concrete armour units for rubble mound breakwaters and sea...
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ftt*attlsResercttMhlingrford
CONCRETE ARMOUR UNITSMOUND BREAKWATERS ANDRECENT PROGRESS
FORSEA
RUBBLEWALLS:
N I . f H Al lsop BSc, C Eng, MICE
Report SR 100March 1988
Registered Office: Hydriulics ResearchWallingford, Oxfordshire OXIO 8BA.Telephone: (X91 35381. Telex: 84.8552
This report describes work jointly funded by the Department of theEnvironment and the l,l inistry of Agriculture Fisheries and Food.
The Department of the Environment contract number was PECD 7 16152 for whichthe nominated officer rras Dr R P Thorogood.
The Ministry of Agriculture Fisheries and Food contribution was lrithin theResearch Connission (Marine Flooding) CSA 557 for which the nominatedoff icer was l{r A J ALl ison.
The work was carried out in the Maritime Engineering Department ofHydraulice Research, lfall-ingford under the rnanagement of Dr S I,l Huntington.
The report is published on behalf of both DoE and I'|AFF, but any opinionsexpressed in this report are not necesearily those of the fundingDepartments.
@ Crown copyright 1988
Publ iehed by permission of the Control ler of l ter Majestyts Stat ioneryO f f i c e .
Goncrete,armour "unite.for' rubble mound breakwaters,sea val,ls and. revetuentsS recent :pfogf,eas,
N lJ H Al leop
Report SR 100, ilarch 1988
Eydraulics Reeearch, Wal lingford
Abetract
ilany deep water breakrvatera constructed in,the laet 2O-50 years are ofrubble sound construction, proteeted againat the effects of rave aetion byconcrete armour nnite. Ttrese units are oftea of complex ehape; Ttrey aregenerally produced in unreinforced concrete ia eizee between around 2-50tonnea depending apon the local water depth, the eeverity of the locel saveeonditione, and on the efficiencl and: stsbiiity of the unit type selected.On any Particular project, unitc may codnonly be required in more than oneeize. ltaay different chapee have been ouggcsted, Uut data euitable for usein design ie avai labte for relet ively few.,- :
Over the last ten Jrears a significant, number of,relative,ly: new breakwatersarmoured rith concrete units bave been severely damaged. Ttre costs of therepair or recoaatruction of these.etracturee ie often close to the originalconstruction coat, in the range C5U-850U per kilometre length. So,ae oftheee atructurea are in exceas of,. 2-3 hn1 and nlaay are.loaler.than 0.5 kmrgiving structure costs arouad'll0ll-f,1001[. ttre failure.rat; ,for breakwatersis so high that the ineurance'industry regard them",ae eoneituting:a riskaround 100-1000 tiuee worae than a building.
One -of the na jor cootributi.ong,, to reeeat'',failuree has. been the displaceuentand/or breakage..of the .concrete arnour unitei ,In perticular exceaaivearmour movement" eombined with the relative.fregil,ity of nany unreinforcedarmour rrnits, .bave been identifted,as na,jor a^reea of seakness.
Thia reporlt sumarisee the, resnltc of a research s,tudy on the design andperformance of concrete arnour rrnite.. It includeg detaile.of hydraulicmodel tests to identify armour unit movenent or dispLaceuent, ev€reflections and Fun-up levele; calculation, of armour units loadsi newmathematical and physical nodelling techniquea; aad analysis of data.'fromPrototyPe e:perieace. Ttre report includee regulte from a number of phyeicaluodel studieer a comprehensive list of refereneesn and a bibliography.
The report recomeads that design procedures for concrete ermour. units muatinclude the identification of the loade applied ton and the strength of, thearmour units, and the report su'n'narises a number of appropriate nethode. Itie further suggested that sl,ender units can only offei ti ltr tevels ofs tab i l i t y i f re in fo rced.
CONTENTS
1 INTRODUCTION
l. L BackgroundL.2 Out l ine o f th is s tudy1.3 Ou l ine o f th is repor t
2 fiPES AND USE OF CONCRETE ARMOURING
2.1 Classi f icat ion of armour unit types2.2 ExampLes of armour units
2 .2 . I Mass ive armour un i ts2.2.2 Bulky armour units2.2.3 Slender armour units2.2.4 Armour placement2.2.5 Single layer armour
3 I{YDRAULIC PERFORMANCE
3.1 Genera l3.2 Wave ref lect ions3.3 l.Iave run-up
4 ARMOUR I]NIT UOVEUENT/STABILITY
4.L Def ini t ions of disptacement and movement4.2 Quantification of armour movements4 . 3 T e s t r e s u l t s
5 ARMOUR UNIT LOADING/STRENGTI{
5 .1 Types o f toads5.2 CalcuLat ions of pr ineipal loads5.3 Ident i f icar ion of uni t strength5.4 t" [odel l ing methods
5.4. I Generel-5.4.2 DeveLopment of strength - scaled mater ials
5 .5 Ana lys is o f s i te exper ience
6 DESIGN METIIODS
6.1 Des ign ph i losoph ies6.2 PreLiminary design6.3 l lodel l ing merhods
6.3.1 Hydraul ic performance6.3.2 Armour movement6 .3 .3 Armour loads /s t rengths
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CONTENTS (CONT'D)
7 CONCLUSIONS & RECOMUENDATIONS
8 ACKNOWLEDGEMENTS
Page
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41,
9 REFERENCES 42
10 BIBLIOGRAPHY 53
FIGURES
1.1- Breakwater types, af ter Owen (Ref l_)L.2 Effects of incident wave energy1.3 Breakwater armour units3.1 Ref lect ion perforuance of Dolos armoured slopes3.2 Ref lect ion performance of Cob armoured slopes3.3 Ref lect ion performance of Tetrapod or Stabit armoured slopes3.4 Reflection performance of shed or Diode armoured slopes4.L Def ini t ion of eroded area4.2 Distr ibut ion of levels of damage, after Partenscky et al (nef eZ)5.1 Lini t ing drop angles for fairure of Dolos or Tetrapod units5-2 Lirrni t ing impact veloci ty for fai lure of Dolosse, Tetrapods or
Cubes
APPENDICES
1. Use of video image processi.ng in the measurements of armourmovement in hydraulic nodel study
Figure
A1.1 System conf igurat ion
2. Effect of nul t i -direct ional waveannour
a t tack on s tab i l i t y o f Do los
Figures
A2.L Damage42.2 Daoage42.3 RepeatA2.4 Repeat42.5 Damage42.6 Dauage42.7 DamageA2.8 Damage
3. Example test
history for 1.36s long crested waveshistory for 1,35s short crested wavestest6 for 1.35s waves, long crestedte6 ts fo r 1 .36s wavesagainst H"/ADrrr long crested waves, rnean valuesagainst H"/ADnr short crested waves, mean valuesaga ins t H" /ADrr r long c res ted waves , a l l va luesaga ins t H" /ADor shor t c res ted l raves , a l l va lues
resu l ts f ro rn s i te spec i f i c s tud ies
NOTATION
A, B Enp i r i ca l coe f f i c ien ts
a , b r l
A Erosion area from cross-sect ioneB Structure width, in direct ion normal to face
CI , Cz , C. Empi r i ca l o r shape coef f i c ien ts
C Coef f i c ien t o f re f lec t iont
Cr( f ) Ref lec t ion coef f i c ien t funcr ion
D par t i c le s ize or typ ica l d imens ion
D' Non ina l par t i c le d iameter , de f ined as (M/pc) t /3
D" Effect ive unit diurension, usual ly pr incipar axis length
E E las t ic modu lus
Ei Incident lrave energy
8 Grav i ta t iona l acce le ra t ion
H Wave height, f rom trough to crest
Ho Offshore wave height, unaffected by shal low water processesH" Signif icant wave heieht, averaqe of highest one-third of wave
he igh ts
HrO l tean of the greatest 102 of the wave heights in a recordHrr* Maximum wave height in a record
h Water depth
Ir Iribarren or surf sirnilarity number
Irr Modif ied l r ibarren number
KO Damage coefficient in Hudson formulak wave number, ?; l r l l . , ; a lso armour layer packing coeff ic ientL l iave length, in the direct ion of propagat ion
Lo Deep water or of fshore wave length, gT2l2n
M Armour unit mass
N, Number of armour units, on the slope, or in an area of the( t e s t ) s e c t i o n
Na Number of armour units displaced
No Number of uni ts displaced per D. width of structureN" Stabi l i ty number, def ined as H"/A Oo
N, Number of armour units rocking
N, Number of sraves in a storm, record or testn poros i ty , usua l l y taken as nv
o., Volumetr ic porosi ty, volume of voids expressed as proport ion
of total volume
n Area porosi tyaa Overtopping discharge, per unit length of sea wal lq* Dimensionless overtopping discharge
go Volume of overtoppingr per wave, per unit length of
structure
qs superf ic ial veloci ty, or specif ic discharge, discharge per
unit area, ueually through a porous matrixR Run-up level, relative to static water 1evelR llean run-up level
R" Run-up 1evel of significant tave
RZ Run-up level exceeded by only 2fl of run-up crestsR* DimensionLess freeboard
Ragg Run-down Level, below which onLy 2% pass
r Roughness value, usuelly relative to smooth slopes
"ro I'Iaist to height ratio for the Dolos, usually around 0.33
S Dimensionless daoage level, defined as A./orrz
Si Incident epectral energy density
S. Ref lected spectral energy density
s Wave steepness, H/Lo
"* Steepness of mean period 2n H"lg T^2
"n Steepness of peak period, 2* H"/e Tr2
T Wave period
T, Mean wave period
tn Spectral peak period, inverse of peak frequency
Tn Duration of storm, sea state or test
ur v Flow veloci t ies, of ten orthogonal components of veloci tyW Armour unit weight
WSO Median armour unit weight
cr Structure front slope angle
B Angle of wave attack
p Uass density, usual ly of f resh water
p\tr Mass density of sea !f,ater
0. Uass density of rock
p. Mass density of concrete
A Re la t i ve dens i ty , <& - r lpw
T Relat ive damage, usual ly def ined as NU/N", but may be(Nu + Nr ) /Na
o Flexural strength, of concretef
o Compressive strengthc
1 . 1
INTRODTTCTION
BackgroundHarbour development on open or part ial ly protectedcoast l ines general ly requires the construct ion of abreakwater, or breakwaters, to provide adequateshelter f rom wave act ion to perni t ef f ic ient operat ionof the harbour. Ttre main types of breakwaterident i f ied by Owen (Ref L) are dist inguished by rheiruain construct ional mater ial or method:
a) blockworkb) ca issonc) rubble moundd) compos i te .
These four types are i l lustrated echematical ly inFigure 1.1. Hydraul ical ly each type performs in adif ferent fashion. The di f ferent neehanisms fordealing with incident wave energy are sunmerised inFigure 1..2. General ly sini lar forms of construct ionare often used for structures in Less deep water, suchas sea wal ls and coastal revetments, and even forreservoir embankment protection. The choice ofconstruct ional type wi l l depend upon local pract icelfoundat ion condit ions; water depth; s i te layout;construct ion plant, mater ials and expert ise avai l .able;speed of construct ion needed; and other local factors;as we l l as hydrau l i c e f fec ts .
Whi lst previously popular, blockwork construct ion isseldom now used for breaklrater construction. Caissonconstruction is more conmonly used in Japan and inother areas where durable rock is not easi tyava i lab le , o r i s economica l l y unat t rac t i ve .Descript ions of the design and construct ion ofblockwork or caisson breakwaters and sea wal ls arepresented by Owen, Goda, and Ronit i et al (nefs 1-3).These structure types are not dealt with further inthis report .
Rubble mound breakwaters, sea walls and armouredrevetments are commonl.y used around the IIK and abroad.They are part icular ly sui table where high levels ofwave reflection are undesirable. They may be armouredwith rock or special ised concrete armour units. Thedesign, construct ion, and performance of rock armoureds t ruc tures has been d iscussed prev ious ly by A11sop,Powell & Bradbury, Allsop & I,Iood and, in a companionvolume to this report , by Bradbury et al (nefs 4-G).In many locat ions the natural s ize of rock avai lablewi l l be l iur i ted to no more than 5-10 tonne at largest.On many structures, part icular ly those in deeper
1 . 2 Outl inestudy
rilater, armour units of targer eize, and/or greaterhydraul ic eff ic iency, wit l be necessary.
A wide variety of specialised concrete armour unitshave been developed. ltoet are produced inunreinforced concrete. Ihe concrete units mostconmonly used are cubes, nodified cubes, Tetrapod,Stabit , and Dolos (plural Dolosse). Theee units arei l lus t ra ted on F igure 1 .3 .
As harbour and other developments have increased inextent, and have beea required in areas with little orno natural protection from ocean wavea, it has becomenecessary to built breakwaters in increasingly severehydraulic conditions. Even in relatively shallowconditiona sea walls, embankmente and f,evetments maybe subject to oneroua lrave conditions. Over the last10 years, Bome notable failures have occurred torubble mound structurea ermoured with concrete units.Many of these are identified in the report onbreakwaters in deep water published by PIANC (nef 8),although a number of recent examples have been omittedfrsn that report. The reaeons for damage on thesestruetures vary widely. One aspect that has givenrise to considerable concern is the relative fragiLityof slender unreinforced concrete units, particularLythe DoLos and the Tetrapod.
this
Under a prograume of research at Hydraulics Researchon the design and performance of rubble moundbreakwaters a study nas therefore conducted toidentify the main linitetions to the performance ofconcrete ermour units. It wae noted that research onsiuilar aopects was being conducted by otherlaboratories and reeearch units, and it was thereforedecided to concentrate the limited resources availableon identifying:
a) cr i t ical l i rni ts to performance;b) appropriate design methods, and/or new modelling
techniques for use in design.
Whenever possible test results or other data fromother laboratories have been used to expand theinformation available. It is noted however thatinformation on the performance of concrete armourunits is widely scattered, and often inconsistent anddifficult to check or verify. Information in thisreport is not Eherefore regarded as suff ic ient fordesign purposes on i ts own.
The work descr ibed in this report was subiect to anumber of s igni f icant modif icat ions during the courseof the project. The or iginal intent ion had been toconduct a short literature review on the hydraulicperformance of concrete armour units; then to developtechniques to measure armour movement during testing,and to develop strength scaled mater iaLs; f inal ly toconduct a ser ies of hydraul ic rnodel tests to descr ibethe hydrautic performance of a lirnited set of armourunits. It was not original-ly anticipated that anysignif icant proport ion of the resources avai lablewould be devoted to rock armour.
Ear!.y work in the development of a video imagingmethod for the measurement of armour movement appearedto be successful. A number of nethods to produce astrength-scaled material for model concrete lrereexplored and a plaster based mixture ident i f ied.However early trial mixes lrere particularlyunsuccessful , with tr ia l test specimens fal l ing apartbefore they coul-d be loaded! During this period italso became clear that the identification of armourmovement alone was unlikely to prove sufficient forthe design of any part icutar concrete armour unit , butthat aspects of the concrete strength and loadingfrequency andlor intensity rnight predominate. Majorresearch programmes on the strength of concrete armourunits were underway in Denmark, Ho11and, and Canada,each requiring considerable expertise and experiencein the design and performance of reinforced andunreinforced concrete. The prograrnme of research wastherefore modified to include a wider review of theresults of these and other research progranmes. Aeeparate research progranne on the performance ofsingle layer ermour systems wittr trigtr porosity, suchas the Cob, Shedn and Diode units was initiated withspec ia l i s t co l tabora tors .
Finally it nay be useful to the reader concerned withthe design and performance of rubble mound structuresto note that the project, of which this study nas apar t , has a lso addressed: -
a) the design, performance and durability of rockarmouring (Refs 4, 6, g, 10 and l l ) ;
b) the hydraulic effects of breakwater croun wa1ls(nee rz ) ;
c) the hydro-geotechnical perforrnance of largemounds (nef S) .
1.3 Out l ine o f th isreport
2 .1
The principal types of concrete armour unit, andexamplee of their use and performance in service aredescribed in Chapter 2. Chapter 3 reviews examptes ofthe main data on hydrautic performance as given byttave run-up leveLs and wave reflections. A number ofsinple empirical methode are described alLowing thecalculat ion of run-up leve1s and ref lect ioncoefficients under random rraves.
The definition and measurement of armour movement, ordamage, is considered in Chapter 4. Examples ofempirical" methods to predict armour movement arepresented together with data on model test resuLts.Chapter 5 examines the catcuLation of loads on arrnourunits and of the etrength of typical types. Some ofthe l i rni ts to use of concrete units are discussed.
Chapters 6 and 7 draw together the main design methodsavailable, and the conclusions of the study.Publ icat ions ci ted in the report are Listed underReferences, whilet others used during the study, andrelevant to the subject matter of this report , ereListed in the Bibl iography.
TTPES AI{D T'SE OFCOI{CPGTEARIIIOURING
Class i f i ca t ion o farmour unit types
A wide variety of concrete armour units have beensuggested or developed for the protection of rubbleuounds. Approximately 50 different types are coveredby the wa1l-chart produced by Hydraulics Research(nef tg) and rhe rable given by Feuiller er al(nef Z). WhiLsr thie table gives 45 arr i f ic ialbLocks, only around 2L of them would nornally betermed rubbl"e mound armour units. This proliferationof armour unit types would appear to orf,e more to theinaginative abilities of sone coastal engineere thanto Logical procesees of design supported bycalculat ions. Of the rnany types suggested, relat iveLyfew are at all well supported by laboratory and sitedata on hydraulic performance. Fewer sti1l have beenwidely used. Even these vary wictely in shape,placement, and performance.
The types of concrete armour units avaiLabLe aretherefore not easi ly classi f ied. I t may however beuseful to descr ibe 5 broad categories, with exampLesof those units in more common use, or of fer ing
part icular advantages. The categories are drawn byunit shape, laying pattern, and performance:-
Category
Massive
Bulky
S lender
Single layerbulky
Single layerporous
Bl.ock Shape
Sinple, cubic orrectangular
Complex, but!f,ithout slenderlinbs
In te rLock ing ,legged
A11 returnsExcl Japan
Placing pattern
Random orientat ion,two layer
Examples
Anti fer cubesimple cube
Regular posi t ion but Accropodeor ien ta t ion genera l l y S tab i trandom, one or two layer
Random or control led Dolosorientat ion, two layer Tetrapod
Close- f i t t ing , Cont ro l led or ien ta t ion , Tr ibargeneral ly cubic one layer Haroor hexagonal Seabee
Hol low cube Regular close placement, Cobone layer Shed
Diode
I'he relative frequency of use of each type may begauged from the listing of breakwaters given by PIANC(Ref 8). Ttre l ist was based on a set of quest ionairesdistr ibuted to coastal engineers worldvidee butsuffered from very low response in many areas. Ttrisreport l ists around L63 breakwaters, embankments,je t t ies , o r re la ted s t ruc tu res . Of these 1 .02 werelonger than l-00n and/or used uore than 1000 units.Of the 102 larger structures, 30 were in Japan andthese were al l aruoured with Tetrapods. This ref lectsboth the popularity of the products of Nippon TetrapodCo Ltdr and the particularly good Japanese response tothe PIANC survey. It should be noted that it is notpossible to weight the frequency by number of unitsused, as this infornat ion l ras often omit ted from thereturns. A simple indicat ion of the frequency of useof Cubes, Tetrapod, Stabit or Accropode, Dolos, androck can be gauged frour the number of structuresl i s ted under each un i t :
Rock Cube Tetrapod Stabit /Accropode Dolos
t07" Lsz 4tz147" 2LZ L77"
L2Z177"
2 2 %327"
2 . 2 Examples ofarmour units
2.2.L t lassive armour units
Uassive arnour units, such as plain or grooved cubes,resist wave forcee pr imari ly by their uni t weight.Unless laid as a pavement, euch blocks generaterelat ively l i t t le inter lock. Conversety, on steepslopes it ruay be difficult to prevent cubes or similarblocks from sliding downslope to form a closely packedlayer. Such an armour Layer will give rise to greaterrun-up, overtopping and reflections than would a moreopen placement. In some instances considerabte efforthas been expended to provide a rough underlayer,specificalLy to promote random orientation and openpacking of the armour layer. An example is discussedby Groeneveld et al (Ref 98) who describe thedeveLopment of the Robloc unit to form such anunderlayer.
Massive blocks are general ly hydraul ical- ly ineff ic ientand require Large unit sizes for given levels of waveattack and armour movement. It has been suggestedthat their bulky shape ellows relatively high levelsof movement to be tolerated, balancing to some extenttheir relative inefficiency. It is aLso claimed thattheir simple shape reduces fornwork costs (surely verymargiaal on a project of any size), and speeds upcasting. Ilovever l-arge conerete blocks, 40-90 tonnes,have been found to euffer from cracking arising duringcasting and setting, and are reLatively prone tofailure under impact and/or fatigue (tefs 14-16, 25).
2.2.2 Bulky armour units
Bulky interLocking units such as the Accropode orStabit are general- ly la id in a singte tayer, withclose packing and random orientation. A relativelytightly packed annour tayer is produced. Both unitshave approximatel-y similar hydraulic performance andstabi l i ty. The unit weight of ei ther night beexpected to be around 6O7. of a cubic unit for the samewave conditions. Taken with some further saving ofconcrete in the single layer placement, both unitshave been claimed to offer significant savings overother types. Both of these units have been patented;the Accropode by Sogreah in Grenoble, and the Stabitby Sir Willian Halcrow & Partners in London.
The Stabit rras developed around 1960 with the f i rstuse at Benghazi, Libya in 1961 (nefs 77, 18). I t maybe estimated from the PIANC report (Ref 8) Lhat around210000 stabits have been placed on about 11breakwaters. Recent ly around 4000 23 tonne Stabits
were used to arrour the new breakwater at Douglas,Is le of I ' {an.
The Accropode was developed by Sogreah around L979.By 1986 about 36000 units had been placed on around 15structures (nef tg). The strength of the Accropodehas been examined by some simple finite element stressmodel l ing at the Universi ty of Grenoble. This isdiscussed further in Chapter 5.
Other units that uay be included in this category arethe Gassho block, patented by Toyo Construction Co inJapan, and used in sizes between 2 atd 8 tonnes onapproximately 30 structures (up to 1981); and theAkmon, patented by the Rijkswaterstaat in ltoLland.The Akmon was first described and compared with otherunits by Paape & walther (nef zo). webby (net zt)describes modeL tests of repairs to an embankment atWellington, New Zealand, armoured with 10 tonneAkmons, and damaged in a storm in 1972.
2.2.3 Slender armour units
SLender interlocking units, such as the Tetrapod andDolos, appear to offer a significant advantage overother types of units by virtue of their high level ofstabi l i ty under wave act ion. They offer high porosi tywhen laid in double layers, giving good run-up andref lect ion performance. A high level of inter lock isgenerated between units, hence al lowing relat ivelyl ight uni ts to resist large rraves. Laboratory testsduring the development and earLy use of both unitsindicated signi f icant ly better resistance to a givenleveL of wave attack than for other units available atrhe t ime (Refs 22, 23).
The Tetrapod was developed and patented by Neyrpic inFrance in 1950 (Ref 24). The Tetrapod has been usedin sizes from around 0.25 tonne to 50 tonnes' oncoastal- protection structures and breakwatersworldwide. The Tetrapod has been particularLy popularin Japan where Nippon Tetrapod Co are the sole agentsfor the use of the patent, and natural rock ofappropriate quality is very scarce. Recentty a numberof Tetrapod armoured breakwaters have been damaged.The most notabl-e examples are Arzew El Djedid,armoured with 48 tonne units, and Tripoli, using 14and 19 tonne units (nefs 25-29).
The Dolos unit was deveLoped by Eric I'terrifield, theengineer to the East London harbour in South Africa.The earty development and testing is described byMerr i f ie ld & Zwamborn (Refs 30, 31). The Dolos wasspecif ical ly not patented in an attempt to al tow i ts
wider use. Whi lst successful in this, the lack of apatentee has resulted in develop'rnent occurring in apiecemeal and uncoordinated fashion. Rubble slopesarmoured with Dolosse have been tested in manylaborator ies, but part icular ly at the US WaterwaysExperiment Stat ion. Test ing using regular waves ledto suggest ions that stabit i ty coeff ic ients up toKO = 31 could be contempLated in design (nefs 22,23).
The Dolos has been used in the UK and elsewhere. Inthe UK i ts use is conf ined to two si tes: the A55 coastroad in north tJales, and the sea wa11 and breakwaterat Torness in southern Scotland. The 1.6km embankmentto the A55, descr ibed by Lunniss (Ref 32), is armouredwith 5 tonne Dolosse in two layers at a 1:2 slope.The design inshore significant wave height is around5n. At Torness both the 1.5km sea wa1l and the 170nlong breakwater are armoured with Dol-osse, at 5.4tonne and 13 tonne respectively (Ref 33). ttinisral-levels of unit breakage have been observed on eithero f these s i tes .
Elsewhere a number of breakwaters have suffered damageand breakage of Dolosse. ltre ?IANC report identifiesaround 11, with unit s izes ranging from 2.0t to 50t(nef g). of the l isted instances of fai lure, 272involved units smal ler then 5t, 452 units less then10t, and. 647. involved Dolosse less than 15t. Magoon &Baird (nef :+) identified armour movement ascontributing to breakage and armour Layer failure inL977. They discussed the extensive breakage of 5 and8 tonne Dolosse at Baie Comeau, Canada, in a storm inOctober 1976. Breakage of 2 tonne Dolosse atCleveLand, Ohio has aLso been discussed by Pope &CLark and Markle & Dubose (Refs 35, 36). The damageto 42t uni ts at Sines, and the 50t dolosse at SanCipr ian, has been discussed very ful ty elsewhere(ne fs 37-39) .
2.2.4 Armour placement
The three categories of uni ts discussed above are al lgenerally laid to a fixed pattern but with randomorientation. An exception to this is the practice inJapan of placing Tetrapods, and other units such asGassho bLocks, to a very t ight ly control led patternand or ientat ions. The last two categories (seeSect ions 2.2.2-3) include those units general ly la idin a single regular ly-placed layer. These units relyheavily on close placement, and hence good interlockor inter-block fr ict ion, to generate restrainingforces. r jn i ts laid in regular pl-acement in a singlelayer may be considered under thro categories, asbefore, bulky or slender.
2.2.5 Single layer armour
Ttre two most typical bulky siagle layer units are theTribar and the Seabee. Ttre Tribar was developed andpatented by Robert Palmer, originally for use inHawai i (ner ao). The Tribar has been used onbreakwaters and revetments in the U$A and Auetralia.Thompson & Abernethy have reviewed oone regular wavestudies with Tribars, and report results of randomweve tests (ner 4t) . Fudson and Baird & Hat l(nefs 42, 43) give some details of experience withTribarsn citing instences of danage to bothun-reinforced and reinforced units. The Seabee,essent ial ly a hexagonal pipe with a cyl indr icalcentraL void, has been developed by Chris Brown(nefs 44, 45). Seabees have been used on a number ofbreakwaters and sea wall revetments. They have provedvery stabLe when close placed.
Nagai (nefs 51) descr ibes two types of regulartyplaced blocks, the hollow square and the N-shapedblocks. Each can be laid in single, or double layer.Both of these units were reinforced. Examples of useltere not reported but it ia believed that these, orsimilar, have been used on a number of coaetalrevetments, Nagai suggests that KO = 13.5 may be usedin design.
The Haro is approximately reetangular in plan withtapered corners. I t is pierced by a vert icat centralopening. The block height is 802 of the narrow sidelength. The Haro has been used on the innerbreakwatera at Zeebrugge laid in two layere. It isclained that the llaro is significantly more robuetthen slender units, dolos or tetrapod, and moreeconomicaL than cubic blocks. De Rouck et al reportthe deveLopment of the llaro and some model tests, buthad not then completed laboratory testing (nefs 52,s3) .
The final category of rubble mound armour unitsconsidered includes al l those of high-poroeity laid inregular placement in a single layer. In the IIK theexamples of this type are the Cob, Shed, and Diode(nefs 46-50). These units offer coneiderably greaterrelat ive stabi l i ty than most other types, togetherwith good run-up and reflection performance. Theseunits are the subject of a further research study, andare not eovered in this report.
3 HYDRAT'LICPERFORUANCE
3.1 Genera lA sea wall or breakwater armoured with concrete ar:rnourunits wi l l exhibi t hydraul ic perforrtrance that isgeneral ly sini lar to that of t t re equivalent rockarmoured structure. Some types of concrete armourunit are more open and permeable to wave action thanrock armouring, and reduced run-up and/or reflectionsmay therefore be expected. Conversely bulky armourunits such as cubes have sometimes been placed veryclosely with low armour layer porosi ty, and hencehigher run-up levels and wave ref lect ions l r i l l resultthan rnight be predicted.
The influencea of the underlayer and core permeabilitymust also not be ignored. I' lhere the lower layers inthe structure are less permeable to rrave action,ref lect ione of longer weves wi l l be greeter. this rnayarise when a very efficient ermour unit is used onsnal l s ized underleyers or core mater ial . Sonemathematical modele of wave-induced flows in porousmounds nay allorr qualitative eomparieons of thiseffect. I t is noted however by Al lsop & Wood (Ref 5)that no Eteesuremente of in-situ permeability, or evenporosi ty, ere avai lable, nor have the standardformulae relating perneability to the ruain flow andmater iel parametere been cal ibreted against theresulte of ei ther f ie ld or large-scale laboratoryinveet igat ione. t i t t le quant i tet ive guidance isavai lable on the effects of underlayer siae, gradingor thickneas on any of the main hydrauliccharec ter is t i cs .
3.2 !{ave ref lect ionsI, Iaves ref lected from a coastal gtructure may interactwith incident waves to give a confused sea in front ofthe structure, v i thin r f i ich occasional steep andunstable rraves may cauEe s€vere hazard to small boats.Reflected naves may also propagste into areas of aharbour previously sheltered from wave action. Lnmost instences the reflection of wave energy from astructure wi l l lead to increased peak orbi talveloci t ies at the sea bed in front of the structure,increasing the l ikel ihood of general bed erosionand/or loca l scour .
Wave ref lect ions are often described in terms of theref lected wave height. The rat io of the ref lectedwave height to incidenr height wi l l g ive a coeff ic ientof ref lect ion. In regular wave terms this may bewr i t ten :
C r = H r / H i
L 0
In random traves it will be more precise to define theref lect ion coeff ic ient funct ion, Cr(f) , over the ful1range of wave frequenciee considerEd. General ly thetotal- reflected and incident energiee, E" and 81, arecompared:
I
c' = (E, /n)z
The reflection performance of any particular structurewill depend on the structure geometry and upon theincident wave conditions. Many different methods toestimate reflection performance have been discussed byA11sop & Hett iarachchi (Ref 54). For simple rockarmoured atructures, the reflection performance may becharacter ised by the coeff ic ient of ref lect ionl C"rcalculated fron:
Armourunit
DolosCobsTetrapodsor S tab i tsSheds orDiodes
Waveact iontes ted
RegularRegularRandom
Randoo
r . 5 -3 .0t . 33 -2 .5I . 33 -2 .0
1 . 33 -2 .0
1 .5 < I r<5 .51 .5< I r<4 .52 .5< I r r <6 .0
(3 .1 )
0 .55 10 .00 .50 6 .540 .48 9 .62
^ - a T t Z
" -
fl[Jwhere a and b are enpir ical coeff ic ients; C.,^ is thecoeff ic ient of wave ref lect ion, def ined in ierms ofwave heights; and Ir is the Iribarren number,tanc,/arz' The reflection performance of Dolosarmoured slopes under reguLar wave action has beendetermined by Whillock & Thompson (Ref 55). Theresulte of those tests have been re-presented by nanyother researches, ineluding Gunbak (nef S0), andLosada & G-Curto (Ref 57). Whi l lock & Ttrompson'sresults have been analysed again, together withSticklandt s meesurements of refleetions from Cobarmoured slopes (nef Sg), and are presented in Figures3.1 and 3.2. Random lrave test results for Tetrapodsand Stabits, and for Sheds and Diodes, fron Allsop etal (nef 0O) and Al"Lsop (Ref 50) are presented inFigures 3.3 and 3.4. Enpir ical equat ions of the forngiven above have been fitted to the data end theresults are surmarised below:-
Range of Range of Coefficients inslope angles Ir or I rr equat ion 3.1
a b
3 ,0< I r r <6 .0 0 .49 7 .94
1 1
3.3 tlave run-upthe prediction of wave run-up levels on armouredrubble -slopes has been discussed previously by Al leopet a1 (nefs 59-50). Sinple empir ical predict ionequatione for 2Z and significant run-up levels, R, andR" respect ively, nere suggeeted for permeable slopesarmoured with cubes or Tetrapods. these werepresented in ferrns of the rnodified lribarren number,Irr = tanc,/soz:
for Tetrapods,
R"1H" = 1 .32R2 /Hs = 1 .83
and for cubes,
R" {H" = 1 .07 [ r -exp ( -0 .+S r r ' ) ]R2 /Hs = 1 .52 [ l - exp ( - 0 .34 I r ' ) ]
Where i t was possible to check, A11sop et al (nef e)found reasonable agreement between their measurementsof R"/H" and reguler wave test measurements of R/H.They also found that the 2Z run-up 1evel R* wasreasonably wel l descr ibed by:
I l -exp ( -0 .31 r r ' ) lI r -exp ( -0 .30 r r ' ) ]
( 3 .2 )(3 .3 )
(3 .4 )(3 .5 )
R Z = 1 . 4 R " . ( 3 .6 )
4 ARUOUR T'NITI.{OVEI{8NT / STAB ILITY
4.L Def in i t ions o fdisplacement andmovement
One of the principal concerne of the designer of arubble breakwater ie to ensure adeguate stabitity ofthe armour units on the front face of the structure.This is generally deemed to be achieved when the tevelof armour unit displacement remains below an acceptedthreshold. Recently, breakage of concrete armourunits has been accepted as a major contribution toarmour layer faiLure. Ttris chapter coneiders themovement and displacement of concrete armour. Thebreakage of concrete units is treated separately inChapter 5.
To date the main method of predicting movement and/ordisplacement of armour units has been the hydraulicscale model. Def ini t ions of uni t displacement ormovement, often termed damage, have been drawn from orstrongly infl-uenced by physical model test procedures.I t must be noted that def ini t ions of daoage di f ferbetween researchers, laborator ies, and even for
l 2
dif ferent armour units. The values cal-culated maydepend upon the stope angle, af,mour layer thickness,design wave height, length of armoured stope, and eventhe width of the test facility. Comparisons betweenvalues presented are extremely difficult and rmrstoften be limited to an identification of a "no damage"condit ion.
The sinplest definition of armour damage ie given asthe number of armour units fully displaced from theiror iginal posi t ion, Nr, expressed as a Percentage ofthe total number of inits in the armour, Nr. Thisdefinition of damage was adopted by Hudson forconcrete armour units, and is impl ic i t in the uie ofthe lludson damage coefficient, Kr.,. In some instances,the totaL number of armour units-used are those laidin a specified zone above and bel-ow the statie atater'level. The extent of this zone is usually related tothe design ltave height. ALternatively the number ofunits displaced, N, l , can be expressed as the numberdisplaced over eacfr width D. of the slope. Thisdefinition of damaB€r Nor i's' l-ess dependent on modelvar iab les .
The definition of damage by reference to theproportion or percentege of units displaced may beextended to quantifying those displacedr or evenmoving, within certain ranges of dimension or ang1e.Owen & Allsop (Ref 61) have suggested five movementcategories to be used in hydraul ic model tests:
O - no discernible movementR - unit observed rocking, but not permanently
displaced- unit displaced by up to 0.5D- unit displaced by betreen 0.5 and 1.0D- unit displaced by more than 1.0D.
In these definitions an actual dimension typical ofthe unit s ize was used, D = Do. Partenseky (nef 52and 63) has extended this appioach by suggesting sizecategories and attaching a weighting factot to eachcategory. Those for doLos units may be wri t ten:-
123
Category Rotat ion Displacement !ileightingfactorr tr'I3
Very small- Iol5 4D l6 -D l3 9D l3 -D lz 16Dl2-D 25>D 36
123456
<5"5 -15"1 3-30 '30-45 "45-90">90 "
13
The numbers of units in each category are aasessed asa percentage of those in the zone 1.5 Ho above andbelow the stat ic nater level. The overi l l damageindex, J, is determined by summing the weighted damagein each category.
An al ternat ive approach that nay be more appropriateto rip rap and rock armour is given by defining danagein terms of the cross-aect ional area of urater ial . -removed from a zone on the slope around the rraterleve l . Th is vas or ig ina l l y used by Hudson (Ref 64) ,and subsequently adopted and refined by Ahrens(Ref 65), Thompeon & Shurt ler (Refs 66 & 67) and Vander Meer (Ref 58). The eroded area, A.1 on 8crosa-e€c t ion is meaeured by pro f i l i ng- the s lopebefore and a f te r a tes t (see F ig 4 .1 ) . Areas o feroaion can then be ident i f ied for each prof i le l ine.A dinensionless damage level1 S, may be def ined usingthe nominal armour unit diameter:
s = A./Drr2 (4 .1 )
where oo = ( ! ) r rs
This rnethod has been used in a number of modelinvest igat ions, al though general ly for rock armouring.I t is relat ively sinple to execute, and can easi ly beautouated in the laboratory. The ident i f icat ion ofsna l l un i t d isp lacements i s d i f f i cu l t , par t i cu la r lywith inter locked and randomly or ientated units. I t isl ikely that this method of neasuring and def iningdamage will remain appropriate only to units tolerantof s igni f icant movement.
4 .2 Ouant i f i ca t ion o farmour movements
It i€ expected Chat ermour layers on all rubble moundatructures wi l l . suffer some deforuat ion, sett lement oradjuetment. I t wi l l be shown later that the magnitudeof eueh Bovements nust be linited for some concretear:rmour unite to avoid structural failure of the units,and consequently of the armoured slope. The extentand magnitude of these movements may be predicted byhydraul ic model tests, ei ther specif ic to the designconcerned, or of a more general nature. The qual i tyand appLicabi l i ty of the measurements wi l l dependpriurar i ly upon:
a) the s ize and soph is t i ca t ion o f the tes tf a c i I i t y ;
b) the equipment and methods used for measuringmovemenf;
I4
c )d )
the mode l eca le se lec ted ;the absolute resolut ion required in the design.
The feci l i t ies commonly used for design studies forrubble structures may convenient ly be divided intoth ree ca tegor ies : -
a) very large f lumes generat ing l raves in excess ofHo = 1 .0 rn ;
b) cSnvent ional laboratory vave f lumes generat ingnaves up to about I Io = 0.3m1
c) laboratory l rave basins, generat ing long-crestedvaves up to about H" = 0.3m.
In the very large f lurnes, model scales of around1:10-15 rnay suff ice for many breakwaters, wtr i let seawal ls may be tes ted a t sca les around 1 :1-5 . Thesefaci l i t ies are extremely cost ly to run, requir ing verylarge quant i t ies of mater iel and other resources. Anumber of special ised studies have been, and cont inueto be conducted in such faci l i t ies, but they arerelat ively seldom used for design studies. Examplesof such f lumes have been buiLt in Hol land, Germany,the USA, and Japan. In conventional wave flumes andbas ins , b ) and c ) , mode l sca les o f a round 1 :30-50 aregeneral ly appropriate for breaknaters, rr i th sea wal lsand s imi la r s t ruc tu res o f ten tes ted a t 1 :10-L5 .
The measurement devices and procedures used toquant i fy the movemente and displacements discussedabove have been previously descr ibed by Owen & A1lsop,Owen & Briggs, Partenscky et al , and others(nefs 61-53, 69). Those most commonly used nay besummarised: -
a) direct v isual observat ions, recorded in wri t ingand/or on a tape recorderl
b) v ideo recording, run cont inuously orinterni t tent 1y;
c) c ine f i ln, again oade cont inuously or as singleframes tr iggered by a sui table receding \rave;
d) st i l l photographs, usual ly 35mn, taken before andafter each part of the test, and pr inted astransparent overlays.
Other devices may be used to quant i fy the effects orconsequences of movement, such as accelerometers, loadtransducers, and/or strain gauges. Accelerometers areexpensive to obtain and deploy, and are relat ivelylarge in relat ion to most model armour units. Theiruse has therefore been conf ined to a few studies inthe very large f lumes. A major disadvantage is thatdata is only provided from those units instrumented.Many units must be so equipped to ensure stat ist ical
15
val idi ty for the results. This aLso appl ies to theload measuring devices. These are, however, of tenrather lese expensive than an accelerometer, allowingmore instrumented units to be deployed. The use ofload measuring devices is discussed in Chapter 5.
The measurement or assesgment of armour movement maybe made continuously during a test, and try before andafter comparisons. Owen & AlLsop (Ref 61) advocatedthe use of 35m uonochrome photographs taken beforeand after each test part from a point perpendicular tothe drained slope. These photographs are then printedas transparent overlays and analysed manually inpairs. In laboratories in Canada and South Africa,movementa have comnonly been identified from singleshot Snrn cine fiLm. Each frame is triggered by apuLse from a wave mea€uring device eet to detect awave dropping below a pre-set 1eve1 on the slope. Inmost instancea these measurements have beensupptemented by visual observations made through theglass sides of the f lume, and frm above (nef 113).
Recently these various methods have been compared intests at the Franzius lnst i tute, Universi ty ofHannover. Partenscky and co-workere (nefs 62163)report tests in a conventional wave fLume usingconcrete Doloese, cubes, and Tetrapods, and eomealuminium Dolosse. During the tests both continuousvideo recordings and single frame cirre film weretaken, supplimented by vieual observations. the testsections were also photographed before and after eachtest on 35mm monochrome fi1n. In these experimentsthe photographs were then printed as positive andnegative overlays. They were then analysed uanuallyto determine displacementa in categories 1-6, definedin Section 4.1 above. In considering the variousmethods used, Partenscky et a1 concluded that theoverlay method was considerably better at evaluatingmovements. It was noted that even small movementawere easily recognised on the overlays, and at no timewere rocking motions observed or recorded during thete6t that did not also result in some noticeabledisplacement in the overlay photographs. It may alsobe noted that the resolution of good quality 35mblack and white filn far surpasses that of 8"- cinefiln or professional quality video recordings.
A possible disadvantege of the overlay photographmethod ie the requirement for a high level of skil1and consistency in the analysis, i teel f a ssmewhatrepet i t ious task. During studies covered by thisreport an attempt was uade to overcome some of thesedisadvantages by the use of a relatively inexpensivecomputer-driven video image proceasor. This attempt
1 6
4 . 3 T e s t r e s u l t s
was not ent i rely successful , and a number ofsigni f icant l i rni tat ions r"r" id"rr t i f ied. Theexperiment did however demonetrate that automatedprocessing of single frame video images would be bothpossible and useful , when suitable eguipment becameavei lable at a reasonable cost. A descript ion ofthese experiments is given in Appendix l.
As indicated previously there are often widevariations in damage definition and meaaurement, andin test procedures. These variat ions make i tdi f f icul t to compare resutts fron di f ferent si tespecif ic studies, and between di f ferent laborator ies.In generaL model test data wi l l exhibi t considerabLescatter. This is due in part to the stochast ie natureof random wavee, the effects of di f ferent foreshorebathynetry, and to spatia!. variations in armour layerconstruct ion. This lat ter is part iculsr:Ly i rnportantfor those units that use interlocking to resistmovement, as relat ively enalL var iat ions in att i tudeand posit ion vi l1 lead to signi f icant changes inapparent stabi l i ty. As a result i t is seldom possibleto compare directly measurernents of damage fromdif ferent studies. A number of s imple empir ical_expressions have been advanced to describe theconditions at the onset of damage, and in a fewinstances, the change in armour movement with changesin wave condition, chiefly wave height. Many of theseformulae have been discussed elsewhere. l{ost of theempirical formulae were originally derived for rockarmouring, see Bradbury et al (nef O). Very few havebeen developed specif ical ly for concrete armour units.The most colrmonly used general expression is thatdeveloped by }ludson (nefs 22,42,64) which may bewritten to give the Eypical armour unit size:
p ^ H 3M = -
KO cotc A3G.2)
Where MpcH
s mass of armour unit= density of concrete= a rrave height, often taken as the
signif icant nave heightr Hor or mean of theh ighes t one ten th , Hrn ;
= a r rs tab i l i t y r t coe f f i i i en t= the structure slope= re la t i ve dens i ty , (p^ / * ) - t= dens i ty o f (sa l t o r FreEt r ) l ra te r .
KDct
APril
The expression may a lso be re-wr i t ten in terms of adimensionLess wave height :
L 7
uqwhere Dr, = the nominal unit
(4 .3 )
. r /3dianeter ( t l lp.) -
lhe lirnitations of the Hudson formuLa heve beenidentified at length in the Shore Protection Uanual(nef ZZ) and eleelrhere. It is well accepted that thewidespread uee of the Hudson formula and stabilitycoeff ic ient, Kgr owes lese to the adequacy of theformula than to the availability of test datapresented as val-ues of Kr.r. It has become comnonpractice to determine a nzeto damagett value of KO for0-52 extract ions. In the use of such values of KOr i thas been inplicit that displacement of more than 0-52wiLl const i tute the most important, and l ikely,failure condition for the armour l-ayer. As will beshom l"ater, this is often not the most importantp r o c e 6 s .
Many researchers have suumarised the results ofhydraut ic model testse and occasional ly prototypeexperience, by using the Hudson formula andcalcul-ating appropriate values of Kr.r. In someinstances the results of di f ferent I tudies, togetherwith site experience, have been assembled to givevaluee of KO suggested for use in design. Thesevalues mav often reflect more caution than thosederived direct ly fron test results. Ini t iaLly al ltest reeulte were based on regular rraves. Values ofKg for concrete armour units under either breaking ornon-breaking waves for 0-52 extractions are given byHudson (Ref 42), summarising regular wave testr e s u l t s : -
= (tro .oto) l /3
Unit
Tetrapod/ quadripodTribarModified cubeDoloe
KDnon-breaking
8 . 31 0 . 4
7 . 82 5 . 0
breaking7 . 29 . 0
2 2 . 0
The rates of damage with increasing wave height forDol.oe, Tetrapod, and Tribar are given by Carver &Davidson, Hudson, and the Shore Protectioa l.fanuaL,(nefs 22,23 & 42). czerniak er a1 (R.ef 70) alsoreport the resulEs of regular wave teats by TetraTech, on Dolos armoured slopes. For 2.52 extract ions,they recornurended K, = 20 with a packing coefficient,k = 1.2. They argue that the rate of increase ofdamage with increasing wave height is relatively low.They include the units displaced, Nd, together withthose rocking, Nr, as a proport ion of the total number
1 8
o f un i t s , No , and sugges t t ha t damage l T1for any wav6 height , H, by:
N ; + N -r - "dN; " r = 0 .053 ( r .+ tz
h - t l
Units
Tetrapod /quadripodTribar (random placed)Modif ied cubeDolos
RockGrooved cubic blocks(Ant i fer cube)Modif ied cubeTetrapodAccropodeDolos
non-breakr.r, *o
breaking
may be given
( 4 .4 )
7 .O9 .06 .5
15 .8
9 . 524
where I lpr the design \rave height, is given by usingthe Hudson formula with XO = 20.
Regular vave test ing was also conducted for the Stabitermour unit, froro which a value of K- = 25 was derived(Ref 18). I t may be noted rhat rhe f iesigners rhensuggested that a factor of l_.5 be appl ied in design,reduc ing the suggested va lue o f KO to 16 .8 .
The values of Kr. , given in the latest edi t ion of theShore Protectiofr ttanual (Ref 22) may be summarised forthe more commonly used concrete units on a structuretrunk under either breaking or non-breaking ldaves.
8 .010 .07 .5
31 .8
The SPM appl ies a number of caveats to the values.Two are of part icular interest here. In relat ion tothe Dolos unit i t is suggested that the value of Kr. , ,should be halved for no rocking (wr/W, < 2Z), c i t i f igthe work of Zwamborn & Van Niekerk-(R6f 71). I t isalso suggested that the appropriate ! i lave height to usein the Hudson formula should be the mean of theh i g h e s t L / 1 0 w a v e s , H t ' .
A s in i la r se t o f resu l ts a re g iven by Feu i l le t e t a l(Ref 7 ) , who or ig ina l l y suggested the use o f Hro :
Unit KDDamage leve l (Z)0 - 1 1 - 5 5 - 1 0 1 0 - 2 0
3 .2I
6 .88 .310
2244
5 .113
7 . 21 8
1 9
Schol"tz et al (nef ZZ) discuss changes to the rat io ofDolos waist thickness to the unit length, the waistratio. They note that some advantage in strength maybe gained by increasing the waiet ratio for Dolossefrom the customary value of around 0.32-0.33r but thatthis rnay reduce the hydraulic stability. They suggestthat for units less than 40 tonne the waist ratioshould be given by:
r , = 0 .34 6o) t " ( 4 .5 )
Hydraulic model test results however suggest that forr . . , > 0.33 the stabi l i ty reduces dramatical ly. Forr] = 0.38 Scholtz et al suggest that Kn should be 2O7",r f ,a for r = 0.48, 602 lower than for r"= 0.33.
Somewhat different conclusions are drawn by Burcharth& Brejnegaard-Nielsen (Ref 73) who tested Dolosse ofw a i s t r a t i o s 0 . 3 2 , 0 . 3 6 , 0 . 4 0 a n d 0 . 4 4 o n a 1 : 1 . 5stope with random waves. They argue that the f,udsonformuta is inappropriate to the Dolos unit, andpresent their damage results for both displaced androcking units against H* and No3, wher. N" = I Is/ADn.They conclude that hydraul ic sEabit i ty decreases withincreasing waist rat io, but only for unreal ist ical lyhigh degrees of damage. At level-s of movement likel"yto be acceptable from reaaons of armour unit strength,they concLude that no reduction of tc' with increasingvalues of r is needed. They note, however, that adisplacement of 5Z corresponds to around 10% rockingat Ko around 6.5-7.5, where Ko is caLculated usingH 8 .
Partenscky and co-workers (Refs 62163) report theresults of random ltave teste on cubes, Tetrapods andDoLos, using the more comprehensive damage classesd iscussed in Sec t ion 4 . t . The i r resu l ts showconsiderable var iat ion in val-uee of Kr. , due, i t isbel ieved, to wave period effects and Ehe inf luence offoreshore bathymetry. ?artenscky et al suggest valuesof K,., for design, together with the raflge and medianof t f rose calculated direct ly from the hydraul ic model-r e s u l t s :
Unit Kl)Range & median Value
measured recoruuended
CubeTetrapodDolos
9 . 5 - 2 2 . O5 . 9 - 1 0 . 67 . 6 - 2 3 . 1
12 .57 .5
11 . 8
7 . O7 . 2
1 0 . 0
20
In the analysis of test results i t was [ot iced thatthe relationships betveen occurence of sma11 andlarge movements was consistent between armour units.A mean frequency distribution was fitted to the damageclasses, and is reproduced as Figure 4.2.
A ser ies of random wave tests on a 1:1..5 Dolosarmoured slope, mentioned previously by Shuttter(nefs 74175), have been re-analyeed for thie project.The tests were intended to explore the relativeeffects of short and long crested wave att,ack, and thevariat ion between repeat tests. Ttre test proceduresand results are deecribed in Appendix 2. For thisproject the results have been described in terme oftwo dimensionless parameters. As before, the waveheight, Ho, has been scaled by the nominal armourdiameterr-D,rr and the relat ive deneity, A. Thedamage, T =-Nd/Na, has been scaled by N_8. Thisscal ing does seem to give a reaaonable i lescr ipt ion ofthe results. The values of scaled damage are plottedagainst the dinensionl-ess wave height for the long andshort-crested seas in Appendix 2. Considering adesign exampte of 2.52 extract ions in a storm of 3000waves, these results suggest a dimeneionless lravehe igh t , H . /AD- = 2 .5 , in tu rn equ iva len t to Kr , , = l l .7fo r the l i l .5 "s tope tes ted . These tes t resu lEs canal-so be presented in terms of the N^ damage paraueterused by van der ueer (Ref 76), and def ined earl ier insect ion 4.1. Not ing that the Dolosse ueed in thesetests have a nominal diameter D- - 0.0304rn and thetotal width of the test sect ion"was 0.85rn, i t can beshown that for these tests No = 27.9 Nd/Na.
Random nave teste on the stability of rubble slopesarmoured sith cubes, Tetrapods, or Accropodes, havebeen reported by van der Meer (Ref 76). Armourmovement for cubee and Tetrapods is presented in termsof the damage Level, No, number of waves, N*, and themean sea steepness, Ir i
fo r Te t rapods a t co tc , = 1 .5 ,
H"
A D,,=(3.rrF+0.85)# G.6 )
Q . 7 )
fo r cubes a t co tc = 1 .5 ,
H"
A D,,=(6.r#+r.o)#
2T
During the tests it was noted that the start of damagecorresponded to N^ = 0. Severe danage to the tetrapodslope occurred at-N^ = 1.5, but for the cube armouredslope at N., = 2. F5r a typical sea steepness,sm = 0.04r-and storm durat ion of 3000 waves, theseresults may be sumnarised:-
Uni t Damage
Tetrapod St,artSevere
Cube StertSevere
No Hs/A Dn KD
a L .621 .5 2 .800 1 .38
2 .O 2 .48
2 .814 .6
1 .810 . 2
For Accropodes the effects of storm duration and seasteepness were found to be relat ively ineignif icant.The stability performance was described solely interms of the dimensionlees wave height:
at the start of damage, No = 0i
H^- 9 - = ? 7A D o
and for severe daoage, No ) 1
H.= 4 .1- " n
( 4 .8 )
(4 .e)
It will be noted that the difference between no damageand severe damage for Accropodes is very small. Vander Meer notes that the designers of the Accropode,Sogreah, suggest that Kr.. = 12, equivalent toI ts/A Dn = 2.5, be used In design. Fron the testresults presented by Van der !1eer, this would appearto aLlow a considerable nargin of safety. I t must benoted, however, that the dauage meaaurements usedincluded only those units fu11y displaced fro'n theiroriginal location. Smaller movementc lrere notrecorded or anaLysed.
During the compilation of this report it was notedthat the results of s i te specif ic studies rnight beuseful in a more general context. A number ofsuitabl.e studies were identified, and the resutts ofarmour movement tests sumnarised. Theee resutts areshown in Appendix 3.
Finally, it rnust again be emphasised that themeasurements of arttrour movement given are all specificto the part icular test procedure; def ini t ion ofdamage; measurement method; etc. It is clear from thedata avail-abLe thaE armour movement depends upon a
22
5 .1
AR}IOUR T'NITLOADING/STRENGTtr
Types of Loads
wide range of parameters, onLy a few of rshich arecovered by the formulae given.
During service on a coastal structure, concrete armourunits wi l l be subjected to a var iety of loads inproduct ion, handLing, placing, and f inal ly in service.If any of these loads exceed the strength of theconcrete, or i f the eumulat ive effects of the Loadsexceed the fatigue resistance, degradation and failureof the armour layer mey occur. The main categories ofloads may be su'nmarised:-
a) dynamic - due to the effecEs of wave drag andmomentum, may also include some handling loads;
b) impact - due to collisions between adjaeentarmour units, with broken units, underlayer rockor other soLid mater ial ;
c) stat ic or quasi-stat ic - due to sett lement and/orcompaction of the structure core, underlayers orarmour layers, wedge or arching effects;
d) abrasion (more correct ly termed attr i t ion) - dueto the impact of particles much smaller than thearrnour units, often sand or shingle insuspension;
e) thermal - due to temperature changes, mainlyduring cast ing, but also in freeze/thawcond i t ions ;
f) chemical - due to reactions at the surface andwithin the concrete, including sal tc rys ta l iea t ion , su lphate a t tack , a lka l i / s i l i careact ion, and reinforcement corrosion.
It may be noted in passing that a brief but usefulsumnary of the origine and effects of !!any co$monloads affecting marine etructures is given byGaythwaite (nef ZZ). Some of the cosmon effecte ofabrasive and chemical loads are discussed by Fookes &Poole (nef Zg). Thermal l -oads result pr incipal ly fromstresses induced by temperature differences in thesetting and hardening phases of nanufacture, and arediscussed by Burcharth and Ligter ingen et al (nefs 79,8 0 ) .
Dynamic, impact, and static forces are l-ikely to becri t ical for s lender and inter locking units, thermal
23
5 . 2 C a l c u l a t i o n o fp r inc ipa l loads
and impact loads will be more important for bulky orb locky shapes. These loads w i l l a r i se in a l l th reephasee of the l i fe of the unit : manufactur€;handl ing, t ransport and placing; and in service. Theload condit ions for the f i rst two phases areessent ia l l y con t ro l lab le , uay be reasonab lywel l-def ined, and are rnainly inf luenced by theself-weight of the unit . Under normal circunstances,careful handl ing wi l l ensure that these phases do notlead to c r i t i ca l load ing cond i t ions . The ab i l i t y o fan aroour unit to resist handl ing loads may be checkedby sinple drop tests or by a numericaL stressanalysis. An example of this is given by patur l .e etal (Ref 19) who deecribe the use of a f in i te elemenrotress analysis package to calculate stressee ! i l i th inan Accropode under a number of idealised loadingcond i t ions .
'lhe remainder of this chapter deals with loads undera) - c). In general the most important are expectedto be those dynamic, impact, and/or quasi-stat icloads, ar is ing during najor storos. I { t r i lst sueh loadswil l be addit ive, techniques present ly al low only avery simple analysie of s ingle load types.
Under wave action the principal types of loads vill beinpact, contact, or quasi-stat ic loads. Those appl iedto a unit by wave slam or drag are unlikely to causeprob lems d i rec t l y , as they are e i rher re la t i ve ly low,or last for too short a time, Such loeds will howeverbe much concentrated at contact points between units.
Galvin & Alexander (Ref 81) developed simple enpir icalexpressions to caleulate crushing loads at contactpoints between armour units under breaking rravesoConsidering the Dolos ae an exanple, they postulatesome simple loading condit ions, and calculate bendingstresses. The analysis suggests that the cr i t icalconditionri are independent of the size and weight ofthe Dolosse, but do depend on the strength of theconcrete. Galvin & Al.exanderre calculat ione suggestthat Dolosse of 3000psi compressive strength(o. = 20.7N/m2) vould break under l raves of 14ft( t t -= 4 .3ur ) , wh i ls t Do losse o f 6000ps i (o^ * 41 . .4W/mn2)would break under waves of 20ft ( t t = 5.1;) . Theysuggest that the equivalent armour unit sizes for suchcondit ions would be 3 to 8 tone respect iveLy. Theanalysis methods involve considerable siupl i f icar ions,in part icular impact loads are not expl ic i t lyconsidered, nor are sett lement or other quasi-stat icloads included. Some qual i tat ive conf irrnat ion is
24
offered by Magoon & Bairdt s report (net 14) ofbreakage to 5 and 8 ton dolosee at Baie Comeau,Canada, shere Dolosse of concrete strength between6700-8700psi (6^ = 46.2 - 6O.0N/um2) broke undet wavecond i t ions es t i ;a red a t 13-15 f t ( " " - 4 .0 - 4 .6n) .
It will- be noted however that Galvin & Alexanderrsnethod does not take account of sett lement toads, norof i rnpacts between units. Ligter ingen & Heydra(nef ZS) have considered laboratory tests at large andsmall scale. They conclude that s lender units largerthan around 40-45 tonne can break under sEatic loadingconditions. Breakage under rocking can affect unitslarger than around 10-15 tonnes. Ttrey furtherconcl.ude that methods then evail-able (1985) wereinsuff ic ient for the design of any concrete unitsgreater than around 10-15 tonne.
These uncertainties may be overcome using either, orboth, of two different methods. Ttre first involvesthe use of instrumented model atrmour units in physicalmodel testing, and has been developed in Canada atQueents Universi ty, King6ton, in associat ion withW F Baird & Associates, Orrawa (nefs 82-84). Thesecond method involves the calculat ion of ideal isedloads using a combination of mathenatical models, andhas been developed at Auburn and Oregon StateUniversir iee in rhe USA (nefs 85-87).
The Canadian method requires the model arrnour unitsbe instrumented to measure the appropriate loadsduring hydraulic model testing. Lindo & Stive(nef Z6) have described very briefly node!. Tetrapodsequipped to measure bending moments in a leg and tomeasure accelerat ions. Scott et al (nefs 82, 83) havedeveloped a simple cyLindrical load cel l capable ofmeasuring bending moments and torsion at themid-sect ion of a Dolos unit . These methode thenrequire the use of finite element methods of stressanalysis to determine peak stresses throughout theunit . Scott et al i l lustrate the use of their loadce1l with examptes of measurements from hydraulicmodel tests. They indicate examptes where Dolossesubjected to l rave condit ions wel l within theirapparent hydraul ic capabi l i ty may fai l structural ly.Their papers do not however describe the finiteelement stress analysis method used; the problems ofthe non-l inear behaviour of concrete, part iculartywhen reinforcedl or the def ini t ion of Loading/react ionpoints for each unit considered. An apparentdisadvantage of this method is the need for manyinstrumented units to be deployed on each model testsec t ion to y ieLd a s ta t i s t i caL ly vaL id descr ip t ion o f
25
both spatial and temporal variations in armour units1oade.
In an early example of the alternative approach,Tedesco & t'fcDougal (Ref 85) derive a simple method toestimate wave loading as wave slam forces on acyLinder, using an approach sini lar to that descr ibedby Apelr & Piorewicz (nef 88):
t r = tC "gD lu2 (5 .1 )
where the slarming coeff ic ient, Co, var ies with t ime,and a depth-averaged veloci ty, ur- is calculated forthe wave front using the wave celerity. Values of Coare estimated for both partial and full iurnersion wi[ha peak value of Co = 3.2. Using ideal ised loading andreact ion patterns; a non-l inear f in i te element methodof etress analysis is used to determine l- imit ingstress values. Tedesco & t lcDougal def ine a designload case for Kn = 22, coto = 2.5, and wave periodgiven by a sea sLeepness from Lr - 2.5. A regularwave condition is used in the calcutations. Threes izes o f Do los are cons idered, hav ing s izes o f 15 .2 ,30.3 and 40.4 tonnes. In calculat ions of the designload the authore meke a numbet of fundamenlal- errorswhich influence the results of subsequentcomputat ions. In caleulat ing valueg of a degign waveheight, Hgr for each armour unit size, a val"ue ofKr,, = 8.8 iias used rather than 22 as stated in thepiper, coincidently rather closer to that recommendedfor use by Partenscky et a1. Also in calculat ing adesign wave period, Ts, a value of I r = 2.0 wasactually used, rather-than the value given in thepaper. Values of II* and T. used for each of thearmour unit sizes c^dnsiderBd rnay be sumarieed:
M( r )v(n3)o- (m)nii('lt ! (s )
SmalL
t 5 .26 .07
L .8247 .35
10 .85
Medium
30 .3L2 .L42 .2989 .L7
12 . 11
Large
40.415 . 182 .52910 .18L2 .77
Using these values, Limit ing stresses are calculatedfor a renge of wave condit ions. I t is interest ing tonote that, even using a most conservative value ofK., = 8.8, these calculat ions suggest that 40 tonneu"nits og 6o = 27.6N/mn2 will fail at wave eonditionsbelow the design load case, and that 30 tonne units ofthe same concrete will be near failure. It will benoted that these calculat ions are generalLy simi lar tothose proposed by Galvin & Alexander (Ref 8L) and donot include ei ther sett lemenE or impact loads.Tedesco & McDougaL ident i fy some of the l imitat ions oftheir methods, and atLempts are made in later work toovercome the more important of these.
2 6
In the more recent work Tedesco et al and McDougal etal (nefs 86, 87) revise their wave force model,although they do perpetuate some of the calculationerrors in their earlier work. Their revised waveforce model includes calcuLations of force on eachl inb of the Dolos, using drag, inert ia, k inet ic andbuoyant force components. They note that the peakslanrning forces are of short duration, and do notoccur simultaneously for each 1imb. As a reeult themaximum total force at any tirne ie lese than the sumsof the peak forces. ResuLts from the revised waveforce model are again used with idealised loadingconfigurations to provide the input toading conditionsfor stress caleutaEions. A sophist icated f in i teelement method devel.oped by ADINA in Watertown,Massachusetts is used to determine def lect ions andstresses. A number of reinforcement conf igurat ionsare considered for 40 tonne Dolos units. Again thecalcutat ions appear to indicate possible fai lure ofconcrete of oc = 37N/nm2 at Less than the design loadcase, st i l l afparenCly determined using Ko = 8.8rather than 22 as given. In these papers a nunber ofsigni f icant l - i rni tat ions are ident i f ied, part icular lyin the def ini t ion of loading and of supporteonf igurat ions. McDougal et al (Ref 87) do, however,indicate some early results of calculat ions of r ig idbody motions, veloci t ies and accelerat ions, whichmight later be used to determine impact 1oads. Ttresehave mainly been studied in relation to armour unitstrength and are considered in sect ion 5.3.
Final ly three other approachea are of interest.Howell- (nef gg) reports the evol-ution of a measurementsystem to ident i fy concrete strains, uni t movements,and accelerat ions, in 42 tonne Dolosse st CrescentCity, CaLifornia. I t is understood that 20instrumented units have been deployed on thebreakwater, but no result has yet been publ ished.
Sini lar ly unpubl ished are the resutts of a regearchstudy at the Universi ty of Leeds in which straingauged epoxy model DoLosse were subjected to lraveaction. The strains measured were then anaLysed usingthe PAFEC f ini te element stress analysis method.Early discussions suggested that for a concrete oftensi le strength, o,- = 3N/mm2, the safe size ofunreinforced Dolossi rnight be as 1ow as 2 tonnesn thatis the size of those broken at CleveLand, Ohio.
Nishigori et al (net gZ) report the resul_ts ofmeasurements of surface strain on model Tetrapods of50kg subjected to rrave action in the very Large fLtrmeof the Central Research Inst i tute of the ELectr ic
2 7
5 . 3 I d e n t i f i c a r i o nunit strength
Power Industry in Japan. They present examplemeesurements of atrains for certain srovements ofTetrapods under regular wave6 of H/ AD^ between 2.6 and4.2. They conclude however that more"information isneeded on the leve1 of etrain at fai lure.
o f
Three major approaches have been taken to identify thestrength of concrete armour units. In the f i rst two,fu1L scale units have been subjected ro a number ofsimpl i f ied loading condit ions, usual ly increased unt iLfai lure is reached. A third, and sometimescomplementary, approach involves the use of variousmethods of stress analysis to calculate stresseswithin units subjected to ideal ised loadingcond i t ions .
Conerete armour units have routinely been subjected tosimple drop tests, ueual ly intended to demonstraterobustness. Burcharth (nefe 90r91) descr ibes thedeveLopment and use of a set of impact and drop testsintended to quantify the reeistance of Dot"osse toimpacts. Sini lar tests with Dolosse are reported byTerao et al, and tin et al (Refs 94-96). Some testswith Tetrapods are discussed very briefly in the CIADreport (Ref 97), and some results for cubes, Tetrapodsand DoLosse ere discussed by Si lva, Groeneveld et aL,and l,[o1 et al (nefs L4, 98n 99). The general trend ofthe resut ts for the drop test for Dolosse andTetrapods may be i l lustrated by est iuat ing theliniting drop height, and hence drop angle for givenunit s izes. The results of s iraple cal_culat ions basedon data in References 15, 90, 91, 97 and 98 arepresented in Figures 5.1 and 5,2. Such l i rai t ing valuecurves might be used to identify perrnitted LeveLs ofannour movement. Sinilar curves ere presented byTimco, and discussed by Burcharth (qef tO+). Thereader is advised to consul. t these References,part icular ly the 1ast, before using Figure 5.1, evenin prel iminary design.
A somewhat different approach has been taken byUzumeri et a1 (nefs 100, 101), who have reviewedprevious l i terature on the design of Dolos units froma structuraL engineerrs viewpoint, and then conducteda series of loading tests on plain and reinforcedunits. Uzumeri et a1 consider previous work on thestrength of Dolosse by Li l levang & Nickola (nef lOZ),Desai (Ref 93) and Burcharth (Refs 91, f03). Theyf ind a number of misconcept ions or errors ofinterpretation in the work of Desai and Lillevang &Nickola. They conclude that a1!- Dolosse, and byextension al l other units that generate high inter l_ock
28
-_..- __-,
forces, should be reinforced. Uzumeri et al arguethat, only by ensuring that the units are strongenough to resist the degree of movement to which modelunits are subject, wi l l the high level_ of armourstabi l i ty seen in the hydraul ics laboratory beachieved in service. They note that the primaryadvantage of the Dolos is i ts inter lock, and suggestthat it is highly 1ikeLy that a number of units in anystructure wi l l be subject to a total loadsignificantLy greater than the dynamic forces on anisolated unit . Should these highly stressed unitsfracture, unless reinforced, they wi l l fa i l . Theoverload wi l l then ei ther be passed to adjoining unitsleading to their fai lure, or i f they areinsuff ic ient ly supported, to their i isplacement. Whenan unreinforced Dolos fai ls, the result ing piecesbecome projectiles carried by the waves, and lead tofurther impact damage. The authors ergue strongly forreinforcement to maintain integri ty in units aftercracking. They describe a ser ies of loading tests on10 ton Dolosse, both pLain and reinforced. They alsodescribe the use of the ADINA f ini te element stressanalysis programs in nodelling the behaviour of theunits under test. They divided the unreinforcedDolosse into 440 sol id elements, 681 nodes. Thereinforced Dolosse required further el"ements. Uzumeriet al concl-ude that this mathematieal model , even whennodif ied to aLlow reinforcement bar sLip, wi l l g ivesuccessful results up to the cracking l_oad, but is notrel iable beyond this point. The authors also addressaspects of cost, which they do not beLieve shouldincrease signi f icant!-y, and of reinforcementcorrosion. In their conclusions the authors make somepoints that are best conveyed verbat im:
"There is a profound difference between the behaviourof reinforced and un-reinforced Dolos units. ForDolos unit s izes fal l ing within the range ofreasonable and economical engineering design,unreinforced Dolosse should not be used. The exactdetermination of the economical range for reinforcingDoLosse can only obtained by examination of the waveregime and safety factors ut i l ized for a part iculardesign, and by considering further informationregarding condit ions exist ing at the si te. ' ,
A number of other researchers have tr ied to usemethods of stress analysis to descr ibe the strength ofunreinforced concrete armour units. At i ts s irnplestthe strength of a concrete armour unit is given byboth i ts shape and the mater ial propert ies of theconcrete, such as the compressive and tensi lestrengths. The uLt imate strength of a Dolos unit wasest imated by Desai (Ret g:) who considered units free
2 9
to rotate. A compressive strength o^ of 35 N/rm2, andmoduLus of rupture of 4.5 N/mz were-used incalculat ions of energy needed to cause fai lure of aunit . Frm the results of the analysis i t wasconcluded that units of 40t or greater would need tobe reinforced against impact loadings. The anal-ysismethod used does not expLici t ly consider the effectsof irnpact loading. Errors in this approach have beendiscussed by Uzumeri (a.et 100). A simple analysis ofbending stresses induced in a Tetrapod subjected torocking movements is given in the CIAD report(ner gz) .
Patur le et a1 (Ref 19) used a f in i te element method totest a simpl i f ied Accropode. This was treated in foursymnetr ic quarters. Each quarter uni t was describedby 353 elements with 608 nodes, rhus giving 1824equations to be eolved. The concrete lras taken ashaving a density of 2400kg/m3, and a Poissons rat io ofO.2. I t was noted that the dynamic elast ic moduluswould be greater than the quasi-stat ic modulus. Avalue of E = 20000t'IPa was taken. The anatysis methodused again did not deal with irnpact loads, which formany randomty-orientated armour units may be expectedto doninate.
I Ia1 l e t a1 (Ref 123) d iscuss br ie f l y the use o fsimi lar f in i te element methods for stress analysis totransfer strain measurements made on model units tos t resses in fu1 l -sca le Do losse. Th is was la te rcovered by Scott et al and Baird et al (nefs 82-84),al though 1i t t1e detai l is given of the f in i te elementmethod used.
5. 4. I General.
One of the major l iur i ta t ions of convent ional hydraul icurodel- tests is that the model_ armour units have astrength that is not scaled, whi l_st the loads are. Asa resul-t the units do not break during testing, forwhich the hydrauLic model1er is of ten gratefut ! Thishas in the past however 1ed the users of such tool"s toignore the probl-ems of the structuraL design of armouruni ts . Two methods may be used to assis t inident i fy ing the possib i l - i ty of fa i lure of uni rs in thearmour l-ayer of a breakwater. The model units may beinstrument,ed to determine 1oads, movements oraccelerat ions. Examples of th is procedure have beendescr ibed in Sect ion 5.2 above, and in References 25,26 , 82 , 83 , 84 . The ca l cu la t i on o f l im i t i ng s t ressescan then be conducted using one of the finite elementmethods deser ibed previously .
5 .4 Mode l l i ngmethods
30
An al ternat ive, aLbeit one of relat ively l i rni tedappl icat ion, is to use model armour units of amater ial of sui tably scaled strength. This was f i rsttried when the National Research Council,, Canadatested the ( fai led) Sines breakwater. l "Jansard & pLoeg(Ref 105) report tests with model Dolosseincorporating a weak section to altow armour unitbreakage. Using these weakened units they obtainedfai lure resul- ts qual- i tat ively sini l -ar to thoseobserved during and after the storm of February 1978.These units lrere not of scaled strength throughout.,and the possible fai lure mode of modeL units wasunreal ist ical ly l in i ted. I t was therefore necessaryto try to deveLop a material that could reproduce theimportant propert ies of concrete at scale aroundI : 20-40 .
The use of scale models to simulate performance ie notconf ined to the f ie ld of hydraul ies. At var iouspoints in time structural analysis of complex formshas been performed using structuraL models. Ingeneral i t is extremely di f f icul t to scale al l theimportant properties of concrete, and it has beennoted that concrete is particularly unusual in thewide difference between its compressive and tensiles t rengths .
5.4.2 Develop'ment of strength - scaled mater ial"s
Dodds (nee tO0) considers the production of armourunits scaled at around L125, having a mo<lel tensilestrength og or = 0.12N/mn2 and an elast ic modulus ofE = 1600N/m2l Loaded thermo-sett ing polymers wereconsidered, and it was concluded that a compound nightbe derived using a phenolic resin Loaded with calciumcarbonate. It was clear, however, from the very briefstudy reported, that considerable care would be neededin handling such units in the moulding, storage andplacing operat ions.
The use of micro-concrete and gypsum pLaster mater ialsfor structural model l ing has been discussed by Preece& Davies (nef tOZ), white (net tOa) and by sabnis eral (Ref 109). Plaster based mater ials reduce strengthon ismersion in lrater. For modeL armour units thiscan be turned to an advanEage. The model units may bemade at a greater strength than needed for test ing.This strength than allows the units to be handled andplaced. Soaking in water for a controt led period maythen reduce the unit strength to the required value.The deveLopment of plaster based mixes to simulate thef lexural strength of concrete at scales around 1:20-40is descr ibed by Timco (nef t tO) and Timco & l fansard(net t t t ) . The use of modeL units made in strengrh
31
scaled materiaLs is reported by Tinco & l-Jansard(ne fs 111, 112) and Mansard & T imco (ne f t t l ) . rndescribing the evolut ion of the mixes, Timco (Aef f fO)notes that the ratio of compressive to flexuralsLrength is anomalously high, hence the failure tofind materials to scale both compressive and flexuralstrengths. A f lexural strength of of = 4.4N/mn2 wasused for the prototype, giv ing target strengths forvar ious sca le ra t ios :
Timco then describes the effects of varying thecomponents of the mix: a cotrmercial plaster of paris,sand; iron ore; and water. It is noted that theconstituents may vary, and is suggested that einilareeries of tests wil-l be needed to derive curves offlexural strength against mix proporti.ons. In thetests at NRC the proportions of materials were givenby :
T o t a l = a + B + y + 6
where c = rrt of plasterB = l r t of i ron ore (density 5000 kg/m3)y = lrt of sand6 = wt of f resh lrater.
( 5 .2 )
f o r a l L t e s t s y = 3 . 0 a n d d = 1 . 0 .
To achieve the correct density B = 1.0 was found toyieLd the target density of about 2250 kglm3. Theproportion of ptaster, c, lras altered to change thes t rength :
Sca le
1 : 11 : 1 5l : 2 51 : 4 0l : 5 0
Sca le
1 : 1 5l : 2 51 : 4 01 : 5 0
Tests were conducted at I{RCanadian test results withUK. As iron ore is not ans tandard mater ia l , in i t ia laluminirmr oxide, producedheavy aggre€iate. This had
og (N/nmrz)
4 .4o .2930 . 1760 . 1100 .088
c
0 . 6 80 . 5 70 . 4 70 . 4 2
to try to reproduce themater ials avai lable in theeasi ly avai labLe ortests used a synthet ic
by Al-ag, as a subst i tutepreviously proved to be
3 2
very useful with ordinary portland cement in theproduction of cement mortar model armour unite. Whenused with pLaster, however, an expansive react ionoccurred which split the units apart over a few days.A number of other probLems were also encountered withthe inclusion of air , and fLash sett ing in mixing.It proved very difficult to obtain strengths in therenge sought. A series of cube compression andcyLinder spl i f t ing tests were conducted at OxfordPolytechnic on a number of mixes by t{alker (nef ftS).The results of these experiments were not usefuL asmany of the test specimens fai led before test ing,having falLen apart during the soaking period.
Subsequent work by Taylor at Teesside Polytechnic inl iason with HR (Ref 116) euggested soLut ions ro manyof the problem areas. An appropriate heavy materialthat is inert in pl-aster mix is barytes. Taylor usedbarytes grade 217 prodtced by the llopton Uining Co inDerbyshire, this had a density of around 4200tg/n3.It was noted that the plaster used at HR was alsodifferent to that avaiLabl-e in Canada, although it wasone of a range used previousLy for structurat nodels.Dental plaster to 3.54722:71 produced by British Gypsumproved more successfut. Many of the problemsencountered in mixing and placing in the moulda lrereovercorne by using an industrial food mixer. The sand,barytes, and plaster (previously mixed) were added tothe water whilst mixing. The materiaL was generallymixed for less than 30 seconds before placing.
Taylor produced 10 mixes using pl-aster, barytes, sand,and water. The proportions of the rnixes rnay besummarised using the terur inology of equat ion 5.2:
Mix
A 1 .0B r l
c r l
D r l
E r l
F r l
G r l
H r l
r r lJ r l
Sand Water
Y6
4 .0 1 .1t f l l
r t t l
t t t l
I t l l
i l 1 . 3r 1 . 6
" 1 .95 . 0 2 .06 . 0 2 .2
Plas tercl
Barytes
B
0 .00 .250 .75t . 25t . 752 .O
l l
t l
t l
t l
Flexural and compressive strengths,respect ivel-y, were evaluated usingTimco. The results of these tests
f6 and f"s imi lar methods tomav be summarised:
33
Mix Dens i ty( tg7rr ;
203020602L50226023302300220021802L20I 8702080206017402160210020102LO71997
Strengthfb
0 .7130 . 7380 .6700 .819B. 863o .6470 .526o .4750 . 8111 . 517o .3220 .3920 .8420 .3350 . 3550 .5000 .2560 .438
(u/rmn2)f"
1 . 7 0L . 5 22 . I 31 . 8 61 . 8 4I . 8 3
- )- )
ABcDEFGG
(c(eHH
(ttII
( rJJ
1 .1L .22 .L2 .21 .1r .22 . 11 . 1t . 22 . 1I . l2 . L
: )
- )
Tests C2L.-2, I I2.1, and I2.1 were performed on dy testspecimens that had not been soaked. Tests cl .1-2,U1.1 , I1 .1 and J1 .1 were per fo rmed a f te r 19 hourssoaking. Teets H1.2 and I1.2 used specioens that hadbeen soaked only 2.5 hours. This reduced soak timeincreased the f lexuraL strength sl ight ly, suggest ingthat a longer period than 2.5 hours is required.Despite the extensive nature of the tests only one mix(J) would have been suitable for a scale ratio smallert h a n 1 : 1 5 .
The use of other strength-scaled mater ials ismentioned br ief ly by Li l levang et al (Ref 114), whoalso used a mixture of plaster of par is, sand andbarite. Prol-onged exposure to water redueed thestrength of this mix. This mater ial was thenreplaced by Modcrete, developed by Arctec Inc frommaterial used to scale the propert ies of ice. Nodetails of this material have been found in thel i te ra tu re .
ALl scaled strength materials suffer from a number ofdisadvantages. They are relat ively expensive toproduce, by virtue of the staff time needed to producearmour units. Each set of uni ts can only be used in asingle short test. A number of propert ies of coneretecannot be scaled wel l - , part icular ly the compressivestrength and elast ic modulus. In using such units i twi l .1 be possible to ident i fy fai lure condit ions andthose of severe armour unit damage. Strength-scaledunits do not however yield the quantitative measuresof stress below faiLure obtained by instrumentedu n i t s .
34
5 . 5 A n a l y s i s o fsi te experience
Dauage to breakwaters and coastal structures has beenwidely reported, and has been covered in some of theearLy chapters of this report . Very br ief detai ls aregiven by PIANC (nef gZ) aLthough this reporr omitssome important structures, such as those at DiabloCanyon and San Ciprian. Very 1ittLe analysis hashowever been conducted. Tvo useful approaches aresuggested by Timco (nefs 117, 118) and Behnke &Raichlen (Ref 119). Ttre methods described have beenconsidered to be usefuL for rock by Allsop & Latham( R e f t o ) .
Behnke & Raichlen (nef 119) suggest that armourdisplacement may be linked to the cumulative energy ofall storrrns above a threshold level. Allsop & Lathamadapt that method to calcutate the energy above thethresho ld :
Erh = cth 9* E2 Hg To T*/16n
where the threshol-d coef f ic ient , Crn, mayin terms of a threshoLd (s igni f ica i t ) waveHs th :
c rh = [ z (u " .n /n " ) , * 1 ] exp [ -2 (Hs rh /H" )2 ]
Behnke & Raichlen use this type of approach toconsider the resuLts of model tests of the damage tothe Tribar armoured breakwater et Diablo Canyon.
Timco (Refs LL7, 118) uses a somewhat simi larapproach, but considers very meny more structures, atLarmoured with Dolosse. From the results of previouspendulum and drop tests it is suggested that theresponse of the units to input energy/fracture area isconsistent over a range of uni t s izes. Timco def inesan incident energy:
Eio" = e, s2 n! r$ l t6n
then def ines a factor O as theenergy to the area of fracturewr i t ten :
o = 0.7328 rx - :s.5rzrc - fIlTrS r-z;-q*J-
Timco calcul -ates values of O for 10 st ructures thathave suffered some armour displacement and/or damageto Dolosse. Values of n range f rom 36x106 J lm7 permetre for Sines breakwater down to 16x105 J lm2 oer
( 5 .3 )
be def inedhe igh t :
( 5 .4 )
(s .5)
rat io of the incidentof a unit . Tbis may be
(s .6)
35
6 DESICN T{ETEODS
6. l - Des ignphi losophies
metre for RiviBre-au-renard, for those structures withbroken Dolosse. Structures, that have suffered onlymoderate damage have values of O less than 10 x106f/n2 per metre. From this analysis Tiurco suggestsa l in i t ing value for O of 12x105 J/m2 per metre, abovewhich i t is l ikely that unreinforced D,olosse wi l lfa i l . I t i s c lear tha t th is reLat ive ly s iu rp leana lys is su f fe rs sone l im i ta t ions . In par t i cu la r i tdoes no t address s ta t i c load ings , o r fa t igue e f fec ts .The method and conclusions are however convincinglyargued and, subject to the l imitat ions discussedappear to be we l l -based.
A number of other authors have reported examples ofarmour unit breakage, including Edge & Magoon (Ref 39)Markle & Davidson (Ref L22) t but have not achieved asconv inc ing an ana lys is as T imcors .
The design phi losophy adopred wi l l i tsel f have asignif icant inf luence on the way in which a design isexecuted, the input data required and the infornat ionprovided by the design process. Two di f ferentphi losophies may be def ined:
a) Determin is t i c ;b ) Probab i l i s t i c .
Detern in is t i c des ign ph i losophy is based essent ia l l yon the ident i f icat ion of a single rnajor event ofpredicted return period, the quant i f icat ion of theloads arising from that event, and the design of thestructure to resist the calculated load with adequatesafety margins. Determinist ic design methods arereasonably sinple and require relat ively 1i t t le inputdata. I t is, however, argued by some researchers anddesigners that deterrninist ic methods often lead roover-design, and that they do not al low the essessmentof r isk levels of danage or fai lure. Msst of thedesign handbooks or manuals used in coastalengi-neering are based on determinist ic phi losophy.
Probabi l ist ic design involves the assessment of theloads ar is ing from many eventa, together with thel ikel ihood of each such event being exceeded. Aprobabi l i ty density funct ion may then be compi led forthe loads on the structures. A sirniLar probabi l i tydensity funct ion may then be described for theres is tance or s t rength o f the s t ruc tu re . Areas o foverlap, where loads exceed resistance, qray then beest imated giving a probabi l i ty of damage or fai lure.Probabi l ist ic methods are claimed to yield noreprec ise ly de f ined des igns w i th we l l idenr i f ied
36
6.2 Pre l im inarydesign
standards of protect ion or safety. Such methods aremore cortpatible with the increasing need for riskassessment , par t i cu la rLy in cos t /benef i t s tud ies .Ful l probabi l ist ic design may, however, be compl icatedto perform, and will require much more data than isoften avai lable. In many examples of the use of suchmethods, the form of the probabi l i ty density funct ionhas simply been assumed to foLl-ow that of the normalprobabi l i ty distr ibut ion. Simple descr ipt ions of theuse of probabi l ist ic design methods for breakwatershave been given by Ligter ingen & Heydra (nef Z5),Dover & Bea (nef tZO) and Burcharrh (Ref 121). A morecomplete discussion of probabi l - ist ic methods is givenin rhe CIAD report (Ref 97).
Whi lst sophist icated probabi l ist ic design phi losophieshave been discussed by an increasing number ofresearchers and designers, part icularLy with referenceto concrete armour units, such design methods are notyet of i rmediate use to the designer. This is duemainly to the lack of understanding, andquant i f icat ion, of the forces act ing upon the armourunits. A third design phi losophy has thereforeevolved, known as quasi-probabi l ist ic. As the ternirnpl ies, this offers a compromise approachincorporat ing elements of probabi l ist ic design methodsin an essent ial ly determinist ic f ramework. Mostprobabi l ist ic design methods suggested for use at themoment are of this form.
At the feasibi l i ty or prel iminary design stage a rangeof sirnpl-e empirical methods are available to addressthe main design parameters. The pr incipat aspects tothe design, such as armour unit s ize, s lope angl-es,and crest leveL may be ident i f ied by addressing:
a) hydraul ic performancelb) armour movement;c) annour unit strength.
Data is general ly avai lable on the hydraul icperformance, principally reLative run-up leve1s andre f lec t ion coef f i c ien ts , fo r a number o f un i ts .Examples are ident i f ied in sec t ions 3 .2 -3 .
A littLe information on armour movement is availablefor a wide range of armour units in vaLues of KO.Much of the data reLates to regular lraves and to otherideal ised condit ions. Detai led information isconf ined to relat ivel-y few units. Other ernpir icalmethods are a lso d iscussed in sec t ion 4 .3 .
37
6 . 3 M o d e l l i n gmethods
The roain types of loads acting on annour units underwave act ion are dynamic, impact, and quasi-stat ic. Afew siupl ist ic methods have been developed to est imatedynamic forces. To date these have been conf ined tothe Do los , and are l i rn i ted to very idea l i sed load ingand support conf igurat ions. Those methods present lyava i lab le a re a t a research leve l on ly . The e f fec tsof impact loads have been considered in terms ofarmour uovement, rather than loads, and are discussedbelow. No methods have yet been ident i f ied toquant i f y the deve lopment o f quas i -s ta t i c loads w i th inthe armour layer. Very l i t t le inforurat ion isava i lab le to a l low the pred ic t ion o f mound se t t lement ,and even less to determine the consequent loads and/ormovements within an anuour layer.
Siur i lar ly l i t t le information is avai lable on thestrength of any unit other than the Dolos. A fewother units, such as the Accropode, have beensubjected to siuple ad-hoc dropping tests to provide ameasure of strength, but no standard test exists, andvery l i t t le da ta has been pub l ished.
T imco (ne fs 1171118) has suggested a s i rup le empi r i ca lmethod to calculate a threshold wave condit ion abovewhich armour unir breakage may occur. This methoddoes not, however, assess ei ther the loads or thestrength of the unit , and is val id only for the Dolos.In general the select ion of the size and robustness ofthe unit rel ies heavi ly upon local experience and oneach designersr part icular knowledge. Any furtherinfornat ion wi l l require the use of physical ormathematical model l ing nethods.
6 .3 .1 Hydrau l i c per fo rmance
Idave run-up on, and reflections from, an armouredslope are measured easi ly in an appropr iate ly scaledhyd rau l i c mode1 . The gene ra l des ign p r i nc ip les f o rsuch models have been d iscussed previously by Owen &Al lsop and Owen & Br iggs (Refs 124, 125) and byo the rs .
Methods and examples of the measurement of wave run-upleve l s have been p resen ted by A l l sop e t a l (Re fs 60 ,126), and ref lect ions by Al lsop & Het t iarachchi(Ref 54) . Mathemat ica l models of wave run-up, andre f l ec t i ons , unde r regu la r waves have been d i scussedby Kobayash i e t a l ( ne f s 127 , 128 ) . These techn iquesa re p resen t l y on l y ab le t o ca l cu la te run -up andre f l ec t i ons f o r a l im i t ed range o f wave s teepnesses .They have yet to be val idated or wel l supported by
38
CONCLI'SIONS ANDRECO}IMENDATIONS
laboratory or si te measurements. They offerconsiderable promise and work is proceeding atHydraul ics Research, the Universi ty of Delaware, andelsewhere to extend and refine them. Thesemathematical modeLling techniques are however not yetsui tabLe for rout ine or economic use in the designp r o c e s s .
6.3.2 Armour movement
Methods for the measurement of armour movement ordisplacement in physical models have been discussedearl ier in this report and in the references.
Very few mathematicaL modelLing methods are availableto estimate armour movements. Kobayashi & Jacobs(nefs 129, 130) report a modeL used to est imatedisplacement of r ip-rap. This modeL suffers somesignif icant l in i tat ions and has not been used for anyconcrete armour units. McDougal et al (Ref g7) reporton rrave force calcuLations on Dolosse and indicate theresults of some sinpLe calculat ions of r ig id bodymotions. Again these techniques show considerablepromise but are not yet suitable for routine uae.
6 .3 .3 Armour loads /s t rengths
The development and use of strength scaLed modelarmour units wi l l a1low dhe ,"""""r .r t of condit ionsthat lead to armour unit faiLure. They do not howeverallow the measurement of toads. Other techniquesmeasure armour movement, acceleration, or inducedstrains on the unit or in a load transducer. Someestimates of loading may be made using appropriatef ini te element methods of stress analysis. fn.detai l -ed descript ion of such methods is however,beyond the scope of this report .
A number of preliminary nathematical modellingtechnigues to determine armour unit loads have beendescribed in References 85-87. The techniques, asdescribed, suffer f rom signif icant l imitat ions, andsome errora. They do, however, show much promise forfurther deveLopment.
The most commonly used concrete armour units on largebreakwaters have been the cube, Tetrapod, Stabit andDolos. For these uni ts , the conclus ions of th is s tudymay be summarised:-
- This unit is relat ively ineff ic ienthydraul ical ly. I t is not general_l_y
Cube
39
suitable for steep slopes, due to atendency to slide down the stope, and forma reLatively smooth pavement. Cubes areoften regarded as robust, but large unitscan suffer from thermal and shrinkagecracks, reducing their resistance toimpacts .
Tetrapod - This unit has been widely used. I t of ferssome hydrauLic advantages over cubes, butis Less robust. Some breakwaters armouredwith Tetrapods have suffered significantarmour unit breakage.
SEabit - Wtren used in a single layer the Stabitappears to offer hydraul ical ly ef f ic ientperformance with relatively less concreteneeded than Tetrapods. No eignif icant dataon in service performance is available. Nodetail.s of the strength of the unit havebeen pubt ished.
Do los - This unit has been used and studiedwortdwide. It has potentially very goodhydraulic performance and economy, but thisis often not achieved due to the apparentfragi l i ty of unreinforced units. I t hasbeen argued that all DoLosse should bereinforced. A sirnple empirical method hasbeen developed from experience of breakageof unreinforced Dolosse in service tosuggest a minimum unit size for a givendesign rrave state.
Other units that have been developed re!.ativel_yrecently incLude the Accropode, Haro, and Seabee.Each of these units appear to offer a number ofadvantages over those considered above. Littlerel iable data is avai lable to ident i fy the hydraul icperformance and unit strength under wave attack.
In the Light of recent failures the design of anyconcrete armour unit cannot be restricted to theidentification of the hydraulic performance and unitdisplacement, but must include armour unit loads andstrengths. This last is not yet poseible solely bycalculat ion, even for the most intensively studiedunits. A range of s imple ernpir ical methods, physicaland mathematical modelling techniques are available toidentify hydraulic performance and armour movement ordisplacement. The model l ing methods avaiLableinc lude:
40
a) photographic and video methods to ident i fymovements and displacements in physical modelt e s t s i
b) instrumented nodel or prototype armour units tomeasure loads , acce le ra t ions , o r s t ra ins ;
c) scaled strength urodel uni ts to ident i fy incidenceof un i t fa i lu re l
d) mathematical models to calculate wave loads onideal ised armour units under very simpl i f iedload ing cond i t ions ;
e) f in i te element methods of stress analysis toexpand data on loads or strains at pointloca t ions .
The strength of ful l scale units may be ident i f ied bysiurple drop or pendulum tests, a control led ser ies oflaboratory loading tr ia ls, or by an anaLysis ofperformance in service.
This report has not covered the design and performanceof high-porosi ty single layer units. These unitsoffer considerable hydraul ic advantages over mostother armour types. They are often, however, viewedas po ten t ia l l y f rag i le . They are the sub jec t o f asepara te rml t i -d isc ip l inary research pro jec t byresearch club members including designers,contractora, and special ists in the design of concretestructures, and Hydraul ics Research.
8 ACKNOT{I,EDGEUENTSThe work at Hydraulics Research covered by this reportwas conducted pr incipal ly by members of the CoastalStructures Section in the l.taritime EngineeringDepartment, and the author is grateful for theass is tance o f h is co l leagues.
Part icular advice and assistance in analysis andconpi l ing this report was also afforded by: J TayLorof Teesside Polytechnicl G Timco of N R C CanadalW McDougal of Oregon State Universi ty;S S L Hett iarachchi of the Universi ty of Moratuwa, SriLankal James tli l l iaurson and Partners; and TraversMorgan and Partners.
4 7
9 REFERBNCES1. Owen I'{ W. rrPorts and harbours.t' In Developments
in Hydraulic Engineering, Vo1 3, Ed p Novak,Elsevier Appl ied Science Publ ishers, Barking,1 9 8 5 .
2. Goda Y. 'rRandom Seas and design of maritimestructures.rr Universi ty of Tokyo press, Tokyo,1 9 8 5 .
3. Ronit i G, Nol i A, & Franco L. "The l tal ianexperience in composite breakwaters.rr proc ConfBreakwaters 85, ICE, London, October 1985.
4. Allsop N W H, PowelL K A & Bradbury A p. "Theuse of rock in coastaL structuresrt . Summary ofseminar, I lydraul ics Research, Wal l ingford,January 1986.
5. Allsop N W Il & t{ood L A. I'Eydro-geotechnical
performance of rubble mound breakwatersrr. ReportSR 98, Hydraul-ics Research, Wallingford, I' larch1 9 8 7 .
6. Bradbury A P, Allsop N W H, Latham J-p, Mannion M& Poole A B. rrRock armour for rubble moundbreakwaters, eea wa1Ls, and revetments: recentprogress.t t Report SR 150 t tydraul ic Research,Wal l ingford, March 1988.
7. Feui l let J, Bernier J, Coef f6 y & Chaloin B. ' r tedimensionnement des digues h talus.tr Col lect ionde la Direction des Etudes et RecherchesdrELectr ic i t6 de France 54, fdi t ion Eyrol l_es,P a r i s , 1 9 8 7 .
8. PIANC. 'rThe stability of rubble moundbreakwaters in deeper water.rr Report of lforkingGroup of Permanent Technical Connittee 2,Supplement to Bultet in No 48, PIANC Brussels,198s .
9. Bradbury A P & Al lsop N W II . I 'Durabi l i ty of rockon coastat structures.t t proc 20th Coastal EngConf, Taipei, November 1986.
10. ALlsop N W tl & Lathau J-p. 'rRock armouring tounconventional breakwaters: the designirnpl icat ions for rock durabi l i tyt t . proc. Seminaron unconventional rubble mound breakwaters, NRCC,Ottawa, September 1987.
11. Latham J-P, Mannion M, poole A B, Bradbury A p &A11sop N W Il. "The influence of armour stone
4 2
shape and roughness on the stabi l i ty ofbreakwater armour layers.rr Queen MaryCo l l ege /Hyd rau l i cs Resea rch , May 1988 .
12. Bradbury A P, Al lsop N I ,1 H & Stephens R V.rrl lydraulic performance of breakwater crovrnwa l l s . " Repo r t SR 146 Hyd rau l i cs Resea rch ,Wa l l i ng fo rd , March 1988 .
13. Hydraul ics Research Stat ion. r rBreakwater armourb l o c k s . r r W a l l c h a r t , 1 9 8 0 .
14 . S i l va M A G . "On the mechan i ca l s t reng th o fcubic armour b locks.r r Proceeding Coasta lS t ruc tu res r83 , ASCE, A r l i ng ton , 1983 .
15. Burcharth H F. ' rFat igue in breakwater concretea rmour un i t s . r r P roc 19 th Coas ta l Eng Con f ,H o u s t o n , 1 9 8 4 .
16. Burcharth H F. I 'The lessons f rom recentbreakwater fa i lures, developments in breakwaterdes ign . r r P resen ted to Techn i ca l Cong ress , I { o r l dFederat ion of Engineer ing Organisat ions,Vancover, May L987.
17 . S tab i t s L td . I 'S tab i t s : a new t ype o f a r t i f i c i a larnour b lock for breakwaters and sea defenceIrorks . f r Stabi t L td, Aldwych, London.
18. Singh K. I ts tabi t , a ne\r armour uni t . , ' proc lL thCoasta l Eng Conf , London 1968.
19. Patur le J-M, Vincent G & Val lon D. ' rRubble moundbreakwaters, a new generat ion of b locks, s t rengthof the Accropode, f in i te e lement s tudy.r r SogreahConsul t ing Engineers, January 1985.
20. Paape A & Wal ther A W. r rAkmon armour uni t forthe cover layers of rubble mound breakwaters. t lProc 8th Coasta l Engineer ing Conf , Mexico Ci ty ,1 9 6 3 .
21. I {ebby M G. "Hydraul ic model s tudy of repai rs toex i s t i ng sea p ro tec t i on o f We l l i ng ton a i rpo r textension.r r Paper No 4, Proc 10th conf of NewZealand Harbour Engineers, Whangarei , NewZ e a l a n d , 1 9 8 4 .
22. Coasta l Engineer ing Research Centre. r rshore
Protect ion Manual . ' r US Govt Pr int ing Of f , 2Vo l s , 4 th Ed i t i on , Wash ing ton , 1984 .
43
23. Carver R D & Davidson D D. rrDolos annour unitsused on rubble-mound breakrdater trunks subiectedto non breaking lraves with no overtopping., lTechn ica l Repor t E 77-L9, WES, V icksburg ,November 1977.
24. Danel P, Chapus E & Dhai l l ie R. rrTetrapods andother precast blocks for breakwaters.rr Proc ASCENo WW3, Vol 86, September 1-960.
25. Ligter ingen H & Heydra G. rrRecent progress inbreakwater design." Dock & Harbour Authori ty,J u l y 1 9 8 5 .
26. Lindo M H & St ive R J H. rrReconstruct ion of mainbreakwater in Tr ipol i harbour, Libya." Dredging& Port Construct ion, February 1985.
27. . . Abdelbaki A & Jensen O J. rrstudy of provisionalrepair of the breakwater in Port drArzew ElDjedid.rr Proc COPEDEC Colunbo, March 1983.
28. Gunbak A R. rrDamage to Tripoli harbour northwest breakwater.rr in Design and construct ion ofmounds for breakwaters and coastal protect ion,E lsev ie r 1985.
29. Barony Y S, Mal ick V D, Gusby M & Sehery F.rrTripoli harbour north west breaklsater, and itsproblems.rr Proc COPEDEC Colunbo, l tarch 1983.
30. Merrifield E M & Zwamborn J A. "Ttre economicvalue of a new breakwater armour unit rDolost.r lFroc 10th Coastal Eng Conf, Tokyo, 1966.
31. Merr i f ie ld E M. rrDolos concrete armourprotect ion.rr Civi l Engineering - ASCE, December1 9 8 6 .
32. Lunnis R. r rConcrete dolos uni ts protect newNorth Wales coast road.r r Concrete, March 1985.
34. Magoon O T & Baird W G. rtBreakage of breakwaterannour units.I Syurposiun on Design of Rubblel " lound Breakwaters, EEL Br i t ish Hovercraf t Corp,Shank l i n , L977 .
3 3 . W i l l A I , W i l l i s T A F & S m i t h D D S . ' r D e s i g nand construct ion superv is ion of sea wa11 andbreakwater at . Torness po$rer s tat ion. ' r Proc ICE,P t I , Oc tobe r 1985 .
44
35 .
36 .
Pope . I & Clark D R. "Monitor ing of a dolosarmour cover; Cl"eveland, Ohio." Proc CoastalS t ruc tures t33 , ASCE, ArL ing ton , 1983.
l ' farkle B G & Dubose W G. t tWave stabi l i ty testsof dolos and stone rehabi l i tat ion designs foreast breakwater, Cleveland, Ohio." TechnicalReport No CERC-85-10, WES, Vicksburg, December1 9 8 5 .
37. Port Sines Invest igat ion Panel- . "Fai l -ure of thebreakwater at Port Sines, Portugal.rr ArnericanSociety of Civi l Engineers, New York, 1982.
38. Zwamborn J A. ' rAnalysis of causes of damage toSines breakwater.rr Proc Coastal Structures 79,Alexandria, ASCE, March 1979.
39. Edge 1'I L & Magoon O R. "A review of recentdamages to coastaL structures.t t Proc CoastalS t ruc tures r79 . ASCE, A lexandr ia , 1979.
40. Palmer R O. rrBreakwaters in the Hawaiianisl-ands.rr Proc ASCE, Jo tr I tways & Ports Vol 2,No 13, December 1952.
4L. Thompson D M & Abernethy C L. rrBanksmeadow
breakwater: model tests on stabi l i ty of Tr ibararmour." Report EX 538, I{ydraul ics ResearchStat ion, Wal l ingford, I ' tarch I97I.
42. Iludson R y (ed). ttConcrete armour units forprotect ion against wave attack.r t l , t isc. Paperg-74-2, I{ES, Vieksburg, January 1974.
43. Baird ! i l F & Hal l K R. "The design of annoursystems for the protection of rubble moundbreakwaters.rr Proc Conf Breakwaters, Design andConst ruc t ion , ICE, London, 1983.
44. Brown C T. rrArmour units - rando'm mass ord isc ip l ined ar ray . t t Proc Coasta l S t ruc tures 79 ,ASCE, Alexandria, l larch 1979.
45. Brown C T. rrseabees in service." proc CoastaLSt ruc tures 83 , ASCE, Ar l ing ton , 1983.
46. Al lsop N W H. rrConcrete armour units."D iscuss ion to Paper No 8977, Proc ICE. P t I ,December 1985.
4 7 . l J i l k i n s o n A R & A l l s o p N w H . , ' H o l l o w b l o c kbreakwater armour units. tr Proc CoastalS t ruc tures r83 , ASCE, Ar l " ing ton , 1983.
45
48. Batt f ie ld A. rrArmour units - unsoundCivil- Engineering, November/December
49. Barber P C & Lloyd T C. r fThe rDiodel
d iss ipa t ion b lock . r r Proc ICE Par t l ,1 9 8 4 .
tes t ing? r l
1 9 8 6 .
rfaveNovember
50. Atlsop N W tt. ttTtre Shed breakwater armour unit,model tests in random !raves." Report EX 1124,I lydraul ics Research, WaLLingford, Apri l 1983.
51. Nagai S. "Stable concrete blocks on rubbLe moundbreakwaters.rr Proc ASCE Jo Wrways and HarbourDiv Vo1 88 WW3, August L962.
52. De Rouck J, Wens F, Van Damne L & Leumers J. 'rA
new type of armour unit: the llaro.rr 20th CoastalEng Conf, Taipei, November 1986.
53. De Rouck J, Wens F, Van Danrme L & Lemners J.rrlnvestigation into the merits of the Harobreakwater armour unit." 2nd Conf COPEDECBeij ing, September 1987.
54. Alleop N W Il & Hettiarachchi S S L. "WaverefLect ions in harbours: design, construct ion,and performance of wave absorbing structuresrr.Report OD 89, Hydraul ics Researeh, Wal l ingford,Apr i l 1987.
55. Whillock A F & Thompson D M. rrHigh IsLand WaterScheme - Ilong Kong - a study on the use of Dolosarmour unit,s for wave protection on the seawardface of the Eastern Dam.rr Report EX 532,Hydraul ics Research, Wal l ingford, 1970.
55. Gunbak A R. ttRubble mound breakwaters.tlNorwegian Inst i tute of Techonology Report 1,L 9 7 9 .
58 .
Losada U A & Gimenez-Curto L A. t'Flow
character ist ics on rough, perrneable slopes underwave act ion." Coastal Engineering 4r ELsevier,1 9 8 1 .
St ickland I W. "COB units - Report on Eydraul icsmodel research." Wimpey Laboratory, Ref Nor r /334, 1969.
59. A11sop N W H, Franco L & Hawkes p J. ttWave
run-up on steep s lopes: a l i terature rev iewt t .Report SR 1, Hydraul ics Research, Wal l ingford,March 1985 .
57 .
46
60. Al lsop N W H, I lawkes P J, Jackson F A & Franco L.t ' l lave run-up on steep slopes: modeL tests underrandom waves". Report SR 2, HydrauLics Research,I , IalLingford, August 1985.
62. Partenscky H W, Rutte J & Schrnidt R. t 'On thebehaviour of armour unit in the coverlayer.ttProc 20th Coastal Engineering Conf, Taipei,November 1986.
63. Partenscky I l W. t tNew invest igat ions on vert ical-and rubble mound breakwaters.r t Proc 2ndChinese-German Symposiurn on llydrology and CoastaLEngineering, l ln iversi ty of l lanover, June 1987.
64. Eudson R Y. "Laboratory invest igat ion of rubblemound breakwaters.rr Proc ASCE Jo Wrways &Harbours D iv . , Vo l 85 WW3, 1959.
65. Ahrens J P. "Large vave tank tests or riprapstabi l i ty.rr Tech tnlemo 51, CERC, Fort Belvoir ,May 1975.
66. Thompson D ! t & Shutt ler R M. "Riprap design forwind wave attack: a Laboratory study in randomnaves.t t Report EX 707, Hydraul ics ResearchStat ion, WalLingford, September 1975.
67. Thompson D M & Shutt ler R M. "Design of r iprapsLope protect ion against wind waves.rr Report No61, CIRIA, London, 1976.
68. Van der l {eer J t{ . rrstabi l i ty of rubble moundreveLments and breakwaters under randon waveattack.rr Proc conf Breakwaters t85, ICE, London,1 9 8 5 .
70. Czerniak t I T, Lord C J and Col l ins J I . , ,Dolosse
armouring design for an offshore airport .rr procCoastal Structures '19, ASCE, Alexandria, l , tarchL979.
Zwamborn J A & van Niekerk M. rrAdditional modeltests, dolos packing densi ty and ef fect ofre lat ive b lock densi ty . r r CSIR Research Report554 , S te l l enbosch , Ju l y 1982 .
SchoLtz D J P, Zwamborn J A & van Niekerk M.t tDolos stabi l i ty , e f fect of b l -ock densi ty andwaist th ickness.r r Proc 18th Coasta l Engineer ingConf , Cape Town, 1982.
Burcharth I I R & Brejnegaard-Nie lsen T. r rThe
inf luence of vra is t th ickness of dolosse on thehyd rau l i c s tab i l i t y o f do losse a rmour . r r 20 thCoasta l Eng. Conf , November 1986.
7r .
72 .
73 .
47
74. Shutt ler R t l . "Some aspects of model l ing slopeprotect ion.rr BNCOLD Conference, Universi ty ofKeele, September L982.
75 . Shut t le r R M. ' rR ip rap s tab i l i t y , a p rogressrepor t - d iscuss ion . t ' p roc ASCE.
76. Van der Meer J W. "Stabi l i ty formula forbreakwaters armoured with accropode.rt ReportH546, Delf t Hydraul ics Laboratory, September1 9 8 7 .
77. Gaythwaite J W. rrstructural designconsiderat ions in the marine environment. tr JoBoston Soc Civi l Eng, ASCE, Vo1 65, October1 9 7 8 .
78. Fookes P G & Poole A B. "Some prel-ininaryconsideraEion on the select ion and durabiLi ty ofrock and concrete uaterials for breakwaters andcoastal protect ion works.t t Ouarter ly Jo of EngGeology 14 , 1981.
79. Burcharth I t F. t tMater ial , structural" design ofarmour units." Proceedings Seninar Rubble MoundBreakwaEers, RoyaL lnst i tute of Technology,BuLlet in No REIRA-VBI-120, Stockholm, Apri l1 9 8 3 .
80. Ligter ingen H, MoL A & Groenevel_d R L. , 'Cr i ter ia
and procedures for the structural design ofconcrete armour units.tt Proc Conf Breakwatersr85 ICE, London, 1985.
81. Gatvin C & Alexander D F. rrArmour unit abrasionand dolos breakage by wave-induced stressconcentrat ions." Paper to ASCE convent ion, NewYork, preprint 8L-I72, ASCE, May 1981,
82. Scott R D, Turcke D J & Baird I , l F. "A uniqueintrumentation scheme for measuring loads inmodel dolos units." Proc 20th Coastal"Engineering Conf, Taipei, November 1985.
83. Scott R D, Turcke D J, Baird I^I F & Readshaw J S.trA rational design procedure for concrete armourunits for breakwaters.rr Dock & l larbourAuthori ty, January 1987.
84. Baird W F, Readshaw J S, Scott R D & Turke D J.rrA procedure for the analysis and design ofconcrete armour unitst t . Proc 20th Coastal Eng.Conf, Taipei, November 1986.
85. Tedesco J W & t lcDougal W G. "Non1inear dynamicanalysis of concrete armour units. t ' Computersand Structures Vol 12, Pergamon Press, 1985.
4 8
86. Tedesco J !f , l 'fcDougal I{ G, }.lelby J A &l{cGill- P B. "Dynamic response of dotos ermourunits. t t Computers & Structures Vo1 26, pergamonJourna ls r 1987.
87. McDougal tI G, l"lelby J A & Tedesco J W. ,'l i lave
forces on concrete armour units.tt proc ASCEConvention, computer aided simulation off lu id-structure interact. ion problems. ASCE,At lan t ic C i ty , Apr i l 1987.
88. Apelt C J & Piorewicz J, rr lmpact force as a partof the total breaking wave force on a verticalcyl inder. t t Research Report No CE 78, Universi tyof Queensland, January L987.
89. Itowell G. rfA system for the measurement of thestructural response of dol_os armour units in theprototype.rr Conf l"leasuring Techniques ofHydraulic Phenomena in Offshore, Coastal andInland ldaters, BIIRA, London, April 1985.
90. Burcharth t t F. "Ful l -scale tr ia ls of dolosse todestruct ion.rr Proc 17th Coastal_ Eng Conf,Sydney, 1980.
91. Burcharth l t F. "Ful l -scale dynarnic test ing ofdolosse to destruct ion.rr Coastal Engineering Vol4 , E l s e v i e r , 1 9 8 1 .
92. Nishigori !{, Endo R & Shinada A. rron stress intetrapods under .trater action." proc 20th Coastal_Engineering Conf, Taipei, November 1986.
93. Desai H C. t tVolume and strength of a doLos.rr JoWrway and Harbours Div, WWl Vo1 102 ASCE, L976.
94. Terao T, Terauchi K, Ushida S, Shiaishi N,Kobayashi K & Gahara H. rrprototype test ing ofdolosse to destruct ion.rr proc 18th CoastalEngineering Conf , Cape Tovn, 1982.
95. Lin W-M, Rau C & Su R-L. 'rThe structuralresponses of dolos armour units under the dynamicloading.rr Proc 20th Coastal Engineering Conf,Taipei, November 1986.
96. Lin W-M, Rau C & Su R-L. rrDSmamic testing ofdoLosse to destruct ion.fr proc Conf l " tar ineConcrete t85, The Concrete Society, London,September 1986.
97. CIAD. rrComputer aided evaluat ion of therel iabi l i ty of a breakwater design.rr CIAD
49
pro jec t g roup, Zoetermeer , the Nether lands ,1 9 8 5 .
98. Groeneveld R L, Mol A and Zwetsloot P A J. rr l lestb reakwater , S ines : nen aspec ts o f a rmour un i ts . "Proc Coasta l S t ruc tures 83 , ASCE, Ar l ing ton ,March 1983.
99. Mol A, L igter ingen H, Groeneveld R L andPi ta C A R M. r rwest breakwater , Sines: s tudy ofa rmour s tab i l i t y . t ' P roc Coas ta l S t ruc tu re " 83 rASCE, A r l i ng ton , March 1983 .
100. Uzumeri S M, Basset R & I4r i11 G T. rrstructuralbehav iour o f 10 ton do los un i ts . r t pb ln . 85-06 ,Dept of Civi l Eng, Universicy of Toronto, August1 9 8 5 .
101. Uzumeri S M & Basset R. rrstructural behaviour of10 ton dolos armour units." Proc 20th CoastalEngineering Conf, Taipei, November 1986.
102. Li l levang O J & Nickola W E. rrExperimentalstudies of stress within the breakwater armourp iece do los . r r Proc 15 th Coasta l Eng Conf ,Hono lu lu , 1976.
103. Burcharth H F. t 'A design method for inpact -loaded slender armour units.rr Paper to ASCEConvent ion, New York, 1981 (also as BuLlet in No18, Inst i tute of Civi l Engineering, AalborgUniversi ty, Denmark.
104. Tirnco G W. rron the structural integri ty of dolosunits under dynamic loading condit ions.,r CoastalEngineering Volume 7, Elsevier SciencePub l ishers , Amsterdam, 1983.
105. Mansard E P D & Ploeg J. rrModel tests of Sinesbreakwater.rr Report LTR-HY-67 Div of Mech EngNational Research Counci l Canada, October 1978.
106. Dodds R. ' rFeas ib i l i t y s tudy o f mater ia ls rosimulate the behaviour of concrete in modelform.rr Conf ident ial Technical Report 6591 tRAPRA, Shrewsbury, July 1981.
107 . P reece B W & Dav ies J D . r rMode ls f o r s t ruc tu ra lconc re te . r r CR Books , London , 1964 .
108 . I l h i t e R N (Ed ) . , rMode ls f o r conc re tes t ruc tu res . r r SP-24 , Amer i can Conc re te I ns t i t u te ,De t ro i t , r ep r i n ted 1980 .
5 0
109. Sabnis G I '1, Harr is H G, Wtr i te R N & Mirza M S.rrstructural model l ing and experimental-techniques.rr Prent ice-t{al1, Englewood CLif fs,1 9 8 3 .
110. Timco G W. "The development, propert ies andproduct ion of strength-reduced model armourunits." Laboratory Technical ReportNo LTR-HY-92, National Researeh Council Canada,Ottawa, November 1981.
111. Timco G W & Mansard E P D. " Improvements inruodelling rubbLe-mound breakwaters.rt Proc 18thCoastal- Engineering Conf, Cape Town, L982.
1I2. Timco G l,il & Mansard E P D. tt0n theinterpretat ion of rubble-mound breakwater tescs.r lProc Coasta l S t ruc tures r83 , ASCE, Ar l ing ton ,1 9 8 3 .
113. Mansard E P D & Timco G W. ' rA review ofbreakwater test ing at NRCC.rr Proceedings 6thCSCE Hydrotechnical Conference, VoL 2, Ottawa,1 9 8 3 .
114. L i t levang 0 J , Ra ich len F R, Cox J C &Behnke D L. rrA detailed model study of damage toa large breakwater and model ver i f icat ion ofconcepts for repair and upgraded strength. ' r Proc19th Coastal Engineering Conf, Houston, 1984.
115. Walker P R. rr l . {odel- armour units: mater iaLss t rength tes ts . r r Repor t No 128, Dept o f C iv i lEng, Oxford Polytechnic, Apri l , 1985.
116. Taylor J. rrFurther invest igat ion in strengthscaled model- l ing of concrete annour units. t , BScFinal year thesis, Teesside Polytechnic, May1 9 8 8 .
117. Timco G t i l . r rAn analysis of the breakage ofconcrete armour units on rubble-moundbreakwaters.rt Technical, Beport No TR-1{Y-001,National Research Counci l Canada, Ottawa, 1983.
118. T imco G W. "On the s tab i l i t y c r i te r ion fo rfracture in dolos armoured breakwaters.rr CoastalEngineering, Vok:me 8, Elsevier SciencePubl- ishers, Amsterdam, 1984.
119. Behnke D L & Raichlen F. rrBreakwater armourd ip lacement th resho l -ds : a poss ib le cor re la t ionwith cumulat ive wave energy." Proc 19th CoastalEng Conf , I {ouston, 1984.
5 1
120. Dover A R & Bea R G. "App l ica t ion o f re l ia t r i l i t ymethods to the des ign o f coas ta l s t ruc tu res . ' lP roc Coasta l S t ruc tures r79 , ASCE, A lexandr ia ,t 9 7 9 .
lzL. Burcharth H F. rron che rel iabi l i ty of rubblemound breakwater design parameters.rr Seminar onrubble mound breakwaters, Copenhagen, DanishSociety of Hydraul ic Engineering, T)ecember 1985.
I22. Markle D G & Davidson D D. r fBreakage of concretearmour units." Proc 18th Coastal EngineeringConf , Cape Town, 1982.
l-23. Hal1 K R, Baird W F & Turcke D J. t rstructuraldesign procedures for concrete armour units. , tProc 19th CoastaL Engineering Conf, Houston,1 9 8 4 .
l-24. Owen M W & Al lsop N W H. rrHydraul ic model l ing ofrubble-mound breakwaters.rr proc ConfBreakwaters, Design and Construct ion, ICE,Londonr 1983.
125. Owen M W & Briggs M G. ' r l in i tar ions ofmode l l ing . r r Proc Conf Breakwaters t85r ICE,Londonr 1985.
126. A l l sop N W H, Franco L & Hawkes p J .rrProbabi l i ty distr ibut ion and levels of waverun-up on armoured rubble slopes.rt proc ConfNumerical and hydraul ic model l ing of ports andharbours, BHRA, Birmingham, Apri l 1985. (11soavai lable as Hydraul ics Research Conference paperN o 1 4 ) .
127. Kobayashi N, Roy I & Otta A K. rrNumericalsimulat ion of wave run-up and armour stabi l i ty."OTC Paper 5088, 18th Offshore TechnologyConference, Houston, May 1986.
128. Kobayashi N, Otta A K & Roy I . i lWave ref lect ionand run-up on rough slopes. i l proc ASCE, Vol L13,WI{3, Uay 1987.
1-29. Kobayashi N & Jacobs B K.under wave act ion.rr proc1 9 8 5 .
130. Kobayashi N & Jacobs B K.un i ts on compos i te s lopes .WW5, September 1985.
"R iprap s tab i l i t yASCE, Vol I I I , WW3, May
rrstabi l i ty of ar:rnourrr Proc ASCE Vol I1I ,
5 2
10 BIBLIOGRAPHY
Abdelbaki A & Jensen O J. "Study of provisional repair of the breakwater inPort drArzew E1 Djedid.[ Proc COPEDEC Columbo, lularch 1983.
Ahrens J P. "Large wave tank tests of r ip rap stabi l i ty. t t Tech Memo 51,CERC, Fort Belvoir , May 1975.
Allsop N l{ H. "The Shed breakwater armour unit, model tests in randomwaves." Report EX 1124, I{ydraul ics Research, I^Ial l ingford, Apri l 1983.
Al lsop N w I{ . rrConcrete armour units. t ' Discussion to Paper No 8977, ProcICE. P t I , December 1986.
AlLsop N I.I H & 
Baird w F, Readshaw J s, scott R D & Turke D J. "A procedure for theanalysis and design of concrete armour units ' r . Proc 20th of Coastal Eng.Conf, November 1986.
Barber P c & Lloyd T c. "The rDioder wave dissipat ion block.r proc rcEPart 1, November 1984.
Barony Y s, Mal ick v D, Gusby M & sehery F. r tTr ipol i harbour north westbreakwater, and i ts probLems.r ' proc copEDEC colunbo, l larch 1983.
Batt f ie ld A. "Armour units - unsound test ing?rr c iv i l Engineering,November/December 1986.
Baumgartner R C, Carver R D & Davidson D D. frBreakwater rehabiLi tat ionstudy, Crescent City harbour, Cal i fornia.r t Technical Report No CERC-85-8,WES, Vicksburg, November 1985.
Beeby A !il. 'rCracking and corrosion.tt Concrete in the Oceans TechnicalReporr No 1, crRIA/IrEc/cAcA, 1979.
Behnke D L & Raichlen F. rrBreakwater armour diplacement thresholds: apossible correLat ion with cumuLative rrave energy.tr Proc 19th Coastal EngConf , Houston , 1984.
Bradbury A P & Al-1sop N W H. trDurabi l i ty of rock on coastal- structures.r tProc 20th Coastal Eng Conf, Taipei, November 1986 (avai labLe as Eydraul icResearch Conference paper No l) .
Bradbury A P, Allsop N w II, Latham J-p, Mannion M & poole A B. t'Rock armourfor rubble mound breakwaters, sea wal ls, end revetments: recent progress.t tReport SR 150 Hydraulic Research, WalLingford, llarch 1998.
Bradbury A P, Allsop N !,I H & stephens R v. rrH.ydrauLic performance ofbreakwater crol tn wal ls.r ' Report SR 146 Hydraul ics Research, Wal l ingford,March 1988.
Brown C T. t tArmour unite - random mass or discipl ined array.t t proc CoaetalStructures 79, ASCE, Alexandria, ! {arch Lg7g.
Brown c r . "seabees in service." proc coastal structures 83, AscE,Ar l - ing ton , 1983.
Burcharth H F' t tFul l -scale tr ia ls of dolosse to destruct ion.rr proc 17thCoastal Eng Conf, Sydney, 1980.
Burcharth I l F. "Fu1l-scale dynanic test ing of dolosse to destruct ion.t lCoas taL Eng ineer ing Vo1 4 , E lsev ie r , 1981.
Burcharth 11 F. "A design method for impact - loaded slender armour units'."Paper to ASCE Convent ion, New York, l98f (a1so as Bul let in No 18, Inst i tuteof Civi l Engineering, Aalborg Universi ty, Denmark.
54
Burcharth t l F. t tMater ial , structuraL design of armour units. t t proceedingsSeminar RubbLe Mound Breakwaters, Royal Insitute of Technology, Bulletin NoREIRA-VBI-I20, Stockholn, Apri l 1983,
Burcharth I I F. t 'Fat igue in breakwater concrete armour units.rr proc 19thCoastal- Eng Conf, Houston, 1984.
Burcharth I1 F. r t0n the rel iabi l i ty of rubble mound breakwater designparameters.rr seminar on rubble mound breakwaters, copenhagen, DanishSociety of Hydraul- ic Engineering, December 19g5.
Burcharth I{ F. "The lessons from recent breakwater failures, devel.opmentsin breakwater design.rr Presented to Technical Congress, ! , Ior l -d Federat ion ofEngineering Organisat ions, Vancover, May 1997.
Burcharth H R & Brejnegaard-Nielsen T. t tThe inf luence of waist thickness ofdolosse on the hydraul ic stabi l i ty of dolosse armour." 20th CoastaL Eng.Conf, November 1986.
Burcharth H F & Thompson A C. t 'stabi l i ty of armour units in osci l latoryf low. r r Proc Coasta l S t ruc tures 83 , ASCE, Ar l ing ton , 19g3.
CIAD. rrComputer aided evaluat ion of the rel iabi l i ty of a breakwaterdesign." crAD project group, Zoetermeer, the Netherlands, 19g5.
carver R D & Davidson D D. trDolos armour units used on rubble-moundbreakwater trunks subjected to non breaking waves with no overtopping.flTechnical Report H 77-Lg, I{ES, Vicksburg, November Lg77.
Coastal Engineering Research Centre. ' tShore Protect ion Manual. t r US GovtPr in t ing Of f , 2 ,Vo ls , 4 th Ed i t ion , l {ash ing ton , 19g4.
cusens A R. rrconcrete and other manufactured mater ials. ' r proc confBreakwaters, Design and Construct ion, ICE, London, 1993.
Czerniak M T, Lord C J and Col l ins J I . t tDolosse armouring design for anoffshore airport . t t Proc CoastaL structures 79, ASCE, Alexandria, l , {arch1 9 7 9 .
Deignan J E. I tBreakwater at crescent ci ty, cal i fornia.r Jo wrway andllarbours Div, I{t{3 Vol 85 ASCE, September LgSg.
Danel P, Chapus E & Dhai l l ie R. "Tetrapods and other precast blocks forbreakwaters.rr Proc AscE No W[' I3, vol- 86, september 1960.
Desai H C. "Volume and strength of a dolos.rr Jo Wtway and Harbours Div,WWI Vo1 102 ASCE, L976.
Dodds R. rrFeasibi l " i ty study of mater ials to simulate the behaviour ofconcrete in modeL form.rr conf ident ial Technical Report 6597, RAPRA,Shrewsbury, July 1981.
Dover A R & Bea R G. "Appl icat ion of rel iabi l i ty methods to the design ofcoas ta l s t ruc tu res . r ' Proc Coasta l S t ruc tures r79 , ASCE, A lexandr ia , 7g lg .
55
Edge ! , I L & Magoon O R. r rA rev iew of recent damages to coasta l s t ructures.r rProc CoastaL Structures '79. ASCE, Alexandr ia, 1979.
Fang T. "Dolos breakwater design improvements." Jo Wrway and llarbours Div,l lt l4 Vo1 108, ASCE, November 1982.
Feui l le t J , Bernier J , Coef f6 Y & Chalo in B. "Le d imensionnement des d iguesI t a l us . t t Co l l ec t i on de l a D i rec t i on des E tudes e t Reche rches d rE l -ec t r i c i t 6de F rance 64 , f d i t i on Ey roL les , Pa r i s , 1987 .
Fookes P G & Poole A B. ' rSome pre l iminary considerat ion on the select ionand durabil ity of rock and concrete materials for breakwaters and coastalprotect ion works. t t Quarter ly Jo of Eng Geol_o* L4, 1981.
Fookes P G, Siutm J D and Barr J l '1. "Uarine concrete performance indi f ferent c l iurat ic envi ronments." Proc Conf I ' lar ine Concrete r86, TheConcrete Soeiety, London, September 1986.
Galvin C & Alexander D F. ttArmour unit abrasion and dolos breakage byweve-induced stress concentrations.tt Paper to ASCE eonvention, New York,prepr int 8L-172, ASCE, May 1981
Gaythwai te J I . l . "Structura l design considerat ions in the mar ineenvi ronment . r t Jo Boston Soc Civ i l Eng, ASCB, Vo1 65n October 1978.
Gebert J A & Clausner J . t tPhotogrammetr ic moni tor ing of dolos stabi l i ty ,Manasquan in let , New Jersey.r r Proc 19th Coasta l Engineer ing Conf , Fouston,1984 .
Goda Y. r rRandm Seas and design of mar i t ime st ructures." Univers i ty ofTgkyo Press, Tokyo, 1985.
Groeneveld R L, Mol A and Zwetsloot P A J. rt l,Iest breakwater, Sines: newaspects of armour uni ts . " Proc Coasta l Structures 83r ASCE, Ar l ington,l larch 1983.
Gunbak A R. ttDamage to Tripoli harbour north west breakwater.rt in Designand construction of mounds for breakwaters and coastal protection, Elsevier1985 .
Gunbak A R. "Rubble mound breakwaters.rr Norwegian Institute of TechonoLogyReport 1. , 1979.
HalL K R, Bai rd !J F & Turcke D J. r rs t ructuraL design procedures forconcrete armour uni ts . r r Proc 19th Coasta l Engineer ing Conf , Houston, 1984.
Hannant B J, Zonsveld J J & Ilughes D C. ttPolypropylene fi ln in cement basedmate r i a l s . ' r Compos i t es , IPC Sc ience & Techno logy P ress , Ap r i l 1978 .
Ilawken D I'1 & Allsop N W H. "Use of the video image peripheral in themeasurement of armour movement in breakwater and sea wa11 models - a usermanual." Report No IT 322, Hydraulics Research, ! i la1-lingford, February1 9 8 8 .
5 6
I lof f G C. "Use of f ibre-reinforced concrete in hydraul ic structures andmarine environments. ' r l r isc paper c-7s-4, concrete Laboratory, wESVicksburg, June 1975.
Howel l G. rrA system for the measurement of the structural response of dolosarmour units in the prototype.rr Conf r{easuring Techniques of Hydraul icPhenomena in Offshore, Coastal and Inland Waters, BHRA, London, Apri l 1986.
Hudson R Y. rr l ,aboratory invest igat ion of rubble mound breakwaters.rr procASCE Jo l , I rways & I larbours Div. , Vol 85 l . l l^r3, 1959.
Hudson R Y (ed). "concrete armour units for protect ion against waveat tack . " Misc . Paper H-74-2 , WES, V icksburg , January 1974.
Hydraul ics Research Stat ion. rrBreakwater armour bl-ocks.r t Wal1 chart ,1 9 8 0 .
IAHR/PIANC. ' r l , ist of sea state parameters.f t Supplement to Bul let in No 52,PIANC, Brusse ls , January 1986.
Jensen O J. 'rA monograph on rubble mound breakwaters.tr Danish Hydraul-icInstitute, Ilorsholm, November 1984
Keer J G. t tBehaviour of cracked f ibre composites under l in i ted cycl icloading.rr Internat ionaL Journal of Cement Composites, Construct ion press,Vo l 3 , No 3 , August 1981.
Kluger J W J. t tThe monitor ing of rubble mound breakwater stabi l i ty using aphotographic survey method.rr Proc 18th CoastaL Engineering Conf, CaDe Town,L982.
Kobayashi N, Roy r & otta A K. ttNumerical simulation of \rave run-up andarmour stabi l i ty.rr OTC Paper 5088, 18th Offshore Technology Conference,Houston, I lay 1986.
Kobayashi N, otta A K & Roy r. ttwave reflection and run-up on roughs l -opes . " Proc ASCE, Vo l 113, Wl f3 , May 1987.
Kobayashi N & Jacobs B K. trRiprap stabit i ty under wave act ion." proc ASCE,Vol I I I , f f i3, May 1985.
Kobayashi N & Jacobs B K. t tstabi l i ty of armour units on composite slopes.t tProc ASCE Vol I I I , WW5, September 1985.
Latham J-P, Mannion M, Pool-e A B, Bradbury A p & Allsop N w II. "Ttreinftuence of armour stone shape and roughness on the siability of breakwaterarmour layers. t t ReportWal l ingford, I ' Iay 1988.
L e M e h a u t e B & K o h R Cto the shore." Jo l tyd
Ligter ingen H & l leydraI larbour Author i ty , Ju ly
Queen Mary Col-1-ege/Itydraul-ics Research,
E. "On the breaking of a wave arr iv ing atRes Vo l - 5 , No 1 , L967 .
G. r rRecent progress in breakwater design. t l1 9 8 5 .
an angle
Dock &
57
Ligter ingen I I , Mo1 A & Groeneveld R t . "Cri ter ia and procedures for thestructural design of concrete armour units.rr Proc Conf Breakweters t85 ICE,Londonr 1985.
Li l levang O J & Nickola I{ E.. "Experimental studies of stress within thebreakwater armour piece dolos.rr proc 15th coastal Eng conf, Honolulu,L 9 7 6 .
Li l levang O J, Raichlen F R, Cox J C & Behnke D L. "A deta i l -ed model- s tudyof damage to a large breakwater and model ver i f icat ion of concepts forrepai r and upgraded st rength. t t Proc 19th Coasta l Engineer ing Conf , l louston,1 9 8 4 .
Lin I{-M, Rau C & Su R-L. rrThe structural responses of dolos armour unitsunder the dynamic loading." Proc 20th coasta l Engineer ing conf , Taipei ,November 1986.
L in W-M, Rau C & Su R-L. t 'Dynamic test ing of dolosse to destruct ion. ! ' Procconf Mar ine concrete r86, The concrete society, London, september 1986.
L indo M H & st ive R J I I . r tReconstruct ion of main breakwater in Tr ipol iharbour, L ibya. ' f Dredging & por t Construct ion, February 1985.
Losada M A & Gimenez-Curto L A. "F1ow characteristics on rough, permeabl-es lopes unde r wave ac t i on . r r coas ta l Eng inee r i iE 4 , E l sev ie r , 1981 .
Lunnis R. r rconcrete dolos uni ts protect new North wales coast road. ' lConcrete, lv larch 1985.
Magoon o T & Baird 
Merrifield E U & Zwamborn J A. "The economic value of a new breakwaterarmour unit rDolosr. t t proc 10th coastal Eng conf, Tokyo, 1966.
McDougal W G, Melby J A & Tedesco J W. ttWave forces on concrete armourunits." Proc ASCE ConvenEion, computer aided simulat ion of fLuid-structurein te rac t ion prob lems. ASCE, A t tan t ic C i ty , Apr i l tgB7.
Mo1 A, Ligter ingen I l & Paape A. t tRisk anal-ysis in breakwater design. ' r procconf Breakwaters, Design and construct ion, rcE, London, 1983.
Mo1 A, Ligter ingen l l , Groeneveld R L and pi ta c A R t{ . rwest breakwater,sines: study of armour stabi l i ty.rr proc coastal- structures g3, ASCE,Ar l ing ton , March 1983.
Nagai S. t tstable concrete blocks on rubbl-e mound breakwaters.rr proc ASCEJo Wrways and Harbour Div Vol 88 ! IW3, August 1962.
Nishigori w, Endo R & shimada A. tron stress in tetrapods under l rateract ion. ' r Proc 20th coastal Engineering conf, Taipei, November 1986.
Normand R. t tReview of long-term performance of concrete coastal structuresin the Gulf area." Proc Conf Marine Concrete r85, Ttre Concrete Society,London, September 1986.
Owen M I'I. rrPorts and harbours." In Developments in llydraul-ic Engineering,vol 3 ' Ed P Novak, Elsevier Appl ied science publ- ishers, Barking, 1995.
Owen M I'I & Allsop N W Il. trllydraulic modelling of rubbl-e-mound breakwaters.rlProc conf Breakwat.ers, Design and consLruct ion, rcE, London, 1993.
_owen.lr W & Briggs M G. ' r l imitat ions of modeLl ing. ' r proc Conf Breakwaters'85 , ICE, Londonr 1985.
Paape A & Ligter ingen I l . t t l ' todel- invest igat ions as a part of the design ofrubble-mound breakwaters.rr Seminar on cr i ter ia for design and construct ionof breakwaters, Santander, July 1980.
Paape A & Walther A W. "Akmon armour unit for the cover layers of rubblemound breakwaters.r ' Proc 8th Coastal Engineering Conf, Mexico City, 1963.
Palmer R Q. rrBreakwaters in the Eawai ian is lands.rr Proc ASCE, Jo ! , l rways &Ports Vol 2, No 13, December 1952.
Partenscky tt I.I. "New investigations on vertical and rubble moundbreakwaters.rr Proc 2nd Chinese-German Symposium on Hydrology and Coastal-Engineering, Universi ty of Hanover, June 19g7.
PartensckY H W, Rutte J & Schrnidt R. "On the behaviour of armour unit inthe coverlayer. ' r Proc 20th coastal Engineering conf, Taipei, November1 9 8 6 .
Patur le J-M, v incent G & val lon D. t 'Rubble mound breakwaters, a ner tgenerat ion of b locks, s t rength of the Accropode, f in i te e lement s tudy.r lSogreah Consul t ing Engineers, January 1995.
59
PIANC. "The stabi l i ty of rubbl -e mound breakwaters in deeper water . r r Reportof Working Group of Permanent Technical Cornoittee 2, Supplement to BulletinNo 48 , P IANC Brusse l s , 1985 .
Pope J & Clark D R. t tMoni tor ing of a dolos armour cover ; Cleveland, Ohio."P roc Coas ta l S t ruc tu res r83 , ASCE, A r l i ng ton , 1983 .
Port Sines Invest igat ion Panel . t tFai lure of the breakwater at Por t Sines,Portugal . r r Arner ican Society of Civ i l Engineers, New York, 1982.
Preece B W & Davies J D. "Uodel-s for s t ructura l concrete. r r CR Books,London, L964.
Ridout G. "Wirra l bui lds on la test . sea defence technology. ' r ContractJournal, 16 September L982.
Romit i G, Nol i A, & Franco L. "T:he I ta l ian exper ience in composi tebreakwaters. r r Proc Conf Breakwaters 85, ICE, London, October 1985.
De Rouck J, Wens F, Van Darnme L & Lemmers J. ttA new type of annour unit:the l laro. r r 20th Coasta l Eng Conf , Taipei , November 1986.
De Rouck J, I{ens F, Van Darme L & Lenmers J. "Investigation into the meritsof the flaro breakwater annour unit." 2nd Conf COPEDEC Beij ing, September1 9 8 7 .
Sabnis G M, I lar r is H G, Whi te R N & t [ i rza M S. r rs t ructura] - modelL ing andexper imenta l techniques." Prent ice-Hal l , Englewood Cl i f fs , 1983.
Schol tz D J P, Zwamborn J A & van Niekerk M. "Dolos stabi l i ty , e f fect ofbLock densi ty and waist th ickness.r r Proc 18th Coasta l Engineer ing Conf , CapTown, L982.
Scott R D, Turcke D J & Baird W F. ttA unique instrumentation scheme formeasur ing loads in model dolos uni ts . r r Proc 20th Coasta l Engineer ing conf ,Taipei , November 1986.
Scot t R D, Turcke D J, Bai rd W F & Readshaw J S. ' rA rat ional designprocedure for concrete armour units for breakwaters.tt Dock & Ilarbourauthor i ty , January 1987.
Seel- ig W N. t t ! ' Iave ref lect ion f rom coasta l - s t ructure. r r Proc Conf Coasta lS t ruc tu res r83 , ASCE, A r l i ng ton , 1983 .
Seel ig W N & Ahrens J P. ' tEst imat ion of wave ref lect ion and energydiss ipat ion coef f ic ients for beaches, revetments and breakwaters. r r CERCTechnical Paper 81-1, For t Belvoi r , February 1981.
Shut t ler R M. r rsome aspects of modet l ing s lope protect ion. t ' BNCOLI)Con fe rence , Un i ve rs i t y o f Kee le , Sep tember 1982 .
Shu t t l e r R M. "R ip rap s tab i l i t y , a p rog ress repo r t - d i scuss ion . t ' P rocASCE.
60
Shirnada A, Jujimoto T, Saito S, Sakakiyaua T & Hirakuchion stabi l i ty and wave ref lect ion regarding armour units.r ,Engineering Conf, Taipei, November 1986.
Silva U A G. rr0n the mechanical strength of cubic armourProceed ing Coasta l S t ruc tures r83 , ASCE, Ar l ing ton , 19g3.
H. t r sca le e f f ec t sProc 20th Coasta l
b locks . r r
Singh K. t tstabi t , a new armour unit . r f Proc l l th Coastal Eng Conf, London1 9 6 8 .
Sorensen T & Jensen O J. "Experience gained from breakwater fai lures.r tProc Conf Breakwaters r85 ICE, London, 1985.
stabits Ltd. "stabits: a nelr type of art i f ic ial armour bLock forbreakwaters and sea defence works.rr stabit Ltd, Al_dwych, London.
Stickland I W. 'rcOB units - Report on llydraulics model research.rr l{irnpeyLaboratory, Ref No I t /334, 1969.
St ickland I w & Eaken I C. "Sea wal ls: survey of performance and designprac t ice . " Techn ica l Note 125, CIRIA, London, 1986.
Taylor J. rrFurther invest igat ion in strength scaled model"Ling of concretearmour units.rr BSc Final year thesis, Teesside polytechnic, May 19g9.
Taylor l^loodrow Construction Limited. 'ruarine durability survey of theTongue sands Tower." concrete in the oceans Technical Report No 5,crRrA/uEc/cace, 1980.
Tedesco J w & McDougal W G. 'rNonlinear dynamic analysis of concrete armourunits. ' r computers and structures vol 12, pergamon press, 19g5.
Tedesco J w, McDougal w G, Melby J A & McGil l p B. *Dlmamic response ofdolos armour units." computers & structures vol 25, pergamon Journals,1 9 8 7 .
Terao T, Terauchi K, ushida s, shiaishi N, Kobayashi K & Gahara II.f rPrototype test ing of dolosse to destruct ion." proc l8th coastaLEngineering Conf, Cape Town, LggZ.
Thompson A C. rrTests on breakwater armour units.'f Technical Note StructRoyal Mi l i tary col lege of science, shr ivenham, March Lgg2.
Thompson A c & Burcharth H F. "stability of arrnour units in fLow throughlayer." Proc 19th Coastal Engineering Conf, Houston, 19g4.
Thompson D u & Abernethy c L. "Banksmeadow breakater: model tests onstabi l i ty of Tr ibar armour." Report EX 538, I{ydraul ics Research Stat ion,Wal l ing ford , March 1971.
Thompson D It & shuttler R M. ttRiprap design for wind wave attack: alaboratory study in random waves." Report Ex 707, Hydraul ics ResearchStat ion, Wal- l ingford, September L975.
6 ,
6 1
Thompson D I ' { & Shutt ler R M. "Design of r iprap slope protect ion againstwind waves.t t Report No 51, CIRIA, London, 1976.
Timco G t{. rrThe deveLopment, properties and production of strength-reducedmodel armour units.tt Laboratory Technical- Report No LTR-Hy-92, NationalResearch Counci l Canada, Ottawa, November 19g1.
Timco G W. rtAn analysis of the breakage of concrete armour units onrubbLe-mound breakwaters.rr Technical" Report No TR-Tly-001, National ResearchCounci l Canada, Ottawa, 1983.
Timco G I{. rron the structurel integrity of dolos units under dynamicloading condit ions.tr coastal Engineering voLume 7, El_eevier sciencePub l ishers , Amsterdam, 1983.
Timco G W. "On the stabi l i ty cr i ter ion for f racture in dolos armouredbreakwaters.rr Coastal Engineering Volume 8, El-sevier Science publ ishers,Amsterdam, 1984.
Timco G w & l{ansard E p D. "rmprovements in rnodeLling rubble-moundbreakwaters.rr Proc 18th coastal Engineering conf, cape Town, 19g2.
Timco G w & Mansard E p D. "on the interpretation of rubblernoundbreakwater tests.rr Proc coastat structures rg3, AscE, Ar1ington, 19g3.
Timco G l,l, Mansard E p D & ploeg J. 'stabiLity of breakwaters withvariat ion in core permeabi l i ty. t t proc 19th coastal Engineering conf,l louston, 1984.
Torum Ar ltathiesen B & Escutia R. I'Scale and model effects in breakwatermodel tests.rr Proc poAC t79, Norwegian rnst i tute of Technotogy, rg7g.
Uzumeri S M & Basset R. rrstructural behaviour of 10 ton dolos armourunits. t ' Proc 20th coastal Engineering conf, Taipei, November 19g6.
Uzumeri S M, Basset R & I{ i l l - e T. rrstructural behaviout of 10 ton dolosunits." PbLn. 85-06, Dept of c iv i l - Eng, universi ty of Toronto, August1 9 8 5 .
van der Meer J w. "stability formula for breakwaters armoured withaccropode. ' r Report 11546, Delf t l lydraul- ics taboratory, September 1987.
Van der Meer J W. rrstability of rubble mound revetments and breakwatersunder random wave attack.rr proc conf Breakwaters tg5, rcE, London, 19g5.
Van der Meer J W & Pilarczyk K W. ttstability of rubble mound sl-opes underrandom l tater attack.rr Proc 19th Coastal Engineering Conf, Houston, 1984.
Walker P R. "Modet armour units: mater iats strength tests. t t Report No 128,Def t o f C iv i l Eng, Oxford po ly techn ic , Apr i l , 19g5.
I ' Iebby M G. rr l lydraul- ic model study of repairs to exist ing sea protect ion ofWel l ington airport extension." Paper No 4, Proc 10th conf of New Zeal-andHarbour Engineers, Whangarei , New Zealand, Lgg4.
6 2
I {erner G (Ed). "Rubble mound breakwaters.* proceedings seminar, RoyalInsi tute of Technology, BuLlet in No TRITA-VBI-I20, Stockholm, Apri l 1983.
weyuouth o F & Magoon o r . ' rstabi l i ty of quadripod cover layers." proc11th Coasta l Eng ineer ing Conf , London, 1968.
whilloek A F & Thompson D M. "High rsland water scheme - Hong Kong - astudy on the use of Dolos armour units for wave protection on the seawardface of the Eastern Dam.rr Report EX 532, Hydraul ics Research, I , la l l ingford,1 9 7 0 .
white R N (Ed). t ' I . {odels for concrete structures.tr sp-24, American ConcreteIns t i tu te , Det ro i t , repr in ted 1980.
I ' I iegal R L. t 'Forces induced by breakers on pi les." Proc 18th Coastal EngConf. Cape Town, 1982.
Wil-kins N J Dt & Lawrence P F. trFundamental mechanisms of corrosion of steeLreinforcement in concrete immersed in sea-water.rr Concrete in the OceansTechnical Reporr No 6, CIRIA/UEF/cICA, 1990.
wi lk inson A R & AlLsop N w I I . t tEol low block breakwater armour units. t t ProcCoasta l S t ruc tures r83 , ASCE, Ar l ing ton , 1983.
I ^ I i L l A I , W i l l i s T A F & S m i t h D D S . " D e s i g n a n d c o n s t r u c t i o n s u p e r v i s i o nof sea wal1 and breakwater at Torness poner stat ion.t t proc rcE, pt I ,Oc tober 1985.
ZonsveLd J J. "Propert ies and test ing of concrete containing f ibres otherthan steel.rr RILEM Synposium, London, 1975.
Zwamborn J A. "Analysis of causes of damage to Sines breakwater.rr ProcCoastal Structures 79, Alexandria, ASCE, t farch L979.
Zwamborn J A. rrDiscussion to Monitor ing of doLoa armour coverl Cleveland.t lProc ASCE.
Zwamborn J A, Bosnan D E & Moes J. rrDoLosse; past, present, future?rr proc17th Coastal Engineering Conf, Sydney, 1980.
Zwamborn J A & SchoLtz J D P. "Dolos annour design considerat ions.rr Proc20th Coastal Engineering Conf, Taipei, November 1985.
Zwamborn J A & van Niekerk M. ttAdditional model- tests, dolos packingdensity and effect of relat ive block density. ' ! CSIR Research Report 554,Stel- lenbosch, July 1982
63
F IGURES.
Shopcd 3lonell_JL L_;l R'hhrr | | .Shop€d 3tone
C Rubble mound breokrvoler
Fig 1.1 Breakwater types, af ter 0wen (Ref . 1)
lncident wave action
Overtopping Transmission
armourmovement
rear slopearmourdamage
tloodtng wave disturbance toe scour
Fig 1.2. Ef f ects of inc ident wave energy
I Rock 2 Ploin cube
Antifer cube 4 Tetropod
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Stobit
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0otosseS l o p e s 1 : 1 . 5 . 1 : 2 . 0 . 1 : 3 . 0
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Fig 3.2 Ref lect ion pef formance of cob armoured stopes
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Fig3.3 Ref lect ion perfomanre of Tetrapod 0r Stabi t armoured s lopes
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APPENDICES.
APPENDIX I
Use of video inageermour movement in
Introduct ion
Eguipment and .method
The priuary requirementsprocessing system may be
proceeeing ia the meeauremente ofhydraulic model studiee
for any video imagesurwnarised: -
During this project an attempt was made to develop anautomated method of comparing before and after imagesof the armoured slope to guantify the occurrence andmagnitude of armour movement. It was anticipated thatthis method would provide a sirnple and rapidassessment. of armour movement, as an alternative tothe photographic 'over lay method. In both methodsimages taken perpendicular to the drained sLope arecompared for the differences arising fromdispl -acements of uni ts in the area analysed. I t washoped that the video image processing technique coul-dthen be developed further to process images takenduring the test, rather than only those taken beforeand af ter the test . A method of t r igger ing thestorage of an image had been developed by theCanadians for use with singl-e frame cine and 35mnst iL1 cameras. In the f i rs t instance ef for ts wereconcentreted on the comparison of before and afterimages.
a) video camera;b) digital image framestore operating at video
r a t e ;c) control computer, with appropriate data storage/
transfer devices such as f loppy and/or hard diskdr ives ;
d) appropriate rnonitor(s) for displaying videoimages, computer control and output signals;
e) hardcopy output device, such as a pr inter.
For sone uses it will- also be irnportant to record thevideo iurages during testing on a high q.uaLity videorecorder. The fulL system conf igurat ion isiL lus t ra ted in F igure A1.1 , and a de ta i ted l i s t ing o fthe equipment used in these experiments is given inthe f inal sect ion of this appendix.
The primary component of the sysEem is the videointerface peripheral, known as the VIp. Thepart icular device used in these experiments wascapable of stor ing and processing black and whiteimages in ei ther of two resolut ion modes. In high
resolution the image was handl_ed as 5l2x5l2 pixets,each pixel having an approximate aspect rat io of 3:4.In Low resolution four images, each of 256x256 pixels,could be etored. In ei ther mode each pixel was storedat one of 64 levels of grey, varying frorn binary blackto binary white, Final ly a single store holds abinary version of the image. I t is the data in thisstore that is used to generate the measured resuLts.
In essence the method used to ident i fy and quant i fythe differences between two images is very sirnpl-e.Consider image 1 taken before a test and image 2 takenafter. These may be stored within the VIp or onsuitable data storage devices controlLed by thecomputer. Each image vilL consist of an array ofpixels, each of a given leve1 of grey. Any areas ofmovement or change between the two images wilL beidentified by subtracting one image from the other. Adescript ion of the use of the VIp to generate adifferenced image is given by Hawken & Allsop inReference 1. At this stage i t should be noted that,only i f the l ight ing of the rest sect ion for bothimages was identicaL at alL points to tess than I in64 levels of greyr.wi lL the di f ferenced image exact lyeorrespond to areas of armour unit movement alone.
For the VIP used in these experiments, the videodif ference between pixels that are ident ical isdisplayed as the 32nd level of grey. il inor changes,corresponding generally to il lumination differences,wi l l be displayed as levels of grey in the appropriaterange either side of the 32nd Level_. Where a changeoccura between image I and image 2, such as thedisplacement of an armour unit, the differenced imagedisplays a lesser or greater level of grey.Intereet ingly this has the effect of doubl ing theresolut ion of the system, as both areas of posi t iveand negat ive di f ference are ident i f ied. At this stagethe differenced image is stiLL stored as a ttgrey,timage. It wou1d, however, require very considerablecomputer power to analyse the image at each of 641eveLs. The differenced image is therefore processedto produce a simple binary image, by using athresholding routine developed for the VIp. lhisconverts aL1 pixels, having a grey leve1 between twoseLected l in i ts, to binary white. The ! . imits may becontrol led manual lyr or rnight be set automaticalLywith suitable software. In these experiments thethreshol.d f.inits vere set oanually either side of the32nd 1evel of grey, with an appropriate range toovercome minor areas of di f ference ascr ibable tochanges in lighting 1eve1. This l_eft the importantareas of di f ference, ei ther posi t ive or negat ive,unchanged.
At this stage the data needed for further analysis areleft in the grey store. The areas of l i t t le or , ,odifference have been written to the binary store.This is the opposite of that required for ef f ic ientfurther analysis! The binary image is thereforeinverted, leaving al l areas of ei ther posi t ive ornegat ive di f ference converted to binary white. Thisbinary image can then be scanned to locate each of theareas of di f ference. A number of analysis rout ineswere supplied with the particular hardware used forthe experiment, and these aLlowed the locat ion, area,and boundary of each block of binary white pixels tobe ident i f ied .
In considering the use of this method, i t is importantto dist inguish between l in i tat ions of the part icularhardware and software available for these experiments,and of the method in general. The VIp used for theseexperiments is made by Sight Systems Ltd andcontrol led by an 8 bi t BBC micro-computer. Datastorage and transfer is handl_ed by twin doubLe-sided80 track f loppy disk dr ives. This system wasprincipally set up to handle images of 256x256 pixels,and aLlowed one such image to be stored on a singlefl-oppy disk. The VIP was set up with four 2562 greystores, aLlowing four low resolut ion images to bestored or processed. The images in any two of thefour quadrents could be differenced to produce a thirdimage. By swapping inages between quadrants 3 imagesof 2562 coul-d be stored and processed rapidly withoutusing the f loppy disc dr ives, see Refs I end 2.
This system is also capable of handl ing a eingle imageof. 5L22 pixels by using all four 2562 quadrants toform a single image. It was not however possibte tostore a 5122 image on a f loppy disc, with thepart icular system used. That would have requiredthe provision of an addit ional hard disc dr ive,together with addit ionaL control software. Nor was i tpossible to di f ference or threshold images at thisresol-ut ion 1evel without considerable nodif icat ion tohardware and software.
Discussion on the use of the VIP
A number of trials were conducted to identify theusefulness of the system as a routine method ofmeasurement for hydraul_ic model studies; to expl_orethe performance linits; and to identify furtherdevelopment needed. In the f i rst instance a ser ies ofsimple experiments were conducted using tr ia l s lopeswith ideal ised armour units, usual- ly simpLe cubes; andwith 35rm monochrome photographs taken on previoussi te specif ic studies. Two maior probl-ems were
ident i f ied, together with a number of minorperformance probleros with the device, and theexperiments nere discont inued before fuLL f lume testswere mounted.
The f i rst problem encountered was that of consistencyin l ight ing levels between photographs. In theory i twas possible to set up l ight ing so that each testsect ion could be consistent ly l_i t , and the l ight ingconditions would be identical for each image. Inpract ice this proved di f f icul- t to achieve, but notinsuperabl-e. I t was clear that f - ight ing for eachstudy would have to be set up with aome care, usingthe VIP system to check consistency. An aspect ofl ight ing that was di f f icul t to overcome was that ofl ight ref lected from armour units, part icular ly thosewith f lat s ides. Such ref leet ions aroae when theslope vas wet, as it would be during or irumediatelyafter a test, and could not be overcome by changes tothe Lighting. The problem was reduced by allowing theslope to drain for around 10-15 minutes. Care had tobe taken to keep al l uni ts vis ible danp, but not wet,to avoid changes in hue. It will be noted that thist ime delay of i tsel f wiLl tend to reduce theattract ion of this method of measurement.
The second main problem concerned the resol_ution ofthe image, and the number of armour units that coul_dbe monitored by the system. It will be seen from thediscussions in Chapters 4 and 5 of the main reportthat even very small degreee of movement can be ofsignificance in the design of structures armoured rsithunreinforced concrete armour units. I t is also clearthat armour movement on a sl-ope varies spatially, aswell as with variations in wave conditions. Anymethod of measurement mlst cover a representativesect ion of the test sect ion. For these tr ia ls i t wasfeLt that the minimum acceptable area would beequivalent to 20 units square, or 2ODx20D, where D isa typical arnour unit dimension. Noting Orsen & ALl"sopand Partenskyrs damage categories, i t was fel t thatthe system must be able to distinguish movements downto about 2o, or 0.04D. At a resolut ion of 20D = 5!2pixels, this is equivalent to 1 pixel only. I t wasnoted earl ier that the video di f ferencing proceduredescribed doubtes the area of di f ference by count ingboth positive and negative differences, a movement of0.04D or 2o wi l - l y ield a di f ference measurement atbeet of 2 pixels. Clearly a resol-ut ion of onl . .y 2562pixels would be unacceptable.
Appendix IReferences 1. Hawken D M & AlLsop N W H. rrUse of the
video image peripheral in the measurement ofarmour movement in breakwater and sea waLl-model-s.rr Report lT 322, Hydraul- ics Research,Wal l ingford, February 1988.
2. Sight Systerns Ltd. rrVideo interface peripheral :instruct ion manual.r ' Sight Systems Ltd, Newbury,undated.
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APPENDIX 2
Effect of nul t i -direct ionalof Dolos ermour
Introduct ion
wave attack on stabi l i ty
Rubble mound breakwaters have, unt i l fa i r ly recent ly ,been bu i l t gene ra l l y i n sha l l ow wa te r . I t has beenassumed tha t t he des ign sea s ta te i s l ong -c res ted w i thno d i rect ional spread. Where waves lengths aregreater than around 5-10 t imes the water depth,re f rac t i on e f f ec t s a re l i ke l y t o reduce d i rec t i ona lspread. However for a breakwater in deep water , thedi rect ional spread of wave energy might be animportant factor in the stabi l i ty of the armour. Abr ief invest igat ion was therefore conducted in to thestabi l i ty of Dolos armour ing under shor t -crested(d i rec t i ona l ) seas , and l ong -c res ted seas . The s tudywas intended to ident i fy and quant i fy any comparat iveef fect in the onset and rate of armour d isp lacernent .
Mode l t es t s
A series of hydraul ic model tests were conducted inHydrau l i cs Researchrs mul t i -d i rec t iona l random seafaci l i ty. Ten paddles were set in an arc centred onthe test s lope. The wave generator was prograsmed toproduce ei ther long crested waves, or short crestedwaves with a cos20 direct ional spreading funct ion.The 3.5m long test sect ion was constructed withgrou ted s tone a t a 1 :1 .5 s lope on an impermeab le base.Over the central 0.85m length the underlayer wasrecessed to take the Do losse. Mode l un i ts o f 55 .5grams, height D = 54mrn; and density 2.32 graur/cm3,were laid in two layer at a placing density of 793un i ts /m3, us ing a to ta l o f 728 un i ts . The up s lopelength of the dolos armoured sect ion vas L.08m, andthe water depth during test ing, h, was 1.5rn. TheDolosse were re - la id fo r each tes t to a care fu l l ycontrol led laying pattern to ensure some consistencyin lay ing .
Each test was run at the specif ied sea state, given byH" and Trr for 5000 waves, or unt i l 150 units (20.62)had been extracted. Damage lras assessed as the numbero f un i ts d isp laced f rom the i r o r ig ina l pos i t ions .Each test was also recorded on video tape whichal lowed the damage assessment to be checked later i fneeded. The tes t cond i t ions used may be summar ised: -
Longu" (m)
0 .0880 . 1030 .1080 . 1130 . 1180 . t29o .147
c res tedr ,o(s)
r .36t f
t l
t l
t l
l l
n
ShortH" (m)
0 .0880 . 1030 . 1080 . 1130 . 118o . t 29
cres tedT,o( s)
1 . 3 5l l
l l
t l
t l
t f
In each instance a Pierson-Moskowi tz speetrum wasu s e d .
Tes t resu l t s
The observat ions made during the f i rst two tesc ser ieshave been plotted in Figures A2.1-4. Some signif icantscatter in the test results is apparent. GeneraLlythe greater proportion of the damage occurs in thef i rst 1000-2000 waves. For aL1 but the Largest waveconditions where damage reaches a failure conditionbefore the end of the test, the rate of damage slonsduring the test. This trend is relat ively welLindicated by scaling the damage, T * Nd/Na, Uy 4.The factor { has been used previousl} bivan der Meer (Ref 68), and Bradbury et a1 (Ref 6),for rock armour.
The scatter of the test results is welL i l lustrated inFigure A2.2, where damage for some of the higher waveconditions are occasionally less than for lower waveheights. Tvo ser ies of repeat tests rrere run, al lw i th long-c res ted naves a t l l s = 0 .118m, T , = 1 .36s .One set of tests were always started at tFe same pointin the seguence, the second used randomty sel-ectedstart ing points. The results of these repeat testsare plotted in Figures L2.3-4.
For each test (at a singl"e wave height) in each set oftests damage, T = N.{/No, was calcul-ated at f requentintervals through tfie Eest up to N.-, = 5000 naves, orT > 2OZ. Each value of T was then"scpled bV f f i . Themean, and scandard deviat ion, of T/N-z were cal iulatedfor each test, and are plotted for tiie long and shortcrested lraves in Figures A2.5-5. A simple empir icalreLat ionship was f i t ted to each data set using aregress ion ana lys is .
For long crested \raves:
h = e.3s x loo nfr lo.13oa-n
w i t h n 2 = 0 . 9 5 .
For shor t c res ted waves :
H ^ r A A - . 0 . 1 2 0( 5 . 6 1 x 1 0 b y ' N w ) v . ! 4 va"n
w i t h n 2 = 0 . 8 3
This sicrple approach is f lawed in two ways:
(a) the analysis had been conducted using meanv a l u e s ;
(b) addit ional data was avai lable but had not beenu s e d .
The ana lys is was there fore re - run fo r ,a l1 re levantdata, using individual values of T/N.?. As one mighthave expected this reduced the correlat ioncoeff ic ients markedly. The increase in the number ofdata values did not however change the empir icalc o e f f i c i e n t s s i g n i f i c a n t l y . ( F i g u r e s A 2 . 7 - B ) .
For long crested waves:
h = e.74 x 106 ,f tro.trt- "n
w i t h n 2 = 0 . 6 1
For shor t crested t raves:
H^ 16 #-0 . rzoT * - = ( 6 . 4 3 x l CA D n " ^ r - v r r w /
w i t h n 2 = 0 . 6 4
@oeo
et
o
ti'l
o
P1 'p:reldstp sltun Jo .oll
c,o
o
anto
o oool.rl
ooo-f
ooo,7t
=-,a-C'
,!t
ct
o < to - .o(\l
ooo
CA
o
3\-+
o
G>€D
Fig A2-1 0amage history for 1.36s long rrested vayes
3== 33 ooou1
ooo-t
orcorYt -
-.
vr'at
att
CI
o c to -o(\l
ooo
oo
P 1 'prreldslp sltun Jo 'oN
€)l/t
Fig A2.2 0amage history for 1.36s short crested wayes
ooorn
oootY!
=-U'C'
ag'
C'
o c to -o(!
ooo
t -\
€)Irt
P1 'pa:e1ds!p sl lun fo'ol{
t-o
,ac r +
ru at} ia u el l Et l t
r U ;= & ,
Fig A2.3 Repeat tests for 1.36s uaves, long mested
ooortl
oeo-$
oootYl
=z.utc,a0'
c!
o c to =oC!
ooo
Itt
$
Ir l
I
oo
P 1 'pueldslp sllun Jo .oN
III\
T'c, 'E
4- C,r a +a, aaa- c,
t,
L cttC ' G
5 C ll/t -l
Repeat tesfs for 1.36s uavesFig Az.t+
lort
ccf
r t f{jE.g(u
(noi g
'T'
=tnvt{U
N c! o
N .;;
c(u
.Ea
rOoi
a$ | . )No9 0 O ( ) Oqqqo6c ic tc idc ;
z7r^ N/ J" 'aEeueg
o o&
o.J oJ-tf, -o
.tJ E
a- a-(o ft,-E -tf,c crc, nt
-a- -t-(u ta 14=
rto
c c cto ft ro(U (U CJ
E E =
I s l 6 f . . t oqaoooctqqqq
oooo
Fig A2,5 0amage against Hs/ABn, long crested uaves, mean values
rort
ccf
r.I tn-1-
.+---E.g(U
oloig
'D
=IAv,q.l
N c. oN . ;
c(U
.ga
r O l @ f . . ( o l O + r C N r Ooooooooooodqqqqqgqqqoooooooo()
qr^ N/ '1 ' 'a6eueg
c c ..9 .o
!
qJ oJ-t) 'o
-tf, Et- L-r0 l!
'E -lf
L U
m r o+ +
(U t L/l
= t _
t0
c , c cfo ro ro(U (U (U
= = =
Fig A2.6 0amage against Hs/40n, short rrested wayes, mean values
r{,rt
cF
r t f€-E
.3(U
ql
oigao=UIar7( u l
t \ c! O
ot -;cqJ
.5a
rOoi
t . g l 6 b t o t f ) + l 0 c { Oqaoao6660oci99qqqqqqq
o o o o o o . c i c t o
ur^ N/,L 'abeu.teo
|__-_r--.T--T*+
ii
!l
lfl-'r g grno o
+ +ro r0
aJ c,-t -13
-L L
tt rct-E 'E
d cao t9
+ &(u vt vl
=F
ro
c , c cfo to toqJ <U (U
E E =
o+o
Fig A2.7 0amage against Hs/A0n, long cfested uaves, atl vatues
lort
a
,vi t/l
&-
.3(U
Ol
oigr0=IAvl(u
f \ C
c.i .9aC.(U
-=G
toCri
=qr@r . . (o ro . f r c lNroqaoooo6c jood9qssgqqqq( f , ( f ooooooo
z7r^N/J 'aEeuJe0
.9 .e+ +ro ro
o-i aJ€ ] f ,
Tl 'r:fc- (-ro fD-E' 'E
d crD TE
+ +(U V7 tJl=to
c c crc' rD ro(u (u (u
= E =
o+o
Fig A2.8 Damage against Hs/40n. short rrested wayes, al l values
APPENDIX 3
Example test results froo si te specif ic studies
The results of ermour movement measurements in si tespecif ic model tests have been summarised in thefo l low ing tab le . In each ins tance the de f in i t ion o fdamage used has been eguivalent to Owen & Al lsoptsca tegory 31 or Par tensckyrs ca tegory 6 , fu l1ex t rac t ion .
The armour unit is ident i f ied by the type, i ts uni tmass, and the prototype concrete density. Thecross-sec t ion s lope ang le , the s lope length , number o fun i ts , and no t iona l permeab i l i t y fac to t t p t a f te r vander Meer, are l isted. Incident wave condit ions aregiven by the signi f icant wave heightr Hor rnean waveper iod , Tr r and s to rm or tes t par t duraE ion , T* .
I t nust be noted that these tables represent acons iderab le s i rnp l i f i ca t ion o f the or ig ina l tes t da ta .The dauage results wi l l have been inf luenced by manyaspects not given here. The reader is advised toconsu l t the or ig ina l tes t repor t , i f ava i lab le , and/orto look at other test results. The data containedhere should only be used for prel iminary designPurposes .
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