TU Delft Design Manual

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C O A S T A L E N G I N E E R I N GVo Lu m e I

B R E A K W A T E R D E S I G N

oas taL E n g i n e e r i n g GroupD e p a r t m e n t of C iv iL E n g i n e e r i n gD e L f t U n i v e r s i t y o f T e c h n o L o g yD e L f t T h e N e t h e r l a n d s


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324.MfiiS 672.

COASTALENGINEERINGVolume I I I - Breakwater Design

edited byW.W. Massie, P.E,

Engineering Group C i v i l Engineering

f t Un iv er si ty o f Technology Netherlands

november 1976 f 3,10


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"He knows enough whoknows to learn".

Abraham L i n c o l n


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TABLE OF CONTENTS - VOLUMEI I IBREAKWATER DESIGN

Page1 . Introd ucti on 1

1.1 Scope 11.2 Contributo rs 11.3 References 11.4 Miscellaneous Remarks 1

2. General Considerations 32.1 Purposes 32.2 General Design Information 62.3 Sources of Design Data 72.4 Performance Requirements 82.5 Review 9

3. Types of Breakwaters 103.1 Int roduct ion 103.2 Comparison of Types 103.3 Conclusions 19

4. Rubble Mound Breakwaters 204.1 D e f i n i t i o n 204.2 Two Distinct Types 204.3 Basic Construct ion Princi ples 21

5. Wave Run-up and Overtopping 225.1 Introdu ction 225.2 Run-up Determination 225.3 Run-up in Relation to Breakwater Design 245.4 Conclusions about Run-up 255.5 Wave Overtopping 255.6 Wave Transmission 26

6. Construct ion Mate rials 286.1 Necessary Prope rties 286.2 Desirable Propert ies 286.3 Characterizing Co eff ici ent s fo r Armor Units 296.4 Armor U n i t Types 306.5 Armor Se lection 356.6 Methods to increase S tab i l i ty 36

7. Armor Computations 377.1 His tory 377.2 Theoretical Background 377.3 The Hudson Formula 407.4 Special Appli cat ions 427.5 Sensi t ivi ty of Hudson Formula 43


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7.6 Choice of Armor Units 447.7 Layer Extent and Thickness 457.8 Crest W i d t h 477.9 Review 47

8. The Core 488.1 Function 438.2 Materials 488.3 Construction Methods 49

9. F i l t e r and Toe Construct ions 509.1 Descript ion and Functions 509.2 The Physical Phenomena Involved 509.3 Design Cr it er ia fo r F il te rs 519.4 Design Cri te ri a fo r Toes 519.5 F i l t e r Layer Constructions 519.6 Toe Constructions 549.7 Other Foundation Problems 57

10. Rubble Mound Breakwater Construction 5810.1 Introduction 5810.2 Construction Methods 5810.3 Specific Construct ional Aspects 6010.4 Special Construction Problems 6210.5 Review 63

1 1 . Optimum Design 6411.1 Introduction 6411.2 Parameters and their Interrelationships 6411.3 Given Data 6511.4 Preliminary Calculations 6811.5 Cost of Quarry Stone Breakwater 7211.6 Damage to the Breakwater 7811.7 Optimization of Quarry Stone Breakwater 8111.8 Additional Remarks 84

12. Example of Rubble Mound Breakwater 8613. Monolithic Breakwaters 87

13.1 D e f i n i t i o n 8713.2 General Features 8714. Construction Materials 91

14.1 Introduction 9114.2 Environmental Dif ferences 9114.3 Consequences for Materials 91


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15. Wave Forces on Vertical Walls 9215.1 Introduction 9215.2 Standing Waves 9215.3 Breaking Waves - Impact 9315.4 Comparative Results ' 9515.5 Other Wave Forces 9615.6 Additional Comments 96

16. Monolithic Breakwater Foundations 9816.1 Fai lu re Types and Causes 9816.2 Types of Foundations 9816.3 Impact Load Response 10016.4 Example of Impact Response 10316.5 Breakwater Sliding 10616.6 Example of Sliding 11116.7 Breakwater Rotation 11416.8 Example of Rotation 115

17. Influence of Breakwater on Waves 11617.1 Int rod uction 11617.2 Standing Waves 11617.3 Local Morphological Changes 116

18. Construction of Monolithic Breakwaters 11818.1 Int rod uction 11818.2 Const ruction Over Crest 11818.3 Use of Float ing Caissons 12118.4 Const ruction in Place 122

19. Optimum Design 12319.1 Int rod uction 12319.2 Design Data 12319.3 Pre liminary Computations 12519.4 Optimizat ion Variables and Philosophy 12819.5 Minimum Crest Elevat ion 13019.6 Construction Costs 13119.7 Determination of Damage 13319.8 The Optimizat ion 14119.9 Additional Comments 151

20. Rotterdam - Europoort Entrance Design 15220.1 Int rod uction 1522.2 Harbor Layout Considerations 15220.3 Proposed Designs 15320.4 Evaluation of Designs 15320.5 Construction Deta ils 154Symbols and Notation 162References 169


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LIST OFTABLES

Table T i t l e Pagenumber

1.1 ContributingStaff 2

7.1 Comparison of armor un it s 4511.1 . Storm data 6711.2 Costs of Materials in place 6811.3 Wave shoaling 7111.4 I n i t i a l cost estimate - stone breakwater 7611.5 Cost as function of Wave height for stone 78

breakwater11.6 Breakwater damage computations 80

8111.7 Cost Summary 8216.1 Response to schematized forces 10416.2 Breakwater sl iding parameters 10916.3 Sliding computation 11319.1 Storm data 12319.2 Costs of Materials in Place 12519.3 Wave computations 12619.4 S ta ti st i ca l cal cu la tion fo r Hd = 8.0 m 12719.5 Element quan ti ti es 13319.6 Wave fo rce Computations 13519.7 Additional breakwater sl iding parameters 13919.8 Optimizat ion computations 14320,1 Overview of breakwater types 154


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LIST OF FIGURESFigure T i t l e Pagenumber2.1 Plymouth Harbor, U,S,A, 42.2 Columbia River entrance 52.3 Influence of cross cur rent on ship 52.4 Current pat tern at Europoort entrance 63. 1 Air bubble cu rtain 103.2 Composite breakwater 113.3 Resonant breakwater 16

4. 1 Overtopping breakwater 204.2 Non overtopping breakwater 215.1 Wave run-up 235.2 Run-up - steepness curves 245.3 Wave transmission fo r submerged breakwaters 276.1 Akmon armor unit 306.2 Cob 316.3 Concrete cube 316.4 M o d i f i e d cube forms 326.5 Dolos 326.6 Tetrapod 346.7 T r ibar 357.1 Force diagram fo r single armor unit 377.2 L i m i t s of Armor Equations 407.3 Equilibrium along contour 437.4 Comparison of armor un it s 45

9.1 Pressures w i t h i n breakwater 509.2 Woven fabric mattress 529.3 Woven fabric mattress w i t h concrete block 539.4 Conventional excavated toe const ruc tion 559.5 Al te rnat ive toe constructi on 569.6 Toe cons truc tion without excavation 56

10,1 Breakwater constructed w i t h core pro tec tio n 6211.1 Storm wave and water level data 6611.2 Wave data at si te 7011.3 Run-up steepness curves af te r Hudson 7311.4 Sketch design of stone breakwater 7511.5 Damage re la ti on sh ip fo r rough quarry stone 7911.6 Cost curves fo r stone breakwater 83


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Figure T i t l e Pagenumber13.1 Typical monolithic breakwater 8713.2 Monolithic breakwater on rough bottom 8813.3 Caisson cross section 8913.4 Caisson w i t h parapet 8913.5 Hanstholm type of monolithic breakwater 8913.6 Composite Breakwater 9015,1 Pressure diagram for standing wave 9316.1 Composite breakwater on moderately s t i f f soil 9816.2 Quicksand condition 9916.3 F i l t e r layer under monolithic breakwater 9916.4 Schmatic representation of eq, 16,01 . 10016.5 Mass-spring system 10216.6 Actual and schematized fo rce diagram 10416.7 Response to example loadings 10516.8 Forces on breakwaters 10616.9 Breakwater sl iding parameters 11016.10 Forces important to ro ta ti on 11417,1 Standing wave and resulting bottom changes 11718.1 Breakwater f r o m Algiers, Morocco 11918.2 Elements and crane fo r secondary breakwater 12018.3 Construction consi sting of cylindrical caissons 12018.4 Plan of construction yard 12119.1 Short period dynamic forces 12419.2 Design wave height as function of annual f r e - 129

quency of exceedance19.3 Element de ta ils 13119.4 Breakwater sl iding parameters 13819.5 Cost curves for various crest elevations 14519.6 Total cost versus height and w i d t h f o r best 148

solutions19.7 Contours of total cost parameter surface as 149

function of w i d t h and height19.8 Sketch of monolithic breakwater 15020.1 New harbor entrance Hook of Holland 15520.2 Proposed designs fo r North Breakwater 15620.3 Optimization curves 15920.4 Cross sections of North Breakwater 16020.5 (construction)phases of North Breakwater 161


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1 . INTRODUCTION W.W. Massie1.1. Scope

This t h i r d volume of the series on coastal engineering concentrates on a single specialized topic: breakwater design. The subdivisions into four categories found in the previous two volumes is notfound here; a l l of thi s volume relate s to harbors in someway. Ofcourse, some information presented here can be used elsewhere. Forexample, knowledge of wave impact forces, important for the designo f monolithic breakwaters, can also be handy when designing of fsho restructures.

Amore direct t i e can be made between the design methods usedfor breakwaters and those needed for coastal defense works - volume I ,chapter 30.

1.2. ContributorsThe primary authors are l i s ted at the beginning of each chapter ;

f i n a l editing and coo rdinat ion was done by W.W. Massie, layout byW. Tilmans, J . van Overeem and'J.D. Schepers. Table 1.1 lists the staffmembers of the Coastal Engineering Group who contributed to this volume.

1.3. ReferencesOne general reference is so handy for breakwater design tha t i t

is not repeatedly mentioned. This book is the Shore Protection Manualpublished in 1973 by the U.S. Army Coastal Engineering Research Center.Information presented w e l l there w i l l not be duplicated here; these notescomplement rather than replace the Shore Protection Manual.

1.4. M isce11aneous RemarksAs in previous volumes, the spelling used is American rather than

English. A l i s t of Dutch translations of the more important technical wordsis available.

The notation used is kept as consistent as possible w i t h previous volumes and w i t h in te rnat io na ll y accepted prac ti ce. A symbol table is i n c l u ded in this volume, even though most symbols are def ined in each chapteras they appear.

Literature is l i s ted in the text by author and year; a more completel i s t ing i s included separately in the book.

More general in troducto ry material may be found in chapter 1 ofvolume I of these notes.


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Table 1.1 Contr ibutors to th is volume

I r . J.F. Agema, Chief Engineer fo r Hydrau lics,M i n i s t r y of Public Works (Rijkswaterstaat),The Hague.

Prof.Dr. ir . E.W. Bijker, Professor of Coastal Engineering,D e l f t University of Technology, D e l f t .

I r . L.E. van Loo, Senior S ci en ti fi c O ff ic e r,D e l f t University of Technology, D e l f t .

W.W. Massie, MSc, P.E., Senior Sci en t if ic O ff ice r,D e l f t University of Technology, D e l f t .

I r . A. Paape, Director of D e l f t Branch',D e l f t Hydraulics Laboratory, D e l f t .


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2. GENERAL CONSIDERATIONS W.W. Massie2 . 1 . Purpose

Most generally speaking, breakwaters are b u i l t to change the coasti n some way.* The development of the need fo r breakwaters has pa ra lleled that of harbor and approach channel development outlined in chapte rs 14 and 15 of volume I .

More spe ci f ic purposes fo r breakwaters were described in chapter 18o f volume I , but shall be treated i n more detail here.

The most obvious purpose of a breakwater is to provide prot ec tionagains t waves. The prot ec ti on may be provided fo r an approach channel oreven for a harbor i t s e l f . This type of protection is necessary in orderto provide quie te r water fo r ships to navigate and moor. Mot i on of mooredships in harbors can be detrimental to cargo handling efficiency, especiall y f or container ships. Wave action in approach channels can increase thedanger f o r tugboat crews and make navigation more d i f f i c u l t . Furthermore,dredging in exposed locations is relat ively expensive - see chapter 16 ofvolume I . Figure 2. 1 shows a small harbor pro tec ted by a breakwater.

Abreakwater can also serve to reduce the amount of dredging requ iredi n a harbor entrance. This can res ul t f r o m the cutting o f f of the l i t t o r a ltranspor t supply to the approach channel, or i t can resu lt f r o m naturalscouring action in an a r t i f i c i a l l y narrowed channel. This purpose washighlighted b r i e f l y in chaper 18 of volume I . Figure 2.2 shows such anapplication constructed in an attempt to increase natural channel scouring.

A t locations where l i t t l e or no natural protection exists, breakwatersoften serve as quay f a c i l i t i e s as w e l l . Such dual usage of the breakwater iseconomical in terms of harbor area but requires a di fferent type of breakwater structure. This aspect w i l l be discussed furt he r in sect ion 4 of thi schapter.

A fourth possible important purpose of a breakwater can be to guidethe currents in the channel or along the coast . I t has already been shown(volume I ch. 18) how the channel currents can be a r t i f i c i a l l y concentratedto maintain depth. On the other hand, a breakwater can also be b u i l t to reduce the gradient of the cross current in an approach channel.

Ships moving at slow speed in a channel are re la t ive ly d i f f i c u l t tohold on course. A constant cross current makes the p i l o t ' s job mored i f f i c u l t but can often be to le ra te d. On the othe r hand, an abruptchange in cross current strength as the ship progresses along thechannel can cause dangerous naviga tio n si tuat ions . This is shownschematically in figure 2.3. One of the primary considerations inthe design o f the Europoort breakwaters in The Netherlands was thel i m i t a t i o n o f the cross cu rrent gradient. The re su lt in g current pat tern, observed in a physical model is shown in figure 2.4.

Obviously, a single breakwater can serve more than one of thesefour main purposes. The design requirements implied by these functionaldemands are discussed in section 4; in the f o l l o w i n g section we examinethe general design data required.* This def in i t ion includes coastal defense works; the rest of the dis

cussion is l i m i t e d to harbor breakwaters, however.


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Figure 2.1PLYMOUTH HARBOR, U.S.A.


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Figure 2.2CO L U M B I A RIVER ENTRANCE

Actual Path

TDesired Poth

1.5 1.3CROSS

11CURRENT

1.0(KNOTS)

1.0 1.0 1.0

SHIP SPEED RELATIVETOWATER (KNOTS)

Angle Relative xto Desired Path 16 13 11.5 10.5 9.5

value increased from 30 by moment generated by abrupt current change.

Figure 2.3 INFLUENCE OF CROSS CURRENT ON SHIP


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Figure l.kCURRENT PATTERN AT EUROPOORT ENTRANCEH A L F AN HOUR BEFORE H.W. HOOK OF HOLLAND

2.2. General Design InformationHydrographic data are obviously important for the design of a break

water. Bathymetry is extremely impor tant; the volume of a rubble moundbreakwater increases quadraticly w i t h water depth. Water level changescaused eithe r by tides or by storm surges can be important for determiningthe crest elevation of the breakwater. These water levels, by inf lue ncin gthe total water depth can also l i m i t the wave attack to some maximum value.

Wave heights and their frequency of occurrence f o r m the most importan t input to an optimum design procedure f o r a breakwater. The s t a t i s t i cal relationships needed have already been presented in chapters 10 and 11o f volume I . When wave data i t s e l f is not available, waves can often bepredicted f r o m meteorological data- see volume I chapter 12 and the ShoreProtection Manual.


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Horizontal tides can also be important. In addition to hindering shipping, these currents can also re su lt in erosion which endangersthe breakwater foundation.

Meteorological data are also important. Winds are not only importantfo r local wave genera tion, but can also be impor tant fo r est ima ting thequantity of overtopping by spray f r o m the broken waves. When the inner sideo f a breakwater serves as a quay, the ship mooring forces - dependent part i a l l y on wi n d influences - can be important in the design.

Temperature data can be important for the selection of constructionma te rial s. Special concrete must be used i f repeated cycles of free zingand thawing are expected.

Special navigational aids may be needed on a breakwater in a lo cat i o n where fog forms frequently. These aids can range f r o m radarreflectors to radio beacon installations.

Since every breakwater must have some so rt of founda tion - however simple - knowledge of the local soil conditions is necessary. Thegrain size d is tr ibu t ion , cohesion, bearing capacity, and consolidationcharacteristics can all influence the design of a structure.

The hi st ory of the coastal morphological changes can be helpfulfor estimating the influence which our structure w i l l have on the coastalenvironment. While not involved direct ly w i t h the breakwater construct i o n , re su lt ing coastal morphological changes can influence the totalproject economics s ignif icant ly . Methods for predicting these changesand reducing th e ir detrimental ef fe ct s are discussed in volume I I .

Information about any special design wishes i s also necessary. Forexample, i t may be required tha t the ent ir e struct ure be vis ib l e f r o mw i t h i n a given distance; thi s has im plica tions fo r the crest el eva tio n.I t may be desirable to design a breakwater sui table fo r use by sportfishermen under certain weather conditions.

One last item involves the avai lab i l i ty of construction materials.Since large volumes of material are needed to construct a breakwater, alocal supply is nearly always required in order to keep transpo rt costw i t h i n reason.

2,3, Sources of Design DataMuch of the preliminary hydrographic data can be obtained f r o m na

vigation charts. They often provide sufficientdata for site selection.The user should keep in mind, however, that indicated depths are usuallyminimum depths; th is is i n keeping w i t h their primary use in navigation.The most up-to-date charts are usually issued by local (national) hydrographic agencies. The B r i t i s h Admiralty, however, issues charts coveringnearly all the coasts of the w o r l d . These same hydrographic survey agencies usually accumulate and publish tidal information as w e l l , .

Meteorological data is usually accumulated most systematically by thelocal (nat iona l) weather forecast ing serv ice. Data on waves are also of ten recorded at coastal and offshore stat ions along w i t h meteorological in


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formation. As an al ter na tive , wave stat i st ics can sometimes be derived f romother information as explained i n chapter 12 of volume I . Storm surge datai s also of te n recorded at coastal stat ions by the weather se rvice. Theoretica l pr edi ct ion is sometimes possible when measurements are lacking; anapproach to the problem is out li ne d in volume I chapter 3.

Information about the soil condit ions at a si te is of ten more d i f f i cult to f i n d . Possibly local publ ic works agencies or dredging contractorswho have worked in the area may be able to provide some information.Even so, a detailed geotechnical survey of the area w i l l very of te n berequired, e special ly i f a large or special p roj ect is involved.

Any information concerning special design specifications, such asrecreational requirements w i l l be provided by the autho ri ty in i t ia t ingthe project.

Data f r o m which an impression of coastal morphological changes canbe obtained may be held by public works agencies or may be derived f r o mcomparison of present and past navigation charts. Librar ies ofte n havemap collections which can be used for these comparison studies.2 . 4 . Performance Requirements

Several factors which can influence our choice of breakwater typehave already been mentioned..These have been grouped under purpose andunder design information in ea rl ie r sections of this chapter. In th issection other factors aff ec t in g the choice of design type w i l l be considered. A catalog o f types o f breakwaters w i t h the i r advantages anddisadvantages w i l l be presented in chapter 3.

In contrast to dikes, the performance requirements for breakwatersare usually much less stringent. For example, a breakwater may be neededonly temporarily such as thoseused to es tabl ish the beachheads in WorldWar I I . On the other hand, a permanent s tr uc tu re may be des irable , butthis structure need only be effective intermittently. One can conceiveof a fer ry harbor entrance which only need be protected f r o m wave actionwhen the ferry is moving in or out.

Available construction and maintenance methods can also result inmodified designs. I f , fo r example, navigational aids and the breakwater i t self must be repaired quickly, then a higher cres t el evation may be dictated by the need to move equipment along the dam during severe weather.Indeed, for some purposes, a breakwater need not be much higher than thes t i l l water level, while f o r others i t must be nearly as high as a dike.I f quay f a c i l i t i e s are to be provided on the inner side of the breakwater,special foundations w i l l be required to withstand the addit ional loadsf r o m cargo handling and to l i m i t settlement.

Another contrast w i t h dike is that a breakwater need not always beimpermeable. Some types of breakwaters such as air bubble curtains orf loat ing breakwaters do l i t t l e to re st ri ct currents.


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2 . 5 . ReviewThe more important purposes and design and performance re qu ire

ments of breakwaters have been outlined in a general way. In the f o l lowing chapter, many types of breakwaters w i l l be described b r i e f l yalong w i t h a summary of their advantages and disadvantages.One of the most important tasks of the designer is to achieve asolution to a problem having the lowest total cost. This total cost caninclude much more than construction and maintenance costs of the breakwater; recreational, environmental, and indirect damages w i t h i n a harbor resulting f rom breakwater fa i lure should also be considered. Thisconcept of optimum design has been introduced in chapter 13 of volume I .


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Advantages: Effective.Use natural materials.Usually very durable.Usually very inexpensive to maintain.Aesthetic - recreat ional value.

Disadvantages: Possible sand loss at exposed locations.Need much space - slopes of 1:10 or f l a t t e r are usuallyneeded.

Examples: Europoort EntranceReferences; Volume I I of these notes.c. Composite - Rubble Mound Front

Description: Permanent structure consisting of some f o r m of monol i t h i c vertical breakwater w i t h a rubble mound f o r m placedbefore and against i t . This is o ften used to re fu rbi sh oldmonolithic vertical breakwaters.

Advantages: Low ref lect ion of waves.Moderate material use.Impervious to water and sediment.Can provide quay f a c i l i t i e s on lee side.Can be b u i l t working f r o m structure i ts e lf .

Disadvantage: Expensive f o r m of new const ruct ion since i t uses amultitude of construction techniques.

Example: Improved old breakwaters at Scheveningen and IJmuiden.d. Composite - Vertical Monolithic Top

Description: Permanent s truc tu re consis ting of a rubble moundbase surmounted by a mono lithi c ve rt ic al st ructure.

Advantages: Moderate use of material.Adapts w e l l to an uneven bottom.Provides a convenient promenade.

Disadvantages: Suffers f r o m impact forces of largest waves.Reflects largest waves. This can damage the lower rubble

mound portion.Rubble mound must be ca reful ly constructed in order to pro

vide a good foundation for the monolithic top.Destroyed when design conditions are exceeded.

Examples: f igure 3,2The slope needed is dependent upon the material grain size; finermaterials need flatter slopes.

Figure 3.2COMPOSITEBREAKWATER


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e. Floating Fle xibleDescription: Temporary f lex ib le bouyant f loat ing device which

absorbs wave energy by f r i c t i o n w i t h water and f r o m internaldeformation.

Advantages: Inexpensive, usually.Easily moved f r o m site to si te .Often very quickly fabricated.Relatively independent of bottom conditions.

Disadvantages: Ine ffe cti ve against long waves.Must be anchored.Some types such as brushwood mattresses require much skilled

labor for fabricat ion.Examples: Brushwood mattresses.

Floating auto t i res ,f loating plastic mats.

References: Wiegel, Friend (1958), G r i f f i n (1972), Kowalski (1974).f . Floating R i g i d

Description: Usually a temporary solution consisting of a largef loating body. This may be a ship or a large shallow pontoon.Advantages: Easily moved to new s i t e .

Usually consume l i t t l e space.Can provide temporary quay f ac i l i t i e s .Independent of bottom except for anchors.

Disadvantages: In ef fe ct iv e fo r long waves.Must be anchored.Can resonate leading to poor performance at some wave f r e quencies.Damaged when design condi ti ons exceeded.

Examples: Large ships or pontoons.References: G r i f f i n (1972), Kowalski (1974).

g. Monolithic "Floating"

Description: Semipermanent concept for a monolithic breakwatersuitable for use on mud coasts where the bottom materialbearing capacity is l i m i t e d . The st ruc tu re consi sts of a largecaisson or ship f loating w i t h i t s h u l l projecting some metersinto the mud.


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Advantages: Easily placed.Well adapted to very sof t bottom.Not prone to settle.

Disadvantages: May move w i t h large mass sl ide s o f the mud - seev o l . I , ch. 27.Subsequent dredging proh ibit ed in the area.

h . Monolithic - Porous FrontDescription: A permanent monolithic structure having a porous

front w a l l which acts to absorb the oncoming wave energy.Advantages: Uses relat ively l i t t l e mate rial compared to rubble mound.

Less wave impact and reflection than conventional monolithicstructure.Needs l i t t l e space.Provides quay on lee sid e.

Disadvantages: D i f f i c u l t to construct.Need high quality concrete and workmanship.Even bottom needed.Intolerant of settlement.Foundation problems on fine sand.Severe damage when design condition exceeded.

Examples: Ekofisk storage tank, North SeaBaie Comeau, Canada

References: Jarlan (1961)Marks & Jar lan (1969)G r i f f i n (1972)chapters 13 through 19.

i . Monolithic - Sloping FrontDescription: Amonolithic structure w i t h the upper portion of the

vertical face sloping back at an angle of in the order of 45 .This is often called a Hanstholm type of breakwater.

Advantages: Economical of material.Rather quickly constructed.Less wave impact and reflection when compared to conventional

monolith.Occupies l i t t l e space.Quay f a c i l i t i e s can be provided on lee side .


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Disadvantages: Needs even bottom.Wave impact forces can be locally severe.Waves are reflected.Erosion can take place near the bottom.Inflexible i f settlement occurs.Needs very heavy construction equipment.Foundation problems on f ine sand, except when on a pile

foundation.Severly damaged when design conditions are exceeded.

Examples: Original breakwaters in Scheveningen and IJmuiden.Reference: Chapters 13 through 19 of th is book.

1 . Oil SlickDescription: very temporary emergency measure used at sea to re

duce spray in heavy seas. Effectiveness derives f r o m surfacetension influences.

Advantages: Inexpensive .Easily implemented under emergency conditions .

Disadvantages: L i t t l e , i f any, actual wave reduction.Aesthetic - pollution source.

m. Pi le RowDescription; Permanent st ru ctur e formed by driving a row of piles

either close together or spaced apart. Suitable fo r groins asw e l l as simple breakwaters.

Advantages: Inexpensive.Uses very l i t t l e space.Well adapted to poor foundation co ndi ti ons.Can be incorporated in quay structure.Can be rather w at er ti ght or open as des ired.

Disadvantages: wave re f l ec t ion .Possible scour at bottom.Wood pi le s attacked by worms and ro t .

Examples: Evanston, U.S.A.

References: Wiegel (1961).


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n . Resonant BreakwaterDescription: Aseries of rectangular basins connected to a harbor

entrance such that each is tuned to absorb energy of a givencommonly occu rring wave period . In contrast to ch. 19 of Vo l.a seiche is encouraged in these basins.

Advantages: Can help reduce seiches in main harbor.Can be b u i l t on soft ground.

Disadvantages: Sharply tuned to sp ec ifi c waves.Takes much space.

Example: Dunkerque near lock.References: Valembois (1953)

figure 3.3.0 . Rubble Mound - Pell - mell A r t i f i c i a l Armor Units

Description: A permanent str ucture consis ting of layers o f stoneand gravel protected on the exposed surfaces by a layer ofrandomly placed a r t i f i c i a l armor un it s. A massive st ructur emay be incorporated in the cres t to save material.

Advantages: Durable.Flexible - accommodates se tt lement .Easily adapted to irregular bathymetry.Needs no large natural units.Functions w e l l even when severely damaged.

Disadvantages: Need factory for armor units.Large quant it ies of material needed.Needs underlayer i f b u i l t on sand.Unsuited to soft ground.

Example: Europoort, The NetherlandsSante Cruz, U.S.A.

References: Agema (1972)chapters 4 through 12,

p. Rubble Mound - Placed UnitsDescription: Permanent structure similar to that w i t h pell - mell

unit placement except that units are now individually placedi n a precise pattern. Amonolithic crest construction is usuall y used.

incident vi /aves

harbor basinFigure 3. 3RESONANT BREAKV^/ATER


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Advantages: Durable.Flexible - adapts to settlement.Uses least material of rubble mound types.Adapts w e l l to irregular bathymetry.Well adapted to "dry" construction.

Disadvantages: Armor units must be fabricatedNeeds much s k i l l in construction.Impossible to place armor under water.Unsuited to very soft ground.Needs underlayer i f b u i l t on sand.

Examples: N a w i l i w i l i Kauai, U.S.A.

References: Palmar (1960), Agema (1972)chapters 4 through 12q. Rubble Mound - Stone

Description: Permanent structure consisting of successive layerso f stone. The exposed surface is covered w i t h heavy armorstones.

Advantages: Very durable - resists severe attack w e l l .Functions even when severly damaged.Adapts to ground set tlement.Uses natural commonly available mat er ials.Easily adapted to irregular bathymetry.Construction possible w i t h l i m i t e d ski-lied labor.Uses common construction equipment.Materials are usually inexpensive.Much experience available.

Disadvantages: Uses the most mater ial of a l l types.Must be adapted for construction on sand.Unsuited to very soft ground.

Examples: Marina Del Rey, U.S.A.Winthrop Beach, U.S.A. - See Vol . I , ch. 28 f i g . 28.7a.

References: Chapters 4 through 12.r . Rubble Mound - Stone w i t h Asphalt Spotting

Description: Astone armored rubble mound breakwater w i t h lighterarmor partially keyed together by scattered patches of asphalt.


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Advantages: Lighter armor units than would otherwise be possiblew i t h stone.Flexible for settlement.Easily adapted to uneven bathymetry.Adapts to ground settlement.

Disadvantages: Asphalt plant needed.Very ski l led labor needed to place asphalt.Asphalt can be in eff ect ive in hot weather.Failure can lead to severe damage.

Submerged - vertical or rubble moundDescription: Permanent structure sometimes used to create an

a r t i f i c i a l tombolo, fo r groins.Advantages: Can be designed for desired wave reduction.

Aesthetic - invisible.Reduces longshore sand transport.

Disadvantages: Prevent onshore sand transport.Hazardous to shipping.Foundation problems on sand sometimes important.

Examples: Groins on Dutch Coast.References: Johnson, Fuchs, Morison (1951)

chapter 5.Vertical Sheet Pile CellsDescription: Permanent breakwater or groin construction consis

ting of sheet pile cells f i l l e d w i t h sand, and usually cappedw i t h pavement.

Advantages: Inexpensive.Can be constructed f r o m land w i t h small equipment.Well su it ed to sand and mud bottom.Usually quite durable.Rather fast construction.Provides road or promenade.Insensitive to bottom settlement.

Disadvantages: High wave reflection.Corrosion can l i m i t l i f e .Possible local bottom scour.

Examples: Presque I s l e , U.S.A.Port Sanilac, U.S.A.


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3.3 ConclusionsI t Is obvious f r o m the previous section that no one type of break

water is always best. Further, the choice of a breakwater for a given s i tu ation is dependent upon so many factor s that i t is nearly impossible t ogive specific rules of thumb for determing the "best" type. A few generalrules can be given, however:

- Rubble mound st ructures are the most durable , and as such are bestsuited to extremely heavy wave attack.

- Monolithic structures use less space and material; this is especiallytrue in deeper water.

- Special types of breakwaters are usually best suited to specificspecial applications.

Detail s o f rubble mound breakwaters are worked out in the f o l l o w i n gnine chapters; problems of monolithic breakwaters are taken up in chapters13 through 19.


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4. RUBBLE MOUNDBREAKWATERS J. F. Agema4 . 1 . D e f i n i t i o n

What is a rubble mound breakwater? The cynic's description "a pileo f junk" is not too bad provided that a couple of qualifications areadded. The f i r s t qual if icat ion is that the "junk" must be some r e l a t i vely dense material such as stone or concrete elements (compressedscrap auto bodies have also been suggested). The second is that the "pile"must be b u i l t up in a more or less orderly fashion. In the remaindero f this chapter we b r i e f l y describe the parts of a rubble mound breakwater and thei r interrelationships.

4.2. Two Distinct TypesThe use to be made of the area directly leeward of a rubble mound

breakwater plays an important role in the choice between an overtoppingor non-overtopping rubble mound st ru ct ur e. In general , the less important or c r i t i ca l the act iv i ty on the lee side , the more overtoppingthat may be allowed. For example, i f containers are to be loaded in theimmediate lee area (an operation very sensitive to harbor wave action),very l i t t l e , i f any, wave overtopping would be acceptable. I f , on theother hand, a breakwater served primarily to guide the current near aharbor entrance, the regular overtopping would be of no consequence.

I f a breakwater is designed to be overtopped, then special measuresmust be taken to assure that the upper portion of the inner slope is notdamaged, Anon-overtopping breakwater, on the other hand, must be sodesigned that i t is , indeed, nearly never overtopped. Typical tross sections of these two types are shown in figures 4.1 and 4.2.

Figure / . . lOVERTOPPING BREAKWATER

Anon-overtopping breakwater is usually somewhat higher - re lat iveto the design s t i l l water level - than an overtopping one. The amounto f wave run-up and overtopping on a given slope o f given height i s discussed in chapter 5.


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Crest

^ MSL

zFILTER LAYERS

Figure 4.2NG N OVERTOPPING BREAKWATER

4.3. Basic Construct ion Princip lesNearly every rubble mound breakwater Is constructed I n layers. These

have already been Indicated I n f lgures 4.1 and 4.2. As a general rule,each layer of the breakwater must be so designed that the adjacent layero f f iner material cannot escape by being washed through Its voids. Obviously, the outer layers - both in f i n a l fo rm and during construction -must be designed to withstand the expected wave at ta ck . This is discussedi n detail in chapter 7. Of course, these layers must also be designedsuch that they can be constructed w i t h the available equipment - seechapter 10.

The choice of construction materials is largely determined byavai labi l i ty in the quantiti es needed. Necessary properties of theseconstruction materials - especially of armor units - are catalogedi n chapter 6,

Many times the outer layers of the breakwater can be supportedby a rather undescribable core material. Usually, the cheapest available material is thrown in - see chapter 8.

The rule that adjacent layers may not be allowed to wash throughvoids applies to the natural bottom materi al laye r under the breakwater as w e l l . There are no problems when a rubble mound is constructedon a rock bottom. I f , on the other hand, the bottom mate rial is finesand, then a f i l t e r must usually be constructed. This f i l t e r is described in detail in chapter 9.

Once a breakwater has been conceived (its general dimensionsand properties are sketched) this concept must be economically evaluated. This application of the optimum design technique, described inchapter 13 of volume I , is handled in detail in chapter 11 .


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5. WAVERUN-UP AND OVERTOPPING A. Paape5 . 1 . Introduction

Reflection of waves against a slope or the breaking of waveson some fo rm of breakwater leads to water level fl uct uat ions on theslope surface which can considerably exceed the amplitude of theincident waves. For example, when waves are f u l l y reflected by animpermeable vertical barrier, the water level fluctuation at thew a l l is t he or et ic al ly two times the height of the incident waves.H i-

When waves break on a slope, a portion of their momentum istransferred to a tongue of water rushing up the slope. The run-up,R, is defined as the maximumvertical elevation reached by thistongue measured relative to the s t i l l water level - see figure 5.1.I t is implied in this def in i t ion that the crest of the slope is higherthan the run-up. Since the run-up is measured relative to the s t i l lwater level , the run-up, R, also includes effects of wave set-up caused by tne radiation stress - volume I I .5.2. Run-up Determination

When regular waves are considered, a unique relationship existsbetween the wave run-up, R, and the wave properties, height and period,and structure characteristics, toe depth, slope angle, roughness, poros i ty , and foreshore slope. These parameters are also shown in figure 5.1.Thus:

R= f ( H. , T, h ^ , a, e, r, n) * (5.01)where:

Hi is the incident wave heigt.ht i s the depth at the toe of the slopen is the porosity of the slope.r is the roughness of the slope.R is the vertical wave run-up.T is the wave period.a is the slope of the structuree is the slope of the foreshore

* I t has been assumed that the wave crests approach parallel to thebreakwater.


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Figure 5.1WAVE RUN-UP DEFINITION SKETCH

The energy of the waves approaching i s , in general , partial lydestroyed by breaking, par t ia l ly reflected, and par t ia l ly expendedi n run-up. The wave height, water depth, and wave period determinethe i n i t i a l wave steepness. This steepness, combined w i t h the slope,a, determines the breaking ch ar ac te ri st ic s of the wave - see volume

I chapter 8. This characteristic determines the ratio of reflectedmomentum to momentum consumed in run-up. Thus, f o r constant slope andforeshore properties ( h ^ , a, p , r , n) and wave period (T) , the run-upw i l l ttot be a linear function of the inc iden t wave height . Experimentaldata is presented in fi gu re 5.2. In th is f igure, is the equivalentdeep water wave height, hadthere been no refraction; and \ is the deepwater wave length - see volume I chapter 5, The slopes listed give therat io ver t ica l : horizontal and correspond, therefore, to the cotangent ofthe slope angle, a. The smooth slopes are impervious. Sand beaches canalso be treated as impervious. The curves for rubble mound slopes arefor complete rubble slopes and not fo r ju st a rubble-covered surface .

The influence of the slope, a, is obvious f r o m figu re 5.2. Forsteep slopes, the re fl ec ti on is greater and the run-up i s , in general,less. On the o ther hand, fo r very f l a t slopes, the up-rush is retardedby f r i c t i o n over the long distance so that the height reached is alsoless than the maximum.

Nearly al l of the run-up information available is of an experimental nature , and most applies to impervious structures such as dikes . Anextensive c r i t i ca l bibl iography can be found in an anonymous report(1972) entitled Golfoploop en Golfoverslag.''^

I t is obvious that a more complicated si tua ti on ex is ts when i r r e gular waves are involved. Because the wave pro pert ies now vary continuousl y the run-up also becomes a stochastic va ri ab le . d'Angremond and vanOorschot (1968) report that the statistical properties of the run-up aredependent upon more than ju s t wave charac te ri st ic s fo r a given slope.

An English translation has also been prepared.


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LOO

The fo rm of the wave spectrum in addition to its characteristic waveheigt and period is important for the statistical description of therun-up. Saville (1962) and Battjes (1974) have made reasonably successf u l attempts to relate run-up data obtained w i t h regular waves to thatobtained w i t h ir re gu la r waves. A l l of thi s was done f o r smooth impermeable slopes.

S t i l l less is known about run-up caused by irregular waves onrough permeable slopes such as found on rubble mound breakwaters. Theprinciples involved are the same, but the roughness and permeabilityalso have a definite influence and tend to make the effect of otherparameters less pronounced. These facts are revealed by figure 5.2.

Obviously, run-up is very important for the design of a dike; itsimportance in breakwater design is highli ghted in the next sec tion .

5.3. Run-up in Relation to Breakwater DesignThree factors are of importance when considering run-up influences

on a breakwater. These are: the s tab i l i ty of the structure, the use ofthe cr es t, and the e f fec t of overtopping on the harbor. Each of theseis examined in more detail below.


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The s tab i l i ty and safety of a structure are only jeopardized byrun-up when the crest and inner slope cannot withstand water runningover the i r surfaces; This is oft en true of dikes. Under such conditions, i t is reasonable to design the structure so as to prevent runup reaching the crest (overtopping), even under except ional wave andwater level conditions such as those used to determine the face stab i l i t y . Such an extreme l i m i t a t i o n is usually uneconomical for a breakwater.

When the crest has a function in the harbor operation, such as acting as a roadway or pipeline s t ree t , then very occasional overtoppingcan usually be allowed. "Occasional" here usually means tha t i t occursunder relatively moderate wave conditions such as might occur once ora few times per year. Obviously, th is resu lts in a lower crest el evation than that determined by the f i r s t criterium. Wi th such a designthe effects of mass overtopping under extreme conditions must be adequately considered in the design evaluation. Resulting damage to ahighway or pipelines must be included, for example.

The e f fec t of overtopping, ei ther by wave run-up or spray is d i f f i c u l t to est imate. Overtopping by run-up w i l l be considered i n section5.5. Overtopping by spray i s more dependent upon the wi n d and breakwate r slope propertie s than on the crest el ev at ion. Spray should pre fer ably be reduced by avoiding the fo rmat ion of "spouting" breaking waves.*

These can be reduced by l i m i t i n g the vertical portions and abrupt discontinuities on the front slope.5.4. Conclusions about Run-up

Wave run-up on rubble mound structure s i s , f ort un ate ly, usually lessc r i t i ca l than on dikes or sea-walls. In spite of it s re st ri ct io ns , datapresented in fi gu re 5.2 can oft en be used. When using th is fi gu re w i t hirregular waves, the si gni f icant wave height is usually used in place ofthe monochromatic wave height . Such an approach yi elds a f a i r , and usuall y safe, prel imina ry design. However, only i f the pro je ct i s of very modest size or the crest elevation of the breakwater must be relativelyhigh for other independent reasons, is i t j u st i fi ab le not to conductmodel experiments to investigate run-up and overtopping effects. Oneshould be espec ia lly care fu l when long wave lengths are encountered.Several model studies have indicated that unexpectedly great overtoppingcan occur then.

5.5. Wave OvertoppingI f the crest e leva tion is lower than that corresponding to maximum

run-up, then up-rushing water w i l l s p i l l on to and over the crest of thestructure. The usual unit o f measurement of overtopping is volume perunit time and crest lengt h. This quan ti ty of overtopping is sometimesused as a damage criterium for sea walls. I t can also be used to dimension a drainage system to remove this overtopping water. The "direct"

This should be compared to chapter 15.


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relevance of overtopping is usually less f or a breakwater than fo r aseawall unless important harbor operations are carried out f r o m or closebehind the structure.

In prin cipl e the factors which lead to a decision on allowable runup also lead to a decision w i t h regard to overtopping. However, somepertinent observations are in order.

Overtopping which may endanger a breakwater's s tab i l i ty has neverbeen related to the quantity of water as such. Model test results r elat ethe wave conditions and crest elevation directly to structural damage orrequired armor unit weights. This is , of course, more straightforward.

The amount of overtopping can be a criterium to evaluate a designemploying the breakwater crest in the harbor operat ion. This evaluationi s para ll el to tha t already mentioned in section 5.3.

When the overtopping f l o w is considerable and the water must return to the sea via the harbor, currents w i l l be generated behind thebreakwater. Obviously the quant ity of overtopping must be appreci able ;the crest e levatio n is r e l at ive ly low. A special model study of over topping was ca rri ed out f o r the Europoort Proj ec t. A few other examplescan be found in the l i t e ra tu re but not enough i s known to es tabl ish ageneral predic tion re la ti on sh ip ; usual ly special model studies areneeded.

When the crest e levati on is s t i l l lower, the overtopping water w i l lgenerate waves in harborbasinsas w e l l . This wave generation is deal tw i t h in the f o l l o w i n g section.5.6. Wave Transmission

When the crest of a breakwater is re la t ive ly low compared to thewave height the resulting large volume of overtopping can generate appreciable waves on the lee side. The f o l l o w i n g rules of thumb are suggested:

fo r -pq > 7]: ; minor waves (5.02)f o r ^ = 0 : (5.03)

1 H, 3f o r ^ < - | : ^ > | (5.04)

where:H j^ is the inciden t wave height ,H, is the transmitted wave height, and

i s the el eva tion of the cres t above the s t i l l water level,The above equations can be used w i t h regular as w e l l as w i t h irregularwaves i f the si gn i fi can t wave height is taken to character ize the spectrum.


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The above rule of thumb is only very approximate. In principle, a l lo f the f ac to rs governing wave run-up as w e l l as the breakwater crest w i d t haffect wave transmi ssion. In prac ti ce , the most important parameters arethe incident wave characteristics - determined by H ^ , T, and h - and thecrest elevation, z^. The slope roughness and angle are only important forgentle slopes and wide crests (10 m or more).

For a submerged structure (z negative), the most importantparameter is -pp . Figure 5.3 shows some experimental r es ul ts . The effect of wave steepness is also indica ted. Longer waves resu lt in greater wave transmission. Figure 5.3 does not disagree w i t h relations 5.03and 5.04, This figure may not be extrapolatedl

When the crest is near the s t i l l water level , or the waves areshort and steep, a more dependable parameter fo r wave transmission isthe ratio - j ^ . Thus, figure 5.3 becomes less dependable near - j ^ equalto zero. Se H a l l and H a l l (1940).Some further data is.presented in the Shore Protection Manual butnot presented in a very handy usuable f o r m . One must be very carefu l whenattempting to use their graphs such as m-fure 7.59 in that book; all ofthe parameters must match those used to make their figures.

A correct conclusion is that too l i t t l e information on wave transmission is available in the literature to allow accurate estimates to bemade during design. A factor which makes the establishment of allowablel i m i t s fo r wave transmission even more d i f f i c u l t is the simultaneous presence of waves which penetrate through the harbor entrance. The resultingtotal wave height is not simply the sum of the wave height componentsEven a sum based upon wave energy proves to be unreliable. Large scalemodel tests can provide insight into the problem for specific harbors.

For completeness, we should realize that waves may also penetratethrough rubble mound breakwater. After a l l , i t is , in principle , often apermeable str uc tu re . In pra ct ice, th is permeability to wind waves isusually low, due to the fa ct tha t the waves are re lat ively short and thepossible presence of a breakwater core consisting of f ine material - seechapter 8. However, i f the breakwater i s b u i l t almost exclusively f r o mcoarse materia l (concrete blocks, for example) and the wave period i slong (more than 12 seconds in order of magnitude), this wave penetrationmay no longer be negligible. Because of the nonlinear character of thef l o w through such a coarse porous medium, scale effects can cause severeproblems for the interpretation of model data. Veltman-Geense (1974) hasattacked the problem of wave penetration both theoretically and experiment a l l y .

Propert ies required of armor units used to protec t the exposed faceso f breakwaters are discussed in the f o l l o w i n g chapter.

0.2 -io


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Materials which pack into rather porous layers (have high v o i drat io) tend to damp the waves more effectively. Also a savings in totalweight of mat eri al result s and wave forces acting on the outer layersare reduced. On the other hand, th is desirable large porosity can be inconf l ic t w i t h the containment property for armor layers lis ted above.Armor units which more or less interlock can prove to be more resistant to wave forces since a locally high wave force is distributedthroughout several uni ts . I f , thi s interlocking is disturbed, however,severe damage can result. Conservatism in the design of breakwater crestsand ends is often advisable, since interlocking effects are least pronounced where an armor layer curves sharply - see chapter 7.

6.3. Characterizing Coeff icie nts fo r Armor UnitsNow that the proper tie s of rubble mound breakwater materials in ge

neral and of armor units in particular are w e l l de fined, we need to translate these properties into quantitative parameter values suitable foruse in computations. L u c k i l y , these properties can be reduced to four parameters, two of which are important for s tab i l i ty . These are each discussed a bi t below; values f or them fo r sp eci fi c armor units are given inthe f o l l o w i n g section. Their use in computations is explaned in chapter 7.

The most straightforward property of an armor unit to express quant i t a t i v e l y is its mass density, p ^ . Since the density is only dependentupon the material used in the armor uni t , densit ie s of the common armorunit materials w i l l be discussed here.

Granite, the most common natural armor stone ranges in density f r o m3 3 32650 kg/m to 3000 kg/m w i t h most sor ts having a densi ty near 2700 kg/m .Basa lt , another commonly used stone, has a density of 2900 kg/m~ . Veryoccasional ly , limestone blocks are used in a breakwater. It s lower re-3sistance to environmental attack and lower density - 2300 to 2750 kg/m -are a handicap.Concrete for armor units usually ranges in density between 2300 and33000 kg/m . Special aggregates needed to achieve even higher concrete dens i t i e s usual ly prove to be too expensive to be economical. The concrete

2used should have a 28 day strength of at le as t 30 N/mm .The remaining properties of an armor unit - shape, degree of interlocking, roughness,location on breakwater, et c. - are combined into one socalled damage coef f ic ien t , K^. This emperically determined coefficientand the density, p ^ , determine the necessary block weight for a givenslope geometry and wave condition - see chapter 7.

Two other parameters are of primary importance fo r dimensioningand pricing a breakwater. The f i r s t of these indicates the degree towhich the armor uni ts pack together and is cal led a laye r co e ff ic i ent ,K^. I t represents the ratio of the length of a typical dimension of thearmor unit to the length of the edge of an equivalent cube and is usedto determine layer thicknesses.

Lastly, the volume of voids in an armor layer is given by i t sporosity, n, the ratio of v o i d volume to total volume. This is used,primarily, in de termining the number of armor uni ts needed for a givenproject.


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Details about a var ie ty of armor un it s, l i st ed in alphabe tical order, are given in the f o l l o w i n g section. Agema (1972) and Hudson (1974)also give summaries of available block forms.

Unless otherwise specified, damage coe ff ic ie nt values are given fo ra double layer of randomly placed armor units subjected to non-breakingwaves in the main body of the breakwater.* "Percent damage" refers tothe percentage of armor units in the area exposed to attack which aredisplaced so far that they no longer f u l f i l l their function as armor. Thisrather arbitrary damage measurement is chosen f or i t s ease of measurement(via counting) and u t i l i t y in optimum design procedures.6.4. Armor U n i t Typesa. Akmon

An anvil shaped plain concrete block - the name comes f r o m the Greekfor anvil - developed in 1962 by the D e l f t Hydraulics Laboratory. A photoo f such a block is shown in figu re 6. 1 . Because of their high value, amassive monoli thic crest is suggested. The density of the blocks is thesame as that fo r concrete. The damage coefficient has be'en found to varyaccording to the allowable damage as follows:

Damage K,m0 4.81 11.2 12.5 ^ 17

Further, slopes of up to 1:1.33 are possible. The porosity, n,is 55 to 60%, and the laye r co ef f ic ient , is about 1.00. The datapresented above are based upon only a l i m i t e d number of model tests.Reference: Paape and Walther (1962)

F i g u r e 5.1AKMON ARMOR UNIT

See chapter 7 and Shore Froteot-Lon Manual.


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b. CobThe cob is a hollow concrete block made by cas ting only the edges

o f a cube - see figure 6.2. They are normally placed in a regular pattern in a single layer; they must be placed w i t h their sides touching.

Preliminary model test data indicates that cobs have very highdamage coe ff ic ie nt values, but give no quant itat ive information. Instead,i t is suggested that model tests be conducted when specific applicationsare being considered. Amonolithic crest construction w i l l be requiredi n order to guarantee the i r s tab i l i ty .

Cobs have a porosity of about 58 and a layer co ef fi ci en t, of1.33. This high porosity implies that a major part of the core containment function must be accomplished by lower armor layers.Reference: Anon (1970): A r t i f i c i a l Armouring of Marine Structures.

c. CubeCubes of stone or concrete have been used as breakwater armor for

centurie s. As such, they are, w i t h natural stone, the oldest uni ts . F i gure 6.3 shows a photo of a concrete cube. Obviously, their density isdependent upon the concrete used. Cut stone cubes are no longer economical now tha t concrete can be worked so e f f ic ien t ly .

Damage coeff ic ient values are l i s ted below:Damage Kr,

(%)0 3.51 7.2 8.5 ^ 14

Randomly placed cubes have a poro si ty o f about 47% and a packingcoeff ic ient , K^, of about 1.10.Reference: Paape and Walther (1962).

Figure 6.3CONCRETE CUBE


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Because of. i t s good in te rlocking ca pabi li ty , the dolos has thehighest damage coefficient value - K Q = 2 2 to 2 5 , Because of this, abreakwater face may f a i l by means other than armor unit displacementdown the slope. A s l i p fa i l u re of the ent ir e slope i s the most probableunless slopes f latter than 1:2(vertical:horizontal) are used.Dolosse have a porosity, n, of 6 3 and a layer coefficient, K ^ - of1 . 0 0 .

f . Quadripod - see Tetrapod

g. Quarry Stone - -RoughThis is natural stone obtained by blasting w i t h i n a rock quarry.

I t is characterized by a very rough, angular, ir re gu la r shape.Such stone has a damage coeff icientdependent upon the acceptable

damage.Damage h{ )

0 - 5 4 . 05 - 1 0 4 . 9

1 0 - 1 5 6 . 61 5 - 2 0 8 .02 0 - 3 0 1 0 . 03 0 - 4 0 1 2 . 24 0 - 5 0 1 5 . 0

Its porosity in a layer, n, is about 3 7 and i t has a layer coeff i c i en t , K ^ of between 1 . 0 0 and 1 . 1 5 .Reference: Shore Protection Manual

h . Quarry Stone - SmoothThis is also stone obtained by blasting w i t h i n a quarry, but more

regularly shaped and smoother than the previous sort. Since its smoothnessreduces i ts ef fect ive f r i c t i o n between armor elements, i t tends to havelower damage coefficients than other stone:

Damage h(%)0 - 5 2 . 45 - 1 0 3 . 0

1 0 - 1 5 3 . 61 5 - 2 0 4 . 12 0 - 3 0 5 . 13 0 - 4 0 6 . 74 0 - 5 0 8 .7


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Smooth stone has a porosity of about 38% and a layer coeff ici ento f 1.02.Reference: Shove Proteotion Manual

i . Tetrapod and QuadripodBoth tetrapods.and-quadripods are plain concrete armor units

consisting of four arms projecting f r o m a central hub. The angularspacing between al l arms of a tetrapod is the same; Three of thefour arms of a quadripod extend horizontallywhile the fourth arm extends ver t ical ly . The tetrapod was developed by SOGREAH in France in1950; the quadripod by the U.S. Corps of Engineers in 1959. These unitsare l i s ted here together because they have identical design properties.Figure 6.6 shows a photo of a tetrapod.

Figure 6.5TETRAPOD

The damage coeff ic ientvalues vary w i t h the allowable damage:

Damage(%) K D *

0-5 8.35-10 10.8

10-15 13.415-20 15,920-30 19.230-40 23.440-50 27.8

* The values lis ted are given by Hudson (1974); Paape and Walther(1962) report much lower values.


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Here, also, because of a high value , a mono lithic cres t construct i o n is usually required to guarantee that the units do not slide up thebreakwater slope.

Tetrapod armor layers have a poros it y, n, of 50% and a layer coeff i c i en t , K^, of 1.04.Reference: Danel, Chapus, and Dhaille (1960)

j . TribarA tri bar is a plain concrete unit consisting of three vertical

cylindrical bars connected to a central hub. I t was developed inthe United States in 1958. Unlike the previous armor units, tribars aresometimes arranged in a single layer w i t h the axes of the three c y l i n ders perpendicular to the slope. Figure 6.7 shows such an armor unit.

I n a single uniformlyplaced layer the t r i bar has a damage c o e f f i ci en t of about 14. When i t i s randomly placed in a double layer then thef o l l o w i n g values have been found:

Damage Kj{ )0-5 10.45-10 14.2

10-15 19.415-20 26.220-30 35.230-40 41,840-50 45,9

Amonoli thic crest cons tructio n is required to prevent the unit s f r o msl iding up the breakwater face, especially when a single uniform layeris used,

Asingle uniform layer of t ri ba rs has a porosity of 47% and a laye rcoeff ic ient of 1.13. The high porosi ty has i mpl ica tio ns fo r the secondary armor layer which must be very eff ect ive at conta ining the lowerlaye rs . See chapter 7 sec tio n 4.

Reference: Hudson (1974)6.5. Armor Selection

As one may conclude f r o m the variety of armor unit shapes available,no single type of armor unit is univ er sal ly acceptable. Quarry stone armoris usually cheapest per ton but a larger volume is needed than when concrete un its are used. Why? - because the lower Kp value re qui res ,fl att erslopes to achieve the same s tab i l i ty . See chapter 7, On the other hand,a concrete plant is not needed when quarry stone is used.


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I f , on the other hand, a r t i f i c i a l armor uni ts are selected, then o ften one having a relatively high value such as tet rapods or dolosse canprove most economical since the breakwater cross section can be mademuchsmaller and/or l ig ht er unit s can be used. The mono lith ic crest const ructi oncan even save total material cost by allowing - sometimes - a lower cres tand lighter lee side armor than would otherwise be possible.

I n the f o l l o w i n g chapter, where computations of necessary armor unitweights are presented, some of these items come up again.6.6. Methods to Increase Stabil ity

I t is conceivable that armor layers having even higher effectivedamage coeff icient values can be economical. What are the methods ava ilable to increase the Kp value of armor unit s?

One technique used on the breakwater extension at IJmuiden was toadd asphalt to the stone armor layer. This served as a binder causingthe armor layer to function as a unit and was, therefore, more resistant to wave attack than the individual stones. Unfortunately, theasphalt was also s uf fi c ie nt to f o r m a wate r- ti gh t covering such as iscommon on dikes. This required that the armor layer r esi st the res ul ti nghydrostatic u p l i f t fo rce s. F urther, the reduced porosi ty increased thewave run-up the slopes. These las t two problems are, of course, detrimental to a design.

Aproposed alt er na ti ve is to use smaller quanti ti es of asphalt placedhere and there on the armor layer surface to t i e individual armor unitstogether into larger units but not to form a closed layer. The hope isexpressed by proponents of thi s tha t s uf fi ci ent proro sit y w i l l be maintained to prevent hydrostatic u p l i f t pressures and to s t i l l absorb thewave energy.

Development of these concepts is proceeding slowly, partially becauseof the d i f f i c u l t y of scaling the elast o-p las tic properties of asphalt ina model.


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7. ARMOR COMPUTATIONS L . E . van LooW.W. Massie

7 . 1 . HistoryU n t i l less than f i f t y years ago, rubble mound breakwaters were

designed purely based upon experience , usually in prototype. Castro(1933) seems to have published the f i r s t modern work on th is subj ect .I n i t i a l attempts to compute necessary armor unit sizes were basedupon the ore tic al considerations of the equilibrium of a single armorunit on a slope. One need only to visualize the complex f l o w patternsi n a breaking wave rushing up a breakwater slope to conclude that apurely theo re ti ca l approach is impossible . The theo re ti cal backgroundo f the currently used formula is indicated in the f o l l o w i n g section.7.2. Theoretical Background

Consider a single armor unit resting on a slope making an angle ew i t h respect to the horizontal as shown in figure 7.1.The wave force, F, acting on the block, can be approximated very

crudely by considering the drag force of the water excerted on the block.This approach yields a force proportional to the unit weight of water,the projected area of the armor unit and the water surface slope. Whenwe fu rt he r l e t the surface slope be proport ional to the wave height(This is reasonable since the wave length i s determined by the wave periodand water depth only.) then i n a mathematical f o r m :

where:F is the drag force,d is a chara ct er is ti c dimension of the block,g is the acceleration of gravity,H is the wave height,p is the mass density of water, anda denotes "is proportional to".Other assumptions about the force description can be made; all run

into d i f f i cu l t i e s somewhere. Therefore, (7.01) w i l l be transformed into anequation by introducing a proportionality constant, a:

This fo rce can act eithe r up (uprush) or down (backwash) the slopeas shown in f ig ur e 7 . 1.

Using f igure 7.1, equilibrium of forces perpendicular to theslope yields:

2Fa ( p , g, H, d ) (7.01)

F = a p g Hd (7.02)

N = Wsub cos 6 (7.03)where N is the normal f orc e.


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This normal force is related to the f r i c t i o n f or ce , f , by thecoefficient of st at ic (Coulomb) f r i c t i o n , v.

f = y N (7.04)Equilibrium para ll el to the slope i n fi gu re 7.1a (uprush case)

yields:

f = F - W^^j^ si n e (7.05a)and fo r backwash ( f i g . 7.1b):

f = F + Wg^jjj si n e (7.05b)or, more generally:

f 1 F - ^sub ^ .(7.06a)and

f 1 F + Wg^j[j sin e (7.06b)respectively. These become:

cos e+ sin 6 ) i a p g Hd (7.07a)

W2y, (y cos e - s in 8) a p g Hd (7.07b)The submerged weight of the armor unit can be expressed as its

unit weight , g, times i t s volume minus the weight of displaced water.I t is assumed, further, that the volume of the armor unit may be expressed as some constant, b, times the cube of it s characteristic d i mension, d. In equation f o r m :

"sub = (P a - P g b d (7.08)Substitution of (7.08) into (7.07) yields:

3 2(P g - p) g b d u cos e + sin e) a p g H d (7.09a)(P g - p) g b d' u cos e - sin 6) a p g Hd (7.09b)

which reduce to:p, P

( ^ ) b d y C O S e + sin 6)^ a H (7.10a)p, - ' P

( - 2 ^ ) b d j i cos 6 - sin e) a H (7.10b)for uprush and backwash re spec ti ve ly .


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Analogous to the notat ion used in densi ty currents (volume I chapter 22),let :

p, - P (7.11)Substituting (7.11) in (7. 10), rearranging, and cubing both sides yieldsb ^ d 3 > - ^ ijl (7.12a)

A (u COS 6 + sin 0)

b3 3 (7.12b)A (u COS G- sin e)

The weight, in air, of our armor unit is:

W= P g g b d (7.13)(7.13) in (7,12) results in:

W 1 3 3 (7.14a)A {\i COSe+ sin e)

for uprush, and 3Pa 97Z h2

W 3 3 (7.14b)A ( y COSe - sin 6)

for backwash,This is e ff ect iv el y the formula derived by Irib arr en (1938).A primary disadvantage of equation 7.14 is i t s abundance of emperical

coefficients; a, b, y, and p^ a l l must be determined f o r a given armor unittype. This has led to many emperical al tern ativ e proposals t o replaceIribarren's formula w i t h a simpler one.

While these alternative formulations have even less of a theoreticalbackground, they often prove to be more handy i n practice. A summary of theseformulas is presented in a Report of the Intemational Commission for theStudy of Wave Effects of the PIANC (1976). I t would serve no purpose to discuss all of these formulas here individual ly. Instead, the shaded area infigure 7,2 shows the range of results obtained using the various availableformulas. Angular stone armor un it s having a given densi ty and exposed to aconstant wave height were assumed.

One of the more convenient alt er na ti ve s to equation 7,14 is developedi n the next section.


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The Hudson Formula was developed fo r use on the outer layer of themain (trunk) p or tion of a breakwater. F urther , as already mentioned, i tapplies only to the front slope. While the formula is very helpful evenw i t h these re st ri ct io ns i t can sometimes be applied to other cases asw e l l ; t hi s is discussed in the f o l l o w i n g section.7.4. Special Applications

Breakwater endsThe convex shape of the end of a breakwater can be expected to i n

crease the exposure o f the armor uni ts to wave at tack . In ad di ti on , theconvexity can reduce the degree of int erl oc ki ng between adjacent armorunits. Both effects can be incorporated in the Hudson Formula, equation7.15, by reducing the value of the damage co e f f i c i en t , K ^, appropriately.This reduction amounts to between ten and f o r t y percent depending uponthe type of armor unit . The reduction is usually greatest for armor unitshaving the higher Kp values (most interlocking). The Shore ProteotionManual tabulates Kp values fo r ends of breakwaters (st ructure head). Often the lower Kp value is compensated by se le ct ing somewhat fl a t t e r slopesat the end so that the same armor size may be used.

ToeThe Hudson Formula can be appl ied di rec t ly to the design of the toe

o f a breakwater exposed to breaking waves. This is discussed in more de tai li n chapter 9.

Secondary armorA breakwater must be stable during const ruct ion as w e l l as after

i t s completion. Thus, i t is necessary that the inner layers directlyunder the primary armor (secondary armor) be dimensioned to withstandthe waves that can be reasonably expected during the constructionperiod. The Hudson Formula may be applied di re ct ly to th is problem inthe same way that i t i s used fo r the primary armor laye r. Because ofthe l i m i t e d exposure time, however, a somewhat less severe storm canbe used. Usually, this secondary layer w i l l be made f r o m stone havinga weight of about 1/10 of that of the primary armor.

When especially porous armor unit placement is used in a singlelayer we must be especially aware of the containment function of thesecondary armor. This extra function is most apparent when cobs ortribars are used for the outer armor. See chapter 6.

Angular wave attackAs we have seen in volumes I and I I , the angle of wave approach

is very important to the s tab i l i ty o f a beach. For a breakwater, however, the angle o f wave attack is not important for the s tab i l i ty ofthe armor. Even waves propagating along orthogonals parallel to thebreakwater axis have been observed to damage the armor layer. The reasonfor this has not yet been su f f ic ien t ly inv es ti ga ted, but may be that theweight of the armor unit no longer contributes directly to its s tabi l i ty


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when equilibrium along a slope contour l ine is being considered - seefigure 7.3 and compare to figure 7 . 1 ,

Inner slopeThe Hudson formula may be used to investigate the s tab i l i ty of theinner slope of a breakwater subject to direat attack f r o m waves on the

lee side of the stru ctur e. These waves may be generated w i t h i n the harbor by winds or passing ships or may enter the harbor through the entranceor by overtopping another portion of the breakwater.

The Hudson Formula is inadequate however, to predict armor weightsnecessary to withstand the attack f r o m waves spi l l ing over the breakwatercrest f r o m the opposite side of the structure.^Detailed model studies are required to inves tigate the behavior ofbreakwaters too low to prevent overtopping.

w,sub INF i g u r e 7.3EQUILIBRIUMALONGCONTOUR

CrestThe Hudson Formula is also inadequate to dimension armor un it s

for the cres t of a breakwater overtopped by waves; Once again, de ta il edmodel tests are required.

Armor units having higher damage coef fi ci en t values need addit ionalsupport at the top of their slope. Monolithic crest structures are thenrequired. Even though these are usually more expensive to construct, inthemselves they can save enough total material to be economical.

7.5, Sensit ivi ty of Hudson FormulaNot al l o f the parameters in the Hudson Formula, equation 7.15, canbe exactly determined for a given design problem. Therefore, i t can beinstructive to examine the inf luence of small changes of the various parameter values upon the r es ulti ng weight of the armor unit . In the f o l l o wing discussion the influ ence of a given change in a parameter is re fl ec ted in a change in the armor weight, W, A l l other parameters are assumedto be constant. For convenience, equation 7.15 is repeated here:

,3W

Kp A cot( e)(7.15)

When the wave height increases by the required armor weightincreases by 33/. A 10%decrease in wave height decreases the block-weight by 27%. Thus, the formula magnifies small er rors in wave height .

Increasing the density of the armor unit by 10%decreases the armor weight needed by about 30% for normal values of armor and water dens i t ies^* Decreasing the density by 10% increases the necessary weightby 55%: What is the effect of substituting Swedish Granite p ^ = 2650 kg/m^)for .Basalt (P g = 2900 kg/m ) for armor units? The ratio of the armor weightsis:* This is the reason that the crest elevation was earlier assumed to

exceed the run-up.1025 kg/m' and p = 2600 kg/m'^.


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'^granite (2900 - 1025) 2650 ,-,'^basalt ^^^^ (2650 - 1025)''

= 1.40 (7.17)The granite blocks must be 40%.heavier than the basalt stone

to achieve the same s tab i l i ty .Increasing the value by 10%decreases the necessary armor

weight by 9%. This change in the damage coefficient could be accomplishedby sele cting a di ff e re nt type of armor or possibly by accepting a greaterdamage to the struc tu re during exposure to a given storm; see chapter 6.7.6. Choice of Armor Units

The sensitivity of the Hudson Formula to wave height changes has beendemonstrated in the previous sec ti on . The wave height chosen for designpurposes is seldom accurately related to a frequency of occurrence.Equivalently, the si gn if ic ant wave height associated w i t h a given frequencyo f occurrence,such as once per ten years,is seldom accurately determined.Thus, i t seems appropriate to select an armor unit which forms a layer mostre si stan t to waves (storms) which may exceed the design condition.

Normally, the Kp values used in equation 7.15 are associated w i t h onlyslight damage to the armor layer - perhaps 1% of the u nits e ff ec ti ve l y removed. Onthe other hand, i f we wish to accept a higher damage to our designwe can account for this by increasing the damage co ef fi ci ent values in theHudson Formula. This i s the background of the tables of Kp versus percentdamage given for some armor unit s in chapter 6. How can this informationbe used to predict damage when the design wave heights are exceeded?

Once v;e have made a design and selected an armor uni t , then the onlyvariables l e f t in the Hudson Equation are Kp and H. Equation 7.15 can betransformed to show the re la ti on sh ip :

Kp = 3' - (7.18)WA co t(e)yielding:

H * = - \ ^ / ? . H (7.19)

where:H* is the unknown wave height causing a chosen experimental ly

determined damage,H is the wave height f o r no damage,Kp is the damage coe ffi ci ent for the damage percentage caused by H,

andKpi' is the damage coefficient for no damage.


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Thus,1/3

TT K, (7.20)DWecan use equation 7.20 to compare tr iba rs to te trapo ds, fo r example.

Using data f r o m chapter 6, we can make the computation shown in tab le 7.1i n which the wave height ratios are computed using equation 7.20. The resultsare also shown in a graph, f igu re 7.4; i t appears that tribars are superior.TABLE 7.1 COMPARISON OFARMOR UNITSDamage Tetrapods

^ TTTribars' D I T

{ ) (-) (-) (-) (-)0-5 8.3 1.00 10,4 1,005-10 10.8 1.09 14,2 1,11

10-15 13.4 1.17 19.4 1.2315-20 15.9 1.24 26.2 1.3620-30 19.2 1.32 35.2 1.5030-40 23.'4 1,41 41.8 1.5940-50 27.8 1.50 45,9 1.64

0 10 20 30 AO 50Damage to A r m o r l a ye r ( )

Figure 74COMPARISON OF ARMOR UNITS

One must be careful about drawing conclusions based solely upon computations of the sort j us t carr ied out. Nothing is i ndica ted about theabsolute block weights required or about diffe rences in capi ta l costs ofvarious armor units.

Data necessary for determining figure 7.4 are available only for a fewtypes of armor units. For other armor, detailed model tests are needed toodetermine the relationship shown in the f igure. Except for very small proje ct s i t is strongly recommended tha t model tests always be used to v e r i f ythe given coefficients for the specific project under consideration.

Armor layer design considerations unrelated to the Hudson Formulaare considered in the f o l l o w i n g two sections of th is chapter.7.7. Layer Extent and Thickness

Since the primary armor layer can be more expensive to constructthan other port ions of the breakwater, i t is advantageous to l i m i t thearea covered by primary armor units as much as possible consis tentw i t h s t ab i l i t y needs. Only a few rules of thumb ex is t to indica te thenecessary extent of this armor layer. These should be confirmed by experiments i f the pro ject is at al l extensive .

Normally the primary armor un it s are extended downward on the breakwater slope to an el evat ion of 1.5 H below the s t i l l water level . Whetheran extreme storm f l o o d water level and a severe storm must be chosen or amoderate storm w i t h low water level depends upon which condition resultsi n the lowest absolute el evat ion fo r the bottom of the primary armor.


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7.8. Crest WidthThe crest w i d t h o f a rubble mound breakwater Is determined by the

degree of wave overtopping and construction requirements. When there Isno overtopping, the waves no longer Influence the choice of crest w i d t h .When overtopping Is expected and primary armor unit s cover the cre st , thenthe crest should be at least wide enough to allow three armor units to beplaced across I t . Thus:

where:B Is the crest w i d t h , andm' Is the number of armor unit s across the crest - usually at least 3.When a breakwater is to be constructed or maintained by construc tion

equipment working f r o m the cre st , then the crest w i d t h w i l l possibly bedictated by the space needed fo r e f f ic ien t use of the chosen equipment.This w i l l be discussed again in chapter 10.7.9. Review

The background and use of the currently popular semi-empericalrelations for rubble mound breakwater armor layer computations havejus t been presented. Because of the ir emperical nature,, the equationsmust be used w i t h caution. Extrapolation, for example, is incorrect andirresponsible.

In practice the formulas presented here and the coefficients listedi n chapter 6 should, at best, be considered to be guide lines. Extensivemodel testing is required for all except the most modest projects.

The requirements for and design of the deeper layers of a breakwaterare discussed in the f o l l o w i n g two chapters.


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8. THE CORE J.F. AgemaE.W. Bijker

8 . 1 . FunctionThe primary function of the core material of a rubble moundbreakwater i s to support the covering armor layers in their proper

position. A secondary function, stipulated when the breakwater mustbe sand-t ig ht , is that the core be reasonably impermeable. I t need,i n f ac t , only be impermeable to sand; water may continue to f l o w throughi t . In prac ti ce , however, a designer should not plan on const ructi ng asandtight damwhich wi.11 allow much water to pass through i t - at leastno t fo r long. Marine growth w i t h i n a breakwater core can reduce i t spermeability s ignif icant ly w i t h i n a few years.

Occasional ly, i t is required that a breakwater be wat er ti gh t. Thisi s of te n true, f or example, when a breakwater must serve to guide thecooling water fo r a thermal power st at io n. In such appl icat ions di re cttransfer of discharged water to the intake water can be detrimental tothe thermodynamic e ff ic iency of the pl an t. Special impermeable core constructions-must then be provided. These types of cores are described inthe l i terature and courses on dikes.

The choice of a core material w i l l have an influence on the armorunits. As the permeability of the core decreases, the portion of thewave energy expended upon the armor layers increases, resulting in ahigher e ff ec ti ve attack on these units. Quantitative information can beobtained only f r o m model experiments.8.2. Materials

Since most any non- floa ti ng material w i l l be su ff i c ie nt to supportthe cover layer, the choice of a core material is.usually dictated byconstructional or economic requirements.

When quarry stone is used for armor, then the f iner tail ings - scrapmaterial f r o m the quarry, oft en cal le d quarry run - can be advantageouslyused in the core. This material, because of its w e l l distr ibuted range ofgrain sizes, (us ua lly) forms a rather impervious core.

I f this sort of w e l l graded material i s not ava il abl e, other coreconst ructions can be conceived. Small (a few hundred kilogram) concreteblocks have been used in some cases. Rubble f r o m razed masonry buildingshas even been used occasionally.

I f an impermeable core is required, but the available core materialsw i n remain too permeable f or sand and water, asphalt or grou t can beinjected into the core to decrease i t s permeability. Of these materials,asphal t is probably to be pre ferre d since i t maintains a degree ofplas t ic i ty during settlement of the str uc tur e.

The core of a breakwater or even tha t o f a seawall is fundamentall y d i f f e ren t f r o m tha t of a dike . F i rs t , the core is usual ly the onlyimpermeable part of a breakwater while a dike usually has several im-


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permeable layers. Second, at best a breakwater need only be absolutely impervious to sand; there is usually no need to prevent waterseepage - something which can be disasterous to a dike.

8.3. Construction MethodsWhen reasonably fi ne material can be used for a core, much of this

core can often be placed simply by dumping the material f r o m bottom dumphopper barges. This sort of construction technique is less advantageouswhen coarser material must be used.

One must be cautious in design to provide adequate protection forthe core material during construction. This w i l l be highl igh ted as parto f chapter 10.


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This damping is a fu nc tion of the breakwater material grain size andwas investigated by de Lara (1955) and by Le Mhaut (1957-58).

The velocities resulting f r o m the pressure fluctuations are evenharder to determine. Physical models run into problems since the porosityof the breakwater material does not f o l l o w simple scaling laws. Veltman-Geense (1974) has investigated this. Even though average f l o w velocitiesnear the bottom of a breakwater may be small, the irregularity of the f l o wchannel f o r m can lead to locally high velocities which result in scourand thus set tlement . Obviously, th is settlement does not continue i n d e f i n i t e ly . As the breakwater material penetrates deeper the damping influencebecome greater; eventually an equilibrium is reached. Unfortunately i f nof i l t e r were b u i l t , settlements of several meters could be possible, re su lt ing in much waste of mate rial . Therefore, i t is usual ly more economicalt o b u i l t a f i l t e r under a breakwater located on an erodible bed. The purpose of this f i l t e r w i l l be to prevent the occurrence of f l o w velocitieshigh enough to cause erosion of fine bed material.

An additional purpose of the toe construction is to prevent the armorunits f r o m sliding down the face of the breakwater. This is also shown infigure 9.1.9.3. Design Criteria for Filters

An adequate f i l t e r construction on a sand bed must satisfy two criteriaa, i t must prevent the erosion of material f r o m under the breakwater

caused by horizontal currents, andb. i t must prevent the formation of a quicksand condi tion caused by

an abrupt vertical f l o w (pressure gradient) in the sand.Most f i l t e r constructions which satisfy one of the above conditions

w i l l satisfy the other as w e l l . Model tests of f i l t e r s run into scale d i f f i cu l t i e s ; often f u l l scale tests are conducted for large or importantbreakwater projects.9.4. Design Criteria fo r Toes

In addition to the criteria already listed for f i l t e r s in the previoussection, toe constructions must also remain stable under the action ofwaves, currents and the lateral load f r o m armor units on the slope. Inaddition, extended revetment type toe construct ions must be f lex ib le enoughto f o l l o w changes in the bottom profile which can result f r o m local scournear the revetment edge.

The currents which cause erosion in this area may result f r o m wavepressure fluctuations, but may also be caused by tides or a longshore current.

9.5. F i l t e r Layer ConstructionsA conventional f i l t e r layer is usually b u i l t up of a few layers o f

progressively coarser gravel. The construction work must be carried outw i t h reasonable care, since a gap in a layer of the f i l t e r can result ineventual fa i lu re . A certain degree of overdimensioning is usually j u s t i f i ed .


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