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FLOATING BREAKWATERS PREDICTING THEm PERFORMANCE

BY

@BRADLEY J. MOREY, B.ENG.

A THESIS SUBMITTED TO THE SCHOOL OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE

REQUIREMENTS FORTHE DEGREE OF MASTER OF ENGINEERING

FACULTY OF ENGINEERING

AND

APPLIED SCIENCE MEMORIAL UNIVERSITY OF NEWFOUNDLAND

JANUARY, 1998

ST.JOHN'S NEWFOUNDLAND CANADA

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ABSTRACT

Current environmental and financial restrictions on harbour developments dictate that alternatives to traditionalfixedrubble mound and caisson breakwaters arerequired.The most common solution is theFloating Breakwarer.a concept which utilizes reflection.

dissipation, and/or transformation to reduce incident wave energy. The design and construction of these for exposed coastal regions present major engineering challenges.

Theprimaryobjective ofthisthesis

was

to develop a comprehensive design rationale to enable the designerpredictlocal wave climate (exceedance probabilities, design spectra), optimize a breakwater design (suuctural parameters, mooring~ems)andestimate costs.

To facilitate this a number of aspects

were

reviewedincluding methods utilizedin predicting the wind-wave climate in fetch funited regions. designcriteriafor inner harbour wave climates. and performance prediction techniques. Based on this review the author developed a simplified deterministic approach to perfonnance prediction based on dimensionalandregressionanalysisof moodtest data..Thisinformation

was

combined into a computer simulalion to predict thelocalwave climate, optimize the nearing breakwater size, design the mooring system, and detennine the cost effective solution.

ACKNOWLEDGEMENTS

I would like to takethisopportunity tothankDr. A.B. Cammaert (co-supttvisor), forhis assistance,guidanceand moral support throughout my studies; Dr. 1.1. Sharp (co- supervisor) for his assistanceinmy studies; Dr. L. Lye forhiscontinued guidance;Mr.G.

Frampton. Mr. Claude Burry,Mr.D. Blundon.andMr.F. Huxter fortheirinterest and assistanceinmy work;andfinally my fellow graduate students and university staff who supported meinmystudies.

No amount of gratitude can repay my wife, who has made many sacrifices sothatI may continue and complete my studies. This thesis is dedicated and truly belongs to her.

CONTENTS

ABSTRACT... . . i

ACKNOWLEDGEMENTS .. . ii

LIST OF RGURES... . vi

LIST OF TABLES .. vii

llST OF SYMBOLS... . _ viii

Chapter I

WIRODUCTION _ I

1.\ Overview,... . _ 1

1.2 Scope... . 2

Chapter 2

STATE OF TIlE ART REVIEW... . .4

2.1 Overview... . _..4

2.2 Classification 9

2.2.1 Reflection.. . 10

2.2.2 Transformation.. . 10

2.2.3 Dissipation... . 11

2.2.4 Hybrid.... . 13

2.3 Nomenclature... .. 14

2.4 Mooring Systems... . 16

2.4.1 Anchors... . 16

2.4.2 Cables... .. 18

2.4.3 Hardware.... 19

2.4.4 Patterns... . 20

2.5 Prototype lnstallations... .. 21

Chapter3

WIND WAVE PREDICTION ...

3.1 WIndClimate Analysis ...

3.1.1 Elevation Correction . 3.l.2 Stability Correction . 3.U Location Correction . 3.1-4 DragCorrection ...

3.2 Wave ClimatePrediction ..

3.2.1 Fetch Limited Climate ...

3.2.2 Duration Limited Climate ....

Chaptet4

PERFORMANCE ANAl.YSIS ...

4.1 Prediction Techniques...

iii

.. 23

. _23

. 25

.. .. 25 ..26

. 28

. 28

. 30

. 31

. 32 .. 32

4.1.1 Previous Experience...•...33

4.1.2 Analytical Methods .. . 34

4.1.3 Numerical Methods.... . 35

4.1.4 Fidd Trials... . 35

4.1.5 LaboruoryTesting... . 36

4.2 Dimensional Regression Technique... . 36

4.2.1 Parametric Revicw.. . 37

4.2.2 DimensionalAnalysis _ 40

4.2.3 Modd Analysis _ _ 43

4.2.4 Multiple Regression.. . 44

4.2.2 RegressionResults... . .48

4.3 PerfOnnanceCriteria... . 52

Chapter 5

PROBABILISTIC MODEL... . 55

5.1 WIlId-WaveClirnate 55

5.1.1 WrndClimate 57

5.1.2 Wave Climate... . 58

5.1.3 ProbabilisticSummary... ..58

5.2 Performance Analysis.. . . .. 59

5.2.1 GeometricStiffness.... ..59

5.2.2 Structural Parameter1... . 59

5.3 ExampleSimulatiOtl... . _ 62

Chaptcr6 CONCLUSIONS ...

REFERENCES_ ...

AppendixA MODEl.. TEST DATA

. 65

. .. _ 68

iv

LIST OF FIGURES

Figure2.1 Figure2.la.

Figure2.2b Figure 2.3 Figure2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure2.8 Figure 2.9 Figure2.10 Figure3.1 Figure 3.2 Figure3.]

Figure4.1 Figure4.2 Figure4.3 Figure4.4 Figure 4.5 FigureS.l FigureS.2

Reid's floating Breakwater 6

loly's Floating Breakwater _ 6

loly's Floating Breakwater .. . . 7

Bombudon Floating BreaJcwater _ 7

A·fram.e Floating Breakwater.. . . 11

Alaskan Floating Breakwater.. . _ 12

Goodyear TU"e Floating Breakwater _ IJ

Screen Rdlector floating Brealcwater 14

Floating BreakwaterNome:nclan.are . 15

Cable Mooring System .. . . 17

Spread Mooring Panem. 21

Rayleigh Cumulative Probability Distributions forWtndspeed. 24 StabilityRatio.Rr^(ResioandVmcent, 1977)... . 27 LocationRatio,Rr(ResioandVtncent, 1971) . 27

Catenary Mooring System.. .. . 40

Caisson Data Summary... . . 44

Measured versus Predicted CT (Logarithmic Model) 50 Standardized Residuals versus Measured CT(Logarithmic Model) " 50 measured versusPredictedCT.. . _... . 51

Wtnd -WavePrediction Algorithm . 56

Performance Analysis Algorithm 61

LIST OF TABLES

Table 2.1 Table 2.2 Table2.3 Table4.1 Table4.2 T1ble4.3 Table 4.4 Table 5.1 Table 5.2 Table 5.3 Table 5.4

Roating Breakwater Classification... . _ 9

Floating Breakwater Nomenclature 15

InstallationtypeSummary... . 22

Intrinsically Linear functions (Devore. 1987)... . 45 SCH Exceedance Criteria (Eastern Designers limited. 1991) 53 Atria Engineering Exceedance Criteria (Fournier etaI.• 1993) 53 OERC Exceedance Criteria (Morey and Cammaen. 1995) ... . ... 54

Dildo Data Summary ... . 62

Exceedance Dinnbution... . _... . . 63

Storm Design Conditions... . __ 63

BreaJcwattt Cost Optimization... . .. . 64

LIST OF SYMBOLS a - regression constant

Po -

regression coefficient 4X - structure displacement (m)

&, --residual

£s - smearing estimate

" " = density of water (1025 kglm^J)

Bs=strueturewidth(m) Ce "'"mooringcablecostperlength($1m) Cr - tnnsmissioncoefficient Ds~strueturedraft (m) Dill' - average water depth over fetch(m) F, - leewarda:nchorline'spretension (N) FJ - seaward anchorline's pre-tension (N) FJ- leeward anchorline's force (N) F4- seaward anchorline's fon:e (N) FA - applied extemal fon:e (N) g - gravitational constant (9.81 m1si He - hoUow caissoncosts($1m)

vii

HI ..incoming wave height (m) Hs:=significant wave height (m) Hr ..transmitted wave height(m) K" ...wave number Lc=mooring cable length (m) L" ""wave length (m) Ms ""structure mass per length (kglm) n:=number ofdatapoinu Mol=numberof mooring lines Pu "" probability ofwind speed V{O-I)

R,z:location amplificationratio Rr

=

stability ampliticarionratio

T,.

:=limitingduration {s}

T,:=peak wave period(s) Ts ""structure sidesway period (s) Tw ""wave period{s}

V - predicted stonn wind speed (mls) Va,=wind speed at 10m elevation (mls) VA=adjusted wind speed (mls) UJ,l ""mean wind speed(mls) Vr ...windspeed adjusted for stability (mls) Vr:=windspeed overwar.er (mls)

Ux "" predicted stonn wind speed (mfs)

Y ..dependent variable YI =v~caJdistance (m) X·fetcl>(Ian)

XI '"original horizontal distance (m) Xl=new horizontal distance (m) X& ..effective fetch (Ian) X. - iodependeot variable

We '""submerged anchorline unit weight(NIm) Z "" anemometer beight (m)

Chapter 1 INTRODUcnON

1.1 Overview

Current environmentalandfinancialrestrictions on harbour developments dictate that alternatives to traditional fixedI1lbble~moundandcaisson brealcwaters are essential to thefutureofcoastal engineering. The Floating BnakwaJeris one such alternative. a concept which utilizes reflection, dissipation and/or transfonnation to reduce wave energy and therefore attenuating incident waves to an acceptable level.

Floating breakwaterscanactasthe primary source of wave protection or supplemental protection where partial shelterisafforded byotherbarrimsuchasreefs.

shoals and traditional fixed structures. Insta.Uation sites include small craft harbours, marinas, yacht clubs., aquaeu1tunJ facilities, industrial waterfronts. and recreational areas.

During ecological emergencies. marine construction,militaryapplications. and special socia1Irecreationai events a temporary structure could prove verybeneficial...

With respect to fixed rubble mound struewres. floating breakwatenpos.sessa number ofdistinct advantages. These include lower capital cost, shaner construction time,suitabilityfor deep watersites.rninimaIimpact on water circulation and marine habitat, accommodation for a variety of bottom conditions.and effective perfonnance where largetidalvariation exists. Some disadvantages include the limitation to short fetches, shoner service life (10 - 20 yeus)and. a portion ofme incident wave is transmitted..

Theengineering involved in the de$ign ofOoating breaJcwaten for exposedcoastal.

regions present major challenges.Inputicular. the forecasting of wave heights and periods ina fetch limited environment and predicting the peri'ormance of a given floating breakwater system are especially rigorous. With recent advances in the use of probabilistic computer models. thisa.n.aIysis canbecompletedina more cost andtime effective manner.

1.2 Scope

The objectives of this thesis allow for an overall assessment of floating breakwater technologyinan effort to develop a probabilistic computer model suitable for preliminary designpurposes.These objectives include the following:

A review of the state of the art in floating breakwater technology. This includes a disawion of the cJassification of floating breakwaters, a summary of mooring systems, and an analysis of existing installations.

Review of methods utilisedinpredicting the wind-wave climateinfetchlimited regions in

an

eJfon to develop

a

deterministic technique to produce thedatarequired to assess floating brealcwater performance.

Review ofcurrent floating brealcwater pttformance prediction techniques and develop a simplified determi.nistic model capable of estimating the struetunl and mooring parameters.

Develop a probabilistic software model to estimate the local wind-wave climate, evaluate 80ating breakwater performance. optimizethestructural parameters. and estimate the costs.

A demonstration ofthe programs capabilities is included by way ofa case study. A current installation site at Dildo, Newfoundland

was

evaluated to determinethelocal wind-wave climate, optimize the floating breakwater system, and determine the most cost- effective solution.

Chapter2 INTRODUCTION

2.1 Overview

Thefirstdocumented example ora floating breakwater

was

recordedin1811.

ProposedbyGeomJBentham.,the Civil Architect of Her Majesty's Royal NavyinGreat Britain, the structure was to provide shelter for the British. fleet at Plymouth. The system wasto consist of 111wooden.triangularfloatingframes.each 18.3 minlength, 9.2 min width and 9.2 m in height., moored with iron chains (Readshaw, 1981)

In1841,thisissue offtoatingbreakwaterswasagain raisedby Captain Taylor of Her Majesty'sRoyalNavy. He proposedthattreated 80ating wooden timber sections of 4.9mdraft and 2.1 m freeboard when connected to piles would provide a measurable degr~ofproteerion(Readshaw.1981).

Once againin 1842. reference to -Reid'sK floating attenuation system was included in theCivil EngineersandArchitectsJournal(1842).Thebreakwater(Figure2.1) consisted of an archedtimbeTframe,witha sloping timber ramp on which the waves

would break. The width of the structure

was

6.1m.timbers 0.6 msquarewere used for framing. and the total length ofa single unit was 18.3 meters. The slopingbeachangled downward at a35·angle with a projected depth of4.6 m. Iron chain was utilized as mooring lines, although problems with the mooring arrangement were anticipated. There is no record of Reid's breakwater ever being built

fn a1905presentation to the Royal Dublin Society entitled "00 Floating Breakwaters", Ioly proposed two floating breakwater concepts (Figures 2a and 2b) for the eastcoast ofIreJ.aod (Joly,1905).The designs were to take adViUltage of the added mass of water enclosed within the walls of mesyst~providing a relatively stiffand unresponsive structure to the ocean waves. Although this system was never constructed, it roused interestinthe concepts oftloating breakwaters,

Funher experiencewasreportedin1941 at LyseIcil. Sweden,wherea 120 m long Ooating concrete breakwater was built for a small cnUls harbour (WCHL, 1981). The eatamannsystem was constructed fromrectangu1arconcrete sections 4.5 m square.

Indications are that during its service the system perfonned satisfactorily.

Onlyminimaleffons were expended on floating brealcwatersuntilthe Normandy Invasion of World War ITin1948, when a floating systemwasrequired to protect the off·

loading area for soldiers and supplies. Referred to as the~Bomba.rdon~.the system (Figure 2.3) was of a simple crucifix cross-section 61 m in length with overall cross dimensions of9 m by9 m(Jellet,1948). The systemwasdesigned towithstandwaves withheights of] m and periodsinthe range of5to 6 s. Preliminary,fullscale.trial sectionsweretested indicating an efficiency in the range of 50 - 70"/0 (Todd, 1948).

Figure 1.1: Reid's Floating Breakwater

'Wo. ter Level

~/~ ~/ ^{. 'WATER~.}

^.

Figure 1.1.: Joly's Roating Breakwater

: [ ] : : . : : ::: 'w'oter Level - - - ; { : AIR ::

.. . .

..

~ ^..• ~

Figure 2.2b: Ioly's Floating Breakwater

Fipre 2..3: Bombardon Floating Breakwater

Duringthe 1970's., there was an explosion of the technologyin whicha lacge number of floating breakwaterswereconstructed to protectmarinasand smallcraft facilities. Thenwnberandvariety of designsincreaseddramatically andin1974. thefirst conference on floating breakwaters was held at the University of Rhode Island (Kowalski.

1974).In1981. a second 80atingbreakwater conference was held at the University of Washington (Nece and Richey, 1981).

There havebeen threesignificant publicatiom concerning floating breakwaters in the pastISyears.Thefirstwas by Lyndell Z. Hales, published in 1981. Sponsored by the U.S. WaterwaysExperiment Station(WES)inVicksburg.Mississippi. this study prov;ded detailed information pertaining to a literature review (142 references).adescription and classification of floating breakwater configurations. and a detailed description of previous model investigations.

The second was conductedbythe WesternCanadianHydraulics Laboratory (WCHL).alsopublished in 1981. Sponsored by the Canadian Depanment of Fisheries andOceans.,thisstudy also providedadetailed lite:rature review (266 references).

description and cla.s.sifications of breakwaters and detailed descriptiom of previous model investigations. One important aspect covered inthisreponwasa summaryof current field installations around the world.

The most recent and extensive StUdy

was

conducted by theOceanEngineering ResearchCentre (OERe) at Memorial University of Newfoundland. A joint project sponsored by the Department ofFisberiesand

Oceans.

Public WorksandGovernment Services Canada. and Fisheries, Food and Agriculture Newfoundland. A database of more

than 800 references. an extensivesurveyof floating breakwater sites worldwide.and a summary of previous experimental results were the most significant results of the study.

These reporn have summarized current breakwater technology to a considerable extent.

2.2 Classification

Floating breakwater systemsreduceincident wave heights through the conversion of wave energyvia reflection, tranSformation and dissipation.1bcseenergy reduction methodscan actinasingular natuee orina combination of one, two, orall threemodes.

The author suggests that the mosteffectiveapproach for classification would involve separating systems by these three methods of wave anenuation, as shown in Table 2.1.

Table 2.1:Floating Breakwater Classific.ation

Classification

A·_

""'" I

"""""

Hollow C o r _

A'i

LogRaftlBWld1c

Gcody<~

-..-

w_~

Pol~-tin

I

T""""'FIoo<

I

Ttubuleoce Geaentor AaJble Membrue

I

Slopi.ngAoat

"""'''''''''''' I

Cenueboard

I cmsoo

2.2.1 Rdlectioa

Reflective breakwaters utilize large vertical orinclinedsurfaces to reflect incoming wave energy back out tosea.Efficiencyismost sensitive to incident wave height and period,depth and angle ofthereflectingsur&ceandtheoverallstruetw'estability.

Adequate stability is provided by a verystiffmooringsystem. Insome

cases.

wave energy maybetransformed intosecondarywavetrains(Eastern Designersand Company Limited (EDCL), 1991). Typical design concepts includetheA-FrameandOffset.

TheA-frame (Figure 2.4) was developedand hasbeenusedex:teasivelyinBritish Columbia. A centerboard (timber)hasbeencombined with stabilizers (steel, plastic, or wood) and framingmembers(steel) to developalarge moment of inertiaas analternative to increasingmass(RicbeyandNece, 1974).Benefits ofthiJsysteminclude its light weigbt andsimplistic design. Thedrawbacksare corrosion of steel frames, damage to end~throughcoUisions with other modules causing loss of buoyancy,and a high cost.

2.2.1 Transfonnarioa

Transformation breakwaters convert incident wave energy through induced motion response into secondary wavetrainsof various beights andperiods.Highestefficiencies occur when these secondary transmitted wave trains are out of phase with the incident waves. Attenuationisinfluenced bymass.natural periods of motion..and stnIeture width to wave length

(Wan..

1981).The degree of restraint afforded by the anchoring system is not as crucial to performance as the reflective brea.lcwa1ers(EOCL. 1991). Concepts grouped under this attenuation method includeCaissonsandLogRaftsIBundJes

'0

Figure 2.4: A-Frame Floating Breakwater

Atypicalcaisson designisthe Alaskan (Figure 2.5), a double pontoon system constructed from concrete and polystyrene foam. The two large pontoons are held in position using a series of braces to provide additional stiffuessandfloatation.This design is currently usedinseveral harbours along the Alaskan coast.

2.2.3 Dissipation

Dissipative breakwaters conven wave energy into heat, sound, nnbulence or friction by breaking waves on sloping surfaces oragainststructural members.Efficiency is governed primarily through geometry and mooring restraints(WeIn..1981). These have limited useinanenuating waves of any significantheightbuthavebeen used extensivelyin

\I

R~-:

Figure l.S: Alaskan Aoating Breakwater

attenuatingwindgenenuedchop (EDCL. 1991). SystemS includedinthis classification areScrapTir~s.Tt.IMred Floal,Fl~rihle M~mbran~s,andTurbulenceG~neralors.

Themostcommon of these designsisthe Goodyear (Figure 2.6), which uses a modular building-block design of 18 tires boundwithflexible beltingwithovera.lliength, width and beight dimensions of2.0 by 2.2 by 0.8 m respectivdy. Each unit is laid outin.

3-2·)-2·3-2-3 combinationandheld together with unwelded open·link galvanizedchain.

Units are COMected to form a breakwater that is 3. 4 or S units in width. Additional floatationis provided by cast-in-place foam positionedintheaowns oftires.Although these breakwaters are cost effective, they need to be I to 1.5 times the design wave length andconsequently utilize considerable space.

12

PLAN VIE...

Figure 1.6: Goodyear Scrap Tire Floating Breakwater

1.1.4 Hybrid

Thethreewave attenuation mechanisms (reflection. transformation.and dissipation) are to some degree incorporated into each floating breakwater. Some systems rely heavily on a combination of these. These breakwaters arehybrid. applyingwave attenuationmec.hanismssimultaneously and/or successively tobeeffective.The moSt common systems includeSloping Float, Senten ReflecrtJ1',andCenterboard Cai.JSOn.

One of these systems. the screen reflector (Figure 2.7), first dissipates incoming wave energy on a inclined porous surface.Energywhichpasses by andthrough this surface are reflected by a wall. Although the structure does provide bener protection. the costs are usually higher

13

Fipr'f: 1.7: ScreenReflectorBreakwater

2.3 Nomenclature

Asthis design classification indicates, there are a significant number of floating breakwatersystems.Thenomenclature associatedwiththesesystems can often imply a different meaningfoteach type, and a generic set of descriptive tenns which relate to StniCtuTaJ, Mooring.andWowparameters were required.Theauthorhasadopted and modified nomenclature from various sources, primarily Kowalski (1974) and Gaythwaite (1988). These parameters, which relate toStnlcnuaJ. MooringandWawchuaeteristics are depictedinFigure 2.8,and timherdefinedinTable2.2.

14

Figu~2.3: Aoating Breakwater Nomenclature

Table 2.2: Aoating Breakwater Nomenclature SlructuraJ

Bs-width As-l~ngth Ds-draft M s -massll~ngth Ts - sicksway~riod

Moorial I.e -chainlength Me - chainmassIl~ngth

D" -waterdepth Xo - horizontal distance

IS

Wave H, - incoming height HIJ, -r~fl~ct~dheight Hr -transmittedheight

L", -Waw!I~ngth T.. - wme puiod

2.4 Mooring Systems

A mooring synem for a typical floating coastal Stnleture generallyfallsundertwo categories;fixedand cable.Ina fixedsystem.piles develop holding capacity by mobilizing the lateral soil pressureandskinfriction inthesurrounding seafloor material. Their advantageisanabilityto resistbothupliftandlaten.lloads. Unfortunately. they require specializedinstallation equipment andtheirunderwater in.staIlarion, particularly in deep flowing water, isveryexpensive. Inaddition,theirdesign requires detailed geotechnical data tofullpile depth,which isdifficultandex:pensiveto obtain(Tsinker, 1986).

Ina cable system (Figure 2.9), thestructureisconnected to a series of anchors to holdthestructureinposition while allowing some verticalandhorizontal movement. For the above noted reasons, the cable system is predominant in tloating coastal Stnleturcs. A review ofthe cable system componentsis includedinthefollowing sections.

2.4.l Ancllon

Anchors canbebroadly classified according to their primary mode of developing lateralresistance. There arethreebasic categories,whichinclude drag embedment, dead- weight.anddirect embedment..

Drag embedment anchors consists of a number of components which include the shank.shackle., fluke., crown,andstock. Themost commonly utilizedtypesincludethe Navy Stocldess, AC-14, Danforth,andLWT. Each of these anchors have associated with them a -holding efficiency-. defined astheratio ofholdingpower to anchor weight.This holding power is generated by activating shear stresses within the soil in which the anchors

16

Figure 2.9: Cable Mooring System

areembedded (Gaythwaite. 1990). This is governedbythemass of soil displaced (a function of flukeareaand penetration depth)andsoilproperties. Detailed geotechnica.l information isnecessaryto accurately detennine thetypeandmassofanchor. In situations where the anchor placementiscrucial great care mustbe takentoensure there are no obstrUctions on or beneath the sea Boor.

The dead.weight or gravity anchor depends on submerged weight and friction to pro"';de venica.l and horizontal resistance. When the block penetrates the sea floor there is addedresistancefrom suctionincohesive soilsand activepressureingranularsoils.

AdditionallateraI resistance can be obtained utilizingshonneedle piles orprojec:tionscast intothe bloclcs to activate soil resistance. The anchorshapealsohelps to penetn.le the

17

bottomandgain passive resistancewithinthe soil (Gaytbwaite. 1990).Minorinformation pertaining to the type of soilisrequired to adequately estimate soil friction.

Directembedment anchors are forciblydriveninto the bottombypile hammers or propeUants. Stake pilesaredrivm beneath the 800r andcanbea.ce:umelylocatedwhile other anchors are propelled to a certain depth and are set by pulling on the anchorwhich opens the fluke developingresistance(Gaythwaite, 1990). Again, some detailed geotechnical information isnecessaryto accuratdy determine the size of anchor and charge. Any obstrUctions onor justbeneath the sea800r couldcausesevere problems.

1.4.2 Cabla

Cablesare usuallyc1usifiedbymaterialwhich include,rynlMtics, winropeand chain. Inthecaseof deep water, itisa common practice to utilize chainsnearthe attachments, and syntheticlines inbetween.Intheca.seof shallow water, chain has been them&1erialofchoice.

The main typeSof synthetic ropes include nylon, dacron., polypropylene, polyethyiene"andKevlar. Nyionisnotable for its elasticity and energy absorption properties while Dacron is attractive foritsmodest elasticity and range of available sizes.

Specially constrUcted plaited, braided.andpre-stretched ciao-on covecedwithprotective polyvinylchloride or polyethylene jackets arealsoavailable. Two of the more common typesinclude "NolaroM_andMMylar" _ Synthetic lines have demonstrated considerable potential for shorHerm operations, due totheirease ofhandling. Thesetypesof materials are not commonly used for long term floating structure installations.

18

Standard wire rope is constructed from very stron& tough. durable sted.

combininggreat strengthwithhigh fatigueresiswtce. Theyconsist ofwireswound into strands and suandswoundinto ropes. ThetJ1Ost.common typeisaregularleft lay, where the winding of the wires into strands and the strands into rope oppose each other,thw preventingthe:rope from unlaying under tension. Inmarine applications., a electrolytic zinc·plating (two to three times the normal coating) is necessary to protect the wire from rapid weight loss and diameter reduction. Due to corrosion, these areDOtnonnally used ina salt water environment, especially wherehighcurrents are present (Skop. 1988).

Chainisavailableinmanygrades, types., andmateria1s. Ca.st·steel studlinkchain is recommended for sha1Iow water aJ:lchoring as it prevents tangling and twisting.Chain has several advantages over the other cable types. Theseinclude theabilitytobe connected to atanypoint along its length.highabrasion resistance, longevity, and its ability to provide energy absorption fromthe:weightandcatenaryshape. Galvanizingis usually reconunended to increase corrosion resistance. Another approach involves using oversizedchainfor corrosionandutilize the additional weight to deepen the catenary improving energy absorption characteristics (Miller, 1974).

1.4.3 Hardware

Varioustypesofshackles..swivels. centrerings,andterminations arerequiredto join the major components of a cable mooring system together. This misceUaneous hardware experiences the greatest fatigue and as a result forms theweakestlinkinthe cable system.Inmany design situations thestrengthof the mooring system is limited by

19

the capacity of these connections and splices (Miller, 1974). There are other accessories including springs. clump weights anddngplales (Wemer-, 1988),whichactto increase tensioninthe mooring lines,therebyreducing breakwater motions andimprovingwave attenuation. Clumpweightsalso increasethecatenaryto provide deeper clearance for passingvessels.

1....4 Pattenl.

Thetypicalcable mooringanugement.is thespreadpattern (Figure 2.10). In most systems,itisconunonpLace to provide rJ}orelinesand beavier aDChon on the seaward side,usuallydouble the leeward side. Another unique feature involves the placement of lines at theendsof theunngementat an angle between 45 to 60 degrees (WesternCanadianHydnulics Limited, 1981). Theseprovideadditionalrestrictions to movementinthe lateral directions.

[n the majority of situations, and where possible,a scopeof 2.5 or 3.0 to 1.0 should be utilited. This servesseven! functionswhichinclude theminimizingofline length and costs, transfers the majority of the force to the anchorina horizontal direction, and

increases

the overall performance ofthe

anchors as

well

as

the structure.

With respect to the arrangement of thelines.thereanumberof options. The most utilized are the crossed non-connected, crossed connected,anduncrossed. Thelinesarc usually connected with a centrering.Anevaluation of the site andtypeof breakwaterwill usually determine anidealconfiguration. For example aossedlinesprovide deeper clearance for passing ships and require less space on the sea Ooor.

20

PLAN VIEW' FilUre 1.10: Spread Mooring Pattern

2.5 Prototype Installations

There have been over 150 floating breakwaters insta.l1ed world·wideincountries such as Austra!i&, New Zealand, Great Britain, Italy.Japan,Norway, Switzerland, United States, and Canada. A survey conducted by OERC identified a total of 135 installations (Table2.3).Most oftheowners/operatorsindicated adegree of satisfactioninthe range of 50 to 65 percent but indicated a demand forincreasedefficiency.

The majority of the problems~relatedto theinadequacyofmooringsystems to reduce motionandhold the breakwater in place. The concepts suggested for future investigations were the caisson, a·frame, screen reflector.andcentreboard caisson.

2\

Table 1.3: lnstallation TypeSummary

Classiji€atUJtI

T_

N_mba

R~fl~ction A,·Framu 5

Off~t I .

TnmsformDnon Cafuons

Hol/qw..c~ntnd J5 Catamaran

.-

1⁴

RaftslBundks 7

-

^J

BundJ~s 14 Dissipation Scrap Tires

Goodymr J2

Pole·TIn 4

WaveMau J

Tedrered Floar 1

Turbulence Generator 2

Flexible MembraM 1

Hybrid InclinrdlSloping Float 2

ScnMReflectDl' 1

CentTeboardCaisson 0

0"',

¹¹

Total JJ5

22

Chapter 3

WIND WAVE PREDICTION

When predicting loca1Iy generated wave beighu andperiodsinfetch limited regions. two important factorsmust beconsidered.Firstly,the designermustbeable to predict wind velocities (direction and speed) representative ofthe location. Secondly, the designer must be able to predict the wave regimebasedonwindspeed..duration, fetch.

andwaterdepth.

3.1 Wind Climate ADalysis

To facilitate any probabilistic analysis. a designer must have statistics for thewind directionandspeed.Therearc sevenJ convenient sources of information available, published by environmental agencies such as Environment Canada.. This data is presented in terms of percentage occurrence and mean hourly wind speed by direction and month.

The data presentedbyEnvironment Canada provides a probability distribution of winddirection by month. which can easily be converted into a cumulative or exc:eedance

23

distribution.Acommonlyusedcumulative distribution forwindspeedpredictionis the Rayleigh distribution. Typical cumulative distributions for 5,0, 7.5 and 10.0 mls mean wind speeds are showninFigure 3.1,andcanberepresented mathematicallybyEquation ].1(ResioandVmcent. 1977).

- - - /0

--,

f ::~Ej~--~~ ..// 3

e " / ¹

~

^{0.6 _}

/~ I

1

^{0.4 .' - / /} - - - -

U /~/

0.1 -:;~.7'-

...-.---.---...---.--..

^-.-~

....----..-...-

., o

/0 IS 20 15 JO Jj

If'iJtdSpud (ws) -···1.j

Figure 3.1: Rayleigh Cumulative Probability Distributions for Wmdspeed

(3.1)

where; U - predicted storm wind speed (mls) Uu - meanwindspeed (mls)

24

Pu ⁼probability of windspeed U (0-1)

The meanwindspeed estimated from this equation mustbecorrected for several factors which describe the atmOSpheric layer abovethewaves. These include elevation.

stability,location, anddrag.

3.1.1 Elevatioa Correctioa

When winds are notmeasuredat the10 melevation, thewind speedmust be adjusted accordingly. lfthe observed elevation does not exceed 20

m.

whichisusuallythe case, a simple approximation (Equation3.2) can be used (SPM, 1984).

(10)'

U'G -

Z

U^r

where; Uu}s windspeedat10 melevation(m1s) Z • anemometer beight (m) Uz •predicted storm windspeed(m1s)

3.l.2 Stability COrnctiOD

(3.1)

Whenthe air-sea temperature difference is zero, the boundary layerhasneutral stability. and no corrections are needed. Whenthe differenceispositive, the layer is stable and the windspeedisless effectiveincausing wave growth.(ftheairisat a lower

25

temperatUre than the layer, then there is increased wavegrowth.Resio and Vmcent (1977) definedilllamplification ra.tio(Rr)toaccountforthe effects of air-sea temperatUre.

Aneffective wind speed is obtainedby Equation 3.3, whereRris determined from Figure 3.2.Inthecases where there isinsufficientdata,.an amplification ratio of 1.1 should be used.

Ur - RrU,.

where; Ur ""wind speed adjusted forstability(mls) Rr - stabilityamplification ratio Uu,= windspeed at 10mdevation (mfs)

{3.J)

3.1.3 LocationCorrec.tion

Overwater winddata is often not available. then data from nearby environmental. stations canbeobtained. These winds can be translated to overwater windsifthey are the result of the same pressure system.Aneffective wind velocity can be calwlated by Equation 3.4. where the location ratio(Rt)isobtained from Figure 3.3. When the fetch is lessthan 15

Ian.

a location ratio ofl.lis recommended (Resio and Vincent,1977).

Uw - ~Ur

where; U.. - windspeedoverwater (mfs) 26

(3.4)

1.1

,.---c

u -=_

----=---

~

[

J',.J r-··

§1.0+~---\r---.--,

~ ~

i:O.9 t---.---~

~

0.8

f---.---c----.---C=-_=.l

"

10 10 -1

-IJ -10

0.7+---'--~---~

-10

TtmprrallUf! DiffireMtiftCllsius (Air· Watlr) Figure 3.1: Stabilitytutio.Rr (ResioandVtneent, 1977)

1.0 ~

1.8

; - - \ - - - 1

1.0

:<

1.6

~

^...

L: +----"<---j

----I

/0 fj 10

{)yeT/and WindsfHld (m/s)

0.8~--~---'

o

FlIUre 3.3: Location Ratio.~(ResioandVmcent.,(977)

27

R,. •location amplification ratio Ur • wind speed adjusted for stability(mI!)

3.1.4 OngCorrection

After the above corrections havebeenmade to the wind data, the wind speed is converted to a wind·stress factorbyEquation3.5 (SPM, 1984).Thisaccounts for the dragover thesur&ceofme water, relating the non-linear relationship between wind stress and wind speed

u. -

0.71

(U.)W

where; UA • adjustedwindspeed(m1s) U. - wind speed overwater (mfs)

[3.5)

These approximations and adjustments reduce bia.ses in winddataandprovide a means of obtaining information where adequate measurements are not available.

However, the collection of over waterwinddata is preferable, even if coUected for a short period, it is of valueinrdating over landwinddatato over water values.

3.2 Wave Climate PredictioD

Prediction of wave height andperiodis normally donethroughthe process of

28

hindcasting, which utilises historicalwinddatato develop a wave climate based upon the availablewindspeed. water depth. fetch and duration.The waves at prospective breakwater sites are primarily the result oflocally generated winds, as fetches do not exceed 10 km. There are a nu.m.ber offormuJaethatcan be applied for wave prediction.

most notably those produced for deepand shallow water waves as described in the Shore ProtectionManual(1984).

Inrecentyears,therehavebeen formulae developedwhich canbe utilized to predict wave heightsandperiods depending on whether the siteisduration or fetch limited,andwhichalsoprovidesasmooth transitionbetweendeepto shallow water, The most recentseriesof equations havebeen developedbySilvester andHsu(1993).

Discussed in detail below, the equations areamajor improvement overthe techniques used in the Shore ProtectionManual

The Silvester andHsuprediction process initiates with the estimate of the critical orlimitingduration (Equation3.6)whichindicates the timerequiredfor fully developed seasto occur for a specific windspeedand fetch. For example,awind speed of 20 mls combined with a3Icmfetch and6 m water depth requires 17,319 s (4.8 hrs) for afull

T.. • J078VU ..Xl

where; T,. - limitingduration (s) V.. -adjusted windspeed(mls)

2.

(3.6)

x -

retch(1an)

J~l Fetcb Limited Wave PredictiOG

When thegivendunben is longerthan the limiting duration the wave growth is limited by the fetch. The significant wave heightandpeale.periodcanbeestimateddirectly from Equations3.7 and 3.8. For example,.thedunrionis18,000 s for a windspeed0(20 mfs, fetch of] ian, and a water depth of6 m, which is lessthanthelimitingduration of 17,319 s. Therefore. the designer can apply these equations directly resultingina significant waveheightand periodorO.S8 mand2.44 s respectively.

H,=0.026U;._JJJ16(O.U;')"j

_--1 ._J --1-'[1J16(o.u;')"1

0.411 XU"

I

^(3.7)

T, =0.846U,t-J IJ89(O.U;')"j

_--1 ._J _--'1 _'[J.789(0.

^{0.401 XU·'}

U;')"I I

^(3.1)

where; Hs - significant wave heightem) T,. -peak:waveperiod($) Dw -average waterdepthover fetch (m) UA ,.adjustedwindspeed (mls) X'"fetch(Ian)

JO

3.2.2 Duration Limited Wave Prediction

Inthiscasethegiven duration is tessthanthelimitingduration. This results in an effective fetch (Equation 3.9)chatis less chan thea.ceuaJfetch.Thiseffective fetch is substituted into Equations 3,7 and 3.8 and the wave height andperiodtalculated. For the same example.,theduntionisreducedto 10,800

s.

which islessthanthe limiting duration of 17.379 s.Aneffective fetch of 1.47 btl is calculated from Equation 3.9, which corresponds to a waveperiodand height of 0.41 m and 1.93 s respectively.

[ ] ^"

X

r...

~. ³⁰⁷⁸

t[iJ;

where; Xs=:effective fetch (Iem) T,- .,limitingduration (s) VA - adjusted wind speed (mls)

One of the shortcomingsinprevious wave prediction techniques for Doating (3••)

breakwater installationshas beento characterise the locally generated wind·wave climate by a particular design wave, such as that produced by a 50 year stann event. The diffia.1ltiesindefining acceptablelimitshave often resultedinunrealistic designs and costs.

The authorhasutilised a more rigorous probabilistic approach to define the appropriate wave regime.Inchapter 5, the author describes how these formulae

were

adopted into a computer modd to conduct such a probabilistic design.

31

Chapter 4

PERFORMANCE ANALYSIS

Oncethe wave regimehasbeen prediaed, the next aucia1 step involves determining the true performance of thet10atingbreakwater under a specific set of conditions.Therehave been numerousattemptstodevdop a prediction technique,seven!

of which havemetwithmodcn1e success. A second keyaspectof performance

analym

relates to the acceptable wave climate the designer aims to achieve. These aspects of performance analysis have been investigated to determine a simplified deterministic approach to performance analysis.

4.1 PredictioD Techniques

There are anumberof techniquesthatWtteemployedbydesigners topredict performance of numerous breakwater types. The primary approaches include previous experience,analyticalmethods, numerical methods. fiddtrials.andlaboratory testing.

These are discussed in some detail in the subsequent sections.

32

4.1.1 Previous ExpuieaU!

There does exist significant infonnation on various types of sysrems currentlyin Unfonunately this information is often biased due to what many refer to as the

~humanmaor". Owners and operators who have observed their systeminthefield indicate the perfonnance tobe 20·25%more effectivethanwhat wouldbemeasured (Richey and Nece, 1984). As a result. this type ofinfonnation canbeverymisleading and should not beusedfor performance prediction purposes.

4.1.2 Analytical Methods

Floating breakwaters were6ntinvestigated utilizing approximations consisting of idealiud forms of wave barriers (rigid structure fixed near the swfa.ce).Anexpression for the transmission coefficient (Equation 4.1) was developed by Macagno (1954).Wiegel (1960)furtherinvestigated this modelwithprime consideration given to wave power transmission (time rate of energy propagation) beneath a thin plate (Equation 4.2).

C _

[J • (

^k.8. sinh(k. D.) ),].;

T 1cosh(k.. D .. - k.. D,)

J2k.. (D., - D,) - sinh (2k. D. -1k.. D,) C^T - 1k.. D.. ... sinh (2 k", D ..)

33

(4.1)

(4.2)

where; Bs .,structurewidth (m) Ds "strueturedraft(m) D.. "wuerdepth(m) Cr c transmission coefficient K.. ..wave number

Thesemodelsdo not account for any effect which the motion of the structure can impan on wave transmission.In anattempt to incorporate motion,Carr(1951) assumed the nansmission coefficient for a rectangular cross section anchored in shallow water- couldbe predicted from linear wave theory, hydrostatic pressure distributions, linear dampingand thesidesway component of motioD (Equation4.3). The motionwas characterized bythewaveandsidesway period.

C •

_r

[I

+

(~)'

_PwLwDw

(Ii)'J;

_T~

where; Cr • transmission coefficient L.. ..wave length (m) Ms -strUcturemassperlength(kglm) Ts ..structure sidesway period (s) T" -waveperiod(s)

34

(4.3)

U.J Numerical Methods

Detailed computermodelshave recently been employed. These utilize simple rectangular shapes where the wave interaction phenomena canbelinearizedand simplifying assumptions taken to reducethe complexity ofthe problem.Numerical prediction nonnallyrequiresatleasttwOsteps of analysis; -hydrodynamic- and -body_

response-. While the body response analysis canbesolved utilizing standard methods of numericalapproximation, the bydrodytwnic analysisismort complicated. A number of numerical modelsforthe bydrodynamic analysishasbeendevelopedinrecentdecades.

Thesehave been reviewedandevaluatedbysevealspecial.istsinthefield (Bando and Sonu, 1986) to determine themostcomputationally economicandeffective method. The most highly recommended techniqueistheHybrid Green FunctionMethod(HGFM), proposed byIjima. and Yoshida (1975).

U.4 FiddTrials

Full scale tests are very expensive and time consuming, and current methods of recordingandmeasuring waves have not been completely verified.Therehave been a number offull scale sections tested, and indications arethatfielddliciencies are genenUy higherthanefficiencies predicted by laboratory or numericalmethocb.

It hasbeensuggestedthat thisisdue to the variability of the wave surface and angle ofattack..Whena waveencounters the structure, therearetwo important factors to consider. Farstly, theeffectivewidth ofthestructureisincreasedastheangle of attack increases.Ithasbeenwellestablishedthatan Mease in width wiUincreaseattenuation.

J5

Secondly, the force on the structure must vary when both wave surface and angle of attack are constamly changing.Thisvariabilityreducestranslation of the suucture which has also been shown[0increase attenuation.

4.1.5LaboratoryTatiDe

Developing and conducting a series of comprehensive [ests to evaluate performance has been used very often. Unfortunately, this tends tobe very costlyand time consuming.Inaddition. there are a finite number of test conditionswhichare available. As a result, the test results are only valid when considering the same structure exposed tosimilarconditions. Despite these sboncomings.it isthisapproachwhichholds the most promise for performance prediction.

4.2 Dimensional Regression Technique

Asmentioned previously. inadequate information on performance of prototype installations exists and undertaking physical, numerical and fuji scale section investigations is not considered feasible in theinitialstages of design.Ofthese predictionmethods,the extrapOlation of results from previous model studies is the most reasonable approach.

The dimensional regression technique the author employed involved four basic steps. FU'St, various breakwater systems were analyzed toascenainwhatparameters were important in the attenuation process. Second, dimensional analysis wasconduaedto isoJar:e the parameters into a series ofdimensionless ratios, relevantindescribingthewave attenuation process. Third, available model test data was coUected and converted into

36

dimensionless ratios developed in step two. Fourth, a regression analysis was conducted to find the most appropriate deterministic model. These steps are described in detailinthe subsequent sections.

4.2.1 Pan.m.etricReview

The primary factor in evaluating floatingbreaJcwa.ter performance is the Transmission Coefficient(CT). defioedasthe ratio oftraDsmitted waveheight(HTlto incoming wave height(HI).Prior parametric studies have utilized the ratios of structure width to wave length(8s/ L r ).wave height to~velength(HI I L ..).stIUClW'edraft:to water depth(Dsl Dr).and water depth to wave length(Drl L,,)are most commonly utilized.Inearly analytical formulae, the ratio of structurem&S$ [0wuer density. wave length~waterdepth(Ms

I""

^LrDr)wasconsidered important.

These tenus relate to twoaspectsof breakwater perfonnance. the structural and wave parameten. A crucialaspectnot covered adequaJ:e1y or even 11allinprevious studies concerns the geometric sriffneu characteristics of the mooring system(K.w). a measure oCtile force required to displacethe breakwater1unitfrom its originaJ or neutral position.

GeO"'ftricSriffnw

Foran llCQ.latedeterministic model tobedeveloped, amethodto evaluate the geometricstiffDe:sswasrequired.Typica1ly.mooring systems corWst ofa series ofchains to bold the structureinposition.Thesechains form a natural catenaryshapeandrequire a

37

series of detailed calculations to determinetheappropriate forces and corresponding displacements.Therewet'e twOprimarysourcesofinfomwion identified«Beneaux.

1976),(Tsinker,1986»fromwNchEquations4.4to4.9 weredeveloped. The tenns used intheseequationsarefurtherclarified byFigure4.1.

[ (xi. r:!' W; xl ]

Lc -

x, --x-,-- -

¹⁴

^{Fi (x: ...} r:/

^J

where; X, - original horizontal distance (m)

38

('.')

('.5)

(•.6)

('.7)

(U)

('.')

Xl -new horizontal distance (m) 4X - structure displacement (m) F, - leewardancborfine's pretensiOIl(N) FI

=

seaward anchorline's pre·tension (N) We - submerged anchortine unit weight (NIm)

Y,

=

verticaldistance (m) Lc - length of mooring line (m) FJ=leeward anchortine's force (N) F. - seawardancbortine's force (N) FA - applied external force (N) Nil= numberof mooringlines Ku=mooring stifthess (NIm)

Consider a simplified scenario. a floating breakwater 30 m in lengthhas6 mooring linesattaChed to the system. Three of these are COMected to the leeward side while the other lines are COMected to the seaward side to form three pairs of lines(Nil).The is 20 mm diameter with a unit weight (We)78.5kN/m..Thewuerdepth(Y,)is10mw the lines are placed with a scope on to I(X,is three (3) times

r,)

to makeX,30 m.[{we arbitrarily select a change in position (L1X) of0.2 m we can apply equations 4.4 to 4.9, which indicate it would take 5kN to move the 30m structure O.2m, for astiffnessof 25kN1m..

39

/ - FBW original position 1- FBW new position

J - anc:horliM'$ original position 4 -anchorliM'snew position

Figure ".1: Catenary Mooring System

4.2.2 DimentioaalADalysis

The resulting basic functional Equation (4.10) contains eight variables. Since this system is a surface dominated phenomenon. the viscous and inenia effects have been considered negligible and excluded from the analysis.

Hr - ; (H,.Lw.D.,. Br. Dr. Mr. KJ>l) (4.10)

where; Hr - transmined wave height (m) HI • incoming wave height (m) L" ...wave length (m)

40

D., - water depth (m) Bs -structurE width (m) Ds - structuredraft(III)

Ms - structure mass per unit length (kglm) KM - mooring stiffness(NIIII)

After a thorough review of dimensional analysis techniques.themethod of synthesis was adopted. The reasoning for doing50was this technique uses linear proportionality's(lengthdimensions) to devel.op adimensionallyhomogeneous equation.

Based on Equation 4.10, six of the eight terms already have linear dimensions (m), while the remaining two terms of massperunitlength(Ms) and geometric stifihess(KM)include dimensions of mass (kg) and time (5).

Inorder to developlinearproportionality's, thesynthesistechnique allowsyouto add the terms relating to gravity(g)and water density (p.,o) wherenecessaryto develop linear tem1S. The structure unit mass term (units of kg/m) was modified by dividing with the water density (units oflcglm^l)andtakingthe square root ofthe term toarrivealinear proponionality (m). The stiffness term (units of kg/5¹)is a little more complex, as it contains both mass (kg) and time (5). The modification involves dividing by both the gravitational constam (units Ofm/5¹)and water density (units ofkg/m') then taJcing the square root to arriveata linear proportionality. These termsthenreplace the structure unit massandstiffD.essinEquation 4.10 to arrive at thefinalfunctional Equation 4.11.

41

where; Hr ""transmitted wave height (m) H,=incoming wave height(m) L..=wave length(m) D,,"waterdeptb.(m) 8s '"structure width (m) D~=strueturedraft(m)

Ms '"structure massper unitlength (kglm)

!GJ ,.

mooring.stiffi1ess(NIm) g"gravitational COllSWlt (9.81mI~) p"2 density of water (l02S

!t&'m)

(4.11)

The6naIstep in the process..isto create a series of dimensionless parameters, by dividingeachtermbyone of the others. This process allows for the modification ofany panuneuic term bydividingor multiplyingaswellassquaring orcubing._Thefinalbasis for the selection ofme terms should bebased.on the particular system under investigation and should reliect the understanding of the process involved. The most common parameters have been shown in Equation 4, 12. and is cort5idered representative for a varietyofBoatingbreakwater types. Other, more unique systems may notbecompletely

42

explained by the results of the analysis.As a result, additional parameters would be required to analyzethe system. Provided the above steps aremaintained,the parameters derivedfrom aseparate analysis wouldstillbe valid.

c

_r

:!!L..

_H,

;(!!.L

_{L" ,}^D"_{L" .}

!!L!!L.!!!.L.~) _£"

_{'D" .}

p"L?,..

'KArL?,.. ^(4.11)

where; Hr^>5tra.nsmittedwave~ght(m) H, - incoming wave height (m) L" ..wavelength (m) D"& waterdepth(m) Bs - strUctUrewidth (m) Ds

=

structure draft (m)

Ms - structure massperunitlength (kg/m) IG.t ..mooring stiffhess (NIro) Kosgravitational constant (9.81mls1 P" ...density of water (1025kg/m)

4.1.3 Model Analysis

Now that we have our dimensionless tenos, the: nextstep was to collectall availablemodeltestdata and amu1ge the resuluwithrespect to these terms. The author has considered one of me: most common designtypes, the caisson. A thoroughreviewof

43

numerousmodelstudies conducted on caissons was coUected andsw:nnuriz.edin AppendixA.Asummary plot of the data is shown in Figure 4.2, which plots the transmission coefficient(Cdas a function oftilewave period(T,.).

Fipr'e 4.2:CaissonData Sumrtwy

4.2.4Multiple RqressiOD

In multiple regression the objective is to build a probabilistic model that relates the dependent variable (in this caseCr)to one or more of the predictor terms as depicted in Equation 4.13. This impliesthateachoCthe predictor terms have a linear relationship with the dependent variable.

44

Y ..a'"P,X, - PIX}+ ..•P,X, ...&

where; Y=dependent variable Cl '" regression constant

p. ,.

regression coefficient X; ..independent variable

(4.13)

When envirorunental variables (wave height, wavelength,wiDd. velocity) are present as the independent variables. the relatioll5hips are not nonnally linear. To correct rorthisnon-linearity, thedatamustbetransformedbyutilizing intrinsicallylinear functions, which include exponential, power, and logarithmic relationships (Table 4.1).

Table 4.1: Intrinsically Linear Functions (Devore, 1987)

The most widdyusedintrinsically linear functionisthe power model. As shown in Table 4.1, this involves taking the logs orboth the dependent and independent variables, then proceedingwith the regression. These single variable regression analysis techniques

45

can easilybee:ttended to include multiple regression.Oncecompletethelinear fonn of the modelcan be convened to a simple power relationship as shown in Equation 4.14.

Y:aXf X:' ... X,A£

where; Y - dependent variable a -regression constant

PI -

regression coefficient

x.

⁼independem variable

(4.14)

Oneofthe problems with the transformationinvolvesthe error tenn(e),whichin the tnnsf"onned modelrepresentsthe medianofthe error, not themean.Therefore,the error term or smearing estimator must be determined for the prediction tobe representative. According to Devore(1987) thisisachievedbyaveragingtheexponentials of the residuals in the transformed model (Equation 4.IS).

where; £s - smearingestimate

46

(4.15)

&. - residual n - number ofdata points

When conducting the regression, the author utilized Microsoft Excel and conducteda.stepwise forwacdlbackward substitutionanalysis. This procedurestaIt5off with no predictorsinthe model and considers finingintumwithcarrierX,. X1•and so on.

The variable whichyields the largest absolutel-nztio(a measure of the influence of the parameter) enters the model provided the ratio exceeds thespecifiedconstant. whichhasa standardvalueof2(t.).SupposecartierX,entered the model, then models with(X,.

X;j.(X,. XJJ....• (X,. XJare considered in tum. The tenn which coupled withX,thathas thehighest t-nUioisthen added to themodelAftereach addition, the previous terms are examined to ensurethattheirt-ratioalso exceeds 2,andifone of the previous tenns no longer have at-ratiowhichexceeds 2 itisdiscarded.

The principa.l behind the forwatdlbackward substitutions. is that a single variable maybemore strongly related to the dependent variable than either of the twO or more variables individually.but in combination of these variables may make the single variable subsequently redundant. Whileinmost. situations these stepswillidentifY a good model, there is no guaranteethat the best or even a nearlybestmodel will result. Close scrutiny shouldbegiventodatasetsforwhich thereappear tobestrong relationships between some of the potential carriers.

41

4.2.S Results

After an e:x.baustive analysis of the transformation mnhods. thepowermodel

was

adopted. The reasoningbeing aptness ofthe model.astheothers did not adequately describe thebehaviourof the wave anenuation process.Basedon thestepwise forwardJbaclcward regression, thefirstterm toenterwas therelative width(Bs1£,,) parameters witha t-ratioof ·13. 78. Thenexttwo terms to enter the relationship were the mooring plU'1Jneter(Ntlgp"L.1and relative depth parameter(D" IL,,) witht-rona'sof

·2.41and2.44respea:ivety.Theregressionanalysiswascontinued ontheremaining;three parameters but, thet-{'atia'sof these terms wereallies.s than2andnot included in the relationslUp. The resulting linearma.the:matica1rdationshipisshowninEquation 4.16.

I{Z~) --2.097+0J51m(~)-O.437~t)-OJ92m(g~M~J

^(4.16)

where; Hr ".tranSmitted wave height (m) HI ...incoming wave height (m) D"=water depth (m)

£" ". wave length (m) Bs .. structure width (m)

KM ".mooring stiffness (NIm) g - gravitational constant (mls²)

pw - density of water(kglm)}

48

To verify aptness oCthemodeltheauthorusedtwodiagnostic plots.Thefirstisa plot ofpredict~ v~ measur~CdFigure 4.3),while the secondisa plot of standardized residuals against the predicted Cr(Figure 4.4). The less the scatterinthese plots thebetterthe fit of the model.Ifthereare uendsinthe residualseitherupwud or downward the aptness of the model has tobequestioned. With respect to the plots in Figures4.3and4.4,therearenoobviousuends so Equation 4.16isvalid.More information,ODmodelaptnessandinterpretation canbefoundinDevroe(1981).

The nextstepis to convert the linear relationship (Equation4.16)into that ofa powerrelationship.Utiliringasmearingestimatorof1.025,calD.1lated byEquation 4.15, the resulting regression constant becomes0.126.The remaining regression coefficients become theexponentsofeach ofthreeparametcnindicatedbyEquation4.16.Thefinal, more useful,powerrelationshipisshowninEquation4.11,whichprovidesareasonable representation of the wave attenuation process for a hoUow caisson floating breakwater.

Aplot of the measuredv~predicted CrisshowninFigure 4.5.

(Dr)"'" ^(B,)~·m ( K. )~.

Cr-OJ26

L; L;;

g~~

where; Cr - uansmission coefficient D" -water depth(m) L" - wave length (m) Bs •^{structurewidth (m)}

49

(4.17)

~

-:::: } . - - . - - - -•.•- ..- ....••..•..•.- . ..._...d>.0"

o~'" ^·-·1

j

-4,50

t~

⁰

- 1

i

^-4.n

^r

---o~

_ _ 00_ _ ---1

u ~ 0000 I

:~ -1.00r·--····_-u-~··_·

__

···_,o~-_

..

···o _..

j

5:

-11S~---

8

- I

~.'SO_o ^0:& _j

!

^.17S

L _ -~--- ---

. 1 o o L -

-].00

·us

./JO -1.15 -1.00 -0.75 .o.SO -0.15 0.00

LogofTro/lsmission eo,jJici,,,rtcr) Fipre 4.3: Measured versus PredictedCr(LogarithmicMood)

i !~ 1-·-~-·"~·-::··~---· ---···-·1

~ :~ L-.-.- .. ~~=:~.::"1'"o-.~~:~~~~:i~~:::~='

~

^-0.5

I 'o-cr--o...~-o---

~-1.0E _ : .~(J".~g--"O"'&"---=-

I

, _ _

~_,,-g0 - - - _

~~:~ {--_ .. __ ._._-~

^..

_

^..

__ ._---

...

_--_._-_

^...

__

^.

__

._--_

_._-

.2.S j..'_-;._~~-~-~_ _+_-~- -___J

-1.00 -1.1S -1.50 ·1.15 -1.00 .(J.7J -0.50 -0.15 0.00 lAgojTrtZ1U1fIwion~ffldclt(Cr)

Figure 4.4: Standardized Residuals venus Cr(LogarithmicMood)

50

/.0~.---=--- 0.9} ..._ ..._._....

0::-08.f....---.---d'---<>-~

~ 0:' -;---.---

~^0.6

t---- -.-.----.---..--

a

^0.5

~

^{tf!-!L-!:..-Q}

i :; E--~· e;;~==-._-=-. --3- ¹

~

^0.1

~--f'''''""':"o_-'---_

~1 _ _ I

0.0 . .

~o ~J ~1 U ae UJ M d] U U to

TrWlsmJuio/l c-/Jidetll(C r)

Fipre4.5: Measured venusPredictedCr (power Mood)

~.., mooring stiffil,ess (NIm) g - gravitational constant (m/52)

AreviewaCthe mechanics ofthebollow caissonisrequired to ensurethat the parametersderivedfromtheregressionanalysisarevalid.Thecaissonutilizes transformation to attenuate incoming wave energy. This requires two imponant aspects; a sufficientwidth (Bs)andmooringstifIDess(~)sothatthe stnJctuceisrdativdy unresponsive tothepassage ofw.ves. Hence, the regression equation is consistentwith thistheoreticalanalysis.Thethird termisrelativedepth(DrIL~).whichis a direct indication ofwhether-the structure isindeep, transitional or shallow waten.Inshallow

51

water depths. more energy is presentDearthesurliwewhichincreasesthe caisson performance, hence the addition of the term is reasonable.

TheexpoDel1lSofthe relative terms are an indication of the sensitivity ofme attenuation, aswellas me effect ofincteasiDgor decreasing the numerators.in this case water depth(D.,),structurewidth(Bs), and mooring stiffness (K.w). The most sensitive tennistherelative width(Bsl L.,)ratio,with

an

exponent of -0.437.Thenegative exponent impliesthatasthestructUrewidth(Bs)increasesrelativeto the wave length (L ..),the transmission coefficient (Cr) dec:reases, improving performance. ASo-~increase inwidm(Bs)causesa corresponding decreaseinthe transmission coefficient(Cr)^by16%.

Thesame is cue of the mooringstiffnes.s(~)ratio,withan exponent of..o.l92.

Thisresultsinonly a7% decreaseinthe transmission coefficient (Cr) for a SOO/a increase inthestiffiJess(K.t).Thethirdand6na1ratio ofre1ative depth(D..I L,,) hasanexponent of 0.151, which causes a 6% increase: in the transmission coefficient (Cd for a SOO/a increase the water depth relative(D.)tothe wave length(L ..).

4.3 Performance Criteria

Aaucia1 design aspect for floating breakwatersisto provide a set of performance criteriatiua. !he structure must be designed to achieve. A number of studies on this criteria have been conducted.Themostusd'iLloftbese include a recentstUdy conducted on behalf oftheSmall Craft.Harbours(SOl)branch of the DepartmeDt ofFisheries and Oceans (DFO) byEasternDesignenLimited (1991). They recommendedthe adoption of exceedance or threshold values (Table 4.2).

52