PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–57–
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.
–58–
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.
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–59–
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
–60–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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)
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–61–
(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.
–62–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–63–
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)
–64–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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)
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–65–
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
–66–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–67–
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
–68–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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.
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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.
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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.
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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)
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
(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
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METROLOGY AND OCEANOGRAPHY
–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
–78–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METEOROLOGY AND OCEANOGRAPHY
–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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METEOROLOGY AND OCEANOGRAPHY
–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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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)
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METEOROLOGY AND OCEANOGRAPHY
–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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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
PART II ACTIONS AND MATERIAL STRENGTH REQUIREMENTS, CHAPTER 2 METEOROLOGY AND OCEANOGRAPHY
–87–
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–
TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN
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.
4