Overtopping performance of different armour units for rubble mound breakwaters

14 Pages·2009·1.42 MB·English

CoastalEngineering56(2009)166–179
ContentslistsavailableatScienceDirect
Coastal Engineering
journal homepage: www.elsevier.com/locate/coastaleng
Overtopping performance of different armour units for rubble mound breakwaters
T. Brucea,⁎, J.W. van der Meerb, L. Francoc, J.M. Pearsond
aSchoolofEngineeringandElectronics,UniversityofEdinburgh,King'sBuildings,Edinburgh,EH93JL,UnitedKingdom
bVanderMeerConsultingB.V.,P.O.Box423,8440AK,Heerenveen,TheNetherlands
cUniver2sityofRome3,Dept.CivilEng.,ViaV.Volterra62,00146Roma,Italy
dUniversityofWarwick,SchoolofEngineering,Coventry,CV47AL,UnitedKingdom
A R T I C L E I N F O A B S T R A C T
Availableonline12June2008 Thispaperdescribesamajorprogrammeofsmall-scalephysicalmodelteststoestablishbettertheinfluence
ofarmourtypeandconfigurationonovertopping.Specifically,179testsdeterminedtherelativedifferencein
Keywords: overtoppingbehaviourfor13types/configurationsofarmour.Roughnessfactorsγ weredeterminedforrock
f
Rubblemoundbreakwaters (twolayers),cubes(singlelayerandtwolayers),Tetrapod,Antifer,Haro,Accropode,Core-Loc™andXbloc™.
Overtopping TheseroughnessinfluencefactorshavebeenincludedintheCLASHdatabaseandareforuseintheneural
Armourblocks
Wavereflection networkpredictionofovertopping.Individualwave-by-waveovertoppingvolumeswereanalysedandfound
tocomparewellwithcurrentpredictionmethods.Measuredreflectioncoefficientsforthedifferentunitsare
Armourroughness
Overtoppingvolumes alsopresentedandcomparedwithrecentformulae.
Meanovertoppingdischarge ©2008ElsevierB.V.Allrightsreserved.
1.Introduction structureshasmostlybeenbasedonallowableovertopping,oreven
onallowabletransmission(low-crestedstructures).Stillanestimation
Theovertoppingdatabaseof theCLASHproject(Steendametal., orpredictionofwaverun-upisvaluableasitgivesapredictionofthe
2004)containsmorethan10,000testresultsonwaveovertoppingat number or percentage of waves which will reach the crest of the
coastalstructuresworldwideandisthereforeconsiderablylargerthan structure and eventually give wave overtopping. This number is
initiallyforeseen.Thedatabasewasusedasinputforaneuralnetwork neededforagoodpredictionofindividualovertoppingvolumesper
which resulted in a generic prediction method for overtopping at wave.
coastalstructures(Pozuetaetal.,2004;VanderMeeretal.,2005b). Fig.1gives2%waverun-upheightsforvariousrocksslopeswith
Interimanalysisoftheovertoppingdatabaseindicatedthattherewere cotα=1.5,2,3and4andforanimpermeableandpermeablecoreof
some“whitespots”wherefurthermodeltestswouldbeadvantageous. the rubble mound. These run-up measurements were performed
Test programmes to fill these “white spots” were devised. This paper duringthestabilitytestsonrockslopesofVanderMeer(1988a).First
describes a major programme of 2D physical model tests to establish ofallthegraphgivesvaluesforalargerangeofthebreakerparameter
bettertheinfluenceofarmourroughnessonovertopping.Specifically,the ξm−1,0duetothefactthatvariousslopeanglesweretested,butalso
objective was to determine the relative difference in overtopping withlongwaveperiods(givinglargeξm−1,0values).Mostbreakwaters
behaviourforvarioustypesofarmourunitsleadingtoroughnessfactors have steep slopes of 1:1.5 or 1:2 and thus the range of breaker
γf for the database and for use in the neural network prediction of parametersisoftenlimitedtoξm−1,0=2–4.Thegraphgivesrockslope
overtopping. In addition to measurements of mean overtopping informationoutsidethisrange,whichmay beusefulalsoforslopes
discharge,wave-by-waveovertoppingvolumesandreflectioncharacter- withconcretearmourunits.
isticswerealsomeasuredandcomparedwithpredictiontools. The prediction for the 2% wave run-up value for rock slopes for
ξm−1,0≤1.8canbedescribedby(EurOtop,2007):
2.Technicalbackground
2.1.Run-upandovertoppingatslopingstructures RHu2k¼1:65gbgfgbnm(cid:2)1;0 nm(cid:2)1;0V1:8 ð1Þ
m0
Waverun-uphasalwaysbeenlessimportantforrockslopesand
rubble mound structures and the crest height of these type of withamaximumof
!
⁎ EC-omrraeislpaodnddreinssg:[email protected](T.Bruce). RHum2k0 ¼1:00gbgf;surginggb 4:0(cid:2)pffin1ffiffimffi:ffi5ffi(cid:2)ffiffi1ffiffi;ffi0ffiffi nm(cid:2)1;0V1:8 ð2Þ
0378-3839/$–seefrontmatter©2008ElsevierB.V.Allrightsreserved.
doi:10.1016/j.coastaleng.2008.03.015
T.Bruceetal./CoastalEngineering56(2009)166–179 167
Notation
α angleofforeshoreslope(measuredfromhorizontal)
γβ influencefactorforeffectofobliquewaveattack
γ influencefactorforeffectofaberm
b
γ influencefactorforeffectofsloperoughness
f
γ influencefactorforeffectofashallowforeshore
h
Δ relativebuoyantdensityofarmourunit(¼qqunit (cid:2)1)
/ armourunitpackingdensity(no.ofunitspewratserquareD )
n
ρ ;ρ densityofwater;densityofarmourunit[kg/m3]
water unit
ξaξmp−1,0 Wbbrreeeaaibkkueelrrl((soocrralsseuuprrffa--rssaiimmmiiellaaterrriitt,yya))nppdaa(rrsaacmmaleeintteegrr)bbfiaatsstieenddguucppoooennffiTTcmpie(−n¼1t,0ptfaoffis(nffioffia¼prffiffi)npeffistffiamwffinffi(cid:2)ffiaffi1ffi;ffif0ffio)rmulaforK
r
b Weibullshapeparameter,and(shape)fittingcoefficientfornewformulaforK
r
Bt breadthoftoeofstructure[m](cid:7) (cid:5) (cid:6) (cid:8)
D armourunitnominaldiameter ¼ unitmass 1=3 [m]
n qunit
D ;D ;D median;85%and15%non-exceedancevaluesofD [m]
n50 n85 n15 n
g accelerationduetogravity[m/s2]
G crestwidthofthestructure[m]
c
h waterdepthattoeofstructure[m]
s
H designwaveheight(i.e.maximumH fordesignofarmour)[m]
0 m0 pffiffiffiffiffiffiffi
H significantwaveheightobtainedfromspectralanalysis(¼4 m )[m]
m0 0
H significantwaveheightofincidentwavesatthestructure[m]
si
K reflectioncoefficient(fromstructure)
r
k layerthicknesscoefficient
t
N totalnumberofarmourunitsdeployed
N numberofarmourunitsperm2perlayer
a
P probabilitythataparticularovertoppingeventvolumeexceedsV
V
q (dimensional)meanovertoppingdischarge[m3/s/m]
R crestfreeboard[m]
c
R waverun-up,2%exceedancelevel[m]
u2%
sm−1,0 wavesteepnessbaseduponperiodTm−1,0
s wavesteepnessbaseduponoffshorepeakperiod
op
Tm−1,0 meanwaveperiodobtainedfromspectralanalysis(=m−1/m0)[s]
T spectralpeakwaveperiod[s]
p
V overtoppingvolumeassociatedwithsingleovertoppingevent(permetrerun)[m3/m]
V meanindividualwaveovertoppingvolume[m3/m](=totalvolumeovertopping/numberofovertoppingevents)
bar
W medianarmourunitmass[kg]
50
W maximumallowablemassforrockformodelcore[kg]
core,max
W ;W maximum;minimumallowablemassforrockformodelfilterlayer[kg]
u,max u,min
whereγb,γf,andγβareinfluencefactorsaccountingforbermwidth, Although there exist many formulae for the prediction of mean
armourroughnessandobliquityofwaveattackrespectively. overtoppingdischargeatslopingstructures,itisnotthepurposeof
Forξm−1,0N1.8theroughnessfactorincreaseslinearlyupto1for thisworktoevaluatetheseformulae.Rather,focusisontheroughness
ξm−1,0=10 and remains 1 for larger ξm−1,0. Over this range, the
roughnessinfluencecanthereforebedescribedby
(cid:3) (cid:4)(cid:3) (cid:4)
gf;surging¼gf þ nm(cid:2)1;0(cid:2)81::28 1(cid:2)gf 1:8Vnm(cid:2)1;0V10 ð3Þ
gf;surging¼1:0 nm(cid:2)1;0N10 ð4Þ
Thephysicalexplanationforthisisthatiftheslopebecomesvery
steep (large ξm−1,0 value) and the core is impermeable, the surging
wavesslowlyrunupanddowntheslopeandallthewaterstaysinthe
armourlayer,leadingtofairlyhighrun-up.Thesurgingwaveactually
doesnot“feel”theroughnessanymoreandbehavesasawaveona
verysteepsmoothslope.
Forsteeperslopes(cotα≤1.5)withapermeablecore,however,a
maximumisreachedforRu2%/Hm0=1.97(atξm−1,0g4.6).
Eqs. (1)–(3) also give a good prediction for run-up on slopes
armouredwithconcretearmourunits,iftherightroughnessfactoris
Fig.1.Relativerun-uponstraightrockslopeswithpermeableandimpermeablecore,
applied. comparedtosmoothimpermeableslopes.
168 T.Bruceetal./CoastalEngineering56(2009)166–179
Table1
Unitpropertiesandmodel/waveparameters
W50 Dn50 D85/D15 ρ Na N Δ H0 hs Rc Bt Wu,max Wu,min Wcore,max
[kg] [m] [–] [kg/m3] [–] [–] [–] [m] [m] [m] [m] [kg] [kg] [kg]
Rock—large 0.1910 0.042 1.54 2650 398 159 1.65 0.103 0.258 0.103 0.125 0.038 0.013 0.0038
Rock—small 0.0720 0.030 1.38 2650 763 305 1.65 0.074 0.186 0.074 0.090 0.014 0.005 0.0014
Cube 0.0620 0.030 2361 660 264 1.36 0.089 0.222 0.089 0.089 0.012 0.004 0.0012
Antifer 0.0850 0.033 2361 535 214 1.36 0.099 0.247 0.099 0.099 0.017 0.006 0.0017
Tetrapod 0.1000 0.035 2350 427 171 1.35 0.104 0.259 0.104 0.105 0.020 0.007 0.0020
Accropode 0.0742 0.032 2361 622 249 1.36 0.107 0.268 0.107 0.095 0.015 0.005 0.0015
Core-Loc™ 0.0605 0.030 2300 632 253 1.30 0.108 0.271 0.108 0.089 0.012 0.004 0.0012
Xbloc™ 0.0620 0.030 2300 607 243 1.30 0.109 0.273 0.109 0.090 0.012 0.004 0.0012
Cubes(1layer) 0.0620 0.030 2361 792 317 1.36 0.089 0.222 0.089 0.089 0.012 0.004 0.0012
Haro 0.0420 0.026 2361 668 267 1.36 0.092 0.231 0.092 0.078 0.008 0.003 0.0008
influence factor γ described above, which can also be applied to whichcanbegeneratedintheflume.Thisdesignwaveheightisgiven
f
overtoppingprediction,e.g.viaEq.(5)(TAW,2002); as
!
qffiffiqffiffiffiffiffiffiffiffiffi¼0:2exp (cid:2)2:6 Rc 1 ð5Þ H0¼stabilityno:(cid:3)DDn ð6Þ
gHm30 Hm0gf Tests with Hm0=H0 would be the maximum significant wave
heightfortesting.OthertestsshouldbecarriedoutwithH =0.5H
m0 0
Inthiswork,theinfluencefactorγ istakentoincludethedirect and0.75H .Eachwaveheightwouldthenberepeatedforthreewave
f 0
effectofarmourroughnessandalsotheeffectofthearmourporosity. steepnesses,s =0.02,0.035and0.05,wheres isthenominalwave
op op
A previous study attempted to separate out these influences on steepness(¼2pH0).Twowaterlevelswouldbetested,giving(formost
overtopping,butfindingswereinconclusive(Franco,2007). tests)Rc=1.3agnTdp2 0.8.Thisleadstoatotalof18testsforonestructure,
H0
covering small to large overtopping. The actual number of tests
2.2.Designofastandardtestsituation howevervariedforeachconfiguration.
2.2.1.Selectionofwaveconditions 2.2.2.Selectionofstandardisedstructurecross-section
Largewaveovertoppingisoftenrelatedtosituationsquitecloseto Most structures are built in fairly shallow water, but in orderto
thedesignwaveconditionsforstructurestability.Forthisstudy,the makethecomparisonbetweentestsfortheroughnessfactoreasier,it
stability of the structure itself is not an issue. In order to compare isbetternottoincludeaforeshore.Ontheotherhand,thewaterdepth
differentunitsofdifferentsizes,astandardtestsituationandstandard shouldnotbetoolarge,becausethestructurebecomesmuchlarger
cross-sectionisrequired. Sucha standardtestsituationcanbest be withalargerwaterdepth.Twowaterdepths(2.5H and3.0H )were
0 0
basedondesignconditionsforthestructures. chosenforthetests.Forsuchwaterdepthsthewavesdonotbreakand
Veryoftenbreakwaterswithasteepslopearedesignedforafixed theycanbegeneratedwithoutaforeshore.Withfocusbeingonthe
n(s¼tuamqbqwuaintbiletriet(cid:2)yr1in)suadmnedfibneDrendDHiDssinfotwhrheeeaurcnehiΔtunnisoitmthainendraelilsda,ittaihvmeeneb,tuethorye(cid:7)a¼bna(cid:5)tusndqiitusmneitafsnso(cid:6)sr1i=3tb(cid:8)yo.otAhfsttthhaeebuitlenitsiytt aisnirmgmpoflauecr,thoporesrr.ifzoAornsmtaasunlfccoher,,etsthhheeoirnestt,eawnnhtdiioacnrhdwwsaatssrutdoceteeuxmrceleudwdaeacsfcuedrptethsaiebgrln,eceoadsmlwponliitcghaatas-
set-upandthecross-section.Furtherdetailsonthedesignofrubble thewaterdepthaboveitforeshorewasatleast2.5H .
0
moundstructurescanbefoundin(e.g.)VanderMeer(1988a),andVan The crest freeboard under design conditions was 1.3H , giving a
0
derMeer(1999). totalstructureheightof3.8H .Forthedeeperwatertests,thestructure
0
Table2givesvariousunitswiththeirstabilitynumberfordesign— height was maintained at 3.8H , with a consequent reduction in
0
the data used for setting up and scaling of the experiments. It was freeboardto0.8H .Fig.2givestheproposedstandardcross-section.
0
originallyanticipatedthatthemodeltestswouldincludeDolosseand Fortheactuallayerthickness,thevaluesinTable1wereused.
Shed, but unfortunately at the time of testing suitably-sized units Theslopeofthestandardstructureis1:1.5(i.e.cotα=1.5),though
couldnotbesourced. testswerealsocarriedoutona1:2(cotα=2)structurewithrockand
Given the stability number, the wave height under design cube armours. All dimensions are related to H or to the nominal
0
conditions (H ) can be calculated. This should be a wave height diameteroftheunit.Thecrestandtoeare3D wide.Theunder-layer
0 n
Fig.2.Standardisedcross-sectionfortests.
T.Bruceetal./CoastalEngineering56(2009)166–179 169
Table2
Stabilitynumbersfordifferentarmourunitsusedtoscaletheexperiments(SPM,1977;
CLI,2007;DMC,2007),togetherwithotherunitdata
Typeofarmour Hsi/ΔDn No.of Layerthickness Porosity(%) Packing
layers coeff.,kt density,/
Rock 1.5 2 1.15 ∼40 1.38
Cube 2.2 2 1.1 47 1.17
Antifer 2.2 2 (1.1) (47) (1.17)
Tetrapod 2.2 2 1.04 50 1.04
Dolosse 2.8 2 0.94 56 0.83
Accropode 2.7 1 1.51 59 0.62
Core-Loc™ 2.8 1 1.51 63 0.56
Xbloc™ 2.8 1 1.49 61 0.58
Cubes(1layer) 2.2 1 1.0 30 0.70
Haro 2 51
container using an electric pump during data collection periods. At
theendofthetesttheload-cellvoltagetracewaspassedthroughan
Fig.3.GeneralviewoftheEdinburghwaveflume.
algorithm which determined that total volume of water which
overtopped the structure during the test. Similarly, wave-by-wave
overtoppingvolumesweremeasuredbydeterminingtheincrement
waschosentobeintherange1/5to1/15oftheweightofthearmour in the mass of water in the collection tank after each overtopping
unit. eventfollowingthegeneralapproachfirstusedbyFrancoetal.(1994).
Todeterminetheincidentwavecharacteristics,threeresistance-
3.Experimentalset-upandprocedure typewavegaugeswereused.Threegaugeswerepositionedseaward
ofthestructureseparatedby0.75and0.3m.Incidentandreflected
3.1.Wavegenerationandmeasurement conditions were separated using the Aalborg University WaveLab™
software (which uses the methodology described by Mansard and
The 2D experimental investigations at small-scale were all Funke(1980)).Thewavegaugeswerecalibratedeachmorning.
completed in the wave channel in the School of Engineering and
ElectronicsatUniversityofEdinburgh,UK(Fig.3).Thechannelis20m 3.2.Structurecoreandfilterlayer
long,0.4mwideandhasanoperatingwaterdepthof0.7m.Theside
walls and the bottom of the flume are made of glass. Waves are The core and filter material was graded into the correct size by
generated by a flap type wave paddle that is capable of generating sievingthematerialthroughtheappropriatemeshsize.Forthecore
regularandirregularwaveswithsignificantwaveheightsupto0.11m layer, the requirement was that the weight was less than 1/50W,
andwaveperiodsupto2.0sforafixedwaterdepthof0.70matthe where W is theweight of the armour unit. As all the armour units
paddle. The paddle is equipped with active absorption which differedinweight,carefulconsiderationwasgivensuchthatthefilter
significantlyreducesreflectedwavesreturningfromthestructure. layer fitted all criteria. Fig. 4 shows the installation of the core and
Overtoppingdischargesweredirectedviaacentrally-placedchute filterlayer.
(width either 0.1 or 0.2 m), which discharged into a measuring Theweightdifferencebetweenthedifferenttypesofarmourunits
containersuspendedfromaloadcell.Individualovertoppingevents wastoolargetoallowasinglegradingoffilterlayersotwofilterand
were detected by two parallel strips of metal tape run along the filterlayergradingsweremade.Thesmallergrading(filterlayer“A”)
structurecrestwhichactedasaswitchclosedbythewater.Forhigher wasusedfortheHaro,whilstthelargergrading(filterlayer“B”)was
discharge conditions, water was removed from the collection used for the Cubes, Antifer, Tetrapod, Rock, Core-Loc™, Accropode,
andXbloc™.Table3showsthecoreandfilterlayercharacteristics.
The standard cross-section was inevitably the result of some
degree of compromise in order that rebuilds could be kept to a
minimum(maximisingtheavailabletestingtime).Thefinalchoiceof
Fig.5.Resultsoftestsforsmoothslope;cotα=1.5.Linesarebestfit(γf=1.05,upper,
blackline)andγf=1.0(lower,greyline).Symbolsdenotedifferentnominalsteepnesses;
Fig.4.Themodelfilterlayerandcorebeforearmourplacement. triangles,squaresandcirclescorrespondingtosop∼0.02,0.035and0.05respectively.
170 T.Bruceetal./CoastalEngineering56(2009)166–179
Fig.6.Resultsoftestsforrock;cotα=1.5—“small”(uppergraph)and“large”(lower).Dashedlinesareforγf=1.
corematerialwithD ∼9mmresultsinacorewhichismarginalin R/H =1.0and1.7,whereR =110mmand187mm.Thedata(Fig.5)
n c m0 c
termsofunwantedviscouseffectsandconsequentconcernsaboutthis agreequitewellwiththeEq.(5)(TAW,2002),thoughwitha5%over-
scaling effect. It is asserted, however, that because these tests are estimationofγ.Itistakenthatγ =1isthetruevalue,andthusall
f f
about comparisons between tests under a fairly narrow range of subsequentvaluesofγ obtainedfromtheexperimentsarereduced
f
conditionswhoseresultsdonotneedtobescaledperse,anymarginal bythis5%.
viscouseffectsinthecorewillhaveminimaleffectontheconclusions.
4.2.Results—rock
3.3.Testingprocedure
Fortherocktests,twostonesizeswereused(Table4).Verysimilar
Prior to each test, the water level was adjusted to the required resultsforthedifferentstonesizesareshowninFig.6.
freeboard (R). For each armour unit type, two freeboards were Testswerecarriedoutusingtwolayersofnaturalrockarmourona
c
investigated.Thesizeofarmourunitdeterminedthedesignoffshore 1:1.5slopingstructure.RelativefreeboardsR/H were1.3and0.9,
c m0
significantwaveheight,H .Astheunitswereofdifferentsize,H withR =134mmand95mm.Thepackingdensity/was1.38.14tests
m0 m0 c
alsovariedaccordingly. used“large”rock,with15using“small”(Table3).
Forthesmoothstructure,relativefreeboardswereR/H =1.0and
c m0
1.7. For the natural rock R/H =0.9 and 1.3, and for all the other 4.3.Results—cube
c m0
armourunitsR/H =0.8and1.3.
c m0
Overtoppingmeasurementsweremadeatthecrestwalledge.The Testswerecarriedoutwithcubesarrangedinasimplepatternwith
propertiesofthearmourunitsaresummarisedinTable2. facesapproximatelyalignedtogiveasmoothprofiletotheslope,and
Thetestshadafixeddurationof1024sandhence,dependingupon also with cubes arranged in an irregular or “rough” pattern. The
thewaveperiod,gavebetween700and1300waves.Forallconditions overtopping performance of a single layer of cubes arranged in the
a JONSWAP (γ=3.3) pseudo-random wave spectrum was used. For “regular” pattern was also investigated. Results are shown in Fig. 7
eacharmour/configuration,thepackingdensity(numberofunitsper which, surprisingly, showed no difference in response between
squareD ),/,wasestimatedandrecorded.Asummaryofeachsetof “regular”and“irregular”patterns.However,comparedtotheequivalent
n
testsforeacharmourunitisgivenonthefollowingpages,together double-layer pattern, the single-layer pattern produced larger over-
with graphs of overtopping data and a photograph to show the toppingdischargesasexpected.
conditionofthearmourattheendofthetestsforthatstructure. Cube—doublelayer,“irregular”pattern:18testswerecarriedouton
For the cubes, it was decided to verify whether the placement a1:1.5slopingstructurearmouredwithtwolayersofcubesarranged
orientation of the cube influenced the overtopping characteristics, with the faces in an irregular manner. Three tests yielded no
hence the cubes were tested in a “flat” or “regular” orientation measurabledischarge.RelativefreeboardswereR/H =1.3and0.8,
c m0
wherebythecubeswereplacedrelativelyflattoeachotherandthe withR =118mmand71mm.Thepackingdensity/was1.17.Towards
c
secondcasewaswhenthecubeswereplacedinamorerough,random
pattern.
4.Meanovertoppingdischarge Table3
Filterandcorelayercharacteristics
4.1.Introduction W50(g) D85/D15
Core 0.86 1.30
The benchmark for the tests with different armour units was FilterA 3.37 1.28
the18testsperformedwitha1:1.5(cotα=1.5)smoothslope,with FilterB 7.42 1.19
T.Bruceetal./CoastalEngineering56(2009)166–179 171
Fig.7.Resultsoftestsforcube—“irregular”(topgraph);singlelayer“flat”(middle);and“flat”(bottom).Dashedlinesareforγf=1.
Fig.8.ResultsoftestsforAntifer,HaroandTetrapod(two-layerarmoursystems).Dashedlinesareforγf=1.
172 T.Bruceetal./CoastalEngineering56(2009)166–179
Fig.9.Resultsoftestsforsingle-layerarmoursystems—Accropode,Core-Loc™andXbloc™.Dashedlinesareforγf=1.
theendofthetestsitwasnotedthatthecubesmovedslightlyfroman with the faces “flat”. One test yielded no measurable discharge.
irregularpatterntoamoreregular“flat”pattern.Noreadjustmentof Relative freeboards R/H were 1.3 and 0.8, with R =116 mm and
c m0 c
theunitswasmadeduringthetesting. 71mm.Thepackingdensity/was0.65.
Cube—single layer, “flat”pattern: 18 tests were carriedouton a Cube—doublelayer,“flat”pattern:18testswerecarriedoutwith
1:1.5slopingstructurearmouredwithasinglelayerofcubesarranged cubes arranged with faces aligned flat, with three tests giving no
Fig.10.Resultsoftestsforsmallrockand“irregular”cubeson1:2slopes.Dashedlinesareforγf=1.
T.Bruceetal./CoastalEngineering56(2009)166–179 173
measurable discharge. Relative freeboard R/H was 1.3 and 0.8, Table5
c m0
whereRc=118mmand71mm.Thepackingdensitywas1.19. Finalγfvaluesfor1:1.5slopingstructures,arrivedatfromsynthesisofnewdataand
othercomparabletests
4.4.Results—othertwo-layerarmoursystems Typeofarmour No.of γf γf γf
layers
Threeotherarmoursystemsthatareconventionallyusedastwo- mean 95%CI,low 95%CI,high
layer systems were tested — Antifer, Tetrapod and Haro. Data and Smooth – 1.00
Rock(twolayers;permeablecore) 2 0.40 0.37 0.43
photographs(aftertesting)areshowninFig.8.
Rock(twolayers;impermeablecore) 2 0.55
Antifer: 18 tests were carried out on a 1:1.5 sloping structure Rock(onelayer;permeablecore) 1 0.45
armoured with two layers of Antifer, arranged with the faces in a Rock(onelayer;impermeablecore) 1 0.60
regular pattern. Three of these tests gave no measurable discharge. Cube 2 0.47 0.44 0.50
Cube(singlelayer) 1 0.49 0.46 0.52
RelativefreeboardsR/H were1.3and0.8,withR =128.7mmand
c m0 c Antifer 2 0.50 0.46 0.55
79mm.Thepackingdensity/was1.17.
Haro 2 0.47 0.44 0.50
Haro: 19 tests were performed on a 1:1.5 sloping structure Tetrapod 2 0.38 0.35 0.42
armoured with two layers of Haro, with faces arranged in a flat Accropode 1 0.46 0.43 0.48
manner.Fourtestsgavenomeasurabledischarge.Relativefreeboards Core-Loc™ 1 0.44 0.41 0.47
Xbloc™ 1 0.44 0.41 0.49
R/H were1.3and0.8,withR =118mmand74mm.Packingdensity
c m0 c Dolosse 2 0.43
/was1.16. Bermbreakwater 2 0.40
Tetrapod: 18 tests were performed on a 1:1.5 sloping structure Icelandicbermbreakwater 2 0.35
a(‘rSmOToRuAreMdEwR’i)t.hEitgwhtoolfatyheersseotfesTtestyraieploddedanrroanmgeeadsuirnabale‘Td’ispchatatregren. Vadadluiteisonhatvoebtheeenmneoarnmavlaisluedeboyfcγofm, vpaalruiseosnawtiltohwsemroaonthdsulopppeertesbtosutnadksenoafstγhfe=19.5I%n
Relative freeboards R/H were 1.3 and 0.8, with R =135 mm and confidenceinterval(CI)arealsogiven.RockarmourvaluesinitalicsfromVanderMeer
c m0 c
83mm. (1988b).Othervaluesinitalicsareestimated/extrapolatedfromdiscussionamongthe
authorsandCLASHcolleagues.
4.5.Results—single-layerarmoursystems
using standard statistical techniques where the intercept of the
Three armour systems that are intended for use as single-layer regression equation can be tested for significance. Reasonable
systemsweretested—Accropode,Core-Loc™andXbloc™.Dataand estimates can be obtained at the 95% significance level using the
photographs(aftertesting)areshowninFig.9. analysisofvariance(ANOVA)with13classesofc.14observations.A
Xbloc™: 14 tests were performed on a 1:1.5 sloping structure statisticalanalysisusingtheRstatisticspackage(RDevelopmentCore
armoured with a single layer of Xbloc™. Two tests yielded no Team,2007)showsthatthereisnosignificantevidencetosupportthe
measurable discharge. Relative freeboards R/H were 1.3 and 0.8, contentionthattheinterceptvarieswithunittype,socancorrectlybe
c m0
withR =142mmand90mm.Packingdensity/was0.58. leftat0.2forallconfigurations.
c
Core-Loc™:16testswereperformedona1:1.5slopingstructure Inadditiontoestimatingtheγ coefficientusinglinearregression
f
armoured with a single layer of Core-Loc™. One test gave no itispossibletocomputethe95%confidenceintervalassociatedwith
measurable discharge. Relative freeboards R/H were 1.3 and 0.8, thisestimate(i.e.therangeinwhichweare95%certainthatthetrue
c m0
withR =86.4mmand140mm.Packingdensity/was0.56. value of γ lies). Table 5 shows the computed values of γ together
c f f
Accropode:15testswerecarriedoutona1:1.5slopingstructure with their lower and upper limits. The authors note that the 95%
armoured with a single layer of Accropode. One test gave no confidence interval for 1:2 rock lies completely outside of the
measurable discharge. Relative freeboards R/H were 1.3 and 0.8, remaining confidence intervals indicating that the performance of
c m0
withR =139mmand86mm.Thepackingdensity/was0.62. this configuration is significantly different from the others tested.
c
Additionally, a further series of single-layer armour tests were Despite their overlapping confidence intervals, γ values for other
f
carriedoutwithsimplecubes—seeSection4.3,above. configurations are given separately (rather than as a single, mean
value)asfurthermeasurementsordatafrommuchlargerdatasets
4.6.Results—structureswith1:2slope mayimprovethedistinctionbetweentheunittypes.
Themarginalinfluenceofscaleonpossibleviscouseffectsinthe
Testswerealsocarriedouton1:2slopedstructuresarmouredwith corehasbeennotedinSection3.2.AssetoutinSection2.2,thetests
rockand simple (two-layer) cubes. Theresults areshown in Fig.10 reportedhereweredesignedasdirectcomparisonsofclosely-related
(upperandlowergraphs/photographsrespectively). configurations.Assuch,fortheobjectivesofthiswork,scalingofdata
toprototypescale(anditsinherentadditionaluncertainty)neednot
4.7.Uncertaintyanalysisandscaleeffects followdirectly.Ifthedataweretobeadjustedformodeleffectsand
scaledtoprototypescaleforalaterpurpose,theproceduregivenby
In this work a total of 179 tests have been conducted over 13 theCLASHproject(DeRoucketal.,2005)shouldbefollowed.
different armour types/configurations (plus 18 tests with smooth
slope)givingtypically14testsperconfiguration.Intheanalysisofthis 4.8.Discussion
dataseveralquestionsneedtobeanswered.Theprimaryquestionis
whethertheinterceptof0.2istrulyfixedorwhetherinsteaditvaries DetailedmeasurementshavebeenmadeinUniversityofEdinburgh
with armour type/configuration. This question is simply answered flume to parameterise the mean overtopping rates q for a range of
different armour units on a 1:1.5 sloping structure. Additional
investigationshave beencarriedouton a 1:2slopeforrock, and for
cube armour units. Within experimental limitations, the results
Table4
demonstrate that the overtopping characteristics follow the general
Smallandlargerockcharacteristics
trendofEq.(5)(TAW,2002).
W50(g) D85/D15 AlllinesstartatRc/Hm0=0andq/(gHm30)0.5=0.2.Forsmoothslopes
Smallrock 72 1.38 γ=1andthevalueforeachunitisderivedbyfittingalinethroughthe
f
Largerock 190 1.54 datapoints.
174 T.Bruceetal./CoastalEngineering56(2009)166–179
Fig.11.GraphshowingsuccessofTAW(TAW,2002)predictorofmeanovertoppingdischargeasafunctionofbreakerparameterξm−1,0.Alldatafromthisstudyareincluded.1:2
configurationsareshownastriangles,with1:1.5dataascircles.
It should be noted that Antifer were not tested in a rougher, γ withtheslopeangleforrock.Inthedatabase,andalsoforuseofthe
f
“irregular”arrangement,whichmighthavegivenasomewhatlowerγ. NeuralNetwork,onlyonevalueforγ isgiven.Thusitwasnotedthat
f f
Moreover, available data from similar previous studies were re- theNeuralNetworkmustbeabletoincludetheslopeinfluenceinits
analysedinthesamewayinordertooptimisethefinalselectionafter prediction.Therefore,inthedatabaseonlystructureswithcotα=1.5
joint discussions among CLASH partners. Specifically, Aminti and andG =3D shoulduseγ fromTable5.
c n f
Franco(1988)(forrock,cubeandTetrapod);FrancoandCavani(1999) When all the mean overtopping data from this studyare viewed
(for Antifer, Tetrapod and Core-Loc™); and the results of parallel together (Fig.11), there emerges some indication that the success of
CLASH tests undertaken at Aalborg University and at University of the predictor has a weak dependency upon the breaker parameter
Ghentwerereviewedanddiscussed.Thisallowedafinalselectionof ξm−1,0.Lookingattheratio,qmeasured:qpredicted,TAW,atendencyforover-
γf values as given in Table 5, which are valid for a rubble mound, predictionatlowerξm−1,0andforunder-predictionforhigherξm−1,0
armouredstructurewithslope1:1.5,withcrestbermwidthGc=3Dn (ξm−1,0≥∼4)isapparent.Thistrendisinlinewiththeobservations
withapermeablecore/under-layer.Additionalgeometries/unittypes fromrun-upmeasurementsthattheroughnessinfluencefactorγ is
f
were tentatively assigned a corresponding γf, based on experience notafixedvalueforagivenslope,butinsteadincreaseswithξm−1,0
from other available model tests identified within the CLASH over- over the range 1.8≤ξm−1,0≤10 (see Section 2.1). This serves as a
toppingdatabase. reminder that the γ values derived and presented in Table 5 are
f
Itisobservedthatthecomparisonwithprevious/parallelstudies representative values for the range of ξm−1,0 covered by the tests,
showedthatfortheRockcase(permeablecore),γ varieswithslope and further work is required to extend these boundaries to lower
f
angle—Table6.Theresultsofthisstudyalsoshowedadependencyof andhigherξm−1,0.Itisworthnoting,however,thatthestudiedrange
Fig.12.GraphshowingsuccessofTAW(TAW,2002)predictorofmeanovertoppingdischargeasafunctionofwavesteepnesssm−1,0.Alldatafromthisstudyareincluded.1:2
configurationsareshownastriangles,with1:1.5dataascircles.
T.Bruceetal./CoastalEngineering56(2009)166–179 175
Fig.13.GraphshowingsuccessofTAW(TAW,2002)predictorofmeanovertoppingdischargeasafunctionofwaveperiodTm−1,0.Alldatafromthisstudyareincluded.1:2
configurationsareshownastriangles,with1:1.5dataascircles.
encompasses the vast majority of practical concrete armoured analysisofmeanovertoppingdischargeonsteep(cotα≤1.5),armoured
structuresundernormaloperatingconditions.Further,itisasserted revetmentswithimpermeablecore.
thatgiventheinherentscatterinovertoppingdata,theuseofasingle
γf over the range ∼2.0≤ξm−1,0≤∼4 is acceptable for engineering 5.Individualwaveovertoppingvolumes
assessmentanddesignpurposes.
Looking more closely at the source of the influence of breaker Until recently, guidance relatingovertopping to direct hazard has
parameterξm−1,0,itcanbeseenthatthegoodnessofthefitofthedata been based upon admissible mean overtopping discharges (see e.g.
tothesimple(γ=constant)modeldependsuponbothincidentwave EA,1999).Althoughithaslongbeenappreciatedthatindividualwave
f
steepness sm−1,0 and wave period Tm−1,0 (Figs.12 and 13). Both of overtoppingvolumesoughttoprovideabettermeasureofdirecthazard
these viewsareagainconsistent withthe premise that γ increases (e.g.Francoetal.,1994),itisonlyrecentlythatnewguidanceincluding
f
(approximately linearly) with ξm−1,0 as per behaviour observed in referencetoovertoppingvolumeshasbeguntoemerge(Allsopetal.,
run-up experiments (Section 2.1) with longer waves “feeling” the 2005;EurOtop,2007).Inadditiontothemeanovertoppingdischarges
roughnessless.Furthertestswillberequired,however,beforethere measuredduringthesetests(reportedinSection4),individual,wave-
wouldbeasufficientlysubstantialbasisforadjustedguidance. by-waveovertoppingvolumeswerealsorecordedthroughout.Results
Looking beyond the structures tested in these studies, it is arefirstpresentedformaximumindividualovertoppingvolumes.Itis
anticipated that these influence factors could also be applied in the however accepted that this is not a particularly stable measure, and
Fig.14.GraphshowingsuccessofEA(EA,1999)predictorofmaximumindividualwaveovertoppingvolumeasafunctionofdimensionlessmeandischarge.