A-CONTRIBUTION-TO-THE-ANALYSIS-OF-STRESS-IN-A-CIRC

DeliveredbyICEVirtualLibrary.comto:IP:222.66.175.213On:Fri,23Sep201112:24:41ACONTRIBUTIONTOTHEANALYSISOFSTRESSINACIRCULARTUNNELbYH.D.MORGAN,M.Sc.(Eng.),M.I.C.E.SYNOPSISInrecentyearsprogresshasbeenmadeintheevolutionofmethodsoftunnelliningwhichrepre-sentamarkeddeparturefromthetraditionalcast-ironlining.Indesigningsuchtunnellinings,itisnecessarytorelatetheeffectsofstiffnessoftheliningtothecharacteristicsofthegroundsincethestrengthoftheliningisrelatedtobothfactors.Inmakingatheoreticalstudyofthisproblemitisnecessaryfirsttoconsidertheeffectsonthestateofstressinthegroundaroundthetunnelduetoitsconstructionandthemannerinwhichsubsequentdeformationofthetunnelliningmayoccur.Equa-tionsarethenpresentedrelatingthestresssetupinatunnelliningdirectlytothestiffnessoftheliningandtheelasticpropertiesofthesurroundingground.Sincethenewerformsoftunnelliningare,onthewhole,lessstiffthanthetraditionallining,itisalsonecessarytoconsiderthequestionofthestabilityofthelining.Knownmethodsofanalysisforcriticalexternalpressureonathintubehavebeendevelopedtorelatetoathintubeinanelasticmedium.Whereatunnelisdriveninclay,long-termeffectsofconsolidationsettlementhavealsotobecon-sideredandrelationshipsareestablishedbetweentheultimatestressinatunnelandtheconsolidationcharacteristicsoftheground.Fieldtestsarebeingcarriedoutwhichareexpectedtoprovideinformationontheapplicationandlimita-tionsofthetheoreticaltreatment.Aucowsdecesdernieresanneesl’evolutiondesmethodesderev&tementdestunnelsafaitdesprogresquirepresententunedeviationnettederevetementstraditionnelsenfonte.Danslacon-ceptiondestelsrevetementsdetunnels,ilfautCtablirunrapportdeseffetsderigiditedurev&m-mentauxcaracteristiquesdusolcarlasoliditdurevetementestenrapportaveccesdeuxfacteurs.Pourfaireuneetudetheoriquedeceprobleme,ilfautconsidererd’abordleseffetssurlaconditiondetensiondanslesolautourdutunnelacausedesaconstructionetdelaman&edontpeuventseproduirelesdeformationsconsecutivesdurevete-mentdutunnel.CommedansI’ensemblelesnouvellessortcsderevetementsdetunnelsontmoinsrigidesquelesrevetementstraditionnels,ilfautconsidereraussilaquestiondelastabilitedurevetement.Desmethodesd’analyseconnuespourlapressionexterieurecritiquesuruntubeminceontet6developpeepourCtablirunrapportavecuntubemincedansunmilieuClastique.Ohonperceuntunneldansl’argile,leseffetsalongtermedetassementdiialaconsolidationdoiventaussietreconsider&etonBtablitdesrelationsentrelatensionlimitederupturedansuntunneletdescaracteristiquesdeconsolidationdusol.Onestentraindefairedesessaisdechantierdontonattenddesrenseignementssurl’applicationetleslimitationsdutraitementtheorique.INTRODUCTIONThetraditionaltypeoftunnelliningwhichhasbeenverywidelyused,particularlyinLondonClay,consistsofflangedcast-ironsegmentsboltedtogetherradiallyandcircumferen-tially.Althoughinpracticethecircumferentialjointwasfrequentlynotfullybolted,greatattentionwasalwayspaidtotheboltingoftheradialjointsoastoachieveastiffring,althoughtheboltedjointcouldneverhavethesamestrengthinbendingastheironsectionitself.Fullboltingofthecircumferentialjointwasseldomadopted,exceptinwater-bearinggroundwhenthejointwascaulked.Inthelate1930satypeofreinforcedconcretesegmentwasintroducedbythelateSirDavidAndersonwhichwasessentiallyaflangedringofthesametypeasthatmadeofcastiron.Thereinforcementwaslightand,infact,hadlittleeffectoncetheringwasinposition.Itschiefvaluewasinthepreventionofdamageduringhandling.Duringthe1939-45warthistypeofliningwasusedwheneverpossible,tosaveiron,andinoneinstanceafairlywidespreadfractureoftheconcreteflangestookplaceaftercompletion.TheAuthorwasaskedtoexaminethetunnelinquestionwithaviewtofindingthereasonforthefracture.Itappearedthatthetroublehadbeencausedbyincorrecterectionofthekeysegmentsanditfollowedthatwherefractureoftheflangeshadoccurredthewholeofthethrustwasbornebytheskin.Themagnitudeofthethrustwasknownfromstrainmeasurementscarriedoutonadjacentcast-ironlining,andtheresultingstressesintheconcretewereestimatedtobeoftheorderof37DeliveredbyICEVirtualLibrary.comto:IP:222.66.175.213On:Fri,23Sep201112:24:4138H.D.MORGAN2,000lb/sq.in.Theconcrete,however,wasofhighquality,itsultimatestrengthbeingupwardsof5,000lb/sq.in.asaminimumandwellover6,000lb.ingeneral.In1946aCommitteeonthedesignoftunnelliningswassetup,itsobjectbeingtore-examinewhethereconomiescouldbeeffectedincast-ironlining.Itwasclearthatintheopinionofmanythestandardofcomparisonbetweendifferenttypesofliningshouldbethemodulusofresistanceofthesection.Asaresultofwar-timeexperiencetheAuthordidnotagreewiththis,believingthatingroundbehavingmoreorlesselasticallythemodulusofthesectionwasofminorimportance.In1944,alsoasaresultofwar-timeobservations,anattemptwasmadeuponarationalapproachtothedesignoftunnelliningswithworksintheLondonClayschieflyinmind,takinginthefirstplacetheextremecaseofclaysinplasticcondition.Itappearedthatthestiffnessofthecross-sectionoftheliningwouldinthecaseinquestionbeofmajorimportancesincethetunnelringwouldbesubjectedtoaconditionanalogoustothatofaloadedstrut.Itsmostimportantpropertythenwouldbestiffnessandthemomentofinert