盾构管片结构设计算例

ADesignofShieldTunnelLiningPartOne:DesignData(1)FunctionofTunnelTheplannedtunnelistobeusedasasubwaytunnel.(2)DesignConditionsDimensionsofSegmentTypeofsegment:RC,FlattypeDiameterofsegmentallining:D0=9500mmRadiusofcentroidofsegmentallining:Rc=4550mmWidthofsegment:b=1200mmThicknessofsegment:t=400mmGroundConditionsOverburden:H=12.3mGroundwatertable:G.L.+0.6m=12.3+0.6=12.9mNValue:N=50Unitweightofsoil:=18kN/m3Submergedunitweightofsoil:=8kN/m3Angleofinternalfrictionofsoil:=30oCohesionofsoil:c=0kN/m2Coefficientofreaction:k=50MN/m3Coefficientoflateralearthpressure:=0.4Surcharge:P0=39.7kN/m2Soilcondition:SandyMaterialsThegradeofconcrete:C30Nominalstrength:fck=20.1N/mm2Allowablecompressivestrength:fc=14.3N/mm2Allowabletensilestrength:ft=1.43N/mm2Elasticmodules:E=3.0×104N/mm2Thetypeofsteelbars:HRB335Allowablestrength:fy=fy’=300N/mm2BoltYieldstrength:fBy=240N/mm2Shearstrength:B=150N/mm2Parametersforjointspring:PK18070/kNmrad(ifinsidepartofliningistensile)NK32100/kNmrad(ifoutsidepartofliningistensile)DesignMethodHowtocomputememberforces?Forcemethod(PartTwo)andElasticequationmethod(PartThree)areusedrespectivelytocalculatememberforces.Howtocheckthesafetyoflining?LimitstatemethodbasedonthenationalcodeGB50010-2002isusedtocheckthesafetyoflining.(3)GeometricDesignofShieldLiningTheshieldliningisfittedwith9segmentalpieces(oneKey-typesegment,twoB-typesegmentsandsixothersegments)asshowninFigure1.Centralangleofeachsegmentpieceis40degrees.KB2A6A5A4B1A1A2A3Figure1ThecrosssectionoftheshieldliningPartTwo:ComputationbyForceMethod(1)LoadConditionsJudgmentofTunnelType(byTerzaghi’sformula)φπFigure2JudgmentoftunneltypemRB227.8)4308cot(75.4)48cot(01)tanexp()]tanexp(1[tan)]/(1[101110BHPBHBCBh)31tan227.83.12exp(7.39)]31tan227.83.12exp(1[31tan]01[227.8mHm3.12986.24Sothedesignedtunnelisashallowtunnel.LoadTypesandPartialFactorsTable1showstheloadsshouldbeconsideredinthedesignandcorrespondingpartialfactors.Table1LoadTypesandPartialFactorsLoadtypesPartialfactorsLoadtypesPartialfactorsSurcharge1.4Earthpressure1.2Deadload1.2Subgradereaction1.2Waterpressure1.2ComputationofLoadsComputationelementisa1.2meter(widthofsegment)partalongthelongitudinaldirection,andFigure3showstheloadconditiontocomputememberforcesofthesegmentallining.Figure3LoadconditionofthedesignedtunnelVerticalpressureattunnelcrownEarthpressure:mkNHPbpe/392.208)3.122.17.394.1(2.1)'2.14.1(01Waterpressure:mkNHbpmkNppqwe/152.39476.185392.208111mkNRbq/471.261875.4215.02.12.1215.02.12mkNqqp/623.420471.26152.394211VerticalpressureattunnelbottommkNtbppc/671.4674.0262.12.1623.4202.112Wherec=UnitweightofRCsegment=26kN/m2LateralpressureattunnelcrownEarthpressure:mkNtbpqee/278.84)24.082.12.1392.208(4.0)2'2.1(11Waterpressure:mkNtHbq)24.09.12(102.12.1)2(2.11mkNqqpwe/918.27264.188278.84113LateralpressureattunnelbottommkNDDbpcwc/973.172)1.9101.984.0(2.12.1)'(2.14mkNppp/891.445973.172918.2724343WhereDc=Computationaldiameter=mtD1.94.05.90Averageself-weightmkNtbpc/976.144.0262.12.1.215Lateralresistancepressure)]0454.0(24/[)24454331ccKREIRpppp（=(2×420.623-272.918-445.891+π×14.976)×103×4.554/[24×(0.8×3.0×104×106×6.4×10-3+0.0454×60×106×4.554)]=2.29104×10-3mmkNbkpk/462.1372.11029104.2105033)cos21(26hpp)434(WhereDisplacementofliningattunnelspringReductionfactorofmodelrigidity=0.8EModulusofelasticityofsegment=3.0×104N/mm2IMomentofinertiaofareaofsegment=1/12×1.2×0.43=6.4×10-3m4kCoefficientofreaction=50MN/m32/602.150mMNbkKtheanglemeasuredfromtheverticaldirectionaroundthetunnel(2)ComputationofMemberForcesFigure4showsthesimplifiedmodelofthesegmentallining.Figure4SimplifiedmodeldiagramforcalculationCalculationdataradmkNKP/18070(ifinsidepartofliningistensile)radmkNKN/32100(ifoutsidepartofliningistensile)2334192000104.610100.3mkNEICoefficientsCalculation521114321nnnnnNote:ifthejointjustlocatedat180degreeofthehalf-ringlining,thenitsstiffnesscontributiontothewholestructureshouldbeconsideredashalfofthetotalvalue.321002180705.219200055.425.211)(11niNPiKKEIRKEIR)/(1075105.24mkNniNPiiKRKREIRKREIR12)(212674.1826.2)cos1(1kN/1028761.13210055.4674.11807055.4826.219200055.432niNPiiKRKREIRKREIR12232)(2322627.1122.523)cos1(123kNm/1022943.93210055.4627.11807055.4122.5192000255.433223)608.065.204sin1214212)(1213111NPiinipKKEIRRpKRpEIRp（52308.0)32100608.01807065.2019200045.545.5423.64202（2)(121231221)sin1(12)243221iinnnipKRppEIRpp（）（）（]00120.0143.02432[212NPKKEIRRpp）（）（02104.0]3210000120.018070143.0243192000255.4[55.4623.420671.4672）（）（)418.0561.243)cos11243232)(1233331NPiinipKKEIRRpKRpEIRp（（25953.1)32100418.018070561.219200045.5435.54918.2722（)45.10792.0245)cos1112245243)(1243441NPiinipKKEIRRpKRpEIRp（