chapter 2 meteorology and oceanography1 meteorology and oceanography items to be considered for...

PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY

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Chapter 2 Meteorology and Oceanography

1 Meteorology and Oceanography Items to be Considered for Performance Verification1.1 GeneralThefollowingmeteorologyandoceanographyitems,shallbeconsideredwithregardtotheperformanceverificationofportfacilities.

① Atmosphericpressureanditsdistributionarefactorsthatgeneratewinds.

②Windsgeneratewavesandstormsurge,andaffectthewindpressurethatactsuponportfacilitiesandmooredvessels,andbecomeafactortointerferewithcargohandlingandotherportoperations.See2 Windsfordetails.

③ The tidal level affects soil pressure andwater pressure,which act onport facilities, andbecomes a factor tointerferewithcargohandlingandotherportoperations.Also,ithasaneffectonwavesinareasofshallowwater.See3 Tidal levelfordetails.

④Wavesexertwaveforceonportfacilities,andbecomeafactortointerferewiththefunctioningofportfacilities.Theyalsoactonmooredvessels,causingthemtomoveandinterferewithcargohandlingandotherportoperations.Theyalsocanraisethemeanwaterlevel,whichhaseffectssimilartothetidallevelasmentionedabove.See4 Wavesfordetails.

⑤ Tsunamiexertswaveforceandfluidforceonportfacilities,andbecomesafactortointerferewiththefunctioningofportfacilities.Italsoactsonmooredships,causingthemtomove.See5 Tsunamisfordetails.

⑥Watercurrentsaffectsedimentsontheseabottomandbecomeafactortointerferewiththefunctioningofportfacilities.See6 Water Currents etc.fordetails.

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TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN

2 WindsPublic NoticeWinds

Article 6Characteristicsofwindsshallbesetbythemethodsprovidedinthesubsequentitemscorrespondingtothesingleactionorcombinationoftwoormoreactionstobeconsideredintheperformancecriteriaandtheperformanceverification:(1) Oceansurfacewinds tobeused in theestimationofwavesandstormsurge shallbeappropriately

definedintermsofwindvelocity,winddirectionandothersbasedonthelong-termwindobservationorweatherhindcasting.

(2) Windstobeusedinthecalculationofwindpressuresshallbeappropriatelydefinedintermsofthewindvelocityanddirectioncorrespondingtothereturnperiodthroughthestatisticalanalysisofthelong-termdataofobservedorhindcastedwindsorothermethods.

(3) Windstobeusedinthecalculationofwindenergyshallbeappropriatelydefinedintermsofthejointfrequencydistributionofwindvelocityanddirectionforacertaindurationoftime,basedonthelong-termdataofobservedorhindcastedwinds.

[Commentary]

1) WindstobeusedintheEstimationofWavesandStormSurge:Windstobeusedintheestimationofwavesandstormsurgeshallbeobservedorhindcastedvaluesfor30yearsormoreasastandard.

2) WindstobeusedintheCalculationofWindPressure:Windstobeusedinthecalculationofwindpressureshallbeobservedorhindcastedvaluesfor30yearsormoreasastandard.

[Technical Note]

2.1 General

(1)Windisoneofthemostdistinctivemeteorologicalphenomena,namely,thephenomenonthattheairmovesduetoatmosphericpressuredifferencesandheat.Theconditionsunderwhichwindsblowovertheoceanareusuallyverydifferentthanforthoseoverland.Windvelocitiesovertheoceanaremuchhigherthanthoseoverlandneartheshore.1)Forperformanceverificationofportfacilities,theeffectsofwindsmustbeappropriatelyevaluated.

(2)GradientWinds

① Thevelocityofthegradientwindcanbeexpressedasafunctionofpressuregradient,radiusofcurvatureofbarometicisolines,latitude,andairdensityasinequation(2.1.1).

(2.1.1)

where Vg :velocityofgradientwind(m/s);inthecaseofananticyclone,equation(2.1.1)givesanegative

valueandsotheabsolutevalueshouldbetaken. ∂p/∂r :pressuregradient(takentobepositiveforacyclone,negativeforananticyclone)(kg/m2/s2) r :radiusofcurvatureofbarometicisolines(m) ω :angularvelocityofEarth'srotation(1/s)ω =7.27×10-5/s φ :latitude(°) ρa :densityofair(kg/m3)

Beforeperformingthecalculation,measurementunitsshouldfirstbeconvertedintotheMKSunitslistedabove.Notethat1ºoflatitudecorrespondstoadistanceofapproximately1.11×105m,andanairpressureof1.0hPais100kg/m/s2.


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② Agradientwindforwhichthebarometicisolinesarestraightlines(i.e.,theirradiusofcurvatureinequation(2.1.1)isinfinite)iscalledthegeostrophicwind.Inthiscase,thewindvelocityisasequation (2.1.2).

(2.1.2)

③ Theactualseasurfacewindvelocityisgenerallylowerthanthevalueobtainedfromthegradientwindequation.Moreover, although the direction of a gradientwind is parallel to the barometic isolines in theory, the seasurfacewindblowsatacertainangleαtothebarometicisolinesinrealityasillustratedinFig. 2.1.2.Inthenorthernhemisphere,thewindsaroundacycloneblowinacounterclockwisedirectionandinwards,whereasthewindsaroundananticycloneblowinaclockwisedirectionandoutwards.Itisknownthattherelationshipbetweenthevelocityofgradientwindsandthatoftheactualseasurfacewindvarieswiththelatitude.ThisrelationshipundertheaverageconditionsissummarizedasinTable 2.1.1.3)

Low

α

High

α

(a) Cyclone (b) Anticyclone

Fig. 2.1.2 Wind Direction for a Cyclone (Low) and an Anticyclone (High)

Table 2.1.1 Relationship between Sea Surface Wind Speed and Gradient Wind SpeedLatitude(°) 10 20 30 40 50

Angleα(°) 24 20 18 17 15

VelocityratioVs /Vg 0.51 0.60 0.64 0.67 0.70

(3)TyphoonWindsIncalculationsconcerningthegenerationofstormsurgeorwavesduetoatyphoon,itiscommontoassumethattheairpressuredistributionfollowseitherFujita’sequation (2.1.3)4)or Myers’ equation (2.1.4) 4);theconstantsinthechosenequationaredeterminedbasedonactualairpressuremeasurementsintheregionoftyphoons.

Fujita’sformula

(2.1.3)

Myers’formula

(2.1.4)

where p :airpressureatadistancer fromthecenteroftyphoon(hPa) r :distancefromthecenteroftyphoon(km) pc :airpressureatthecenteroftyphoon(hPa) r0 :estimateddistancefromthecenteroftyphoontothepointwherethewindvelocityismaximum

(km) ∆p :airpressuredropatthecenteroftyphoon(hPa) ∆p=p∞-pc p∞ :airpressureatr =∞(hPa); p∞=pc+∆p

Thesizeofatyphoonvarieswithtime,andso r0and∆p mustbedeterminedasthefunctionsoftime

(4)MeteorologicalGPVOrganizations such as the Japan Meteorological Agency, the European Center for Medium-Range Weather

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Forecasts(ECMWF),andAmerica’sNationalCenterforEnvironmentalProtection(NCEP),calculatethevaluesofitemssuchasairpressure,windvelocity,winddirection,andwatervaporflux,basedoncalculationmodelsformeteorologicalvaluesthatuseathree-dimensionalcalculationgrid,andthevaluesatthegridpoints(GPV:gridpointvalues)aresaved.TheseGPV’smaybeusedinsteadofwindhindcastingsbasedonequation (2.1.1) throughequation (2.1.4). However,whenagridwithlargespacingisusedformeteorologicalcalculationstheatmosphericpressureandwindsmaynotbesatisfactorilyreproducedatplaceswheremeteorologicalconditionschangedrasticallywithposition,suchasnear thecentersof typhoons. Therefore,whenGPV’sareused, it ispreferabletouseobservationalvaluestoverifytheprecision.

(5)WindEnergyIfwindsareconsideredasthemovementoftheairthenthewindenergythatcrossesaunitcross-sectionalareainunittimeisgivenbyequation(2.1.5).1) Winds forestimating thewindenergyshallbeappropriatelyspecifiedwith jointstatisticdistributions forvelocity and direction for a fixed time (usually, one year), based on long-term (usually, three years ormore)observedorhindcasteddata.

(2.1.5)

where P :windforceenergyperunitcross-sectionalarea(W/m2) ρa :airdensity(kg/m3) V :windvelocity(m/s)

Inotherwords,thewindforceenergyisproportionaltothecubeofthewindvelocity,soasmalldifferenceinwindvelocitycanmeanabigdifferenceinenergy(powergeneration).Therefore,duringperformanceverificationoffacilitiesthatusewindforceenergy,itisimportanttoaccuratelyunderstandhowtheconditionschangewithregardtotimeandspace. Inthecoastalzonethewindconditionsvariesdrasticallybetweenlandandsea.Also,windvelocityshowsgreatvariationonlandduetoaltitude,butovertheseathechangesinwindvelocitywithaltitudearegradual,soitispossibletoobtainhighlystabilizedwindsthatareappropriateforpowergenerationatrelativelylowaltitudes.Forexample,theresultsofmeasurementsinthevicinityoftheKansaiInternationalAirport,showthatthewindenergyoverthecourseofayearatameasurementtower(MTstation)placedataheightof15metersovertheoceanwereroughlythesameasatalandstation(Cstation)withanaltitudeof100meters,andaboutfivetimesgreaterthanatalandstationwithanaltitudeof10meters.5)

2.2 Characteristic Values of Wind Velocity

(1)DeterminationofWindCharacteristicsTheelementsofwindsaredirectionandvelocity,wherethewinddirectionisexpressedasoneofsixteendirectionsand thewindvelocity is themeanvelocityover10minutes. Thevelocityofwinds thatactsdirectlyonportfacilitiesandmooredshipsisspecifiedingeneralasavelocityforacertainperiodofoccurrence,asestimatedfromtheprobabilityofoccurrencedistributionofwindvelocitybasedonlong-termmeasuredvaluesover30yearsormore.Usingtheannualmaximum10-minutemeanwindvelocitiesoverabout35years,basedonMeasurementTechnicalDataSheet#34oftheJapanMeteorologicalAgency,7)andassumingadoubleexponentialdistribution,theexpectedwindvelocitiesover5,10,20,50,100,and200yearshavebeencalculatedat141meteorologicalstations. Forperformanceverificationoffacilities, thesedatacanbeusedasreferencevalues,however if thelocationofstudyhasdifferenttopographicalconditionsfromtheclosestofthesemeteorologicalstationsthenitisnecessarytotakemeasurementsforatleastoneyeartodeterminetheeffectofthetopography.8)

(2)Thewindvelocitiesobtainedatthemeteorologicalstationsarethevaluesatabout10metersabovetheground.Therefore,whenusingthemeasuredvaluestoestimatethewindsovertheocean,iftheheightofthetargetfacilityisverydifferentfromtheheightmentionedabove,thencorrectionoftheheightshallbeperformedforthewindvelocity.Theverticaldistributionofwindvelocityisusuallyshownonalogarithmicscale,howeverforsimplicityanexponentialscaleisoftenusedduringperformanceverificationofvarioustypesoffacilities.

(2.2.1)

whereUh:windvelocityatheighth(m/s)U0:windvelocityatheighth0(m/s)


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(3)Theexponentn inequation (2.2.1)varieswiththeroughnessof thenearbyterrainandthestabilityof theair,but ingeneral it ispossible touseavalueofn=1/10to1/4forperformanceverificationwhenspecifyingthewindvelocityforpurposessuchascalculatingwindpressure,andavalueofn≥1/7isoftenusedovertheocean.Statisticaldataforwindvelocityisusuallythemeanwindvelocityover10minutes,howeverdependingonthefacilitythemeanwindvelocityoverashortertimeperiodmayberequired,orthemaximuminstantaneouswindvelocitymayberequired,andinsuchcasesoneshouldunderstandthecharacteristicsoftheregionsuchastherelationshipbetween themainwindvelocityand themaximumwindvelocity, and thegust factor (definedasthe ratio between themaximum instantaneouswind speed and the 10-minutemeanwindvelocity) shouldbeestimated.

2.3 Wind Pressure

(1)Wind pressure shall be appropriately specified by considering items such as facility structure and facilitylocation.

(2)Windpressurethatactsonsheds,warehouses,andcargohandlingequipmentshallbespecifiedasfollows.

(a) Structuralstandardformobilecrane

InArticle 9, Structural Standard For Mobile Crane, it is specified that thewind loadshallbecalculatedasfollows:

① Thevalueofthewindloadiscalculatedfromequation(2.3.1):

(2.3.1)

where W :windpressureforce(N) q :velocitypressure(N/m2) C :windpressurecoefficient A :pressure-receivingarea(m2)

② Thevalueofthevelocitypressureinequation(2.3.1)canbecalculatedfromeitherequation(2.3.2) orequation 2.3.3dependingontheconditionofthecrane:

(2.3.2)

(2.3.3)

where h :height(m)abovegroundofthesurfaceofthecranethatreceivesthewindsuseh :16miftheheightislessthan16m.

③ Forthevalueofthewindpressurecoefficientitispossibletousethevaluefoundinwindtunneltestsofthecrane,orthevaluegiveninTable 2.3.1forthecategoryofthesurfaceofthecranethatreceivesthewinds.A“surfacecomposedofflatsurfaces”inTable 2.3.1meansthesurfaceofastructurewithabox-likeshapesuchasaboxgirder,operator’scab,machinechamber,orelectricalchamber.A“cylindricalsurface”includesthesurfaceofawirerope.The“facearea”meanstheareaoftheshadedportioninFig. 2.3.1.

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Table 2.3.1 Wind Pressure Coefficients for the Wind Load on a Crane

Classificationofcranesurfacesthatreceivewinds ValueSurfacescomposedwithhorizontaltrusses(Otherthanhorizontaltrussesmadewithsteelpipe)

W1 < 0.1 2.00.1 ≤ W1 < 0.3 1.80.3 ≤ W1 < 0.9 1.60.9 ≤ W1 2.0

Surfacescomposedofflatsurfaces W2 < 5 1.25 ≤ W2 < 10 1.310 ≤ W2 < 15 1.415 ≤ W2 < 25 1.625 ≤ W2 < 50 1.750 ≤ W2 < 100 1.8100 ≤ W2 1.9

Surfacescomposedofcylindricalsurfacesorhorizontaltrussesmadewithsteelpipe

W3 < 3 1.23 ≤ W3 0.7

Note:Inthistable,W1,W2,andW3representthefollowingvalues,respectively:W1:AreaOccupyingRatio(thevalueobtainedbydividingtheprojectedareaofthesurfaceofthecrane

thatreceivesthewindsbytheareaofthesurfacethatreceivesthatsamewinds)W2:Thevalueobtainedbydividingthelengthinthelongitudinaldirectionofthesurfaceofthecrane

thatreceivesthewindsbythewidthofthesurfacethatreceivesthatsamewinds.W3:Thevalueobtainedbymultiplyingtheprojectedwidthofthecylinderorsteelpipe(unit:m)bythe

squarerootofthevalueshownin2)forthevelocitypressure(unit:N/m2)whenthecranestops.

hProjected Area Ar : Area of the shaded portion

Area Occupying Ratio W1 = Arh

Fig. 2.3.1 Projected Area

④ Thepressure-receivingareainequation (2.3.1)shallbetheareaofthesurfaceofthecranethatreceivesthewindsprojectedontoasurfaceperpendiculartothedirectionofthewinds(hereafterinthissectionreferredtoas“projectedarea”).Whentherearetwoormoresurfacesofthecranethatreceivethewinds,theareasubjecttowindpressurecalculationisdeterminedbysummingupthefollowing;

1) theprojectedareaofthefirstsurfaceinthedirectionofthewinds

2) theareasobtainedbymultiplying theportionsof thesurfaceareasof thesecondand latersurfaces inthedirectionofthewinds(hereafterinthisparagraph“secondandlatersurfaces”)thatoverlapthefirstsurfaceinthedirectionofthewindsbythereductionfactorsshowninFig. 2.3.2

3) theprojectedareasoftheportionsofthesurfaceareasofthesecondandlatersurfacesthatdon’toverlapthefirstsurfaceinthedirectionofthewinds.

InFig. 2.3.2,b,h,φ,andη representthefollowingvalues,respectively:

b :distancebetweenthebeamsofthecranethatreceivethewinds(seeFig. 2.3.3)h :heightofthefirstbeaminthedirectionofthewinds,amongthebeamsthatreceivethewinds(see Fig. 2.3.3)φ : theareaoccupyingratioof thefirstbeamin thedirectionof thewindsamongthebeamsfor the surfacesofthecranethatreceivethewinds(forsurfacesthatareformedofhorizontaltrussesφ isthe valueW1specifiedinthenoteofthetableoftheprevioussection,andforsurfacesformedofflat surfacesorcylindricalsurfacesitis1)η :reductionfactor


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b/h=6

b/h=5

b/h=4

b/h=3

b/h=2b/h=1

b/h=0.5

10.80.60.40.20φ

0.2

0.4

0.6

0.8

1

0

η

Fig. 2.3.2 Reduction Factors for Projected Areas

hb hb

(b) Beams of Box Type Structure(a) Beams of Steel Structure

Fig. 2.3.3 Measurement of b and h

(b) StructuralstandardsformobilecraneInArticle 9, Structural Standard For Mobile Crane,itisspecifiedthatthewindloadshallbecalculatedasfollows:

① Thevalueofthewindloadcanbecalculatedfromequation(2.3.1).

② Thevelocitypressurecanbecalculatedfromequation (2.3.2).

③ Forthevalueofthewindpressurecoefficientitispossibletousethevaluefoundinwindtunneltestsofthemobilecranethatreceivesthewinds,orthevaluegiveninTable 2.3.1ofSection a), Structural Standard For Mobile Crane”.ForthevalueofvelocitypressureinW3calculation,thevaluefromequation (2.3.3) shallbeused.

④ Thepressure-receivingareacanbecalculatedbythemethodof4)inSection a) Structural Standard For Mobile Crane.

(c)StructuralstandardforderrickcraneInArticle 11, Structural Standard For Derrick Crane,itisspecifiedthatthewindpressureforceshallbecalculatedasfollows:

① Thevalueofthewindpressureforcecanbecalculatedfromequation(2.3.4).Inthiscasethewindvelocityistakentobe50m/satthetimeofstorms,and16m/satallothertimes.

(2.3.4)where

W :windpressureforce(N) q :velocitypressure(N/m2) C :windpressurecoefficient A :pressure-receivingarea(m2)

② Thewindvelocitypressurecanbecalculatedfromequation (2.3.5):

(2.3.5)

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where q :velocitypressure(N/m2) U :windvelocity(m/s) h :height(m)abovegroundofthesurfaceofthecranethatreceivesthewinds (useh=15m,iftheheightislessthan15m)

③ ForthevalueofthewindpressurecoefficientitispossibletousethevaluefoundinwindtunneltestsorthevaluegiveninTable 2.3.2forthekindofthesurfaceandthecompletenessratioofthesurfacethatreceivesthewinds.

Table 2.3.2 Wind Pressure Coefficients for the Wind Pressure Force of a Derrick

Classificationofthesurfacethatreceivesthewinds CompletenessratioWindpressurecoefficient

Surfacescomposedofhorizontallatticesorhorizontaltrusses W1<0.1 20.1≤W1<0.3 1.80.3≤W1<0.9 1.6

0.9≤W1 2Surfacescomposedofflatsurfaces --- 1.2

Wireropesurfaces --- 1.2Note:Thevalueoftheareaoccupyingratioisthevalueobtainedbydividingtheprojectedareaofthesurfaceofthecranethatreceivesthewindsbytheareaofthesurfacethatreceivesthatsamewinds.

④ Thepressure-receivingareaistheareathatreceivesthewindprojectedontoasurfaceperpendiculartothedirectionofthewinds.Whentherearetwoormoresurfacesthatoverlapinthedirectionofthewinds,itshallbecalculatedasfollows;Theareasubjecttowindpressurecalculationisdeterminedbysummingupthefollowing;

1) Incasetherearetwooverlappingsurfacesthatreceivethewinds

i) theprojectedareaofthefirstsurfaceinthedirectionofthewinds

ii)60%oftheareasoftheportionsofthesecondsurfaceinthedirectionofthewindsthatoverlapthefirstsurface

iii)theprojectedareasoftheportionsofthesecondsurfaceinthedirectionofthewindsthatdon’toverlapthefirstsurface.

2) Incasetherearethreeormoresurfacesthatreceivethewinds

i) 50%oftheprojectedareasoftheportionsofthethirdandlatersurfacesinthedirectionofthewindsthatoverlapthefirstsurface

ii)theprojectedareasoftheportionsofthethirdandlatersurfacesinthedirectionofthewindsthatdon’toverlapthefirstsurface.

ThewindpressurethatactsuponstructuressuchashighwaybridgesandelevatedhighwayscanbespecifiedaccordingtotheHighway Bridge Specifications and Commentary.10)IntheHighway Bridge Specifications and Commentary,thewindpressureforcethatactsuponabridgeisspecifiedbyappropriatelyconsideringthelocation,topography,andgroundconditionsofthebridgeconstruction,thestructuralcharacteristicsofthebridge,anditscross-sectionalshape.

a) SteelbeamsThewindpressureforcethatactsonasteelbeamisthevaluegiveninTable 2.3.3,whichisthevalueperonemeteroflengthinthebridgeaxialdirectionforonespan.

Table 2.3.3 Wind Pressure Force for Steel Beams (Units: kN/m)

Cross-sectionalshape Windpressureforce1≤B/D<8 4.0-0.2BDD≥6.08≤B/D 2.4D≥6.0

where B=thetotalwidthofthebridge(m)(seeFig. 2.3.4) D=thetotalheightofthebridge(m)(seeTable 2.3.4)


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B

Fig. 2.3.4 Measurement of B

Table 2.3.4 Measurement of D

Bridgeguardfence

Walltyperigidguardfence

Otherthanawalltyperigidguardfence

MeasurementofD

D

0.4m

D

(b)DualmaintrussThewindpressureforcethatactsonadualmaintrussisthevalueshowninTable 2.3.5,per1m2oftheeffectiveperpendicularprojectedareaonthewindwardside.ForastandarddualmaintrussitisalsopossibletousethewindpressureforceshowninTable 2.3.6peronemeteroflengthofthearchmaterialonthewindwardsideinthebridgeaxialdirection.

Table 2.3.5 Wind Pressure Force on a Dual Main Truss (Unit: kN/m2)

Truss WhenthereisaliveloadWhenthereisnoliveload1.25/√—φ2.5/√

—φ

Bridgefoundation WhenthereisaliveloadWhenthereisnoliveload1.53.0

0.1≤φ≤0.6whereφ=areaoccupyingratioofthetruss(theratioofthetrussprojectedareatothetrussenvelopedarea)

Table 2.3.6 Wind Pressure Force on a Standard Dual Main Truss (Units: kN/m)

Archmaterial Windpressureforce

Loadedarch WhenthereisaliveloadWhenthereisnoliveload1.5+1.5D+1.25√—λh≥6.0

3.0D+2.5√—λh≥6.0

Notloadedarch WhenthereisaliveloadWhenthereisnoliveload1.25√—λh≥3.02.5√—λh≥3.0

7≤λ/h≤40whereD:totalheightofthebridgefloor(m)(notincludingtheheightoftheportionthatoverlapsthearchportionasseenfromthehorizontaldirectionperpendiculartothebridgeaxis)(seeFig. 2.3.5)h:heightofthearchportion(m)λ:maintrussheight(m)fromthecenterofthelowerarchportiontothecenteroftheupperarchportion

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h

D1

D=D1–h

D

0.4m

Wall type rigid guard fence

(a) Upper roadway truss (b) Lower roadway truss

Bridge protective fence otherthan a wall type rigid guard fence

Verticalbeam

Floorbeam

Archportion

Verticalbeam

Floorbeam

Archportion

Fig. 2.3.5 Measurement of D for a Dual Main Truss

(c) OthertypesofbridgesEither(a)or(b)dependingonthebeamshapeshallbeappliedtoobtainthewindpressureforceonothertypesofbridgebeams.Thewindpressureforceonmembersnotdescribedunder(a)or(b)isthevaluegiveninTable 2.3.7dependingonthecross-sectionalshape.Whenthereisaliveload,thewindpressureforceistakentobe1.5kN/mfortheliveloadataposition1.5mfromthebridge’suppersurface.

Table 2.3.7 Wind Pressure Force Acting on Bridge Members other than Steel Beams and Dual Main Trusses (Unit: kN/m2)

Cross-sectionalshapeofmembersWindpressureforce

Membersonthewindwardside

Membersontheleewardside

Circularshape WhenthereisaliveloadWhenthereisnoliveload0.751.5

0.751.5

Polygonalshape WhenthereisaliveloadWhenthereisnoliveload1.53.0

0.751.5

(d)ParallelbridgesWhenthesteelbeamsareparallel,appropriatelycorrectthewindpressureforceofTable 2.3.3byconsideringthateffect.

(e) Thewindpressureforcethatactsdirectlyonthelowerportionofthestructureistakentobeahorizontalloadthatiseitherperpendiculartothebridge’saxialdirectionorparalleltothebridge’saxialdirection.Itisassumedthatitdoesn’tactsimultaneouslyinbothdirections.ThemagnitudeofthewindpressureforceshallbethevalueshowninTable 2.3.8fortheeffectiveverticalprojectedareainthewinddirection.

Table 2.3.8 Wind Pressure Force Acting on the Lower Portion of the Structure (Unit: kN/m2)

Cross-sectionalshapeofthebody Windpressureforce

Circularorellipticalshape WhenthereisaliveloadWhenthereisnoliveload0.751.5

Polygonalshape WhenthereisaliveloadWhenthereisnoliveload1.53.0

References

1) Nagai,T.,K.Sugahara,K.SatoandK.Kawaguchi:CharacteristicofJapaneseCoastalWindPowerbasedonLongTermObservation,TechnicalNoteofPHRI,No.999,p.59,2001

2) Nagai,T:ObservedOffshoreWindCharacteristicsfromaViewofEnergyUtilization,TechnicalNoteofPHRI,No.1034,p.34,2002

3) Takahashi,K:Studyonquantitativeweatherforecastingbasedonextrapolation(Part1),StudyBulletinNo.13,19474) JSCE:TheCollectedFormulaofHydraulics(1985Edition),JSCE,Nov.1985


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5) Nagai,T.,H.Ogawa,A,Nakamura,K.SuzukiandT.Nukada:Characteristicsofoccurrenceofoffshorewindenergybasedonobservationdata,JSCEProceedingsofCoastalEng,.,pp.1306-1310,2003

6) Nagai,T,I.Ushiyama,Y.Nemoto,K.Kawanishi,T.Nukada,K.SuzukiandT.Otozu:Examinationoffieldapplicationoflightingsystemutilizingcoastalwindforce,JournaloftheJapanSocietyforMarineSurveyandTechnologyVol.17No.1,JSMST,2005

7) JapanMeteorologicalAgency,Catalogueofannualmaximumwindspeed (1928-1966)atvariousplaces inJapanand theprobabilityofoccurrence,MeteorologicalAgencyobservationTechnicalNoteNo.34,1971

8) JSCE,CivilEngineeringHandbook,Giho-doPublications,1974,pp.541-5449) IndustrialHealthDivision,IndustrialSafetyandHealthDept.,LabourStandardsBureau,MinistryofHealth,Labourand

Welfare:Commentaryofstructuralstandardsofvarioustypesofcranes,JapanCraneAssociation,200410) JapanRoadAssociation:Specificationsandcommentaryofhighwaybridges,PartIGeneralandPartIISteelBridge,2002

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3 Tidal LevelPublic NoticeTidal Level

Article 7Thetidelevelshallbeappropriatelyspecifiedasthewaterlevelrelativetoadatumlevelforportandharbormanagementthroughthestatisticalanalysisoftheobservedorhindcasteddataand/orothers,bytakingintoaccounttheastronomicaltides,meteorologicaltides,wavesetup(riseofwaterlevelbywavesneartheshore),andabnormaltidallevelsduetotsunamisandothers.

[Commentary]

(1) TidalLevel:Whenspecifyingthetidallevelfortheperformanceverificationoffacilitiessubjecttotechnicalstandards,appropriatelyconsiderhowthetidallevelaffectstheactionofwavesandwaterpressure.Also,whenspecifyingthecombinationoftidallevelandwavesintheperformanceverificationoffacilitiessubjecttotechnicalstandards,amongthetidallevelsthathaveahighlikelihoodofoccurringsimultaneouslywithwaves,takeasastandardthetidallevelthatwouldbemostdangerousfromtheviewpointoftheperformanceverificationofsuchfacilities.

(2) AstronomicalTides:Withregard toastronomical tides thatareconsidered in thespecificationof the tidal level, takeasastandardthespecificationofchartdatumlevel,meansealevel,meanmonthly-highestwaterlevel,andmeanmonthly-lowestwaterlevel,basedonmeasuredvaluesforoneyearormore.

(3) StormSurge:Whenspecifyingstormsurge,appropriatelyconsiderlong-termmeasuredvalues.Asastandard,long-termmeans 30 years ormore. When specifying storm surge, if long-termmeasured values cannotbe available, then appropriately consider items such as hindcasted values of storm surge based onmeteorologicalconditionsandrecordsinpastdisasters.Inthestormsurgehindcasting,wave-stepupduetowavebreakingneartheshoreshallbeappropriatelyconsideredasnecessary.

[Technical Note]

3.1 Astronomical Tides

(1)Definitions1),2),3)Astronomicaltidesaretidesproducedbythegravityofthemoonandsunandcanbeviewedasasumofcomponentsknownastidalconstituents.Thedefinitionsfortherepresentativetypesofwaterlevelareasfollows:

①Meansealevel(MSL)Theaverageheightofthesealeveloveracertainperiodisreferredtoasthemeansealevelforthatperiod.Forpracticalpurposes,themeansealevelistakentobetheaverageofthewaterleveloveroneyear.

② Chartdatumlevel(CDL)Thestandardwaterlevelobtainedbysubtractingthesumoftheamplitudesofthefourprincipaltidalconstituents(M2,S2,K1andO1)fromthemeansealevel.Thisisusedasthestandardforwaterdepthinnauticalcharts.

③Meanmonthly-highestwaterlevel(HWL)Theaverageofthemonthly-highestwaterlevel,wherethemonthly-highestwaterlevelforaparticularmonthisdefinedasthehighestwaterleveloccurringintheperiodfrom2daysbeoreto4daysafterthedayofthelunarsyzygy(newmoonandfullmoon).

④Meanmonthly-lowestwaterlevel(LWL)Theaverageofthemonthly-lowestwaterlevel,wherethemonthly-lowestwaterlevelforaparticularmonthisdefinedasthelowestwaterleveloccurringintheperiodfrom2daysbeforeto4daysafterthedayofthelunarsyzygy.

⑤Meanhighwaterlevel(MHWL)Themeanvalueofallofthehighwaterlevels,includingthespringtideandtheneaptide.

⑥Meanlowwaterlevel(MLWL)Themeanvalueofallofthelowwaterlevels,includingthespringtideandtheneaptide.


–69–

⑦ Nearhighesthighwaterlevel(NHHWL)Thewaterlevelobtainedbyaddingthesumoftheamplitudesofthefourprincipaltidalconstituents(M2,S2,K1andO1)tothemeansealevel.

⑧ Highwaterofordinaryspringtides(HWOST)ThewaterlevelobtainedbyaddingthesumofahalfamplitudeofthetidalconstituentsM2andS2tothemeansealevel.TheheightoftheHWOSTasmeasuredfromthechartdatumisknownasthespringrise.

⑨ Lowwaterofordinaryspringtides(LWOST)ThewaterlevelobtainedbysubtractingthesumofahalfamplitudeofthetidalcomponentsM2andS2fromthemeansealevel.

⑩MeansealevelofTokyoBay(TP)MeansealevelforTokyoBaydeterminedduringtheMeijiperiodfromtidallevelobservations.Sincethen,TPhasbecomethestandardformeasuringaltitudeinJapan.ThebenchmarkislocatedinNagata-cho,Chiyoda-ku,Tokyo.Incidentally,TPdoesnotcorrespondtothepresentdaymeansealevelofTokyoBay.

Therearefourprincipaltidalconstituents,namely,theM2tide(theprincipallunarsemi-diurnalcomponentof tides, period = 12.421 hours), the S2 tide (the principal solar semi-diurnal component of tides, period =12.00hours),theK1tide(theluni-solardiurnalcomponentoftides,period=23.934hours),andtheO1tide(theprincipallunardiurnalcomponentoftides,period=25.819hours).

(2)SeasonalandAnnualChangesinMeanWaterLevel2)ThemeanwaterlevelforeachmonthvariesovertheyearduetofactorssuchastheoceanwatertemperatureandtheatmosphericpressuredistributionneartheJapaneseislands,andinmanyplacesthemeanwaterlevelcanvaryby±5to20cmovertheyear.TypicallyalongtheJapanesecoastitishigherinthesummerandlowerinthewinter. Theannualmeanwaterlevelisalsoaffectedbyfactorssuchastheoceanwatertemperatureandatmosphericpressuredistributionforthatyear,andtheremaybevariationsof±10cmdependingontheoceanregion.

(3)OccurrenceProbabilityDistributionofAstronomicalTidalLevels4)Astronomicaltidallevelshaverepeatedhightidesandlowtidesabouttwiceperday,andrepeatedhighesttidesandlowesttidesabouttwicepermonth.Theshapeoftheoccurrenceprobabilitydistributionoftheseastronomicaltidallevelsvarieswithlocation,andthetidallevelsthathavethehighestprobabilityofoccurrencearethetidallevelsthatareclosetothemeansealevel,whiletheoccurrenceprobabilityofhightidallevelssuchasthemean-monthlyhighestwaterlevel,orlowtidallevelssuchasthemeanmonthlylowestwaterlevel,aresmall.

3.2 Storm Surge

(1)DefinitionsBesidesastronomicaltidesthatarecausedbythegravityofthemoonandsun,theheightoftheoceansurfacecan change due to factors such as changes in atmospheric pressure andwinds accompanying the passage oflowatmosphericpressuresystems(includingtyphoons,hurricanes,andcyclones)andhighatmosphericpressuresystems. Suchmeteorological changes in the sea surface are calledmeteorological tides, and the differencebetweenthemeasuredtidallevelandtheforecastedastronomictidalleveliscalledthetidallevelanomaly.Inparticular,amongmeteorologicaltides,theriseintidallevelduetothepassageofalowpressuresystemiscalledastormsurge.

(2)CausesofStormSurgeIftheatmosphericpressureattheseasurfaceislowered1hPaforasufficientlylongtimesothattheseasurfaceisinequilibriumwiththeatmosphericpressureattheseasurface,forexample,thentheoceansurfacerisesbyabout1cmhigherthannormallevel.Or,ifthewindsblowataconstantwindvelocityforalongtimefromtheentranceofaninternalbaytowardthethroatofthebaysothattheseasurfacerisestowardthethroatofthebayandreachesequilibriumthentheamountofsealevelriseatthefurthestpointinsidethebayisroughlyproportionaltothesquareofthewindvelocity,anditisalsolargerwhenthebayislongerorshallower.Duringanactualtyphoontheatmosphericpressure,windvelocity,andwinddirectionontheseasurfacechangesinacomplicatedwayatdifferentlocationsandtimes.

(3)EmpiricalFormulatoPredictStormSurgeThetideanomalyduetoatyphooncanberoughlyestimatedfromanempiricalformula,suchasequation (3.2.1).5)

(3.2.1)

–70–


where ξ :tideanomaly(cm) p0 :referenceatmosphericpressure(1010hPa) p :lowestatmosphericpressureatthetargetlocation(hPa) W :maximumvalueofthe10-minuteaveragewindspeedatthetargetlocation(m/s) θ :anglebetweenthemainwinddirectionforthebayandthatofthemaximumwindspeedWa, b, c:constantsdeterminedfrompastobservationalresultsatthetargetlocation

(4)NumericalCalculationofStormSurgeAnumericalcalculationisconductedtoanalyzethephenomenonofstormsurgeinmoredetail.Inthisnumericalcalculation,itemssuchastheatmosphericpressurethatactsontheseasurface,thefrictionalstressontheseasurfaceduetowinds,thefrictionalstressthatactsonthecurrentsattheseabottom,andtheeddyviscosityoftheseawateraretakenintoconsideration,andthechangesintidallevelandfluxflowatthegridpointsarecalculatedateachtimestepfromthetimethetyphoonapproachesuntilitpasses.8) Thedistributionsoftheatmosphericpressureandthewindvelocityofthetyphoonarecalculatedfromthecentral(atmospheric)pressure,theradiusofmaximumwindvelocity,andtheforwardingspeedofthetyphoon. Theseabottomtopographyofabayisapproximatedusingagridwithaspacingofseveralhundredmeters,orfinerthanthat,givingthewaterdepthateachgridpoint.Therearevariousmodelsforthenumericalcalculationofstormsurge,thereforeanappropriatecalculationmethodthatsufficientlyreproducesstormsurgesinthetargetsearegionshallbeused. In recentyears,numericalcalculationmodelshavebeendeveloped thatconsiderdensity layersandwaterdischarged from rivers, aswell asmodels that do not treat storm surge, astronomical tides, andwaves as anindependentphenomenabutratherconsidertheirinteractions,andsuchmodelsmaysometimesbetterreproducetheactualphenomena.9),10),11),12)

(5)StormSurgeandAstronomicalTidesStorm surge is caused bymeteorological disturbances such as typhoons,while astronomical tides are causedmainly by the gravity of themoon and sun. Since storm surge and astronomical tides are phenomenawithindependentcauses,thetimeofmaximumtideanomalyduetostormsurgemightoverlapeithertheastronomicalhightideorthelowtide. Inparticular,theastronomicaltiderangeislargeatinternalbaysattheSetoInlandSeaandalongthecoastoftheEastChinaSea,sothateveniftherehadbeenaremarkabletideanomalyitmighthavebeenpossibletoavoidgreatdamageifitoverlapslowtide.Whenspecifyingthedesigntidallevel,inorderthatonedoesnotoverlooksuchastormsurge,oneshouldnotconsiderthetidallevelobtainedbycombiningthestormsurgewiththeastronomicaltide,butratheroneshouldconsiderthecharacteristicsoftheoccurrenceoftideanomaliesjustduetostormsurge.

(6)CoincidenceofStormSurgeandHighWavesAstormsurgeinaninternalbaymainlyoccursdueto thesuctioneffectofdepressionandwindsetupeffect.Usually,atthebayentrancethesuctioneffectpredominates,andthetideanomalyismaximalwhenatyphoonis closest and the atmospheric pressure has dropped themost. At the bay throat often thewind setup effectpredominates,sothatthetidallevelanomalyisgreatestwhenthetyphoonwindsareblowingfromtheentranceofthebaytowarditsthroat.Ontheotherhand,wavesarenotdirectlyrelatedtosuctioneffect,butrathertheydevelopduetowinds,andtheirpropagationisaffectedbythetopographyoftheseabed.Wavesarealsoaffectedby thesurrounding topography,andcaneasilybeshelteredbycapesor islands. Sincestormsurgediffers inthesewaysfromwaves,thepeakofthetideanomalyandthepeakofthewavesmaynotoccursimultaneously,dependingonthetrackandthelocationofthetyphoonwithinthebay.13)

(7)MeanWaterLevelRiseduetoWaveBreakingInthesurfzone,regardlessofwhetherthesealevelisbeingdrawnupbydepressionorwindsetupeffect,thereisariseofthemeanwaterlevelduetowavebreaking,andthereislongperiodoscillation.Aspartofthisprocess,theriseofthemeanwaterleveliscalledwavesetup.Theamountofrisedependsonfactorssuchastheslopeoftheseabottomandthesteepnessoftheincidentwaves,andittendstobelargerneartheshoreline,andmaybe10%ormoreofthesignificantwaveheightatoffshore.Therefore,attheshorethatisdirectlyhitbywaves,theabsolutevalueoftheamountofriseofthemeanwaterlevelislarge,thisisalsoanimportantfactorofthetideanomaly. Fortheperformanceverificationofportfacilitiesinthesurfzoneitisnecessarytoconsidertheriseofthemeanwaterlevelduetowavebreakingaswellastheoscillation,howeverusuallythecalculationformulasanddiagramsforfactorssuchaswaveheightinsurfzone,waveforce,andwaveovertoppingrateincludetheeffectof riseof themeanwater level, therefore it isnotnecessary toseparatelyadd theamountof riseof themeanwaterlevelintothedesigntidallevel.However,inareaswherereefshavewidelyformedtheriseinwaterlevelisespeciallylarge,sometimesevenonemeterormore,soinsuchplacesitispreferabletoincludetheriseinmeanwaterlevelinthetidallevelforthepurposeofperformanceverificationinsuchlocations.


–71–

3.3 Harbor Resonance

(1)DefinitionIn locationssuchasa lakewhoseperimeter isclosedorabaywhoseentrance isnarrowso that there is littleexchangeofwaterwiththeouteroceantheinternalwaterhasanaturaloscillationwithaconstantperiodduetovariationsinactionssuchaswinds.Thisphenomenoniscalledseiche.Ontheotherhand,theoscillationthatoccursinabayorharborwhereonepartisopentotheouteroceansothatwatercangoinandoutiscalledharborresonance.Harborresonanceisthemainproblemforperformanceverificationofportfacilities,whereonemustconsidertheoscillationperiodandamplitude. Harborresonanceisdividedintotwomaintypes.Oneiswhenitoccurswithinabayduetosuctioneffectofdepressionandwindsetupeffect.Fig. 3.3.1showstheobservationalrecordsoftidallevelinTokyoBayduringTyphoon2001/5(Danas),whenremarkableharborresonanceoccurredasshownbythearrows. Theotheristhetypeofoscillationthatoccurswithinabayorharborduetowavesthatimpingefromtheouteroceanandtheiraccompanyinglong-termwaterlevelvariationsandcurrents.Thistypeofoscillationcancausealargeresonancewithanoscillationperiodthatisuniquefortheshapeandsizeofthebayorharbor.Inparticular,inplaceswheretheshapeislongandnarrow,suchasanartificiallyexcavatedport,andthewaterareaissurroundedbythefacilitieswithahighrefractioncoefficientsuchasquaywalls,remarkableharborresonanceoftenoccurs. Theperiodforharborresonanceisusuallyfromseveralminutestoseveraltensofminutes,andtheamplitudemayreachseveraltensofcentimeters.NagasakiBayhasseenamplitudesofabout2meters.Eventhoughtheverticalamplitudeofthewaterlevelduetoharborresonancemayonlybeseveraltensofcentimeters,thecurrentvelocityinthehorizontaldirectionislarge,sothiscanbeagreatproblemforshipmooringandcargohandlingoperations.Wavesthatcontaincomponentwaveswithaperiodof30to300secondsinthefrequencyspectrumasanalyzedfromcontinuousmeasurementrecordingsof20minutesormorearedefinedaslongperiodwaves(forlong-periodwaves,seeSection 4.4, Long-period Waves). Therefore,itisnecessarytoknowanaturalfrequencyperiodofaportforperformanceverificationofportfacilities. Unoki 17)hasconducteda researchon thecharacteristicsofharbor resonance in themajorportsofJapan.Itisalsopossibletousenumericalcalculationsofwaveswithfrequenciesfromseveralminutestoanhourthatimpingeonportstocalculatetheiramplituderatios.18)

Fig. 3.3.1 Tidal Level Observational Recordings During Typhoon 2001/5 (Danas)(Japan Coast Guard home page)

(2)HarborResonancePeriodsForharborswhichcanbemodeledbysimpleshapetheirnaturalfrequencyperiodandamplitudeamplificationratio canbe foundby theoretical calculations. However, shapes andboundary conditionsof real harbors areextremelycomplicated,soitispreferablefortheirnaturalfrequencyperiodsandamplitudeamplificationratiostobefoundbyon-siteobservationsornumericalcalculations.18)Forreference,formulasforthenaturalfrequencyperiodsinthesimplestcasesaregivenasfollows:

–72–


① Rectangularharborofconstantdepth(surroundingsareclosed,nowaterentersorleaves,Fig. 3.3.2 (a)):

(3.3.1)

where T :naturalfrequencyperiod(s) l :lengthofthewatersurface(thelongitudinaldirection)(m) m :modeoftheoscillation(1,2,3,...) g :gravitationalacceleration(9.8m/s2) h :waterdepth(m)

② Rectangularharborofconstantdepth(asinFig. 3.3.2 (b),watercanfreelyentersandleavesinoneplace,andtheharborisnarrowandlong):

(3.3.2)

Theamplitudeamplificationratiooftentakesitsmaximumwhenmis0or1,soinpracticeitisacceptabletojustinvestigatethiscase.Inreality,notonlytheseawaterwithintheharborbutalsotheseawaterintheouteroceanneartheharborentrancealsooscillatestosomeextent,thereforethevalueofthenaturalfrequencyperiodbecomessomewhatlongerfromthatgivenbyequation(3.3.2)andbecomesthevaluegivenbyequation (3.3.3) 19):

(3.3.3)

where l :longitudinallengthofaharbor α :harborentrancecorrection,givenbyequation(3.3.4):

(3.3.4)

where π :ratioofthecircularconstant b :widthofaharbor

Table 3.3.1 shows values of the harbor entrancemodification coefficientα for representative values ofb/l, ascalculatedfromequation(3.3.4).

Table 3.3.1 Harbor Entrance Modification Coefficients

b/l 1 1/2 1/3 1/4 1/5 1/10 1/25α 1.320 1.261 1.217 1.187 1.163 1.106 1.064

③ Rectangularharborofconstantdepth(asinFig. 3.3.2 (c),watercanfreelyenterandleaveinoneplace,andtheharborentranceisnarrow):

(3.3.5)

where b :widthofaharbor(m) l :lengthofaharbor n :numberofnodesinthewidthdirectionofaharbor(n=0,1,2,...)

Inactualcases,thenaturalfrequencyperiodhasasomewhatsmallervaluethanthatcalculatedfromequation (3.3.5) duetotheeffectoftheharborentrance.


–73–

b

(a) (b) (c)

Fig. 3.3.2 Models of Harbor Shapes

(3)AmplitudeTheamplitudeofharborresonanceisdeterminedbythewaveperiodthatcauseitaswellasbytheaccompanyinglong-periodwater levelvariationsandcurrentvariations, andtheamplificationratiofor thoseperiods. If theperiodoftheactionequalsthenaturalperiodfortheharborthenresonanceoccurs,sothattheamplificationratiotakesonahighvalue.However,bottomfrictioncausesirregularwavesandeddiesattheharborentrance,leadingtoalossofenergy,sothattheamplitudeoftheharborresonancedoesnotincreasewithoutanylimitation.Aharborresonancewithasmallamplitudestillformseveniftheperiodoftheactionisdifferentfromthenaturalperiodoftheharbor. Ifthewidthoftheharborentranceisnarrowedinordertoincreasethecalmnesswithintheharbor,itmayinsteadmakeharbor resonancemore likely tooccur. Thisphenomenon is called theharborparadox. Whentheshapeof theharbor ischanged,suchasbyextending thebreakwaters,onemustbecarefulnot tocausearemarkableharborresonance. Iftheenergylossattheharborentranceisneglected,theamplitudeamplificationratioRattheinsidecornersofabaywitharectangularharborcanbecalculatedfromtheratioofthelengthoftheharborandthewavelength,usingFig. 3.3.3 20)andFig. 3.3.4.20)AccordingtotheseFigs,forthelongandnarrowrectangularharborofFig. 3.3.3,resonanceoccursmoreeasilyforlengthsthataresomewhatlongerthantheresonanceconditions.InFig. 3.3.4theresonancepointsareroughlythesameastheresonancepointsforacompletelyclosedrectangularshapedlake,asapproximatedbyequation(3.3.6):

m, n=0,1,2,... (3.3.6)

Am

plitu

de A

mpl

ifica

tion

Rat

io R

Relative Length of the Harbor k = 2π/L Relative Length of the Harbor k = 2π/L

Am

plitu

de A

mpl

ifica

tion

Rat

io R

002468101214161820

1 2 3 4 5 6 7

2b/ =0.2

8 9 10

d/b=0.01 0.1 1.0

3π2π

2b2d

m=

1n=

0

m=

0n=

0

m=

2n=

0

m=

3n=

0

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

102b/ =0.2

d/b=0.01 0.1 1.0

π 3π2π

2b

2d

m=

1n=

0

m=

0n=

0

m=

1n=

2 m=

2n=

0m=

2n=

2

m=

2n=

4m=

3n=

0

π

Fig. 3.3.3 Resonance Spectrum for a Fig. 3.3.4 Resonance Spectrum for a Long and Narrow Rectangular Harbor 20) Wide Rectangular Harbor 20)

(4)CountermeasuresAgainstHarborResonanceHarborresonanceisthephenomenonwherebylong-periodwavespenetrateintoaharborfromtheentrance,repeatperfectreflectionwithintheharbor,andincreasetheiramplitude.Inordertoholddowntheamplitudeofharborresonance,itisnecessarytominimizereflectancearoundtheinnerperimeteroftheharbororaltertheshapeoftheharbortoreduceresonancegeneration,orincreasetheenergylosswithintheharbor.Forthisreason,itisnotadvisabletobuilduprightquaywallsaroundthewholeperimeterofaharbor.Ifapermeablerubble-moundbreakwaterwithagentleslopeisused,wavereflectioncanbereducedtosomeextent,andinadditiononecan

–74–


expectacertainenergylossinaslopingbreakwater.Furthermore,byinstallinganinnerbreakwaterclosetothepositionofanodeoftheharborresonanceinaharbor,theamplitudeoftheharborresonancecanbesomewhatreduced.Regardingtheshapeoftheharbor,itisconsideredthatanirregularshapeisbetterthanageometricallyregularshape.

3.4 Abnormal Tidal Levels

(1)CausesofAbnormalTidalLevelsBesidesstormsurgebytyphoonsandtsunamis,variousotherreasonscanbegivenforabnormaltidegeneration,suchascurrentvariationsoftheKuroshiocurrent,riseintheoceanwatertemperatureduetotheinfluxofwarmwater,andthelong-termcontinuationofwestward-movingwind-drivencurrents.Suchabnormaltidallevelsmaycontinuefromseveraldaystoseveralmonths,andincasessuchaswhenthemonthly-highesttidesoverlapwithstormsurgetherecanbedamagefromwaterflooding. Theanalysisofabnormaltidallevelsrevealsnotonlyabnormallyhightidallevelsbutalsoabnormallylowtidallevels.Itisimportanttoclarifytheircausesforeachoceanregion.

(2)EffectsofAbnormalTidallevelsTheeffectofabnormaltidallevelsonthestabilityofportfacilitiesandtheverificationoftheabilitytowithstandeventssuchaswaveovertoppingcanbeconsideredbyreflectingthemindesigntidallevels.Forexample,withregardtothestabilityofbreakwaters,anabnormallyhightidallevelcanincreasethebuoyancyofbreakwatersandtherebydecreasestability.21) Yoshiokaet. al.haveevaluatedtheprobabilitydistributionofabnormaltidallevelsat97placesthroughoutJapanbasedontideobservationaldataincludingasmuchasfor29years,andtheyhaveperformedareliabilityanalysisbasedonthis,tostudytheeffectontheslidingandoverturningstabilityofbreakwaters.Withinthescopeoftheirresults,thedecreaseinthesafetyindexduetoabnormaltidallevelsissmallenoughthatitcanbeneglected.22)

3.5 Long-term Variation in the Mean Sea Level

(1)PredictionofVariationsintheMeanSeaLevelSeparatefromtheconsiderationsofastronomicaltidallevelsandstormsurgeinthespecificationofdesigntidallevels,therehavebeenstudiesbothwithinJapanandabroadofthelong-termriseintheleveloftheoceansurface. According to the evaluation report of the IntergovernmentalPanel onClimateChange (IPCC), 23), 24) theglobalmeansea level ispredicted torisebetween0.09and0.88meters from1990 to2100. Fig. 3.5.1 showsIPCC’spredictedfuturevariationinthemeansealevel.

Rise

in th

e Wat

er L

evel

of t

he O

cean

Sur

face

(m)

Year

SRES ScenarioComplete SRES Envelope Including the Uncertainties Concerning Continental Ice

Bars show the range of prediction results for the year 2100 according to several models.

Complete SRES Scenario Envelope According to Several Models

Mean Model Envelope for Complete SRES Scenario

CompleteIS92

Fig. 3.5.1 Predicted Future Variation in the Mean Water Level of the Earth’s Ocean SurfaceAccording to IPCC’s Third Evaluation Report

(From the Third IPCC Evaluation Report, First Operating Committee Report, Climate Change 2001, Scientific Basis, Summary for Government Policy Makers)


–75–

(2)EffectoftheMeanSeaLevelRise,anditsAdaptationIfthemeansealevelrises,andastormsurgeortsunamioccurs,theheightsoftheshoresandriverbankswillbeinsufficient,therebyloweringthesafetyoftheirfacilitiesandincreasingtheriskofdisasters.Also,therewillbeaneffectonthelogisticsinfrastructure,suchasusagelimitationsonportfacilities. Measurestotakeagainstameansealevelriseincludesuchmeasuresasfacilitydevelopment,changesinlanduse,andstrengtheningofdisasterpreventionsystem,and it isnecessary toclearlyunderstand theadvantagesanddisadvantagesofsuchmeasures, taking intoaccount factorssuchas thesocialcharacteristicsandnaturalconditionsofthetargetareas,andcombiningallsuchmeasuresintoanadaptableplans.26)Inordertodevelopfacilities,suchasportfacilities,sewerfacilities,androads(bridges),itisnecessarytocompensatefortheeffectsofmeansealevelrise.However,itisnecessarytokeepinmindfacilityplanning,theaccompanyingdesignworkingtime,cost-effectiveness,theeffectonthesurroundingenvironment,andtheuncertaintiesinthepredictionsofthesealevelrise.

3.6 Underground Water Level and Seepage

(1)Asnecessary,performanceverificationofportfacilitiesmustappropriatelyconsidertheundergroundwaterlevelatsandycoastalareas.

(2)As necessary, performance verification of port facilitiesmust consider the velocity and discharge of seepagewithinpermeablefoundationsandfacilities.

(3)GroundwaterLevelinCoastalAquiferTheelevationofbrackishgroundwaterintrudinginacoastalaquifermaybeestimatedusingthefollowingequation(seeFig. 3.6.1).

(3.6.1)

where

h :depthbelowtheseasurfaceoftheinterfacebetweenfreshwaterandsaltwateratthedistancex(m) h0 :depthbelowtheseasurfaceoftheinterfacebetweenfreshwaterandsaltwateratx=0(m) hl :depthbelowtheseasurfaceoftheinterfacebetweenfreshwaterandsaltwateratx=L(m) ρ1 :densityofthefreshwater(g/cm3) ρ2 :densityofsaltwater(g/cm3) ζ0 :elevationoffreshwaterabovetheseasurfaceatthecoast(x=0)(m) ζ :elevationoffreshwaterabovetheseasurfaceatx=L(m) L :distancefromthecoast(x=0)tothereferencepoint(m) x :landwarddistancefromthecoastline(m)

Equation(3.6.1)cannotbeappliedifanimpermeablelayerexistsclosetothegroundsurfaceorintheaquifer:Fortherelationshipbetweentheriseofgroundwaterlevelduetowaverunupandbeachprofilechange,seein10.1General[TechnicalNotes](8)

x=0

xL

hh0

h1

ζ ζlζ0

ρ2

ρ1

Fresh waterlevel

Fresh water

Salt waterlevel

Salt water

Sea

Fig. 3.6.1 Schematic Drawing of Groundwater at Coast

–76–


(4)SeepagewithinFoundationsandFacilities

① FormulaforCalculatingtheSeepagedischargeWhenthefluidthatisflowingintheseepagelayerisasteadylaminarflow,thedischargeofseepagecanbecalculatedfromtheDarcyformula.Steadyflowswithintheusualseepagelayersmadeofsoilandsand,suchassurfacelayersandfiltrationlayers,areextremelyslow.InsuchcasestheflowfollowstheDarcyformulaofequation (3.6.2)

(3.6.2)

where q :dischargeofwaterflowinginaseepagelayerperunittime(cm3/s) k : permeabilitycoefficient(cm/s) i : hydraulicgradient

Lhi =

h : headloss(cm) L : lengthofseepagecurrentpath(cm) A : cross-sectionalarea(cm2)

TheapplicabilitylimitsforthisformulaaredeterminedbythediametersoftheparticlesthatformtheseepagelayerandtheReynoldsnumberfortheseepagerate,howeveritisbettertoverifythisbymeasurementbecausetherestillisnosufficientlyagreeduponsolution.31)FortheapplicablerangesandpermeationcoefficientsseeChapter 3, 2.2.3, Hydraulic Conductivity of Soil.

② PermeationthroughasheetpilewallTheflowrateofpermeationthroughasheetpilewallisnotdeterminedpurelybythepermeabilityofthewall;rather,thepermeabilityofthesoilbehindthewallhasadominatinginfluence.Shojietal.13)examinedthisproblem, and carriedout comprehensivepermeation experiments inwhich theynot onlyvaried the tensionof the joints,butalsoaddedthecaseswithandwithoutsandfillingin the jointsection. Theyproposedthefollowingexperimentalformula:

(3.6.3)

where q :flowrateofpermeationthroughasheetpilejointperunitlengthintheverticaldirection(cm3/s/

cm) K :permeationcoefficientforthejoints(cm2-n/s) h :pressureheaddifferencebetweenthefrontandbackofajoint(cm) n :coefficientdependingonthestateofthejoints

(n ≒0.5whenthejointsarenotfilledwithsand,andn ≒1.0whenthejointsarefilledwith sand)

Whentherewassandonbothsidesofthesheetpileandthejointswereundertension,Shojietal.obtainedavalueof7.0×10-4cm/sforK intheirexperiments.However,theyalsopointedoutthatifthepermeationflowisestimatedwiththisvalue,thentheflowrateturnsouttobeasmuchas30timesthatobservedinthefield.Foractualdesign,itisthusnecessarytopaycloseattentiontoanydifferencebetweenthestateofthesheetpilewallusedintheexperimentsandthoseusedinthefield.

③ PermeationthroughrubblemoundTheflowrateofpermeationthrougharubblemoundfoundationofagravitytypestructuremaybeestimatedusingthefollowingequation:

(3.6.4)

where q : flowrateofpermeationperunitwidth(m3/s/m) U : meanpermeationvelocityforthewholecrosssectionofrubblemound(m/s) H : heightofthepermeablelayer(m) d : rubblestonesize(m) g : gravitationalacceleration(=9.81m/s2)ΔH/ΔS : hydraulicgradient ζ : resistancecoefficient


–77–

Equation (3.6.4) hasbeenproposedbasedontheexperimentalresultsusingeightdifferenttypesofstonesofuniformsize,withthediameterrangingfrom5mmto100mm.ThevirtualflowlengthΔS maybetakentobeasthetotalofthe70%to80%ofthepermeablelayerheightandthewidthofthecaissonbase.ThecoefficientofresistanceisshowninFig. 3.6.2.WhenRe(=Ud /ν)>104,itisacceptabletotakeζ≒20

.

d(mm) ∆S(cm)

5 – 10 1005 – 10 7510 – 15 10010 – 15 7515 – 20 10020 – 25 10025 – 30 9930 – 35 10095 104100 102

1010

102 103 104

Re =Udv

102

103

ζ

Fig. 3.6.2 Relationship between Resistance Coefficient ζ and Reynolds Number

References

1) JapanCoastGuard:TideTable,Vol.1,19962) JapanMeteorologicalAgency:TideTable2004,2003,3) StudyGroup ofAnalysis and utilization of coastal wave observation data,:measurement of tide, Coastal Development

InstituteofTechnology,CoastaldevelopmentTechnicalLibrary.No.13,2002.4) Kawai,H.T.Takayama,Y.SuzukiandT.Hiraishi:FailureProbabilityofBreakwaterCaissonTidalLevelVariation,Rept.of

PHRIVol.36No.4,1997.12,pp.3-425) JapanMeteorologicalAgency:TideTable2004,JapanMeteorologicalAgency,2003,6) Takahashi,H.A.Takeda,K.TanimonoY.TsujiandI.Isozaki:Predictionandpreventivemeasureofcoastaldisaster-Howto

preparefortsunamisandstormsurges,HakuaPublishing,408p.19887) Hiraishi,T.K.Hirayama andH.Kawai:AStudyonWave-0vertoppingbyTyphoonNo. 9918,TechnicalNoteofPHRI,

No.972,2000.12,19p8) Shibaki,H.,T.Ando,T.MikamiandC.Goto:Developmentof integratednumerical researchsystemforpreventionand

estimationofcoastaldisaster,Jour.JSCENo586/11-42,pp.77-92,19989) Yamashita,T.,Y.Nakagawa:SimulationofastormsurgeinYatsushiroSeaduetoTyphoonNo.9918bywave-stormsurge

coupledmodelconsideringshearstressofwhitecapbreakers,ProceedingofCoastalEng.No.48,pp.291-295,200110) Takigawa,K..andM.Tabuchi:Preparationofhazardmapsofstormsurgesandhighwavesunderthemostprobableoccurrence

basedontide-waveinteractionanalysis,probableassumption,ProceedingofCoastalEng.No.48,pp.1366-1370,200111) Shibaki,H.andA.Watanabe:StudyonMulti-levelsimulationmodelforestormsurgeconsideringdensitystratificationand

wavesetup,JournaloftheJSCE,No.719/IIpp.47-61,200212) Kawai,Y.,K.KawaguxhiandN.Hashimoto:Modelingofwave-stormsurgetwo-wayjointhindcastingandcasestudyfor

Typhoon9918hindcasting,,ProceedingofCoastalEng.No.50,pp.296-300,200313) Kawai,Y.,S.TakemuraandN.Hara:Characteristicsofstormsurge-highwavejointoccurrenceanddurationinTokyoBay,

ProceedingofCoastalEng.No.49,pp.241-245,200214) Konishi,T.:Situationsofdamagesofstormsurgesandstatusofthestudyforforecasting,OceanographicSocietyofJapan,

CoastalOceanographyResearchVol.35No.2,199815) TatsuoKonishi:ACauseofStormSurgesGeneratedatthePortsFacingOpenOceans-EffectofWaveSetup-,Seaandsky

Vol.74,No.2,199716) Shibaki,H.,F.KatoandK.Yamada:HindcastingofabnormalstormsurgeinTosaBayconsideringdensitystratificationand

wavesetup,ProceedingofCoastalEng.No.48,pp.286-290,200117) Unoki,S:Onseicheandlongperiodwavesinharbours,Proceedingof6thconferenceoncoastalEngineering,pp.1-11,195918) Takayama, T. and T. Hiraishi: Amplification Mechanism of Harbor Oscillation Derived From Field Observation And

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NumericalSimulation,TechnicalNoteofPHRINo.636,pp.70,198819) Honda,K,,Terada,T.,Yoshida,Y.andlshitani,D.:Secondaryundulationofoceanictides,Jour.CollageofScience,Univ.of

Tokyo,Vol.26,194320) Goda,Y:Secondaryundulationoftideinrectangularandfan-shapedharbour,JSCE10thconferenceonCoastalEng.,pp.

53-58,196321) CoastalDevelopmentInstituteofTechnology(CDIT):SurveyreportonExtra-hightidelevelFiscal2002,pp.86,200322) Yoshioka,K.,T.Nagao,E.Kibe,T.ShimonoandH.Matsumoto:Effectofextra-hightideontheexternalstabilityofcaisson

typebreakwaters,TechnicalNoteofNationalInstituteforLandandInfrastructureManagement,No.241,200523) IPCC:ClimateChange2001,ScientificBasis,CambridgeUniversityPress,p.881,200124) AssemblymeninchargeofEnvironment,SyntheticScienceandTechnologyConferenceand,CabinetOfficeDirector-general

forPoliticsonScienceandTechnologyCondition:StudyReportonClimateChange,SyntheticScienceandTechnologyConference, GlobalWarming Study Initiative, Frontier of Climate Change Studies, Knowledge and Technology in theCenturyofEnvironment,2002,p.142,2003

25) Nagai,T.K.Sugahara,H.WatanabeandK.Kawaguchi:LongTermObservationoftheMeanTideLevelandLongWavesattheKurihama-Bay,Rept.OfPHRIVol.35No.4,1996.12,pp.3-36

26) TaskForceoftheStudyonLandconservationagainstsealevelriseduetoglobalwarming:ReportoftheLandConservationTaskForceonsealevelriseduetotheglobalwarming,,p.35,2002

27) Todd,D.K.:Groundwaterhydrology,JohnWiley&Sons,Inc.,196328) JSCE:TheCollectedFormulaofHydraulics(1985Edition),JSCE,Nov.198529) Ishihara,T.andH.Honma:AppliedHydraulics(Vol.IINo.2),MaruzenPublishing,196630) Sakai,G:Geohydrology,AsakuraPublishing,196531) Iwasa,Y.:Hydraulics,AsakuraPublishing,p.226,196732) Yamaguchi,H:SoulMechanics,Giho-doPublishing,p.76,196933) Shoji,Y.M.KumedaandY.Tomita:ExperimentsonSeepagethroughInterlockingJointsofSheetPile,Rept.PHRIVol.21

No.41982.12

PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METEOROLOGY AND OCEANOGRAPHY

–79–

4 WavesPublic NoticeWaves

Article 8Characteristicsofwavesshallbesetbythemethodsprovidedinthesubsequentitemscorrespondingtothesingleactionorcombinationoftwoormoreactionstobeconsideredintheperformancecriteriaandtheperformanceverification:(1)Wavestobeemployedintheverificationofthestructuralstabilityofthefacilities,thefailureofthe

sectionofastructuralmember(excludingfatiguefailure),andothersshallbeappropriatelydefinedintermsofthewaveheight,periodanddirectioncorrespondingtothereturnperiodthroughthestatisticalanalysisofthelong-termdataofobservedorhindcastedwavesorothermethods.

(2)Waves tobeemployed in theverificationof the assuranceof the functionsof a structuralmemberandthefailureofitssectionduetofatigueshallbeappropriatelydefinedintermsofthewaveheight,period,directionandothersofwaveshavingahighfrequencyofoccurrenceduringthedesignworkinglifethroughthestatisticalanalysisofthelong-termdataofobservedorhindcastedwaves.

(3)Wavestobeemployedintheverificationoftheharborcalmnessshallbeappropriatelydefinedintermsof the joint frequencydistributionsof thewaveheight, periodanddirectionofwaves for a certaindurationoftimethroughthestatisticalanalysisofthelong-termdataofobservedorhindcastedwaves.

[Commentary]

(1)Wavesemployedtoverifythestabilityoffacilities,toverifythefailureofthesectionofastructuralmember.

①ReturnperiodofvariablewavesWhensettingthewavestobeconsideredintheverificationofserviceabilityforavariablestatewheredominatingactionisvariablewaves,thepurposeofthefacilitiesandtheperformancerequirementsmust satisfied, and in addition the returnperiodof thewavesare set appropriatelybyconsideringsuitablythedesignworkinglifeanddegreeofimportanceofobjectivefacilities,aswellasthenaturalconditionofobjectivelocation.

②ReturnperiodofaccidentalwavesWhensettingthewavestobeconsideredintheverificationofserviceabilityforaaccidentalsituationwheredominatingactionisaccidentalwaves,thewavesthatbecometheseverestamongthewavesthatcanoccurinobjectivemarinewatersorwaveswithareturnperiodof100yearsorlongeraresetappropriately.

③PeriodofobservedvaluesorestimatedvaluesAperiodof30yearsorlongerisusedasthestandardforthelong-termobservedvaluesorestimatedvalues.

(2)Wavesemployedtoverifytheassuranceofthefunctionsandthefailureofsectionsduetofatigueofthefacilitiesrelatingtostructuralmembers

①Theverificationoftheassuranceofthefunctionsofthefacilitiesrelatingtostructuralmembersreferstoverificationofthelimitstateinwhichfunction-relatedtroubleoccursinstructuralmembers,andinadditiontheverificationoffailureofsectionsduetofatiguereferstoverificationofthelimitstateinwhichdestructionofasectionoccursinastructuralmemberduetorepeatedaction.

②Thewavestobeconsideredintheverificationoftheassuranceofthefunctionsofthefacilitiesrelatingtostructuralmembersemployasthestandardwavesforwhichthenumberoftimeswhichthewaveswithawaveheightgreaterthanthatstrikeinthedesignworkinglifeisabout10,000times.

③Whensettingthewavestobeconsideredintheverificationofdestructionofasectionduetofatigue,the various conditions such as the natural condition of objective facilities are considered, and thenumberoftimesofappearancerelatingtothewaveheightandperiodofthewavesthatoccurduringthedesignworkinglife.Theperiodoftheobservedvaluesandestimatedvaluesisbasedon(1)③above.

(3)WavesemployedtoverifyharborcalmnessAperiodof5yearsorlongerisusedasthestandardforthelongterm(observationorestimation).Inaddition,

–80–


when setting thewaves tobe considered in theverificationofharbor calmness, longperiodwaves shouldbeincludedinareaswhereoccuranceoflongperiodwavesispredicted.

[Technical Note]

4.1 Basic Matters Relating to Waves

(1)DefinitionofWavesThewavesoftheoceansareoneoftheprincipalactionsactingontheportfacilities,andareinprincipletreatedasrandomwaves,andaresetappropriatelybasedtothegreatestpossibleextentonpastobservationdataandthelatestfindings.Fig. 4.1.1showsthedefinitionofwaves.Here,theheightfromthetroughtothepeakofonewaveisthewaveheightH,thespatiallengthisthewavelengthL,andthespeedatwhichitispropagatedisthewavecelerityCcalculatedbythezero-upcrossmethod.ThelengthoftheperiodfromthestartofawavetothestartofthenextwaveexpressedinacaseobservedatafixedpointistheperiodT.Reference1)canbereferredforthespecificsonthebasicnatureofwaves.

-4

-3

-2

-1

0

1

2

3

4

00 10 20 30 4040 50 6060 70 80 90 100100

Time (s)

Wat

er le

vel (

m)

Wave height H (m)

Period T

Fig. 4.1.1 Definition of Waves

(2)IntroductionofRandomWavesThewaveheightandperiodofoceanwavesvaryforeachwave.Suchwavesarecalledrandomwaves,anditispreferableinprinciplethatrandomwavesareemployedintheperformanceverification.Itispossibletoconsiderrandomwavestobetheoverlappingofregularwaveswithvariousperiods,andtherespectiveregularwavesarecalledcomponentwaves.Itisthefrequencyspectrumofawavethatindicatesthedegreeoftheenergyofthecomponentwaves,andaspectrumshapecorresponding to thepropertiesofoceanshouldbeemployed in theperformance verification. Basedon observed cases to date on Japan’s seacoast, theBretschneider-Mitsuyasuspectrum2)iscommonlyemployed. TheBretschneider-Mitsuyasuspectrumshapeisexpressedbythefollowingequation.

(4.1.1)

whereS( f ) :frequencyspectrumofthewaveH1/3 :significantwaveheight T1/3 :significantwaveperiod f :frequency

However,ininnerbayareaslikeTokyoBay,thepeakofthespectrumoftenbecomespointed,soitispreferabletointroduceaspectrumshapeoftheJONSWAPtype3)basedonobservationstothegreatestextentpossible,ortoemployaspectrumthatcanreflectappropriatelytheobservationresults.

(3)IntroductionofMultidirectionalityofWavesInshallowwaters,thewaveheightofthecomponentwavesbecomesorthogonaltotheshorelineduetorefractioneffects,andthenatureofthewavesbecomesclosertouni-directionalrandomwaves.Accordingly,acaseinwhichthewaterdepthtothewavelengthratioofoffshorewaves(h/L0)becomes0.1orsmallerisusedasthebenchmark,andinwatersshallowerthanthisitmaybeapproximatedasawavethatactsbyanuni-directionalrandomwavecomposedofcomponentwaves thatareunidirectionalonly, limited tocaseswhereawaveisemployedas thevariable action. In deeperwaters, its character as amulti directional randomwavewhere the energy of thecomponentwavesadvances invariousdirectionsbecomesstronger, and it ispreferable to treat thewaveasamultidirectionalrandomwave.Inaddition,sincethemultidirectionalityofthewavehasamajoreffectinthe


–81–

performanceverificationofthestabilityofthebreakwaterheadofabreakwaterorfloatingfacilities,sothemultidirectionalityofthewavesinwatersshouldbeexaminedbeforehandwithappropriateobservationdata.Thewavedirectionhasamajoreffectontheresultsinthecalculationofthedegreeofcalmness,sothewavesarecalculatedasmultidirectionalrandomwaves. Adirectionalwavespectrumisemployedasanindexforshowingthemultidirectionalityofawave.Thedirectionalwavespectrum is theproductof theabove-described frequencyspectrum S( f )and thedirectionalspreadingfunctionG( f,θ),andisexpressedasS( f,θ)=S( f )G( f,θ).TheMitsuyasutypedirectionalspreadingfunction is commonly employed inmost cases as the directional spreading function. Fig. 4.1.2 shows thedistributionshapeoftheMitsuyasudirectionalspreadingfunction.f,fpandl inthefigurearerespectivelythefrequency,peakfrequencyofthefrequencyspectrumandcoefficientemployedwhencomputingthedirectionalwavefunctionincosineshape.TheparameterofthedirectionalwavefunctionSmaxisthedirectionalspreadingparameterintroducedbyGodaandSuzuki,4)andthefollowingnumericalvaluescangenerallybeused.

Windwaves Smax=10 Swellwithashortattenuationdistance Smax=25 Swellwithalongattenuationdistance Smax=75

However,thevarianceofthedirectionalspreadingparameterislargeon-site,andwhenthedirectionalwavespectrumisobservedon-site,thesevaluesshouldbeusedasareference.

ℓ= 5

ℓ=13ℓ=11ℓ= 9

f*1(f/fp=0.80)f*0(f/fp=1.00)f*2(f/fp=1.38)f*3(f/fp=1.65)

G( ) 2.5

-90° 0° 90°

θ

θ

ℓ

(1)WhenSmax=75

-90° 0° 90°

2

1

G( ) f*1(f/fp=0.80)f*0(f/fp=1.00)f*2(f/fp=1.38)f*3(f/fp=1.65)

ℓ=1ℓ=3

θ

θ

(2)WhenSmax=25

-90° 0° 90°

2

ℓ=1

ℓ=5ℓ=3

f*1(f/fp=0.80)f*0(f/fp=1.00)f*2(f/fp=1.38)f*3(f/fp=1.65)

G( )θ

θ

11

(3)WhenSmax=10

Fig. 4.1.2 The Distribution Shape of the Mitsuyasu Type Directional Spreading Function

–82–


ThedirectionalspreadingparameterSmaxofoffshorewavesthatexpressesthedirectionalspreadingofwaveenergyvariesdependingonthewaveshapesteepness,anditcanbeestimatedwithFig. 4.1.3intheeventthatadequateobservationdataisnotobtained.Inaddition,inshallowwaters,thedirectionalspreadingofwavesvariesdependingontheseabottomtopography,soitispreferabletoestimatethisbyawavedeformationcalculation,butinthosecaseswherethecoastlineisclosetolinearhavingsimpletopographyandthewaterdepthcontourisdeemedtobeparalleltotheshoreline,thechangesinSmaxmaybeestimatedbythediagraminFig. 4.1.4.

200

100

20

50

10

5

2

1

H0/L00.005 0.01 0.02 0.05

S max

Fig. 4.1.3 Changes in Smax due to Wave Shape Steepness

10

20

30

405060708090

100

0.02 0.05 0.1 0.2 0.5 1.0

( p )0= 0°30°60°

(Smax)0= 25

(Smax)0= 10

(Smax)0= 75

h/L0

S max

α

* (Smax)indicatesthevalueofoffshorewaves,and(αp)0indicatestheprincipalwavedirectionofoffshorewaves.L0indicatesthewaveheightofoffshorewaves,andhindicatesthewaterdepth.

Fig. 4.1.4 Changes in Smax due to Water Depth

(4)WavesRepresentedinPerfomanceVerificationSincethewaveheightofrandomwavesvariesdependingonthetime,representativewavesshallbeemployedin theperformanceverification. Significantwavesarenormallyemployedasrepresentativewaves. SincethesignificantwaveheightH1/3 is calculatedbycalculating thewaveheight for eachwaveobtainedby the zero-upcrossmethod,andthencalculatingthemeanvalueof1/3oftheuppervalueofwaveheightthatarerearranged


–83–

indescendingorder.AndthesignificantwaveperiodT1/3isthevalueaveragingtheperiodofthewaveemployedforcalculationofthesignificantwaveheight.Themeanoftheindividualwavesincludedinalldataareexpressedasthemeanwaveheight R andmeanwaveperiodT .Thewavewiththegreatestwaveheightamongaseriesofwavesiscalledthehighestwave,itswaveheightandperiodarerespectivelycalledthehighestwaveheightHmaxandhighestwaveperiodTmax,andtheactionduetothewavesemployedintheverificationofstabilityofabreakwatershallbecalculatedfromthedimensionsofthehighestwave.Ontheassumptionthatwaveenergyisconcentratedintheextremelynarrowrangeofacertainfrequency,theoccurrencefrequencyofthewaveheightsincludedinthewavegroupofoffshorewavesfollowstheRayleighdistribution.IntheeventthattheoccurrencefrequencyofwaveheightsfollowstheRayleighdistribution,thefollowingrelationshipexistsbetweenthehighestwaveheightHmaxandthesignificantwaveheightH1/3.5)

(4.1.2)

Thefollowingrelationshipexistsfortheperiod.

(4.1.3)

TheRayleighdistributionisexpressedbythefollowingequation.

(4.1.4)

whereH isthemeanwaveheightofallwavesinthewavegroup.

Asinthecaseofthemethodforcalculatingthesignificantwaveheight,thewaveheightcalculatedwith1/10oftheuppervalueofwaveheightiscalledthehighest1/10waveheight.Thefollowingformulasareestablishedbetween H ,H1/3andH1/10.

(4.1.5)

(5)DeformationofwavesinshallowwatersThephenomenonwherethewaveheightordirectionofprogressofwavesvariesduetotheeffectsofthewaterdepthiscalledthedeformationofwaves,andadeformationofwavesinwatersthatareshallowerthan½ofthewavelengthL0(=1.56T02)ofoffshorewavesshouldbetakenintoconsideration.Thedeformationofwavesincludessuchphenomenaasrefractionordiffraction,waveshoaling,breakingand,reflection,andcalculationoftheseisdonewiththerespectiveappropriatenumericalcalculationmethods.Sincetheserespectivephenomenaoccurbymutuallyaffectingoneanother,theapplicationofacalculationmethodthatcantakeallofthemintoconsiderationat once is preferable, but at present there is no calculationmethod that can consider all of these phenomenasimultaneouslyinpracticaluse.Inprinciple,thewavesthatactontheportfacilitiesarethoseappropriatewavesthataremostdisadvantageousforthestabilityofthestructureoftheportfacilitiesortheutilizationoftheportfacilities,inviewofrefraction,diffraction,shoaling,andbreakingduetothepropagationofoffshorewaves.

(6)ShallowwatersanddeepwatersInwaterswherethewaterdepthisatleast½thewavelength,thewavesarehardlyaffectedbytheseabottom,andproceedwithoutdeforming.However,wavesaregraduallyaffectedbytheseabottomwhentheyinvadewaterswherethewaterdepthislessthan½thewavelength,andthewaveceleritybecomesslower,thewavelengthshorten,andthewaveheightalsochanges.Giventhisfact,waterswherethewaterdepthisatleast½thewavelengthiscalleddeepwaters,andthewatersshallowerthanthisiscalledshallowwaters.Whensettingthewavesinshallowwaters,dueconsiderationmustbegiventothedeformationofthewaves.Forthedistinctionbetweenshallowwatersanddeepwatersforrandomwaves,thewavelengthL0ofoffshorewavesiscalculatedbyL0=1.56T02(m),andthenthewatersmaybedistinguishedbythewaterdepthrelativetothiswavelength.Moreover,itisnecessarytotakeintoconsiderationthefactthattheshapeofthespectrumandthefrequencydistributionofthewaveheightdiffer fromthestateofoffshorewaves,due to theeffectsof refraction,diffraction, shoaling,andbreaking inshallowwaters.

(7)LongperiodwavesandharborresonanceLongperiodwaves,whichhaveawatersurfacefluctuationwhosefrequencyisseveraltensofsecondsorlonger,mayexertamajorimpactonthemooringfacilitiesortopographyoftheseabottom,anditispreferabletoexamineasnecessary,basedonon-siteobservationsandtheanalyticalresults todate. Harborresonance,whichis the

–84–


naturalresonanceofharborsandbays,haseffectsonnotonlymooredshipsbutalsothewaterleveloftheinnerpartofthebay,sointheeventthatclearharborresonanceisfoundfromthetiderecordstodate,orintheeventthat thetopographyoftheharborvarieswidely, it ispreferabletoexaminethiswithanappropriatenumericalcalculationmethod.6)

(8)WavedirectionThewavedirectionisanimportantparameterfordeterminingthedirectionoftheforcesactingonthefacilities.It ispreferable todetermine theprincipalwavedirection to thegreatest extentpossiblebyobservationof thedirectionalwavespectrumoroftheflowspeedoftwocomponents.7)Theprincipalwavedirectionistheorientationwherethepeaksinthewavetrainaredistributedmostdenselyonawaveformofacertaindirection,anditisconsideredasananglewherethepeakindirectionalwavespectrumappears.However,intheeventthattheswellsfromoutside theharboror thewindwaves thatoccur inside theharboroverlap,bidirectionalwaves thathavetwopeaksforthedirectionalspreadingfunctionappearfrequently.8)Inthesecases,eveniftheprincipalwavedirectionisdetermined,itisseldomthatthisprincipalwavedirectionrepresentsthedirectioninwhichtheenergyofthewaveproceeds,sooneshouldexaminespecialmeasuressuchascarryingouttheperformanceverificationofthefacilitiesatthewavedirectionthatismostdangerous,orcarryingouttheperformanceverificationfortherespectivewavedirections,andsettingthefacilitiestobestableforboth.

(9)SettingofwavesIntheperformanceverification,theabove-describedpropertiesofwavesshallbeconsidered,andfirstofalltheoffshorewavescomposingvariableactionoraccidentalactionshallbedetermined,inaccordancewiththefunctionofthefacilities.Thedirectionalconcentrationoftheenergyofthewaveisset,inadditiontothesignificantwaveheight,significantwaveperiodandwavedirection,astheconditionsofthewaves.Next,thewavedeformationcalculationshowninthenextchapteriscarriedoutinshallowwaters,andtheconditionsofthewavesthatactonthefacilitiesshallbedetermined.

4.2 Generation, Propagation and Attenuation of Waves

(1)SummaryoftheWaveHindcastingMethodWavehindcastingestimatesthetemporalandspatialchangesinwinddirectionandwindvelocityoftheprescribedwaterareafromthetopographyandthemeteorologicaldata,andestimatesthewavesunderthewindfield.Therearevariousmethodsforwavehindcasting,butingeneralthesecanbedividedroughlyintothesignificantwavemethodandthespectrummethod,andthemainstreammethodatpresentisthespectrummethod.

(2)WaveHindcastingbytheSignificantWaveMethodThemodernwavehindcastingmethodthatwasfirstdevelopedintheworldtreatstheseriesofphenomenaknownasthegeneration,development,propagationandattenuationofwavescollectively,andestimatesthewaveheightH1/3(m)andperiodT1/3(s)withthewindvelocityU10(ms)valueat10mabovetheseasurface,winddurationt(s)andfetchlengthF(m)astheparameters.ItsforerunneristheS-M-Bmethod,whichwasproposedbySverdrupandMunk9)inthe1940sandrevisedbyBretschneider.10),11)

Currently,theimprovedWilsonIVformula,12)isgenerallyemployed:

(4.2.1)

(4.2.2)

Fig. 4.2.1illustratestheserelationalexpressions(theunitofthefetchlengthFinequation(4.2.1)andequation(4.2.2)isexpressedbykilometerunitsinFig. 4.2.1).However,theserelationalexpressionsareforcaseswherethewindiscontinuouslyblowingconstantlyforanadequatelylongtime,andforawhileafterthewindstartsblowing it doesnot reach thiswaveheightorperiod. The time required for awave thatoccurs at theupperextremityofthefetchtoreachthepointatdistanceF(m)whileitdevelopsiscalledtheminimumwinddurationtmin(s),andisexpressedbythefollowingequation.

(4.2.3)

whereCg(x)isthegroupvelocityofthewaves.Inaddition,itispossibletomakearoughestimatebymeansofthefollowingequation.13)


–85–

(4.2.4)

Where,tmin’istheminimumwindduration(hr),andF’isthefetchlength(km),anditisnecessarytopayattentiontothefactthattheunitsdifferfromequations(4.2.1)and(4.2.2).Whenthewinddurationisshorterthantheminimumwindduration,thewavesareintheprocessofdevelopingwithtime.Therefore,inthosecaseswherethefetchlengthandthewinddurationaresimultaneouslyprovided,thesmallerwareofthetwocalculatedwavesmustbeadopted. TheSMBmethodfundamentallyappliestoconstantfetch,butintheeventthatthewindspeedischanginggradually,thewavescanbehindcastedbyusingtheequi-energyline(thelineshowingH1/32·T1/32=const). Intheeventthatthewidthofthefetchisnarrowerthanthefetchlengthinalakeorbay,orintheeventthatthefetchlengthisdeterminedbytheoppositeshoredistance,andtheoppositeshoredistancevarieswidelyrelativetominutefluctuationsofthewinddirection,equation(4.2.1) andequation(4.2.2)provideawaveheightorperiodthatismuchlargerthanitreallyis.Insuchcases,itisbesttoemploytheeffectivefetchlength14)providedbythefollowingformula.

(4.2.5)

Here,Feffistheeffectivefetchlength,Fiistheoppositeshoredistanceinthenumberithdirectionfromthehindcastingpointofthewave,andθiistheangleformedbythedirectionoftheoppositeshoredistanceFiandtheprincipalwinddirection,andis-45°≤θi≤45°.

Win

d ve

loci

ty U

(m/s

)

Fetch length F (km)

1 2 3 4 6 108 2 3 4 6 1028 2 3 4 6 1038 2 3 4 6 1048

1

60

50

40

35

3028262422201816

14

12

10

9

8

7

6

52 3 4 6 108 2 3 4 6 1028 2 3 4 6 1038 2 3 4 6 1048

=0.25

H

=0.50

t

=1.5T

0.5

2.5

3.5

1.5

1.5 2.5

2.5

3.5

10

10

10 12 14 18 20 25 30 40 50 60 70 80 90 100 15

0

200

300

400

12

12

14

14

16

18

2022

2426

2830

1618

2022

3035

4045

50

24

1

1 2 3 4 5

6 7 9

2

3

4

5

6

78

9

3

4

5

67 8

9

2

0.75

0.75

8 16

2628

Wave height H1/3 (m) Period T1/3Minimum wind duration t (h) Equi-energy line (H1/32 • T1/3) = const.

Fig. 4.2.1 Wind Hindcasting Diagram by the S-M-B Method

IntheSMBmethod,whenthevariationofthewindfieldissignificantasinthecaseofatyphoonorextratropicalcyclone,itisdifficulttoprovidesuitablythevaluesforwindvelocityU10,fetchlengthForwinddurationt.AmethodthatsolvesthisproblemisWilson’sgraphicalcalculationmethod,15)andthemethodsofIjimaandHorikawa,16),17)whichsolveWilson’sequationnumerically,arecommonlyemployed. Asshowninequation(4.2.1)andequation(4.2.2),thesignificantwavemethodisnothingmorethanformulathat linksexperientially thedevelopmentofwindwaveswith thebasicparameters, and isnot formula that isconstructedinlinewiththemechanismsofgenerationanddevelopmentofwaves.Owingtothisnature,itleavesanumberofvaguepoints,suchashowtohandlecaseswherethewindgraduallydeflects,thetransitionfromwindwavestoswells,themethodforsynthesizingwindwavesandswells.Inaddition,thereisalsotheproblemthatthewavedirectionobtainedbyhindcastingdisplaysthewinddirectionofthefinalstepofcalculation.However,compared toa casewhere thewindfieldhasa simplenatureand theeffectsof swells canbe ignored, it is apracticalestimationmethodthatissimplerthanthespectrummethodandwhosecalculationtimeisalsoshort.

–86–


As far as the swells that wind waves propagate distant from the generation and development areas areconcerned,

(4.2.6)

(4.2.7)

Here,(H1/3)Fand(T1/3)Farethewaveheightandperiodofasignificantwaveattheterminusofthefetch,(H1/3)Dand(T1/3)Darethewaveheightandperiodofaswell,Fministheminimumfetchlengththatgeneratesthewave,Distheattenuationdistance,thatisthedistanceterminusofthewindfieldtothearrivalpointofaswell,andk10.4,andk2 2.0.Inaddition,thepropagationtimetofaswellisgivenbythefollowingequation.

(4.2.8)

Awavehindcastingmethodforshallowwaterareahasalsobeenproposed.19)

(3)WaveHindcastingbytheSpectrumMethodIngeneralthefollowingformulaisemployedforwavehindcastingbythespectrummethod.

(4.2.9)

Here,Cgisthegroupvelocity,thefirsttermatleftstandsforthelocaltemporalchangeinspectrumenergyE(ω,θ),andthesecondtermstandsforthechangesduetothetransmissioneffectofthespectrumenergy.Inaddition,Snet(ω,θ)ontherightsideisthetermexpressingthetotalamountofchangeinenergyrelatedtothechangeofthespectrumcomponents,andingeneralisprovidedbythefollowingformula:

(4.2.10)

Here,Sinistheenergytransmittedfromthewindtothewaves.Snlisthegainandlossofenergythatoccursbetween the four componentwaveswith differentwave numbers, and is called transport ofwave energy bynonlinear interactions(hereinafter,“nonlinear transportofwaveenergy”). Thenonlinear interactionsdue tothesefourwavescausetheshapeofthedirectionalwavespectrumtovary,withthetotalsumofenergythatthewaveshaveconstant.Sdsstandsfortheeffectswheretheenergyofthewavesdissipatesduetowhite-capbreakingwavesortheinternalviscosityofseawater. Modelsbasedonthespectrummethodareclassifiedintothedisjoinedpropagation(DPmodel),thecoupledhybrid(CH)modeland thecoupleddisjoined(CD)model,dependingonhowthenonlinear transportofwaveenergySnlistreated.IntheDPmodel,thenonlineartransportofwaveenergytermisnotintroduceddirectly,andtherespectivefrequencyanddirectionalcomponentsarenotcoupledtoeachother. IntheCHmodel,thenonlinear interactions between component waves are parameterized and introduced. In the CD model, thenonlinearinteractionsareintroduceddirectlyinsomeformorother. Ontheotherhand,themodelsarealsoclassifiedbytheperiodwhentheyweredeveloped.TheDPmodel,whichwasdevelopedfromthe1960s to thebeginningof the1970s, is thefirstgenerationmodel,andtheCHmodelandCDmodel,whichweredevelopedfromthe1970stothe1980s,aresecondgenerationmodels,andtheCDmodel,whichwasdevelopedfromthelatterhalfofthe1980stothepresent,andwhichhandlesthenonlinearinteractionswithhigheraccuracythanpreviously,iscalledthethirdgenerationmodel.Inthethirdgenerationmodel,thedegreeofflexibilityoftheschemeofthenonlineartransportofwaveenergytermishigh,anditispossibletohindcastwithgoodaccuracyeveninthecaseofwaveswherebidirectionalwaves,windwavesandswellsareallpresent. ThewavehindcastingmodeloftheJapanMeteorologicalAgencystartedfromMRI,20)thefirstgenerationmodel,anddevelopedintoMRI-II21)andMRI-IInew,22)thesecondgenerationmodels,andcurrentlyMRI-III,23)the thirdgenerationmodel, isbeingemployed. Inaddition to these, the Inouemodel 24) and theYamaguchi-Tsuchiyamodel25)areknownasafirstgenerationmodel,andtheTohokumodel26)isknownasasecondgenerationmodel.Inaddition,inthefirstgenerationmodels,aonepointmethodwherethewavesatonespotarecalculated


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fromacalculationalongthewaverayofeachcomponentwavethatarrivesatonespothasbeendeveloped.

(4)MRIModel20)TheMRImodelthatwasdevelopedin1973isthemodelthatwasemployedforthenumericalwavereportserviceoftheJapanMeteorologicalAgencyoverapproximatelyadecadefrom1977. IntheMRImodel,thelineardevelopmentandexponentialdevelopmentofwindwavesduetowind,andthephysicalmechanismsofenergydissipationduetotheeffectsofbreakingwavesandinternalfrictionandheadwinds,aretakenintoconsideration.TheeffectsofnonlineartransportofwaveenergySnlarenotconsideredformally,buttheeffectsofon-lineartransportofwaveenergyareexpressedindirectlybyemployingthedevelopmentequation24)forwindwaves,whichdoesnotseparatethenonlineartransportofwaveenergySnlfromthetransportofwaveenergySin fromthewindtothewave. Thetotalamountofchangeinenergy Snet(ω,θ)isdividedintothecasesoftailwindsandheadwinds,andisexpressedasfollows.

(4.2.11)

Here,fisthefrequency,θ isthewavedirection, θw isthewinddirectionandE=E( f,θ)isthedirectionalspectrum of thewave. EPM is the Pierson-Moskowitz spectrum, and is employed as the standard form of asaturatedspectrum.Inaddition,Γ(θ-θw)isthedirectionalwavefunctionthatisproportionatetocos2θ,AandBarethelinearandexponentialdevelopmentrates24)ofwindwavesperunittime,andDisthecoefficientofinternalfriction(eddyviscosity). InaDPmodelincludingtheMRImodel,thespectrumshapeofthewavesisexpressedsoastograduallyapproximateasaturatedspectrum,bymultiplyingthetermoftheform{1–(E-EPM)2},and–(E-EPM)2expressestheformalenergydissipation.Inaddition,intheDPmodel,thecalculationtimeisshort,andithaspracticalaccuracywithrespecttowaveheight,soitisemployedcurrentlyasawavemodelthatcanbeusedsimplyandconveniently.

(5)WAMModel28)TheWAMmodelisarepresentativethirdgenerationwavehindcastingmodelthatdirectlycalculatesthenonlinearinteractions of fourwave resonance, by the discrete interaction approximation 29) of S. Hasselmann andK.Hasselmann.

Inthemodelofthespectrummethod,thetransportofwaveenergyfromwindtowaveisgenerallyprovidedbythefollowing.

(4.2.12)

Here,A correspondstothePhillipsresonancemechanism,andBEtotheMilesinstabilitymechanism.ThePhillipsresonancemechanismisamechanismwheretherandompressurefluctuationsofwindthatblowsoverastillwatersurface,andthecomponentwavesthathaveaspatialscaleandphasevelocitythatmatchestheformer,cause resonance, andowing to thephenomenaawave isgenerated. On theotherhand, theMiles instabilitymechanismisamechanismwheretheairflowonthewatersurfaceisdisturbedandbecomesunstableowingtotheunevennessofthewatersurfaceduetothewaves,andenergyisefficientlytransmittedfromwindtowavesduetothisphenomenon.IntheWAMmodel,thefollowingequation,fromwhichtheitemsrelatedtothePhillipsresonancemechanismareomitted,isadopted:

(4.2.13)

However,inthismethod,iftheinitialvalueofthespectrumenergyofthewavesisassumedtobe0,nowavesaregenerated,soitispossibletoprovideastheinitialvalueaspectrumcalculatedfromthefetchlengthandinitialvelocity. InCycle4oftheWAMmodel,Janssen’squasi-lineartheory30),31)hasbeenincorporatedinthecalculationequationforthetransportofwaveenergytermfromwindtowaves.Owingtothis,evenintheeventthattheconditionsoftheoffshorewindsareidentical,itispossibletocalculateclosertoreality,suchthattheamountofwaveenergytransportedisgreaterforwaveswhosewaveageisyounger. IntheenergydissipationtermoftheWAMmodel,theeffectsofwhite-capbreakingwavesandseabottomfrictionhavebeentakenintoconsideration. Inthenonlineartransportofwaveenergyterm,thenonlinearinteractionsofthefourwaveresonancehave

–88–


beentakenintoaccount.Nonlinearinteractionsareaphenomenonwherethecomponentwavesmakingupthespectrumexchangetheenergythat theyrespectivelyhave,andalthoughnochangeis imparteddirectly to thetotalenergyofthewave,effectsappearthemselvesontheamountofenergytransportfromwindtowavesandtheamountofenergydissipationduetothefactthatthespectrumshapechanges.Then,thenonlineartransportofwaveenergyoffourwaveresonanceisexpressedbythefollowingequation.32)

(4.2.14)

Here,n(k)=E(k)/ωstandsforthewaveactiondensity,Q()thejointfunctionofthespectrumcomponents,δ thedelta function,k thewavevector,and thesubscriptsare the fourwavecomponents. Thedelta functionexpressestheresonanceconditions,andnonlinearinteractionsoccurbetweenthecomponentwavesthatsatisfythefollowingexpression.

(4.2.15)

However,anincalculablenumberofcombinationsofresonancethatsatisfiesthisexpressionexist.Owingtothis,animmensecalculationburdenisinvolvedincalculatedallofthesecombinations,sointheactualmodelonerepresentativecombinationisdecidedon,andSnlisapproximated. AmodelexpandedsothattopographicalbreakingwavesandwavesetupbasedonWAMcanbeconsideredisSWAN,33)andthisisemployedforwavehindcastinginshallowwaters.

4.3 Wave TransformationsIngeneral,thewavestobeconsideredtoexertactionsonportfacilitiesshallbethewavesthataremostunfavorablein terms of the structure stability or the usage of the port facilities. In this consideration, appropriate attentionshall begiven towave transformationsduring thepropagationofwaves fromdeepwater toward the shore,whichincluderefraction,diffraction,shoaling,breaking,andothers.Thewavetransformationstobeconsideredshallbemultidirectional randomwaves, 34) and thesewillhave tobecalculatedafterassigning themwithanappropriatedirectionalwavespectrum35)whileindeepwater.However,whendeterminingtheroughwaveheightoftheaction,anapproximatesolutionmaybecalculatedusingregularwaveswithrepresentitivewaveheightsandwaveperiods(forexampleH1/3,T1/3)ofrandomwaves.

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