有關(guān)隧道方面外文文獻(xiàn)與翻譯資料

Aconvection-conductionmodelforanalysisofthefreeze-thaw

conditionsinthesurroundingrockwallofa

tunnelinpermafrostregionsHEChunxiong（何春雄），（StateKeyLaboratoryofFrozenSoilEngineering,LanzhouInstituteofGlaciologyand

Geocryology,ChineseAcademyofSciences,Lanzhou730000,China;DepartmentofAppliedMathematics,

SouthChinaUniversityofTechnology,Guangzhou510640,China）WUZiwang（吳紫汪）andZHULinnan（朱林楠）（StatekeyLaboratoryofFrozenSoilEngineering,LanzhouInstituteofGlaciologyandGeocryologyChineseAcademyofSciences,Lanzhou730000,China）ReceivedFebruary8,1999

AbstractBasedontheanalysesoffundamentalmeteorologicalandhydrogeologicalconditionsatthesiteofatunnelinthecoldregions,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:3x°3x°W$電°；wheret，x，rarethetime，axialandradialcoordinates;U，Vareaxialandradialwindspeeds;Tistemperature;pistheeffectivepressure(thatis，airpressuredividedbyairdensity);visthekinematicviscosityofair;aisthethermalconductivityofair;Listhelengthofthetunnel;Ristheequivalentradiusofthetunnelsection;Disthelengthoftimeafterthetunnelconstruction;，S(t),S(t)arefrozenandthawedpartsinthesurroundingrockmaterialsfurespectively;九,九andC,Carethermalconductivitiesandvolumetricthermalfufucapacitiesinfrozenandthawedpartsrespectively;X=(x,r),g(t)isphasechangefront;Lhisheatlatentoffreezingwater;andToiscriticalfreezingtemperatureofrock(hereweassumeTo=-0.1°C).usedforsolvingthemodelEquation(1)showsflow.Wefirstsolvethoseconcerningtemperatureatthatthetemperatureofthesurroundingrockdoesnotaffectthespeedofairequationsconcerningthespeedofairflow,andthensolvethoseequationseverytimeelapse.2.1ProcedureusedforsolvingthecontinuityandmomentumequationsSincethefirstthreeequationsin(1)arenotindependentwederivethesecond

equationbyxandthethirdequationbyr.Afterpreliminarycalculationweobtainthefollowingellipticequationconcerningtheeffectivepressurep:0<x<L0<x<L,0<r<R.Thenwesolveequationsin(1)usingthefollowingprocedures:(i)AssumethevaluesforU0，V0;(ii)substitutingU0，V0intoeq.(2)，andsolving(2)，weobtainp0;solvingthefirstandsecondequationsof(1)，weobtainU0，V1;solvingthefirstandthirdequationsof(1)，weobtainU2，V2;calculatingthemomentum-averageofU1，v1andU2，v2，weobtainthenewU0，V0;thenreturnto(ii);iteratingasaboveuntilthedisparityofthosesolutionsintwoconsecutiveiterationsissufficientlysmallorissatisfied，wethentakethosevaluesofp0，U0andV0astheinitialvaluesforthenextelapseandsolvethoseequationsconcerningthetemperature..2.2EntiremethodusedforsolvingtheenergyequationsAsmentionedpreviously，thetemperaturefieldofthesurroundingrockandtheairflowaffecteachother.Thusthesurfaceofthetunnelwallisboththeboundaryofthetemperaturefieldinthesurroundingrockandtheboundaryofthetemperaturefieldinairflow.Therefore，itisdifficulttoseparatelyidentifythetemperatureonthetunnelwallsurface，andwecannotindependentlysolvethoseequationsconcerningthetemperatureofairflowandthoseequationsconcerningthetemperatureofthesurroundingrock.Inordertocopewiththisproblem，wesimultaneouslysolvethetwogroupsofequationsbasedonthefactthatatthetunnelwallsurfacebothtemperaturesareequal.Weshouldbearinmindthephasechangewhilesolvingthoseequationsconcerningthetemperatureofthesurroundingrock，andtheconvectionwhilesolvingthoseequationsconcerningthetemperatureoftheairflow,andweonlyneedtosmooththoserelativeparametersatthetunnelwallsurface.Thesolvingmethodsfor

theequationswiththephasechangearethesameasinreference[3].2.3Determinationofthermalparametersandinitialandboundaryconditions2.3.1Determinationofthethermalparameters.Usingp=1013.25-0.1088H，wecalculatePairpressurepatelevationHandcalculatetheairdensitypusingformulap=,whereTistheyearly-averageabsoluteairtemperature，andGisthehumidityconstantofair.Lettingcbethethermalcapacitywithfixedpressure,九thethermalconductivity，and卩thedynamicviscosityofairflow,wecalculatethethermalconductivityandofthesurroundingrockaredeterminedfromthetunnelsite.kinematicviscosityusingtheformulas九a=kinematicviscosityusingtheformulas九a=—CpPandv=.Thethermalparameters2.3.2Determinationoftheinitialandboundaryconditions.Choosetheobservedmonthlyaveragewindspeedattheentryandexitasboundaryconditionsofwindspeed，andchoosetherelativeeffectivepressurep=0attheexit(thatis，theentryofthedominantwindtrend)andp=(1+kL/d)xv2/2[5]onthesectionofentry(thatis，theexitofthedominantwindtrend)，wherekisthecoefficientofresistancealongthetunnelwall,d=2R，andvistheaxialaveragespeed.WeapproximateTvaryingbythesinelawaccordingtothedataobservedatthesceneandprovideasuitableboundaryvaluebasedonthepositionofthepermafrostbaseandthegeothermalgradientofthethawrockmaterialsbeneaththepermafrostbase.AsimulatedexampleUsingthemodelandthesolvingmethodmentionedabove，wesimulatethevaryinglawoftheairtemperatureinthetunnelalongwiththetemperatureattheentryandexitoftheXiluoqiNo.2Tunnel.Weobservethatthesimulatedresultsareclosetothedataobserved[6].TheXiluoqiNo.2TunnelislocatedontheNonglingrailwayinnortheasternChinaandpassesthroughthepartbeneaththepermafrostbase.Ithasalengthof1

160mrunningfromthenorthwesttothesoutheast,withtheentryofthetunnelinthenorthwest，andtheelevationisabout700m.Thedominantwinddirectioninthetunnelisfromnorthwesttosoutheast,withamaximummonthly-averagespeedof3m/sandaminimummonthly-averagespeedof1.7m/s.Basedonthedataobserved，weapproximatethevaryingsinelawofairtemperatureattheentryandexitwithyearlyaveragesof-5°C,-6.4°Candamplitudesof18.9°Cand17.6°Crespectively.Theequivalentdiameteris5.8m，andtheresistantcoefficientalongthetunnelwallis0.025.Sincetheeffectofthethermalparameterofthesurroundingrockontheairflowismuchsmallerthanthatofwindspeed,pressureandtemperatureattheentryandexit,werefertothedataobservedintheDabanshanTunnelforthethermalparameters.Figure1showsthesimulatedyearly-averageairtemperatureinsideandattheentryandexitofthetunnelcomparedwiththedataobserved.Weobservethatthedifferenceislessthan0.2'Cfromtheentrytoexit.Figure2showsacomparisonofthesimulatedandobservedmonthly-averageairtemperaturein-side(distancegreaterthan100mfromtheentryandexit)thetunnel.Weobservethattheprincipallawisalmostthesame,andthemainreasonforthedifferenceistheerrorsthatcamefromapproximatingthevaryingsinelawattheentryandexit;especially,themaximummonthly-averageairtemperatureof1979wasnotforJulybutforAugust.F更.1.F更.1.Conpmsoinofsimulatedandobseivedajritinp^r-atuneinXohuoqiW?2TurtiielinJ979,LSimulateFal-(I帕；打obse'ivedrdneauFig*2,Th.cwmperi和nofEmulatedanddbs&ervedAiri-m-peraium&insidetheXiJioqiNo.2TuhkeIin1979a11Siminvduc^f2,obaeiveilvulur^.Predictionofthefreeze-thawconditionsfortheDabanshanTunnel4.1ThermalparameterandinitialandboundaryconditionsUsingtheelevationof3800mandtheyearly-averageairtemperatureof-3C,wecalculatetheairdensityp=0.774kg/m3.SincesteamexistsIntheair,wechoosethethermalcapacitywithafixedpressureofairC=1.8744kJ/(kg.oC),heatpconductivityX=2.0x10-2W/(m.oC)andandthedynamicviscosity卩=9.218x10-6kg/(m.s).Aftercalculationweobtainthethermaldiffusivitya=1.3788x10-5m2/sandthekinematicviscosity，v=1.19x10-5m2/s.Consideringthatthesectionofautomobilesismuchsmallerthanthatofthetunnelandtheauto-mobilespassthroughthetunnelatalowspeed，weignorethepistoneffects，comingfromthemovementofautomobiles，inthediffusionoftheair.WeconsidertherockasawholecomponentandchoosethedryvolumetriccavityX=2400kg/m3,contentofwaterandunfrozenwaterW=3%andW=1%,andthedthermalconductivityX=1.9W/m.oc,X=2.0W/m.oc,heatcapacityufC=0.8kJ/kg.ocandV廠(0.8+4.128w)廠(0.8+4.128w)C=lxy,C=lxyf1+Wdu1+WdAccordingtothedataobservedatthetunnelsite，themaximummonthly-averagewindspeedisabout3.5m/s，andtheminimummonthly-averagewindspeedisabout2.5m/s.Weapproximatethewindspeedattheentryandexitasv(t)=[0.028x(t一7)2+2.5](m/s),wheretisinmonth.TheinitialwindspeedinthetunnelissettobeU(0,x,r)=U(1-(】)2),V(0,x,r)=0.aRTheinitialandboundaryvaluesoftemperatureTaresettobewheref(x)isthedistancefromthevaulttothepermafrostbase，andR0=25mistheradiusofdo-mainofsolutionT.Weassumethatthegeothermalgradientis3%，theyearly-averageairtemperatureoutsidetunneltheisA=-30C，andtheamplitudeisB=120C.AsfortheboundaryofR=Ro，wefirstsolvetheequationsconsideringR=Roasthefirsttypeofboundary;thatisweassumethatT=f(x)3%0ConR=Ro.Wefindthat,afteroneyear,theheatflowtrendwillhavechangedintherangeofradiusbetween5and25minthesurroundingrock..Consideringthattherockwillbecoolerhereafteranditwillbeaffectedyetbygeothermalheat,weappoximatelyassumethattheboundaryR=Roisthesecondtypeofboundary;thatis，weassumethatthegradientvalue，obtainedfromthecalculationuptotheendofthefirstyearafterexcavationunderthefirsttypeofboundaryvalue,isthegradientonR=RoofT.Consideringthesurroundingrocktobecoolerduringtheperiodofconstruction，wecalculatefromJanuaryanditeratesomeelapsesoftimeunderthesameboundary.Thenwelettheboundaryvaluesvaryandsolvetheequationsstepbystep(itcanbeprovedthatthesolutionwillnotdependonthechoiceofinitialvaluesaftermanytimeelapses).4.2CalculatedresultsFigures3and4showthevariationsofthemonthly-averagetemperaturesonthesurfaceofthetunnelwallalongwiththevariationsattheentryandexit.Figs.5and6showtheyearwhenpermafrostbeginstoformandthemaximumthaweddepthafterpermafrostformedindifferentsurroundingsections.Fif.).ITm=nHmthfjr-tirvFragE陽mjwrff巾EapIhesprfer-ftnfD^bsfluhanTunnel,人除屜nwiidsFif.).ITm=nHmthfjr-tirvFragE陽mjwrff巾EapIhesprfer-ftnfD^bsfluhanTunnel,人除屜nwiids12…衛(wèi).Dr^tHnwfhwn哮nlryZm自q[i€￥<ba-su*^?g

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寸bidMMFit，6?ThsmaxunuiDehod<tep<hafterj^rmaj'mtfrnnftJ祜yMR；4.3PreliminaryconclusionBasedontheinitial-boundaryconditionsandthermalparametersmentionedabove,weobtainthefollowingpreliminaryconclusions:1)Theyearly-averagetemperatureonthesurfacewallofthetunnelisapproximatelyequaltotheairtemperatureattheentryandexit.Itiswarmerduringthecoldseasonandcoolerduringthewarmseasonintheinternalpart(morethan100mfromtheentryandexit)ofthetunnelthanattheentryandexit.Fig.1showsthattheinternalmonthly-averagetemperatureonthesurfaceofthetunnelwallis1.2°ChigherinJanuary,FebruaryandDecember,1ChigherinMarchandOctober,and1.6ClowerinJuneandAugust,and2qClowerinJulythantheairtemperatureattheentryandexit.Inothermonthstheinfernaltemperatureonthesurfaceofthetunnelwallapproximatelyequalstheairtemperatureattheentryandexit.2)Sinceitisaffectedbythegeothermalheatintheinternalsurroundingsection，especiallyinthecentralpart,theinternalamplitudeoftheyearly-averagetemperatureonthesurfaceofthetunnelwalldecreasesandis1.6°Clowerthanthatattheentryandexit.3)Undertheconditionsthatthesurroundingrockiscompact,withoutagreatamountofunder-groundwater,andusingathermalinsulatinglayer(asdesignedPUwithdepthof0.05mandheatconductivity九=0.0216W/mC,FBTwithdepthof0.085mandheatconductivity九=0.0517W/m°C),inthethirdyearaftertunnelconstruction，thesurroundingrockwillbegintoformpermafrostintherangeof200mfromtheentryandexit.Inthefirstandthesecondyearafterconstruction,thesurroundingrockwillbegintoformpermafrostintherangeof40and100mfromtheentryandexitrespectively.Inthecentralpart，morethan200mfromtheentryandexit,permafrostwillbegintoformintheeighthyear.Nearthecenterofthetunnel，permafrostwillappearinthe14-15thyears.Duringthefirstandsecondyearsafterpermafrostformed，themaximumofannualthaweddepthislarge(especiallyinthecentralpartofthesurroundingrocksection)andthereafteritdecreaseseveryyear.Themaximumofannualthaweddepthwillbestableuntilthe19-20thyearsandwillremaininsrangeof2-3m.4)Ifpermafrostformsentirelyinthesurroundingrock，thepermafrostwillprovideawater-isolatinglayerandbefavourableforcommunicationandtransportation.However,intheprocessofconstruction，wefoundalotofundergroundwaterinsomesectionsofthesurroundingrock.Itwillpermanentlyexistinthosesections，seepingoutwaterandresultinginfreezingdamagetothelinerlayer.Furtherworkwillbereportedelsewhere.附2.外文資料翻譯嚴(yán)寒地區(qū)隧道圍巖凍融狀況分析的導(dǎo)熱與對(duì)流換熱模型何春雄吳紫汪朱林楠(中國科學(xué)院寒區(qū)旱區(qū)環(huán)境與工程研究所凍土工程國家重點(diǎn)實(shí)驗(yàn)室)

(華南理工大學(xué)應(yīng)用數(shù)學(xué)系)摘要通過對(duì)嚴(yán)寒地區(qū)隧道現(xiàn)場(chǎng)基本氣象條件的分析，建立了隧道內(nèi)空氣與圍巖對(duì)流換熱及固體導(dǎo)熱的綜合模型;用此模型對(duì)大興安嶺西羅奇2號(hào)隧道的洞內(nèi)氣溫分布進(jìn)行了模擬計(jì)算，結(jié)果與實(shí)測(cè)值基本一致;分析預(yù)報(bào)了正在開鑿的祁連山區(qū)大坂山隧道開通運(yùn)營后洞內(nèi)溫度及圍巖凍結(jié)、融化狀況.關(guān)鍵詞嚴(yán)寒地區(qū)隧道導(dǎo)熱與對(duì)流換熱凍結(jié)與融化在我國多年凍土分布及鄰近地區(qū)，修筑了公路和鐵路隧道幾十座.由于隧道開通后洞內(nèi)水熱條件的變化;，普遍引起洞內(nèi)圍巖凍結(jié)，造成對(duì)襯砌層的凍脹破壞以及洞內(nèi)滲水凍結(jié)成冰凌等，嚴(yán)重影響了正常交通.類似隧道凍害問題同樣出現(xiàn)在其他國家（蘇聯(lián)、挪威、日本等）的寒冷地區(qū).如何預(yù)測(cè)分析隧道開挖后圍巖的凍結(jié)狀況，為嚴(yán)寒地區(qū)隧道建設(shè)的設(shè)計(jì)、施工及維護(hù)提供依據(jù)，這是一個(gè)亟待解決的重要課題.在多年凍土及其臨近地區(qū)修筑的隧道，多數(shù)除進(jìn)出口部分外從多年凍土下限以下巖層穿過.隧道貫通后，圍巖內(nèi)原有的穩(wěn)定熱力學(xué)條件遭到破壞，代之以阻斷熱輻射、開放通風(fēng)對(duì)流為特征的新的熱力系統(tǒng).隧道開通運(yùn)營后，圍巖的凍融特性將主要由流經(jīng)洞內(nèi)的氣流的溫度、速度、氣—固交界面的換熱以及地?zé)崽荻人_定.為分析預(yù)測(cè)隧道開通后圍巖的凍融特性，Lu-nardini借用Shamsundar研究圓形制冷管周圍土體凍融特性時(shí)所得的近似公式，討論過圍巖的凍融特性.我們也曾就壁面溫度隨氣溫周期性變化的情況，分析計(jì)算了隧道圍巖的溫度場(chǎng)[3].但實(shí)際情況下，圍巖與氣體的溫度場(chǎng)相互作用，隧道內(nèi)氣體溫度的變化規(guī)律無法預(yù)先知道，加之洞壁表面的換熱系數(shù)在技術(shù)上很難測(cè)定，從而由氣溫的變化確定壁面溫度的變化難以實(shí)現(xiàn).本文通過氣一固禍合的辦法，把氣體、固體的換熱和導(dǎo)熱作為整體來處理，從洞口氣溫、風(fēng)速和空氣濕度、壓力及圍巖的水熱物理參數(shù)等基本數(shù)據(jù)出發(fā)，計(jì)算出圍巖的溫度場(chǎng).數(shù)學(xué)模型為確定合適的數(shù)學(xué)模型，須以現(xiàn)場(chǎng)的基本情況為依據(jù).這里我們以青海祁連山區(qū)大坂山公路隧道的基本情況為背景來加以說明.大坂山隧道位于西寧一張業(yè)公路大河以南，海拔3754.78?3801.23m,全長1530m，隧道近西南一東北走向.hh由于大坂山地區(qū)隧道施工現(xiàn)場(chǎng)平均氣溫為負(fù)溫的時(shí)間每年約長8個(gè)月，加之施工時(shí)間持續(xù)數(shù)年，圍巖在施土過程中己經(jīng)預(yù)冷，所以隧道開通運(yùn)營后，洞內(nèi)氣體流動(dòng)的形態(tài)主要由進(jìn)出口的主導(dǎo)風(fēng)速所確定，而受洞內(nèi)圍巖地溫與洞外氣溫的溫度壓差的影響較?。欢酒钸B山區(qū)盛行西北風(fēng)，氣流將從隧道出曰流向進(jìn)口端，夏季雖然祁連山區(qū)盛行東偏南風(fēng)，但考慮到洞口兩端氣壓差、溫度壓差以及進(jìn)出口地形等因素，洞內(nèi)氣流仍將由出口北端流向進(jìn)口端.另外，由于現(xiàn)場(chǎng)年平均風(fēng)速不大，可以認(rèn)為洞內(nèi)氣體將以層流為主(r?If涼十(r?If涼十3U莎+0<x<Zj?□<r<Hi矢dISIX1<?/二一+^X\UJa)+r'升廠0<t<D,0<x<L,<r<R:Bp“f1n{yV1(“T\r畀*~)'r)*x<Z,D<r<R;一卄宀云i石丿七匚喬("^7)-70<t</),0<x<L1(“T\r畀*~)'r)*x<Z,D<r<R;心)?0<t</)>〔a；,廠)E￡「(e)；6勢(shì)皆仏彗卜第以斜Mb-u恥丿0<t<Dt〔jc、r)G5U(t};了'「(r,牢($))-7\i〔』、年D)-Tq+0-gx;Eh士，0W/W刀，其中t為時(shí)間，x為軸向坐標(biāo)，r為徑向坐標(biāo);U,V分別為軸向和徑向速度，T為溫度，P為有效壓力(即空氣壓力與空氣密度之比少，V為空氣運(yùn)動(dòng)粘性系數(shù),a為空氣的導(dǎo)溫系數(shù)，L為隧道長度，R為隧道的當(dāng)量半徑，D為時(shí)間長度S(t),fS(t)分別為圍巖的凍、融區(qū)域.九,九分別為凍、融狀態(tài)下的熱傳導(dǎo)系數(shù)，C,Cufufu分別為凍、融狀態(tài)下的體積熱容量，X=(x,r),g(t)為凍、融相變界面,To為巖石凍結(jié)臨界溫度(這里具體計(jì)算時(shí)取To=-0.100C)，L為水的相變潛熱.求解過程由方程(1)知，圍巖的溫度的高低不影響氣體的流動(dòng)速度，所以我們可先解出速度，再解溫度.2.1連續(xù)性方程和動(dòng)量方程的求解由于方程((1)的前3個(gè)方程不是相互獨(dú)立的，通過將動(dòng)量方程分別對(duì)x和r求導(dǎo)，經(jīng)整理化簡(jiǎn)，我們得到關(guān)于壓力P的如下橢圓型方程：01%+r3r\a」〔耳兀3r3r2Jp1⑵0<x<L,0<t<R.于是，對(duì)方程(1)中的連續(xù)性方程和動(dòng)量方程的求解，我們按如下步驟進(jìn)行：⑴設(shè)定速度U0,V0；將U0,V0代入方程并求解，得P0聯(lián)立方程(1)的第一個(gè)和第二個(gè)方程，解得一組解U1,V1；聯(lián)立方程((1)的第一個(gè)和第三個(gè)方程，解得一組解U2,V2；⑸對(duì)(⑶,(4)得到的速度進(jìn)行動(dòng)量平均,得新的U0,V0返回⑵；(6)按上述方法進(jìn)行迭代，直到前后兩次的速度值之差足夠小?以P0,U0,V0作為本時(shí)段的解，下一時(shí)段求解時(shí)以此作為迭代初值.2.2能量方程的整體解法如前所述，圍巖與空氣的溫度場(chǎng)相互作用，壁面既是氣體溫度場(chǎng)的邊界，又是固體溫度場(chǎng)的邊界，壁面的溫度值難以確定，我們無法分別獨(dú)立地求解隧道內(nèi)的氣體溫度場(chǎng)和圍巖溫度場(chǎng).為克服這一困難，我們利用在洞壁表面上，固體溫度等于氣體溫度這一事實(shí)，把隧道內(nèi)氣體的溫度和圍巖內(nèi)固體的溫度放在一起求解，這樣壁面溫度將作為末知量被解出來.只是需要注意兩點(diǎn)：解流體溫度場(chǎng)時(shí)不考慮相變和解固體溫度時(shí)沒有對(duì)流項(xiàng)；在洞壁表面上方程系數(shù)的光滑化.另外，帶相變的溫度場(chǎng)的算法與文獻(xiàn)［3］相同.2.3熱參數(shù)及初邊值的確定熱參數(shù)的確定方法：用p=1013.25-0.1088H計(jì)算出海拔高度為H的隧道現(xiàn)場(chǎng)的大氣P壓強(qiáng)，再由P=—計(jì)算出現(xiàn)場(chǎng)空氣密度P，其中T為現(xiàn)場(chǎng)大氣的年平均絕對(duì)溫GT度，G為空氣的氣體常數(shù)?記定壓比熱為Cp，導(dǎo)熱系數(shù)為九，空氣的動(dòng)力粘性系數(shù)為「按8二丄和v=^計(jì)算空氣的導(dǎo)溫系數(shù)和運(yùn)動(dòng)粘性系數(shù).圍巖的熱物理CPPP參數(shù)則由現(xiàn)場(chǎng)采樣測(cè)定.初邊值的確定方法:洞曰風(fēng)速取為現(xiàn)場(chǎng)觀測(cè)的各月平均風(fēng)速.取卞導(dǎo)風(fēng)進(jìn)曰的相對(duì)有效氣壓為0主導(dǎo)風(fēng)出口的氣壓則取為p二(1+kL/d)Xv2/2［5］，這里k為隧道內(nèi)的沿程阻力系數(shù)，L為隧道長度，d為隧道端面的當(dāng)量直徑，v為進(jìn)口端面軸向平均速度.進(jìn)出口氣溫年變化規(guī)律由現(xiàn)場(chǎng)觀測(cè)資料，用正弦曲線擬合，圍巖內(nèi)計(jì)算區(qū)域的邊界按現(xiàn)場(chǎng)多年凍土下限和地?zé)崽荻却_定出適當(dāng)?shù)臏囟戎祷驕囟忍荻?計(jì)算實(shí)例按以上所述的模型及計(jì)算方法，我們對(duì)大興安嶺西羅奇2號(hào)隧道內(nèi)氣溫隨洞曰外氣溫變化的規(guī)律進(jìn)行了模擬計(jì)算驗(yàn)證，所得結(jié)果與實(shí)測(cè)值［6］相比較，基本規(guī)律一致.西羅奇2號(hào)隧道是位十東北嫩林線的一座非多年凍土單線鐵路隧道，全長1160m，隧道近西北一東南向，高洞口位于西北向，冬季隧道主導(dǎo)風(fēng)向?yàn)槲鞅憋L(fēng).洞口海拔高度約為700m，月平均最高風(fēng)速約為3m/s,最低風(fēng)速約為1.7m/s.根據(jù)現(xiàn)場(chǎng)觀測(cè)資料，我們將進(jìn)出口氣溫?cái)M合為年平均分別為-5oC和-6.4。C，年變化振幅分別為18.9oC和17.6。C的正弦曲線.隧道的當(dāng)量直徑為5.8m,沿程阻力系數(shù)取為0.025.由于圍巖的熱物理參數(shù)對(duì)計(jì)算洞內(nèi)氣溫的影響遠(yuǎn)比洞口的風(fēng)速、壓力及氣溫的影響小得多，我們這里參考使用了大坂山隧道的資料.圖1給出了洞口及洞內(nèi)年平均氣溫的計(jì)算值與觀測(cè)值比較的情況，從進(jìn)口到

出口，兩值之差都小于0.20C.圖2給出了洞內(nèi)(距進(jìn)出口l00m以上)月平均氣溫的計(jì)算值與觀測(cè)值比較的情況，可以看出溫度變化的基本規(guī)律完全一致，造成兩值之差的主要原因是洞口氣溫年變化規(guī)律之正弦曲線的擬合誤差，特別是1979年隧道現(xiàn)場(chǎng)月平均最高氣溫不是在7月份，而是在8月份溫不是在7月份，而是在8月份.Fig■1..CoenparieonofBLoulaledand：servedairtemperatureinXilixxjiNg,2Tumdin1979.1$Simuktedval-U啊丨2才cbscEVEdvslges.Fi?2?The-eomparifrOihof^ninuhleJsim!dbseivtd?iri#m-peratuirein/dg?lh*Xiluccp.No.2Tunnelih19741+SHhiinlak