有關(guān)隧道方面外文文獻(xiàn)與翻譯

conditionsinthesurroundingrockwalloftunnelinpermafrostregionsHEChunxiong（何春雄）,（StateKeyLaboratoryofFrozenSoilEngineering,LanzhouInstituteofGlaciologyandGeocryology,ChineseAcademyofSciences,Lanzhou730000,China;DepartmentofAppliedMathematics,SouthChinaUniversityofTechnology,Guangzhou510640,China）WUZiwang（吳紫汪）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.Anumberofhighwayandrailwaytunnelshavebeenconstructedinthepermafrostchangedafteratunnelwasexcavated,thesurroundingwallrockmaterialsoftenfroze,thefrostheavingcauseddamagetothelinerlayersandseepingwaterfrozeintoicediamonds,whichseriouslyinterferedwiththecommunicationandtransportation.SimilarproblemsofthefreezingdamageinthetunnelsalsoappearedinothercountrieslikeRussia,NorwayandJapan.Henceitisurgenttopredictthefreeze-thawconditionsinthesurroundingrockmaterialsandprovideabasisforthedesign,constructionandmaintenaneeofnewtunnelsincoldregions.Manytunnels,constructedincoldregionsortheirneighbouringarea,spassthroughthepartbeneaththepermafrostbase.Afteratunnelisexcavat,edtheoriginalthermodynamicalconditionsinthesurroundingsareandthawdestroyedandreplacedmainlybytheairconnectionswithouttheheatradiation,theconditionsdeterminedprincipallybythetemperatureandvelocityofairflowinthetunnel,thecoefficientsofconvectiveheattransferonthetunnelwall,andthegeothermalheat.Inordertoanalyzeandpredictthefreezeandthawconditionsofthesurroundingwallrockofatunnel,presumingtheaxialvariationsofairflowtemperatureandthecoefficientsofconvectiveheattransfer,LunardinidiscussedthefreezeandthawconditionsbytheapproximateformulaeobtainedbySham-sundarinstudyoffreezingoutsideacirculartubewithaxialvariationsofcoolanttemperature?Wesimulatedthetemperatureconditionsonthesurfaceofatunnelwallvaryingsimilarlytotheperiodicchangesoftheoutsideairtemperature.Infact,thetemperaturesoftheairandthesurroundingwallrockmaterialaffecteachothersowecannotfindthetemperaturevariationsoftheairflowinadvance;furthermore,itisdifficulttoquantifythecoefficientofconvectiveheatexchangeatthesurfaceofthetunnelwall?Thereforeitisnotpracticabletodefinethetemperatureonthesurfaceofthetunnelwallaccordingtotheoutsideairtemperature.Inthispaper,wecombinetheairflowconvectiveheatex-changeandheatconductioninthesurroundingrockmaterialintoonemode,Iandsimulatethefreeze-thawconditionsofthesurroundingrockmaterialbasedontheinsituconditionsofairtemperature,atmosphericpressure,windforceattheentryandexitofthetunnel,andtheconditionsofhydrogeologyandengineeringgeology.MathematicalmodelInordertoconstructanappropriatemodel,weneedtheinsitufundamentalDabanshanTurinelislo-totedonthehighwayfromXiningtoZhangye,southoftheDatongRiver,atanelevationof3754.78-3801.23m,withalengthof1530mandanalignmentfromsouthwesttonortheast.Thetunnelrunsfromthesouthwesttothenortheast.Sincethemonthly-averageairtemperatureisbeneathO'}Cforeightmonthsatthetunnelsiteeachyearandtheconstructionwouldlastforseveralyears,thesurroundingrockmaterialswouldbecomecoolerduringtheconstruction?Weconcludethat,afterexcavation,thepatternofairflowwoulddependmainlyonthedominantwindspeedattheentryandexit,andtheeffectsofthetemperaturedifferencebetweentheinsideandoutsideofthetunnelwouldbeverysmall.Sincethedominantwinddirectionisnortheastatthetunnelsiteinwinter,theairflowinthetunnelwouldgofromtheexittotheentry.Eventhoughthedominantwindtrendissoutheastlyinsummer,consideringthepressuredifference,thetemperaturedifferenceandthetopographyoftheentryandexi,ttheairflowinthetunnelwouldalsobefromtheexittoentryAdditionally,sincethewindspeedatthetunnelsiteislow,wecouldconsiderthattheairflowwouldbeprincipallylaminar.Basedonthereasonsmentione,dwesimplifythetunneltoaroundtube,andconsiderthattheairflowandtemperaturearesymmetricalabouttheaxisofthetunnel,Ignoringtheinflueneeoftheairtemperatureonthespeedofairflow,weobtainthefollowingequation:X+7★亦…at/r/AU-Z—+(/—+dt%T 亦(“狂+7 a?J產(chǎn)'0<t<

77,0<x<fjJOcr3/R7\1 3/Ar\

/?j喬*左石+) 殆入己 artdsat 亠張［

3?=27芥(snc-,一r\c小弓訂⑺丹，0<f<Z>f(ir>Sf{t):

-口nUiz*=ru(f*3TA-九昇)1

0<I<

.(x(r)6Su(<)；?r010/Z)Z“屠0WY6wheret,x,rarethetime,axialandradialcoordinates;U,Vareaxialandradialwindspeeds;Tistemperature;pistheeffectivepressure(that,isairpressuredividedbyairdensity);visthekinematicviscosityofair;aisthethermalconductivityofair;Listhelengthofthetunnel;Ristheequivalentradiusofthetunnelsection;Disthelengthoftimeafterthetunnelconstruction;St(t),Su(t)arefrozenandthawedpartsinthesurroundingrockmaterialsrespectively;f,uandCt,CUarethermalconductivitiesandvolumetricthermalcapacitiesinfrozenandthawedpartsrespectively;X=(x,r), (t)isphasechangefront;Lhisheatlatentoffreezingwater;andToiscriticalfreezingtemperatureofrock(hereweassumeTo=-0.1C).2 usedforsolvingthemodelEquation(1)showsflow.Wefirstsolvethoseconcerningtemperatureatthatthetemperatureofthesurroundingrockdoesnotaffectthespeedofairequationsconcerningthespeedofairflow,andthensolvethoseequationseverytimeelapse.2.ProcedureusedforsolvingthecontinuityandmomentumequationsSincethefirstthreeequationsin⑴ arenotindependentwederivethesecondequationbyxandthethirdequationbyr.Afterpreliminarycalculationweobtainthefollowingellipticequationconcerningtheeffectivepressurep:Thenwesolveequationsin(1)usingthefollowingprocedures:「齢空仃' J裂工『3r\AssumethevaluesforUO

njflQsubstitutingUO,VOintoeq.(2),andsolving(2),weobtainpO;solvingthefirstandsecondequationsof(1),weobtainUO,V1;solvingthefirstandthirdequationsof(1),weobtainU2,V2;calculatingthemomentum-averageofU1,v1andU2,v2,weobtainthenewUO,VO;thenreturnto(ii);iteratingasaboveuntilthedisparityofthosesolutionsintwoconsecutiveiterationsissufficientlysmallorissatisfied,wethentakethosevaluesofpOUOandVOastheinitialvaluesforthenextelapseandsolvethoseequationsconcerningthetemperature..2.2EntiremethodusedforsolvingtheenergyequationsAsmentionedpreviously,thetemperaturefieldofthesurroundingrockandtheairflowaffecteachother.Thusthesurfaceofthetunnelwallisboththeboundaryofthetemperaturefieldinthesurroundingrockandtheboundaryofthetemperaturefieldinairflow.Therefore,itisdifficulttoseparatelyidentifythetemperatureonthetunnelwallsurface,andwecannotindependentlysolvethoseequationsconcerningthetemperatureofairflowandthoseequationsconcerningthetemperatureofthesurroundingrock.Inordertocopewiththisproblem,wesimultaneouslysolvethetwogroupsofequationsbasedonthefactthatatthetunnelwallsurfacebothtemperaturesareequal.Weshouldbearinmindthephasechangewhilesolvingthoseequationsconcerningthetemperatureofthesurroundingrockandtheconvectionwhilesolvingthoseequationsconcerningthetemperatureoftheairflow,andweonlyneedtosmooththoserelativeparametersatthetunnelwallsurface.Thesolvingmethodsfortheequationswiththephasechangearethesameasinreferenee[3].2.3Determinationofthermalparametersandinitialandboundaryconditions2.3.1Determinationofthethermalparameters.Usingp=1013.25-0.1088H,wecalculatepressurepatelevationHandcalculatetheairdensityusingformula

Pair,whereTistheyearly-averageabsoluteairtemperatureandGisthehumidityconstantofair.amicviscosityofairflow,wecalculatethethermalconductivityandofthesurroundingrockaredeterminedfromthetunnelsite.kinematicviscosityusingtheformulasa—and —.ThethermalparametersCP.3.2Determinationoftheinitialandboundaryconditions.Choosetheobservedmonthlyaveragewindspeedattheentryandexitasboundaryconditionsofwindspeedandchoosetherelativeeffectivepressurep=0attheexit(that,istheentryof2 thedominantwindtrend)andp(1kL/d)v/2onthesectionofentry(thatis,theexitofthedominantwindtrend),wherekisthecoefficientofresistaneealongthetunnelwall,d=2R,andvistheaxialaveragespeed.WeapproximateTvaryingbythesinelawaccordingtothedataobservedattheseeneandprovideasuitableboundaryvaluebasedonthepositionofthepermafrostbaseandthegeothermalgradientofthethawrockmaterialsbeneaththepermafrost2 AsimulatedexampleUsingthemodelandthesolvingmethodmentionedabove,wesimulatethevaryinglawoftheairtemperatureinthetunnelalongwiththetemperatureattheentryandexitoftheXiluoqiNo.2Tunnel.Weobservethatthesimulatedresultsareclosetothedataobserved[6].TheXiluoqiNo.2TunnelislocatedontheNonglingrailwayinnortheasternChinaandpassesthroughthepartbeneaththepermafrostbase.Ithasalengthof1rthwest,andtheelevationisabout700m.Thedominantwinddirectioninthetunnelisfromnorthwesttosoutheast,withamaximummonthly-averagespeedof3m/sandaminimummonthly-averagespeedof1.7m/s.Basedonthedataobservedweapproximatethevaryingsinelawofairtemperatureattheentryandexitwithyearlyaveragesof?5°C，?64Candamplitudesof189Cand176Crespective!y.Theequivalentdiameteris5.8m,andtheresistantcoefficientalongthetunnelwallis0.025.Sineetheeffectofthethermalparameterofthesurroundingrockontheairflowismuchsmallerthanthatofwindspeed，pressureandtemperatureattheentryandexit,werefertothedataobservedintheDabanshanTunnelforthethermalparameters.Figure1showsthesimulatedyearly-averageairtemperatureinsideandattheentryandexitofthetunnelcomparedwiththedataobserved.Weobservethatthediffereneeislessthan0.2、Cfromtheentrytoexit.Figure2showsacomparisonofthesimulatedandobservedmonthly-averageairtemperaturein-side(distaneegreaterthan100mfromtheentryandexit)thetunnel.Weobservethattheprincipallawisalmostthesame,andthemainreasonforthediffereneeistheerrorsthatcamefromapproximatingthevaryingsinelawattheentryandexit;especially,themaximummonthly-averageairtemperatureof1979wasnotforJulybutforAugust.Pig■11:阿嚴(yán)1齡no(simulAtedanddrivedair左afurrinXihioqag2Tunnelin1979,1、SicniilMedvib

Tic凹聽(tīng)阿弊口ofsitnuhiedandabserv回?irlera-peraruirinaidetheXihi呦No,2Twindin19791*Simi-vdu￡A；2,uLMrvedvadiiiA.Pisusefromtheemr>/miPs,diarvlijafreeze-thawconditionsfortheDabanshanTunnelPisusefromtheemr>/miUsingtheelevationof3800mandtheyearly-averageairtemperatureof?3C,weandandthedynamicviscosity9.21810kg/(m.s).After6calculationweobtainthecalculatetheairdensityp=0.774kg/m3.SineesteamexistsIntheair,wechoosetheandandthedynamicviscosity9.21810kg/(m.s).After6calculationweobtainthethermaldiffusivitya=1.378810m/sandthe5kin2ematicviscosity,Consideringthatthesectionofautomobilesismuchsmallerthanthatofthetunnelandtheauto-mobilespassthroughthetunnelatalowspeed,weignorethepistoneffects,comingfromthemovementofautomobiles,inthediffusionoftheair.Weconsidertherockasawholecomponentandchoosethedryvolumetriccavityd2400kg/m'contentofwaterandunfrozenwaterW=3%andW=1%,andthethermalconductivityu,f 2.0W,heatcapacityCv0.8kJand

(0.84.128Wu)(0.84 128Wu)1W 1WAccordingtothedataobservedatthetunnelsitethemaximummonthly-averagewindspeedisabout3.5m/s,andtheminimummonthly-averagewindspeedisabout2.5m/s.Weapproximatethewindspeedattheentryandexitasvt)[0.028(t7)tunnelissettobeU(O,x,r)Ua(1

2.5](m/s),wheretisinmonth.Theinitialwindspeedinther2(R)2),V(0,x,r) 0.TheinitialandboundaryvaluesoftemperatureTaresettobe(X=.1■潔和汕,aT(OtX,/t)=af

? Jto)XO.OJ-C,-r)xO.D3?t./i r

FWKWwheref(x)isthedistaneefromthevaulttothepermafrostbas,andR0=25mistheradiusofdo-mainofsolutionT.Weassumethatthegeothermalgradientis3%,theyearly-averageairtemperatureoutsidetunneltheisA=-3,andtheamplitudeisB=12°C.AsfortheboundaryofR=Ro,wefirstsolvetheequationsconsideringR=Roasthefirsttypeofboundary;thatisweassumethatT=f(x)onR=Ro.Wefindthat,afteroneyear,theheatflowtrendwillhavechangedintherangeofradiusbetween5and25minthesurroundingrock..Consideringthattherockwillbecoolerhereafteranditwillbeaffectedyetbygeothermalheat,weappoximatelyassumethattheboundaryR=Roisthesecondtypeofendofthefirstyearafterexcavationunderthefirsttypeofboundaryvalue,isthegradientonR=RoofT.Consideringthesurroundingrocktobecoolerduringtheperiodofconstructio,nwecalculatefromJanuaryanditeratesomeelapsesoftimeunderthesameboundary.Thenwelettheboundaryvaluesvaryandsolvetheequationsstepbystep(itcanbeprovedthatthesolutionwillnotdependonthechoiceofinitialvaluesaftermanytimeelapses).4.2CalculatedresultsFigures3and4showthevariationsofthemonthly-averagetemperaturesonthesurfaceofthetunnelwallalongwiththevariationsattheentryandexit.Figs.5and6showtheyearwhenpermafrostbeginstoformandthemaximumthaweddepthafterpermafrostformedindifferentsurroundingsectionsHfVTTlPh/iHTftpihfBijrhfi*rtff=k9un\19

tAfwrwrdftkrfmnh】廠肌'"iPEIMfewrMMirfAcetiiiubel*rtkthutihchAntl.1,Jnnti(JiManccA100aframcfUi｝血eiLI)tcviperatmconrfcr<ufiic<*i2.uwHrurlemperifuft.氐□hsun氐

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Fig,6.Tk；KJiimiflEthweddepihH!!e(Tpennatrafitfrrfuwdin y*snj42086420864■■IB—■■-于9C昭巧QjOmV總町 LhsoI2I【尸匚gtjnt2產(chǎn)—njAlx二471藥—工一匚v、WFIddEul—二二2即ncu2二.WQCOOPuEIHooor二DrsScrfnwrirwiy-4.3PreliminaryconclusionBasedontheinitial-boundaryconditionsandthermalparametersmentiabove,weobtainthefollowingpreliminaryconclusions:Theyearly-averagetemperatureonthesurfacewallof thetunnelisapproximatelyequaltotheairtemperatureattheentryandexit.Itiswarmerduringthecoldseasonandcoolerduringthewarmseasonintheinternalpart(morethan100mfromtheentryandofthetunnelthanattheentryandexitFig.1showsthattheinternalmonthly-averagetemperatureonthesurfaceofthetunnelwallis1.2°ChigherinJanuary,FebruaryandDecember,1ChigherinMarchandOctober,and1?6ClowerinJuneandAugust,and2qClowerinJulythantheairtemperatureattheentryandexit.Inothermonthstheinfernaltemperatureonthesurfaceofthetunnelapproximatelyequalstheairtemperatureattheentryandexit.especiallyinthecentralpart,theinternalamplitudeoftheyearly-averagetemperatureonthesurfaceofthetunnelwalldecreasesandis1.(6lowerthanthatattheentryandexit.3)Undertheconditionsthatthesurroundingrockiscompact,withoutagreatamountofunder-groundwater,andusingathermalinsulatinglayer(asdesignedPUwithdepthof0.05mandheatconductivity=0.0216FBTwithdepthof0.085mandheatconductivity=0.0517W/mC),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.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(guó)科學(xué)院寒區(qū)旱區(qū)環(huán)境與工程研究所凍土工程國(guó)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(guò)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(kāi)鑿的祁連山區(qū)大坂山隧道開(kāi)通運(yùn)營(yíng)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)換熱凍結(jié)與融化在我國(guó)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(kāi)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內(nèi)滲水凍結(jié)成冰凌等，嚴(yán)重影響了正常交通 類(lèi)似隧道凍害問(wèn)題同樣出現(xiàn)在其他國(guó)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(kāi)挖后圍巖的 凍狀況，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穿過(guò)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(kāi)放通風(fēng)對(duì)流為特征的新的熱力系統(tǒng)隧道開(kāi)通運(yùn)營(yíng)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、氣一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(kāi)通后圍巖的凍融特性，Lu-nardini借用Shamsundar研究圓形制冷管周?chē)馏w凍融特性時(shí)所得的近似公式，討論過(guò)圍巖的凍融特性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)

我們也曾就壁但實(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(wú)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(guò)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(lái)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)1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)大山公路隧道的基本情況為背景來(lái)加以說(shuō)明 大坂山隧道位于西寧一張業(yè)3754.78-3801.23m1530m,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(zhǎng)8個(gè)月,加之施工時(shí)間持續(xù)數(shù)年，圍巖在施土過(guò)程中己經(jīng)預(yù)冷，所以隧道開(kāi)通運(yùn)營(yíng)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??；冬季祁連山區(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)氣體將以層流為主基于以上基本情況，我們將隧道簡(jiǎn)化成圓筒，并認(rèn)為氣流、溫度等關(guān)十隧道中心線軸對(duì)稱(chēng)，忽略氣體溫度的變化對(duì)其流速的影響，可有如下的方程(duvdvca7+T

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0<I<D?0<x<L.0<r<R;VC竺Di"警卜+訊嘰Upa/<7v\in/aC竺Di"警卜+訊嘰r二~芥耳j耳丿* Jr\rar 0<t<O90<x<L.0<r<Hi/ 3T\I3/c?T\卜 二右(4右丿+V57\37/*0<x<D,(xrr)€5f(x);0<l<D.(x?)G(t);r(j,0MfW0$二厶節(jié)，0w/w6其中t為時(shí)間，x為軸向坐標(biāo)，r為徑向坐標(biāo)；U,V度，P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(zhǎng)度，RSf(t),Su(t)分別為圍巖的凍、融區(qū)域f,U分別為凍、融狀態(tài)下的熱傳導(dǎo)系數(shù)，Cf,Cu融狀態(tài)下的體積熱容量，X=(x,r), (t)為凍、融相變界面,ToTo=-0.10<),Lh為水的相變潛熱2求解過(guò)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(guò)將動(dòng)量方程分別對(duì)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：3UBV3(JdV\21nL升drdxir2O<i<Zf>O<r<jR

xr于是，對(duì)方程⑴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⑵將U0,V。代入方程并求解，得P。(3)二個(gè)方程，解得一組解(4)

聯(lián)立方程(1)的第一個(gè)和第U1,W;聯(lián)立方程((1)的第一個(gè)和第U2,V2;三個(gè)方程，解得一組解⑸對(duì)(， (4得到的速度進(jìn)行動(dòng)量平均，得新的U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,V。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(lái)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(méi)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)的大壓強(qiáng)，再由

PP計(jì)算出現(xiàn)場(chǎng)空氣密度GT

,其中T為現(xiàn)場(chǎng)大氣的年平均絕對(duì)溫度，G為空氣的氣體常數(shù)記定壓比熱為Cp,導(dǎo)熱系數(shù)為，空氣的動(dòng)力粘性系數(shù)為按a

和一計(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CP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(1kL/d)v2/2[5],這里k為隧道內(nèi)的沿程阻力系數(shù)，L為隧道長(zhǎng)度，d為隧道端面的當(dāng)量直徑， 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2(6)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(zhǎng)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)度約為700m,

洞口海拔高月平均最高風(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50C和的正弦曲線隧道的當(dāng)量直徑為5.8m,0.025.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.1.

從進(jìn)口到2給出了洞內(nèi)（距進(jìn)出口100m以上）月平均氣溫的計(jì)算值與觀測(cè)值比較的情19