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Aconvection-conductionmodelforanalysisofthefreeze-thawconditionsinthesurroundingrockwallofatunnelinpermafrostregionsHEChunxiong(何春雄)，(StateKeyLaboratoryofFrozenSoilEngineering,LanzhouInstituteofGlaciologyandGeocryology,ChineseAcademyofSciences,Lanzhou730000,China;DepartmentofAppliedMathematics,SouthChinaUniversityofTechnology,Guangzhou510640,China)WUZiwang(吴紫汪)andZHULinnan(朱林楠)(StatekeyLaboratoryofFrozenSoilEngineering,LanzhouInstituteofGlaciologyandGeocryologyChineseAcademyofSciences,Lanzhou730000,China)ReceivedFebruary8,1999AbstractBasedontheanalysesoffundamentalmeteorologicalandhydrogeologicalconditionsatthesiteofatunnelinthecoldregions,acombinedconvection-conductionmodelforairflowinthetunnelandtemperaturefieldinthesurroundinghasbeenconstructed.Usingthemodel,theairtemperaturedistributionintheXiluoqiNo.2Tunnelhasbeensimulatednumerically.Thesimulatedresultsareinagreementwiththedataobserved.Then,basedontheinsituconditionsofsirtemperature,atmosphericpressure,windforce,hydrogeologyandengineeringgeology,theair-temperaturerelationshipbetweenthetemperatureonthesurfaceofthetunnelwallandtheairtemperatureattheentryandexitofthetunnelhasbeenobtained,andthefreeze-thawconditionsattheDabanshanTunnelwhichisnowunderconstructionispredicted.Keywords:tunnelincoldregions,convectiveheatexchangeandconduction,freeze-thaw.AnumberofhighwayandrailwaytunnelshavebeenconstructedinthepermafrostregionsandtheirneighboringareasinChina.Sincethehydrologicalandthermalconditionschangedafteratunnelwasexcavated，thesurroundingwallrockmaterialsoftenfroze,thefrostheavingcauseddamagetothelinerlayersandseepingwaterfrozeintoicediamonds，whichseriouslyinterferedwiththecommunicationandtransportation.SimilarproblemsofthefreezingdamageinthetunnelsalsoappearedinothercountrieslikeRussia,NorwayandJapan.Henceitisurgenttopredictthefreeze-thawconditionsinthesurroundingrockmaterialsandprovideabasisforthedesign，constructionandmaintenanceofnewtunnelsincoldregions.Manytunnels，constructedincoldregionsortheirneighbouringareas，passthroughthepartbeneaththepermafrostbase.Afteratunnelisexcavated，theoriginalthermodynamicalconditionsinthesurroundingsareandthawdestroyedandreplacedmainlybytheairconnectionswithouttheheatradiation,theconditionsdeterminedprincipallybythetemperatureandvelocityofairflowinthetunnel，thecoefficientsofconvectiveheattransferonthetunnelwall，andthegeothermalheat.Inordertoanalyzeandpredictthefreezeandthawconditionsofthesurroundingwallrockofatunnel，presumingtheaxialvariationsofairflowtemperatureandthecoefficientsofconvectiveheattransfer,LunardinidiscussedthefreezeandthawconditionsbytheapproximateformulaeobtainedbySham-sundarinstudyoffreezingoutsideacirculartubewithaxialvariationsofcoolanttemperature.Wesimulatedthetemperatureconditionsonthesurfaceofatunnelwallvaryingsimilarlytotheperiodicchangesoftheoutsideairtemperature.Infact，thetemperaturesoftheairandthesurroundingwallrockmaterialaffecteachothersowecannotfindthetemperaturevariationsoftheairflowinadvance;furthermore，itisdifficulttoquantifythecoefficientofconvectiveheatexchangeatthesurfaceofthetunnelwall.Thereforeitisnotpracticabletodefinethetemperatureonthesurfaceofthetunnelwallaccordingtotheoutsideairtemperature.Inthispaper,wecombinetheairflowconvectiveheatex-changeandheatconductioninthesurroundingrockmaterialintoonemodel，andsimulatethefreeze-thawconditionsofthesurroundingrockmaterialbasedontheinsituconditionsofairtemperature，atmosphericpressure，windforceattheentryandexitofthetunnel，andtheconditionsofhydrogeologyandengineeringgeology.MathematicalmodelInordertoconstructanappropriatemodel,weneedtheinsitufundamentalconditionsasaba-sis.HereweusetheconditionsatthesceneoftheDabanshanTunnel.TheDabanshanTunnelislo-totedonthehighwayfromXiningtoZhangye,southoftheDatongRiver,atanelevationof3754.78-3801.23m,withalengthof1530mandanalignmentfromsouthwesttonortheast.Thetunnelrunsfromthesouthwesttothenortheast.Sincethemonthly-averageairtemperatureisbeneath0`}Cforeightmonthsatthetunnelsiteeachyearandtheconstructionwouldlastforseveralyears，thesurroundingrockmaterialswouldbecomecoolerduringtheconstruction.Weconcludethat,afterexcavation,thepatternofairflowwoulddependmainlyonthedominantwindspeedattheentryandexit，andtheeffectsofthetemperaturedifferencebetweentheinsideandoutsideofthetunnelwouldbeverysmall.Sincethedominantwinddirectionisnortheastatthetunnelsiteinwinter,theairflowinthetunnelwouldgofromtheexittotheentry.Eventhoughthedominantwindtrendissoutheastlyinsummer,consideringthepressuredifference,thetemperaturedifferenceandthetopographyoftheentryandexit，theairflowinthetunnelwouldalsobefromtheexittoentry.Additionally，sincethewindspeedatthetunnelsiteislow，wecouldconsiderthattheairflowwouldbeprincipallylaminar.Basedonthereasonsmentioned，wesimplifythetunneltoaroundtube，andconsiderthattheairflowandtemperaturearesymmetricalabouttheaxisofthetunnel，Ignoringtheinfluenceoftheairtemperatureonthespeedofairflow,weobtainthefollowingequation:wheret，x，rarethetime，axialandradialcoordinates;U，Vareaxialandradialwindspeeds;Tistemperature;pis