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46200612South2to2NorthWaterTransfersandWaterScience&TechnologyVol.4No.6Dec2006:2006211222:(973)(2005CB724202):(19792),,,,,,(,100084):Froude,,,Yarnell,:;;;Yarnell:TV131.4:A:167221683(2006)0620053203ComparisonofExistingBackwaterModelsforBridgePiersinSubcriticalFlowsWANGKai,FUXu2dong,WANGGuang2qian(StateKeyLaboratoryofHydroscienceandEngineering,TsinghuaUniversity,Beijing100084,China)Abstract:Bridgepiersinwater2diversionopenchannelswillobstructtheflowandmaycauseanincreaseinwaterlevelsupstreamofthebridgestructure.Thewaterlevelincreasecausedbythepresenceofbridgepiersiscalledbackwater.Themaximumbackwaterisaffectedbytheratiooftheflowareaobstructedbythepierstothetotalflowareadownstreamofthepiers,theFroudenumber,thepiershapeandconfiguration,andthechannelgeometryandfrictionfactor.Thispaperexaminedseveralexistingmodelsforbridgebackwaterthroughusingexperimentaldatafromphysicalmodels.Yarnell’sequationshowsagoodagreementwithexperimentaldata,andcanbeappliedforcalculatingbridgebackwaterinsub2criticalflowswithlargeflowrate.Keyword:Bridgepier;Backwater;Subcriticalflow;Yarnell’sequation1,,,,[122],1270km,,100m,,700,,,[325],,,,DpAubuisson[627]Yarnell[728]Henderson[3][3,9],,,,,,,,,,2Froude,,1,Zh1h3,v1v2v3h:h=h1-h3+1v232g-3v232g=Z+1v212g-3v232g(1)35:131-13-3h1-13-3,,hZ,hZ1,(Z)DpAubuisson[627]Yarnell[728]Henderson[3][329]B;b;Q;A1A31-13-3;,:(1)DpAubuisson[627]Z=12(b-B)2h23-1b2(h3+Z)2Q22g(2)::Z=12(A3-h3B)2-1A21Q22g(3)Z=827K2DA(1+0.5Fr23c)3Fr23c-11+Z/h32v232g(4):KDA,1;Fr3c()Froude,:=1-3-KL2+(1-KL)Fr23c3/2Fr3c(5):KLDpAubuisson,1-12-2[7],DHIMIKE11(2)Yarnell[728]Z=2KY(KY+10-0.6)(+154)v232g(6):KY,1;=v23/2g;h3Yarnell=11.7%23.3%35%50%,2600,HEC-2HEC-RASMIKE11(3)Henderson[3]Z=v222g-v212g+v222g=(1+)v222g-v212g(7):Henderson0.35,0.18Henderson,1KDAKY1KDAKY1=0.9=0.8=0.71.0790.900.940.920.951.0510.900.9660.950.910.890.880.9911.050.910.890.88901.051.050.950.940.921.0651.250.910.870.86(4)[3,9]Z=Q22g21A22-v212g(8):1,(),1;A2;,A2=(b-B)h3,A2=(b-B+mh3)h3;m;=A2/A30.95,Z[9](5)Yarnell[7]CharbeneauHolley[7]99,(Froude,Yarnell33.5m()1.52m()0.81m(),=0.0580.108,8.916.5cm;19.853.3cm,Froude0.120.85:Z=KY(KY+10-016)(a+15a4)v232g(9):,2b:v1=Qbh1,v2=Q(1-)bh3,v3=Qbh3(10)20.650.691.240.40m,b:v1=Q(b+mh1)h1,v2=Q(1-a)(b+mh3)h3,v3=Q(b+mh3)h3(11)5,Yarnell,,[3]YarnellHenderson,,Yarnell,4542720066[5],DpAubuissonYarnell,,Yarnell3[4],,,130,0.200.23m/s,0.24m,Froude0.150.18500550m3/s,m=2.5,3.03.9mm,9.99.0mm;m=430m,12.611.4mm=0.075[4],[3][4],b=40m,m=2.5,7.2m1.2m/s;,2.15mQ=501m3/s,FroudeFr=0.143,=0.074130,0.24m0.22m/s,[4],(1)DpAubuisson=0.074,Fr3c=0.85,KDA=0.966,v3=1.2m/s,Z=0.0081m(2)Yarnell=0.074,KY=0.95,v3=1.2m/s,=0.073,Z=0.011m(3)Henderson=0.074,=0.18,v2=1.296m/s,=0.073,Z=0.040m(4)=0.074,1=0.91(=0.1),A2=386.7m2,Z=0.043m(5)CharbeneauHolley[7]Yarnell,=1.24,=0.40,=0.074,KY=0.95,v3=1.2m/s,=0.073,Z=0.0083m,Henderson,0.04m;3,0.01m[4],500m3/s,9.0mm,DpAubuissonYarenllYarnell,Henderson0.1;Henderson,,CharbeneauHolley[7]99DpAubuissonYarnellNaglerRehbockAl-NassriYarnell6FroudeFr3c,KL0.5=0.0250.05,DpAubuisson=0.15,Al2Nassri,,(0.1),HendersonYarnell0.1,0.1,(0.1)Yarnell=0.0580.108,(0.1),DpAubuisson,Froude,,,Yarnell4Froude,,DpAubuissonYarnellHendersonYarnell,,Yarnell,:(973)(:2005CB724202),,:[1]Hunt,J.,Brunner,G.W.,andLarock,B.E.Flowtransitionsinbridgebackwateranalysis[J].JournalofHydraulicEngineer2ing,1999,125(9):9812983.[2]Seckin,G.,Yurtal,R.,andHaktanir,T.Contractionandex2pansionlossesthroughbridgeconstrictions[J].JournalofHy2draulicEngineering,1998,124(5):5462549.[3],.[J].,1997,18(5):124.[4],,.[J].,2000,33(6):16219.[5].[R].:,1994.[6]DHIWater&Environment.MIKE11ReferenceManual:AModellingSystemforRiversandChannels[K].DHISoftware,2003.[7]Charbeneau,R.J.,andHolley,E.R.Backwatereffectsofbridgepiersinsubcriticalflow[R].ResearchReportNo.02180521,Austin:TheUniversityofTexasatAustin,2001.[8].(.)[K].:,1982.[9].[K].:,1980.55