DOC

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

By Sue Ford,2014-02-18 23:07
12 views 0
Stability analysis of shallow tunnels subjected to seepage with strength reduction theoryof,to,To,with

    Stability analysis of shallow tunnels

    subjected to seepage with strength

    reduction theory

    J.Cent.SouthUniv.Techno1.(2009)16:10011005

    D0I:10.1007/sl1771-009-0166-4

    Stabilityanalysisofshallowtunnelssubjectedtoseepagewith

    strengthreductiontheory

    YANGXiao.1i(杨小礼),HUANGFu(黄阜)

    Springer

    (SchoolofCivilandArchitecturalEngineering,CentralSouthUniversity,Changsha410075,China)

    Abstract:Basedonstrengthreductiont}leory,thestabilitynumbersofshallowtunnelswereinvestigatedwimintheframeworkof

    upperandlowerboundtheoremsoflimitanalysis.Stabmtysolutionstakingintoaccountofwaterseepagewerepresentedand

    comparedwiththosewithoutconsideringseepage.Thecomparisonsindicatethatthemaximumdifferencedoesnotexceed3.7%.

    whichprovesthepresentmethodcredible.TheresultsshowthatstaHtynumbersofshallowtunnelsconsideringseepagearemuch

    lessthanthosewithoutconsideringseepage.andthatthedifferenceOfstabi1itynumbersbetweenconsideringseepageandwithout

    consideringseepageincreasewithincreasingthedepthratio.Thestabjlitynumbersdecreasewithincreasingpermeabilitycoecient

    andgroundwaterdepth.Seepagehassignificanteffectsonthestabilitynumbersofshallowtunnels.

    Keywords:strengthreductiontheory;seepage;permeabilitycoefficient;stabilitynumbers

1lntrOductiOn

    Limitanalysis.characteristicsandlimitequilibrium methodsarethetraditiona1methodsfordeterminingthe stabiljtynumbersofshallowtunnels.Thesemethodsare commonlyappliedtotunnelstabilityanalysissincethey wereproposedfortheirsimplicityandexactness. However,eachofthesemethodsalsohasitsown

    deficiencies.Forexample.therelationshipofsoil betweenstressandstrainisignored.andthehypothetieal criticalfailuresurfaceshouldbesetatthebeginningof analysis[1-4].Strengthreductiontheorynotonly overcomesthesedisadvantagesbutalsotakesinto accountofthenonlinearconstitutiverelationforsoil. Thismethodcansimulatethedeformationprocessin stabilityanalysisofearthstructuressuchasslope, foundationbearingcapacityandearthpressureof retainingwalls.anditissuitableforanycomplex boundaryconditions.Consequentl~thenumericalresults usingthestrengthreductiontheoryaremoreaccuracy. Thestrengthreductiontheorywasappliedtostudying stabilityproblemsofearthstructuressuchassoi1slope andretainingwalls[57.Itisobviousthatstrength

    reductiontheoryiswidelyusedinslopestabilityanalysis anddevelopedasamaturetheory.However,therehas beennoreasonableandreliablecriteriontoassessthe stabilityoftunnelsforalongperiod.Thefactorofsafety andfaiiuresurfacefortunnelscannotbecalculated simplybasedonthestress,displacement,andplastic regionbytheaditionalfiniteelementmethod.Asa

    result,strengthreductiontheorybeginstoapplytotunnel

stabilityanalysis.

    Theaforementionedresearchfortunne1stability analysisbystrengthreductiontheorydoesnottakeinto accountoftheefrectofundergroundwaterseeDage. However.undergroundwaterisoneoftheenvironmental factorsforrockmasses,andstressfieldanddisplacement fieldaroundtheundergroundopeningareconstantly affectedbyseepagefield.Fortunnelsdeeplyburiedin waterrichrockmassesorbearinghighhydraulic

    pressure,theeffectofseepagefieldonsurroundingstress anddisplacementfieldswillreachapointthatcannotbe ignored.Takingintoaccountofseepage,LEEand NAM[8]calculatedtheupperboundsolutionoftheface stabilityforacirculartunneldriventhroughsandysoil bylimitanalysis.Consequently,reasonabledesign conceptsapplicabletothedesignoftunnelliningandto theevaluationofthesuppo~pressurerequiredfor maintainingthestabilityofthetunnelfacewere suggestedforunderwatertunnels.Aproposedmodelto predictthedisturbanceofhydraulicconductivitycaused byexcavatingaroundtheSyueshantunnelinfractured rocksbyLINandLEE[9].Theclosureoffractureswas assumedtobethesolefactorthatcausedhydraulic conductivitychanges,andahyperbolicrelationship betweennormalstressandclosurewasintroduced insteadofusingalinearrelationintheirresearch. Foundationitem:Project(200550)supportedbytheFoundationfortheAuthorofNationalEx

    cellentDoctoralDissertationofChina;Project(09JJ1008) supportedbyHunanProvincialNaturalScienceFoundationofChina;Project(20063187855

    7)supportedbyWest~afficofScienceand

Tec}lnol0gyofChina

    Receiveddate:20O9O3O2:Accepteddate:2009~06-06

    Correspondingauthor:YANGXiaoli,Professor;Tel:+8673

    82656248;E-mail:yxnc@yahoo.com.cn

    J.Cent.SouthUniv.Techno1.(2009)16:10011005

    Theinstabilityofsurroundingrockaroundtunnel causedbyundergroundwaterseepageisoneofthe significantfactorsamongvariousinfluencingfactorsfor tunnelstabilityanalysis.andthedocumentsconsidering seepageeffectbystrengthreductiontheorywasrare. Takingaccountofseepageeffect,thestrengthreduction theorywasappliedtocalculatingthefactorofstability f0rtunnelinthiswork.Bycomparingthedifferenceof factorsofstabilityfortunnelbetweentakingaccountof seepageandwithouttakingaccountofseepage,the influenceofseepageeffectforsurroundingrockaround tunllelwasinvestigated.

    2Stabilitynumberbylimitanalysis

    TheconstructionofashallowtunneIinsoilsisoften excavatedbyshieldmachine.Thesoilsareremoved fromthetunnelfaceeitherbyhandorbycuaer,andthe tunnelstabilityiscontrolledbythemachinewith compressedair,bentoniteorclayslurry.Underthese conditions.itispossibletoidealizetheconstructionof tunnel[1O].Accordingtoaseriesofexperimentresults, anequationwasusedtocalculatethestabilitynumbers ofshallowtunnelsincohesivesoil.Theequationisas follows:

    =

【一at+?(C+D/2)]/Cu

    thenthelpadswillbelowerthanthoseforcollapse.The upperboundtheoremstatesthatifaworkcalculationis performedforakinematicallyadmissiblecollapse mechanism.thentheloadsthusdeducedwillbehigher thanthoseforcollapse.DAVISeta1l11arguedthat,the

    stabilitynumberwasaapproximatefunctionofc|Dand D|Cmthustheproblemcouldberegardedasfindingthe valueof(at)lCainitslimitoncethevaluesof

    parametersC|DandyO/Cuwerefixed.Consequently, lowerandupperboundsolutionsforvaluesofrD/CI from1t02werecalculatedrespectively,andthen stabilitynumberswerecomputed.

    3Stabilitynumberbystrengthreduction

    Ifthemodelisunstable,

    reductioncalculationwill

    thefiniteelementstrength

    notconvergeinstatic

    computation.Basedonthetechnique,whenthesoil reacheslimitequilibriumstatetheelementstatic computationwillundergotheprocessfromconverging tononconvergingthroughreducingthestrength parameterofsoil.andthereductioncoecientisthe

    factorofsafetyforshallowtuunelatthetime.Herein. thecohesionofsoilischosenforthereductionstrength parameter,andthereductioncoe~cientisdefinedas: (1):Co/F~

    whereCisthetunneldepth,Disthetunneldiameter, istheuniformpressureactingonthesoilsurface.atis theuniforlTlfluidpressureorshoringactingonthetunnel

    face,istheunitweight,andG.istheundrainedshear strength.Inthefollowinganalysis,itisassumedthatCu isconstantwithdepthvarying,althoughinpracticeCa increaseswithincreasingdepthforthereasonofthesite history.Thesimplifiedmechanicalmodeloftheshallow tunnelisillustratedinFig.1.whereHisthedistance fromthegroundwaterleveltothetunnelcrown. Fig.1Planestrainunlinedcirculartunnel

    Stabilitysolutionscanbeobtainedusingtheupper boundtheoremandlowerboundtheoremofplasticlimit analysistheory.Thelowerboundtheoremstatesthatif anystressfieldsupportingtheloadscanbefound,andis everywhereinequilibriumwithoutyieldbeingexceeded, (2)

    whereisthereductioncoefficient,Coistheactual cohesionofsoil,andrepresentsaseriesoftrial cohesionsthathavebeenreduced.Then,simulationsare runforaseriesoftrialcohesionsuntilthetunnelreaches limitequilibriumstate.andthecorrespondingreduction coefficientistheminimumfactorofsafetyforshallow tunnelatthetime.Thedetailedprocessisasfollows: denotesasequenceofnumbersfromF1to,soCn

    correspondingtoalsodenotesasequenceofnumbers thatarerepresentedas,C1=F1,C2=,F2,,

    CCFThen,C,C2',Cnaretested.Ifthe

    maximumunbalancedforceislessthan1×10when

    1istested,andthemaximumunbalancedforceis largerthanl×10whenistested,thelimit

    equilibriumstatewillbereached,andwillbethe criticalvalueofcohesion.Accordingtothefactorof

    safetyasdefinedbyBishop,factorofsafetyisthe ratiooftheactualsoilshears~engthtothecriticalshear strengthwhenlimitequilibriumstateisreached.The factorofsafetyisgivenby

    =

    =(3)

    Thestrengthreductiontechniquebasedonfinite elementmethodhasbeenappliedmostlytoslope stability,whichillustratesfailuremechanisminvolving deformingwedges.Theresultsusingthetechniqueagree J.Cent.SouthUniv.Techno1.f2009)l6:l001-1005 wellwiththeslicesolutionsof1imitequilibrium.which showstheeffectiveness12141.

    However,howtoiudgewhetherthesimulation

    reacheslimitequilibriumiscmcialforcalculatingthe factorofsafety.Inthisworkthe1imitequilibriumstateis determinedbytheconvergenceoffiniteelement calculation.Ifthedistinctionofunbalancedforcecannot meettherequiredconvergentcondition.thesoilwill reachthe1imitequilibriumstateunderthegiven reductioncoefficient.

    1003

    4Resultsofstabilitynumberwithseepage

    4.1Stabilitynumberforsaturatedsoils

    Thecomputercodeistheexplicitfinitedifference program,anditispossibletoperformtheseepageaswell asthemechanicalanalysis.Inordertostimulatethe percolationcharacteristicofsurroundingrockaround tunnelundertheconditionoffullsaturation.the boundaryconditionissetasfollows.Thegroundwater

    1eve1islocatedatthetopofthegrid.andthepore pressureisfixedtobezeroatgridpointsalongthetopof thegrid.Thenthesaturationissettolatthesame positionHsthefullysaturatedconditionis

    established.Theexcavatingboundaryisfreedraining boundaryandtheporepressurearoundthisboundaryis fixedatzero.Asaresult.thegroundwaterinfiltratesinto thetunnelundertheeffectofporepressures.Theleft. fightandbottomboundariesofthegridaresettobe impermeable,sincetheinfluenceofseeDageonthe stabilityofsurroundingrockaroundtunnelintheregion isextremelysmal1.Besides.theinitialporepressureis assumedashydrostaticpressureanddistributedalong depthaccordingtolinearlaw.Thewholesimulating processisdividedintotwosteps.Firstly,theflowand mechanicalcalculationisturnedoff,andthefully saturatedsoilissolvedtomechanicalequilibrium.Then tunnelisexcavated.Secondly,tumontheflowand mechanicalcalculation,andsolvethecoupledfluid. mechanicalproblemuntiltheconvergenceoffinite elementcalculationisreached.

    Withoutconsideringtheeffectofundergroundwater seepagewhenD{Cu--2,frictionangle=o,C

    varyingfromlto4,thestabilitynumbersofshallow tunnelarecalculatedbystrengthreductiontheory.By comparingwiththesolutionsofDAvISetal[11using

    limitanalysis,itcanbeseenthat.whetheritisupper boundsolutionorlowerboundsolution,themaximum differencebetweenstrengthreductionandlimitanalysis solutionofstabilitynumbersforshallowtunnelwillnot

    exceed3.7%.Therefore.thestabilitynumberscalculated bystrengthreductioniscredible.WhenyD/C~=2,friction angle=0.,C,lDvaryingfromlto4andtakingaccount ofundergroundwaterseepage,thesimulationsarerun fordifferentvaluesof(as)/Cubyusingstrength

    reductiontheoryuntilthefactorofsafetyreachesan approximatevaluethatisthesignoflimitequilibrium state.Thenthestabilitynumbersofshallowtunnel,witll effectofseepagetakenintoaccount,canbecomputedby substitutingtheaforementionedvaluesintoEq.(1).As showninFig.2.thestabilitynumbersofshallowtHanel consideringseepagearemuchlessthanthosewithout consideringseepage,andthedifferenceofstability numbersunderthesetwoconditionsincreaseswiththe increaseofC/D.WhenC,D=1.thestabilitynumbersof shallowtunnelconsideringtheseepageare9.6%less thanthosewithoutconsideringseepage.However,when C/D--4.thestabilitynumbersofshallowtunnelwi?l

    consideringofseepageare41.5%1essthann1atwithout consideringseepage.Asaconsequence,withtheincrease oftunneldepthandthedecreaseoftunnelradius.the efrectofseepageonsurroundingrockaroundtunnel increases.

    0

    E

    :

    =

    =

    ?

    Fig.2Comparisonofstability

withoutconsideringseepage:

    Upperboundsolutions

    numbersconsideringseepageor

    (a)Lowerboundsolutions;(b)

    4.2Stabilitynumbersofshallowtunnelwith

    permeability

    BasedonBiotconsolidationtheorythecoupled fluid-solidtheoremisusedtocalculatethestability numbers,andthecorrespondinggovemingdifferential equationcanbedescfibedbyDarcy'slaw.Foran anisotropicporousmedium.Darcy'slawcanbereduced DLu:c五若D要?

:!!:!:!12!!

    andtunnelsurroundingrockbecomesunstable.to: q,--,op/Oxj(4)

    whereqiisthespecificdischargewhichisthesame meaningofaverageseepagevelocity,kisthepermeability coefficient,ap/axjishydraulicgradient,andPispore waterpressure.Eq.(4)showsthatthepermeability coefficientkisthedirectproportioncoefficientbetween seepagevelocityandhydraulicgradientinthestateof laminarflow.andmatitsdimensionisthesameas velocity.Whenthehydraulicgradientisgiven,the permeabilitycoefficientincreaseswithincreasingthe velocity.Theseepagevelocityreflectsthepermeabilityof soil,sothepermeabilitycoefficientcanbeusedasa criteriontoassessthepermeabilityofsoil.The permeabilitycoefficientofsoilislarge,andthewaterin soiliseasytoflow.Thecontourdiagramsofhydraulic

Report this document

For any questions or suggestions please email
cust-service@docsford.com