tr
lmpactof Bi-modalSeason Beachesand
ControlStructures
P J Hawkes
T T Coates
R J Jones
Report SR 507
February1998
{
ar
HRWallingford
Address and RegisteredOtfice: HR wallingford Lld. HowberyPark, Wallinglord,OXON OX10 8BA
Tel: +44 (0) 1491 835381 Fax: +44 (0)'1491 832233
G.otp Ltd.
is a wtpllyom€d srbskliaryof HRWallinsford
Regid€redin EnglandNo.2t'6209s.HRWallingford
sR 507 16/02198
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sB 507 16/02198
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Contract
Fisheriesand Foodunder
This reportdescribes
workfundedby the Ministryof Agriculture,
and FD07(BeachManagement).The HR
Commissions
FD02(MarineFloodProtection)
job numberswereCCS14 andCCS15. Publication
by
impliesno endorsement
Wallingford
or
the Ministryof Agriculture,
Fisheriesand Foodof the report'sconclusions
ProjectOfficerwas Mr A C Polson.The HR
recommendations.
The Ministry'sNominated
Wallingford
Nominated
ProjectOfficerwasDr S W Huntington.
Preparedby
Approvedby
KMdril"
?re.oe
Datelt kbqs tQQq
@
Ministryof Agriculture,
Fisheriesand Food,copyright1998
ill
sR 507 16102/98
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iv
sR 507 16/02198
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Summary
lmpactof bi-modalseas on beachesand controlstructures
P J Hawkes
T T Coates
R J Jones
Report SR 507
February1998
A sea state is madeup of eitherwind-sea,swell-seaor a combinationof the two. Wind-seasare
generatedby localwinds;their impactsat the coastin termsof overtopping,beach movement,
armourdamage,etc, are relativelywell understoodfor manysimpleconfigurations.Swell-seas
resultfrom the transferof energyto lowerfrequenciesas wind-seasdecay;their magnitudesand
impacts at the coast are more difficultto predictthan wind-seas.
Often duringthe transitionfrom wind-seato swell,the wind speedwill rise and begin generating
new wind-sea.This situationis characterisedby a bi-modalwavespectrum,in which the lower
frequencypeak is the swell-seacomponentand the higherfrequencypeak is the wind-sea
component. These types of conditions,and the responsesoccurringat the coast, are probably
the hardestof all to predictaccurately. Very few physicalmodel tests of sea defences, and no
establishedempiricalmethods,deal specificallywith the impactsof bi-modalsea conditions.
The Ministryof Agriculture,Fisheriesand Foodhas fundeda seriesof studiesat HR Wallingford
on swelland bi-modalseasand their impacts.This reportdescribesphysicalmodeltestson
beachesand structuresunderswelland bi-modalsea conditions.The first projectinvolvedthe
impacton shinglebeachesin terms of crestelevationand crest roll-back.The second project
involvedmeasurementof overtoppingon differenttypesof seawall. In both cases, resultswere
analysedin detailand guidelineswere developedfor futureassessmentof the effectsof bi-modal
seas. In an oppoftunisticthird project,additionalmeasurementswere taken of run-up,run-down,
armourmovementand reflection;theseare presentedin the presentreportbut are not analysed
in detail.
The reportconcludesby listingphysicalsituationsand locationsin which swell and bi-modalseas
shouldbe consideredas potentialdesignconditions.lt also summarisesthe knowledge
gatheredfrom the test programmeand the areas where further researchis needed. A
companiontechnicalreport gives full detailsof the structures,sea states and measurements
taken.
For further informationon this repofi, pleasecontact Dr Peter Hawkes or Mr Tom Coates of the
CoastalGroupat HR Wallingford.
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VI
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Contents
Title page
Contract
Summary
Contents
I
iii
vii
. . . . . . . . . . - . . . .1. . . ' .
.....,.1
1
..-..........'.
2
...............'......
Introduction
1.1
Background
1.2
Projectdescription
1.3
Reportoutline
Effectsof bi-modalseas on shinglebeachresponse
2.1
Fieldobservations.........
2.2
F l u m es t u d y . . . . . . . . . .
2.2.1 Objectives
2.2.2 Methods
2.2.3 Results.......
2.3
Discussion..
with Powell(1990)........
2.3.1 Comparison
2.3.2 Equalenergytests........
2.3.3 Equalreturnperiodtests...........
2
.........-.........2
. . . ' . . . . . . . .3. . .
...............3
. . . . . . . . . . . . ' .4. . . '
......--.-...4
'-.-...4
..-....-....4
5
....-........
5
...-....'...........
6
.................
Effectol bi-modalseason overtoppingof slopingseawalls.....
.....'.6
Introduction
3.1
6
..-.........'.
3.1.1 Purposesof the overtoppingtests and analysis
6
......'.....'.....
..............
3.1.2 The flumetestsand measurements
8
.......'....
Analysisof the resu1ts.................
3.2
8
'..........-......
3.2.1 Outlineof the ana|ysis................
8
..........
measurements....
the
overtopping
3.2.2 Presentation
of
9
3.2.3 Analysisof wind-seaand swell-seaovertopping............-...............-...
-...'...I
3.2.4 Use of the Owenformulafor swell-seaovertopping
10
............'...
3.2.5 Analysisof bi-modalseaovertopping'...........
..".......11
and waysforward
3.3
Observations
3.3.1 Observationson measurementsand predictionsof swell-sea
11
...........
overtopping
predictions
bi-modalsea
of
and
3.3.2 observationson measurements
--'-'.....'12
overtopping
design?........'.......--.........12
in
important
seas
Are
bi-modal
and
swell
3.3.3
Effectof bi-modalseason otherparameters...........
4.1
lntroduction
Armourmovements
4.2
4.3
Run-up/run-down
..........
4.4
W a v et r a n s m i s s i o n . . . . . . . . .
4.5
Wave reflection.............
13
.............
..'..13
13
...........
.....16
. . . . . . . . . . . . . . . . .1. 6
..-.
-..--17
Practicalapplications
of researchresults
5.1
Shinglebeachprofiles
5.2
Overtopping
in swell-seas..........'.....
5.2.1 Overtopping
in bi-modalseas...........
5.2.2 Overtopping
..'--..-..17
.--..-.17
. . . . . . . . ' . . . . ' . . .1. .8. . .
......."'18
.'...'..'.18
'19
.......'.........
'tg
..........
-.....-...'.20
Conclusions
processes
Hydraulic
6.1
Design
significance
6.2
....-21
ldentificationof furtherresearch
vii
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Contents continued
8
Acknowledgements...............
9
References......
Tables
Table 2.1
Table3.1
Table 3.2
Table3.3
.........21
............22
Wave conditionsused in the shinglebeachtests
Summaryof waveconditions
usedin the flumetests..........
purposes
Divisionof the testsintofive setsfor presentation
Factorsto be appliedto SWALLOWpredictions.............
Figures
Figure1.'1
Figure2.1
Figure2.2
Figure2.3
Figure2.4
Figure2.5
Figure2.6
Figure2.7
Figure2.8
Figure2.9
Figure2.10
Figure3.1
Figure3.2
Figure3.3
Figure3.4
Figure3.5
Figure3.6
Figure3.7
Figure3.8
Figure3.9
Figure3.10
Figure3.1'1
Figure3.12
Figure3.13
Figure3.14
Figure3.15
Figure3.16
Figure3.17
Figure3.18
Figure4.1
Figure4.2(a)
Figure4.2(b)
Figure4.3
Figure4.4
Figure4.5
Figure4.6
........7
.......8
...........
10
Spectraldefinitionof wind-seaand swell
'1994
Beachprofiles- Highcliffe,December
Beachprofiles- Hordle,December1994
Wave spectraat peak water levelsduringstorm event of
7-8 December1994
Wave spectraat peak water levelsduringstorm event of
29-30December1994
Swellinfluenceon cresl elevation:Hs = 2.12m
Swellinfluenceon crestcut back:Hs = 2.12m
Swell influenceon crest elevation:Hs = 2.83m
Swell influenceon crest cut back: Hs = 2.83m
Swellinfluenceon crestelevation:Hs = 3.53m
Swellinfluenceon crestcut back: Hs = 3.53m
'l
Spectrafor Test Series
Measuredmean ovedoppingrate - set 1
Measuredmean overtoppingrate - set 2
Measuredmean overtoppingrate- set 3
Measuredmean overtoppingrate- set 4
Measuredmean overtoppingrate- set 5
Measuredmean overtoppingrate- test series1 and 4, water level
14m,two structureslopes
Owen and van der MeerComparisonbetweenmeasurements,
set 1
Owen and van der MeerComparisonbetweenmeasurements,
set 2
Owen and van der MeerComparisonbetweenmeasurements,
set 3
Owen and van der MeerComparisonbetweenmeasurements,
set 4
and Owen - set 5
Comparisonbetweenmeasurements
in Owenformulaas a f unctionof lribarrenNumber(1:50
Discrepancy
foreshoreshore;wind-seaand swellonly)
and modifiedOwen - set 1
Comparisonbetweenmeasurements
and modifiedOwen - set 2
Comparisonbetweenmeasurements
and modifiedOwen - set 3
Comparisonbetweenmeasurements
and modifiedOwen - set 4
Comparisonbetweenmeasurements
and modifiedOwen - set 5
Comparisonbetweenmeasurements
Uni-modalwaves,armourdisplacements
Exampleof wave shoalingand breaking
Uni-modalwaves,predictedarmourdamageS
Uni-modalwaves,comparisonof measuredand predicted
displacements
Uni-modalwaves,
comparisonof measuredand predicted
displacements
allowingfor steepapproachslopes
Bi-modalwaves, armourdisplacements
Bi-modalwaves,comparisonof measuredand predicted
displacements
vill
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Contents continued
Figure4.7
Figure4.8
Figure4.9
F i g u r e4 . 1 0
F i g u r e4 . 1 1
Figure4.12
Figure4.13
Figure4.14
Figure4.15
Figure4.16
Figure4.17
Run-upperformance
performance
Run-down
"equalenergy''
waves,run-upperformance
Bi-modal
performance
waves,run-down
Bi-modal
"equalenergy''
period"
waves,run-upperformance
"equalreturn
Bi-modal
period"
waves,run-downperformance
"equal
Bi-modal
return
performance
"equalenergy''
waves,transmission
Bi-modal
performance
Bi-modal"equalreturnperiod"waves,transmission
performance
and bi-modalspectra
of uni-modal
Reflection
performance
Bi-modal"equalenergy''waves,reflection
performance
Bi-modal"equalreturnperiod"waves,reflection
sB s07 1€,/02198
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1 Introduction
1.1
Background
It is well knownthat wave period,as well as wave height,can be importantin determiningthe
actionof waves on beachesand coastalstructures.In the commonsituationof waves being
depth-limitedat the toe of a sea defenceafter breakingover a gentlyslopingforeshore,wave
periodand waler levelmay both be more importantthan wave height. Swellwaves, produced
as wind waves decayafter a storm,have longerperiodsthan locallygeneratedstorm waves
(wind-sea),althoughusuallylowerwave heights. Becauseof the effectof wave period in
determiningcoastalresponse,it is possiblethat extremeswell wave conditions(or a mixtureof
wind-seaand swell)representa worstcase sea statelor some aspectsof design. However,
littleis known aboutthe effectof bi-modalsea conditionson sea defencesor beaches,and
swell is rarelyconsideredexplicitlyin the designor assessmentof shorelinemanagement
operations.
This lack of knowledgeprovokeda seriesof researchprojectson swell and bi-modalseas
funded by the Ministryof Agriculture,Fisheriesand Food (MAFF). One productof the earlier
studieswas a swellwave atlasfor Englandand Wales (Hawkesef a/, Reference1). As wellas
lookingat commonlyoccurringand extremeswellsall aroundthe coast of Englandand Wales,
the atlas divided the coast into 25 sectionsand providedmore detailedoffshore swell wave
climatedata for each one. The informationincludeda distributionof swell wave height,period
and directionfor each area,and extremeswellsand bi-modalseas for a range of returnperiods.
The bi-modalsea conditionsare specifiedin terms of a significantwave heightand a mean
wave period for both the wind-seacomponentand the swell-seacomponent (i.e. four
parameters in all); if necessary,separatemean wave directionscan also be specifiedfor each
component,givingup to six parametersin all. A methodfor generatingthe correspondingbimodalspectrumis also givenin the swellatlas.
It was intendedthat the swell wave informationwould provide input to nearshoretransformation
models,physicalmodels,and designcalculations,in the same way that deep water wind-sea
data would be used. A potentialdifficultyis that applicationsand designmethodsdeveloped
usingwind-seaconditionsmay notworkwellwithswellwaveconditions.
A more obviousdifficultywith the bi-modalsea data arisesfrom the separateparameters
neededto specifythe separatewind-seaand swellcomponents(Figure1.1). These could be
used withina randomwave numericalor physicalmodelin which a spectrumcan be fully
specifiedby the user. However,mostdesign methodsuse a singlewave heightand period (or
equivalent)and it is far from obvioushow to representbi-modalsea data in this form before it
can be used in such methods. This problemhas been addressedintuitivelyin differentways in
the past, but withoutrelevantphysicalmodelor field data for validation,it is difficultto say which
(if any) of those approacheswere correct. The simplestapproach,for example,is just to
calculatethe significantwave heightand mean wave period(and mean wave directionif
required)in the usualway by spectralanalysis,withoutregardfor the possibilitythat the sea
may be bi-modal. This has on occasionbeen demonstratedto be incorrect,because the mean
wave period (or direction),at which there may be little wave energy, produces a different
responseto the combinedeffectdue to the two very differentmodesof the spectrum. An
exampleof beach responseto bi-modalseas was obseryedduringa MAFF-fundedlield study
in ChristchurchBay;these observationsare discussedin Chapter2.
1,2
Projectdescription
relatingto
HR Wallingfordwas commissioned
by MAFF to conducta seriesof investigations
the impacts of bi-modalseas on coastaldefencesand beaches. The objectiveswere:
.
o
to investigatethe influenceof bi-modalseason shinglebeachprofiles,produceguidance
for beach managementand, if possible,to derivegenericpredictionmethodscompatible
with existingbeach profileresponsemodels
to investigatethe influenceof bi-modalseason wave run-up,wave overtoppingand the
structuralstabilityof coastalstructures,and to developpracticalguidelinesfor modifying
existingdesignapproaches.
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The work was undertakenin a waveflumeat HR Wallingfordas part of a rollingprogrammeof
MAFF research.Detailsof the methodsand resultsfor all of the flume studiesare presented
in the companionTechnicalReport(Reference2).
1.3
Reportoutline
describedin the
This reportpresentsanalysisand discussionof the flume investigations
TechnicalReport(Reference2), and presentsguidanceon the applicationof the results.
Resultsfor shinglebeachesand structureovertoppingare presentedin Chapters2 and 3.
Resultsfor other parameters(run-up,structuralstability)are presentedin Chapter4. Chapter5
whileChapters6 and 7 presentthe conclusionsand
sets out the practicalapplications,
recommendationsfor furtherresearch.
All dimensionsused in this reportare prototypeunlessothenvisespecified.
Effects of bi-modal season shingle beach response
2
2.1
Fieldobservations
The responseof shinglebeachesto long periodwave conditionshas been noted and
observed many times, but quantitativedata regardingsea conditionsand beach profilesare
not generallyavailable. An exceptionto this is the data set collectedunder a MAFF field
researchcommissionundeftakenin ChristchurchBay, as reportedin Coates & Bona (1997 Reference3).
Profileswere collectedfrom sites at Highcliffeand Hordle beachesin ChristchurchBay
betweenJanuary1993and April1995,whilewave conditionsand water levelswere recorded
continuouslyat a nearshorelocation. A numberof the profilesurveyswere carriedout
following identifiablestorm events,two of which can be comparedto illustratethe potential
impact of bi-modalseas.
ChristchurchBay is protectedf rom severewave attackby the DolphinBank and the lsle of
Ledgeand HengistburyHeadto the southwest.Much
Wight to the east,and by Christchurch
PooleBay, is undergoinglong term
Bay,and the neighbouring
of the coastlineof Christchurch
headlandsare stilldeveloping.
major
erosionas equilibriumbay plan shapesbetweenthe
and increasesin rate in the same
to
east
west
from
Wave induced nett longshoretransportis
direction. The area has a low tidal range relativeto much of the UK, with a springtide range
of about 1.4m, and experiencesan extendedhigh water stand or double high water.
The lengths of shorelineinvestigatedwere:
.
.
the easternend of the rechargedand groynedbeach at Highcliffe
the natural,open beachat Hordle.
The beach at Highcliffeis discussedin some detail in Reference3. Briefly,the beach
comprises loweisand, upper shinglein front of formerlyunstablecliffs of flint, sand and clay
strata. lt has undergonerechargesin 1984and 1992and is controlledby largerock groynes,
whichpreventany significantlongshoretransport.The 1992
builtover earliertimbergroynes,
-by
rechargewas designed HR Wallingford,making use of a parametricmodel developedfrom
a wave flume researchprogramme(Powell,Reference4) which is discussedlater in this
report. The easternsectionof the beachbuiltup intoa relativelystablebeachfollowingthe
rechargeof 1984,and receivedvery littlenew materialin 1992. The beachwas consideredto
be nearingmaturityin termsof its profile,shapeand dimensions.The shinglehas a D5eof
about 25mm and a gradingrangefrom 10mmto 100mm. The interfacebetweenthe lower
sand beach and the shinglecomprisesa zone of constantlychanginglayersof sand and
shinglethat can be erodeddown to form a deep scourchannelor built up to form a sandytoe.
The beach at Hordleis natural. lt comprisesa wide shinglebank with a steepface running
down to about -2m OD where the gentlyslopingsand nearsha(ezone begins. The shingle
grading rangesfrom 1Ommto 50mm and has a D5sof about 16mm. The sectionof beach
sR 507 16/02/98
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investigatedhas no groynesand can be consideredto have reacheda state of dynamic
equilibriumwiththe wave and tidalclimateover manyyears.
DuringDecember1994two majorstormsaffectedChristchurchBay. The first ran from the
3rd to the 8th, whilethe secondran from the 25thto the 30th. Beachprofileswere surveyed
on the 19th and the 3'lst. Figures2.1 and 2.2 presentthe profiles.
The profilesfor Highcliffeshowthatthe beachcrestincreasedin elevationf rom 4.0m OD to
4.3m OD betweenthe two surveys,whilethe Hordleprofilecrestsremainedunchanged.As
the Highcliffecresthad remainedrelativelystaticat the designlevelof 3.9m OD (+ 0.1m) over
the 2/z years since the 1992 recharge,then this change in elevationwas considered
noteworthy.
Initialassessmentof the wave and water level recordsindicatedthat the peak energy
between the two surveysoccurredat high water on the morningof 30 December,when water
levels reached 1.35mOD (07:22)and wave heights(H") were between2.88m (06:00)and
Bay, but a reviewof conditionsduring
3.14m (09:00).These levelswere highfor Christchurch
the previousstorm event earlierin Decemberindicatedthat very similar conditionshad
alreadybeen experienced:
on the morningof 8 Decemberthe water levelreached1.31mOD
pa',221and wave heightswere between2.93m (03:00)and 3.'17m(06:00).
As the basic sea state conditionswere so similarthen it was consideredthat other factors
must be involved. Previousobseruationsat other sites, such as Chesil Beach, had suggested
that swell waves might be importantin beach profileresponse,so a more detailedanalysisof
the wave recordwas undertaken.The wave recordswere analysedspectrallyfor each high
water period throughoutthe two storm events. The resultsfor the two highestwater levels
are presentedin Figures2.3 and 2.4.
During the early Decembereventthe wave energyspectrawere distinctlypeaked within the
different
wind-seaf requencies(0.11-O.14Hz
or 7-9s). The latereventshowedsignificantly
spectra, with much higher proportionsof total energy in the swell f requencyband. During the
high water of 29 Decemberthe spectraseparatedinto two disiinct peaks, with the swell peak
'l
at 0.O5Hz(20s)and the wind-seapeak between0.1 -0.14Hz (7-9s).
A simplifiedmethodof separatingswellfromwind-seawas appliedto those spectrabased on
the Pierson-Moskowitz(Reference5) approach:
f (wind-sea)
=
0.139/U
where f (wind-sea)is the lowestfrequency([z) for waves generatedby local winds
g is accelerationdue to gravityin m/s'
U is the localwindspeedin m/s.
This approachwas derivedfor fully developedseas, but providesa convenientseparationfor
this application. As localwinds were around 17mlsthen the separationfrequencyis taken as
0.075H2. Calculationsfor the two storm eventsare presentedin Figures2.3 and 2.4. Swell
energy lor the first storm was around 1O"/"of total energy,while the second storm had much
more obvious swell accountingfor about 2O"/"of total wave energy.
The apparentresponseof the beachto wave conditionswith a large low frequency
componentor a bi-modaldistribution
suggestedthat the existingmethodof predictingbeach
responsecould be inadequate.This conclusionled to the presentflume studyon shingle
beaches.
2.2
Flumestudy
2.2.1 Objectives
A wave flume study was proposedto investigatethe field observationsdiscussedabove, and
io improve existingbeach managementtools for use by coastal engineers.
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Existingmethodsfor predictingshinglebeachprofilesare basedon an extensivewave flume
study r-portedby Powell(199b,Reference4). Powellrecordedthe responsesof a physical
model beach to a rangeof wave conditionsbasedon JONSWAPspectra. The parametric
modeldevelopedfrom the resultsusesa singlewave height(H")and a singlewave period
(T.) as the inputwave parameters.The modelhas been used in the designof many beach
rechargeand beachmanagementschemesaroundthe UK. Althoughthe model is widely
discussedabove indicate
acknowledgedas a successfuldesigntool,the fieldobservations
beachcrestdevelopmentundersea conditionswith distinct
that the resultsmay under-predict
bi-modalspectra.
The intentionof the presentstudywas to buildon Powell'swork by extendingsome of his
originaltestconditionsto considerbi-modalseas.Severalsequencesof tests were run in
which the total wave energy level was kept constant,but the energy levels within the swell
frequencieswere variedfrom near zero (as in the originalwork) through several levels to near
100% swell energy. In addition,a sequenceof tests was run using a set of wave conditions
with an assumedconstantreturnperiod,based on the 2:1 year return period conditionsfor
GreatYarmouth.This sequenceincludedtotalwind-sea,totalswelland a rangeof
intermediateconditions;total energylevelsdiminishedfrom wind-seato swell.
2.2.2 Methods
The study methodsare describedin the companionTechnicalReport (Reference2). The
followingis a briefsummary.
Tests were undertakenin the Wave AbsorbingFlume at HR Wallingfordat a notionalscale of
1:20. The requiredwave conditionswere calibratedat the outset of the study, and were
monitoredthroughouteach test to ensurecorrectgeneration.The shingle beach was
modelledusing irushed and graded anthracitecoal, scaledaccordingto well established
proceduresthat correctlysimulatethresholdof motion,onshore-offshoretransportand
permeability. Beach responsewas recordedon video,photographsand by an automated
beach profiler. Test sequencesincluded:
.
.
.
initialverification
againstthe work of Powell
six sequencesof equalenergyconditions,withthreeenergylevels(H" = 2.12m,2.83m
and 3.53m)and three peak swellf requencies(To= 11s, 14s and 19s)
one sequenceof constantreturnperiodconditions.
Table 2.1 summarisesthe test conditions,whilstSection3.1 describesthe backgroundto
their selection.
2.2.3 Hesults
The full set of beach responseprofilesare presentedin the TechnicalReport. The results
discussedin this reportare changesin crest elevationand crest position,presentedin
Figures2.5-2.10. Changesof crestelevationand positionfor each bi-modalor swellwave
conditionare non-dimeniionalisedas percentagevariationsrelativeto the crest responsefor
the appropriatewind-seaonly condition. Elevationsare relativeto the still water level and
crest positionsare relativeto the positionof stillwateron the wind-seaonly profiles.
2.3
Discussion
2.3.1 ComparisonwithPowell(1990)
A major objectiveof the beach study was to extendthe work of Powell (Reference4) by
investigating
bi-modalwaveconditions.The firststepto achievingthis objectivewas to
of flumemodelresultsby repeatinga numberof tests from the original
ensurecompatibility
researchprogramme.The modelfacility,mobilebed and wave/waterlevelconditionswere all
set up to replicatePowell'swork. The scaleof the new modelwas slightlysmaller,at 1;20
refativeto the original 1:17. In addition,the new work was run with a pistontype paddle
rather than the previouswedge paddle. Theoreticallythese two differencesshould not have
affectedthe resultsas the scale change was carriedthroughall aspects of the model and the
performancecapabilitiesof the paddlesare equal.
sR s07 16/02198
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Comparisonof the measuredprofilesunderthreedifferentconditionsshoweda substantial
differencein post-testbeach profiles. Crest elevationsmeasuredin the new series were
between0.3m and O.7mlowerthanthose recordedby Powell. Despitenumerousrepetitions
and sensitivityteststhe differencesremainedtoo largeto concludethat the two sets of results
were compatible.
Differencesmay be attributedto differencesin wave generationor in sedimentdistribution.
The originalspectralanalysesof individualwaveconditionsare no longeravailable,and nor
are the details of the originalsedimentdistributions.Atthoughthere are no apparent reasons
for differences,these two factorsare the only variablesthat could not be thoroughlychecked.
Ratherthan abandonthe project,it was concludedthat data analysisshould concentrateon
the relativedifferencesbetweenbeach profilesunder differentwave conditions,rather than on
the absolutevalues. Powell'swork has been validatedagainstsite informationon a number
of occasionsand is consideredto be a reliableprediclivetool. Therelorethe relative
influencesof differentwave spectraon beach responsederivedfrom this study can be
appliedto Powell'smodeldespitethe lack of compatibility.
2.3.2 Equalenergytests
Six test sequences(Tests 6-32) were run to investigatethe influenceof alteringthe
distributionof wave energyfrom wind-seafrequencies,throughbi-modalspectra to swell
f requencies. The tests includeda representativerangeof energy levelsand frequencies;
considerationwas not given to the probabilitiesof occurrenceat this stage. Test sequences
comprisedan initialtest ol wind-seaonly followedby three combinationsof wind-sea and
swell, ending with a lest of swell only. The wind-seaonly tests are the base against which
each of the others is compared.
The key parametersselectedfor analysiswere the profilecrest elevationand position. These
are two of the criticalparametersin beach rechargedesignas they are importantto bolh
volumeand in assessingriskto the backshore.Figures2.5-2.10presentthe results.
Figures2.5,2J and 2.9 showthe importanceof long periodenergyon crest elevation. In all
sequencesthere is a trendof increasingelevationwith percentageswell and with increasing
swell period. The rate of elevationincreasereduces atler 50"/"swell energy relativeto total
energy. The influenceof swell period is greatestbetween11 secondsand 14 seconds;the
rate of increasereducesbetween14 secondsand 19 seconds.
A similarpatternis seenfor the changein crest positionin Figures2.6, 2.8 and 2.10. The
influenceof swell is greatestup to about 20%, with change beyondthat level being variable
and, in some cases, showinga reversalin trend. The 19 second period swell appears to
have a much greaterinfluencethan the 11 secondand 14 secondconditions.
The conclusionsfrom these sequencesare simple and agree with the field measurements
from the Highcliffestudy (Reference3). Sea conditionswith between2Ot" and 507oswell
energy at periodsof 14 secondsor greatermay be importantdesignconditionsfor beach
managementschemes,dependingon the probabilityof occurrence.
2.3.3 Equalreturnperiod tests
The importanceof swell at a specificlocationis dependenton the probabilityof occurrenceof
swell in conjunctionwith largewind-seaand high waterlevels,plusthe durationand
sequencingof the storm events. An exampleof the potentialimportanceof a probabilistic
approachwas consideredin a singletest sequence(Tests1-5). Wave conditionsof equal
return period were derivedfor a specificsite (GreatYarmouth)so the resultsare not of
generic value and are not presentedin this report(a full set of resultsare presentedin
TechnicalReportTR 24, Reference2). The testsare not conclusive,exceptfor the specific
for all sites.
site, bul illustratethe importanceof consideringbi-modalconditions
sR 507 16/02198
tr
Effect of bi-modal
3.1
of sloping seawalls
Introduction
3.1.1 Purposes of the overToppingfesfs and analysis
The main purposesof the swelland bi-modalsea overtoppingtests are:
changesas sea conditionschangefrom
1. To observein generaltermshow overtopping
wind-sea,throughbi-modalsea, to swell. This is to help determinewhetheror not bi-modal
and swell seas are potentialworstcasesfor UK sea defences,and hence whetheror not
they shouldbe consideredin design.
2. To demonstratea desk studyapplicationof the bi-modalsea data providedby the swell
atlas (Reference1). The hopewas to producea workablemodificationof a uni-modal
designformulafor predictingone aspectof coastalresponseunder bi-modalsea conditions.
The tests {ocusedon mean overtoppingrate on plainseawalls,sincethis is a commonlyused
design parameterwith wellestablishedmethodsfor measurementand prediction,which
dependsstronglyon wave period. Associatedmeasurementsof run-up,run-down,reflection
coefficientand armourdamage,are analysedin less detail in Chapter4.
The resultspresentedin Chapters3 and 4 shouldbe appliedwith caution. They are not
intendedto providedefinitiveguidanceon structuralresponsesunder swell and bi-modalseas,
but they do have relevanceto designcriteriacoveredby the scope of the tests, namely:
.
.
.
ovenopping,run-up,run-down,reflectioncoefficientand armourmovement;
on plainslopesin the range1'.21o1:4;
for breakingand non-breakingwavesarrivingon a foreshoreslope of about 1:50.
3.1.2 The flumetestsand measurements
The overtoppingtests were designedto includecases easily representedby the SWALLOW
(SeaWALL Overtopping
underWaves)empiricalpredictionmodel,namelystormwaveson a
plainsteepslopefrontedby a plainshallowforeshoreslope. Additionaltestswouldcover
for
relatedbi-modalandswell-seaconditions.The SWALLOWmodelappliesa simplification
wave shoalingand breakingon a foreshoreslope beforeapplyingOwen's (1980)formulafor
mean oveftoppingrate (Reference6).
The six seriesof wave conditions
The individualtests withineach of six seriesfolloweda similarformatto assist in interpretingthe
results. Each seriesincluded:
o
a pure wind-seawith givensignificantwave height(H.1)and peak period(Tpr);
.
a pure swell-seawith a givensignificantwave height(Hr2)and peak period(Tpz);
.
three (six for Series2) intermediateor bi-modalsea conditionsin which the peak periodsof
the two separatemodeswereTo1and Tpz.
TypicallyTpz(forswell)was two to threetimeshigherthanTor(forwind-sea)to givewell
separatedmodes and to covera wide rangeof conditions:the valuesof the H" and To
parametersfor eachof the six seriesare listedin Table3.1.
sR 507 16/02198
tr
Table 3.1 Summary of wave conditions used in the flume
fesfs
Series
No
'l
Relationshipbetweentests
Equalenerqv
Wind-sea
H"r
T^t
H.z
T^,
5
3.53
2.83
7
3.53
11
7
2.83
14
2.12
4.40
4.40
7
8
I
2.12
19
2.76
111/z
1.50
15
4.40
8
0.70
21
3
Equalenerqv
Equalenerov
4
Equalreturnperiod
8
5
5
5
Eoualreturnoeriod
5
6
period
Equalreturn
2
Swell-sea
No of
tests
5
The "equalenerqv"series
Thewavespectrafor eachtestwithinSeries1 (Figure3.1)werearrangedto haveequalenergy
(i.e. H"1 = H"z)l
Test 1a Test 1b Test 1c Test 1d Test 1e -
pure wind-sea
20% swell
50% swell
80% swell
pure swell.
Series2 and 3 were arrangedthe same way. Series2 includedthree additionaltests:
Test 2a1 Test 2a2 Test 2b3 -
2% swell
8% swell
32% swell.
The "equal returnperiod"series
The wave heightsfor each test withinSeries4 (Tor--11.5s)were arrangedto have equal return
period,based on expectationsfor the east coastof England(in practiceHs1> H"2):
Test 4a Test 4b Test 4c Test 4d Test 4e -
e)dremewind-seaalone
more extremewind-seathan swell
equallyextremewind-seaand swell
more extremeswellthanwind-sea
extremeswell-seaalone.
Series5 (fpe= 15s)and 6 Ope= 21s) were anangedthe same way. However,since Tests 4a,
5a and 6a would be identical(H"r= 4.4m,To1= 8.0s),Tests 5a and 6a were not actuallyrun in
the flume tests:instead(wherenecessary)resultsfor Test 4a serve for all three.
The flumetests
Nearlyall of the 33 test conditionswere run for each of:
two seawallslopes
two offshorewater depths
-
one foreshoreslope
-
1:2 and 1:4
1am (highfreeboard)and
16m (low freeboard)
1:50.
Series1 was re-runfor someadditional
foreshoreslopesof 1:7, 1:10 and 1:20. About150 tests
were run altogether.
The wave spectraand measurements
The wave spectra needed to drive the wavemakerwere based on two superimposed
JONSWAPspectra(Reference1), one with the H" and To of the wind-seacomponentand one
with the H" and To of the swellcomponent(Figure3.1). Wave conditionswere measuredin the
sR 507 16,/02198
approachesto the foreshoreand at the toe of the wall;the meanovefioppingrate was
calculatedfrom a measurementof the totalvolumeof overtoppingduringthe test.
tr
Full detailsof the tests and measurementsare givenin the companionTechnicalReport
(Reference2).
3.2
Analysisof the results
3.2.1 Outlineof the analysis
Existingpredictionmethods(Owen,1980- Reference6; van der Meer & Janssen,1995 Reference7) for overtoppingwere shownto matchthe measurementsunder wind-sea
conditionsreasonablywell. Section3.2 describesthe attemptto find a workableempirical
methodfor predictionof the mean overtoppingrate underswelland bi-modalsea conditions.
The hope was to demonstratea possibleuse for bi-modalsea data withina desk study
approach. The analysisfell into two main stages:
1. Stage 1 involvedthe applicationof existingpredictionmethodsto the swell wave tests, and
when they provedto be inadequate,the developmentof rule-of-thumbadjustmentsto
producebetteragreement(predictionof swellwave overtoppingwas not the primary
purposeof this project,and it may be worth returningto this topic in further researchat a
laterdate).
2. Stage2 stadedfrom the position(at the end of Stage 1) of havingadequatepredictionsof
the hean overtoppingrate underboth wind-seaand swell-seaconditions. lt attemptedthen
to predictthe overtoppingfor the intermediatebi-modalconditions,based on the separate
predictionsfor wind-seaand swelland a knowledgeof the relativeamountsof energy in the
two modes.
3.2.2 Presentationof the overtoppingmeasurements
thischapter,thetestsweresplit
throughout
of presentation
Forconvenience
andconsistency
in Table3.2.withabout30 testsin eachone.
intofivesetsas described
Tabte 3.2 Division of the tests into five sets for presentation
Set No
Waveseries
Foreshore
Seawall
Water deoth
Set 1
Series1-6
1:50
1:2
14m
Set2
Set3
Series1-6
1:50
1:50
1:50
1:7.10.20.50
1:2
1:4
1:4
16m
14m
16m
1:2.1:4
14m
Set 4
Set 5
Series1-6
Series1-6
Series1
The measuredmean overtoppingratesare plottedin Figures3.2-3.6;naturaldimensional
scalesare used so as to highlightrelativelysmalldifferenceswithineach group of tests. Tests
within each groupof aboutfive are relatedeitherby havingequalenergy (Series1-3) or equal
returnperiod(Series4-6), label"a" indicatingwind-seathroughto label "e' indicatingswellWhere relatedtests had equal energy,overtoppingclearlyincreasedwith the move from windsea, throughbi-modalsea,towardsswell. However,the rate of increasewith wave period,
particularlyfor the steeperwall slope,was ratherlessthan expectedbased on tentative
predictions
usingOwen'sformula. Forthe serieswithequalreturnperiod,the resultswere
in the wind-seaconditionswas higherthan for the
mixed:for the 1:2slope,meanovertopping
swell conditions;for the 1:4 slope,lhere was littledifferencein overtoppingwithinsome of the
series,but oftenthe wind-seawas the worstcase.
sR 507 16,/02198
tr
There was clearlyan effectof wave period,but ratherlessthan had been expected,and very
much less in the case of the 1:2wallslope. Figure3.7 focuseson this by contrastingresultsfor
Series 1 and 4, for each of the two structureslopes,at the same water level.
The effectsof foreshoreslope can be seen in Figure3.6. Overtoppingincreasesslightlyas the
foreshoreslope increases(so allowinga slightlyhigherdepth-limitedwave heightat the toe of
the wall) whilstat the same time the dependenceon wave periodreducesslightly.
3.2.3 Analysis of wind-sea and swell-sea oveftopping
Two commonlyused empiricalmethodswere usedas the basisfor a predictionschemefor
mean oveftoppingin the wind-seaand swell-seatests (excludingthe bi-modaltests at this
stage). These are the Owen (Reference6) and van der Meer and Janssen (Reference7)
formulae,whichare describedand discussedin Besley(1997- Reference8))'.
test cases, and the resulting
The two methodswere appliedto allof the non-bi-modal
predictionswere comparedwith measuredratesof overtopping.The resultsfor the 1:50
foreshoreslope are shown in Figures3.8 to 3.11;measurementsfor steeperforeshoreslopes
(Set 5) are given in Figure3.12, in this case comparedonly with predictionsby Owen's method
as van der Meer is inappropriatehere. The meanwaveperiod(T,n)requiredby SWALLOW
was taken to be 0.8T0,a slightlylowervaluethantheorywould suggest,but using a ratio
between T, and To fairly typical of coastalseas.
There seems littleto choose betweenthe two methods.As would be expected,both work well
for the wind-seaconditionsfor whichthey weredeveloped.Owen's method,which assumes
that overtoppingwill increase indefinitelyas wave period increases,over-predictsthe mean
overtoppingrate in swell,by a factorof up to aboutfour. Conversely,van der Meer'smethod,
which includesmuch less dependenceupon waveperiod,under-predictsby up to a factor of
one hundred.
Neithermethodis adequatefor predictingovertoppingunderswell wave conditionswithout
significantmodification.To take the analysisforward(and guidedpartlyby a recommendation
in Reference8 to continueusingthe Owenformula)the next sectiondescribesthe searchfor a
simple modificationof the SWALLOWmethodto produceworkableovertoppingpredictionsfor
swell-seas.
3.2.4 Use of the Owenformulafor swell-seaoveftopping
Owen's methodwas developedfrom basintestsrepresentingstorm wave conditionsin the
SevernEstuary,reportedby Owen (Reference6). The range of wave steepness(2nHr,/gT'z)
tested was 0.035-0.055(comparedto 0.005-0.020forthe present swell wave tests). The
methodis drivenby the deep watersignificantwave heightand mean period,althoughthe
height is modifiedfor wave breakingon the foreshorebeforebeing used in the Owen formula.
Owen's "breakingwave height"(at the toe of the structure)was not specificallyintendedto be a
best estimateof the real breakingwave height,but rathera realisticvalue designedto give the
correctanswerwhen used in the overtoppingformula. The same is true to some extenteven
where breakingdoes not occur, in that the deepwaterwave heightis used directlyin the
formula,even thoughshoalingmay have occurred.
The searchfor an adjustmentto Owen'smethodto producea workablemethodfor swell seas
involvedthree alternativeapproaches,all of them havingsome physicalbasis ratherthan simply
using arbitrarycorrectionfactors.
The first approachconsideredthe use of the measuredwaveheightat the toe of the structure
(availablefrom the presentmeasurements,but not recordedduringOwen'stests) as inputto
the Owen formula. For these tests,the differencebetweenthe measuredwave height,and the
wave heightused by Owen's methodwas relativelysmall,and the generallyhighermeasured
This approachwas not pursuedfufiher, and the
valueswould lead to increasedover-prediction.
t
Subsequentto publicationof SR 507, the formulaeof van der Meer and Janssen (Reference
7) have been changed(Reference14). The new formulaealterthe resultsof some of the
tests but the conclusionsdrawn here remainvalid.
sR 507 16/02198
tr
were
resultsare not reproducedhere. lt was, however,concludedthatOwen'sover-predictions
in
error
to
any
than
rather
seas,
for
swell
primarilydue to the Owenformulabeinginappropriate
the wave heightat the toe.
The secondapproachnotesthe implicationof Owen'sformulathat overtoppingwill continueto
increaseindefinitelyas a functionof wave period. lt seems more likelythat beyond some limit,
the rate of increasewill graduallyreduceto a pointat which no furtherincreaseoccurs. With
this in mind,the wave periodsfor all of the individualswell wave testswere reducedto the
values neededfor Owen's methodto matchthe measuredmean overtoppingrates. This
approachwas quite promisingin that theredid appearto be a limitingwave period (in the range
6-10 seconds)for each groupof aboutfive tests,beyondwhich measuredovertoppingdid not
increasefurther. Althoughit was notedthat the limitingwave periodwas consistentlyhigherfor
the 1:4 slopethan for the 1:2 slope,its value seemedotherwiseunpredictablewithout resod to
modeltests. This approachwas thereforenot takenfurther.
The third approach,and the one eventuallyadopted,notesthat Owen'sformulaover-predicts
for long wave periods,especiallyon steeperslopes. lt also notesthat the surf similarity
parameteror lribarrenNumber(0, often used as a guideto the way in which waves behave in
the surf zone,combinesthese two parametersin a convenientway. For each of the wind-sea
and swell-seatests,the degreeof over (or under)prediction(F) and ( were calculatedfrom:
f = (predicted- measuredovertopping)/(measuredovertopping)
€=tang/t/s'
wheretang = structureslope,
and s, = mean wave steepness2nHlgT'2
Values of F and ( for all the tests (arrangedin orderof increasingO are plottedagainsteach
other in Figure3.13. The physicalimplicationsof Figure3.13 are that the Owen's predictionsof
dischargeire reasonablycloseto targetvaluesfor plungingwaves (E< 2.3), but increasingly
above measuredvalues{or highervaluesof ( correspondingto collapsingand surgingwaves.
(This effectis incorporatedin van der Mee/s methodby the use of two separateformulaefor
the two ranges.) The empiricaladjustmentfactorsfor Owen's predictionsof mean ovedopping
rate listedin the table belowwere derivedas a functionof lribarrenNumber.
Tabte3.3 Factors to be applied to SWALLOWpredictions
Ranoeof lribarrenNumber
0.0<E,<2.5
2.5<E<3.0
3.0<E<4.3
4.3<E
Adiustmentfactor(F)
4 *.fe
0
d|2.5
?<p
'11','i*-,.
j 13
14.5
jt/ 8.0
The promisingpossibilityof using inshorewavelength,as opposedto the offshorewave length
implicitin the use of the normal lribanenNumber,was also consideredbrieflyas a way of
limitingthe effectof the largestwave periods. Thoroughanalysisof swell wave overtopping,
and thl developmentof new types of method,are beyondthe scopeof the presentproject,but
may repayfufiher researchinihe future. At presenthowever,the approachsummarisedin
Table 3.3 is sufficientto be able to move on to the main thrustof the analysisdescribedin the
next section.
3.2.5 Analysis of bi-modalsea oveftopping
Severalapproachesto the predictionof overtoppingdischargeunderbi-modalsea conditions
were tested. The following"weightedaverage"methodwas the most successful,althoughit
does rely on the existenceof adequatemethodsfor wind-seaaloneand swell-seaalone.
10
sR 507 t6/02198
tr
Step 1
Start with valuesof H"1and T.1 for the wind-seacomponentof a bi-modalsea, and values of
H"2and Tn.2for the swell-seacomponent.These can be obtained,for example,with reference
to the swellatlas(Reference1).
Step 2
Calculatethe overallsignificantwave heightH" = {(H'"1 + H2"z)by summingthe energiesof the
two components.
Step 3
Run SWALLOWusingT,n1(wind-seaperiod)and the overallH" as input,to obtain mean
ovedoppingrate Q1.
Step 4
Run SWALLOWusingTn2(swell-seaperiod)and the overallH"as input,to obtaina mean
overtoppingrate;calculatean lribarrenNumber,basedon H., T,n2and the wall slope,and
estimatea SWALLOWreductionfactor F from Table 3.3; hencecalculatemean overtopping
rate Q2 as the productof these two values.
Step 5
Estimatean overallmean overtoppingrate (Q), calculatedas an energy-weightedaverageof
the two separate predictionsQr and Qz:
Q = (Q1H2"r+ QrH2"r)/ (H2"1+ H2"2)
Figures3.14-3.18show the measuredovertoppingratesfor all tests (the same values already
presentedin Figures3.2-3.6and 3.8-3.'12)togetherwith the correspondingpredictionsfrom lhe
modifiedOwen method. Predictionsfor the wind-seatestsare taken directlyfrom Owen's
formula;predictionsfor swell are basedon Owen's methodwith a reductionfactor based on
Table 3.3; predictionsfor bi-modalseas are derivedas describedin Steps 1-5 above.
The comparisonsbetweenmeasurementsand predictionsare adequatethroughoutthe range
of tests (perhapsnot surprising,giventhe way that the empiricaladjustmentfactors listed in
Table 3.3 were derived).The predictionsfor bi-modalseas can (at best) only be as good as ihe
individualpredictionsfor wind-seaand swell,which were themselvessubjectto some
uncertainty.The largerpart of the differencebetweenmeasurementsand predictionsfor the bimodal sea tests is carriedthroughfrom the separatepreliminarypredictionsfor wind-seaand
swell. The main purposeof the analysisand comparisonswas to demonstratea prediction
method for bi-modalseas,and the part of the methodspecificallyrelatingto bi-modalseas
worked well.
3.3
Observationsand ways forward
3.3.1 Obseruationson measurementsand predictionsof swell'sea
oveftopping
Overtoppingincreases,for a givenwave height,with the increasein wave periodfrom wind-sea,
throughbi-modalseato swell. The measurementsshowedthe degreeto which the overtopping
increased,and the approximateproportionof swell neededto cause a significantincrease.
Generallythe overtoppingdid not increasewith wave periodas much as had been expecled.
Above a mean wave periodof aboutsix to ten seconds(the exactvalue being dependenton
wallslope and water level)therewas littlefurtherincreasein overtopping.Owen'sformula,
which assumesthat overloppingincreasesindefinitelywith increasingwave period,significantly
over-predictedswellwave overtopping.Conversely,van der Meer & Janssen'smethod,which
has no effectof wave periodonce wave breakinghas enteredthe surgingrange,significantly
under-predictedswellwave overtopping.Neithermethod,as it stands,providedan adequate
comparisonwith measurementsin swell-seaconditions.
Variousmodificationsof Owen'smethodwere investigated,and a numberof promising
possibilitieswere identifiedas describedin Section3.2.4. ln order to take the presentproject
11
sR 507 16,/02198
forwards,an empiricaladjustmentfactorwas derived,as a functionof lribarrenNumber(and
hence implicitlythe form of wave breaking)to be appliedto the directSWALLOWpredictions.
In practice,no adjustmentwas made in the rangeof plungingwave breaking(6 < 2.3) but
reductionswere made at valuesof ( above2.5. There is no theoreticalbasisfor this
adjustment,and it may not be generallyapplicable,but it did providereasonablygood
agreementbetweenSWALLOWand the presentswell-seamodeltests.
andpredictionsof bi-modalsea
on measurements
3.3.2 Obseruations
oveftopping
Simple visual inspectionof the measurementsshownin Figures3.2-3.6showsthat the rate of
overtoppingin bi-modalseas is usuallysomewherebetweenthe ratesfor wind-seaand swellsea. The rate of overtopping(at leastfor the equalenergytest series)increasesroughlyin
proportionto the percentageof swell in the spectrum,even for quite small amountsof swell.
This in turn suggeststhat a simplefunctionof the two separateovertoppingratesfor wind-sea
and swell-seamightprovidean adequatepredictionof overtoppingin a bi-modalseacondition.
A reliableand physicallyplausibleapproachwas developedfor predictionof overtoppingrate in
bi-modalseas. All of the wave energyin the spectrumwas appliedfirstlyat the mean wave
periodfor the wind-seacomponentand secondlyat the mean wave periodfor the swell-sea
averageof the two separaterates was then calculated'
component;a simpleenergy-weighted
In practice,predictionof overtoppingunderbi-modalseas is thereforea two-stageprocess:
prediction(or measurement)of overtoppingfor wind-seaand for swell-sea,and then the
weighted averagingof the two rates. There appearsto be far more uncertaintyassociatedwith
the iirst stage than with the second,but a workablemethodgivingfair agreementwith the
presentmeasurementsis detailedin Section3.2.5.
It should be stressedthat the simplemethodsof Sections3.2.4 and 3.2.5 apply only to
overtoppingrate (and strictlyonly to the rangeof situationsstudiedin the physicalmodel). They
would not necessarilywork well for othercoastalresponseparameters,and do not obviatethe
need for physicalmodeltestsof bi-modaland othersea states. Nevertheless,they do providea
workablefirst estimateof overtoppingrate underswell and bi-modalsea conditions,where
theseare consideredto be importantin design.
3.3.3 Are bi-modaland swell seasimpottantin design?
uYes". The mean
As might have been expected,the answerto this questionis a qualified
overtoppingratefor a swell-seais significantlyhigherthan for a wind-seawith the same wave
height,althoughnot as much higheras mighthave been expectedbased on the commonly
used Owen formula. However,for the test seriesbasedon an equal frequencyof occurrence
on the east coast of Englandfl-est Series4-6),the wind-seaoften producedhigherovertopping
than equivalentbi-modaland swell-seatests.
These observationstend to supportthe presentintuitiveapproachto the use of swell beginning
to be used in HR's coastalengineeringconsultancystudies. In geographicalareas where swell
is consideredto be impoilant,it may be treatedas a separatedesigncase. In areas where the
highestswell significantwave heightsare lessthan half that of the highestwind-seas,it may not
need specificconsideration.As a roughguidewe would suggestthat coastalengineering
studiesin exposedlocationsin the south-westpad of the UK, south ol Holyheadand west of the
lsle of Wight, shouldconsiderswellas a potentialworstcase for design. In other areas,it is
probablynot the worstcase in terms of overtoppingrate, but see below.
A less obvious,but quitecommonsituationin whichswell may be important,is where wave
heightsare depth-limitedat the toe of a seawall. lf wave heightsare limitedto some fairly low
value (say one metreor so) by the maximumwaterdepth at the structure,then the fact that
wind-seawave heightsmay be much higheroffshoreis largelyirrelevant.A metre or so of swell
may be a significantlyworsecase than a metreor so of wind-sea,as shown by the resultsfor
Test Series t-S. tnerefore, wherewavesare severelydepth-limitedat a structure,swell is quite
likelyto be a worstcasefor designin terms of overtopping,even in geographicalareas not
particularlyexposedto swell.
12
sR 507 16'/02198
The difficultyin makingreliablepredictionsof overtoppingrate for swell-seasconfirmsthe
continuingneedfor physicalmodeltestsof theseconditions.
tr
The flume test results(bothfor the equalenergyand the equal retum periodseries)show that
thanwhicheveris the higherof the equivalent
bi-modalseas do not causehigherovertopping
wind-seaand swell-seaconditions.This impliesthat for calculationof mean overtoppingrate,
bi-modalseas are not likelyto be a potentialworstcasefor design. This does not necessarily
mean,of course,that they may not be more importantin other aspectsof design.
The one situationwhen bi-modalseas may be importantfor overtoppingis where a small
amountof swell is concealedwithinwhat appearsto be a severewind-sea. Tests 1b, 2b and 3b
(with20% swell) at the lowerwaterdepthon the lesssteepwall slopegive roughlytwice as high
overtoppingas equivalentTests 1a,Zaand 3a (withno swell). (Admittedly,pure swell with the
same spectralenergywould be an even worsecase, but this may not be consideredin design
as it may not be a realisticsea conditionat most sites.)
4 Effect of bi-modal seas on other parameters
4,1
lntroduction
werealso
otherhydraulicparameters
In additionto waveovertopping
andbeachresponses,
armourmovements,
of waveinducedpressures,
studiedduringthis research.Measurements
were
andwavereflection
waverun-up/run-down
levels,wavetransmission
exceedance
given
was
obtained.A description
of theseresearchmeasurements
and presentation
previouslyby Coates,Jones& Bona(Reference
2).
of the
the currentunderstanding
The purposeof thischapterof the reportis to consolidate
influenceof bi-modalseasupontheseotherhydraulicresponses.Waveinducedpressures
9).
& Allsop(Reference
by McGonnell
are not reportedhere,butwill be reportedseparately
The resultspresented
in Chapter3 andin the presentchaptershouldbe appliedwithcaution.
underswellandbiresponses
guidance
on structural
Theyare notintendedto providedelinitive
of thetests,
the
scope
by
covered
modalseas,buttheydo haverelevance
to designcriteria
namely:
.
.
.
andarmourmovement;
reflection
COefficient
overtopping,
run-up,run-down,
plain
1:4;
on
slopesin therange1:2to
for breakingandnon-breaking
wavesarrivingon a foreshoreslopeof about1:50.
4.2
Armour movements
Armour movementswere determinedfor a simple 1:2 non-overtoppingseawall structureusing
uni-modaland bi-modalwave conditions.Approachseabedslopesof 1:50 and 1:20were
studied. The nominaloffshorewave steepness,smo,of the uni-modalwave conditionswas
either 0.02 or 0.04. The percentageof armourdisplacementswas determinedusing a
detailedphotographicmethod describedby Coates,Jones & Bona (Reference2).
Correspondingarmour damage levels,S, were estimatedaccordingto a method describedby
van der Meer (Reference10).
Van der Meer devised{ormulaeto calculatearmourdamage which includethe effects of
and
randomwaves,storm duration,a wide rangeof core/ underlayerpermeabilities,
distinguishbetweenplungingand surgingwave conditions.For plungingwaves:
= 6.2 Po'18(S/./Nr10'2
H./ADn5q
E,n'o's
and for surgingwaves:
HJaDnso= 1.0 P-0'13(sdN,)02icota (,P
Where the parametersare definedas:
13
sR 507 16/02/98
A
p,
p*
Dnso
P
S
A.
N,
6,
sm
(p/p*)- 1
relativebuoyantdensityof materialconsidered,
mass densityof rock
mass densityo{ sea water
nominaldiameterof armour
notionalpermeability
factor
designdamagenumber= AJDnso'
erosionareafrom profile
numberof waves
lribarrennumber= tano/s*t"
wave steepnessfor meanperiod=2nHJgT^'(H" and T, were derivedusinga
statisticalanalysis)
tr
and the transitionfrom plungingto surgingwaves is calculatedusinga criticalvalue of (,:
1tana10'5
)1(P{0's)
E = (6.2 P0'31
Beforeconsideringthe influenceol bi-modalseas uponarmourmovement,it is necessaryto
considerthe armour movementscaused by uni-modalwave action. The percentageof full
displacementsobservedusinguni-modalwaveconditionsis shownin Figure4.1a. Data has
been re-presentedin termsof armourdamagelevel,S, in Figure4.1b. Three groupsof unimodalwave conditionswere consideredin the analysis,two shallowwater groups (measured
at the seawalltoe) describedby s'o=9.92 & 0.04; and one moderatewater group, smo=0.04
(where s,nois the offshorewave,' steepness). The data has been normalisedby the offshore
significantwave height,thus tests with the same identifierhad the same nominaloffshore
wave height (whileperiodvaried with sea steepnesses).When consideringFigures4.1a & b
ii should be notedthat an armour damage of 307o,or damagelevel S=25, representsfailure
of the seawallslope.
Two conclusionscan be drawnfrom Figures4.1aand 4.1b. More armourmovementswere
seen with a 1:20 approachslope when comparedwith the 1:50 approachslope. Less
damagewas observedon boththe 1:50and 1:20approachslopesat s'o=9.64for the
moderatewaterdepthcase. An analysisof the inshorewave heightstatisticsindicatesthat
consistentlylargerwave heightswere presentin the test withthe lowerstaticwater level,due
as demonstrated
to greaterwave shoaling,leadingto greaterlevelsof armourdisplacements
the distance
against
wave
height
gives
significant
ihe
in Figure4.2a. The examplefigure
from the offshorewave probe for Test Ob4/3A in water depthsof 12m and 14m, using a
foreshoreslope of 1:50. The structurewas built 580m from the offshoreprobe. Wave heights
with the shallowwater are consistentlyhigherthan those with moderatewater level in the
area of the structure.
The armourdamagelevelspredictedby van der Meerfor approachslopesof 1:50 and 1:20
have been presentedin Figure4.2b. The inshoresignificantwave height,Hsi,and the
offshore mean wave period,Tn.o,and an assumedpermeabilityfactor, P=0.1, were used to
predictarmourdamage,S, given in the figure. Figure4.2b can be comparedwith Figure
4.1b. Predictedvaluesof S were greaterfor the 1:20slopecomparedwith the 1:50 approach
slope, but predicteddifferenceswould not accountfor the large differencesseen earlier in
F i g u r e4 . 1 b .
Armour damage,S, predictedusing both the offshoreand inshoresignificantwave heights,
has been comparedwith movementsrecordedduringthe tests in Figures4.3a & b.
Movementsrecordedwith an approachslopeof 1:50are shownin Figure4.3a, whilethose
recordedwith a 1:20approachslopeare shownin Figure4.3b. Van der Meer'stests were
completedfor shallowapproachslopes: good agreementbetweenthe measuredand
for a 1:50approachslope.
predicteddamagelevelswouldnormallybe anticipated
Throughoutthe tests usingthe 1:50approachslope,measureddamagewas less than
predicteddamage,indicatingthat the researchmodelwas morestablethan those of van der
Meer. lt wouldbe feasibleto adjustthe armourdamagelevelsin accordancewith the
predictionmethod,but, it would then be necessaryto make the same adjustmentto both the
1:20 and bi-modalwave tests. That adjustmenthas not been made. On the whole,
measured damage on the steeper 1:20 slope was greaterthan predicteddamage and an
adjustmentwouldfurtherincreasethe difference.
14
sR 507 16,/02198
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The increasedlevelsof armourdamageobservedon the 1:20approachslopewere also
observedin an earlierresearchstudyconductedby Allsop& Jones (Reference11). In their
researchAllsop& Jonessuggesta modification
to the van der Meerformulaeto take account
of increasedlevelsof armourdamagewith steepapproachslopes.
For plungingwaves:
qr-o's
H"ADnso= 4.8 P018(S/r/N;0'2
and for surgingwaves:
= o.77 t-o'te1s/i N,)02{cotcr (,P
H"/ADn5e
These new formulaehave been used to predictarmour damage,S, for the 1:20 approach
slope data presentedin Figures4.4a and b. The data presentedin Figure 4.4b have been
expressedin non-dimensionalterms.
The data pointsplottedat S/N'. = 0.80 were described
as slopefailureand may well resultin highervaluesthan 0.80. In practicea seawalldesigner
mightperhapsdesignusingan armourdamageS=2, and mightallowfor a storm durationof
20OOwaves, resultingin S/Nu'"=0.05.The van der Meer predictionequationgiven in Figure
4.4b offers an upper bound (limit)to the data from the 1:50 approachslope, while the
modificationsuggestedby Allsop & Jones offers a similarupper bound for the 1:20 approach
slope data leadingto the conclusionthat the armour movementsproducedby uni-modal
waves follow previouslypublishedcriteria.
Having consideredthe influenceof uni-modalwavesupon armour movements,it is now
possibleto considerthe influenceof bi-modalwaves. The percentageof full displacements
observedfor tests conductedusingthe bi-modalwave conditionsare shown in Figure 4.5a.
The data has been re-presentedin terms of armourdamage level,S, in Figure 4.5b. Two
groups of bi-modalwaves were studied. The first group studiedwas defined as the "equal
energ/ test series,while the second group studiedwas classifiedas the "equal return period"
series(seegroupingexplanationsection3.1.2).
It is possibleto drawthreeconclusionsf rom Figures4.5a and b. The steepnessof the
approachslopeinfluencedthe numberof armourmovements.As was seen in the uni-modal
wave test series,there were more movementswith the 1:20 approachslope than with the
1:50 approachslope. The amountof armour damage increasedwith an increase in the
percentageof swell-seaduringthe "equal energy''tests. Duringthe "equal returnnperiod
tests the levelof armourdamagesustainedby the seawallremainedrelativelyconstant
despitethe range of differentswell-seacombinationstested.
The measuredvalues of S have been comparedto predictedvalues of S for both the 1:50
and 1:20 approachslopes in Figure4.6a. The same data have been presentedin nondimensionaltermsin Figure4.6b. Againvan der Meer'spredictionmethodhas been applied
to the 1:50 approachslope data, while the modificationof Allsop & Jones has been applied to
the 1:20 data. ln all cases the measureddamagewas less than that obtainedfrom the
predictionmethods.Test identifiershave been includedfor the datafrom individualtests on
Figure 4.6b. The "equal energy"test series data gives a clear trend of increaseddamage
level, S, with an increasedproportionof swell-seacomponent. The "equal return period"
series data was groupedtogetherand showed no such relationship.
It is possibleto comparethe resultsof the uni-modaland bi-modalwave tests by comparing
plotsgivenin Figures4.4b and 4.6b. There is evidenceto suggestthat
the non-dimensional
bi-modalwaves produce no worse armour movementsthan comparableuni-modalwave
conditions,i.e.those with the same significantwave heightand mean wave period.
ln summary,these tests have demonstratedthat:
.
More armour movementswere observedwith the 1:20 approachslope compared with the
1:50 approachslope;
15
sF|507 16/0298
tr
.
.
.
More armourmovementswereobservedwiththe shallowwaterdepthcomparedwith the
moderatewaterdepth;
were withinlimitsdefinedpreviouslyby van de Meer (for
Armourmovementobservations
the 1:50approachslope)and modifiedby Allsop& Jonesfor steepapproachslopes(1:20
approachslope);
Bi-modalseas did not influencearmourstabilitybeyondthat whichwould be givenby
existingpredictionmethods.
4.3
Run-up/run-down
werestudiedon 1:2 and 1:4 simpleseawallsusingan
Wave run-up/run-down
measurements
approachslopeof 1:50. Two differentstaticwaterlevelswere studied,14 and 16m,
(annotatedas 7 or 8 respectivelyin the followingpresentation).Statisticsof wave excursions
were determinedusingsoftwarewrittenat HR Wallingford.A summaryof the resultswas
presentedpreviouslyby Coates,Jones & Bona (Reference2); and summarisedin this
chapter in Figures4.7 and4.8. The levelexceededby only 2"/" ol wave run-up/run-down
events for bolh bi-modaland uni-modalwaves has been plottedseparatelyin the figures.
Investigations
by Ahrensand Allsopreportedin the CIRIA/CUR'RockManual"(Reference
12) used simple empiricalrelationshipsbetweenthe 2"h run-up levelsand the lribarren
numberin the form:
0< 6'n< 2.'18
€ m> 2 . 1 9
2 . 4 4< \ ^ < 5 . 2 2
Ref12 Eq 5.12,fromAhrens
Ref12 Eq5.13,fromAhrens
Ref12 Eq 5.16,fromAllsoPet al
R,2"7.
/ H. = 1.84E.
R,2"/./Hs=4.5-0.236m
R,2"7.
/ H. = 3.39-0'246r
for run-uplevelsare givenon Figure4.7. A comparisonof the
These empiricalrelationships
run-up/run-downresultspresentedin Figures4.7 and 4.8 indicatesthat bi-modalwave
uni-modalwave conditions.
conditionsproducehigherlevelsthancorresponding
Two groupsof bi-modalwaveswerestudied,an "equalenergy''groupand an "equalreturn
period"group (section3.1.2).The analysishas been continuedconsideringthe bi-modal
in Figures4.9to 4.12. The graphs
wave groupsseparately,in non-dimensionalterms,
underthe influenceof the "equalenergy''bi-modalwave group
obtainedfor run-up/run-down
levelsincreasedwith
are given in Figures4.9 and 4.10. As expected,run-up/run-down
increasedwave period(increasedlribarrennumber)for both structureslopesstudied. This
may be seen by comparingtests identifiedon the figureswith "a", wind sea only, throughto
swell-seaonly, "e". The bi-modalwave tests "b", "c" and "d" fallingbetweenthese 2,.extremes
followthe same trend,but thereis evidenceto suggestthat the bi-modalwave conditions
providedslightlyhigher levelsof run-up/run-down.A similartrend was identifiedin tests of
;'equalreturnperiod"bi-modalwaves,Figures4.11 and 4.12. Again,run-up/run-down
levels
increasedwith increasedwave period.
4.4
Wavetransmission
Wave transmissionmeasurementswere studiedusing bi-modalwaves for a 1:2 non-porous
breakwaterand a 1:2 bermedstructurebuilt with a 1:50 approachslope. Static water levels
of 14 and 16m were studied.Thesesimplebreakwaterstructuresincorporateda smallcrest
and a simple 1:2 rearslope. A summaryof the wave transmissiondata was presented
previouslyby Coates,Jones& Bona(Reference2).
The bi-modalwave data has beenconsideredin either"equalenergy''or "equalreturnperiod"
data is given in Figure4.13 ior the "equal
groups. A presentationof the wavetransmission
'l
energy"groupand Figure4.14 tor the "equalreturnperiod"group. (The simple :2
a smallcresthas been annotatedwith a "c" on the figures,whilethe
breakwaierincorporating
freeboard,R/H.i, has been
bermedstructurehas been annotated"b".) The dimensionless
coefficient,Cr. The bermedstructure
plottedin the figuresagainstthe wavetransmission
thanthe simpleseawall. Testsconductedusingboth water
sufferedless wave transmission
levels suffered higher levelsof transmissionunderthe higherwater level. An examinationof
both figures revealsthat for the two bi-modalwave groupingsa reductionin dimensionless
freebolrd usually resultedin a correspondingincreasein wave transmission.There is,
16
sR 507 16/02/98
tr
however,no evidenceto suggestthat bi-modalwavesprovidemorewave transmissionthan
correspondinguni-modalwaves.
4.5
Wave reflection
The reflectionperformances
of 1:2and 1:4 simpleseawallswere studiedfor both uni-modal
and bi-modalwaveconditions. A summaryof the wave reflectiondata was presented
previouslyby Coates,Jones& Bona(Reference2).
Uni-modaland bi-modalwave reflections
obtainedfor tests usingan approachslope of 1:50
by Allsop(Reference13) used a simple
have been summarisedin Figure4.15. lnvestigations
empiricalrelationshipbetweenthe reflectioncoefficientC,.,and the mean lribarrennumber (,,
in the form:
cr=d1^2 lb+1^2
where a and b are empiricallyderivedconstants.
The resultsof tests at HR Wallingfordsuggestvalues for coefficientsa = 0.96 and b = 4.8 for
is shownas a predictionline in Figure4.15.
a smoothstructure.The empiricalrelationship
Both uni-modaland bi-modalwavespossessedsimilar reflectionperformances,although
there appeared to be less data scatter with the bi-modal waves, and they appeared to provide
a better fit to the empiricalrelationship.
The reflectionanalysishas been taken a stage further in Figures4.16 and 4.17, where the bimodal wave data has been presentedin groups of "equal energy''in Figure 4.16 or "equal
return period"in Figure 4.17. Like the run-up/run-downanalysiswave reflectionsincreased
with increasedwave period (increasedlribarrennumber)for both structureslopes
investigated.There is evidenceto indicatethat for some bi-modalwaveconditions,wave
reflectionincreasedby approximately10% comparedwith correspondinguni-modalwaves
(see Figure4.16).
5 Practical applications of research results
findingsaredescribed
of the research
ln thischapterof the report,thepracticalapplications
for the two mainareasunderconsideration,
shinglebeachresponseand waveovertopping
performance
underthe influence
of bi-modalseas.
5.1
Shinglebeachprofiles
A genericmethodof predictingthe impactof swell energyon shinglebeach responsehas not
been achieveddue to the lackof compatibilitybetweenthe resultsfrom this study and those of
earlierwork by Powell(Reference4). However,impoilantconclusionscan be drawn that
provideguidancefor the designof shinglebeaches.
For sites that experiencesignificantswellthe worst case designconditionsmay be those with a
bi-modafspectrumor a spectrumwith a broad range includinga significanl(2O"/"or greater)
proportionof low frequencyenergy. The graphspresentedin Figures2.5-2,10can be used in
conjunctionwith Powell'soriginalworkto give a first estimateof the requiredcrest elevationand
width to preventfailureof the beachas a part of a coast defencescheme. lt should be noted
that wave conditionsused in this studyare unbrokenwaves at the toe of the shinglebeach.
The swell wave atlas (Reference1) providesoffshoreconditionsfor the coastsof Englandand
Wales which can be transformedinshore.
Preliminarytrialsof the methodusingwave conditionswith a constantreturnperiodsuggestthat
20% swell eventscan be importantin crest leveland cut-backpredictionsfor sites where swell
waves occurfrequently. Sensitivitytests for specificsites will be requiredto establishthe
most promisingdesigns,whichcan then be testedfully in a physicalmodel.
Limitationswith this approachare:
17
sR 507 16,/02/98
tr
of lessthan 0.01 and is thereforenot
Powell'swork did not includewavesteepnesses
validfor long periodswell;
shallownearshoreconditionsor low wave heights,
the presentstudydid not investigate
needed
to predictbeachresponsewhere waves are depth
so some extrapolation
will be
limitedby the nearshorebathymetry.
5.2
Overtopping
5.2.1 Oveftoppingin swell-seas
Desionsituation1: Geoqraphical
In geographicalareaswhereswell is consideredto be important,it shouldprobablybe
consideredas a separatedesigncase; in areaswherethe highestswell significanlwave heights
are less than half that of the highestwind-seas,it may not need specificconsideralion.As a
rough guide we would recommendthat coastalengineeringstudiesin exposedlocationsin the
south-westpart of the UK, southof Holyheadand west of the lsle of Wight,shouldconsider
swell as a potentialworstcase for design. This is broadlyin line with currentpractice,but we
would suggestthat it be made a moreformalrequirement,since its neglectmay leadto an
underestimateof the risk due to overtopping.
Swell is also importantin otherexposedareassuch as south and west lrelandand Scotland,
but as yet there is no swellwave atlasoutsideEnglandand Wales.
Desionsituation2: Depthlimitation
Swell may be importantwhere wave heightsare severelydepth-limitedat the toe of a seawall:
the fact that wind-seawave heightsmay be much higherthan swell-seawave heightsoffshore
is largelyirrelevant.A metreor so of swell may be a significantlyworse case than a (depthlimited)metre or so of wind-sea.Therefore,wherewaves are stronglydepth-limitedat a
structure,we would recommendthat swellbe consideredas a potentialworst case for designin
terms of overtopping,even in geographicalareas not particularlyexposedto swell. This tends
not to be done at present,and resultsfor Test Series1-3 suggestthat the risk due to
as a result.
overtoppingmay be underestimated
Overtoppinqrate for swell
Overtoppingincreaseswith wave period,but not by as much as had been expected. Above a
mean wave periodof aboutsix to ten seconds(the exactvalue beingdependenton wall slope
and water level)therewas littlefuftherincreasein overtopping.The SWALLOW(Owen,1980,
with
whichassumesthat overtoppingincreasesindefinitely
Reference6) empiricalformula,
swell wave ovedopping. Conversely,van
increasingwave period,significantlyover-predicted
der Meer and Janssen's(1995,Reference7) method,which has no effectof wave periodonce
wave breakinghas enteredthe surgingrange,significantlyunder-predictedswell wave
overtopping.
Workableempiricalpredictionmethod
An empiricaladjustmentfactorwas derived,as a functionof lribarrenNumber (and hence
implicitlythe form of wave breaking),to be appliedto the directOwen's predictions.In practice,
no adjustmentwas neededin the rangeof plungingwave breaking(E< 2.3) but reductionswere
made at highervaluesof (. There is no theoreticalbasisfor this adjustment,and it may not be
generallyapplicable,but it did providereasonablygood agreementbetweenSWALLOWand
the presentswell-seamodeltests. The difficultyin makingreliablepredictionsof overtopping
rate for swell-seasconfirmsthe continuingneedfor researchand physicalmodeltests of these
conditions. (A possiblealternativeto the empiricalmethodsusuallyused would be to apply
modelswellwaveovertoppingusinga empiricalwave
ANEMONE-OTTwhichcan numerically
flumeapproach.)
5.2.2 Oveftoppingin bi-modal seas
Overtoooinqrate for bi-modalseas
in bi-modalseas is usuallysomewherebetweenthe ratesfor wind-sea
The rate of over.topping
and swell-sea. The rateof overtopping(at leastfor the equal energytest series)increases
roughlyin proportionto the percentageof swell in the spectrum,even for quite small amountsof
18
sR 507 16,/02198
rate,wherepurewind-seaand pure
of meanovertopping
swell. This impliesthatfor calculation
swell have alreadybeen considered,bi-modalseasare not likelyto be a potentialworst case for
design. This does not necessarilymean,of course,that they may not be more importantin
other aspectsof design.
Desiqnsituationfor bi-modalseas
One situationin which bi-modalseas may be importantfor overtoppingis where a small amount
of swell is concealedwithinwhat appearsto be a severewind-sea. Tests 1b, 2b and 3b (with
20% swell)give up to twice as muchovertoppingas equivalentTests 1a,2a and 3a (with no
swell). A probabilisticapproachto assessingwaveconditionswould be requiredlo determine
the importanceof these pafticularbi-modalconditions.
Workableempiricalpredictionmethod
A reliableand physicallyplausibleapproachwas demonstratedfor predictionof overtopping
rate in bi-modalseas. All of the wave energy in the spectrum was applied firstly at the mean
wave periodforthe wind-seacomponentand secondlyat the mean wave periodforthe swellaverageof the two separaterateswas then
sea component;a simpleenergy-weighted
calculated.There appearsto be far less uncedaintyhere than in predictionof ovefioppingdue
to swell wave energyalone.
Warninoabout the empiricalmethod
It should be stressedthat the simple methodfor swell and bi-modal seas detailed in
Sections3.2.4 and3.2.5 appliesonly to overtoppingrate (and strictlyonly to the rangeof
situationsstudiedin the flume model). lt wouldnot necessarilywork well for other coastal
response parameters,and does not obviatethe need for physical model tests of bi-modal and
other sea states.
6
6.1
Conclusions
Hydraulicprocesses
Beach responseto bi-modalseas
Flume model resultsconfirmedfield observationsof the importanceof long periodenergyas a
significantinfluenceon beach response.A genericpredictivemethodhas not been developed,
but graphs are presentedthat provideguidancefor preliminarybeach design. Designthat does
not considerthis work may resultin beachfailure.
Overtoppinorate in swell-seas
Overtoppingincreaseswith the increasein wave periodfrom wind-sea,throughbi-modalsea,to
swell,althoughnot by as much as wouldbe predictedby Owen's method (Reference6). An
empirical adjustmentfactor was derived (as a function of lribanen Number) to be applied to
predictionsusingOwen'sequationsof swell-seaovertopping.The difficultyin makingreliable
predictionsof overtoppingratefor swell-seasconfirmsthe continuingneed for researchand
physicalmodeltestsof theseconditions.
Overtoopinorate in bi-modalseas
The rate of overtoppingin bi-modalseas is usuallysomewherebetweenthe ratesfor wind-sea
and swell-sea. The rate of overtopping(at leastfor the equal energytest series)increases
roughlyin proportionto the percentageof swellin the spectrum,even for quite small amountsof
swell. A workableapproachwas developedfor predictionof overtoppingrate in bi-modalseas.
All of the wave energyin the spectrumis appliedfirstlyat the mean wave periodfor the windsea componentand secondlyat the meanwave periodfor the swell-seacomponent;a simple
energy-weightedaverageof the two separateratesis then calculated.There appearsto be far
less uncertaintyherethan in predictionof overtoppingdue to swell wave energy alone.
Armour movements
Armour movementswere studiedusing a 1:2 seawallconstructedwith approach slopes of
either 1:50 or 1:20. The seawallwas tested using both uni-modaland bi-modalwave
conditions. Under uni-modalwave actionmore movementswere detectedwith the 1:20
approachslopethan with the 1:50approachslope. A standardpredictionmethod,developed
19
sR 507 16/02198
by van der Meer,providedan upperlimitto armourmovementsundertests on the seawall
with a 1:50approachslope. A secondpredictionmethod,developedby Allsopand Jones
allowingfor steeperapproachslopes,providedan upperlimitto armourmovementsfor tests
conductedon the seawallwith the steeper1:20approachslope. The "equalenergy''group of
associatedwith
bi-modalwavessuggesteda trendof increasingarmourdisplacements
increasedproportionof swell-sea.
Wave run-up/run-down
As expected,wave run-up/run-downexceedancelevelsincreasedwith increasingwave
period. There was evidencethat bi-modalseas producedslightlyhigherexceedancelevels
than corresponding
uni-modalwave conditions.
Wave transmission
Wave transmission
was studiedusinga simpleseawallstructureand a structureincorporating
a berm. Both structureswere constructedwith 1:2 f ront slopes. The level of wave
transmissionwas reducedbehindthe bermedstructurecomparedwith the transmission
freeboardresultedin a
behindthe simpleseawallstructure.A reductionin the dimensionless
correspondingincreasein wave transmission.There was, however,no evidencethat bimodalwave conditionsproduceddifferentlevelsof wave transmissioncompared with unimodalwaveconditions.
Wave reflections
Wave reflectionperformanceswere studiedusing 1:2 and 1:4 simple seawalls. Both bi-modal
and uni-modalwavespossessedsimilarreflectionperformances,althoughthere appearedto
be less data scatterwith the bi-modalwave conditionsstudied. There was evidence
indicatingthat under some bi-modalwaveconditionsthe reflectionwas increasedby about
1O%comparedwith correspondinguni-modalwaveconditions.
6.2
Designsignificance
Desiqnsituationswhere swellmav be important
In geographicalareas where swell is consideredto be important,it shouldprobablybe
consideredas a separatedesigncase. As a roughguidewe would recommendthat coastal
engineeringstudiesin locationsexposedto the Atlanticshouldconsiderswell as a potential
worstcasefor design.
Depth limitations
Swell may be impodantwhere wave heightsare severelydepth-limitedat the toe of a seawall:
the fact that wind-seawave heightsmay be much higherthan swell-seawave heightsoffshore
is largelyirrelevant.A metreor so of swellmay be a significantlyworse case than a (depthlimited)metreor so of wind-sea. Therefore,wherewavesare stronglydepth-limitedat a
structure,we would recommendthat swellbe consideredas a potentialworst case for designin
lerms of overtopping,even in geographicalareas not particularlyexposed to swell.
Desiqnsituationwhere bi-modalseas may be important
Bi-modalseas may be importantfor overtoppingwherea smallamountof swell is concealed
withinwhat appearsto be a severewind-sea. ln some tests,conversionof 2O"/"of the wind-sea
energyto swell producedup to twice as muchoverlopping.A probabilisticapproachto
assessingthe occurrenceof bi-modalconditions,is requiredto determinethe worst case
conditions.
Which hvdraulicprocesses?
fn bi-modalsea conditionscontaining 2O%swell,typicalof exposedoceanicshorelines,the
followingchecklistshows which processeswouldbe affectedby the presenceof the swell
component.
.
.
.
.
.
.
Shinglebeachprofile
Overtopping
Run-up
Armour
Transmission
Reflection
yes
probably
probably
probably
no
yes
20
sF 507 16,/0298
tr
7 ldentification of further research
The swellwaveatlas(Reference
1) providesguidanceon the predictionof bi-modalwaves
around Englandand Wales. However,littlework has been devotedto analysingwave records
to verify the predictions.As bi-modalwaves have been shownto be importantto beach and
seawalldesign,then it is recommendedthat work be undertakento addressthis gap.
The presentstudyon beachresponseconsidersa very limitedrangeof wave conditionsand
does not addressdepth limitedwaves. Work is neededto improvepredictionof wave spectraat
the beach face and, if necessary,to revisitthe flumestudyto determinethe effectof shallow
nearshorebed slopes.
The inabilityof existingformulaeto predictovertoppingin swell-seaconditionscame as a
surprise. Althoughnot directlyrelevantwithinthe presentresearchproject,this was perhaps
the single most interestingconclusionto come f rom the overtoppingtests. The reasonsfor this
were brieflyexploredin Sections3.2.3 and 3.2.4,but there is much more that could be done
with the presentdata. The empiricaladjustment
of SWALLOWfor use with swell-seas
describedin Section3.2.4was enoughto be able to completethe subsequentbi-modalsea
analysis,but is ratherunsatisfactory
for wider use. A numberof promisingpossibilitieswere
identifiedin Section3.2.4tor improvedpredictionsof overtoppingat swellwave periods. This
appears to be a priorityfor further researchbased on continuinganalysis of the existing data,
preferablyas soon as possiblewhilstthe ideasare stillfresh.
Furtheranalysisand developmentof empiricalmethodsfor the uother"parameters,i.e. run-up,
run-down,armourdamageetc, consideredin Chapter4 would be useful. However,it seems
more efficientto delaythis untildiscussionof the presentrepon is completeand untilthe
recommendedfurtherresearch(if any) on swell wave overtoppingis complete. Furtherwork on
empiricalpredictionmethodsfor overtoppingunderbi-modalseas shouldalso be delayeduntil
very much bettermethodsare availablefor swell alone.
8 Acknowledgements
The work describedhere is basedon studiescompletedby membersof the CoastalGroup of
HR Wallingford,for the Ministryof Agriculture,Fisheriesand Food,under Research
CommissionsFD02and FD07,and in part undersupportfrom the EuropeanUnionMAST lll
Project PROVERBSunder contractMAS3-CT95-0041.
This study was supervisedby Dr P J Hawkes,MrT T Coates and ProfessorN W H Allsop.
The flume work and data processingwas conductedby Mr R J Jones, Mr B Gouldbyand Mr
P F D Bona. The authorsare pleasedto acknowledgethe supportand assistancein testing
and analysisby Mr M Cavanna,Ms J Gilland Mr N P Keshwala.
21
sF 507 16i02/98
tr
9
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H a w k e sP J , B a g e n h o l m A CG, o u l d b y BP & E w i n g JA ( 1 9 9 7 ) .S w e l l a n db i - m o d a l
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wave climatearoundthe coastof EnglandandWales. HR Wallingford,
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on waveflumestudies.
CoatesTT, JonesR J & BonaP F D (1997).Technicalreport
HR Wallingford,
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CoatesTT & BonaP F D (1997).Rechargedbeachdevelopment-Afield studyat
HighcliffeBeach,Dorset. HR Wallingford,ReportSR 438.
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PowellK A (1990). Predictingshortterm profileresponsefor shinglebeaches.
HR Wallingford,
ReportSR 219.
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PiersonW J & MoskowitzL (1964). A proposedspectralform for fully developedwindseas basedon the similaritytheoryof S A Kitaigorodskii.Journalof Geophysical
Research,Volume69, ppS'l81-5190.
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Owen M W (1980). Designof seawallsallowingfor wave overtopping.HR Wallingford,
ReportEX924.
7
van der MeerJ W & JanssenP F M (1995).Wave run-upand wave overtoppingat
dykes. Publishedin Wave forces on inclinedand veftical structures,Ed. Z Demirbilek&
N Kobayashi,ASCE, New York.
B
BesleyP (1997). Overtoppingof sea defences. Publishedby HR Wallingfordas
EnvironmentAgencyR&D ProgressReportW5/006/1.
9
McConnellK J & AllsopN W H (1998).Wave pressureson inclinedslopes:the effect
of wind / swellseas and steepapproachslopes. HR Wallingford,ReportSR 511.
10
van der MeerJ W (1988). Rockslopesand gravelbeachesunder wave attack. PhD
No' 396, 1988.
Thesis,publishedas DelftHydraulicsCommunication
11
AllsopN W H &Jones R J (1994).Stabilityofrockarmouredbeachcontrol
structures.HR Wallingford,RepodSR 289 (revisedOctober1995).
12
Simm J D (Editor)(1991). Manualonthe use of rock in coastalandshoreline
engineering. Special Publication83, ConstructionIndustryResearchand Information
Association,London.
'13
AllsopN W H (1990). Reflectionpedormanceof rock armouredslopesin random
waves. 22ndInternationalConferencein CoastalEngineering,Delft (also published
paper No 37, HR Wallingford).
14
van der MeerJ W, TdnjesP & de WaalJ P (1998).A code for dike heightdesignand
on Coastlines,Structuresand Breakwaters,
examination.lnternationalConference
lCE. London.
22
sB 507 l6i02a8
tr
Tables
sR 507 16/02198
tr
Table2.1 Waveconditions used in the shingle beach tests
Test
Condition Wave conditions
number reference Wind-sea
H"t
(m) T^, (s)
Depth of
water (m)
Swell
H",(m)
T"o (s)
Testsfor comparisonwith SR219
0a
K02
o.75
5
14
0b
K04
1.5
5
14
0c
K06
2.4
5
14
0a1
K02
0.75
5
14
Oa2
KO2
0.75
5
14
0b1
K04
1.5
5
14
Testswithconstantreturnperiod 1 in 6 months)
14
1
0q6
4.4
8
2
5b
4
7.63
1.08
15
14
3
5c
3.4
7.03
1.27
15
14
4
5d
2.6
6.15
1.39
15
14
5
5e
1.5
15
14
1a
0q6
4.4
14
I
Tests with constanttotal spectralenerqy H. = 3.53m and Tn2 !]g
14
0e6
3.53
7
1b
3.12
8
2.5
I
1c
'1d
1.67
10
1e
6 reoeat
0e6
3.53
7 repeat
1b
3.12
7
1.67
11
14
9 repeat
1d
1.67
7
3.12
11
14
1.67
11
14
7
2.5
11
14
7
3.12
11
14
3.53
11
14
14
Tests with constanttotal spectralenerqy H" = 2.12m and To2= 19s
14
7
11
0b4
2.12
12
3b
1.91
0.94
19
13
3c
1.5
1.5
19
14
3d
0.94
1.91
19
14
15
3e
2.12
19
14
1.91
19
14
14 reoeat 3d
0.94
7
7
14
'14
sR 507 16/02198
tr
Table2.1 continued
Tests with constanttotal spectralenergyH" = 2.83m aAdfpe-l!9
14
16
0d6
2.83
17
2b
2.56
7
1.2
14
14
18
2c
2
7
2
14
14
19
2d
1.2
7
2.56
14
14
20
2e
2.83
14
14
16 repeat 0d6
2.83
14
7
Tests with constanttotal spectralenergy H" = 2.83m and Tr2 = !!q
21
7b
2.56
7
1.2
11
14
22
7c
7
2
11
14
23
7d
2
'1.2
7
2.56
11
24
7e
2.83
11
't4
14
H" = 2.83mand To2= 19s
Tests with constanttotalspectralenerqy
25
8b
2.56
7
1.2
19
14
26
8c
2
7
2
19
14
27
8d
1.2
7
2.56
19
14
28
8e
2.83
19
14
'l
Tests with constantlotal spectralenerqv H" = 2.'l2m and To2= I5
29
9b
1.91
30
9c
1.5
31
9d
0.94
32
9e
0.94
11
14
7
1.5
11
14
7
1.91
11
14
2.12
11
14
sR 507 16/02/98
tr
Figures
sR 507 '16/02/98
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tr
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tr
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Figure 2.2 Beach profiles - Hordle,December1994
sR 507 16/O2i98
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02
0.3
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3.17m
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Highwater= 1.31mODalO4.22hrs
=1'O3m
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Figure2.3 Wavespectra at peakwaterlevetsduring storm event of
7-8 December1994
sR507 16/02/98
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03
(Hz)
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=1 .13m
Hrm(sudr)
=2.37m
Hmooind)
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30/t2le4o9o0!0
30/12/9406S0$0
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=1 .42m
Hms(s!,,ell)
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Hmo(wino)
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Figure 2.4 Wave spectra at peakwater levels during storm event of
29-30December{994
sR 507 16,/02198
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tr
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sR 507 t6/02/98
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Figure2.10 Swell influenceon crest cut back: Hs = 3.53m
E'
o
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=
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tr
Test 1a: Wind-sea
Hs=3.53Tp=7s
o
o
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0.00
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frequency
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