有关隧道方面外文文献与翻译

conditionsinthesurroundingrockwalloftunnelinpermafrostregionsHEChunxiong（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.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产'0<t<

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

/?j乔*左石+) 殆入己 artdsat 亠张［

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:阿严1龄no(simulAtedanddrivedair左afurrinXihioqag2Tunnelin1979,1、SicniilMedvib

Tic凹聽阿弊口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■洁和汕,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】厂肌'"iPEIMfewrMMirfAcetiiiubel*rtkthutihchAntl.1,Jnnti(JiManccA100aframcfUi｝血eiLI)tcviperatmconrfcr<ufiic<*i2.uwHrurlemperifuft.氐□hsun氐

from

NuanceMiniemAinP 5[he-jeuwrieopemafrffilbeputcfarmLFI

Fig,6.Tk；KJiimiflEthweddepihH!!e(Tpennatrafitfrrfuwdin y*snj42086420864■■IB—■■-于9C昭巧QjOmV总町 LhsoI2I【尸匚gtjnt2产—njAlx二471药—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.严寒地区隧道围岩冻融状况分析的导热与对流换热模型何春雄吴紫汪朱林楠(中国科学院寒区旱区环境与工程研究所冻土工程国家重点实验室)(华南理工大学应用数学系)摘要通过对严寒地区隧道现场基本气象条件的分析，建立了隧道内空气与围岩对流换热及固体导热的综合模型；用此模型对大兴安岭西罗奇2号隧道的洞内气温分布进行了模拟计算，结果与实测值基本一致 ；分析预报了正在开凿的祁连山区大坂山隧道开通运营后洞内温度及围岩冻结、融化状况 关键词严寒地区隧道导热与对换热冻结与融化在我国多年冻土分布及邻近地区，修筑了公路和铁路隧道几十座 由于隧道开通后洞内水热条件的变化普遍引起洞内围岩冻结，造成对衬砌层的冻胀破坏以及内渗水冻结成冰凌等，严重影响了正常交通 类似隧道冻害问题同样出现在其他国家（苏联、挪威、日本等）的寒冷地区如何预测分析隧道开挖后围岩的 冻状况，为严寒地区隧道建设的设计、施工及维护提供依据，这是一个亟待解决的重要课在多年冻土及其临近地区修筑的隧道，多数除进出口部分外从多年冻土下限以下岩穿过隧道贯通后，围岩内原有的稳定热力学条件遭到破坏，代之以阻断热辐射、 开放通风对流为特征的新的热力系统隧道开通运营后，围岩的冻融特性将主要由流经 洞内的气流的温度、速度、气一固交界面的换热以及地热梯度所确定 为分析预测隧道开通后围岩的冻融特性，Lu-nardini借用Shamsundar研究圆形制冷管周围土体冻融特性时所得的近似公式，讨论过围岩的冻融特性面温度随气温周期性变化的情况，分析计算了隧道围岩的温度场

我们也曾就壁但实际情况下，围岩与气体的温度场相互作用，隧道内气体温度的变化规律无法预先知道，加之洞壁表面的换热系数在技术上很难测定，从而由气温的变化确定壁面温度的变化难以实现本文通过气一固祸合的办法，把气体、固体的换热和导热作为整体来处理，从洞口气温、风速和空气湿度、压力及围岩的水热物理参数等基本数据出发，计算出围岩的温度场1数学模型为确定合适的数学模型，须以现场的基本情况为依据这里我们以青海祁连山区大山公路隧道的基本情况为背景来加以说明 大坂山隧道位于西宁一张业3754.78-3801.23m1530m,由于大坂山地区隧道施工现场平均气温为负温的时间每年约长8个月,加之施工时间持续数年，围岩在施土过程中己经预冷，所以隧道开通运营后，洞内气体流动的形态主要由进出口的主导风速所确定，而受洞内围岩地温与洞外气温的温度压差的影响较小；冬季祁连山区盛行西北风，气流将从隧道出曰流向进口端，夏季虽然祁连山区盛行东偏南风，但考虑到洞口两端气压差、温度压差以及进出口地形等因素，洞内气流仍将由出口北端流向进口端另外，由于现场年平均风速不大，可以认为洞内气体将以层流为主基于以上基本情况，我们将隧道简化成圆筒，并认为气流、温度等关十隧道中心线轴对称，忽略气体温度的变化对其流速的影响，可有如下的方程(duvdvca7+T

-°-

0<x<L^0<r<Rta?du a?V3rS

ai3u

J9/ou\iiy

0<I<D»0<x<L.0<r<R;VC竺Di"警卜+訊叽Upa/<7v\in/aC竺Di"警卜+訊叽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$二厶节，0w/w6其中t为时间，x为轴向坐标，r为径向坐标；U,V度，P为空气运动粘性系数，a为空气的导温系数，L为隧道长度，RSf(t),Su(t)分别为围岩的冻、融区域f,U分别为冻、融状态下的热传导系数，Cf,Cu融状态下的体积热容量，X=(x,r), (t)为冻、融相变界面,ToTo=-0.10<),Lh为水的相变潜热2求解过程由方程(1)知，围岩的温度的高低不影响气体的流动速度，所以我们可先解出速度，再解温度2.1连续性方程和动量方程的求解由于方程((1)的前3个方程不是相互独立的，通过将动量方程分别对求导，经整理化简，我们得到关于压力P的如下椭圆型方程：3UBV3(JdV\21nL升drdxir2O<i<Zf>O<r<jR

xr于是，对方程⑴中的连续性方程和动量方程的求解，我们按如下步骤进行⑴设定速度⑵将U0,V。代入方程并求解，得P。(3)二个方程，解得一组解(4)

联立方程(1)的第一个和第U1,W;联立方程((1)的第一个和第U2,V2;三个方程，解得一组解⑸对(， (4得到的速度进行动量平均，得新的U返回⑵;(6)按上述方法进行迭代，直到前后两次的速度值之差足够小以P0,U0,V。作为本时段的解，下一时段求解时以此作为迭代初值2.2能量方程的整体解法如前所述，围岩与空气的温度场相互作用，壁面既是气体温度场的边界，又是固体温隧道内气体的温度和围岩内固体的温度放在一起求解，这样壁面温度将作为末知量被解出来只是需要注意两点：解流体温度场时不考虑相变和解固体温度时没有对流项；在洞壁表面上方程系数的光滑化另外，带相变的温度场的算法与文献[3]相同.2.3热参数及初边值的确定热参数的确定方法：用p=1013.25-0.1088H计算出海拔高度为H的隧道现场的大压强，再由

PP计算出现场空气密度GT

,其中T为现场大气的年平均绝对温度，G为空气的气体常数记定压比热为Cp,导热系数为，空气的动力粘性系数为按a

和一计算空气的导温系数和运动粘性系数围岩的热物理CP参数则由现场采样测定.初边值的确定方法：洞曰风速取为现场观测的各月平均风速取卞导风进曰的相对 有效气压为0,主导风出口的气压则取为p(1kL/d)v2/2[5],这里k为隧道内的沿程阻力系数，L为隧道长度，d为隧道端面的当量直径， 为进口端面轴向平均速度进出口气温年变化规律由现场观测资料，用正弦曲线拟合，围岩内计算 区域的边界按现场多年冻土下限和地热梯度确定出适当的温度值或温度梯度3计算实例2(6)西罗奇2号隧道是位十东北嫩林线的一座非多年冻土单线铁路隧道，全长1160m,隧道近西北一东南向，高洞口位于西北向，冬季隧道主导风向为西北风度约为700m,

洞口海拔高月平均最高风速约为3m/s,最低风速约为1.7m/s.根据现场观测资料，我们将进出口气温拟合为年平均分别为50C和的正弦曲线隧道的当量直径为5.8m,0.025.内气温的影响远比洞口的风速、压力及气温的影响小得多，我们这里参考使用了大坂山隧道的资料.1.

从进口到2给出了洞内（距进出口100m以上）月平均气温的计算值与观测值比较的情19