 5.49

116

Appendix C

Cumulative wave heights per

direction

To determine the wave height with a 95% probablity of occurence H95%, the data was first

sorted according to the 16 directions of the wind rose. After this, the cumulative wave height

for each direction was plotted. From these graphs, H95% can easily be read. These plots are

shown in figures C.1 to C.16.

Figure C.1: Cumulative wave height - direction N

117

Appendix C. Cumulative wave heights per direction

Figure C.2: Cumulative wave height - direction NNE

Figure C.3: Cumulative wave height - direction NE

118


Figure C.4: Cumulative wave height - direction ENE

Figure C.5: Cumulative wave height - direction E

119


Figure C.6: Cumulative wave height - direction ESE

Figure C.7: Cumulative wave height - direction SE

120


Figure C.8: Cumulative wave height - direction SSE

Figure C.9: Cumulative wave height - direction S

121


Figure C.10: Cumulative wave height - direction SWS

Figure C.11: Cumulative wave height - direction SW

122


Figure C.12: Cumulative wave height - direction WSW

Figure C.13: Cumulative wave height - direction W

123


Figure C.14: Cumulative wave height - direction NWW

Figure C.15: Cumulative wave height - direction NW

124


Figure C.16: Cumulative wave height - direction NWN

125

Appendix D

Extreme wave heights per direction

The significant wave heights calculated by ACES are presented here graphically. For case 2

boundary conditions, as defined in chapter 3, a return period of 50 years is assumed.

126

Appen

dix

D.

Extrem

ew

ave

heigh

tsper

directio

n

Figure D.1: H1/3 North to East

127

Appen

dix

D.

Extrem

ew

ave

heigh

tsper

directio

n

Figure D.2: H1/3 East to South

128

Appen

dix

D.

Extrem

ew

ave

heigh

tsper

directio

n

Figure D.3: H1/3 South to West

129

Appen

dix

D.

Extrem

ew

ave

heigh

tsper

directio

n

Figure D.4: H1/3 West to North

130

Appendix E

Diffraction diagrams

In this chapter, a comparison will be made between using Wiegel diagrams for regular waves

and Goda diagrams for irregular waves, to determine the necessary breakwater length. The

hydraulic boundary conditions are presented in table E.1

Table E.1: Hydraulic boundaries case 1

Hdes Tdes water depth

2,5m 9s 30m

Making use of the linear wave theory, these input parameters lead to a wave length of 117 m.

The maximum value for the attenuation coefficient equals 0,4. Using the approach described

in the Shore Protection Manual (US Army, 1984), this means the diffraction coefficient for

waves around the right or left tip on the diagrams should be 0,28.

131

Appendix E. Diffraction diagrams

E.1 Regular waves: Wiegel (1962)

Figure E.1: Wiegel Diagram head on waves

The Wiegel diffraction diagrams show that a length of 0,75 times the wave length is needed

to ensure a sheltered environment.

132

Appendix E. Diffraction diagrams

E.2 Irregular waves: Goda (2000)

Figure E.2: Goda Diagram head on waves

The diffraction diagrams developed by Goda show that a length in the order of the wave length

will be needed.

The difference between these two results is only 15m, which is negligibly small compared to

the total breakwater length.

133

Appendix F

MILDwave testcases

In chapter 6 it is examined what the best approach is to model a FB in MILDwave. This is

done by modeling three testcases in two ways: a homogeneous approach and a heterogeneous

approach. In the homogeneous approach, the breakwater is modeled with a constant coefficient

of absorption, S. This is done for S ranging from 0,94 to 0,99. In the heterogeneous approach

the breakwater is divided into layers over its width, and each layer is assigned a different value

of S. This value ranges from 0,90 to 0,99, and the smallest value is assigned to the side of the

incoming waves. The resulting contour plots of these testcases are presented in this appendix.

A detail of the area surrounding the FB is shown in each figure.

F.1 Testcase 1: Tolba (1999)

The input parameters in the Tolba (1999) testcase are shown in table F.1. The experimentally

observed value for Ct by Tolba equals 0,21.

Table F.1: Dimensions experiments Tolba (1999)

Width (W) 25 m

Draught (D) 8,3 m

Wave period (T) 7 s


Water depth (d) 50 m

134

Appendix F. MILDwave testcases

Figure F.1: Results MILDwave model, Tolba testcase, Model with S = 0,94


135




136




137


Figure F.7: Results MILDwave model, Tolba testcase, Heterogeneous model

138


F.2 Testcase 2: Koutandos et al. (2005)


observed value for Ct by Koutandos et al. (2005) equals 0,39.

Table F.2: Dimensions experiments Koutandos et al. (2005)

Width (W) 2 m

Length (l) 2,8 m

Draught (dr) 0,4 m



Water depth (d) 2 m

Figure F.8: Results MILDwave model, Koutandos et al. (2005) testcase, Model with S = 0,94

139




140




141



Figure F.14: Results MILDwave model, Koutandos et al. (2005) testcase, Heterogeneous model

142


F.3 Testcase 3: Nakamura et al. (2003)


observed value for Ct by Nakamura et al. (2003) equals 0,16.

Table F.3: Dimensions experiments Koutandos et al. (2005)

Width (W) 0,304 m

Draught (dr) 0,136 m



Water depth (d) 0,95 m

Figure F.15: Results MILDwave model, Nakamura et al. (2003) testcase, Model with S = 0,94

143




144




145



Figure F.21: Results MILDwave model, Nakamura et al. (2003) testcase, Model with varying S

146

Appendix G

MILDwave optimization

In chapter 7 the preliminary design is modeled in MILDwave. Firstly, the breakwater length is

optimized. Secondly, the layout of the FB is studied. The resulting contour plots are included

in this appendix. In every figure, a detail of the area surrounding the FB is added. If this

image is unclear because of contour lines lying too close together, a coloured basin plot is

added as well.

147

Appendix G. MILDwave optimization

G.1 Influence of the FB length

In this section, the results of the study of the breakwater length are shown. A C value of

0,4 is intended. It this case, a breakwater length of 150 is found to suffice. These results are

summarized in table G.1

Table G.1: Results MILDwave simulations to study the FB length

Length C

100m 0,50

150m 0,35

200m 0,30

Figure G.1: FB length 100m

148




149


G.2 Beam shaped FB

The first layout tested here is the beam shaped FB. This breakwater is designed for waves

coming from the segment SE to NW. Considering the symmetry of the breakwater, the only

directions that needed to be studied here were SW, WSW, W, WNW, and NW. Table G.2

summarizes the results of these simulations. The resulting plots are presented in figures G.4

to G.8.

Table G.2: Influence of different wave incidence angles for the beam shaped FB


N 1,30 0,40 S 0,40 0,56

NNE 1,20 0,50 SWS 0,40 0,40

NE 1,20 0,50 SW 0,35 0,40

ENE 1,20 0,50 WSW 0,40 0,40

E 1,30 0,68 W 0,40 0,40

ESE 1,20 0,80 WNW 0,45 0,40

SE 0,90 0,80 NW 0,90 0,37

SSE 0,45 0,68 NWN 1,20 0,40

Figure G.4: Beam shaped FB - Wave direction: SW

150


Figure G.5: Beam shaped FB - Wave direction: WSW

Figure G.6: Beam shaped FB - Wave direction: W

151


Figure G.7: Beam shaped FB - Wave direction: WNW

Figure G.8: Beam shaped FB - Wave direction: NW

152


G.3 L/150/150

The first L shaped layout that is studied, is a symmetrical configuration with both legs mea-

suring 150 m. Detailed results are presented in table G.3.

Table G.3: Inlfuence of different wave incident angles for the symmetric L shaped FB 150x150


N 0,40 0,40 S 0,40 0,56

NNE 0,50 0,50 SWS 0,30 0,40

NE 1,30 0,50 SW 0,25 0,40

ENE 1,50 0,50 WSW 0,15 0,40

E 1,70 0,68 W 0,15 0,40

ESE 1,50 0,80 WNW 0,15 0,40

SE 1,30 0,80 NW 0,25 0,37

SSE 0,50 0,68 NWN 0,30 0,40

Detailed contour plots are shown in figures G.9 to G.19

Figure G.9: L/150/150 - Wave direction: SW

153


Figure G.10: L/150/150 - Wave direction: WSW

Figure G.11: L/150/150 - Wave direction: W

154


Figure G.12: L/150/150 - Wave direction: NWW

Figure G.13: L/150/150 - Wave direction: NW

155


Figure G.14: L/150/150 - Wave direction: NWN

Figure G.15: L/150/150 shaped FB - Wave direction: N

156


Figure G.16: L/150/150 - Wave direction: NNE

Figure G.17: L/150/150 - Wave direction: NE

157


Figure G.18: L/150/150 - Wave direction: ENE

Figure G.19: L/150/150 - Wave direction: E

158


G.4 L/150/100

In this chapter, the results for the MILDwave simulations with an asymmetrical L shape are

documented.

Table G.4: Inlfuence of different wave incident angles for the asymmetric L shaped FB


N 0,50 0,40 S 0,40 0,56

NNE 1,00 0,50 SWS 0,30 0,40

NE 1,30 0,50 SW 0,25 0,40

ENE 1,30 0,50 WSW 0,15 0,40

E 1,40 0,68 W 0,20 0,40

ESE 1,50 0,80 WNW 0,30 0,40

SE 1,00 0,80 NW 0,35 0,37

SSE 0,50 0,68 NWN 0,35 0,40


159




160


Figure G.23: L/150/100 - Wave direction: NWW

Figure G.24: L/150/100 - Wave direction: NW

161



Figure G.26: L/150/100 - Wave direction: N

162




163


Figure G.29: L/150/100 - Wave direction: ESE

Figure G.30: L/150/100 - Wave direction: E

164


G.5 L/100/100

The final L shaped FB is a symmetrical layout, with both legs measuring 100 m. The results

of the MILDwave simulations are presented here.

Table G.5: Inlfuence of different wave incident angles for the symmetric shaped FB 100x100


N 0,45 0,40 S 0,45 0,56

NNE 0,60 0,50 SWS 0,35 0,40

NE 1,20 0,50 SW 0,35 0,40

ENE 1,40 0,50 WSW 0,20 0,40

E 1,50 0,68 W 0,20 0,40

ESE 1,40 0,80 WNW 0,20 0,40

SE 1,20 0,80 NW 0,35 0,37

SSE 0,60 0,68 NWN 0,35 0,40


165




166



Figure G.35: L/100/100 - Wave direction: N

167




168


G.6 U shaped FB

This section contains the results of the MILDwave simulations performed for a FB layout with

a U-shape. The parallel sides each measure 100 m, and the longitudinal side has a length of

155 m. Table G.6 contains detailed results of these simulations. Figures G.38 to G.44 show

the contour plots for each simulation. When these plots are not clear enough, a detail of the

coloured basin plot is added.

Table G.6: Inlfuence of different wave incident angles for the U shaped FB


N 0,15 0,40 S 1,00 0,56

NNE 0,20 0,50 SWS 0,50 0,40

NE 0,35 0,50 SW 0,35 0,40

ENE 0,50 0,50 WSW 0,20 0,40

E 1,00 0,68 W 0,15 0,40

ESE 1,10 0,80 WNW 0,15 0,40

SE 1,30 0,80 NW 0,10 0,37

SSE 1,10 0,68 NWN 0,15 0,40

Figure G.38: U shaped FB - Wave direction: SW

169


Figure G.39: U shaped FB - Wave direction: NW

Figure G.40: U shaped FB - Wave direction: NE

170


Figure G.41: U shaped FB - Wave direction: ENE

Figure G.42: U shaped FB - Wave direction: E

171


Figure G.43: U shaped FB - Wave direction: ESE

Figure G.44: U shaped FB - Wave direction: SE

172

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176


List of Figures

1.1 General approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Seadrome (Armstrong, 1929) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Bombardon Floating Breakwater (Martin, 2004) . . . . . . . . . . . . . . . . . 7

2.3 Semi-submersible structure (Minnes, 2003) . . . . . . . . . . . . . . . . . . . . . 8

2.4 Mega float structure (Watanabe et al., 2004) . . . . . . . . . . . . . . . . . . . 9

2.5 Tension leg platform (Siddiqui and Ahmad, 2001) . . . . . . . . . . . . . . . . 10

2.6 Catamaran floating breakwater . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.7 Dual pontoon floating breakwater . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.8 Mat floating breakwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.9 Aframe floating breakwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.10 Tethered floating breakwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.11 Diffraction process (US Army, 1984) . . . . . . . . . . . . . . . . . . . . . . . . 14

2.12 Transmission process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.13 Six independent motions of a freely floating structures (Ardakani and Bridges,

2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.14 Model Gesraha (2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.15 Models Pena et al. (2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.16 Breakwater Layout Nakamura et al. (2003) . . . . . . . . . . . . . . . . . . . . 18

2.17 Martinelli Layout: I-shapes and J-shape (Martinelli et al., 2008a) . . . . . . . 19

2.18 Hydrodynamic mass-spring system (Fousert, 2006) . . . . . . . . . . . . . . . . 21

3.1 Storm demands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 Wave rose (probablity of non exceedance) . . . . . . . . . . . . . . . . . . . . . 27

177

List of Figures

3.3 Directional significant wave height (m) . . . . . . . . . . . . . . . . . . . . . . . 29

3.4 Influence threshold value - northern direction . . . . . . . . . . . . . . . . . . . 30

3.5 Table of occurrence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.6 Extreme water levels (IMDC, 2005) . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.7 Thorntonbank North current forecast MUMM . . . . . . . . . . . . . . . . . . . 33

3.8 Extreme value distribution for the wind speed (IMDC, 2005) . . . . . . . . . . 34

4.1 OWA support vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Six degrees of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.1 Diffraction process (US Army, 1984) . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2 Definition of the parameters in equatino 5.5 . . . . . . . . . . . . . . . . . . . 43

5.3 Transmission coefficient for rigid, rectangular surface barrier, L/d = 1.25 (Jones,

1971) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44


1971) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44


1971) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.6 Comparison equation 5.6, 5.8, 5.10. T = 9 s, h = 12 m, d = 30 m . . . . . . . . 46

5.7 Tolba (1999). Restrained body. D/d = 1/6, Hi/L = 0,014-0,048, B/d = 1/2 . 47

5.8 Koutandos et al. (2005) Ct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.9 Sketch of the preliminary design . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.1 Preprocessor MILDwave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.2 Calculator MILDwave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.3 Homogeneous model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.4 Non homogeneous model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.5 Contour plot MILDwave model, Tolba testcase, model with heterogeneous S . . 56

6.6 Results MILDwave model, Tolba testcase . . . . . . . . . . . . . . . . . . . . . 57

6.7 Results MILDwave model, Koutandos testcase . . . . . . . . . . . . . . . . . . 58

6.8 Results MILDwave model, Nakamura testcase . . . . . . . . . . . . . . . . . . . 58

7.1 Input MILDwave preliminary design . . . . . . . . . . . . . . . . . . . . . . . . 61

178

List of Figures

7.2 MILDwave: contour plot of the preliminary design . . . . . . . . . . . . . . . . 61

7.3 Results for the beam shaped floating breakwater. —: CMILDwave, - - -: Cmax . 64

7.4 Reflection in the case of the beam shaped FB . . . . . . . . . . . . . . . . . . . 64

7.5 Results for L/150/150. —: CMILDwave, - - -: Cmax . . . . . . . . . . . . . . . . 66



7.8 Comparison L/150/150, L/150/100, and L/100/100 . . . . . . . . . . . . . . . 70

7.9 Comparison L/150/150, L/150/100, and L/100/100 for the NNE direction . . 70

7.10 Results for the U shaped FB. —: CMILDwave, - - -: Cmax . . . . . . . . . . . . . 71

7.11 Comparison between L/100/100 and the U-shaped FB layout . . . . . . . . . . 72

7.12 Reflection in the case of the U shaped FB, direction SE . . . . . . . . . . . . . 73

7.13 Comparison between the beam shaped FB, L/100/100, and U-shaped FB . . . 75

8.1 Definition angle of incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

8.2 RAO modulus - Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

8.3 RAO modulus - Roll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

8.4 RAO modulus - Heave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

8.5 Definition sketch of a moonpool . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

8.6 Definition sketch of a skirt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

9.1 Regions of applicablity according to Deo (2007) . . . . . . . . . . . . . . . . . . 87

9.2 Wave force per meter in depth . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

9.3 Wave pressure distribution on an upright section of a vertical breakwater (Goda,

2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

9.4 Wave pressure distribution on the FB . . . . . . . . . . . . . . . . . . . . . . . 91

9.5 Wave force on one pile in function of time . . . . . . . . . . . . . . . . . . . . . 95

9.6 Forces acting on one pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

9.7 Lateral bearing capacity (De Vos, 2008) . . . . . . . . . . . . . . . . . . . . . . 98

9.8 Heave Floating Breakwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

10.1 Non homogeneous model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

10.2 Comparison between the beam shaped FB, L/100/100, and U-shaped FB . . . 104

179

List of Figures

A.1 Concessions Belgian coast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

C.1 Cumulative wave height - direction N . . . . . . . . . . . . . . . . . . . . . . . . 117

C.2 Cumulative wave height - direction NNE . . . . . . . . . . . . . . . . . . . . . . 118

C.3 Cumulative wave height - direction NE . . . . . . . . . . . . . . . . . . . . . . . 118

C.4 Cumulative wave height - direction ENE . . . . . . . . . . . . . . . . . . . . . . 119

C.5 Cumulative wave height - direction E . . . . . . . . . . . . . . . . . . . . . . . . 119

C.6 Cumulative wave height - direction ESE . . . . . . . . . . . . . . . . . . . . . . 120

C.7 Cumulative wave height - direction SE . . . . . . . . . . . . . . . . . . . . . . . 120

C.8 Cumulative wave height - direction SSE . . . . . . . . . . . . . . . . . . . . . . 121

C.9 Cumulative wave height - direction S . . . . . . . . . . . . . . . . . . . . . . . . 121

C.10 Cumulative wave height - direction SWS . . . . . . . . . . . . . . . . . . . . . . 122

C.11 Cumulative wave height - direction SW . . . . . . . . . . . . . . . . . . . . . . 122

C.12 Cumulative wave height - direction WSW . . . . . . . . . . . . . . . . . . . . . 123

C.13 Cumulative wave height - direction W . . . . . . . . . . . . . . . . . . . . . . . 123

C.14 Cumulative wave height - direction NWW . . . . . . . . . . . . . . . . . . . . . 124

C.15 Cumulative wave height - direction NW . . . . . . . . . . . . . . . . . . . . . . 124

C.16 Cumulative wave height - direction NWN . . . . . . . . . . . . . . . . . . . . . 125

D.1 H1/3 North to East . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

D.2 H1/3 East to South . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

D.3 H1/3 South to West . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

D.4 H1/3 West to North . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

E.1 Wiegel Diagram head on waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

E.2 Goda Diagram head on waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

F.1 Results MILDwave model, Tolba testcase, Model with S = 0,94 . . . . . . . . . 135





180

List of Figures


F.7 Results MILDwave model, Tolba testcase, Heterogeneous model . . . . . . . . . 138

F.8 Results MILDwave model, Koutandos et al. (2005) testcase, Model with S = 0,94139






F.14 Results MILDwave model, Koutandos et al. (2005) testcase, Heterogeneous model142

F.15 Results MILDwave model, Nakamura et al. (2003) testcase, Model with S = 0,94143






F.21 Results MILDwave model, Nakamura et al. (2003) testcase, Model with varying S146

G.1 FB length 100m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

G.2 FB length 150m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

G.3 FB length 200m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

G.4 Beam shaped FB - Wave direction: SW . . . . . . . . . . . . . . . . . . . . . . 150

G.5 Beam shaped FB - Wave direction: WSW . . . . . . . . . . . . . . . . . . . . . 151

G.6 Beam shaped FB - Wave direction: W . . . . . . . . . . . . . . . . . . . . . . . 151

G.7 Beam shaped FB - Wave direction: WNW . . . . . . . . . . . . . . . . . . . . 152

G.8 Beam shaped FB - Wave direction: NW . . . . . . . . . . . . . . . . . . . . . . 152

G.9 L/150/150 - Wave direction: SW . . . . . . . . . . . . . . . . . . . . . . . . . . 153

G.10 L/150/150 - Wave direction: WSW . . . . . . . . . . . . . . . . . . . . . . . . 154

G.11 L/150/150 - Wave direction: W . . . . . . . . . . . . . . . . . . . . . . . . . . 154

G.12 L/150/150 - Wave direction: NWW . . . . . . . . . . . . . . . . . . . . . . . . 155

G.13 L/150/150 - Wave direction: NW . . . . . . . . . . . . . . . . . . . . . . . . . 155

181

List of Figures

G.14 L/150/150 - Wave direction: NWN . . . . . . . . . . . . . . . . . . . . . . . . 156

G.15 L/150/150 shaped FB - Wave direction: N . . . . . . . . . . . . . . . . . . . . 156

G.16 L/150/150 - Wave direction: NNE . . . . . . . . . . . . . . . . . . . . . . . . . 157

G.17 L/150/150 - Wave direction: NE . . . . . . . . . . . . . . . . . . . . . . . . . . 157

G.18 L/150/150 - Wave direction: ENE . . . . . . . . . . . . . . . . . . . . . . . . . 158

G.19 L/150/150 - Wave direction: E . . . . . . . . . . . . . . . . . . . . . . . . . . . 158




G.23 L/150/100 - Wave direction: NWW . . . . . . . . . . . . . . . . . . . . . . . . 161

G.24 L/150/100 - Wave direction: NW . . . . . . . . . . . . . . . . . . . . . . . . . 161


G.26 L/150/100 - Wave direction: N . . . . . . . . . . . . . . . . . . . . . . . . . . . 162



G.29 L/150/100 - Wave direction: ESE . . . . . . . . . . . . . . . . . . . . . . . . . 164

G.30 L/150/100 - Wave direction: E . . . . . . . . . . . . . . . . . . . . . . . . . . . 164





G.35 L/100/100 - Wave direction: N . . . . . . . . . . . . . . . . . . . . . . . . . . . 167



G.38 U shaped FB - Wave direction: SW . . . . . . . . . . . . . . . . . . . . . . . . 169

G.39 U shaped FB - Wave direction: NW . . . . . . . . . . . . . . . . . . . . . . . . 170

G.40 U shaped FB - Wave direction: NE . . . . . . . . . . . . . . . . . . . . . . . . 170

G.41 U shaped FB - Wave direction: ENE . . . . . . . . . . . . . . . . . . . . . . . 171

G.42 U shaped FB - Wave direction: E . . . . . . . . . . . . . . . . . . . . . . . . . 171

G.43 U shaped FB - Wave direction: ESE . . . . . . . . . . . . . . . . . . . . . . . . 172

182

List of Figures

G.44 U shaped FB - Wave direction: SE . . . . . . . . . . . . . . . . . . . . . . . . . 172

183

List of Tables

3.1 Directional H95% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Directional probability of occurrence (m) . . . . . . . . . . . . . . . . . . . . . 28

3.3 Directional significant wave height (m) . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Summary peak wave periods (IMDC) . . . . . . . . . . . . . . . . . . . . . . . . 31

3.5 Hydraulic boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1 OWA support vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 Motion Criteria (Pianc, 1995) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1 Hydraulic boundaries: case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Dimensions experiments Tolba (1999) . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 Analytical results testcase Tolba . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.4 Dimensions experiments Koutandos et al. (2005) . . . . . . . . . . . . . . . . . 48

5.5 Analytical results testcase Koutandos et al. (2005) . . . . . . . . . . . . . . . . 49

5.6 Dimensions experiments Koutandos et al. (2005) . . . . . . . . . . . . . . . . . 49

5.7 Analytical results testcase Nakamura et al. (2003) . . . . . . . . . . . . . . . . 49

5.8 Boundary conditions preliminary design . . . . . . . . . . . . . . . . . . . . . . 51

5.9 Dimensions preliminary design . . . . . . . . . . . . . . . . . . . . . . . . . . . 52


7.2 Influence of the floating breakwater length . . . . . . . . . . . . . . . . . . . . . 62

7.3 H95% per direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

7.4 Influence of different wave incidence angles for the beam shaped FB . . . . . . 63

7.5 Inlfuence of different wave incident angles for the symmetric L shaped FB 150x150 65

184

List of Tables

7.6 Inlfuence of different wave incident angles for the asymmetric L shaped FB . . 67

7.7 Inlfuence of different wave incident angles for the symmetric shaped FB 100x100 68

7.8 Inlfuence of different wave incident angles for the U shaped FB . . . . . . . . . 71

8.1 Motion Criteria (Pianc, 1995) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

9.1 Parameters for wind and current force calculation . . . . . . . . . . . . . . . . . 84

9.2 Dimensions Heave FB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

9.3 Parameters for wind and current force calculation . . . . . . . . . . . . . . . . . 85

9.4 Wind and current load calculation . . . . . . . . . . . . . . . . . . . . . . . . . 85

9.5 Parameters for wave load calculation . . . . . . . . . . . . . . . . . . . . . . . . 89

9.6 Wave pressures according to Goda . . . . . . . . . . . . . . . . . . . . . . . . . 92

9.7 Results wave force calculation according to Chakrabarti and Goda . . . . . . . 92

9.8 Total force acting on the FB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

9.9 Total force acting on one pile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

9.10 Forces on heave floating breakwater . . . . . . . . . . . . . . . . . . . . . . . . 96

9.11 Pile properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99


E.1 Hydraulic boundaries case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

F.1 Dimensions experiments Tolba (1999) . . . . . . . . . . . . . . . . . . . . . . . 134

F.2 Dimensions experiments Koutandos et al. (2005) . . . . . . . . . . . . . . . . . 139

F.3 Dimensions experiments Koutandos et al. (2005) . . . . . . . . . . . . . . . . . 143

G.1 Results MILDwave simulations to study the FB length . . . . . . . . . . . . . . 148

G.2 Influence of different wave incidence angles for the beam shaped FB . . . . . . 150

G.3 Inlfuence of different wave incident angles for the symmetric L shaped FB 150x150153

G.4 Inlfuence of different wave incident angles for the asymmetric L shaped FB . . 159

G.5 Inlfuence of different wave incident angles for the symmetric shaped FB 100x100 165

G.6 Inlfuence of different wave incident angles for the U shaped FB . . . . . . . . . 169

185

Floating BW

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