wave forces on vertical and composite breakwaters · 2020. 4. 2. · r roughness or run-up...

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Wave Forces on Vertical andComposite Breakwaters

N W H AllsopD VicinanzaJ E McKenna

Report SR 443March 1995, revised March 1996

g"- WattingfordAddress and Registered Office: HR Wallingford Ltd. Howbery Park, Wallingiford, Oxon OX10 8BATel: + 44 (0)1491 835381 Fax: + 44 (O11491 832233

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sR 443 0209/96

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sR 443 0209/96

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The work described in this report was part-funded by the Department of Environment ConstructionSponsorship Directorate under research contracts PECD 7161263 and716/312. and part by theEuropean Union MAST programme under contracts MAS2-CT92-0047 and MAS3-CT95-0041.Additional research support was given by the University of Sheffield, Queen's University Belfast, and bythe Department of Hydraulics of the University of Naples, with further funding for visiting researchers atWallingford from the Department of Education of Northern lreland, DENI, the TECHWARE programmeof COMETT, and the National Councilfor Research in ltaly, CNR.

The project co-ordinator for the MAST ll MOS-Project under contract MAS2-CT92-0047 was Dr-lng H.Oumeraci of Franzius Institute of Hannover UnMersity. The project officer for European CommissionDirectorate General Xllwas Mr C. Fragakis.

The project co-ordinator for the MAST lll project PROVERBS under contract MAS3-CT95-0041 wasProfessor H. Oumeraci of Leichtweiss Institute of University of Braunschweig. The project officer forEuropean Commission Directorate General Xll was Mr C. Fragakis.

The DOE nominated officer for research contracts PECD 716/263 andT/6/312 was Mr P.B. Woodheadand HR Wallingford's nominated officers were Dr W.R. White and Professor N.W.H. Allsop. This reportis published by HR Wallingford on behalf of the DOE, but any opinions expressed are those of theauthors, and not necessarily those of the funding department.

The research described in this report was conducted within the Coastal Group of HR Wallingford, atQueen's University of Belfast, and at the University of Naples, under the overall supeMsion of ProfessorN.W.H. Allsop. The HR Wallingford job numbers were CAS 41, CAS 58, and CAS 169. The HRWallingford file was ClEll/3.

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IV sR 443 02109/96

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Wave Forces on Verticaland Composite Breakwaters

N W H AllsopD VicinanzaJ E McKenna

Report SR 443March 1995, revised March 1996

This report gives information on wave loadings on vertical and composite breakwaters and relatedharbour or coastal strucfures. The report reviews types of vertical breakwaters used around the UK, inEurope, and further overseas, and identifies design methods in use in the UK, Europe, and Japan.Analysis of performance in service, and of research studies, shows that present design methodsunderpredict wave loads under wave impact conditions, and are not able to identify reliably geometric /wave conditions which lead to such impacts.

ComprehensMe 2-dimensional hydraulic model tests were conducted in a random wave flume at HRWallingford to measure wave pressures on a wide range of simple and composite vertical walls, undernormal wave attack (9=0"). The test results have been used to:r Assess the reliability of existing prediction meithods;r ldentify the ranges of geometrb and wave conditions which lead to wave impacts;r Develop simple methods to estimate wave forces under impact conditions.

The results of the tests have been compared with predictions by a number of different methods.Analysis of the percentage of impacts relative to all waves has been used to define a new decisiondiagram which summarises parameter regions in which wave conditions and wall/ mound geometrieslead to breaking wave impacts. For pulsating wave conditions, Goda's method has been found to begenerally appropriate, but lor wave impact conditions, it under-estimates loads significantly, even wheneXended by Takahashi. Up-lift forces are generally well predicted by Goda's method for pulsatingconditions, but again under-estimated for impact conditions. For wall configurations that most resemblecrown wall sections, the method in the CIRIA Rock Manual developed by Bradbury & Allsop givesgenerally saf e predictions.

The results of these studies are intended to be of direct use to engineers analysing the stability ofvertical or composite walls in deep water, in harbours, or along the shoreline. The prediction methodsderived here, and/or the test results themselves, may be used to estimate wave loadings on a widevariety of structures, existing or in design. The report is also written for other researchers working in thisfield, to illustrate the range of data available for more detailed analysis, identify regions of continuinguncertainties, and to assist set priorities for future studies.

The work reported here was part{unded by the Department of Environment Construction SponsorshipDirectorate under research contracts PECD 7161263, PECD 7161312 and Cl 39/5/96, and part by theEuropean Union MAST programme under the MCS-Project, contract MAS2-CT92-A047, and later thePROVERBS project, contract MAS3-CT95-0041. Additional support was gMen by the University ofSheffield, Queen's UnMersity Belfast, and by the Department of Hydraulics of the University of Naples,with further funding for visiting researchers at Wallingford from the Department of Education ofNorthern lreland, DENI, the TECHWARE programme of COMETT, and the National CouncilforResearch in ltaly, CNR.

For any further information on these and related studies, please contact N.W.H. Allsop, in the CoastalGroup at HR Wallingford.

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VI sR44302t09,86

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A"a

Armour crest freeboardEmpirical coefficient

Bb Crest width of rubble mound bermB" Width of caissonB"* Width of crown wallB"q Equivalent width of rubble mound in front of wall, averaged over height of moundB'' Structure width at static water levelBt Width of rubble mound at toe levelb Empiricalcoefficient

C. Coefficient of wave reflectionC,(f) Reflection coefficient functionCr Coefficient of wave transmission

D Particle size or typical diameterDn Nominal particle diameter, defined (M/p)t") for rock and (M/p")18 for concrete armourDnso Nominal particle diameter calculated from the median particle mass Muod Water depth over toe mound in front of wall

Ei Incident wave energyE, Reflected wave energyq Transmitted wave energy

FB Buoyant up-thrust on a caisson or related elementFF Earth pressure force on a caisson lrom the seaward part of the moundFR Earth pressure force on the caisson from the harbour side of the moundFs Factor of safetyFh Horizontalforce on caisson or crown wall elementFnrr.r* Horizontalforce at 99.8% non-exceedance levelFn.'ouo Mean ol highest 1/250 horizontalwave forcesFu Up-lift force on caisson or crown wall elementFuo.*r. Up-lift force at 99.8% non-exceedance levelFunso Mean of highest 1/250 up-lift wave forcesf Wave frequencyf, Frequency of peak of wave energy spectrum, = llTo

g Gravitationalacceleration

H.* Maximum wave height in a recordH,o Significant wave height from spectral analysis, defined 4.0m005H"o Otfshore significant wave height, un-affected by shallow water processesH" Significant wave height, average of highest onethird of wave heightsHo^ Wave height exceeded by 2"/o of waves in a recordH'uo Mean height of highest 1/10 of waves in a recordh Water depthhb Height of berm above sea bedh" Height of rubble mound / core beneath caisson / wallh, Exposed height of caisson or crown wall over which wave pressures acth. Water depth at toe of structure

k Permeability (Darcy), also used as wave number = 2nlL

vtl sR 443 02/09196

trL Wave length, in the direction of propagationL. Offshore wave length of mean (T.) periodLo Deep water or offshore wave length - gllZnLe Offshore wave length of peak (To) periodLps Wave length of peak period at structure

Mh Overturning moment due to horizontalwave forceM, Overturning moment due to up-lift forceMt Overturning moment due to allwave loadsMuo Median mass of armour unit derived from the mass distribution curuemo Zeroth moment of the wave energy density spectrumm2 Second moment of the wave energy density spectrum

N*o Number of waves overtopping expressed as proportion or "/" of total incidentN. Number of zero-crossing waves in a record = TRff,nv Volumetric porosity, volume of voids expressed as proportion of total volume

P Encounter probabilityP, Target probability of failurep Wave pressure

q Mean overtopping discharge, per unit length of structureQ" Superficial velocity; or specific discharge, discharge per unit area, usually through a

porous matrix

R" Crest freeboard, height of crest above static water levelRu Run-up level, relative to static water levelR," Run-up levelof significant waveRuex Run-up levelexceededby 2/" of run-up crestsr Roughness or run-up reduction coefficient, usually relative to smooth slopesSF Shear force at caisson / rubble boundaryS(f) Spectraldensitysm Steepness of mean wave period = 2nHlgTfsp Steepness of peak wave period = zn{lgTp"

T, Mean wave periodT* Return period = (1 - (1 - PJln)-lTo Wave period of spectral peak, inverse of peak frequencyTR Length of wave record, duration of sea stateT" Wave period associated with H", not statistically significant

u, v, w Components of velocity along x, y, z €xesx,y,z Orthogonalaxes, distance along each axis

z Level in water, usually above seabed

c (alpha) Structure front slope angle to horizontalB (Beta) Angle of wave attack to breakwater alignmentp (rho) Mass density, usually of fresh waterp* Mass density of sea waterP,, 9", 9" Mass density of rock, concrete, armour unitsA (delta) Reduced relative density, eg. (p/p,)-lA (lambda) Model/ prototype scale ratio (Froude); also used as fraction of aerationp (mu) Coefficient of friction, particularly between concrete elements and rock; also p(x) =

mean of x€ (xi) lribarren number or surf similarity parameter, = lano.lsla

vi i i sB 443 02109196

trq., Eo lribarren number calculated in terms of s, or so0 (phi) Angle of internal friction of rock or soilr (tau) Shear strength of rock mound or soil, also used as the time interval between sampleso (sigma) Stresso(x) Standard deviation of xo' Normalised standard deviation o/pon Normal stress

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sR 443 02/09/96

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Title pageContractSummaryNotationContents

Page

iiiiv

viixi

I n t r oduc t i on . . . . . . . . . . . 11 .1 The p rob lem . . . . . 11 .2 Te rmso f re fe rence fo r thes tudy . . . . . . . 21 .3 Ou t l i neo f t hes tud ies . . . . . . . . . . 21 .4 Ou t l i neo f t h i s repo r t . . . . . 3

Vert lcalbrealrwatersandrelatedstructures ... . . . .52 .1 Pu rposeand fo rmo fs t ruc tu res . . . . . . . . 52.2 Developmentof ver t ica lbreal<waters . . . . . . . . . 6

2.2.1 Historicalbackground .. . ... .. 82.2.2 Construction of breal<waters, piers, and seawalls . . . . I2.2.3 Construction of vertically-composite breaktaters . . . 10

2.3 Performance in seruice .. -. . . . 14

Des ign me thods . . . . . . . 173.1 Design considerations and failure modes ... . . 17

3.1.1 Structura l fa i lures . . . . .173.1.2 Functionalfai lures .. . .173.1.3 Design approaches .. . 18

3.2 Designformulaeforwaveforces/pressures . . . . . . . . 193.2.1 Horizontaltorces ... . .203.2.2 Up-liftforces ...263.2.3 Seaward or suction forces . . . . 27

3.3 Hydraulic modeltests . .. . .. . . 273.3.1 Selection of modelscale .. . . . . . . . . . 28

Design of research studies . . . 314 .1 Ove ra l l p l ano f s tud ies . . . . . . . . 314 .2 Des igno fmode l t es t s . . . . . . . . 33

4 .2 .1 Tes ts t ruc tu res . . . . . . . 334.2.2 Testfaci l i ty .. . .354.2.3 Testcondi t ions. . . . . . .35

4.3 Instrumentationandtestmeasurements .. . . .364.4 Test procedures . . . . . . . 37

4.4.1 Wave measurements . . . - . . . . 374 .4 .2 Waveove r topp ing . . . . . . . . . . 374.4.3 Pressures . . . . . 37

Resu l t so f t es tmeasuremen ts . . . . . . . 395 .1 Examp lep ressu remeasuremen ts . . . . . . . . . . 395.2 Definition of pressure / force events . . . 435 .3 Da taqua l i t yand repea tab i l i t y . . . . . . . . 445.4 Datahandl ing/s torage/arch iv ing . . . .45

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trContents continued

Analysis of wave force / pressure results . . . 476.1 Stat is t ica ld is t r ibut ionof forces . . . . . . .486 .2 Ana lys i so f impac tsand fo rces . . . . . . . 51

6 .2 .1 S imp leve r t i ca lwa l l s . . . . . . . . . 526.2.2 Compositestructures,horizontalforces ..... 536.2.3 Compositewalls,up-l i f t forces ... . . . .56

6.3 Compar isonwi thdesignmethods . . . . .596 .3 .1 S imp leve f t i ca lwa l l s . . . . . . . . . 596.3.2 Composite walls, horizontalforces . . . 606.3.3 Compositewalls,upJift forces ... . . . .636 .3 .4 C rownwa l l s . . . . . . . . . 646.3.5 Overallstability of caissons on rubble mounds . . . . . 66

6.4 Pressure gradientsand localpressures . . . . . .706.4.1 Verticaldistributionsof pressures ....706.4.2 Pressuregradients .. . .72

6 .5 P ressu re r i se t imes / impu l ses . . : . . . . . . . . . . 73

App l i ca t i ono f r esu l t s . . . . . . . . 757 .1 fn f l uenceo fsca lee f fec ts . . . . . . 75

7.1.1 Studies on scaling ... . 757.1.2 Scaling of impacts from HR Wallingford/ Bristol studies .. . . . .. .. 76

7.2 Response periods and impact durations ' ... . 79

Conc lus ionsandrecommenda t ions . . . . . . . . 818.1 Conclusions . . . . 818.2 Recommendat ionsfordesign/analys is . . . . . .828.3 Recommendat ionsfor fu ture research . . . . . . .82

Acknowledgements .. . . 85

References . . . . . 8710

TablesTable 4.1Table 4.2

FiguresFigure 1.1Figure 2.1Figure 2.2Figure 2.3Figure 2.4Figure 2.5Figure 2.6Figure2.7Figure 2.8Figure 2.9Figure 2.10Figure 2.11Figure2.12

Main geometrical parameters for walls and moundsTest conditions, wave steepness, wave height, and water levels .

Ver t ica landcomposi tebreakwaterconf igurat ions. . . . . . . . ' . 1Stone blockwork, StCatherine'sbreakwater,Jersey 1996 . . . ' . . . . . 6Concreteblockwork,EastArmBreakwater ,Dover . . . . . . . . . 7Tra in ingwal l lbreakwater , Nor thTyne . . . . . . . .7Layout of Alderney harbour, after collapse of breakwater outer section . . . ' . ITimbercaisson orGreate Chest used forthe Mole, Tangier, 1677 ... . . . . . . ICircularcaissons used at Hantsholm and Brighton Marina . .. ... .. 10Cross-section of Aldemey breakwater during construction, 1855 . . . 11Cross -sec t i ono f A lde rneyb reakwa te t , . . . . . . . . . . . . 11Concretecaissonsforprotectionof Sestri lndustrialAirport, 1938 . . . .-. . . 12Caisson breakwater with set-back crest wall, Bagnara, 1985 . . . . - . 12PerforatedchambercaissonbreakwateratPonza . . . . . . . . 13Tsunamiprotect ion breakwateratOfunato . . . . . . . . 13

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Figure 2.13Figure 2.14Figure 3.1Figure 3.2Figure 3.3Figure 3.4Figure 3.5Figure 4.1Figure 4.2Figure 4.3Figure 4.4Figure 4.5Figure 4.6Figure 4.7Figure 5.1Figure 5.2Figure 5.3Figure 5.4Figure 5.5Figure 5.6Figure 5.7Figure 6.1Figure 6.2

Figure 6.3Figure 6.4Figure 6.5Figure 6.6Figure 6.7Figure 6.8Figure 6.9Figure 6.10Figure 6.11Figure 6.12Figure 6.13Figure 6.14Figure 6.15Figure 6.16Figure 6.17Figure 6.18Figure 6.19Figure 6.20Figure 6.21Figure 6.22Figure 6.23

Figure 6.24

Figure 6.25

Figure 6.26

Tsunamiprotect ion breakwateratKamaishi . . . . . . . . 14Harbourb reakwa te rw i thw ideca issona t . . . . . . . . . . 14Decision tree for impulsive breaking conditions . . . . . 20Pressure distribution and definitions for caissons, after Goda (1985) . . . . . . 21Verticaldistributions of pressures using Goda, Minikin, and SPM methods . 23Horizontal / up-lift forces on crown wall, after Simm (1991) . . . . . . . . 26Formsof up- l i f td is t r ibut ions,af terMcKenna(1996) . . . . . . . . 27Deepwave f l ume . . . . . 31Caisson/mound geometricalparameters . ... 32Pressuret ransducerposi t ions . . . . . . .32S t ruc tu re 1 . . . . . . . . . . 33S t ruc tu re2 . . . . . . . . . . 33S t ruc tu re 3 . . . . . . . . . . 34S t ruc tu re I . . . . . . . . . . 34Typical pressure events from test 10003 on Structure 1 . . . . . . . . . . 39lmpactevent f romtest 10003on Structure 1 . . . . . . .40Small impact event from test 10003 on . . . . . . 40Double-peaked eventfrom test 10003 on Structure 1 . . . . . . . . . . . . 40Pu fsa t i ngeven t f romtes t10003onSt ruc tu re l . . . . . . . . . . . 41Exampfe pressure / time series over height of caisson . . . . . 42Exampfe fo rce - t imeser ies . . . . . . . . 43Main parameter regions ... . . . 47Example Weibulldistribution of horizontalforces for pulsating andimpac tcond i t i ons . . . . . 48Weibulldistribution of horizontalforces, vertical and composite walls . . . . . 49Weibulldistribution of horizontalforces, effect of berm width . . . . . . 51fnffuence of H./d on % impacts, P,, verticalwall . . . . . 52fnffuenceof Hrn.rr lHoon%impacts, P,,vert icalwall . . . . . . . . 52Dimensionless horizontal forces against H"/d, vertical wall . . . . . . . . 53Influence of H./h" on % impacts, P,, high mound . . . . 53fnfluence of Ho/h" on % impacts, P,, low mound . . ... 54Dimensionless horizontal forces against H",/d, low mound . . . . . . . . 54Influence of H"/h" on o/o impacts, P,, high mound . . . . 55Influence of H"n/d on o/o impacts, P,, high mound . . . . 55Influence of B"ol\ on 7" impacts, P,, high mound . . . . 55Flow chart of parameter regions for wave impacts . . . 56Weibull distribution of up-lift forces, s,=0.04, H"/d=0.45 . . . . 56Weibufl distribution of up-lift forces, s,=0.04, H"/d=0.62 . . . . 57Weibull distribution of up-lift forces, s,=0.04, Ho/d=0.98 . . . . 57Weibuff distribution of up-lift forces, s.=0.04, H"{d=2.54 ... . 57Up- l i f t f o rces fo r0<H. /d<3 .5 . . . . . . . . 58Dimensionless up{ift forces against H"/d, 0<HJd<1.5 . . . . . 58Dimensionless up-lift forces against H./d, 2<H./d<3.5 . . . . . 58Measured / predicted horizontal forces, Goda, vertical walls, H"/d<0.35 . . . 59Dimensionless horizontalforces against H",/d, verticalwalls, A & V's predictionHJd>0 .35 . . . . . 59Measured / predicted horizontal forces, Goda and A & V, vefticalwa l l s ,H r /d<0 .35 . . . . . . 59Measured / predicted horizontal forces, Goda & Takahashi, lowmounds, H"/d<0.65 ... 60Measured / predicted horizontal forces, Goda & Takahashi, low mounds,0 .65<H" /d<1 .2 . . . . . . . 60

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Figure 6.27

Figure 6.28

Figure 6.29

Figure 6.30

Figure 6.31

Figure 6.32

Figure 6.33

Figure 6.34

Figure 6.35

Figure 6.36

Figure 6.37Figure 6.38Figure 6.39Figure 6.40Figure 6.41Figure 6.42Figure 6.43Figure 6.44

Figure 6.45

Figure 6.46

Figure 6.47Figure 6.48Figure 6.49Figure 7.1

Figure 7.2

Figure 7.3Figure7.4Figure 7.5Figure 7.6Figure7.7Figure 7.8

Appendix

Measured / predicted hirizontal forces, Goda & Takahashi, high mounds,. 30<H" /d<0 .55 . . . . . . . . 61Measured / predicted horizontal forces, Goda & Takahashi, high mounds,.650<H" /d<1 .3 ,sho r tbe rm. . . . . 61Influence of B*/\ on horizontalforces, high mounds, intermediate bermw id ths . . . . . . . . 61Dimensionless horizontal forces against H./d, high mounds, G & T'sp red i c t i ons ,0 .65<H" /d<1 .3 . . . . . . . . . 62Dimensionless horizontal forces against Ho/d, high mounds, G & T'sp red i c t i ons , 0 .65<HJd<1 .3 . . . . . . . . . 62Measured / predicted horizontal forces, G & T and V's upper limit, highmounds , w ide be rms . . . . . . . . 62Dimensionless up-lift forces against H"/d, low mounds, Goda's predictions,0 .65<H" /d<1 .4 . . . . . . . 63Dimensionless up-lift forces against H"/d, high mounds, Goda's predictions,0 .65<Hs /d<1 .4 . . . . . . . 63Dimensionless up-lift forces against H"/d, high mounds, Goda's predictions,0.65<HJd<2,pulsatingcondit ions ... .63Dimensionless up{ift forces against H"/d, high mounds, Goda's predictions,0.65<HJd<2, impactcondi t ions . . . . . .64Dimensionless horizontalforceson crownwalls, -4<H./A"<B . ..... 65Dimensionless up-lift forces on crown walls, -4<Hn/Ao<8... . . . . ... 65Forces/reactionsforoveral lstabil i tyanalysis .. . . . . 66Simpl i f iedmodel forovera l ls tab i l i tyanalys is . . . . . . .67Verticaldistributions of pressures, verticalwall, H"/d<0.35 . . . ..... 70Verticaf distributions of pressures, vertical wall, H",/d>0.35 . . ...... 71Etfect of berm width on vertical distributions of pressures, composite walls . 71Measured distributions and goda / Takahashi predictions for pulsatingcond i t i ons (S t ruc tu re3 ) . . . . . . 71Measured distributions and Goda / Takahashi predictions for impactconditions (Structure 4l . .. .. . 72Measured distributions at exceedance levels of 11250,99.6% and 99.8%,impact conditions (Structure 1) . . . . .. 72Maximum pressures and rise times (after Hattoriet al) . .. . . 73Comparison of experimentaldata and Hattori's predictions for rise times . . 74Experimental data (this study) and Hattori's prediction lines . ...... 74Pressure impulses from field and model for wave impacts on armour unit,f i nea r . . . . . . . . . 76lmpact pressures from field and model for wave impacts on armourun i t , l i nea r . . . . . 76Weibull probabilities for pressure impulses from field and model . . . 77Weibull probabilities for wave impact pressures from field and model . . . . . 77Cor rec t i on fac to rs fo rp ressu res . . . . . . . . . . . 77Pressurer iset imes,modelandf ie ldmeasurements . . . . . . . 78Weibullprobabilities of impact pressure rise times from modeland field . . . 78Correct ionfactorsforr iset imes. . . . . .78

Summary of test conditions, structural configurations and results.

xtv sR 4€ qz09l96

trIntroduction

Harbour breakwaters and related marine structures may be of two generalforms:

a) lmpermeable and solid with vertical or very steep faces;b) Rubble mound with permeable and rough side slopes.

Much research effort has addressed the stability and hydraulic performance of rubble moundbreakwaters, but relatively less effort has been directed towards the stability of vertical walls. Relativelyliftle reliable information is available on wave forces / pressures on vertical / composite walls.

This report presents results from new research studies to derive information on wave forces acting onvertical and composite walls and related maritime structures, Figure 1.1. The studies were targetedprimarily at vertical breakwaters, especially those formed by monolithic caissons, or by large concreteor stone blocks joined to act monolithically. Some results of these studies can also be applied tocoastal seawalls or other steep or vertically faced structures, and some results can be applied to crownwalls on rubble mound breakwaters or seawalls, although the eperimental work was not specificallyconfigured to address those structures.

HWL

Figure 1.1 Vertical and composite breakwater configurations

1.1 The problemBreakwaters and related structures are built primarilyto gMe protection against wave attack on shipmoorings, manoeuwing areas, port facilities, and adjoining areas of land. Design methods for suchstructures are generally well established, but some important aspects of those design methods are nowseen to be uncertain or of limited application for some configurations. Recent research studies inEurope have confirmed that design methods for wave forces based on studies in Japan on caissonbreal<waters are limited in their application; give little data on local wave pressures; and may severelyunder- or over-estimate loadings in some important cases. Using such methods, some structures maybe over-designed, and hence too expensive. For others risks of failure may be under-estimated,leading to danger to personnel and property.

European engineers including UK consultants and contractors are involved in analysis, design,rehabilitation, and construction of harbour and coastal structures worldwide. UK design methods /codes are used internationally. lt is therefore particularly important that such methods are well-basedand reliable.

sR 443 02/09196

tr1.2 Terms of reference for the studyThe primary objective of the work commissioned by DOE under contractT16/312 was to provide designdata for vertical faced breakwaters and related structures on the stability response under wave attack.The programme of work described at the start of the studies was summarised:

a) describe the strength and hydraulic properties of the principalstructure types andcomponent elements;

b) identify the principal failure modes for such structures, and each of the main elements;c) describe the design methods used internationally;d) carry out parametric model studies to quantify the responses of selected structure cross-

sections to the appropriate range of input conditions;e) identify the remaining areas of uncertainty, specification of future work needed for further

improvement in economy and/or safety;0 describe general design rules for vertical wall structures, identifying the range of application,

and suggesting target factors of safety.

These terms of reference were expanded to allow the basic test set-up to be shared with two relatedprojects. Studies under the Harbour Entrance project supported by DOE under contract7161263addressed the hydraulic performance of vertical walls. Under the European Union MAST researchprogramme on Monolithic Coastal Structures (MCS-Project), HR Wallingford assisted by otherEuropean researchers extended those studies on hydraulic performance of simple vertical walls toinclude a range of 'low reflection" alternative structure types. These included caissons with voidedchambers, perforated wave screens, and armoured slopes in front of vertical walls. Results of thosestudies have been presented separately, see Allsop (1995), Allsop et al (1995b), McBride et al (1995a),and McBride & Watson (1995).

The studies on wave loadings and breakwater stability discussed here were expanded to includecontributions from researchers from Belfast and Naples developed in collaboration with HR andUniversity of Sheffield. The Ph.D project by McKenna at Queen's University Belfast was intended toaddress in more detailwave up-lift pressures on caisson breal<waters and related elements onpermeable foundations, but the final project title adopted was slightly less specific as "Wave forces oncaissons and breakwater crown walls". This study was started in October 1993, and is to be completedin September 1996. A further Ph.D project by Vicinanza at the University of Naples addressedtemporal and spatial variation of wave impact pressures on vertical and composite walls with a projeettitle of *Pressioni e forze di impatto di onde frangenti su dighe a paramento verticale e composte".Vicinanza's collaboration in these research studies started in November 1994, and his Ph.D studies aredue to be reported in 1997.

The studies discussed in this report were conducted in a 2-dimensional (2-d) wave flume under normalwave attack. A later project supported by Department of Environment under contract Cl 39/5/96 andEU MAST lll under contract MASS-CT95-0041, extended work reported here to cover effects of obliqueand short-crested wave attack using a 3-dimensionalwave basin, the UK national Coastal ResearchFacility. These tests are reported in HR report SR 465 by Banyard et al (1996).

1.3 Outline of the studiesDivision of experimental work within this project was relatively straight-forward. Design of the modelstudies, the test sections, measurement systems, and the test programme were completed atWallingford with assistance from Sheffield and Belfast during 1993 / 94. Model tests by the HR /Sheffield / Belfast team were completed in December 1994.

Expansion of the project to meet requirements of the other partners had however increased the number/ complexity of tests substantially, and therefore the volume of data collected. Analysis therefore tookmore resources than anticipated, but did generate both more data and more reliable information thancould otherwise have been expected. The main activities of each partner may be summarised:

sR44302l09l

trHR Wallingford - overall design of studies; provision of test facility, measurement equipment, teststructures, technical and computing support; lead analysis and reporting; and overall superuision.McKenna from Belfast supervised by Whittaker and Allsop extended the study to include moredetailed analysis of up-lift pressures; assisted in test design; conducted many of the tests; andanalysed up-lift forces and overall forces / stability.

Vicinanza superuised by Benassaiand Calabrese from Naples modified and extended theanalysis programs, and assisted in detailed analysis of wave pressures / forces and statisticalanalysis of wave forces, of pressure gradients and impulses.

Allsop at Sheffield reviewed much of the historical information on vertical breakwaters in the UK;provided support and supervision for the visiting researchers at Wallingford particularly in analysisof wave forces; and compiled and edited research papers and this report.

Studies under the MAST MCS project were divided into four areas covering: Task 1, impact forces andstructure / foundation interaction; Task 2, scaling problems and air entrainment; Task 3, localmorphologicalchanges; and Task 4, wave overtopping and constructional measures. HR Wallingfordwere contracted to contribute to Task 3.1 on wave reflections, Task 3.3 on scour at vertical walls, andwas scheduled to lead Task 4.3 on constructional measures to reduce reflections and overtopping.

During early stages in the MOS-Project, it became apparent that additionalwork was needed on impactforces / pressures. Analysis by Oumeraci et al (1995) demonstrated that impact loads are of criticalimportance in the stability of caisson breakwaters against progressive movements, and Allsop & Bray(1994) demonstrated that short duration impacts are of considerable importance to the integrity ofblockwork walls. ln the light of these findings, the Wallingford / Sheffield / Belfast / Naples teamexpanded their contribution to the MCS project with new studies on wave impact pressures added toTask 1 and discussed here. Work under Task 4.3 was also expanded, and has been reported in detailin the MCS and Harbour Entrances reports, see McBride et al (1996) for a summary.

1.4 Outline of this reportThe main types of vertical walls in use in harbours or along coastlines are described in Chapter 2, anddesign methods available lo determine the main hydraulic and structural responses are discussed inChapter 3.

The design of research studies developed under this project, the structure configurations tested, andthe test equipment and procedures are described in Chapter 4.

Resulls of the wave pressure I lorce measurements are first described in Chapter 5, which discussesthe form and handling of the data collected, and definitions of wave pressure / force events needed toreduce the large volumes of data to more manageable proportions. The detailed analysis of thesemeasurements are lhen discussed in Chapter 6, covering the distinctions between pulsating andimpact conditions, and exploring the different prediction methods needed for these different responseregions.

Application of the wave force results, and the prediction methods derived from them are discussed inChapter 7, including a discussion on the effects of any scale corrections needed for wave pressures.Overall conclusions, and recommendations for design / analysis practice, and for future research, areaddressed in Chapter 8.

sR 443021c'91916

tr

sR 443 f2y09196

tr2 Veftical breal<waters and related structures

This chapter describes the types and purposes of vertical and composite walls / breakwaters in use inthe UK, in ltaly and Japan, and elsewhere. The historical development of such structures is reviewed,illustrated by examples drawn from UK and overseas. Key features are identified from existingstructures around the UK using stone or concrete blockwork, as well as for monolithic structures usingconcrete caissons around ltaly and Japan.

The review draws on a number of sources identified below, but particularly on previous reviews byAllsop & Bray (1994), Franco (1994), Lamberti & Franco (1994), Oumeraci (1994c), and Tanimoto &Takahashi (1994a, b).

2.1 Purpose and form of structuresBreakwaters or seawalls have been built since the earliest development of the coastal zone. Theprimary purposes of such structures are to protect areas of water for navigation, anchorages orsheltered moorings; to protect working areas within and around harbours; or to defend land againsterosion or flooding. Many such structures are required to serve a number of different purposes, andthese may often change in time. The composition and construction of these structures owes much tolocal practice, taking particular account of local conditions and/or materials. The main types of harbourand coastal structure may be summarised:

o harbour breakwaterso entrance channel breakwaters or moleso cooling water breakwaterso nearshore breakwaters, reefs, or sillso groynes, bastions, and other beach control structureso coastalseawallso coastal or shoreline revetments

These structures may be of three general forms:

a) impermeable / solid with vertical or steeply battered faces;b) rubble mound with permeable and rough side slopes; orc) composite construction incorporating a caisson or wall section on or behind a mound of

armour.

The principal concem in the design process for a brealcwater is to achieve required levels of waveprotection in the harbour during service and extreme wave conditions. The degree of shelter requiredwilldepend on harbour usage, and will be most strongly influenced by the economics of the portoperation. Wave protection is achieved by ensuring that the plan configuration, breakwater length andheight, are suflicient to limit wave penetration to sensitive areas of the harbour at selected retumperiods or probabilities. These considerations influence the position and length of the breakwater,principally set by levels of wave diffraction, and its freeboard, generally set so that wave transmissionover the structure is not excessive.

The main requirements for seawalls are essentially similar, with the structure required to limit toacceptable levels any wave overtopping, but also to protect the material behind or below the wall fromerosion by direct or indirect wave forces.

A secondary consideration, but often presented as the major design case, is that any such structureshould remain stable up to a given design condition, and/or that any damage should be restricted togiven limits. Again ditferent levels of damage / movement or safety factor may be accepted at ditferentprobability levels.

sR 443 0209/96

EAround the UK, seawalls and revetments have been constructed to defend parts of the coastlineagainst erosion, termed "coast protection"; or to reduce the level and/or risk of flooding of low-lying landby inundation from the sea, termed "sea defence". Seawalls may be generally vertical or steeplysloping, or they may be formed by embankments protected against erosion by armouring. Structuressuch as seawalls are substantially more numerous than large breakwaters, but many of the designmethods and much of the technology derive from studies for breakwaters. Analysis / design methodsin this report therefore focus primarily on larger structures used to defend coastlines and harbours,primarily harbour breakwaters for commercial/ naval harbours or marinas; sometimes entrancechannels for lagoons; or cooling water basins for power stations. They may be constructed in 5 to 50mof water and, where exposed to severe waves, rubble or composite breakwaters may be armoured byspecial concrete armour in sizes from 1 to 200 tonnes, although rarely above 40 tonne. Caissons maybe constructed in sizes up to 3,000 tonnes, or even up to 10,000 tonnes.

Choices between different configurations are influenced by economics and availability of materials; bylocal construction practice and availability of plant; performance standards required from the structureand local environmental concerns; and client / designer preferences. ln the UK, blockwork walls onrubble foundations were preferred during the last century, but rubble mounds have been more stronglyfavoured over the last 50 years. Caisson breakwaters are rare in the UK, although some structuresuse slice blockwork or sheet piles to form vertical walls. Designers elsewhere in Europe have alsogenerally preferred rubble breakwaters for their relative ease of construction, less brittle failure modes,reduced susceptibility to wave impacts, and potentially reduced environmental impact, except in ltalywhere construction of vertical blockwork and caisson breakwaters dates back to the Roman era, andremains prevalent today. Engineers in Japan also strongly favour vertical caissons or, where waveforces may be parlicularly strong, horizontally composite breakwaters with a mound of armour units infront of the caisson.

2.2 Development of vertical breakwatersln analysing the performance of veftical breakwaters or seawalls in the United Kingdom, it is useful toconsider the design and construction of many historic structures, particularly those built during themajor period of harbour development in and around the UK between 1830 and 1900. Manybreakwaters constructed during that period still survive, and their stability is important to the continuingoperation of the harbours protected.

";*Ki:!#;!r:&ile*raf;"bl'3s 3,"s 9 i ol i oi p;p; ; ;Solsol,iojrb',"?liclX'*-i.q

Stone blockwork, St Catherine's breakwater,Jersey 1996

The more common types ofbreakwater or seawallaround theUK are of simple verticalor batteredslope, with walls formed of stone orconcrete blocks. Such structureswere relatively cheap to constructwhen labour costs were low, andused a minimum of material.Breakwater walls were usuallydouble-sided, but many quays orseawalls are backed by natural orimported materials. An examplebreakwater section from StCatherine's harbour on Jersey,constructed at about 1856, showsthe dry masonry walls, the rubblefilling between the walls, and therubble mound on which the wallsare founded, Figure 2.1.

Figure 2.1

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trQuarried stone is not naturally available in the rectangular shapes needed to form a coherent andstable wall. Production of stone blocks to acceptable sizes and tolerances used to be a routine task in

civil engineering, but became significantly less economic as labour costs increased. Manybreakwaters before 1900 therefore used large stone blocks to form the outer skin of the wall, with thecore formed from smaller blocks and/or rubble infill. The use of concrete blocks to replace dressedstone blocks became more prevalent in the UK after 1850, see section of Dover breakwater inFigure 2.2.

y'qartryed

K"

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Figure2.2 Concrete blockwork, East Arm Breakwater, Dover

Blockwork walls were constructedwidely around the UK to formbreakwaters, dock or quay walls,and seawalls. Whilst the mainpurposes of the breakwaters wereto give quiet water for moored ormanoeuvring vessels; and provideshelter for cargo handlingoperations, they were also oftenused as quays, support for cranesand other equipment, and additionalspace for cargo. Somebreakwaters known as'Moles' or'Piers', Figure 2.3, also acted astraining walls at the mouth of a riveror estuary.

Figure 2.3 Trai ning wall/breakwater, North Tyne

Seawalls around the UK were also constructed using similar techniques to halt erosion of beaches,dunes, or soft cliffs, and/or to limit wave overtopping and flooding during storms. Such structures arenot the primary interest of this report, but examples are cited where they give particular information ondesign techniques or construction methods.

sR 443 02109/96

E2.2.1 HistoricalbackgroundAncient breakwaters around the Mediterranean were constructed of stone blocks, sometimes withconcrete or cementitous infill. Roman engineers used undenvater construction with timber forms(sometimes sunken ships), and filling with cement, pozzolana, and brick. Franco & Verdesi (1993)describe a version of caisson construction used by Herod the Greal's engineers at Caesarea around20 BC, where wooden forms were filled by concrete / mortar lowered in baskets into the forms.

Little evidence remains of such construction around the UK, although some foundations of quay wallshave been dated to Roman times. The use of concrete to form blocks in the UK was probably startedby the Romans, but disappeared again from UK construction practice for marine / coastal structuresuntil about 1850. Few details of construction of breakwaters or coastal walls are recorded before thelate 1600's, and much of the information available to Bray & Tatham (1992) dates from the 1700 and1800s. One notable exception is provided by the account of the construction by British engineers ofthe Greate Mole at Tangier by Routh (1912), discussed in section 2.2.2below.

The main purpose of many harbours in the most exposed areas around the UK was defence, withnaval requirements setting the position, orientation and plan for harbours at Dover, Portland, Plymouth,Holyhead, St Catherine's and Alderney, see layout in Figure 2.4. Other harbours were constructed as"harbours of refuge", to be used by fishing boats and trading vessels during storms. These new, andoften much larger, harbours were much easier to enter than the small coastal harbours. Then, as now,narrow entrances and reflective walls of these small harbours caused very dangerous conditions closeto the harbour entrance, problems that still persist for many harbours in the UK. These aspects arediscussed in more detail in the harbour Entrances project, see particularly McBride et al (1996).

Figurd 2.4 Layout of Alderney harbour, after collapse of breakwater outer section

Many vertical breakwaters or piers were constructed between 1830 and 1900, including Alderneystarted in 1846, Dover started in 1847,Tynmouth 1855, Holyhead 1876, Fraserburgh 1877. Most ofthese have survived in their original form, except Alderney which is discussed more by Allsop & Bray(1994) and Allsop et al (199'l). Many of the naval harbours constructed in this period have since beenabandoned by the navy, and are now used for commercial, fishing or leisure activities.

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sA4430210,9,l

tr2.2.2 Construction of breakwaters, piers, and seawallsThe most common form of construction used in the UK for breakwaters or piers was a rubble moundbrought up to a level slightly below low water, and surmounted by blockwork walls. Hewn stone, oftengranite, was laid in bond, generally at a slight batter off vertical. Blocks were laid dry or in lime orpozzolana mortar up to about 1900. Concrete filling was rarely used, and cement mortars becamewidely available only after about 1900, although lime and other modars were used at least from 1650.Concrete rather than stone blocks was more widely used after about 1880. Various methods weredeveloped to assist transfer tensile, bending, or shear loads between adjoining blocks, or betweencourses of blockwork, including iron cramps, keys or joggle joints between blocks.

Caissons were rarely used in the UK before 1900. One of the first uses by British engineers ofcaissons is described by Routh (1912) who relates the construction of the main breakwater or GreateMole to shelter a harbour at Tangier from the Atlantic. The town was occupied by British troops, andprotection was urgently needed for the vessels supplying the garrison. The Mole was started inconventional fashion, with rubble foundations placed ahead of blockwork construction. Constructionstarted in August 1663, but had only reached 350m by August 1668 due to adverse wave conditions atthe site; loss of rubble fill. into the sand bed; the small and occasional nature of the workforce who wereoften diverted to other (military) duties; difficulties in obtaining materials; and significant delays inpayment for work completed.

After the contract had been re-negotiated, the contractor returned in April 1670 to find the blockworkwalls damaged and breached in at least two places. The construction method was re-considered, anda type of caisson construction used at Genoa was proposed using ogreat wooden chests" bound iniron, and filled with stones and mortar or concrete. After much debate, some of it reported in SamuelPepys' diaries, a new contractor was appointed to eltend the existing structure using caissons'

Wooden caissons of 500 to 2000 tons (Figure 2.5) were towed out from England, and once on site theywere sunk onto the foundation by being filled with stone bound in a local mortar of Roman Tarras.Progress on the new construction was more rapid and less subject to damage than the earlierblockwork sections, and the prognostications were for a longer life than the earlier sections.

Figure 2.5 Timber caisson or Greate Chest used for the Mole, Tangier, 1677

Work on the Mole continued until 1678 when Tangier was attacked and all energies were diverted to itsdefence. Peace was concluded in 1680, and it was then decided that the breakwater should bedestroyed lest it provide shelter to a later enemy. This was completed in 1684 with more ditficulty thananticipated, and marked an apparent halt in significant breakwater construction by British engineers,and certainly in the use of caissons, until the early 1800's.

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sR 443 0209/96

trThe use of concrete for filling breakwater walls, and/or to form the facing started to be usedoccasionally again after about 1830, becoming more prevalent after about 1870. There is no record ofconcrete being used for the North Pier at Eyemouth , 1767; the Old Pier at Wick, 1823; the piers atHynish, 1843, Buckie, 1855, and West Hartlepool, 1858.

Pre-cast concrete blocks were however used at North Tyne in 1855, Figure 2.3; tor Dover breakwater,1866, Figure 2.2: and at Cork in 1877. Concrete filled bags formed a foundation to Fraserburghbreakwater in 1877, and for the Winton Pier, Ardrossan in 1892. Concrete filling was used for the laterstages of Alderney breakwater 1849-1866, the South Breakwater at Aberdeen, 1873; for the North Pierat Aberdeen, and the Fraserburgh breakwater, both in 1877. lt is interesting to note that Lamberti &Franco (1994) credit the ltalian engineer Coen Cagli with re-introducing vertical wall breakwaters toItaly after a visit to Britain in 1896 where he saw the blockwork breakwaters at Dover, Sunderland,North Tyne, Peterhead, and Wick.

The development of so many harbours around the UK between 1850 and 1900, and sulival of many ofthose breakwaters, have significantly reduced the need to construct new harbours around the UK, andhas thus resulted in relatively few breakwaters being constructed since 1900. Those new structureshave generally been formed as rubble mounds to their full height, protected by rock or concrete armourunits, see particularly Port Talbot, Douglas, Bangor, and Peterhead. Many similar structures have alsobeen designed and constructed by British engineers working overseas.

Exceptions to this were the new harbour at Brighton, protected by breakwaters using circular concretecaissons, Figure 2.6, based on the design used at Hanstholm in Denmak; and the vertical wavescreen breakwaters at Sutton Harbour, Plymouth, and Cardiff Bay Barrage.

Brealavater

Cross beams

Access manhole

I

f Crane rail

Figure 2.6 Circutar caissons used at Hantsholm and Brighton Marina

2.2.3 Construction of veftically-composite brealouatersStone or concrete blockworkBefore the advent of advanced underwater working, construction of blockwork walls was chiefly limitedby the depth to which diver-assisted placement of closely-fitted blocks was possible, and by theknowledge and equipment available for placing mass concrete. Rubble materialwas placed by barge,allowed to consolidate, then trimmed to accept the foundation stones.

In 1850, the water depth at which the foundation stones could be laid was usually limited to 12ft (3-4m)below low water level, but by 1900, depths of up to 50ft (15m) had been reached. After dressing themound by divers, blockwork was then founded using the largest blocks available. The breakwater wallwas carried upwards in plain or mortared blocks to the top of the wave wall. The block size oftenreduced as construction climbed, as increased time between immersion allowed more time to fittogether smaller blocks, and/or in laying the mortar bedding / jointing. lndividual blocks were oftenbonded together by keys, by iron or steel dowels in holes through the blocks, or by lead or mortar

1 0 sB 1430210'9,l

trpoured to form keys between blocks, although these complications were more often reserved for theouter end of the breakwater. The use of iron or steel rail cramps to hold together the outer end of abreakwater is discussed by Bray & Tatham (1992). Timber piles were sometimes used to take bendingor tensile forces, and were occasionally incorporated within the breakwater structure.

The sections of St Catherine andAlderney Breakwaters shown inFigures 2.1 and 2.7-8 are relativelytypical of the larger breakwatersconstructed between 1850 and1880. Of these two, Alderney isexposed to substantially moresevere wave conditions, hassuffered significant, provides us withmore information on failure modesand responses, and has thereforebeen given more attention, recentlyby Allsop et al (1991) and Allsop &Bray (1994).

At the landward end of the Alderneybreakwater, the foundation was setno more than 3.5m below low waterlevelon spring tides. Along theouter sections, the lowest intendedlevelwas 7.3m (2aft) below lowwater, but consolidation of themound increased this to 9.1m (30ft)towards the seaward end. Largeblocks of stone, later of concrete,were laid on the rubble after it hadbeen allowed to settle for about 6

Figure 2.7

months. The batter of the wall of 2 (vertical) :1 (horizontal) at the inner end is rather shallower than formany contemporary breakwaters, and was steepened for the outer sections. Walls at St Catherine'swere battered at 3:1, and at Aberdeen at 8:1.

Blocks facing most of the breakwaters considered here were generally of dressed stone. Typical sizesare in the ranges 1m x 0.3m x 0.5m up to 2.5m x 1m x 1.5m. The sizes used were strongly dependenton the stone available, and the stone-working skills available. Very fine tolerances were possible, butwould generally have been reserved for elements on the top of the breakwater, those that could easilybe seen. Stone used as facing on the breakwater wallcould be dressed to give joint gaps typically ofno more than 1-2", about 25-50mm. At lower levels, where inspection was more difficult, and placingtimes shorter, tolerances may have been wider, and joint gaps of up to 75mm might be expected.

The gaps between adjoining blocks would generally have been negligible where blocks were laid inmortar. The mortar will however deteriorate over the structure life, the joints then open up, allowingwater into the hearting or core, and sometimes allowing the blocks to move. Many failures of suchwalls have been associated with the loss of bond / filling between blocks. The use of concrete blocks,eg at Dover shown in Figure 2.2, avoided many of the problems of bonding stonework, and made itmuch easier to make special provisions for joining blocks, such as keyways or other stepped joints, orcut-outs for key blocks.

Once production of concrete blocks became economic, block sizes increased dramatically, sometimesto sizes approaching 400 tons. Stoney (1874) records the use of blocks of approximately 3.5m x 6m x7m lor quay construction in 1871, and suggests their use at Alderney. lt was however agreed that the

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Cross-section of Alderney breakwaterduring construction, 1 855

Figure 2.8 Cross-section of Alderney breakwater,completed,1864

1 1 sF 443 0209/96

trcapital costs of the equipment needed to produce, move and place such blocks, would restrict their useto large projects.

Concrete caissonsOver the last 40-50 years, there have been considerable advances in design methods for verticalbreakwaters; in construction technology for prefabricated concrete caissons; in placement of rubblefoundations at depth; and these changes have altered the balance of advantages and disadvantagesbetween rubble and vertical breakwaters.

The most common form of caisson is rectangular ( or square) in plan and front elevation, andrectangular or near square in end elevation. Caissons may typically be 15-30m long, divided internallyinto cells. An example ltalian caisson is shown in Figure 2.9. The caisson itself is designed to befloated out, ballasted with water to sink it into position, then filled by sand. ln this low tidal range, thelow crest section is then cast insitu.

, 15.00

t '-

Figure 2.9 Concrete caissons for protection of Sestri Industrial Airport, 1938

The slightly more complexbreakwater at Bagnara (1985) isshown in Figure 2.10. The crestwall is shaped to return anyovertopping waves, and is set backto reduce impact forces andovertopping. The toe armour to thisbreakwater was damaged in 1991,but only along its most outer endwhere Tetrapod armour was usedat the toe. The toe armour alongthe main trunk was 5 t modifiedcubes. Figure 2.10 Caisson breakwater with set'back crest wall,

12

Bagnara,1985

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trOne of the main disadvantages of a vertical wall breakwater is the high level of reflections. Thisproblem, and potentialsolutions have been studied in the companion Harbour Entrance and MCSprojects, see discussions by McBride et al(1996), Allsop (1995), Allsop et al (1995b), McBride et al(1995a), and McBride & Watson (1995). One approach is to modify the seawrd chambers of thecaisson to allow wave energydissipation in the first row ofchambers, or in a few instances inthe first 2 or even 3 chambers. Anexample of a 2-chamber perforatedcaisson is shown in Figure 2.11.This illustrates the higher floorlevels in the inner perforatedchambers, the vent through thecrown wall to reduce air pressureswithin the rear chamber, and theuse of concrete fill to increasestrength and density in the seawardcells. ln a few instances, perforatedchambers are also used on theharbour side to reduce reflectedwave action within the harbour. seethe section of Bagnara breakwater in Figure 2.10. lt should however be noted that caissons with asingle perforated chamber are unlikely to achieve reflections below C,=0.5 for any significant range ofwave periods.

High wave reflections may combine with currents along the structure increased by interruption of tidalor wave-induced currents. These may precipitate local scour of the sea bed, a problem that hasafflicted a number of caisson breakwaters. In the UK, Ganly (1983) reports that the circular caissons atBrighton placed directly onto chalk bedrock, Figure 2.6, were subject to substantial early scour leadingto settlement of 3 caissons by up to 0.65m during construction. Extensive scour protection measureswere then included during the remainder of the construction period. Despite these measures, scourholes have continued at Brighton, with significant expenditure being needed to reinforce the toe detailby pumping concrete into flexible bags at the seaward edge of and beneath the caissons. Elsewhere,scour remains one of the more ditficult design problems, and substantial anti-scour measures haveoften been required to avoid localcollapse or loss of support. The hydro-dynamic processes involvedin scour are reviewed by Oumeraci (1994a), but little information is given on potential preventionmeasures. Practical advice derived from analysis of service performance is given by Funakoshi et al(1994), and is discussed in 2.3 below.

Most vertical breakwaters in Europehave been constructed around ltaly.Comprehensive reviews of manyItalian breakwaters, design,construction, failures and repairs,have been described by Franco(1994) and Lamberti& Franco(1994). Around the world, moreharbours and breakwatershavebeen constructed recently in Japanthan anywhere else, perhaps evenmore than in the rest of the world together. The scale of such construction is illustrated by the port ofOnahama where the caisson construction yards completed 1500 caissons in 1932 - 1992, with 131constructed in 1971. Much further information on caisson breakwaters in Japan is given by Tanimoto &Takahashi (1994a, b) who describe the development and historical progress of vertical breakwaters inJapan, and give details of many example structures. Of those relevant to this report, three examplesare shown in Figures 2.12 - 2.14.

12.oom

Figure 2.11 Perforated chamber caisson breakwater atPonza

Figure 2.12 Tsunami protection breakwater at Ofunato

13 sR 443 02@/96

trThe tsunami protection breakwaterat Ofunato, 1967, shown in Figure2.12 is in relatively deep water at35m, but is required to resistrelatively low wave heights. Theperforated chamber caissons usedat Kamaishi, Figure 2.13, is built in60m of water using a mound of35m, and is the deepest breakwaterbuilt in Japan. This structure againseryes as tsunami protection so thedesign wave heights are relatively low.

The widest caisson in Japan at 3Bmis shown in Figure 2.14. Thisbreakwater at Hedono port is in lessthan 30m of water, but is designedto resist a design wave of H" =9.7m. Here the toe armour uses 64tTetrapod units in a layer about 6mthick. The longest caisson built inJapan up to 1994, was 100m long,about 20m wide, and was used as atemporary breakwater at Kochi port.This caisson was cast in a shipdock, and towed 370 km to site.

Figure 2.13 Tsunami protection breakwater at Kamaishi

L.w. to.o H'w-+2'o

Figure 2.14 Harbour breakwater with wide caisson atHedono

More details on vertical breakwaters based on work up to 1992 were presented in a special edition ofCoastal Engineering by Oumeraci (1994), Franco (1994), Tanimoto & Takahashi (1994b), Hattoriet al(1994), Chan (1994) and Oumeraci& Kortenhaus (1994). These papers concentrate on informationfrom research studies, with some comments on design, and with a little information on practicalexamples. More practical information is given in the Workshop on Wave Barriers in Deep Waterspresented at the Port and Harbour Research Institute in Japan, see particularly Tanimoto & Takahashi(1994a), Lamberti & Franco (1994), Allsop & Bray (1994), Xie (1994), Juhl (1994) and Ligteringen(1 ee4).

2.3 Performance in seruiceAnalysis of reports of damage or failure of breakwaters suggests that there are three main periods ofpotential concern during the life of the structure: the construction period; initial seruice; and theextended service period, often well beyond the normal economic life used in present design lifecalculations. Much of the damage reported appears to occur early in the life of the structure, evenduring construction, so it would appear that if a breakwater suryives the first 5 years without damage itis generally likely to survive the next 40-50 years. This confirms the premise that damage / failures aregenerally avoidable if sufficient information is available on the main failure processes.

Relatively little information on service performance of breakwaters was derived from the CIRIA projectreported by Bray & Tatham (1992). Of those owners from whom information on breakwaters wasrequested, only 8% responded, perhaps suggesting that these structures have given little obviouscause for concern in recent years. In their report however, Bray & Tatham note that incrementaldegradation of such walls is often overlooked, and that the apparent lack of problems may be dueprimarily to lack of inspection. ln some instances, it might be concluded that damage occurred so earlythat the structure was abandoned, or was replaced at a relatively early stage in its life. In otherinstances, it might be concluded that historical rates of deterioration have been so slow that the needfor maintenance expenditure is small. This would ignore the brittleness of the failure modes for many ofthese structures, and Bray & Tatham concluded that there is a significant requirement for inspection

1 4 sR 443 0209/96

Eand monitoring to avoid those sudden failures that occur when the structure has degraded to a failurepoint.

Various publications between 1850 and 1900 give details of breakwater pedormance, but often failtodistinguish clearly between cause and response. A good example of this problem is given by reports ofdamage to Wick breakwater. Stevenson (1874) describes the start of breakwater construction in 1863using dry-placed blocks of 5 to 1O tons. During storms in 1870, a section of about 380 ft (1 15m) of thebreakwater was destroyed, presumably by breaching the breakwater wall. This section was thenrebuilt using Portland cement to bond the block facing, and iron dowels between courses. A storm inFebruary 1872 gave wave impact pressures so severe that facing stones were shattered, althoughStevenson's report does not identify whether this was by direct wave impact, or could have been bystones from the mound being hurled against the face, see discussion by Allsop et al (1991) onAfderney. In December 1872 a section of blockwork bonded together and estimated as weighing 1350tons slid into the harbour. This was followed by a similar fate to another section weighing 2600 tons in1873. These are cited by other authors including Cornick (1969) as evidence of impact forces frombreaking waves. Shield (1895) however refers to informal discussions at Wick, and suggests thatdamage was strongly infiuenced by foundation failure, but gives little other data.

Instances are rarer now where the design or construction seems to have incorporated a significant flawfrom the start, and severe damage or failure has become apparent during the construction period. Theprime historical example of this in the UK is the Alderney breakwater where a design that had workedwell in a low wave environment at St Catherines on the sheltered side of Jersey was used again for anextremely exposed site, subject to frequent and severe storms. Potential weaknesses of the Alderneybreakwater were noted during the construction period, leading to steepening of the front face toincrease restraining loads on individual blocks; use of mortar/ concrete to fill between blocks to reduceinternal pressures; reduction of the mound level to place the foundation at greater depth.

Also during construction of the breakwater at Catania in Sicily in 1930, very large blocks slid backwardsinto the harbour under wave aftack. This weakness was ascribed to the absence of the crest blocks,and no changes were made to the design. The damage was however repeated in 1933 when much ofthe upper part of the breakwater slid backwards. Analysis of this failure identified the lack of horizontalconnectivity between layers, hence the relative ease with which successive layers slid over thatbeneath. All later structures built in ltaly include keys, or other connections to resist horizontal forces.Despite this, few if any existing structures were re-appraised or strengthened, and collapses of suchbreakwaters continued at Genoa (1955), Ventotene(l966), Palermo (1973), Bari (1974), and Naples(1e87).

One of the major durability problems of these types of structures arises from scour along the seawardface of the breakwater. Lamberti & Franco (1994) ascribe collapse of the Mustapha breakwater atAlgiers primarily to foundation failure, initiated or aggravated by local scour. Funakoshi et al (1994)anafysed breakwaiers of total length 77km al13 Japanese ports, and found scour up to 2m in nearly allexamples, including examples where scour prevention / alleviation measures had been included fromthe start of construction. Generally such scour abated after the first 1-2 years. Funakoshi et al (1994)recommend repeated bed surveys, and that scour protection measures for the toe mound should bestaged over the first 2 years after construction.

In the use of most practical design methods, it is assumed that wave impacts will either not occur, orthat the pressures will be so brief as not to allow time for massive caisson sections to respond.Limitations of these assumptions are exposed by the examples of breakwater damage by impactsdescribed for Mutsu-Ogawara by Hitachi (1994), for Sakata and Mutsu-Ogawara by Takahshi et al(1994a), and for Amlwch by Allsop & Vicinanza (1996).

Mutsu-Ogawara port on the Pacific coast of Japan was under construction in February 1991, when itwas hit by waves which at H"=9.9m substantially exceeded both the construction period designcondition (1:10 year) of H"=/p1, and the 1:50 year design condition of H;7.6m. Damage wasparticularly severe where mounds of armour blocks intended to cover the front face were incomplete

1 5 sR 44St2lo9l

trand/or had been damaged. These part-height mounds acted to trip the waves causing impact forcesso severe that two 24m long caissons suffered structural damage, one of them losing most of its upperpart. Photographs taken during the storm show breaking waves being thrown many tens of metres intothe air above the breakwater, very similar to the process seen at Alderney under severe waves

Sakata port is on the Japan Sea, and is therefore in theory less exposed than the Pacific coast. Evenso, wave conditions during the winter of 1973 | 74 reached H.o=7'2m and exceeded H"o=4'$6 9;1 4other occasions. In a water depth no more than 9-10m, these conditions would have reached orexceeded the breaking limit, and a high toe mound to protect against possible scour would also haveincreased the probability of impacts. Nearly all of the 39 caissons, each 20m long and 17m deep, slidduring these storms, some by nearly 4m.

ln a storm in 7 December 1990, a small breakwater was damaged at Amlwch port on Anglesey, northWales. The breakwater is about 60m long, runs out approximately eastwards from the coastline, andthe breakwater axis is slightly curved. The structure was constructed before 1977 using concreteblocks laid in slices onto a mass concrete foundation plate into the rockhead. Each block is thus inter-locked with its neighbouis by keyways. The breakwater crest wall is at +7.7mODN, and the structuretoe at approximately -11mODN. During the storm, the outer end of the breakwater slid backwards byabout 0.1-0.2m, leaving cracks down through the slice blockwork in three places of up to 0.075m width.

Wave conditions at Amlwch during this storm are not known, but are estimated as at least H"o=4[],probably with a mean wave period of T,=gs. The foreshore approaching the structure is very steep,approximately 1:13, so falls outside of any established design method. The water level during thestorm probably reached at least +3.4mODN, giving water depths at the toe of 1 1 -14m. Allsop &Vicinanza (1996) estimated limiting inshore wave conditions as H.i=4m at MHWS, but reducing toH"i=3.6m at MLWS. Using the simple method of Vicinanza et al (1995), the horizontalforce wascalculated as 1O4okN/m at MHWS. With no up-Iift, for the blocks direct on concrete, and p=0.5, thesegive a factor of safety of F, = 0.9 at high water, contrasted by predictions using the Goda method whichgives F" = 1.2 at high water, and F" = 2.3 at low water. These factors of safety would be reduced if up'lift pressures could act on or beneath the blocks.

It is claimed by many researchers, particularly in ltaly, Japan and Germany that vertical breakwaterswith pre-cast caissons have lower construction costs and much shorter installation times whencompared with rubble mounds. The form of their installation may also reduce environmental impact inthe form of noise or dust pollution, on site, at the quarry, and in trdnsport to the site. Once constructed,vertical breakwaters often have less visual and spatial impact which is particularly attractive tonavigators who strongly dislike navigating close to rubble slopes. Caisson breakwater sections alsohave the potential to be removed at the end of the project life by simply emptying the fill material and re-floating the empty caisson sections for re-use elsewhere.

It is clear from the examples of damage reviewed above, and the many other examples described inthe literature, that there remain significant uncertainties in methods to analyse and design vertical andcomposite breakwaters. The arguments in favour of these types of structure suggest however that it isnow appropriate to re-examine the relative advantages and disadvantages of vertical breakwaters, andparticularly to re-examine methods to determine wave loadings on such structures.

1 6 sR 443 02,09196

tr3 Design methods

3.1 Design considerations and failure modesThe main activities in the design process, strictly the analysis process, are to identify the main failureprocesses, and then to dimension the selected structure type to ensure that the principal loadingsremain below the structure's resistance when suitably factored. In the design of vertical breakwatersand related walls, the main emphasis has historically been on balancing the horizontal ( and perhaps

up-lift) forces against the caisson weight and hence friction forces. This chapter generally follows thatapproach.

3.1.1 Structural failuresThe main failure modes for these types of structures may be summarised:

Sliding (backwards) of the wall elements relative to the foundation;Rotation or overturning, backwards, of the wall;Forward rotation of the wall;Gross settlement of wall;Structural failure of breakwater elements;Loss of integrity / continuity of structure.

The main loadings acting on these types of walls arise from direct wave pressures; up-lift forces; quasi-hydrostatic forces from internal water pressures; and geotechnical forces / reactions from backing orsupporting materials. Some of the failure modes above may themselves be initiated or accelerated bycontributing failures, including particularly local or global foundation failures. These structures resistwave and geotechnical forces essentially by their own weight, and by friction with the underlyingmaterials. Under local pressures / gradients, interlock or bonding forces between component elementsmaintain continuity and avoid movement or loss of elements and/or fill.

The most commonly addressed failure mode for monolithic vertical structures is sliding backwardsunder direct wave forces. This depends primarily on the horizontal loads, but may also be influencedby up-lift forces. Failure by overturning (backwards) may theoretically be examined by assumingrotation about the rear heel of the caisson / wall. In practice, the point of rotation is not fixed, dependingupon the bearing capacity and geotechnical characteristics of the rubble mound and foundation.Analysis of foundation failure modes has been studied under the MAST ll MCS research project,summarised by de Groot et al (1995), and constitutes a major part of the MAST lll project PROVERBS,so further discussion on these issues within this report will be very limited.

Blockwork breal<waters may also fail by loss of integrity where a block is removed (seaward) by netsuction forces, followed by progressive damage and then catastrophic collapse. Detailed analysis ofthe high local pressures / pressure gradients that may influence this failure mode will be described bythe Naples / Sheffield / Wallingford team in forthcoming reports to PROVERBS.

This report is therefore primarily concerned with the (horizontal) wave loads acting on the seaward faceof the wall, and with the contribution of up{ift forces to overall stability of caisson or similar elements.Peak local pressures will also be discussed, but detailed analysis of these effects will be limited in thisreport, as they are discussed more fully in the Ph.D theses of McKenna (1996) and Vicinanza (1996).

3.1.2 FunctionalfailuresVertical or composite walls may alternatively suffer functional failures when they fail to give adequateprotection despite surviving structurally. In harbours, such a functional failure will generally be due toexcessive wave overtopping which leads to transmission of wave activity into the (previously) shelteredparts of the harbour. A related functional failure may occur if the breakwater structure is adopted toserve other functions as well. This often leads to requirements to limit wave overtopping under

1 7 sR 443 02/09196

trfrequently occurring conditions to allow safe working on / behind the breakwater, vehicle of pedestrianaccess, and perhaps avoidance of damage to buildings or other fixtures on the breakwater.

A particular disadvantage of vefiical walls is these structures do not themselves dissipate anysignificant propoftion of the incident wave energy. Plain vertical walls will either reflect or transmit waveenergy, primarily depending on the relative crest freeboard, and as such structures are primarilyintended to reduce wave transmission, the majority of wave energy incident on the structure is reflectedback away from the structure. These increases in wave activity may cause problems to navigation, ormay initiate / accelerate local bed scour or beach movement. This area is not considered further in thisreport as it has been covered very fully in the accompanying Harbour Entrances project, summarisedby McBride et al (1996), and under the MAST MCS project. Results of those and related studies havebeen presented by Allsop (1995), Allsop et al (1995a, 1995b), Allsop et al (1994a, 1994b), Allsop &McBride (1994), Bennett et al (1992), McBride et al (1996), McBride et al (1995a, 1995b), McBride et al(1994), McBride et al (1993), and McBride & Watson (1995).

3.1.3 Design approachesThe analysis of stability of such structures requires the identification of all significant failure modes, andthe derivation or use of appropriate analysis methods for each failure mode. These analysis methodsmay be conducted at widely different levels of complexity or rigour. They may include detailedcalculations of loadings and structure resistance; calculation of a given response parameter and testingthat it falls below some given limit; comparison of the main features / dimensions of the proposedstructure against those of similar structures in the geographic region, or in the experience of theengineer.

Considerable design information on the stability and hydraulic performance of rubble moundbreakwaters has been derived from research at HR Wallingford and elsewhere, and has been includedin design manuals such as the CIRIA / CUR rock manual edited by Simm (1991), and in parts of BritishStandard 8S6349, BSI (1984, 1991). There is however substantially less information available inEurope on the stability and hydraulic performance of vertical breakwaters, despite their historicalpreponderance around the UK and elsewhere. 856349 Pt 1 (1984) as amended summarises Goda'smethod for predicting non-impulsive wave forces. The CIRIA rock manual notes however that verticalor composite walls can suffer high impulsive or impact forces, with local pressures substantially greaterthan suggested by some design formulae. These impact pressures are limited spatially and temporally,and have usually been regarded as of relatively little effect on the overall stability of the structure.Damage to breakwaters in the UK, and to others in ltaly and Japan, and recent studies under theEuropean Union MAST research programme on the dynamic responses of caissons to impactpressures, have illustrated that there are circumstances where present design methods for wave forcesare insutficient.

The failure modes which vertical walls are required to resist may be re-presented under four headings:

a) Sliding or overtuming of the breakwater wall as a single entity;b) Removal of elements from the (blockwork) wall, resulting in a loss of continuity, and hence

destruction of the wall;c) Gross failure of the rubble mound and/or foundation, allowing movement of the wall;d) Local failure of the mound or supporting seabed, allowing movement of blocks, loss of fill

ancl/or continuity of the blockwork.

Of these, sliding or overturning of single elements a), and gross foundation failure c), have beenrelatively rare in the UK in recent years, but have been more common in ltaly and Japan. Local failuresleading to loss of continuity, and thence to overall failure b) or d), may have been more common in theUK, although records of early failure of minor breakwaters are sparse and incomplete.

Aspects of scour leading to mode d) relate principally to the design of any armour to the seaward faceand berm of the rubble mound, and to the stability of the seabed material in front of the structure.

1 8 sR 443 0209r'96

trScour is not considered further in this project, but has been addressed separately under the MAST llMCS project, see particularly Oumeraci (1994a).

Breakage of (small) elements, and/or the loss of integrity of blockwork walls, have not been muchstudied, and few if any data are available on local pressures / pressure gradients. Allsop & Bray (1994)noted failures of Alderney breakwater, and other related walls in the UK, and suggested that localfailures of the wall, may perhaps be caused by extreme local pressures / pressure gradients. Allsop &Bray suggested an idealised stability analysis for a single block within a wall, but noted that noinformation is available to identify the magnitudes and frequencies of occurrence of severe localpressures and/or pressure gradients. Individual blocks or other small elements are much more likely torespond to rapidly changing pressures, both spatially and temporally than are large elements /caissons, so more detailed data are needed to analyse the stability of small elements.

3.2 Design formulae for wave forces / pressuresIt is often convenient to treat pressures or forces that act on these structures under wave action in twocategories:

Quasi-static, or pulsating;Dynamic, impulsive or impact

Quasi-static or pulsating wave pressures change relatively slowly, varying at rates of the same order ofmagnitude as the wave crest. Two principal quasi-static forces may be considered here. ln the first, awave crest impinges directly against the structure applying a hydro-static pressure difference. Theobstruction of the momentum of the wave causes the wave surface to rise up the wall, increasing thepressure difference across the wall. The net force is approximately proportional to the wave height,and can be estimated using relatively simple methods.

The second case is the opposite of that above, arising as the wave reflects back from the structure,inducing a net negative force or suction on the wall. Again the magnitudes of the forces are relativelylow, and the process is relatively easy to predict.

Dynamic or impact pressures are caused by the special conditions that arise where a wave breaksonto the structure. lmpact pressures associated with breaking waves are of substantially greaterintensity than pulsating pressures, but are of shorter duration. The detailed processes of wavebreaking are not well understood, the occurrence of breaking cannot be predicted with reliability, andthese pressures are therefore extremely ditficult to calculate.

It has generally been accepted that dynamic loads can be very important, but it has been argued thatmany structures are substantially un-affected by such short duration, high intensity loads. Schmidt et al(1992) remind us that despite more than 80 years of research work on impact loading on verticalstructures subject to breaking waves, there are two basic attitudes related to the role of wave impactloadings in the design of such structures. The first attitude simply assumes that impact pressures arenot important and thus should not be adopted in the design. The second attitude is to skip the problemof evaluating the design impact load by assuming that the structure can be designed in such a way thatimpact pressure will not occur.

A third approach is to conduct a dynamic analysis of the structure, and its foundation, and of theapplied loads. This approach is strongly argued by Oumeraci (1995a), Oumeraciet al (1994a & b) andOumeraci & Kortenhaus (1994). Problems arise in the high level of data required, both on the timeseries of loadings, but also on the geotechnical characteristics of the mound and foundation. Thedevelopment of these overall stability models are at relatively early stages. This approach thereforepresently remains the purview of researchers, although it is to be expected that dynamic designmethods and example data will become available during or after the completion of the PROVERBSresearch project, (1996 -1999).

1 9 sR 443 02y09196

trThese problems are compounded by uncertainties in defining those conditions that lead to waveimpacts. Schmidt et al (1992) and later Oumeraci (1994a) define 7 different breaker classif ications interms of Hold. Unfortunately, the breaker height Ho is extremely difficult to predict with any certainty, so

these classifications are of limited practical use. Goda (1985) describes a number of rules to identifywhether particular structures or sea states willcause a risk of impulsive wave conditions, and thatmethod is reinterpreted here as the flow diagram in Figure 3.1.

Figure 3.1 Decision tree for impulsive breaking conditions

The review of design methods below will therefore concentrate primarily on methods used in designmanuals and codes, but will include information on dynamic of impact effects, on the definition of theonset of impact conditions, and on dynamic responses where generally available. This review drawson material also considered by McKenna (1996) and by Vicinanza (1996), and in some instances refersthe readers to those reviews for greater detail.

3.2.1 HorizontalforcesThe main methods used in design manuals to estimate wave forces on upright walls, breakwaters orseawalls, have been derived by:

Goda for simple wallsGoda / Takahshi for composite breakwatersMinikin for composite breakwatersJensen / Bradbury & Allsop for crown walls

ls wave attack oblique?Beta > 20 degr. ?

ls mound large ?0 .1 <Bb/Lp<0.3

Hmax/h > 0.6hb/hs > 0.5

ls sea bed slope shallow?m < 1 / 5 0 ?

ls crest level low?RdHs < 0.3 ?

ls crest level low?Rc/Hs < 0.3 ?

+F"y"is"ifi*il;"drlI hb/hs > 0.1 ? |

20 sR 443 02/09196

trThe most widely used prediction method for wave forces on vertical walls was developed by Goda(1974,1985). This method was primarily developed to calculate the horizontal force for concretecaissons on rubble mound foundations, and was calibrated against laboratory tests and back-analysisof historic failures. lt assumes that wave pressures on the wall can be represented by a trapezoidaldistribution, see Figure 3.2, with the highest value at stil l water level, regardless of whether waves arebreaking or non-breaking. In Europe, Goda's method is cited by British Standard 856349 Pt 1, BSI(1984), and by the CIRIA / CUR rock manualedited by Simm (1991). Before considering Goda'smethod in detail, it is however usefulto review briefly previous methods, particularly those by lto, Hiroiand Sainflou, see lto (1971), and by Minikin (1963).

Figure 3.2 Pressure distribution and definitions for caissons, after Goda (1985)

Hiroi's formula gives a uniform wave pressure on the front face up to 1.25H above stillwater level:

p = 1.5p*gH (3.1)

where p = the average wave pressure, and H the wave height.

Sainflou's method derives a pressure distribution with maximum, pl at static water level, tapering off tozero at a clapotis height above s.w.l. of H+6o, and reducing linearly with depth from pt to p, at therubble base:

pr = (pz + p,gh)(H + 6o) / (h + H + do)pz = p*9H / (cosh(2nhlL))6o = (nH2/L) coth(2nhll))

(3.2a1(3.2b)(3.2c)

Shore Protection Manual (1984) suggests that Sainflou's method may over-estimate wave forces forshorter non-breaking waves, and uses the Miche - Rundgren formulae to derive the height of theclapotis from which an (assumed) linear hydrostatic pressure is calculated. The accompanying up-liftpressure is assumed to be triangular from the front face, with the pressure at the seaward corner

21 sF 4€ C2r'09l96

trconsistent for front face or underside. For long waves of low steepness, SPM recommends Sainflou'smethod, showing design curves varying with H/gT'z.

Ito discusses the use of Hiroi's formula where the water depth over the mound, d, is less than 2H',., and

Sainflou's methods when d>2H,,.. lt is interesting to note that Sainflou's method generally givespressures of about 0.8-1.0p*gH, rather smaller than Hiroi's.

In use in Japan, lhere was some uncertainty whether Hiroi's method gave safe results, particularly

when using H=Hrs, and over the effects of waves breaking over the mound. A simple method by lto,discussed by Goda (1985) gave a rectangular distribution of horizontal pressures acting on the front

face of the caisson, calculated in terms of H,",. The value of H,", is 2H", or Ho if waves are depth-

limited. The pressure, p, is then determined for 2 different regions of relative water depth, H/h.. lto

assumed a triangular up-lift pressure distribution, but uniform pressures on the vertical face. Bruiningapproximates lto's method by:

P = 0.7P,9H.", for H<dp = p*gH,*(O.15 + 0.55H/d) for H>d

The Shore Protection Manual (1984) distinguishes between breaking and non-breaking waveconditions, recommending that loads under non-breaking conditions be estimated by Miche-Rundgrenwith an assumed triangular distribution of up-lift pressures.

Minikin's and related methodsIn Europe, Sainf lou's (1928) simple hydro-dynamic method had been judged as giving too lowpressures for waves breaking onto structures. Engineers had noted but not been able to measure verylarge forces on some walls, and it was well established that the momentum of the wave could berelated to the pressure impulse. Unfortunately it was clear that some conditions led to very short impactdurations, coupled with very large pressures, perhaps larger than could be accommodated byengineering of that era.

Bagnold (1939) postulated a conceptual model of air compressed by the piston of water, wheremomentum from the wave crest compresses the air pocket. The wave slows and slops as the pressurein the air pocket rises. At maximum pressure, the wave momentum has been converted to pressureover the impact rise time. Bagnold's approach however required the identification of the thickness ofthe air pocket, and of the virtual length of the water piston. Neither of these could be measured.

Minikin's (1963) method was developed in the early 1950s to estimate local wave impact pressurescaused by waves breaking directly onto a vertical breakwater or seawall, and therefore addressed theproblems of impact pressures. Minikin used Bagnold's piston model and calibrated a version of thismodel with Rouville et al's (1938) pressure measurements on a sea wall at Dieppe to give maximumpeak pressures for Wpical wave impact events. The resulting epression for p,* may be written:

P^u=hC^xn P* g H* (1+d/h) (d/L) (3.4a)

where C,* is a coefficient defined to allow fitting to Rouville's data, and accounting for the typical size of

an air pocket. Minikin suggests a value of C.*=p, which is then cancelled within eqn. 3.4a to gMe thesimpler version used by 856349 Pt1 (1984):

P.* = fl9*9H,*(1+d/h) (d/L) (3.4b)

Unfortunately, this expression was then re-written by Minikin with np*g replaced by 2'9! The resultingexpression has units of tons (force) per square foot. This (mis-)use of dimensioned coefficients waslater compounded by other authors, including the Shore Protection Manual, which re'writes Minikin'sformula with ng replaced by 101, but adds confusions over the use of tons or tons force, or perhapssome other (un-stated) units.

(3.3a)(3.3b)

22 sR 443 fz09l96

trThe confusions over the use of Minikin's method is exaggerated by mis-calculations by Minikin himselfin the quasi-hydrostatic element of the overall wave force, discussed in more detail by McKenna (1996).Minikin takes the vertical distribution of dynamic wave pressures to be parabolic about the static waterlevel. The total force is given by approximating the impact force as p,*H/3, and then adding thecontribution of hydrostatic pressures at the point of run-up to Hl2. The final expression for the totalhorizontal force may be then be written in dimensionally correct terms:

Fr,.* = /zc^*n g,9 H,* d { (1+d/h) H(3L) + 1l(2n )+ H/(8nd) } (3.4c)

It appears that all later versions of Minikin's formula for total horizontal force, except that used in8S6349 Pt 1 (1984), included the factor of 101, but without the appropriate qualification on the units.These later interpretations were therefore dimensionally incorrect, and give rather larger forces than theoriginal method, see discussion by McKenna (1996). This otherwise minor error becomes much moreserious when later authors imply that the version using 101 can be used in other units than f .p.s, andhave thus propagated the erroneous version of Minikin's formulae ever since!

As if this was not enough, another serious confusion is introduced in the use of the (quasi) hydro-staticelement in the total horizontal force in eqns 3.4c, and this confusion was compounded by errors byMinikin himself in applying the e><ample calculations. The overallforce prediction method described inthe SPM includes a full triangular hydro-static pressure without explaining whether this is balanced byequMalent pressures on the other side of the structure, or by pore / ground water within the structure.The reader of the SPM may therefore be left uncertain as to whether the full triangular distributionshould be applied, so may in many cases have done so. The resulting forces are often very large, butincrease change markedly with increasing water depths.

The effect of these various methods can be contrasted by plotting the different vertical distributions ofpressures for identical wave conditions. An example which matches one of the test conditionsdiscussed later in Chapters 5 and 6(test 10003) has been used tocalculate the pressure distributionsshown in Figure 3.3. Goda'smethod yields a simple trapezoidaldistribution with the maximumpressure at still water level, and thismethod is discussed further below.Pressures calculated by twoversions of Minikin's methoddiscussed above are also plotted.The lowest pressures are given bythe corrected version using eqns.(3.4b) and (3.4c). The largestpressures are given by the SPMversion of Minikin, demonstratingthe substantially greater peakpressure, and the triangular hydro-static element.

ln practice it has been found by other reviewers, and perhaps by practising engineers, that the SPMversion of Minikin's method gave substantially greater pressures than other formulae, and its use forcalculations of wave forces for practical design has been very limited. This is epitomised by Godawriting on wave force formulae in Herbich (1990) who summarises the prevalent view on Minikin'sformulae 'can be considered to belong to a group of pressure formulae of historical interest".

Other methods fo,r impact pressuresMuch attention has been devoted to pursuing the goal of quantifying impact pressures. At small scale,very large (comparatively) pressures may be measured if small fast-responding transducers aresampled very rapidly. There has however been much doubt that this would be found at large scale.

toP.sm in ld.l/.n^2

Figure 3.3 Vertical distributions of pressures usingGoda, Minikin, and SPM methods

23 SR /143 0209196

trPartenscky (1988) quoting Oumeraci uses results from the large wave channel at Hannover /Braunschweig (GWK) to suggest that impact pressures of very short durations (0.01 to 0.03s) may becalculated from:

Payn = Ks P* I Ho (3.sa)

where Ho is the breaking wave height, and the coefficient ( is given in terms of the air content a" of lhebreaking wave:

Kr_ = 5.4 ( (1/a") - 1) (3.5b)

Partenscky also derMes formulae for the vertical distribution of wave impact pressures, but theseformulae take no account of air content. Blackmore & Hewson (1984) conducted field measurementsat four sea walls in the UK, from which they developed a model based on momentum exchange.lmpact pressures p, depend on the shallow water wave velocity, v"; the wave period, T; and an aerationfactor, J\, which depends on the roughness of the foreshore:

P i = J \ P T v " 2 (3.6a)

A value of I = 0.3 is recommended for a rough and rocky seabed, and A = 0.5 for a regular seabed.Breaking wave heights are indirectly considered by using shallow water wave velocities calculated fromthe breaking water depth, ho, and breaking wave height, Ho:

v " = [ g ( h o + H o ) ] o ' s (3-6b)

This method was developed for vertical seawalls, and no up-lift pressures were discussed. Wherethese methods can be used to estimate up-lift pressures / forces, these are implicitly assumed to occurat the same time as the peak horizontal force.

Goda's methodGoda's method represents wave pressure characteristics by considering two components, the breakingwave (impacts) and the deflected wave (slowly-varying or pulsating pressures), represented in themethod by coefficients o1, o2, and o.. The influence of relative depth to wavelength on the slowly-varytng component is represented by c,; the effect of impulsive wave breaking due to the relative levelof the mound is represented by or; and c. accounts for the relative crest level of the caisson and therelative water depth over the toe mound.

This method is one of the few to give estimates of the up-lift forces, and hence of the overturningmoments for the caisson. Wave pressures on the front face are distributed trapezoidally, reducing fromp, at s.w.l. to p. at the caisson base, see Figure 3.1. Above s.w.l. the pressure reduces to zero at thenotional run-up point given by a height q*. The up-lift pressure at the seaward edge is determined by aseparate expression, and may therefore be less than the pressure calculated for the toe of the seawardface. Up-lift pressures are distributed triangularly from the seaward edge to zero atthe rear heel. Themain response parameters are determined from:

rl* = 0.75(1+cosp)H*pr = 0.5(1 +cosp)(a,+orcos2p)p*gH,*pz=pr/(cosh(2nhlL))

Pg = dsPrpu = 0.5(1 +cosp)(o,a.)p*gH,*

(3.7a)(3.7b)(3.7c)(3.7d)(3.7e)

Where q* is the maximum elevation above s.w.l. to which pressure could be exerted, taken by Goda asn* = 1.5H,*, p is the angle of wave obliquity, in plan, and the design wave height, H.",is taken as 1.8H.for all positions seaward of the surf zone. In condltions of broken waves, H.", should be taken as Ho.

The parameters c,, dr, and q3 are determined from:

24 sR 443 gz09196

trGr = 0.6 + 0.s [(4nh/L)/sinh(anh/L) ]'?oz = Inin { ((hb-dy3hbxH.Jd)' , 2dlH.* }0s= 1 - (h7h) t 1 - 1/cosh(2nhll) l

(3.8a)(3.8b)(3.8c)

(3.ea)(3.eb)

(3.10a)(3.10b)

(3.11a)(3.11b)(3.11c)(3.11d)

(3.12a)(3.12b)

The water depth h is taken at the toe of the mound, and d over the mound at the front face of thecaisson, but ho is taken 5H" seaward of the structure.

The caissons on rubble foundations considered by Goda (1974) had natural periods around 0.1 to 0.3s.When subjected to loads of durations shorter than the natural period, the effective load will itself besmaller than the applied load. Thus for the very short peak pressures caused by breaking waves, theGoda formula does not give the actual peak pressure, but pressures which give the equivalent staticload for the dynamic system of caisson, mound and foundation. This method was not intended topredict pressures of short duration, or of limited restricted spatialextent. Goda (1974) noted thatimpulsive pressures caused by waves which break in front of or onto the wall may rise to 10p*9H, butjudged that vertical breakwaters would not be designed to be exposed to direct impulsive pressures.

Various researchers have found uncertainties with the Goda' method, and some have identifieddifferences with measurements of forces / pressures. Bruining (1994) has discussed many of theinconsistencies in the derivation of the Goda method, and particularly of the parameters o1, o2, and c..Despite these limitations, the methods developed by Goda (1975, 1984) and others constitute the bestmethods available, and include many points of good advice.

Takahashi's extensionMore recently, Takahashi(1994) developed an e*ension to the Goda method to include the effect ofbreaking wave impacts. This modification was obtained by re-analysing the results of comprehensivemodel tests ol caissons sliding under wave impacts, together with analysis of the breakwatermovements at Sakata Port, Japan 1973-74. The modification is applied to the Goda method bychanging the formulation for the o, coefficient. Takahashi introduces a new coefficient which is themaximum of o, or a new impulsive coefficient c,, itself given bytwo coefficients representing the effectof wave height on the mound, and mound shape. The modification is applied by changing the o.coefficient to be the maximum of o, or a new impulsive coefficient o,, itself given bytwo coefficientsrepresenting the effect of wave height on the mound, and mound shape, oo, €tod o11l

on = cos6z / cosh6, for 6, < 0, ordrr = 1 / (cosh 6,(cosh6.)0's for 6. > 0

dro = H/dd w = 2

6r = 20 6rr6 r = 15 6r r6z= 4'9 6'e6 e = 3 6 2

for H/d s 2, orfor H/d > 2

for 6', < 0for 6.'.' > 0fo r6 , ,<0for 6r, > 0

6rr = 0.93 ( (B/L)-0.12) + 0.36 ( (h"-dyh.) - 0.6 )6lz= - 0.36 ( (B/L)-0.12) + 0.93 ( (h.-dyh") - 0.6 )

This modification only operates where the water depth over the toe mound, d, is relatively small, and themound is therefore most likely to precipitate wave breaking onto the wall. Takahashi's method does notalter peak pressures near the water level relative to those above or below, but simply increases allpressures by the same factor. lt does not change up-lift pressures calculated by Goda's method. ltincludes the effect of mound width, Bo, but not of the slope angle to the mound.

Crown wallsWave forces on a crown wall section on rubble mound may be treated as an extension of forces on acomposite wall with extremely high mound. The CIRIA Rock Manual, Simm (1991) recommends the

25 sR 443 0209196

trempir ical formulae derived from model tests by Jensen (1984) and Bradbury & Al lsop (1988) for theevaluation of wave forces on crown walls, Figure 3.4:

Fr,se.gz = p* g hr Lo (a (H"/A") - b)Fugg.sy. = 0.5 p* g B"* Lo (a (H./A") - b)

(3.20a)(3.20b)

These formulae were derived from model tests by Jensen and Bradbury & Allsop on a number ofrubble mound / crest configurations, leading to a range of values of the coefficients a and b derivedfrom regression analyses on forces using simple force tables to measure the horizontal forces only.The maximum force in 1000 waves was divided by the height of the front face of the crown wall, h,, togive an assumed rectangular pressure distribution on the front face.

On the underside of the crown wall,this pressure was assumed to betransferred with no losses to theforward edge, with the upliftpressure decreasing linearly overthe element width, B"*, to zero at therear edge. These assumptionswere used to calculate the uplfftforce acting on the structure.

These formulae give a simpleempirical fit to the original data fromwhich they were derived, butconsiderable scailer suggests thatsome parameters may have beenomitted, or the governing processeshave not been fully described. Oneexample of potential over-simplification of the physicalprocesses is that the horizontalpressure is assumed to act over thefull height of the crown wall.

F" l \L.-*"

Figure 3.4 Horizontal/ up'lift forces on crown wall,after Simm (1991)

Hamilton & Hall (1992) conducted an extensive study on crown wall stability, but did not propose anyamendments or alterations to the above formulae. They described quantitatively the effects ofchanging a range of parameters in terms of the stability of the model structure, but did not provide anyspecific design guidance.

3.2.2 Up-lift forcesRelatively little information is available on up{ift forces acting on the underside of caissons or crownwalls. Those design methods which give guidance on up-lift forces generally assume that the up-liftpressure at the seaward edge is equal to that acting at the base of the vertical wall. lt is then usuallyassumed that up-lift pressures are distributed triangularly, reducing to zero at the rear of the caisson /crown wall. There are however few data to describe the shape of this pressure distribution, which maydepend on parameters such as: the structure geometry; permeability of the rubble mound; siltationalong the rear side of the structure; and the incident wave conditions.

Goda's method uses a further equation, see eqn (3.7e) in section 3.2.1, to determine the up-lifipressure at the seaward edge, potentially disconnecting it from that acting horizontally at the base ofthe caisson. The distribution of pressures under the caisson follows the assumed triangular distributiondiscussed above.

ln few if any instances are methods to predict these pressures based on any measurements. Yet theoverall loadings on the structure, and pore pressures acting in the foundation materialand contributingto its strength, all depend upon reliable estimates of up-lift forces. Franco (1994) notes particularly that

26 sR 443 02/09196

Efield measurements of pressures on a breakwater at Genoa had demonstrated that up-lift pressures

could vary rectangularly if drainage of pressures at the rear side is inhibited by siltation in the harbour.This effect could increase the total up-lift force above that assumed by a factor of 2.

o) Rectongulo. b) T.opezoidol

Oumeraci (1 991 ) describedcaisson modeltests where uP-liftpressure distributions differedfrom the simple assumptions, andnoted that the effective point ofapplication of the up-lift force is ofparticular importance whenovefturning stability of a structureis considered. An exponentialdecay of up-lift pressure couldmove the point of applicationforward, thus increasing theoveilurning moment. McKenna(1996) describes four differentforms of up{ift pressuredistribution that have been seen in

Figure 3.5 Forms of up-lift distributions, after McKenna the results of these tests,(1996) summarised here in Figure 3'5.

The simplest two are therectangular and trapezoidal forms a) and b) in Figure 3.5 discussed earlier, but two other forms havebeen seen in measurements. The convex form shown in c) probably occurs at a short time after b) andolten coincides with the maximum up-lift force rather than with the maximum horizontal force. Theconcave form in Figure 3.5d) generally occurs at the time of maximum horizontalforce, but thereforedoes not necessarily indicate maximum up-lift force, nor the lowest overall stability.

3.2.3 Seaward or suction forcesA substantial proportion of failures of vertical walls are by overturning or sliding forward, that is in theopposite direction to the horizontal forces discussed above. Further, most blockwork breakwaters orseawalls fail by progressive movement seaward of individual blocks.

Despite the occurrence of these two effects, there few generally established methods to estimateseaward forces or suction on a vertical wall. A simple graphical method to estimate the quasi-staticpressure difference across a caisson breakwater at the point of maximum wave draw-down issuggested by Goda (1985).

Goda writing in Herbich (1990) gives a very simple method to estimate the pressure under a wavetrough at a vertical wall:

p - p * gand

f o r - 0 . 5 H , * < z < 0 (3.21a)

(3.21b)p - -0.5p* 9H.", tor z < -0.5H,*

3.3 Hydraulic model testsThe evidence of damage / failure of structures identified in Chapter 2 suggests that design methods inuse internationally do not always give reliable estimates of loadings or responses for these types ofstructures. The discussions in section 9.1 - 9.2 on prediction methods have identified different design /analysis methods which give varying estimates of the different loadings or responses, and whoseregions of application ditfer widely. Both the evidence of damage / failures, and the variabilities inprediction methods, lead to significant uncedainties in the analysis / design of these types of structures'and demonstrate that more reliable methods are needed to give engineers improved predictions ofwave loadings and of structure responses.

27 sa44Bo2l@l

trThe most reliable methods to predict wave loadings have been for many years, and still remain,hydraulic model tests at scale ratios that allows the correct reproduction of wave forces and / orstructure responses. The main purpose of such tests, outside of those conducted for research studieson particular responses, has been to determine whole body forces or, less often, wave pressures, thusallowing the designer to set the main caisson dimensions / weight. Hydraulic responses of wavetransmission, wave overtopping, and/or reflections may also be measured. These measurementscommonly use hydraulic models of scales between 1:20 and 1:70.

Typical model studies of the hydraulic performance / stability of a caisson breakwater would beconducted in a 2-dimensional wave flume (2-d), and/or in a 3-dimensional wave basin (3-d). ln eachinstance, a range of different wave conditions would be used to quantify the performance over a rangeof retum periods / risk levels. Random wave tests might typically cover 1000 to 5000 waves.Measurements that made during such tests might include:

a) Wave forces and moments acting on a section of caisson using a force table, dynamometer,or other force measuring devices;

b) Wave pressurgs at points on the front face, and/or on the underside;c) Wave overtopping, mean discharges and/or wave by wave;d) Number / proportion of waves overtopping;e) Transmitted wave energy / heights;0 Reflected wave energy / heights;g) Movement / displacement of toe armour elements;h) Scour changes to bed levels in front of the structure.

It is unlikely that any particular study would include all of these measurements, but would certainlyinclude a) or b), and probably c) and/or d). Examples of such studies using force measurements havebeen discussed by van der Meer et al (1994), and using pressure transducers by Franco (199a) andNoli et al (1995). Franco et al (1994) discuss wave overtopping measurements in such studies.

3.3.1 Selection of modelscaleThe size of the model will be set to avoid any unnecessary scale effects, and to fit the test facilitiesavailable. lt is worth noting that the scale ratio itself is of little relevance in the avoidance of scaleeffects. Most scale effects in breakwater models may be minimised by ensuring that flow conditionsare in the same regime in model and prototype. Owen & Allsop (1983) and Owen & Briggs (1985)reviewed studies of armour stability in laboratories in the USA, Denmark, and UK, and concluded thatscale effects in the flow in the primary armour on rubble brealcwaters are insignificant provided that theReynolds number, defined by the nominal armour diameter, is kept above Re = 3x104. For rubblebreakwaters, this is achieved by ensuring that model wave conditions do not fall below H"=0.15m.

A similar argument may be pursued for flow in / around perforated wave screens, where the Reynoldsnumber may be defined in terms of the screen thickness, t". In studies of wave reflections from verticaland perforated walls, by Allsop et al (1994b) assessed data from a perforated screen in a wavedisturbance model to determine the lowest (model) wave height below which levels of energydissipation start to change significantly. Allsop et al (1994b) plotted the sum of relative reflected andtransmitted wave energies (C,2 + C,'?) against modelwave height. The energy dissipation response isgenerally flat, but rises for Re < 4x103, as flow resistance of the screen increases giving greaterreflections and less relative dissipation within the screen.

The remaining responses which may suffer from scale effects, even in models that meet therequirements outlined above, are wave impact pressures. Such pressures are likely to be greater inmagnitude in small scale hydraulic model tests, but shorter in duration than their equivalents at fullscale in (invariably aerated) sea water. Peak pressures measured in hydraulic model tests thereforerepresent over-estimates of those likely to occur at full scale, thus providing some (as yet un-quantified)safety factor.

28 sR 443 02y09/96

EThe argument on scaling these peak pressures requires information not presently available on therelationships between the statistics of the pressure time gradients and the magnitude of the pressureimpulses. Major research programmes have been underway at University of Plymouth with supportfrom EPSRC, and at Hannover / Braunschweig under the MAST lI-MCS project, but these studies hadnot at the time of these studies resulted in any significant guidance on the scaling of wave impacts.New research by HR Wallingford and Bristol University on concrete armour units on breakwaters, seeHowarth (1996), has however been used here to address this problem in Chapter 7 of this report

It should be noted that the use of a force table or dynamometer to measure horizontal loads, a) above,generally precludes the reliable determination of up-lift forces, and hence of total overturning moments.A force table must usually be mounted close to the base of the (model) structure on which loads are tobe measured, thus placing the device within the (model) mound or foundation. Conversely, adynamometer may be mounted above the measurement caisson, removing any sensing elements frombelow the caisson. Unfortunately, these devices still require that the measurement caisson be free tomove, if only slightly, without restraint from the under-lying mound / foundation material. This inevitablyleads to a preferential flow path, substantially distorting any up{ift forces on the caisson.

These particular problems can be overcome by using pressure transducers mounted in the front faceand underside of the caisson. The pressures may then be summed to give horizontal and up-lift forces,and moments about a chosen point, usually the rear heel point of the caisson. Correct reproduction offlow / pressure conditions beneath the caisson can be ensured by scaling (model) mound / foundationmaterials to reproduce the correct permeabilities, and construction the model carefully to avoidunrealistic flow condiiions along the lower face of the caisson. The up{ifl transducers must bemounted and protected to avoid any possible damage by stones protruding from the mound /foundation.

29 sB 44302109l

E

sR 4€ 02rc9l9630

tr4 Design of research studies

It is apparent from previous work in the laboratory and in the field that there remain considerableuncertainties in determining wave forces on composite walls; in predicting conditions that lead to waveimpacts; and in estimating the loadings themselves. Analysis of recent laboratory and field datasuggests that impact loadings are considerably more important than had previously been presumed,and have probably been implicated in damage or movement of a number of structures. lt was thereforeclear that new research studies were needed to provide a consistent and comprehensive source ofdata on wave loads on veftical and composite walls / breakwaters.

Model studies alone will not complete the gaps in information, but resources available in this two yearproject did not permit field measurements, nor the extended laboratory studies needed to resolveuncertainties in model / prototype scaling etfects. lt was expected, however, that these issues werealready being addressed by other researchers in the MCS and PROVERBS projects under the EU'sMAST ll and lll research programmes.

ln the event, an (informai; extension of the reporting of this project has allowed the inclusion of newinformation on scale effects on wave impact pressures measured in hydraulic modeltests, thus yieldingguidance on scale corrections for the measurements in this study.

4.1 Overall plan of studiesHydraulic model tests were therefore conducted to measure wave loads on a range of simple verticaland composite breakwater configurations. tn designing these tests, it was noted that many previousmodel studies, particularly those used to derive Goda's and Takahashi's prediction methods, had beenbased primarily on studies of the sliding distance of model caissons. No force measurements hadbeen made. ln other studies, the overall force on the front face had been determined by a force plateor dynamometer, but the need to ensure clearance for (slight) displacement of the sensing elementprecluded reliable measurement of up-lift forces. lt was determined therefore that the only way to avoidthese limitations was to measure wave pressures on both the front and underside of model caissonsections.

Figure 4.1 Deep wave flume

31 sa 44302lo9l

trThe modeltests were conducted inthe Deep Random Wave Flume atWal l ingford, Figure 4.1, which is52m long and operates with waterdepths between 0.8m and 1.75m.The flume is configured to reduceany reflection of wave energy fromthe test section in its absorbing sidechannels. The bed level at theposition of the structure was +1.00mrelative to the flume floor, and thebathymetry approaching the testsection was formed to a uniformslope with a gradient of 1:50. Themain caisson was formed as ahollow box in marine plywood withpressure transducers mounted flushwith the front face and theunderside, Figures 4.2 and 4.3.The design and construction of themodel caissons, and of themeasurement systems, werediscussed with the MCS project byMcKenna et al (1994) andVicinanza et al (1995).

Figure 4.2 Gaisson/mound geometrical parameters

Figure 4.3 Pressure transducer positions

The geometric and wave parameters that influence wave forces include:

a) significant offshore or inshore wave heights, H"o and H,,;b) water depth in front ol structure, h"; and crest freeboard, R"c) wave steepness, sm, and wave length at structure toe, \;d) water depth over mound in front of wall, d; and berm height, ho;e) berm width, Bo, and front slope of mound, q;

0 depth of embedment of caisson into mound, ho-h"

Studies to vary each of these systematically would have required up to 1500 tests, equivalent to some55-65 weeks testing. The contract period for the DOE supported work was however limited to 2 yearsincluding: study design; construction and installation of all test sections and instrumentation; andanalysis of the results; so drastic reductions of the programme were required. These were achieved byconcentrating on those dimensionless parameters believed to be most important to the processes,particularly the relative wave height, H"/d, the relative berp length, Bo/L, and the relative berm height,ho/h". The main geometric parameters are defined in Figure 4.2.

These tests were not intended to reproduce any particular structure, nor was any particular modelscale implied in the study design. Most of the design and analysis was intended to be conducted indimensionless terms, in which case no scale is needed. lt is however often convenient to bear in minda scale or range of scales, both to check for any potential scale effects, and to calculate thesignificance in prototype terms of particular measurements. These studies generally relate to prototypesituations at model scales between 1 :10 and 1:50, giving incident wave conditions up to H"=2m or 10m,so many practical situations may be covered by a scale of say 1:30. After completion of these tests, itwas noted that related tests conducted by Politecnico di Milano and Delft Hydraulics were alsoassigned a nominalscale of 1:30, see Franco (1996).

Storm waves around the coastlines of UK and Europe generally give wave steepnesses of about s'o=0.04 to 0.06. lt is known that some response functions are strongly geared to wave steepness, so testswere also run for a lower wave steepnoss, s,o= 0.02, corresponding approximately to diffracted waves

32 sB 443021091

trwithin a harbour, to reduced wave heights / growth of wave length following a storm, or in some areaspreceding the arrival of a storm. Tests were limited to three nominalwave steepnesses, s,o= 0.02,0.04 and 0.06.

Water depth is important for its effects on incident waves, in the position of action on the wall, and indetermining the effects of any approach slope or mound. The model was designed to be tested at up to5 water levels (each 0.09m apart in the model). All5 water levels were used during these tests, but notfor all structures.

The wave heights used in the test facility were limited in magnitude by the capacity of the wavegenerator, but were varied to give intermediate and shallow water conditions. For the simple verticalwall, values of relative wave height H",/h" varied between 0.1 to 0.6, but this range was restricted to0.15 to 0.4 for some other structures.

For the simple wall, the parameters varied were limited to the wave conditions and the local waterdepth. The crest level of the wall was not changed, although its freeboard R" varied as a consequenceof the changes to the water level. For the composite walls, the main change was to the relative height /depth of the rock mound in front of the wall, both by varying the absolute height of the mound, and byvarying the water level. The other changes were to the width of the berm, 3 widths were tested, and tofront slope angle of the mound, varied between 1:1.5 and 1:3 with most tests using 1:2.

The level of the caisson base was varied to study the influence of relative embedment on up-lift forcesacting on the underside of the caisson. The caisson base was set at 3 different levels, equivalent to 3depths of embedment, but giving 7 different values of the submerged depth, h', used in Goda'sprediction method.

4.2 Design of modeltests4.2.1 Test structuresEleven structures were tested in thisstudy. Structure 0 was a simpleverticalwall, tested to describe thehorizontal loadings on the simplestconfiguration. The main compositewalls were Structure 1 with a smallmound, Figure 4.4; Structures 2 or 3with intermediate mounds, Figures4.5 and 4.6; and Structures 9 and10 with large mounds, Figure 4.7.The remaining structures werevariations from these intended toyield a coherent data set from whichthe influence of each parametercould be identified. Thecombinations to investigate certainparameter influences may besummarised:

berm width, Bofront slope, cotccore depth, h"mound depth, ho

Figure 4.4 Structure 1


structures 3, 6, 7, and indirectly 4 and 5structures 3, 4,5structures 2,3,9, (8, 10)structures 3, I (1, 2) (9, 10)

33 sR 443 0209/96

trStructure 0, the simple verticalwallwas placed with the toe of thecaisson at +1.000m, themeasurement caisson was itselfelevated by 0.112m to give a crestlevel at +1.802m, 0.802m above thetoe level. The main geometricfeatures of the test structures aresummarised in Table 4.1.

When considering the influence ofthe berm width Bo, and the frontslope angle cot q, it was found thata single parameter could be definedto include the influence of bothparameters. The equivalent bermwidth, B"o, is defined halfway up theberm, rather than at its crest:

B* = Bo + (ho/2tanc) (4.1)

The model caisson was formed as ahollow box in marine plywood, andwas secured to the seabed by 8screw rods. The front face and the



underside of the model were stiffened with stainless steel plates. For each of these structures, thecaisson boxwas mounted onto two longitudinal timber beams which gave the desired mound heightbeneath the caisson and ensured that the caisson could be restrained rigidly. For Structure 0 wherethere was no mound, the void between the narrow beams beneath the caisson was blocked by a plate

flush with the front face. For the composite structures, this space was filled by the rubble mound.

for walls and mounds

Pressure transducers were installed at 8 positions on the front face of the caisson, 4 on the undersideand 4 just below the surface of the rubble mound. The use of a hollow box enabled overtoppingcollection and measurement equipment to be installed inside the bo)q reducing the need for externalcollection or measurem ent devices.

The rubble mound consisted of three rock gradings: the core (2-77g\;the filter layer (164-2739); and

the armour layer (1.0-1.2kg). During construction of each model configuration, the model caisson was

able 4.1 Main

Structure cot q hb hc Bb Crest level

(m) (m) (m) (m above bed at toe)

0 vertical 0.802

1 2.0 0.187 0.112 0.25 0.802

2 2.O 0.367 0.112 0.2s 0.892

3 2.O 0.367 0.202 0.25 0.892

4 3.0 0.367 o.202 0.25 0.892

5 1 . 5 0.367 o.202 0.25 0.892

6 2.O 0.367 0.202 0.375 0.892

7 2.O 0.367 0.202 0.50 0.892

I 2.0 0.457 0.202 0.25 0.892

9 2.0 0.367 o.292 o.25 0.982

1 ( ) 9 0 o 457 o 992 o 2 5 o-982

34 SR /143 02/09196

trlowered onto a bed of core at the appropriate level, and any gaps at the caisson / mound interface werefilled by careful addition of core material. The berm and front slope were then formed in core material,to which filter and armour layers were added.

4.2.2 Test facilityThe test flume is 52m long, and operates with water depths at the paddle between 0.8m and 1.75m.The flume is configured to reduce re-reflection of unwanted wave energy from the test section by theuse of absorbing side channels on either side of, and separated from, the central channel by perforateddividing walls. The two outer (absorbing) channels are each 0.9m wide and 42m long; and the central(test) channel is 1.2m wide and 52m long.

The bathymetry in the flume was formed by moulding cement mortar over fill in the central channel tothe required shape. From deep water near the paddle, the seabed sloped initially at 1:10 with agradual transition to a more gentle slope of 1:50, and terminated in a 5m horizontal section where themodel was placed. The bed level at the test structure was +1.00m relative to the flume floor at thewave paddle.

Waves were generated by a sliding wedge paddle, driven by a double acting hydraulic ram. Thepaddle movements are computer controlled using software developed at HR Wallingford (HRWAVEGEN), enabling regular or random waves to be produced. The random wave signals aregenerated using a white noise filter technique with a single shift register, to match any wave spectrumthat can be specified at 16 equal frequency ordinates. JONSWAP spectra were generated for all of thetests. The nominal wave heights in Table 1 were generated and measured in the deep water section ofthe flume. The wave conditions in the central section of the flume approaching the test section weremeasured during the calibration tests described in section 4.4.

4.2.3 Test conditionsA range of wave conditions at five water levels were used to investigate the performance of thedifferent structure types under different relative wave conditions. These were chosen so that theinfluences of significant wave height and mean sea steepness could be investigated separately, anddirect comparisons could be made between different water levels. Wave conditions and water levelsare summarised in Table 4.2. At each point marked with a water level (eg +1.43) waves were run thenominal wave heights indicated

hble 4.2 Test conditions, wave steepness, wave height, and water levelssm H-=0.10m H-=0.20m H*=0.25m H.^=0.30m

0.02 +1.43

0.02 +1 .52

0.02 +1.61

0.02 +1.70

0.04 +1.34 +1.34 +1.34

0.04 +1.43 +1.43 +1.43 +1.43

0.04 +1.52 +1.52 +1.52 +1.52

0.04 +1 .61 +1.61 +1.61 +1 .61

0.04 +1.70 +1.70 +1.70 +1.70

0.06 +1.34 +1.34 +1.34

0.06 +1.43

0.06 +1.52

0.06 +1.61o 0 6 +'l 7O

35 sR 4€ q2l09196

tr4.3 Instrumentation and test measurementsThe main measurements made during these tests may be summarised:

a) Instantaneous water levels used to determine wave height / period, using standard HR twinwire wave probes and logging modules;

b) Volumes of water collected in the overtopping tanks, using a continuously recorded load cellunder the collection tank, and/or volumetric measurement of total volume collected over(usually) 500 waves;

c) Number of overtopping waves detected by short wave probes mounted on the structurecrest;

d) Wave reflections derived by analysis of the output from an array or 3 wave probes in front ofthe test structure;

e) Wave pressures on the front face (8) and underside of the caisson (4);0 Wave pressures at (4) positions in the seaward face of the mound;g) Video record of wave profiles obserued through a side window of the wave flume.

Three computers were used during testing. On the first of these, data were acquired from all 16pressure transducers at 400 Hz using the DATS package. The second computer collected data fromthe wave gauges (one offshore, three for reflections and one at the toe of the structure), and from theovertopping cell, using HR WAVES. The third computer was used for random wave generation usingHR WAVEGEN.

The pressure transducers installed on the front face of the caisson were supplied by ControlTransducers and were Model AB with a rated capacity of 0 - 6 psi and up to 2x over-load, but with 4xover-load betore permanent damage to the devices. These transducers gave an upper limit for highresolution measurements equivalent to about 8m (fresh) water head, and a maximum pressure beforedamage on the transducers equivalent to 15m. The transducers on the underside of the caisson wereDruck PDCR 810 with a range of 0 - 2.5 psi.

Before testing started, each set of transducers were checked and calibrated. The AB pressuretransducers on the front face were set up so that 1m of (fresh) water head was equivalent to about 1volt. With a range of 0-10v on the analogue to digital computer board (A/D card), this ensured that allpressure signals that could be measured at high resolution would be recorded in O-8volts, theremaining range being available for any further over-load conditions. The up-lift and moundtransducers were set up so that 1m of (fresh) water head was equivalent to about 5 volts.

The principal recording parameters used here necessarily represented compromises between theneed to measure fast-acting events; the need to collect statistical information over a realistic number ofwaves; and restrictions on data volumes which could be recorded, stored, and processed.

It is generally agreed that faster sampling rates will yield greater wave pressures / forces, provided thatthe transducers are able to respond quickly enough. Some researchers interested in impacts haveused sampling rates up to 5,000 or 10,000H2, see particularly MUller (1993) and Kirkg6z (1995), butsuch rates have been restricted to very short test durations, often limited to regular waves or pre-determined wave packets. In contrast, most engineering studies have used force plates, tables, orframes, with sampling rates limited to no more than 25H2, see particularly van der Meer et al (1994).Oumeraci et al (1994a) provide a graph based on experiments at Hannover which suggests reductionfactors for impact pressures, impact forces, and impulses, as functions of the sampling frequency. Thisgraph suggests that sampling at 400H2 may give under-estimates of maximum pressures by up to50%, but that the equivalent reduction for horizontal force would be limited to 2O"/". At these rates, thetotal impulses are not significantly affected.

The statistics of wave pressures / forces are improved with longer test durations, and increasednumbers of events sampled will tend to increase the maximum pressures / forces recorded. Theoriginal test design had specified l OOO waves, although previous tests described by Meer et al (1994)used 1000 - 3000 waves. During early tests, it was found however that 1000 waves at4OOHz

36 sR 443 02109196

trgenerated files that were too large for the recording computer / software. The test length was thereforerestricted to 500 waves.

4.4 Test procedures4.4.1 Wave measurementsBefore the model breakwater was installed in the flume, wave conditions at the position of the structurewere measured during calibration tests. Short sequences of waves were generated during calibrationand were determined using spectral analysis. Measurements of water surface elevations were madeusing 8 twin wire wave probes, located along the approach to the caisson.

Once the nominalwave condition had been achieved, more comprehensive measurements were thenmade using longer sequence lengths, analysed using statistical methods. This ensured that extremewaves were reproduced correctly, and that the statistical distribution of wave heights was recorded.Statistical analysis allowed the significant, 0.17", and other extreme values of the wave heightdistribution to be determined at each wave probe position, together with the mean wave periods.

These long wave sequences were used during testing to ensure that extreme waves were correctlyrepresented. Incident and reflected wave conditions were measured using 3 wave probes, locatedapproximately 2 wave lengths seaward of the structure. The overall reflection coefficient, C,, wasdetermined by summing energies for each test condition.

4.4.2 Wave overtoppingDuring most of these tests, the number of waves overtopping the structure, the wave by waveovertopping volumes, and the mean overtopping discharges, were each determined. The numbers ofwaves overtopping the structure were counted using four overtopping probes spaced across the widthof the flume. The mean overtopping discharge was calculated from overtopping volumes measuredusing a weighing mechanism located inside the caisson which formed the vertical wall. A 100mm widechute directed overtopping water into the tank. The sensitivity of the weighing mechanism allowed themeasurement of wave by wave overtopping discharges. The mean overtopping discharge wascalculated at the end of each test. When a high mean overtopping discharge was expected during atest, the weighing cell was removed and a large reseruoir was used to collect the water. The water wasthen pumped into calibrated volumetric cylinders. These results have been analysed by Madurini &Allsop (1995), and have already been discussed further by McBride et al (1995), so are not included inthis report.

4.4.3 PressuresPressure data from the 16 transducers were acquired at a rates up to 400H2. Wave impacts recordedby the 8 front face transducers were recorded at 400H2. Pressures measured by 4 slower transducerson the underside, and the further 4 in the seaward face of the rubble mound were filtered at 20H2, yetstill sampled at 400H2 to avoid excessive complication in the logging and computation procedures.Data were acquired continuously for all channels through each test for about 500 waves to prevent thedata loss which occurs with selective acquisition systems. The files generated were very large even inmultiplexed binary format, and had to be expanded by de-multiplexing before analysis. Once de-multiplexed, these files were then put through a preliminary analysis process, in which interesting datawere selected for further analysis.

Within the analysis program, pressure measurements in volts were notionally converted to metres headof fresh water, and these values were then converted to pressures in kN/m2 by multiplying the pressurehead values by p,g.

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E

5.1

5 Resu/fs of test measurements

The principal responses of interest here are the individualwave pressures acting on the front face andunderside of the caisson. As individual pressure records, these data are very difficult to handle and toassimilate, so values of the horizontal and up-lift forces, Fn and Fu, are calculated by integrating thesepressures over the front face and underside of the test caisson.

Pressure data were collected at 400 Hz from 16 channels for 500 waves, giving about 30 Mbytes ofresults per test. With over 200 tests, the initial analysis task was therefore to extract key information foreach test. This need to reduce data volumes had however to be balanced by the need to avoidimposing any particular prejudice on the information likely to be of most interest and/or utility. Theanalysis approach therefore tried to balance these conflicting needs to maintain as much information aspossible, whilst compressing data sufficiently to allow judgements to be made on the occurrence andmagnitude of particular responses. Later analysis therefore operated at various levels of detail.

The analysis program described in report 1T430 by Centurioni et al (1995) was used to identify "waveforce eventsu, about 500 per test. After all such events had been defined in a particular test, theprogram read each pressure channel to detect peak pressures and rise times (At) for each event oneach transducer. Pressures on the front face, and on the underside, were also summed to give totalhorizontal and up-lift forces, and overturning moments using the approach derived by McKenna et al(1994) and modified by Centurioniet al (1995). Results are given, with a summary of test conditions, inthe Appendix to this report.

This chapter describes the form of the pressure measurements, how the data were handled; thederivation of 'force events'; and aspects of data quality, handling and archiving.

measurements

Figure 5.1

Before discussing the detailedanalysis of parameters derived fromthe pressure signals in Chapter 6, it ishelpful to consider a few examPlesselected from the (in excess of 1million) waves sampled. Pressuresmeasured by a transducer mounted atthe static water level are shown inFigure 5.1 for about 9 waves. Thisexample from tests 10003 onStructure 1 with a low rubble mound infront of the wall, shows some waveswith sudden pressure rises and highpeaks termed, impact events; andothers with substantially smallerpressures with much longer rise times,termed pulsating events.

The forms of these wave pressure traces vary widely, depending most strongly on the type of wavebreaking, and the position of the pressure transducer. The shape of the pressure / time records maybe broadly classified in four types shown in Figures 5.2 - 5.5, and described below:

Typical pressure events from test 10003on Structure 1

1

3.5

2-S

o

* . .

I

0.5

o

{.5

39 sR 443 0209196

trType 'l lmpact pressure on the

vert icalwal lcharacterised by a shortrise time, At<0.01T0, andhigh pressure peak,followed by a muchlower, but longerpressure peak, Figure5.2:

Type 2 Less severe impactpressure, or up-lift /mound pressure at thetime of impact, withsimilar characteristics asType 1, but with smallerpeak pressures andlonger rise times,At<O.1To, Figure 5.3;

Type 3 Double peakedpressures from steepnear-breaking waveswith both pressure peaksof similar magnitude, andwith long rise times,At'0.2To, Figure 5.4;

Figure 5.2 lmpact event from test 10003 on Structure 1

Figure 5.3 Small impact event from test 10003 onStructure 1

Figure 5.4 Double-peaked event from test 10003 onStructure 1

5 0 .5

40 sR 443 02109/96

trType 4 Non-breaking or

pulsating wave pressureswith single peaks, andwith long rise times,At'0.2To, Figure 5.5.

Figure 5.5 Pulsating event from test 10003 onStructure 1

I The requirement to describe as fully as possible the pressure peaks in Types 1 and 2 as shown inFigures 5.2 and 5.3, as well as giving a full description of the longer events in Types 3 and 4 motivatedthe requirement for rapid sampling, chosen here at 400H2. l

Individual pressure events are of little practicalapplication without information on the overall levelofforces acting on the wall, and information on the distributions of pressures on the structure. Theexamples shown in Figure 5.6 illustrate how pressures vary in time, and between the different pressuretransducers, with transducers 12 and 13 above the water level, 14 at s.w.l. and 15 and 16 below.lnspection of these impacts show how the peak pressures tended to propagate away from the point ofmaximum pressure, moving both spatially (up and down the wall) and thus temporally. This illustratesthe potential for phase lags between different peak pressures, or forces.

Initial stages of the main analysis of these results concentrated on the total horizontal and up-lift forcesacting on the caisson, Fn and F". These forces were determined by summing pressures over the heightor width of the caisson as appropriate, see section 5.2tor more details. Each test gave approximately500 force events, which were then ranked by magnitude to give probability or exceedance distributionsof force for each test. These exceedance distributions of horizontal and up-lift forces were plotted onWeibull axes to identify the form of the force statistics; to check for any inconsistencies; and to identify il/ where changes of wave breaking altered the type / distribution of loads. These are discussed morefully in section 6.1.

At an early stage in the analysis, there was some discussion as to the statistical level at which the mainresponses should be analysed. lt was noted during testing, and during the statistical analysis, that allfour types of wave pressure event shown in Figure 5.1 could occur in any single test. The use of theWeibull presentation of the force statistics however reduced the data to much simpler form, but did notresolve which statistical level would be representative of the complete distribution. Inspection ol thestatistics revealed that no single value would give the full distribution, and that at least 4 parameterswould be needed to give the full description. lt was therefore decided to concentrate on the statisticallevel used by Goda, and therefore inherently accepted in the British Standard, CIRIA / CUR manual,and by other researchers comparing with Goda's prediction. Most latdr analysis has therefore used themean of the highest 1/250 values, so for tests with 500 values this corresponds to the average of thehighest 2 values, or here to the average of 99.6 and 99.8% non-exceedance levels.

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E' I

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395 395.5 396 396.5 397 397.5 398 398.5 399 399.5 40t (sec)

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{.5395 39s.s 396 396.5 397 397.5 398 398.5 399 399.5 400

t (sec)

3.5c 3* z.u7 2

E t.st lI o.s

v J

-0.5 '

395 395.5 396 396.5 397 397.5 398 398.5 399 399.5 40t (sec)

Figure 5.6 Example pressure / time series over height of caisson

42 sR 443 02/09196

tr5.2 Definition of pressure / force eventsThe first problem in the analysis of the data was to reduce the files to a manageable volume,particularly with over 200 tests each with data files of 1.5-2.0Mbyte x 16 transducers = about 30Mbytes.The first part of the analysis identified those parameters to be recorded for each impact "event", andthus reduce the volume of data to be processed.

Measurements of wave pressure were processed using a new program by Centurioni et al (1995) todefine each "event", so that every time there is a wave impact, the analysis program found a rapidpressure rise to mark the beginning of the event. This involved a series of steps to threshold the signal,then to search for a rise past the threshold that large enough to exclude noise on the pressure signal.Once the start of the event had been identified, another section of the program checked if the signal isdecreasing and falls below an appropriate threshold which is a function of the zero level. When thisdouble condition is verified, the program starts again to look for a new event so that, if a signal has twopeaks or is stepped, the program will only record a single start of event. The event definition ischecked only for the record from the still water level pressure transducer. The very first event is alwaysdiscarded because the measurements might begin somewhere inside it.

The level dnd sign of the noise level (value and sign) needs to be identified to define a threshold forevent processing. A somewhat complex procedure has been developed, but tests have shown that acareful definition of this threshold is needed to avoid errors, particularly if the set-up of the transducer isat all uncertain. A parameter proportional to the noise level is also added to the signal so that themaxima are always positive.

The algorithm used for event definition calculates 2 running averages, and their ratio. When this ratio isgreater then 1.1 for (T./6).400 consecutive times, the program recognizes an event and transferscontrol to another section. The program later seeks an *end of event", after which the programsearches for the next event.

After all events have been identified, the program reads through all the channels and the pressure

Figure 5.7 Example force - time series

peaks are detected for alltransducers. For each event andfor each transducer, the routinefinds the time interval between thepressure peak and when the signalis 2O"/" of the peak (At). Beforemoving to the next event, theprogram derives the main outPutparameters: the horizontaland uP-lift forces, and the ovefturningmoments. Pressures on front faceand under side are summed usingthe trapezium rule, and examPleforce results are shown in Figure5.7. The program also records themaximum pressure for each event,and for each channel.

The forces and moments acting on the (model) caisson at each timestep were calculated from thepressure measurements using an approximate integration method. The positions of the transducers donot cover the full height or width of the caisson, and are not spaced at even intervals. Someinterpolation and indeed extrapolation is therefore necessary. The trapezium rule was chosen inpreference to the staircase method or Simpson's rule since it permits flexibility in the spacing of theinteruals, yet gives results which are in good agreement with analytical integration methods. lntegrationby the staircase method tends to over-estimate forces and moments where there is a high localpressure since it assumes that pressure acts over the whole area between the measurement points.Simpson's rule might have improved accuracy in integration, but the parabolic distribution over three

F

z.YEu-

-1

400

43 sR 443 02109196

tradjacent points might also have given erroneous results in some cases, so the simpler method waspreferred.

5.3 Data quality and repeatabilityOne of the major concerns in research is always to establish the quality / reliability of the dataproduced. In this work, lhis procedure was of particular importance due to:

a) The direct link between these measurements and the development of new / revised designmethods for wave loadings, and hence impact on the safety ol structures designed usingthem, as in BS 6349.

b) The highly variable nature of many previous measurements of wave loadings, particularly

those laboratory tests using repeated regular waves from which conclusions have beenbased on pressures / forces at extreme exceedance levels, see Mttller (1993) or Kirkgoz(1 ees).

During the model testing programme, a number of checks were made to evaluate data reliability, fallinginto four main areas.

At the end of data acquisition, measurements were de-multiplexed and a module within the DATSsoftware package was used to view pressure - time traces. This procedure gave an instantconfirmation that there were no major problems with the data, and that the pressure traces were of thetype and level to be expected from the obseruations made during the test.

The same procedure was used to inspect pressure traces for signs of 'clipping', and to check that thesample rate was sufficient to cope with the very fast rise times. Analysis at this stage also included thepropagation effect of the wave pressures, where the maximum pressure first occurred at one point onthe front wall, then (say) one timestep later had moved to the neighbouring transducers. Times atwhich large impacts had been observed in tests had been noted in the model diary, and these timescould be compared with the pressure traces to check that these times coincided with impact pressuresignals.

During tests on Structure 1, a number of particularly severe impacts were noted, giving pressures up toat least p=4Op*gH". These excited significant interest, particularly as previous research studies byM0ller (1993) and Kirkgoz (1995) had suggested that such severe impacts might be very variable.Demonstration tests (without pressure measurements) were performed on a number of occasions forvisitors to the tests. As the times of the first few big impacts had been recorded in the test diary,impacts observed in subsequent runs of the test chosen for these demonstrations could be comparedwith that in the original test. These comparisons confirmed that severe impacts always occurred at thesame point in the test.

Tests were later repeated using more sensitive transducers and a faster scan rate for some of the testswhich had given high pressures in the originaltest series. A comparison of pressure - time historiesagain showed that peak pressures occurred at the same point in the corresponding tests and thegeneral form of the pressure traces from corresponding tests in each series were very similar. Therewere some ditferences in the peak pressures where the second series of tests recorded lower valuesthan in the first. This was not fully explained, but was ascribed to changes in the acquisition systemand signal conditioning electronics.

Within the original test series, the only differences between some tests were in the core depth (ie thecaisson base was raised, but all other dimensions remained the same). The pressure - time traces forspecific transducer locations relative to water level (as opposed to specific transducers) werecompared for the same incident wave conditions, and were found to agree very well. Again, thesecomparisons confirmed that measurements of wave pressures at specific locations under tests with thesame wave conditions were repeatable.

44 sR 443 02l09r'96

tr5.4 Data handling / storage / archivingDuring each of the tests in this study, measurements were recorded at rates up to 400H2 using a datarecording and analysis software package DATS. These data values, from up to 16 channels weremultiplexed to give a data acquisition file of up to about 20-30 Mbytes per test. With over 200 testsbeing conducted, and a computer limited to about 200-300 Mbytes storage, it was clear that therewould be several problems associated with holding and analysing these data.

The problem was compounded as each multiplexed file had to be de-multiplexed into 16 individualbinary files containing the time series data for each pressure transducer before any analysis could becompleted. The de-multiplexed data files then occupied twice the disk space volume of the acquisitionfiles. Initially data were to be recorded for 1000 waves, but this was soon reduced to 500 waves toreduce storage requirements.

The acquisition computer was equipped with a relatively small hard disk, so it was only possible tostore one or two data acquisitions on the computer before down-loading them to another device. Thiswas particularly important as the sampling / writing speeds used here approached practical constraintson disk access speed, particularly when such a small disk was more than about half-full. Testing,therefore, had to be interrupted regularly in order to transfer the data files. The files were transferredfrom the logging computer to the HR network for short term storage, de-multiplexing and analysis. Boththe multiplexed and de-multiplexed files were then written to the HR magnetic tape archive system forlonger term storage. The capacity of each magnetic tape was 100 Megabytes. For security reasons itwas necessary to make duplicate copies of each archive tape. Over 200 tests were completed duringthis study resulting in some 50+ archive tapes being written. During late 1995 and early 1996, themajority of this data was also transferred to compact disks (with each of 650 Megabyte capacity).

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tr6 Analysis of wave force / pressure results

The general form of the wave force / pressure data collected in these studies has been discussed inChapter 5. Here the results are analysed in more detailto:

a) Describe the form of the statistical distributions of forces;b) ldentify the occurrence of wave impacts;c) ldentify parameter regions of significantly different wave behaviour at the wall.

Later sections then discuss:

d) Prediction of horizontal and up-lift forces at a given exceedance level;e) Comparisons of measured forces with those predicted by methods described in Chapter 3;0 Examples of vertical pressure distributions;g) Wave impulses and impact rise times.

This chapter also discusses an approach to the calculation of overall stability of monolithic caissons onrubble mounds.

The early analyses by Vicinanza et al (1995) and Allsop et al (1995b) of results from these tests tried todescribe the response of F6, Fu, and later the total overturning moment M' to the main wave andgeometry parameters using simple formulae, each intended to apply across the full range tested. Thatinitial analysis developed simple equations to predict horizontal and up-lift forces, and overturningmoments at the 99.6% non-exceedance level, Fn*.u*, Fu*.u* and M"n.u*. Those equations appeared togive reasonable predictions for the initial set of structures considered by Vicinanza et al (1995), but thereliability of the prediction methods reduced when tested against the full data-set. The methodssuggested by Allsop et al (1995b) extended this initial approach, but scatter in some regions of theparameter space covered factors of up to 2-3 times, and it became clear that these simplisticapproaches were concealing important aspects of the wave / structure interaction.

It was then concluded that such simple methods are unlikely to givereliable predictions, and the approach of Allsop et al (1995b) wasabandoned. Careful consideration of the initial data analysis showed thatthe simplifications had disguised significantly different hydro-dynamicprocesses. Two major improvements were therefore developed in theanalysis described here: distinguishing the relative structureconfigurations; and then the types of wave breaking / loading conditions.

In the first change, the relative structure configurations tested in the studywere divided into three ranges, as illustrated in Figure 6.1:

O < H"/d < 2 and d > 0, when the mound is relatively small, and isalways submerged;

2 < H"/d < 3, and d > 0, when the mound is relatively large, but issti l lsubmerged;

-7 < H./d < -1, and d < 0, when the top of the mound is emergent.

Most of the analysis described in this chapter concentrates on the first ofthese configurations (163 tests out of 217\. Analysis of tests covering thethird range has been conducted under crown walls, section 6.3.3.

In the second change to the analysis method, the measured wave forceswithin each of the above datasets were further divided into 'impact' or'pulsating' conditions, in many ways analogous to the 'breaking' and 'non-

d ,

o4t.i /d<2

d>o24\t/d4

d>o-74r/d<-1

Fig.6.1 Main parameterregions

47 sR 443 0209/96

trbreaking'conditions used by the Shore Protection Manual, CERC (1984). This revised analysistherefore proceeded in 3 steps:

a) ldentify parameter ranges over which wave action at the structure leads to 'pulsating' or'impact' conditions;

b) For conditions identified hers as pulsating, compare wave loads with predictions by Sainflou,Hiroi, Goda, or perhaps Goda modified by Takahashi;

c) For impact conditions, compare wave loads with predictions by Goda modified by Takahashi,or suggest new methods.

6.1 Statistical distribution of forcesWave impact forces acting upon any coastal structure are highly variable, sometimes more so than thewaves that cause them, so wave forces may best be described by their statistics rather than by singlevalues. Most design methods in common use are however deterministic, so single values are requiredfor design calculations. An appropriate probability level must therefore be derived at which to calculatethe important parameters. In doing so, it is important to establish the extent to which any singleprobability level is indicative of the full distribution.

For each test, the analysis program gave a peak horizontal force for each event. These values of Fnwere ranked, allowing the exceedance distribution to be plotted on Weibull probability axes to examinethe statistical distribution. These axes, given by plotting ln(-ln(l-P)) against In(Fn) where P is theprobability level, were selected to give a good description of forces at low levels of exceedance (high

levels of non-exceedance). The Weibull distribution may also be used to examine any link with thestatistics of wave heights within a random sea, as wave heights generatly fit a Rayleigh distribution,itself a special case of the Weibull.

1

0

c 'TC

-2

-3

4

9 o o

1,1*+,t . hnp@t

In(F)

These exceedancedistributions allowed waveforces to be divided into thetwo zones: 'pulsating' or'impact' i l lustrated in Figure6.2. Pulsating forces weredefined as those varyinglinearly with exceedanceprobability on a Weibulldistribution. These forcesgenerally lie in rangescalculated by Hiroi orSainflou's methods. lmPactforces however increasemuch more rapidly over theupper part of the distribution,corresponding aPProximatelYwith those waves that breakdirectly against the wall.

Figure6.2 ExampleWeibulldistr ibutionofhorizontalforcesfor pulsating and impact conditions

In any general analysis, the factors that influence the force or pressure responses must be non-dimensionalised in away that identifies the different form of wave breaking at the wall. Before doing so

below, it is helpfulto review example measurements, here plotted at modelscale. The measurementsconsidered here were limited to cases with moderate mound heights, 0 < H"/d < 2, as discussedabove. Each of the distributions shown in Figure 6.3a-e is derived from a test of 500 waves at a singlesea state and water level, and all those shown have s.o=9.64.

48 sR 443 0209/96

tr(b)

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Figure 6.3 Weibull distribution of horizontal forces, vertical and composite walls

Distributions of wave forces on vertical wallsWave forces at the plain vertical wall (Structure 0) shown in Figure 6.3a are generally pulsating.Forces from two comparative tests which differ only in water level giving relative wave heights ofH"/d=O.25 and H"/d=0.29 show close agreement with a Weibull distribution.

lncreasing the relative wave height from H"/d=0.3 to H"/d=0.4 in Figure 6.3b shows that a few of theforces (about 2"/"1 deparlfrom the main Weibull distribution for H"/d=0.4, as larger waves break onto

49 sR 443 0209196

trthe wall. The overall level of wave forces are not greatly increased by this number / severity of impacts,but extreme loads at non-exceedance levels of 99.6% and 1/250 are increased significantly. Theoverall level of forces increases further as the wave condition approaches the breaking limit for shallowbed slopes around H"/h" = 0.55 to 0.6. For simple vertical walls with no mound, d=h", so depth-limitedbreaking is approached at H"/h" = H"/d = 0.55.

It is then probable that further increases in offshore wave heights would lead to more significantproportions of broken waves. These broken waves would probably not further increase the proportionof impacts, as aerated broken waves generally give lower wave forces.

Distributions of forces on comoosite wallsIt has been noted previously that a mound in front of a wall may significantly increase the proportion ofimpacts, and this effect is well illustrated in Figures 6.3c-e for composite walls with rubble mounds. Inthese discussions, the effect of the rubble berm is related chiefly to its level below the water surface, d,and its effective width given by B*. Each of these parameters is non-dimensionalised by the waveheight, H",, or the wave length, Lo, hence the use of the relative wave height H"/d and berm lengthB"/Lo.

The test on Structure 3 with a small mound in front of the wall, and with a high water levelwhereH"/d=0.8 and B*/Lo=0.13 gives pulsating forces in Figure 6.3c which fit the Weibull distribution.Reducing the water level to give a relative wave height over the mound of H"/d=l.31 significantlyincreases the proportion of impacts to about 157o, and thus increases the magnitude of the extremeforces.

Somewhat similar increases in forces are seen in Figure 6.3d for Structure 4 where the mound slopeangle has been slackened to 1:3, giving an increased mound volume. The test at H"/d-0.8 andBJ\"0.t0 gives about 4% impacts, but the lower water level at H"/d=1.3 significantly increasesimpacts to about 25%.

This effect is illustrated by comparing results for three structures with different mounds. Tests with thesame wave height, period and water levelon Structures 4, 6 and 7 compare the effect of relative bermwidth, BJL',thus including the effect of mound slope angle. Forces plotted in Figure 6.3e showrelatively close agreement for Structures 4 (BJl-er0.18) and 7 (BJl-e'O.19) where the outer toepositions of the mounds are very close. The proportion of impacts are very similar, and other than atthe most extreme level, the wave forces are much the same.

The other mound, Structure 6, with a slightly smaller relative berm width, BJI-''0.t0, shows similarbehaviour in Figure 6.3e, but the proportion of impacts is a little less and most of the wave forces onthis structure are smaller.

A similar approach in Figures 6.4a-c compares responses to different structures under the same wavecondition and relative water level, H"r=O.2rTl, s,o=0.04, and H",/d=1.3. The etfect of the relatively shortmound (B*/L'=O.14) in Structure 3 is compared with that of the simple wall in Figure 6.4a. Waveimpacts on Structure 3 reach about P,=g/o, and wave forces at the higher non-exceedance levels aresignif icantly increased.

lncreasing the relative berm width to B"*l\=0.19 in Structure 7 further increases the extreme forces inFigure 6.4b, and impacts increase to Pi=357o. A similar effect is shown in Figure 6.4c for Structure 4,where the berm width is increased but the seaward slope angle is significantly shallower at 1:3. Thissimilar effective berm width, B"d/+0.18 gives impacts at about PF2O9/" for Structure 4.

50 sR 443 02/09196

tr

- sr|@F 3 llru.a - w&1.31 - &qn+o.l{- sr|@EohM.4

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(c)

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Figure 6.4 Weibull distribution of horizontal forces, effect of berm width

These statistical distributions of forces are useful in identifying the form of the wave loads, but are muchless convenient to use in practice than a single representative force. Most of the remaining discussionon wave forces will therefore concentrate on single values of Fn derived for each test, allowing moredirect comparisons of the effects of structure geometry, and relative wave conditions. ln previousanalysis of these measurements, forces were represented by the 99.6% exceedance level. Forcespredicted by Goda's method are based on the average of the highest 1/250 waves, and if based on astandard sample size, Fn,o* may be more stable than Fnrr.ur.. Values of Fno.* are statistically moremeaningful, but comparisons with Goda's and Takahashi's methods will use values of Fnlo*. Thisexceedance level was chosen for consistency with previous work, particularly design methods basedon work by Goda and analysis by van der Meer et al (1 994). The proportion or o/o of impacts P, willcontinue to be used to distinguish impact from pulsating conditions.

6.2 Analysis of impacts and forcesThe combined influences of wave conditions and structure geometry on wave forces are particularlycomplicated. Initial simplifications in analysis of this dataset by Vicinanza ei al (1995) and Allsop et al(1995b) did not reflect fully the complex nature of the hydro-dynamic process of wave interaction atthese structure, and the initial prediction methods did not therefore give wholly reliable predictions. Theanalysis presented here has therefore concentrated on dividing the tests into those for which pulsatingor impact conditions have most influence on the more eltreme forces in the distributions. The casesanalysed are further divided between the simple vertical wall with no toe mound, Structure O, andcomposite walls, Structures 1-10. This analysis was started in a paper in ltalian to the Ravennaconference by Allsop et al (1995c), and is developed further in this report.

5 1 sB 443 0209196

tr6.2.1 SimpleverticalwallsHorizontal pressures only were measured on the simple vertical wall, so this analysis considers theoccurrence of impacts, and the total horizontalforce. The proportions (%) of impacts P,are illustratedin Figure 6.5, where P, is plotted against H"/d (equivalent to H",/h. because d=h. for simple vefticalwalls). This shows a very clear onset of impacts for H"/d > 0.35, suggesting that this may give a simplelimit for the onset of impact conditions.

An alternative approach has been explored in which the largest wave heights from the statisticaldistributions measured in the calibration tests (represented here by H*.u*) are expressed as aproportion of the limiting breaking wave height (calculated here as Ho(uoo")). Results of this comparisonare illustrated in Figure 6.6, and suggest that an alternative limit for the onset of impacts might be givenby H*.ur./Ho,noo"1)0.8, but this approach is not as clear, nor as simple as the limit of H"/h"=9.35 g;vsnabove, and is not pursued further in this report.

1 0

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65Hsi / hs

Figure 6.5 Influence of H"/d on % impacts, P,, verticalwall

7

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0

r r l

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0.6 0.8H99.6% / Hb(Goda)

Figure 6.6 Influence of Ho.u*/Ho on 7o impacts, P,,verticalwall

This value of H"/h"-0.35 is ratherlower than the relative wave heightgiven by the simple rule of thumbfor wave breaking over shallow bed,H"/h"=0.55. lt is howeverreasonable to expect that a fewwaves will break at wave conditionsbelow H,/h,=Q.$$. lt maY be notedthat the upper few waves in thedistribution may be approximately1.8 to 2 times greater than H", andthat the limiting conditions for singlewaves over shallow slopes isH/h"=Q./$. These suggest that alimit for the onset of breaking mightwellbe given by H./h.=0.35.

These limits are potentially useful inidentifying different types of wave /structure interaction, but do not ofthemselves permit predictions offorces. Values of lhe measuredhorizontalforce non-dimensionalised as Fn.,^o/P*gd'have therefore been plotted againstH"/d in Figure 6.7. Values of thehorizontal force predicted by Goda'smethod are also shown, illustratingrelatively good agreement forrelatively smallwaves in the regionH"/d<0.35, but significant errors forlarger waves, H"/d>0.35.

52 SR 4€ q2r09/96

trFor the simple wall with no mound,Goda and Takahashi's predictionsare equal and for H"/d<0.35,generally fall above themeasurements in Figure 6.7.Goda's method may therefore betaken as giving a safe estimate ofwave loads on simple walls forH"/d<0.35.

For waves closer to breaking givenby 0.35<H"/d<0.6, the predictionmethods under-estimate measuredforces. The differences aregreatest where the incident waveconditions approach the breakinglimit, approximated for shallowslopes by H"/h"-Q.55. This

uncertainty can be partially overcome by a simple prediction curve of the form discussed by Vicinanzaet al (1995) fitted here to results covering the range 0.35<H./d<0.6:

Fn,oul(P*gdt) = 15 (H"/d)t'tto for 0.35<H"/d<0.6 (6 .1)

6.2.2 Composite structures, horizontalforcesThe responses of composite structures are significantly more complex than for simple vedical walls,being influenced by the height, width and seaward slope of the rubble mound berm, as well as by therelative water depth and wave conditions. Some of these complexities were discussed earlier insection 6.1 where example responses to H"/d, and B* were illustrated for particular wave conditions.The overall analysis here uses a similar approach to that in section 6.2.1, but is substantially extendedto reflect the further geometric parameters, and hence the greater complexities of the processes.

The first distinction used in the analysis was to separate data by the relative berm height, hr/h" into'low' and "high" mounds. The lower mounds studied here were described by 0.3<ho/h,<0.6, and highermounds by 0.6<ho/h"<0.9. These limits are not themselves of great significance, but give convenientdivisions between regions of somewhat different response characteristics.

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Low mounds. 0.3<hJh^<0.6For low mounds, the onset of wavebreaking and hence the changefrom pulsating to impact conditionsappears to be maintained at H"/h"=0.35, see Figure 6.8. Thisimpression is however not wellsupported by data, as there are nomeasurements for Structure 1below H"/h"= 0.35. lt willalso beshown later that increased moundlevels move the onset of impacts tolower values of Hlh.. lt is howeveruseful to note from Figure 6.8 thatthe combined influence of near-breaking waves and the moundtogether give a significantly higherproportion of impacts than for asimple vertical wall. An alternative

40

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Figure 6.8 tnfluence of H",/h" on o/o impacts, P,, highmound

53 sB 443 0209/96

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trapproach is shown in Figure 6.9,where P,is plotted against H"/d,thus including more directly theeffect of the relative berm level.This figure suggests that the onsetof impacts is shifted by thepresence of the mound toH",/d=0.65, rather than H"/d=0.35noted for the simple wall.Within the range 0.3<H"/d<0.6, withthe data examined covering0.11<H"/h"<0.33 and0.07<Bsq/Le<0.23, wave loads arepulsating, and the Goda equationsgenerally give slightly conservativepredictions of the overall horizontalforces, see Figure 6.'10.

For higher relative wave conditions,0.6<H"/ds 1 .3, the influence ofseabed and mound combine toincrease the proportion of impacts,as shown in Figures 6.8 and 6.9.The forces have been plotted inFigure 6.10 in the same form asFigure 6.7 for the simple verticalwall. Also shown is the simpleprediction method of eqn (6.1),developed for the simple wall andH,/d>0.35. Surprisingly, thisequation seems also to give a gooddescription of the horizontal forcesfor low mounds given by0.3<hb/h"<0.6, and higher relativewave heights given by0.6<H"/d<1.3.

Hioh mounds. 0.6<hJh-<0.9.

Influence of H"'/h" on 7o impacts, Pr, lowmound

Figure6.10 DimensiQnlesshorizontalforcesagainstH",/d, low mound

Figure 6.9

Wave loads are again pulsating for high mounds with relative wave heights in the range 0'3<H"/d<0.6,for datacovering relatively deep water 0.11<H;/h"<O.16 and moderate berm widths 0.2<B"q/Le<0.34.Over these regions, Goda's equations give conservative predictions for horizontal wave forces.

As relative wave heights H"/h" or H"/d increase, more waves are likely to break on the structure, and

the situation becomes more complex. The test results suggest that there is a transition zone around0.55<H"/d<0.65, but few data are available to describe the processes reliably, so it is recommendedthat this zone is treated as the more conservative of the two adjoining zones.

Within the last zone examined here, covered by the largest waves tested given here by 0.65<H./d<1'3,the influence of berm width expressed as B*/Lo is substantially more important. For shofi berms, given

by 0.08< BJ\<O.14, the waves are still pulsating with few if any impacts, and again Goda's methodcan be used to estimate wave forces. At the opposite end with long berms given by B*/Lo>0.4, wave

breaking occurs over the berm before the wall, and wave loads on the wall are due to broken waves.Again the use of Goda's method gives a safe estimation of forces.

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54 sR 443 0209/96

trThe remaining region of moderateberm widths covered by0. 1 4<B"q/Le<0.4 shows significantlevels of impacts, and wave forcesare much larger. lf P,is presentedagainst H"/h" using the form ofFigure 6.8, it can be seen in Figure6.11 that impacts start to occur atvery low values of H"/h". Theseresults may alternatively bepresented in Figure 6.12 in relationto H",/d, as in Figure 6.9, coveringthe region 0.65<HJd<1.3.

An alternative way to present theeffects of B"ol\ is to plot P,againstB"ol\ for constant values of H",/h",as in Figure 6.13. The proportion ofimpacts, P,, increases as therelative berm width increases. ltmay be expected that this will reacha limit for very wide berms wherethe waves are broken before theyreach the vertical wall, and theproportion of impacts, and theoverall level of peak wavepressures would then decrease.This limit was not reached in theseexperiments, although there aresome suggestions that Boq/lT > 0.4or 0.5 would give lower impacts.

The overallpicture of the differentwave loading conditions over theseregions is summarised in a type offlow chart in Figure 6.14. Theparameter regions are divided bythe type of wave breaking onto thestructure, chiefly inlluenced by therelative berm height h/h", therelative wave height H"/d, and therelative berm lengfth B*l\. Thischart represents a considerablesimplification of the overallprocesses, but renders decisionson the type of wave loadingsubstantially more tractable.

Influence of H"/h" on % impacts, Pr, hlghmound

Figure 6.11

Figure 6.12

Figure 6.13

Influence of H"n/d on % lmpacts, P,, highmound

tnfluence of B*Q on % impacts, P,, highmound

40

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55 sR 443 02/09196

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6.2.3 Composite walls, up-lift forcesUp-lift forces were analysed in two ways. ln the first instance, the influence of the depth of the core, h",was explored to investigate the influence of these parameters on the overall level of up-lift forces. Theoverall level of up-lift forces, generally expressed as Fu1256, were then considered using similarapproaches as used for horizontal forces in 6.2.2 above.

The influence of core depth, h", wasexplored by inspecting the up-liftforces for three structures, identicalexcept for the level of the caissonbase: Structure 2, h" = 0.112ffi,Structure 3, h" = O.2O2m, and forStructure 9, h. = 0.292m. Up-liftforces were plotted for each test onWeibull axes, as for the horizontalforces earlier. Example sets areshown in Figures 6.15 - 6.18 for thesame (offshore) wave height andwave steepness, but decreasingwater depths, and hence increasingH"/d.

At H"/d=0.45 and H"/d=0.62, up-liftforces are generally low, withStructure 2 with the lowest caisson base giving the lowest values of Fu12se, Figures 6.15 - 6.16. AtH"/d=0.98 and H/d-2.54, up-lift forces have increased significantly, by 2 to 4 times at 1/250 level,Figures 6.17 - 6.18. Structure 2 with the lowest caisson base still generally gives lower forces thanStructures 3 or 9, although the form of the distribution over the higher non-exceedance levels is oftencomplex.

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,''"'i

Figure 6.15 Weibull distribution of up-lift forces,sr=0.04, H"/d=0.45

56 sR 443 0209196

trInspection of similar graphs forother configurations and waveconditions suggests that up-liftforces are generally greater forincreasing core depth, where thecaisson base is higher, but that thistrend is only clear for pulsatingconditions. Under impactconditions, both horizontal and up-lift are more variable, and no clearinfluence of core depth wasdiscerned.

Taking the analysis more generally,the results were split into threeareas of H"/d. For H.,/d<0, theconfigurations tested most closelyrelate to crown walls on rubblemounds, and forces on thesestructures are discussed in section6.3.2 below. The other two regionsconsidered here were defined aslow mound, 0.3<hb/h"<0.6; or highmound,0.6<hd/h"<0.9; as used insection 6.2.2 above. Whereappropriate, regions are fudherdivided into pulsating or impactconditions.

In general, Fu increases with greaterincident'wave height H",, brltdecreases with lower mounds, iegreater d, Figure 6.19. The up{iftforces appear to cover two regions,given approximately by 0<H"/d<0.8or perhaps 1.5, and 2<Ho/d<4, andthese are discussed further below.It is interesting to note thesignificant variation of Fu for thesame values of H./d, suggestinginfluence of other parameters,perhaps including wave steepnessand/or relative core depth.

Weibull distribution of up-lift forces,s-=0.04, H"n/d=0.62

Figure 6.16

Figure 6.17

Figure 6.18

Weibull distribution of up-lift forces,sr=0.04, H"/d=0.98

Weibull distribution of up-lift forces,s.=0.04, H"ld=2.54

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57 sA4430AOy96

trThe scatter of results can be muchreduced by non-dimensionalisingup-lift forces as Fulp*gd2, and agenerally increasing trend ofincreasing F,/p*gdt with increasingH"/d. The results still appear tocover two different regions, so havebeen split into 0<H",/d<1.5, and2<H"/d<3.5 in Figures 6.20 and6.21.

It has been shown earlier thathorizontal force are more likely tobe increased by impacts forHJd>0.6 as the effect of the bermon the form of the wave breaking isincreased, Figure 6.14. For up-liftforces, a slightly higher limit ofH"/d=0.8 in Figure 6.20 appears tobetter describe the transition frompulsating to impact conditions. Thisincrease in the limit of pulsatingbehaviour for up-lift forces can beexplained by damping of wavepressure propagation in the rubblemound for small proportions ofimpacting waves. As the wavesincrease and thus change frompulsating to impact conditions,horizontal forces respondimmediately, but a small percentageof wave breaking is not sutficient tosignificantly increase up-lift forces.When the percentage of breakingwaves increases (say to H"/d = 0.8)up-lift forces begin to respond to thechange of regime.

For the larger relative wave heightsin Figure 6.21, variations of Fu at thesame values of H"/d are reduced,particularly at higher relative waveheights.

0<Hs/d<1.5

Figure 6.21 Dimensionless up-lift forces against H"/d,2<H"/d<3.5

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58 sR 443 0209/96

tr6.3 Comparison with

design methods6.3.1 SimpleverticalwallsHorizontalforces on simple wallswith no mounds were discussedbriefly in section 6.2.1 above. Theresponses were divided into tworegions, h"/d.0.35 or h*/d > 0.35 .For the lower relative wave heights,hJd < 0.35 , Goda's methodgenerally over-estimates thehorizontal force, but not veryseverely, so this prediction methodmay be taken as giving a safeapproach. The degree ofagreement is illustrated in Figure6.22, showing an average bias orover-estimate of about 40%. lt isinteresting to note that the use of afactor of safety of 1.5 with Goda'sprediction method for the horizontalforces would give a mean safetyfactor of 2 relative to theexperimental results.

For higher relative wave heights,H"/d > 0.35, Allsop & Vicinanza(1996) suggested a simple equationto estimate wave forces, given insection 6.2.1 above as eqn (6.1).The region of application, andexperimental data are summarisedin Figure 6.23. A direct comparisonbetween measurements andpredictions in the form of Figure6.22 is then given in Figure 6.24.This shows wider scatter than forthe smaller forces covered byFigure 6.22, but that any over- orunder-estimate (bias) is small. lt isalso interesting to compare theexperimental results withpredictions from Goda's method inthis region. Here the scatter is stilllarge, but the average under-estimate or bias is about 30%.

Measured / predicted horizontal forces,Goda, vertical walls, H"/d<0.35

Figure 6.22

Figure 6.23

Figure 6.24

Dimensionless horlzontal forces againstH"/d, vertical walls, A & V's predictionH"/d>0.35

Measured / predieted horizontal forces,Goda and A & V, vertical walls, H"/d<0.35

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59 sR 443 @/@/96

tr6.3.2 Compositewalls, horizontalforcesThe comparison of measured and predicted forces using Goda / Takahashi on composite structuresfoffows the general form used in section 6.2.2 above, and the results are therefore treated in theregions summarised in Figure 6.14.

Low mounds. 0.3<h/h"<0.6For low mounds, the onset of impactconditions is shifted to H"/d=0.65,rather than H"/d=0.35 noted for thesimple wall. Over the region ofpulsating loads, H"/d<0.65, themeasured wave forces are safelypredicted by Goda's method, seecomparison in Figure 6.25.Takahashi's method makes verylittle difference for the conditionsconsidered here. The singleoutlying point falls in the transitionzone identified in Figure 6.14, 0.55. HJd < 0.65. Figure 6.25 Measured / predicted horizontal forces,

Goda & Takahashi, low mounds, H"/d<0.65

Wave loads increase substantially with the onset of impacts for greater relative wave heights, H"/d t0.65, as was shown previously in Figure 6.10. Here the simple prediction equation for wave impactforces, eqn (6.1) gives reasonable estimates in the range of 0.65 < HJd < 1.2, although there is someindication that this simple method may over-estimate forces at higher values of H"/d.

The comparison betweenmeasurements and prediction usingthis simple equation shown inFigure 6.26 shows very little bias,but quite wide scatter. Thecomparison between measuredloads and Goda / Takahashipredictions also in Figure 6.26,shows much greater bias,equivalent to an under-estimate withrespect to the measurements ofabout 60%.

Further comparisons between themeasurements and predictionsbased on Minikin's method aregiven by McKenna (1996). Threealtemative versions of Minikin /Shore Protection Manual methodswere tested by McKenna, but none of these approaches gave any improvement over the methodsreviewed above. The use of Minikin's method as correctly (dimensionally) phrased, and as used in8S6349, always gave very low forces, well below those measured. Conversely, the SPM version withtriangular hydro-static pressure always gave much greater forces for pulsating conditions, yet failed tomatch forces under impact conditions.

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Figure 6.26 Measured / predicted horizontal forces,Goda & Takahashi, low mounds,0.65<H"/d<1.2

60 sR /t4t q2rc9€6

trhioh mounds. 0.6<hJh^<0.9.Relative wave heights in the range0.3 < H"/d < 0.55 generally givepulsating loads, and Goda'sequations give conservativepredictions, Figure 6.27. Over thisregion, Takahashi's modificationhas much more effect, but this givessubstantial over-estimates of loads.Again the outlying points in Figure6.28 fall in the transition regionidentified in Figure 6.14,0.55<H"/d<0.65.

The higher relative wave height givegreater possibility of wave impacts,but here the response is moreinfluenced by the relative bermwidth, BJlr. For the smallerrelative berm widths tested here,0.08 < BJh.0.14, Goda's methodagain over-estimates the loads, butsignificantly less so than Takahshi'smethod, Figure 6.28, so Goda'smethod should be preferred. Forboth methods, the higher forcesmeasured in these experiments areless severely over-estimated.

For the longest relative bermlengths considered here, B*/\ >0.4, waves are more likely to breakon the mound, reaching the wall asbroken waves. In these studies,only one test falls in this region, andthe wave force is quite close to thevalue predicted by Goda's method.

Measured / predicted hlrizontal forces, Goda& Takahashi, high mounds, .s0<H"/d<0.55

Measured / predicted horizontal forces,Goda & Takahashi, high mounds,.6s0<H"/d<1.3, short berm

Figure 6.27

Figure 6.28

Figure 6.29 Influence of B"o\ on horlzontalforces, hlghmounds, Intermediate berm widths

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61 sF 443 02109196

trIn the intermediate region, thecombination of greater moundheight and width is sufficient toinitiate wave breaking against thewall, the increase in wave impactsgiving substantially greater forces.The resultant forces depend uponBJ\,see Figure 6.29, and on H",/d,see Figures 6.30 and 6.31, but therelationships are complicated, andno reliable and simple method canbe devised. An upper limit estimateappears to be given by a simpleequation in H"/d:

Fn(p,gdt) = 22 (H"/d\4's (6.2) Figure 6'30 Dimensionless horizontal forces againstH"/d, high mounds, G & T's predictions,0.65<H"/d<1.3

Closer inspection of the comparisonbetween measurement andprediction in Figure 6.32, suggestshowever that this upper limit is muchtoo conservatMe, but it is also clearthat neither Goda nor Takahshi'smethods give safe predictions. Anextremely crude, and safe approachfor wave forces in this region is touse the Takahashi predictionmultiplied by 2. This gMes agenerally sate result for thecombinations of conditions testedhere, but has little other merit exceptits relative sim plicity!

Figure 6.31 Dimensionless horizontal forces againstH"/d, high mounds, G & T's predictionS,0.65<H"r/d<l.3

Again, McKenna (1996) makescomparison's between themeasurements and predictionsbased on the alternative versions ofMinikin / Shore Protection Manualmethods. The use of Minikin'smethod as used in 856349 againgave forces well below thosemeasured. Conversely, the SPMversion with triangular hydro-staticpressure always gave much greaterforces for pulsating conditions, yetfailed to match forces under impactconditions.

Figure 6.32 Measured / predicted horizontal forces, G &T and V's upper limit, high mounds, wideberms

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62 sR 443 q2lo9/9€

tr6.3.3 Composite walls,Low mounds. 0.3<h/hu<0.6For composite walls with lowmounds, Goda's method givesgenerally safe predictions of up-liftforce for pulsating and transitionconditions H"/d<0.65, Figure 6.33.Above that however, the non-dimensional up-lift force Fr/(p*gd2)increases rapidly to 2-3 times thatpredicted by Goda's method.

For the region of Hsi/d > 0.65,where the measurements givegreater up-lift forces than predictedby Goda, a simple regression linewas fitted to the results: .

F,/(p,gd') = 23.2 (H"/d) -15.2(6.3a)

This line is however strongly biasedtowards a set of data points withvery low up-lift forces, which werejudged not to be representative ofthe overalldata set. An altemativeprediction line was therefore fitted togive a more appropriate estimate ofthe upper bound to the results inFigure 6.33 over the range 0.65 <Hsi/d < 1.3:

F,/(p*gdt) = 19.7 (H./d) -11.1(6.3b)

High mounds. 0.6<ho/h"<0.9As was seen for horizontalforces,and discussed in 6.2.3, theinfluence of high mounds is morecomplicated. For pulsating andtransition regions covered byHJd<0.65 and perhaps up to 0.8,the non-dimensional up-lift forceF,/(p,gdt) remains relatively low,and agrees wellwith that predictedby Goda's method, Figure 6.34.

Again for HJd>0.8, the non-dimensional up-lift force Fn(p*gd2)increases rapidly, and here theregion is most usefully split usingvalues of B"ol\ to divide intopulsating or impact regions, Figures6.35 and 6.36.

up-lift forces

Figure 6.33

Figure 6.34

Figure 6.35

Dimensionless up-lift forces against H"t/d,low mounds, Goda's Predictions,0.65<H"/d<1.4

Dimensionless up-lift forces against HJd'high mounds, Goda's Predictions,0.65<H"/d<1.4

Dimensionless uplift forces against H.'/d,hlgh mounds, Goda's Predictions,0.65<H,/d<2, pulsating condltions

o E)eerimental data

a Godal prediction

Fu,/rlrc.g.d 2=t 9.72'Hsi/d-l I.(\8/ n

o/

o l o9

o / ^ a^ l

o/o ^

_ ^

/ o o

t . ' f l ^!^

q,9 1 0

0.2 0.1 0.6 0.8Ari /d

1 . 2 1.1 1.6

f rb*-*-lI 0 . 6 < h b / h s < 0 . s I

I;;**Al^ *"p'"o",*l o e

o ! O

o a o

o

r l

e

a

e 8o c

oo Oo a0

, i!l

eC O

cl

€' i

1 0

i g

0o-2

F-rr"*r '"gi*I|

0 . 6 < k i / d < 2 |

t ".."r"*-lI

B.q/Lp 4.15or{.3 |

F.*'";l| ^ codasetcdidid

I

c

o o^

o o

0

r l

9

9

r l6

t

sq9 l 0

:

l

00.a

63 sR443fi2l@19t6

tr

Figure 6.36 Dimensionless up-lift forces against H"'/d,high mounds, Goda's Predictions,0.65<H"/d<2, imPact conditions

6.3.4 Crown wallsPrediction methods for wave forces on crown walls developed by Jensen, Bradbury & Allsop havebeen included in the CIRIA rock manual, Simm (1991), and these were summarised in Chapter 3.Horizontal forces were non dimensionalised as Fn,oro/p*gh,Lp , and were related to dimensionlessmound depth given as H"/Ao, where A!=-d. Up-lift forces were expressed as Fupsol0.5p,gB"\, whichwas based on assumptions that up-lift pressures at the front edge are equal to horizontal pressures atthat corner, and that the distribution is triangular from the front edge. Simple empirical equations, givenearlier as eqns (3.20a) and (3.20b), used coefficients derived for different configurations of rubblemound and crown wallto relate the dimensionless forces to HotA".

Whilst not a main objective of these studies, the expansion of the tests by McKenna (1996) allowed theconfigurations to be extended to include tests on structures which closely resembled a crown wall on arubble mound. The results from these tests were divided from those representing standard caissonson rubble foundations and were analysed separately. This analysis therefore consideredconfigurations where the depth of water on top of the rubble mound (d) was small, or where the waterlevel was below the top of the berm (d is negative).

Horizontal forces from these configurations did not agree well with predictions by Goda or Takahashi,but the method of Bradbury & Allsop (1988) for crown walls as used in the CIRIA manual was usedhere to compare measured and predicted forces at 1/250 level.

Fnraso = p, g hr I (a (H"/A") - b) (6.4a)

F,raso = 0.5 p* g B" L (a (HJA") - b) (6'4b)

Sections A and C in the CIRIA manual were selected as most representative of the crown wallconfigurations tested here, lor which coefficients a and b had been derived previously for the 99.9%exceedance level:

Section a bA 0.054 0.032c 0.043 0.038

|r'pu"t"sr;|I

0 . 6 < H s i / d < 2 |

r;;;lI

0 . 1 s < B o q / L P < 0 . 3 |

F.,***;l|

^ Goda's pfodic{im I

o o

o

l O

a

o

e 8o o

o OO Oo

I r8 r aa

1 5

tP l 0

(

0.4

64 sR443V2t09t98

trThe initial comparisons of predictedand experimental forces wereconfined to the parameter rangestudied by Bradbury & Allsop ie 0 <H"/A" < 2.5. Only four tests fell intothis narrow range, all for Structure10 with the lowest water level, sothe region of interest was extendedto cover the wider range of -4 <H./A". 8. Horizontal forces arecompared with predictions forBradbury & Allsop's Sections A andC in Figure 6.37, and up-lift forcesare compared in Figure 6.38.Surprisingly, the simple predictionsgiven by Bradbury & Allsop'sequations with a=0.054 andb=0.032 gave reasonable

lr.roRrzoNrAl FoRCEsl

L-. ...r r

r \$..t \ . ' .

I I - l \ .

: j' .io.: t

t .

. ' /,: //

,'(- . 4

t a rl r !

l al r l Ia t rf,

, t

I

0.3

!

I

0.1

i 02

lbi / Ac

Figure 6.37 Dimensionless horizontalforces on crownwalls, -4<H./A"<8

o.3

5

E

€ n ,:L

I

tr.r-rFrFoRcEd

| ..i /'| ./ "/l . : /t . : /... | ./| .'i ,"l : ' t ' l

:'. I ..:' ,'u r tf i . | , . . -

T\l'.. , ...r',..,,/ ::: .,rr o\ | .... 'I I

i ''..r1

;1","' I t: r

r r | , / I

o 2t&i/

4

Figure 6.38 Dimensionless up-lift forces on crown walls'.4<H"/4"<8

estimations for the horizontal forces,although this method over-estimates Fhl,,so at higher values of H"/A".

At negative values of H"/A", the measurements are scattered, but the simple prediction method gives areasonable upper limit for most of the results. These configurations where the mound is just below thewater level represent fairly unusual cases, and it is not surprising that no standard prediction methodapplies here.

Up-lift forces in Figure 6.38 werewellpredicted by Bradbury &Allsop's method at lower values ofH"/A", but significantly over-estimated at high values of H"/Ao.At negative values of H"/A", up-liftforces are again scattered, but thesimple prediction method againgives an upper limit.

Bradbury & Allsop's coefficients a &b are the same for horizontalandup{ift forces, thus assuming that thepressure at the bottom of the frontface of the crown wall equals that atthe front edge of the underside.The absolute magnitudes of theforces then depend on the height orbreadth of the wall over which the pressures act and on the assumed shape of the pressuredistribution. Goda's method suggests that a reduction factor be applied to the pressure at the bottom ofthe wall to give the corresponding up-lift pressure. The results considered here, however indicate thatup-lift forces may be higher than these simplifying assumptions suggest. Initial inspections of up-liftdistributions from tests here and at the large wave flume at Hannover/ Braunschweig suggest that thismay be because the up{ift pressures do not reduce linearly from front to rear. lt is also clear thatpressures at the rear heel may not always reduce to zero. The most conservative approach mighttherefore require the assumption of a rectangular distribution of up-litt pressures, although this wouldprobably be excessive in those cases where the crown wall or caisson is placed on relatively free-draining materials.

65 sR443o2|OSpa

tr6.3.5 Overall stability of caissons on rubble moundsPrevious sections treated horizontal and up-lift forces independently. The use of these forces in anystability analysis therefore assumes that peak horizontal and up-lift forces occur simultaneously. Inpractice, there will always be a lag between peak horizontal and peak up-lift forces, so it is possible thatthe structure would then be more stable than indicated by this simple approach. This analysistherefore uses a simple analysis of the stability of a monolithic caisson against sliding. Factors ofSafety F, against sliding are calculated using measured forces, and are contrasted against thosepredicted using Goda's formulae with Takahashi's modification.

The sliding stability analysis was carried out in three stages to investigate the most appropriate valuesof the horizontal and uplift forces to use, and to determine the consequences of simplifying thehorizontal and uplift forces to single values. The first, and simplest, stage consisted of calculations of asingle Factor of Safety per test, using the 1/250 values of the horizontal and up-lift forces together.These values do not occur at the same time, and do not even necessarily occur for the same wave,since the statistics of the horizontal and up{ift forces were treated separately in this study. The secondstage was therefore to calculate a single Factor of Safety per test using the 1/250 value of thehorizontal force with the concurrent value of the up-lift force. This was done to evaluate the etfect ofsimplifying the forces to their 1/250 values in the first analysis. The third stage of the analysis was thecalculation for selected tests of the Factor of Safety at each timestep using time series. The purpose ofthis analysis was to determine the effect of using averaged single values as input rather than the actualvalues of the forces over each wave event.

These simplifying approaches did not consider failures by overturning, or by local or gross foundationfailure which would require significant modelling of the geotechnical response of the mound.Enhancement of stability by embedment of the caisson into the rubble has also been neglected.

tn the modeltests, the test structure was not free to move, so the Factor of Safety against sliding Fwas calculated for a caisson of the same size and shape as that used in the modeltests, assuming thatthe mean density of concrete and fill was 20@kg/m3, and that the coefficient of friction between rubbleand the base of the caisson could be represented by !r = 0.5 in accordance with the minimumrecommended by BS 6349 (1991).

These simplifications allow the use of data discussed earlier in this chapter. Transient phenomenawere not modelled in this analysis as this would require a dynamic stability model, with force - timeseries as inputs, and inertia and damping of the system (including the soil behaviour) being correctlymodelled. Models of this type are under development, but are not yet validated. Recent work byKortenhaus (1994), lbsen (1994), and the MCS GeotechnicalGroup edited by De Groot (1994) hasindicated the way in which such models may be developed, and it is probable that such models may bevalidated during the later stages ofthe PROVERBS project (1996-1999). Until such sophisticatedmodels are available, determinationof stability of caisson breakwaterswill continue to require use of staticloadings, with appropriate factors ofsafety to compensate forsimplifications in the processes anduncertainty in estimation of inputparameters.

Static Slidino ModelThe forces acting on a compositebreakwater section, where the

Figure 6.39 Forces / reactlons for overall stabllltyanalysls

66 sR 4l|3 q209l96

trsuper-structure is embedded a small amount into the rubble mound, are as shown in Figure 6.39, andmay be summarised as follows:

Fn, horizontal wave force, and Fu, up-lift force underneath the caisson,Mg, dry weight of the caisson,Fr, buoyant up-thrust on the caisson,S' the shear force at the rubble / caisson boundary,Fr, earth pressure force on the caisson from the seaward part of the mound,F", earth pressure force on the caisson from the harbour side of the mound,

The simple sliding stability modelconsidered these forces for thecaisson tested in this study. Thestability model employs a simplifiedcross section (as shown in Figure6.40) where the caisson is notembedded in the rubble mound.Contributions of the earth pressureforces, F, and F^ to the overallstability of the structure aregenerally small, and were omitted inthis analysis. At the point of sliding,the stability of the caisson isexpressed in terms of the Factor ofSafety F, against sliding, defined asthe ratio of resistance forces todisturbing forces, with F. = 1denoting the point of failure:

1700k9/mg

F = 0.5 38%P = 0.6 31o/"

rA+

Figure 6.40 Simplified modelfor overall stabilityanalysis

Fs =U(Mg-F , -FJ /Fh (6 .5 )

Results of Sliding Stability AnalysisThe first stability analysis with Fn.'*o and F,'*o used F"< 1 to identify that 28% of the structure / waveconditions would have failed. In practice, the factor of safety would be required to exceed at least 1.2,and 856349 suggests the use of Fr= 1.5 to 2.0 in design to account for the uncertainties in estimatingthe wave loads and structure response. The percentage of failures for various levels of F, weretherefore determined from the measured loads, and are summarised below:

Limiting F, % failures

1 .01 .21.52.O

The sensitivity of this analysis to the assumed parameters was explored and the 7" failures aresummarised below for different densities of the caisson /fill, and different coetficients of friction. Theseresults confirm that the response of the analysis to the values selected is reasonably gentle, so theoverall conclusions drawn from this analysis will not be significantly influenced by the particular valuesselected.

Friction factor Caisson / fill bulk density

28384253

2000kg/m3

28%2Oo/o

67 sR 44n 02rc8p6

trIt has been noted previously that this analysis does not take into consideration any extra resistanceprovided by embedment of the caisson into the rubble mound, nor take account of the dynamicresponse characteristics. Initial inspection of example force - time series for horizontal and up-lift loadsappear to demonstrate that peak (1/250) horizontal and up-lift forces do nol generally occursimultaneously as assumed in this simple analysis. Up-lift at the time of peak horizontal force isgenerally less than the peak up-lift force. This is however complicated by a phase lag introduced bythe 2OHz filter applied to the up-lift pressures, and it may be unsafe to assume that the actual phaselags between peak horizontal and up-lift forces will be the same as those measured in these pressurerecords

Comparisons of F. used forces measured in these tests, and those predicted using Goda's methodwith Takahashi's extension for horizontal forces and Goda's method for up-lift forces. The comparisonsaddressed each branch of the overall impact response diagram given in Figure 6.14. ln each branch,measured and predicted Factors of Safety were compared to indicate the degree of under- or over-estimate that might be given. The results of these comparisons may be summarised:

For composite structures with low mounds, Goda & Takahashi's method will give safe predictionsfor 0.3 . ho/h" < 0.6 except for those larger mounds and/or wave heights which lead to impacts.

For composite structures with high mounds, Goda & Takahashi's method give safe predictions for0.6 < hu/h" < 0.9, except for 0.65 . H"/d < 1.3 when the mound again causes wave impacts.

Stability analysis with Fnraso-@.,It is very likely that maximum values of horizontal and up-lifi forces will not occur simultaneously due tothe damping effect of the rubble mound on the up-lift pressures. The actual Factors of Safety for astructure subjected to specific loading conditions might therefore be higher than those given by thesimple analysis described above. The implication of this in design would be the rejection of structureswhich would in fact be safe.

The second stage of the analysis explored the consequences of the assumption in the first stage thatpeak horizontal and up-lift forces occur simultaneously, comparing the factors of safety obtained fromthe first analysis with those calculated using values of Fn,o* and F, at the same timestep. This analysisshowed that, although the Factors of Safety changed by about 1O-2O"/" if the concurrent values of forcewere used, the percentage of structures which failed did not change appreciably. In general, structureswhich failed using the simplest analysis (Fn'* and Fu'^o) also failed using the more accurate method(Fn'o* and F, at the same time), so there is no benefit to be derived from this refinement of the forceinputs.

Stabilitv analvsis with F- and F.. for time seriesBoth analyses described previously used averaged values of the maximum forces over more lhan oneevent. The combination of the actualvalues of the forces in an event may result in a greater instabilitythan would be indicated by average values.

The third and most rigorous stage of this analysis calculated Factors of Safety F, at each timestep inselected tests. This required a number of tests to be re-processed to produce force-time series (eachabout 3OMbytes) so this analysis was restricted to a few which fallwithin parameter ranges defined inFigure 6.14. Tests with large or negative H"/d were excluded. The selection procedure aimed toinvestigate the following hypotheses:

1. Conditions which the second analysis indicated were Just safe' (F, just > 1) might actuallybecome'unsafe'at some time during the wave event. This corresponds to cases where the useof the simple analysis would give a marginally safe result. lt would be normal for an engineer toreject a design with a factor of safety so close to 1.0, and this part of the analysis seeks todetermine whether this is justified.

68 sB 4€ q2lool96

tr2. Conditions which the second analysis indicated were 'safe', F, t 1, but for which the Goda and /

or Takahashi predictions gave substantially greater factors of safety, might become 'unsafe' atsome time during the wave event. This situation arises due to the significant uncertainty in theprediction of the forces in certain parameter regions. lt investigates the importance of selecting anappropriate method for determining the input forces for the stability model.

Conditions which the second analysis indicated were 'just safe', F, > 1, but for which thecalculations with the Goda and / or Takahashi predictions gave 'unsafe' results, might become'unsafe'at some time during the wave event. This is important for determining the extent (if any)to which the Goda and / or Takahashi predictions are over-conseruative in certain parameterranges. lf the calculations using Goda and / or Takahashi predictions were consistently'unsafe'when in fact the structure was 'safe'then some reduction in the factor of safety might be justified.

The duration of the 'unsafe' period for cases for which the second analysis showed would just fail(Fs < 1) might be close to the natural period of the caisson. This hypothesis was investigated onlyfor marginal cases, where the static stability analysis was indicating that the structure would be'unsafe'. The possibility exists of a short period of low stability not causing failure, as the dynamicresponse of the stnicture would reduce the effective force applied. lf however the duration of theunstable phase approaches the natural period of the caisson, no allowances of this nature can bemade.

The time-series stability analysis was carried out using a simple FORTRAN program to calculate theFactors of Safety against sliding for every timestep in the force-time histories. The program outputlisted those times during the tests when F, had fallen below and then come back above 1.0, thusallowing the duration of the unsafe period to be calculated. The results of this were compared withthose from the second stability analysis (using Fn,,oo and F, at the same time) to investigate the issueslisted above.

1. Structures which the second analysis indicated were just safe (F. just > 1) might actually becomeunsafe at some time during the wave event.

Here 8 tests were analysed, of which 5 failed, that is gave Fr<1 using the time series analysis.Failure durations were between O.0O25s to 0.0075s (model), which would scale (by Froude) at1:30 to 0.014s - 0.04s. These results suggest that the hypothesis was correct and if F" calculatedfrom Fh,o* and Fu at the same time was just safe, the structure might actually fail. lt is howeverlikely that a structure with values of F, this low would be rejected as well below the safety marginsrecommended in 856349.

2. Structures which the second analysis indicated were safe, and for which the Goda & Takahashipredictions indicated that the structure was very safe, might become unsafe at some time duringthe wave event.

A single test was analysed, and it failed for 0.0025s (model), equivalent to 0.014s by directscaling. This suggested the hypothesis to be true. lf Goda and Takahashihad been used F.would have indicated a very safe structure (Fr>2), whereas in fact the structure might have failed.The second analysis had shown F. from the measurements to be lower, and if these forces hadbeen used, the design would have been rejected as F. was then less than 1.2. The simpleapproach would therefore have been sufficient if appropriate force values had been used as inputparameters.

3. Structures which the Goda & Takahashipredictions indicated were unsafe, but measurementsindicated were safe, might become unsafe at some time during the wave event;

Of 12 tests, only 2 failed, with durations of 0.0025s to 0.005s (model) equivalent to 0.O14s toO.O3s. The use of Goda and Takahashi's methods would generally be conseruative. Values of F

4.

69 sR 443 02109/96

trcalculated from measurements were close to unity, and so would have failed the 'Factor of Safety'test. Again therefore the use of the simple approach can be justified.

4. , The duration of the unsafe period for structures which the second analysis showed would failmight be close to the natural period of the caisson.

Of four tests considered here, all failed, and 2 tests failed twice. Failure durations were short at0.O02Ss to 0.0050s (model) equivalent to 0.014s to 0.027s at prototype if scaled directly. Againthese calculations suggest that the hypothesis was untrue. The analysis however concentratedon those structures where F. was close to 1.0, and did not consider those structures where therewas an obvious failure. In those cases the duration of the unsafe period would be expected to berather longer.

Conclusions from sliding analysisThis analysis has shown that a simple sliding stability analysis based on the values of the horizontaland uplift force maxima at an appropriate probability level (eg 11250) is a usefuland valid method. Theapproach however requires the use of force prediction methods which are suitable for the parameterrange describing the conditions, and the implementation of a safety margin. There is no significantincrease in reliability to be gained by the use of time-series information or more sophisticateddescriptions of the forces than the maxima.

The only reliable altemative involves a full dynamic analysis with elastic-plastic characterisation of themound / foundation, such as is discussed by Kortenhaus et al (1994). Such approaches will improvethe accuracy with which the caisson response can be determined, and may thus permit the reduction ofsafety factors and therefore lead to more cost-etfective design. Until reliable dynamic models arereadiiy available, there would appear to be no particular benefit in'pursuing marginal improvements ofthe simplest analysis approach described here.

6.4 Pressure gradients and local pressuresThe major emphasis in any study of wave forces / pressures is on the overall or average level ofpressures needed to determine the overall stability of the structure. Data on local pressures andpressure gradients are also needild in any analysis of conditions leading to local damage or instabilityof blockwork. Very little information is available from conventionalmethods on the spatialvariability ofpressures, or on local pressure gradients.

6.4.1 VerticaldistributionsGoda's method assumes that wavepressures are distributedtrapezoidally. For pulsatingconditions this assumption isreasonably well-supported, as isillustrated by the example pressuresat pruso levelplotted in Figure 6.41for a simple verticalwallatH"/d=0.3. For this case, the wavesare pulsating, and the verticaldistribution of pressures follows thegeneralform assumed by Goda.Pressure magnitudes are relativelyclose to those predicted by Goda'smethod.

of pressurest .3

1 2

t . l

I

o.0

0.9

E " '

lE 0..

0.4

0.3

o2

0.1

0

P GrVm^2)

Figure 6.41 Vertical distrlbutions of pressures, vertiealwall, H./d<0.35

70 sF 443 02109/96

trAgreement with this simplification ismuch less good for impactconditions. The distribution ofpressures in Figure 6.42 is derivedfor the same simple vertical wall, butat greater relative wave height,H"/d=0.4. Here the peak pressureis substantially greater thanpredicted, and for this case isslightly above the static water level.

The onset of impacts therefore notonly increases the overallforce asdiscussed in earlier sections of thischapter, but also substantiallyincreases local pressures andhence pressure gradientg. Thisetfect is illustrated dramatically inFigure 6.43 where the only physicaldifference between the tests wasthe effective berm width, B*. Asseen earlier, even quite smallchanges in the structure maysignificantly alter the proportion ofimpacts, and the overall force onthe wall. The lowest and mostuniformly distributed pressures inFigure 6.43 occur for the simplevertical wall, Structure 0, and for thecomposite structure with moderateberm, 3. Structures 4 and 7 haveonly slightly larger berms, yet thelocal pressures and pressuregradients increase signif icantly.Here increasing the berm width hasinitiated the breaking process,

These effects are compared withpredictions by Goda andTakahashis in Figures 6.44 - 6.45where the difference between thestructures compared is again ofberm width. The structure with ahigh mound, Structure 3, givespulsating conditions, and pressuresbelow Goda's prediction in Figure6.46 for B/h = 0.13. A smallincrease of relative berm width toBJ\ = 0.16 is however sufficient toinitiate impact conditions, withsubstantially greater wavepressures at the static water level,Figure 6.45.

Vertical distributions of pressures, verticalwall, H",/d>0.35

I

0.9

0.9

o-7

e 0.6

0.5

0.4

o.3

o2

o.l

- fiai4t=0.8 .t| $netuB 0

aStrctuE3-B€CI.P=0.13

oSircturo4.B€qnP=0.16

r. Stnrturs 7 - B€CLP = 0.t I

10 12 14 16 18 N 22 21 2A 2S 30

Figure 6.43 Effect of berm width on vertical distributionsof pressures, comPoslte walls

Figure 6.42

giving greater impact forces for greater relative berm width, and dramatically greater peak pressures.

E

E

l 2

I

0.8

0.8

l+rinre=O.3. HsVaa.g, 1|b/184.62, B€qLp4 tq

. 'a '

1I,

6

A

t0.4

o.2

0

Figure 6.44 Measured distributlons and goda /Takahashl predictions for pulsatingcondltions (Structure 3)

r .2

I

0.9

0.8

o.7

9 0.6=

_--.):=,="tl--''"-

t'o.4

0.3

o2

0.t

o5 6

P (kiuiilz)

71 sR443U2lO9lS6

trThese discussions have beenconfined to pressures at 1/250 level,but it should be noted thatpressures at more extremeexceedance levels are greater.This is illustrated in Figure 6.46where the vertical pressuredistributions for an impact conditionare given for non-exceedancelevels of 99.6 and 99.8%, and for1 1250, lying approximately between99.6 and 99.8%. These confirm thateven the use of prpso may not leadto the highest estimate of localpressures or pressure gradients.

Figure 6.45

Figure 6.46 Measured distributlons at exceedanceof 1125O,99.6% and 99.8%' imPactconditions (Structure 1 )

Measured distributions and Goda /Takahashi predictions for impact conditions(Structure 4)

6.4.2 Pressure gradientsAnalysis by Allsop & Bray (1994) onthe stability of blocks in blockwokwalls subject to wave action hassuggested that large pressuregradients may be particularlyimportant in determining the onsetof movement of such blocks. Thissection considers example pressuregradients calculated from thepressures measured in these modeltests.

For ease in scaling andmanipulation, the results ofcalculations of pressure gradientshave been expressed as pressurehead (in metres of water) divided bythe spacing between themeasurement points (in this instance between adjacent pressure transducers). Values of the pressurehead gradient, dp/dz, discussed below are therefore dimensionless.

The analysis in section 6.4.1 demonstrated that pulsating wave conditions give relatively low absolutevalues of the wave pressure, so pressure gradients are relatively mild, seldom exceeding values ofdpldz >1. The situation is however dramatically ditferent for impact conditions.

For impact conditions on the simple vertical wall, values of the peak local pressure gradients variedover dp/dz=2to70. These values increased slightly for low mounds to dp/dz=S to 90, and for highmounds to dpldz=2to 80. The mean value of these results, the standard deviations (s.d.) andcoetficients of variation are summarised below:

levels

o.9

0.8

0.7

0,8

I o.s=

0.4

0.3

02

0.t

I t|,roo.ss: ttiltoo.sg; lbvGl.31; BeqLp=o.l0I

Structure range mean(dp/dz)

s.d. (dp/dz) coef. varn. (dp/dz)

Vertical 2 - 7 0 13.2 15 .9 1. '19

Low mound 5 - 9 0 29.5 25.9 0.879

Hirrh mnilnr{ 2 - A O 21 .6 1 7 5 o-814

72 sA1/.302109196

trFor impact waves, the greatest relative local pressure measured in these tests was given by:

p,*/(p*gH"J < 50

and the steepest pressure gradient was given by:

max (dp / dz) < 90

6.5 Pressure rise times / impulses

(6.6a)

(6.6b)

The rate at which wave pressures rise is important for two reasons. The first point is that a caisson orrelated structure will only react to a wave force by moving if the duration of the force impulse is close toor greater than the response period of the structure. At a smaller level, this may also be applied to thecomponent elements of a structure. lf the wave impulse is of short duration, as might be characterisedby a very short rise time, then the structure or element may respond only slightly to the loading, even ifthe loading intensity is very high. lt is therefore important to characterise wave forces / pressures bytheir durations. This was not possible directly, but the rise time to peak pressure could be determinedfrom the measurements of pressures, and this was taken as giving a good indication of impulseduration. I lt may be useful to note that within the PROVERBS project in early 1996, the workingassumption was that the duration of the impact impulse was about 3 At.l

The second issue is of scaling from smallscale to prototype. lt is generally accepted that wave impactsin small scale models may be greater in magnitude, but shorter in duration than their equivalents at fullscalb. Despite significant programmes of research, at for instance University of Plymouth or Hannover/ Braunschweig Universities, researchers there have not yet been able to develop reliable or robustscaling methods. This issue will be discussed further in Chapter 7, using information from the field andlaboratory on pressures and rise times.

The classification of pressure risetimes, and the interaction with anylimits on pressures have beendiscussed by Hattori (1994) andHattori et al(1994) who suggestthat, at their particular modelscaleor size, an upper limit may beapplied to individual peak pressuresplotted against rise time. Theselimit curues are summarised inFigure 6.47 where the effects ofthree ditferent sizes of air pocketbetween waves and wallarepresented by the three limit curves.These curves were derived forregular / single waves, and the unitsof pressure and rise time are notscaled from Hattoriet al's original

Figure 6.47 Maxlmum pressures and rise times (afterHattori et al)

measurement. For no air pocket, Hattori suggests a limit oh P,o given by:

P.a' = 320 At'zr3

whilst for a small air pocket, Hattori suggests:

P'* = 300 afl/2

and for a large air pocket, Hattori suggests:

P'r, = 24O At1r3

(6.7a)

(6.7b)

(6.6c)

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ta

trf n each instance, values of p,* are in grams torce lcm2, and At is in milli-seconds.

These curves are re-presented inFigure 6.48 where some of theshorter rise times measured in theWallingford experiments are alsoshown. Hattori et al'smeasurements covered rise timesbetween 0.2 and 10 milliseconds,whereas the Wallingford resultscover from 5 milliseconds to 1second.

A fuller set of Wallingford data froman impact condition is shown inFigure 6.49, where Hattori's threelimit curves are compared withmeasurements. There is goodagreement at longer rise times, butthe measurements appear to lieabove Hattori's curves at higherpressures, shorter rise times. Inpart this will be due to the lower limitto rise times calculated from thesetest results using 3 points, ie 2 x1/400s = 5 milliseconds. Some ofthese records may well relate torather shorter rise times, whichwould place the plotted pointsfurther to the left on the graph, andthus closer to Hattori's limit. Thistendency to give longer rise timesmay also have been compoundedby the somewhat slower responseof the transducers used in theWallingford tests.

It is however most probable that

Comparison of experimentat data andHattori's predictions for rise times

tr E)e.dala (tst 10003 - 500 mv@)

a single.p€kod irpact (fHtoti €t 81., 1994)

* lrpact fap > 120 Hz (tlatlod €t.1., tS94)

v lrpact fap < 120 Hz (Hattqi ol al., I 994)

0.1{tt{s)

Figure 6.49 Experlmental data (this study) and Hattori'sprediction lines

Figure 6.48

Haftori's limits are themselves strongly influenced by the relatively small wave heights that were used inthose experiments, and the scaling of Hattori's limit curues to other model scales, and hence toprototype, have yet to be addressed. The comparisons in Figures 6.47 - 6.49 should therefore betreated with some circumspectiqn.

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tr7 Application of results

The main restrictions to the application of these test results are given by the limits of data covered,distortions of the responses arising from scale effects / uncertainties in scaling from model tests toprototype, and differences in the response characteristics of ditferent structures or elements relative tothose used in making / analysing the measurements.

The ranges of parameters, and of the main dimensionless parameter groups covered by these studieshave been summarised in earlier chapters of this report. Limits to the application of the designmethods are suggested in Chapter 6. Application of the results of this study depend critically on thereliability with which the measurements of pressures made in these modeltests may be applied to fullscale in sea water. The use of such hydraulic models must therefore be subject to analysis of theinfluence of scale etfects of concern where flows in porous layers may be unrealistically influenced byviscous flow effects, and where the pressures produced by hydro-dynamic actions are themselvesinfluenced by the scale of the experiment. In the studies discussed here, the main influence of scaleeffects is on the magnitude of the wave impact pressures, and on their durations.

7.1 lnfluence of scale effectsThe principal results of this study are the wave forces / pressures. The analysis of these pressuremeasurements made at laboratory scale using lresh water has not explicitly assumed any particularscale conversion, but the use of other parameters scaled implicitly by Froude scale has thereforeimplicitly assumed that the forces / pressures measured here can be so scaled.

In the case of pulsating wave pressures where the relationships between wave momentum, pressureimpulse, and total horizontal force are relatMely simple, the assumption of Froude scaling is realistic,and will not alter the key conclusions for pulsating load conditions over the range of scales that may beused from these experiments.

For wave impact pressure, scaling is less simple. lt has long been argued and is well accepted thatwave impacts in smallscale hydraulic modeltests will be greater in magnitude, but shorter in durationthan their equivalents at full scale in (invariably aerated) sea water. lt is very probable therefore thatthe higher impact pressures measured in these model tests can be scaled to lower values, but that theimpulse durations must be scaled to longer values. lt may be noted in passing that the largestpressures may occur when there is least air entrained or trapped, and these impacts may thereforeactually be less influenced by scale effects on air compression.

7.1.1 Studies on scalingMany ol these uncertainties have been studied by researchers working at large scale in the LargeWave Channel (GWK) at Hannover / Braunschweig Universities, and using salt and fresh water inexperiments at Plymouth University. lt has previously been argued by reference to early work byBagnold, von Karman, and others, that the addition of only small fractions of air may dramaticallychange pressure transmission characteristics of the water, thus substantially modifying pressures thatmight be experienced by the structure. Two studies have however suggested that the etfect is verymuch smaller. There is some indication from studies at Plymouth described by Walkden et al (1995)that even quite high levels of aeration in the modelonly reduced wave pressures measured in themodelby about 20%. Numericalmodelling studies by Peregrine and co-workers, see for instancePeregrine & Thais (1996), can be used to suggest that scale errors due to air effects might be limited toabout 50%.

In contrast, the results of analysis described in Chapter 6 of this report suggest that even smallchanges of relative mound levelwill change wave impact pressures by factors of 5 or more. Thissuggests that the influences of small changes to relative geometry may be of greater eflect than theuncertainties introduced by scale effects. lt is however still necessary to assess the likely contributionto overall uncertainties arising from any scale errors.

75 SB /|43 q2l0gl96

trThe argument on scaling wave impact pressures requires information on relative statistics of waveimpact pressures, p, impact rise times At, and pressure impulses, estimated here perhaps by (p xAt).These data must be measured in model and field with equivalent definitions of events. lf comparativedatasets can be compiled, it may then be possible to compare the magnitudes of pressure impulsesscaled by Froude. lf these show good agreement over the exceedance range of interest, say from 90or 95o/o non-exceedance upward, then equivalent comparisons of pressures and rise times will giveestimates of the appropriate scale corrections.

7.1.2 Scaling of impacts froFieldwork measurements on hollowcube concrete armour units havebeen described by Allsop et al(1 995c), who detail fourdeployments of wave pressure andother recording equipment on LaCollette breakwater, Jersey. ln thelast deployment, wave impactpressures were monitoredthroughout winter 1993/4 at eightpoints on a typical Cob concretearmour unit at 500H2. Intelligentmonitoring techniques were used toreduce the volume of data recordedwhilst retaining all significant waveimpact data. Statistics of waveimpact pressures and rise timeswere retained for the completewinter period, see Allsop et al(1995c). During this deployment,3270 impact events were recorded,but it was not possible to analyse allof this data. Howarth et al (1996)discuss 15 sets of recordings giving7417 waves, of which 632 wereimpacts, so Pr=8.57o. Forthese 15storms, values of impact pressure(p), and rise time (At) can be plottedfor the top 8.5% of waves, that isfrom 91.5-100%.

Following previous modeltests atWallingford reported by Herbert &Wafdron (1992), a1:32 modelof thebreakwater cross-section wastestdd by Howarth (1996) at Bristol.The model was subiected to tests each of about 200 waves chosen to represent wave conditions /water levels measured in the field at Jersey. lmpact pressures were measured on a model Cob unit inthe same position as on the instrumented unit. Pressures were collected at lOkHz using a miniaturetransducer scaled from the prototype transducer size. A totalof 37 random wave tests gave 6389waves of which 1310 gave impacts, so here PF2Oo/o, thus allowing values of p, and At to be plotted forthe top 20"/" of waves, that is from 80-100%.

Comparisons of these statistics give a dataset of impact pressures and rise times for full scale in seawater and small scale (1:32) in fresh water. These may be used to calculate pressure impulse, hereestimated by pressure (p) multiplied by the rise time (At). Values of this estimate of pressure impulseare compared at the same exceedance levels in Figure 7.1, and show close agreement over the region

Figure 7.1 Pressure impulses from field and model forwave imPacts on armour unit, linear

Figure 7.2 lmpact pressures from field and model forwave lmPacts on armour unit, linear

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trof 92-99.9% non-exceedance. Thisagreement suppoils the thesis thatthe pressure impulse can be scaledby Froude, even where pressuresor rise times cannot be socompared.

Using the same dataset, impactpressures are compared in Figure7.2, confirming that at the sameexceedance levels, wave impactpressures in the field are lower thanwould be predicted by scalingdirectly pressures from the model.

The presentation of Figure 7.1 and7.2 does not easily show.the form ofthe distribution of impulses orpressures, so these data are re-presented on Weibullaxes inFigures 7.3 and 7.4. Comparison ofimpact pressures from field andmodel in Figure 7.4 suggests ihatthere is a relatively constantrelationship between field andlaboratory pressures over theexceedance levels studied here.Measurements of impact pressuresscaled by Froude need to becorrected by factors between about0.40 to 0.45 over non-exceedancesfevefs of 92 - 99"/", shown inFigure 7.5.

A similar approach may be taken inexamining the effect on pressurerise times, taken here to indicatealso the effect on impact durations.lmpact rise times are plofted onlinear axes to the same exceedancelevels as before in Figure 7.6, andon Weibullaxes in Figure 7.7. Thedifferences here are wider thanseen for impact pressures, andmore care will be needed ininterpreting these results to takeaccount of limitations in the data.For instance, it will be noted thatsteps are introduced into data onthe shortest rise times by theminimum time intervalneeded todefine a rise time, 1-2 samplingintervals. As for wave impact

Figure 7.3 Weibull probabilities for pressure impulsesfrom field dnd model

2In (pressure)

Flgure 7.4 Weibull probabilities for wave impactpressures from field and model

96Non-€xceedance (%)

Figure 7.5

77

Correctlon factors for Pressures

sB 443 0209196

trpressures, a correction factor maybe derived for impact rise times /durations, as in Figure 7.8, but moreinformation willbe needed beforethese correction factors can beapplied with the same confidenceas can be ascribed to the use ofthose in Figure 7.5.

Figure 7.6 Pressure rise times, model and fieldmeasurements

Figure 7.7 Weibull probabilities of impact pressure risetimes from modeland field

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Correction factors for rise times

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trThe correction factors derived above may be summarised:

7.2 Response periods and impact durationsAnother issue in interpreting the use of these measurements is the relationship between the period ofthe wave loading and the response time of the structure. lt has been shown by Muraki (1966) thattypical natural periods of oscillation for (Japanese) caissons is 0.2 - 0.4 seconds. lt is probable thatsmall elements such as stone or concrete blocks in older walls will respond to much shorter periods,but this has not yet been studied. In experiments at large scale in the GWK at Hannover/Braunschweig, Schmidt et al (1992) measured pressure rise times in the regions of 0.05 -0.02s (sic) inthe model. (This may have been mis-typed and should have been 0.005 - 0.02s.) Schmidt et althensuggest that the total wave force rise time is 5-10 times longer at 0.05 to 0.2 seconds, and convertthese times by an un-explained scale (of 3) to prototype rise times of 0.15 to 0.6 seconds. They thencompare these times and the response periods of caissons to confirm that these measurements ofimpacts are stillable to cause movement of even large caissons.

Non-exceedancelevel

lmpact pressurecorrection factor

Rise time / durationcorrection factor

92% 0.44 I

95"/o 0.45 6.8

98% 0.43 5

99"/o 0.41 4.2

79 SR .143 02109196

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sB 443 02109/9680

tr8 Conclusions and recommendations

8.1 Conclusions1. Of the prediction methods for wave forces on vertical and composite walls identified in this study,Goda's method is the most reliably based, and generally best accepted. The determination of waveforces in Goda's method was however derived from tests or field data on sliding distances for caissons,and should not necessarily be expected to give accurate estimates of wave pressures. Goda's methodhas been extended by Takahashito take greater account of impulsive wave forces.

2. Since its publication in 1951 / 1963, Minikin's method for impact forces has almost always beenquoted erroneously (except in British Standard 6349 Pt 1), particularly when the (dimensioned)coefficients have been (mis-) translated from British lmperial units to metric units. The 1963 version towhich most later users refer includes a significant error in the example calculations of hydro-staticpressures. Many later versions of Minikin's method are dimensionally inconsistent, and this has lead toconsiderable uncertainties in the values of the dimensioned or dimensionless coefficients. The methodgiven in the Shore Protection Manual departs significantly from Minikin's method, and generally givessubstantially greater forces.

3. Wave forces on vertical and composite walls are strongly influenced by the type of wave breakingonto the wall. The forces measured in this study may be divided between pulsating and impactconditions. A response diagram (Fig 6.14) has been developed from these measurements to identifyranges of dimensionless parameters that distinguish the different types of wave breaking, and hencethe different types of wave loadings.

4. Pulsating loads are relatively slow-acting. lmpact loads are almost always substantially larger thanpulsating loads, and of much shorter duration.

5. Analysis of overall stability with a simple model of caisson sliding was used to estimate factors ofsafety for all configurations tested in these studies. This model identified some cases where simpleanalysis using Fn,o* and F,r*o showed a Factor of Safety above unity, but full time series data showeda Factor of Safety below unity. These cases were however well below the ranges of F = 1.5 to 2suggested by 856349 Pt 1, and little increase in reliability was given by using loads other than Fn'ouoand Fu'o*. Any increase in sophistication of modelling stability is therefore probably not merited unlessthe full dynamic structure / foundation processes can be reproduced.

6. For pulsating conditions, the vertical distribution of pressures on the front face generally conform tothe simple distribution suggested by Goda, but changes dramatically at the onset of impacts. lmpactconditions give very intense pressures at or near to the static water level, conforming with the generalvertical distribution suggested by Minikin. lmpact conditions have less etfect on pressures much aboveor below static water level.

7. Forces on breakwater crown walls are reasonably well described by the simple method developedby Jensen / Bradbury & Allsop and used in the CIRIA / CUR manual.

8. Under impact conditions, local pressure gradients on vertical walls can be very severe, reachingeltreme pressure head gradients up to dp/dz = 70 to 90.

9. Pulsating loads may be converted directly from model tests at appropriate scales by Froude scalingwithout signif icant scale effects.

10. lmpact loads are potentially influenced by scale and other modeleffects, so impact loadsconverted directly by Froude scaling willover-estimate prototype loads. A new method has beenderived in this study from field and modeltest data on wave impacts to correct wave impact pressuresfor scale / model effects.

81 SB ,143 02/09196

tr8.2 Recommendations for design / analysis1. Combinations of structure configuration and wave / water level conditions that may lead to impactconditions should be identified using the parameter map in Figure 6.14. Where practical, the structureconfiguration should be revised to reduce the potential for high intensity wave impact loads.

2. For pulsating conditions, the statistics of wave forces fit the Weibull distribution. At the 1/250 level,horizonalwave loads can be predicted by Goda's method with reasonable safety. Goda's method mayhowever over-estimate wave forces for low relative wave heights and large mounds. Up-lift forces arepredicted relatively safely by Goda's method

3. For impact conditions, wave forces depart from the Weibull distribution that fits the rest of the(pulsating) forces. Under these conditions, forces at the 1/250 level are substantially greater thanwould be predicted by Goda's method. Takahashi's extension of Goda's method has little effect inincreasing wave impact loads in relation to those measured in these studies. For simple vertical wallsand composite structures with low mounds, horizontal forces under impact conditions may beestimated by the simple formula in eqn. 6.1 and up-lift forces by eqn. 6.3b. Methods for otherconfigurations are discussed in Chapter 6, but within this study no general prediction method forimpacts has been developed for all structure configurations.

4. Wave forces on breakwater crown walls can generally be estimated safely using the simpleprediction method in the CIRIA / CUR manual.

5. The stability of caisson or sections against sliding may be simulated using a simple static analysisprovided lhat wave forces are predicted at 1/250level using an appropriate method; and Factors ofSafety of at least 1.5 - 2.0 are used.

6. Predictions of pulsating loads derived from hydraulic modeltests, therefore including thosemeasured in this study, may be converted to full scale by simple Froude scaling with little scale effect.

7. Predictions of impacts loads derived from hydraulic modelstudies in fresh water are significantlyinfluenced by model and scale effects, and should be corrected to avoid over-estimating wave loads. Anew correction method has been derived here and is presented in Chapter 7.

8.3 Recommendations for future researchFuture analysis / design methods for vertical and composite breakwaters are more likely to useprobabilistic approaches rather than the deterministic methods used to date. Static stability analysismethods willalso be replaced by dynamic analysis of structure and foundation. These newapproaches will therefore require substantially greater levels of detail on variabilities / uncertainties inresponses than available hitherto. The present study, whilst more comprehensive than any otherrecent work in this field, has not covered the full range of possible structure eonfigurations or relativewave conditions. Future research studies should therefore include the following:

1. Gaps in the present parameter map should be filled by supplementary testing. Existing and newdata should be used to improve the reliability of prediction methods for the onset of impact conditions,and for the prediction of the magnitude and durations of wave impact forces.

2. Further detailed testing and analysis is needed to determine more reliably the spatial extent of highimpact pressures, and to describe their spatial variability.

3. The present study was unable to determine correctly the phase lags between horizontal and up'liftforces. Information on these forces and their phasing is needed as input to dynamic modelling ofcaisson / foundation responses. Future model studies and field measurements should record theseforces un-filtered to a common time base to permit phase lags to be determined.

4. These studies have generally supported simple prediction methods for forces on breakwater crownwalls, but do not identify the effects of various configuration parameters. Further testing may be

sR 43 q2l09196

trmerited to identify more fully the influence of crest geometry and armour configuration on wave loadson the crown wall.

5. Typical time series of pressures on the wall and within the rubble mound / foundation will berequired for dynamic structure / foundation simulations. The development of such (standard) timeseries from the data collected in this study, and from future studies, will require information on typicalfrequency ranges for the structural responses of caissons, crown walls, and elements of blockworkwalls.

6. The development of probabilistic simulations of stability will require more reliable estimates ofeltreme force stalistics. Future tests should be extended to 1000 waves, and additional testing shouldquantify the effects of long (test or storm) durations on the extreme force statistics.

7. A simple engineering approach to the derivation of scale correction factors for impact pressures hasbeen presented for the first time in this report. the method is relatMely simple, and omits some of themore complex aspects of the scaling problem. lt is hoped that future studies under the PROVERBSproject will refine this approach, and will present more robust methods to scale impact rise times anddurations.

83 SR .143 @/09196

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sR 44I! O2lO9/9€84

tr9 Acknowledgements

The work discussed here is based in part on studies completed by members of the Coastaland Ports &Estuaries Groups of HR Wallingford for the Construction Sponsorship Directorate of the UKDepartment of Environment, under research contracts PECD 7161263, PECD 7161312, and Cl 39/5/96;in part under support from the MCS project of the EC's MAST ll programme under contract MAS2-CT92-OO47, and the PROVERBS project in MAST lll under contract MAS3-CT95-0041.

This report also draws on the results of research supported by the MAST I programme of the EuropeanUnion, and by the Construction Policy Directorate of the UK Department of Environment under contractPECD 7161312. The development of the numerical models of internaland externalflows used in studieson Alderney breakwater was supported by the Department of Environment under contract PECD7161108.

Substantial additional support to the testing and data analysis has been given by the Queen'sUniversity of Belfast; thei Department of Hydraulics of the University of Naples; and University ofShetfield. Funding support for visiting researchers at Wallingford from TECHWARE, the internationalexchange programme of the University of Naples, and the Department of Education Nl is also gratefullyacknowledged.

The authors are also pleased to acknowledge assistance in testing and analysis by Phil Besley,Daniela Colombo, Chris Jones, and in the compilation of this report by Kirsty McConnell. They aregratefulfor assistance in processing data by Luca Centurioni, visiting researcher at HR Wallingford,and by Siva Sathiamoorthy of the National University of Singapore.

HR Wallingford are also grateful for advice and assistance provided by Mike Chrimes, librarian of theInstitution of Civil Engineers, in researching some of the historical information cited here; to GeraldM0ller of Queen's University of Belfast for early discussions on wave impacts, and advice onmeasurement devices; to Mario Calabrese of the University of Naples for significant assistance in thedevelopment of the flow diagram dividing parameter regions and pulsating / impact responses; and toAndreas Kortenhaus of Universities of Hannover and later Braunschweig for advice on analysis andevent definition methods.

The senior author is grateful for the interest and support shown by the Port and Harbour ResearchInstitute at Yokosuka, Japan, and to JISTEC for supporting pariicipation in the 1994 Wave Barriersworkshop, and to his colleagues in the PROVERBS research project.

85 sR 4€qz0sl96

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sR 4€ @rc9/9086

tr10 References

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Allsop N.W.H. & Bray R.N. (1994) "Vertical breakwaters in the United Kingdom: historical and recentexperience' Proceedings of Workshop on Wave Barriers in Deep Waters, pp76-100, Port and HarbourResearch lnstitute, Yokosuka, Japan.

Allsop N.W.H., Besley P., McBride M.W., & McKenna J.E. (1994a) "Hydraulic performance of verticalwalls: tests on caissons and'low-reflection'walls.' Paper 3.7 to 2nd MCS Workshop, Milan, publnUniversity of Hannover.

Allsop N.W.H., MG Briggs, T Denziloe, & AE Skinner (1991) "Alderney breakwater: the quest for a'final'solution' Conference on Coastal Structures and Breakwaters, Institution of Civil Engineers, London.

Allsop N.W.H., Calabrese M. & Vicinanza D. (1995c) "Analisideicarichi impulsivisu una diga aparamento verticale" Giornate ltaliane di lngegneria Costiera, Ravenna, Ottobre 1995, ltaliana PIANC.

Allsop N.W.H., Calabrese M., Vicinanza D. & Jones R.J. (1996)'Wave impact loads on vertical andcomposite breakwaters" Proceedings 1Oth Congress of the Asia and Pacific Division of IAHR, 26-29August 1996, Langkawi lsland, Malaysia

Allsop N.W.H. & McBride M.W. (1994) 'Reflections from vertical walls: the potential for improvement invesselsafety and wave disturbance" Proceedings of Workshop on Wave Barriers in Deep Waters,ppl01-128, Port and Harbour Research Institute, Yokosuka, Japan.

Allsop N.W.H., McBride M.W., & Colombo D. (1994b) 'The reflection performance of vertical walls and'low reflection'alternatives: results of wave flume tests." Paper 3.4 to 3d MCS Workshop, Emmeloord,publn Universlty of Hannover.

Allsop N.W.H., di Leo M. & McBride M.W. (1995a) "The effect of wave reflections on local wavesteepness" Paper 11.4.3 to the final MCS Project Workshop, Aldemey, publn University of Hannover.

Allsop N.W.H., McBride M.W., & di Leo M. (1995b) oWave reflections from verticalwalls and lowreflection altematives.' Paper 4.7 in Final Report of MCS Project, publn University of Hannover.

Allsop N.W.H. & MUller G. (1995) Discn to Technical Note 2575: 'Comparative study on breaking waveforces on verticalwalls'by Ergin A. & Abdalla S., Proc ASCE, Jo Waterway, Port, Coastaland OceanEngineering Division, September/ October 1995, ASCE, New York

Allsop N.W.H., Vann A.M., Howarth M., Jones R.J. & Davis J.P. (1995c) 'Measurements of waveimpacts at full scale: results of fieldwork on concrete annour units' pp287-302, Conf. on CoastalStructures and Breakwaters'95, Institution of Civil Engineers /Thomas Telford, London.

Allsop N.W.H. & Vicinanza D. (1996)'Wave impact loadings on verticatbreakwaters: development ofnew prediction formulae ' Proceedings of 11h Intemational Harbour Congress, pp 275-284, RoyalFlemish Society of Engineers, Antwerp, Belgium.

Allsop N.W.H., Vicinanza D., Calabrese M. & Centurioni L. (1996)'Breaking wave impact loads onvertical faces' Paper to 6h International Offshore and Polar Engineering Conference, Los Angeles,California, USA.

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trAllsop N.W.H., Vicinanza D, & McKenna JE (1995c). 'Wave forces on composite breakwaters andseawalls: analysis of horizontal and up-lift forces and overturning moments" Paper 1.5 in Final Reportof MCS Project, publn University of Hannover.

Bagnold (1939) "lnterim report on wave pressure research" Jo. Institution of Civil Engineers, Vol 12, pp202-226,1CE, London.

Banyard L., Calabrese M. & Allsop N.W.H. (1996) "Forces on verticalbreakwaters: effects of obliqueor short-crested waves" Research Report SR465, HR Wallingford, Wallingford.

Besley P., Allsop N.W.H., Colombo D & Madurini L. (1994). "Overtopping performance of verticalwallsand 'fow reflection alternatives'- Results of wave flume tests' Paper 4.4 to 3n MCS Workshop,Emmeloord, publn University of Hannover.

Bennett G.S., Mclver P. & Smallman J.V. (1992) "A mathematical modelof a slotted wave screenbreakwater" Coastal Engineerin g, Volume 1 B, Elsevier, Amsterdam.

Blackmore PA & Hewson P (198a) "Experiments on full scale impact pressures" Coastal Engineering,Vol8, pp 331-346, Elsevier, Amsterdam.

Bishop RW (1950) "Maintenance of some rubble breakwaters: Alderney breakwater" ICE Maritime &Waterways, Paper 16, Session 1950-51, pp 16-35 & 36-53, lCE, London.

Bradbury A.P. & Allsop N.W.H. (198e) "Hydraulic effects of brealcwater crown walls" ProceedingsConference on Design of Breakwaters, pp 385-396, Institution of Civil Engineers, London.

Bradbury A.P., Allsop N.W.H. & Stephens R.V. (1988)'Hydraulic performance of breakwater crownwalls" HR Report SR 146, Hydraulics Research, Wallingford.

Bray RN & Tatham PFB (1992) "Old waterfront walls: management, maintenance and rehabilitation"CIRIA/ E & FN Spon, London.

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Appendix

Summary of test conditions, structural configurations and results

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