有关隧道方面外文文献与翻译

Aconvection-conductionmodelconditionsinsurroundingrockapermafrostregionsHEChunxiong(何雄)，KeyofFrozenSoilGeocryology,ChineseAcademyofLanzhouofAppliedUniversityofTechnology,China)WU吴汪ZHULinnan(朱林楠keyofFrozenSoilChineseAcademyofLanzhouChina)ReceivedFebruary8,Abstractonanalysesoffundamentalhydrogeologicalconditionsofinthecombinedmodelforflowinfieldinhasbeenconstructed.thetemperatureinthe2hasnumerically.resultsinagreementwiththebasedinconditionsofsirpressure,windhydrogeologyengineeringgeology,betweenonofthetunnelwallandtheexitofthehasthefreeze-thawconditionsatDabanshanwhichnowconstructionisKeywords:incoldheatexchangeconduction,AofhighwayrailwaytunnelsbeeninregionsneighboringinChina.thethermal

conditionsaftertunnelwasexcavatedsurroundingwallrocktheheavingcausedtolinerseepingwatericewhichwithtransportation.SimilarproblemsthefreezingdamageinthetunnelsappearedinlikeRussia,Japanitispredictfreeze-thawconditionsinthesurroundingrockprovideabasisforthedesign，maintenanceofnewincoldregions.Manytunnels，inregionsortheirneighbouringareas，throughthebeneathpermafrostbase.Aftera，theoriginalthermodynamicalconditionsinthawreplacedmainlybyairconnectionswithouttheheatconditionsprincipallybyofflowinthetunnel，thecoefficientsofconvectiveheattransferwall，geothermalheat.Inordertopredictfreezeandconditionsofwallof，theaxialvariationsofairtemperatureandcoefficientsofconvectivetransfer,Lunardinidiscussedconditionstheapproximateformulaeobtainedinofoutsidecircularwithof.Wetheconditionsofatunnelwallsimilarlytheperiodicchangesofthetemperature.Infact，thetemperaturesofthesurroundingwallaffectotherfindvariationstheinfurthermore，isdifficulttoquantifyofconvectiveexchangeattheofwall.Thereforeitisnottodefineonofthetunnelwallaccordingtooutsideaircombineflowconvectiveheatex-changeheatconductioninthesurroundingrockmaterialinto，theconditionsofrockmaterialinconditionsofair，pressure，windatentryexitofthetheconditionsofgeology.Mathematical

Inordertoconstructappropriatemodel,weneedtheinsitufundamentalconditionsaba-sisusesceneofDabanshanDabanshanisonthefromofRiver,atanof3754.78-3m,withof1530analignmentfromsouthwesttonortheast.tunnelrunsfromthesouthwesttheSincemonthly-averagetemperatureisbeneathforattunneltheconstructionwouldforseveral，therockmaterialswouldbecomeduringtheconstructionconcludepatternofflowwouldmainlydominantwindspeedat，andofthetemperaturebetweentheinsideoutsideoftunnelwouldbe.Sincedominantwindnortheastatinwinter,airinthewouldgotoentry.thewindtrendisinsummer,pressuretheoftheexittheflowinthetunnelwouldbefromthesincespeedatsiteislowwecouldthatflowwouldbeprincipally，simplifytheto，thatflowaretheaxisofthetunnel，Ignoringinfluenceofaironthespeedofairflow,obtainthefollowingequation:

wherexaretimeandcoordinates;Uandspeeds;Tistemperature;is，pressuredividedbydensity);vair;aofLtheofRistheequivalentoftunnelDtheoftimeaftertheconstruction;，S(t),S(t)thawedpartsinrockfrespectively;

f

,

u

Cf

u

thermalconductivitiesvolumetricthermalcapacitiesinfrozenandthawedpartsrespectively;(x,(t)phasechangefront;Lhheatlatentoffreezingwater;Tocriticalfreezingof(assumeTo=℃).2forsolvingWefirstconcerningatthattheofthesurroundingrockdoesaffectspeedofconcerningthespeedofairflow,andthensolveeveryelapse.2.1usedfortheSincefirstthreein(1)thesecond

byxthethirdequationbyr.Afterpreliminaryobtainfollowingellipticconcerningp:in(1)usingthefollowingprocedures:(i)Assumefor，V0;(ii)substituting，V0into(2)，(2)，weobtainp0;(iii)solvingfirstsecond，U0，(iv)thefirstthirdof(1)，U2，V2;(v)themomentum-averageofv1andU2weobtainnewU0，returnto(ii);(vi)aboveuntildisparityofthosesolutionsiniterationsissufficientlysmallissatisfiedweofp0V0asinitialforelapseconcerning2.2EntireusedforsolvingmentionedthetemperaturefieldofrocktheairflowaffectThusoftunneltheboundaryoffieldintheboundaryoffieldinairflowitisdifficultseparatelyidentifythetemperaturewallindependentlyconcerningthetemperatureofairflowthoseconcerningofthe.Inordertowiththissimultaneouslyofbasedonfactthatthetunnelwallsurfacebothequal.Weshouldinthephasewhileconcerningthetemperatureofrockthewhilesolvingofairflow,onlyneedtorelativeatwall.Thefor

thewithphasesamein2.3DeterminationofboundaryoftheUsingp=H，calculatepHairusing

PwhereTisabsolutetemperature，andGthehumidityconstantofLettingC

P

becapacitywithfixedpressure,thermalconductivity，dynamicofcalculatetheusingformulasａ

CP

and

.Thethermalofrockfromtunnel2.3.2oftheconditionsobservedaveragewindspeedtheexitasboundaryconditionsofwind，andchoosethe(that，theofthewindtrend)and

pkLd)/[5]theof(thatexitofthedominant)wherektheofresistancealongthetunnelwall,d=2R，andvistheaverageWeapproximateTbythesinethethesceneprovideasuitableboundarybasedthepositionofthegeothermalofthawrockbeneathpermafrostbase.3Asimulatedthethemethodmentionedabove，welawofinthewiththeattheentryexitofNo.2thatthesimulatedresultsaretothedataTheXiluoqiNo.2locatedtheinpassesthroughbeneathpermafrostbase.Ithasaof

160fromnorthwesttowiththeofinthenorthwest，andelevation700Thedominantwindinthefromtowithamaximumspeedofm/sandminimummonthly-averagespeedof1.7.Basedthedataobserved，approximatesinelawofwithyearlyaveragesof，℃of℃17.6respectively.Thediameteris5.8mtheresistantcoefficientthetunnelwalliseffectofthermalparameteroftheonairmuchthanthatofwindspeed，temperaturetheexitwereferdataobservedinDabanshanTunnelforthethermalparameters.1thesimulatedairtemperatureinsideatentryoftunnelwithdata.Wethatisthan0`Cfromthe2showsacomparisonofobservedmonthly-average(distancegreater100fromentryexit)tunnel.Wethattheisthesame，themainreasonfortheistheerrorsthatfromvaryingatentryexit;,monthly-averagetemperatureofnotforJulyfor4Predictionoffreeze-thawconditionsforDabanshanTunnel4.1Thermalparameterandtheelevationof800mtheyearly-averageairtemperatureof-3℃,we

ddcalculatetheairp=0.774kg/m

.SincesteamIntheair,wechoosethethermalcapacitywithfixedofair/(0),heatp

W/(0C)thedynamic

9.218

).Aftercalculationthethermala=1

2

/skinematic，

2

/sConsideringthattheofautomobilesisthatoftheauto-mobilespassthroughtunnellowspeedweignorecomingfrommovementautomobilesinofair.Weconsiderrockaandchoosecavity

d

/

3

ofwaterwaterW=3%W=1%,thermal

1.9W/.

c

,

f

2.0/

o

capacity0.8kJ/.V

candCf

w)uu11

dtodatathesitemaximummonthly-averagespeedisabout3.5m/s，theminimummonthly-averagespeedis2m/s.Weapproximatethewindspeedattheexitv(t)to

m/s,tisinmonth.ThespeedinrU(0xr)U()R

),(0xr)TheoftemperatureTaresettobewheref(x)fromthepermafrostofdo-mainofsolutionassumethatthe3%，theairoutsidetunnelis

0

，amplitudeis

B=120foroffirstsolveR=Rothefirsttypeofthatisassumethat3%

0

findthat,theheatflowwillhaveinrangeofradiusbetween5andinthesurroundingthewillbecooleritwillaffectedbygeothermalappoximatelythattheboundaryR=Roisthesecondtypeofthatis，thatfromcalculationtotheoffirstexcavationthefirstofboundaryvalue,isthegradientonR=RoofConsideringsurroundingrocktoduringperiodofconstruction，calculatefromJanuaryanditerateofunderboundary.lettheboundaryvarysolvebycanbeprovedthesolutionwillnottheofaftermanytimeelapses).4.2CalculatedresultsFigures3and4showtheofmonthly-averagetemperaturesonofwallalongwiththevariationsatentry.Figs.5and6thepermafrostbeginstoformandthethawedafterpermafrostformeddifferentsections.

4.3Preliminaryconclusionthermalparametersabove,wefollowingpreliminary1)Theonthesurfacewallofapproximatelytoairatentryexit.Itwarmerthecoldandcoolerduringseasonintheinternal100mfromtheexit)ofthe.1thattheinternalonofthetunnelis℃higherinDecember,1℃higherinMarchOctober,1.6lowerinJuneandandlowerinJulythetemperatureattheentryInotherinfernaltemperatureonofwallapproximatelythetemperatureatentryexit.2)Sinceitisbythegeothermalintheinternalsurrounding，inthecentralofthe

onofwalldecreasesand1℃thatatentryexit.3thethatthesurroundingiscompact,withoutaamountalayer(asPUwithofmand

=0.0216℃，FBTwithofmconductivity=0.0517W/m℃，inyeartunnelconstruction，thesurroundingrockwillbegintoformpermafrostintherangeofmfromexitfirstsecondyearthewilltoformpermafrostintheof40andfromtheentryexit.Incentral，fromentrywillformtheeighthNeartheofthe，permafrostwillappearintheyears.Duringfirstsecondafterpermafrostformed，maximumofannualdepth(especiallythecentralpartoftherocksection)thereafteritdecreasesTheofannualthawedwillstablethe19-20thyearswillremaininof2-34)Ifpermafrostentirelyinsurrounding，thepermafrostwillprovidebefavourablefor.However,intheprocessofconstructionlotofinsomeofwillinseepingwaterresultinginthelinerworkwillbereportedelsewhere.

严寒地隧道围岩冻状况分的导热与对换热模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立了隧道内空气与围岩对流换热及固体导热的综合模型;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

导热与对流换热

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;，普遍引起洞内围岩冻结，造成对衬砌层的冻胀破坏以及洞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结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题.在多年冻土及其临近地区修筑的隧道数除进出口部分外从多年冻土下限以下岩层穿过隧道贯通后，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—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.我们也曾就壁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而由气温的变化确定壁面温度的变化难以实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坂山公路隧道的基本情况为背景来加以说明.大山隧道位于西宁一张业公路大河以南，海拔3754.78~3801.23，全长m道近西南—东北走向.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个月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受洞内围岩地温与洞外气温的温度压差的影响较小季祁连山区盛行西北风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，可有如下的方程其中t为时间x为轴向坐标r为径向坐标U,V分别为轴向和径向速度T为温度，有效压力(即空气压力与空气密度之比少，V为气运动粘性系数，a空气的导温系数L隧道长度隧道的当量半径D为时间长(t)f

()别为围岩的冻区域u

f

分别为冻状态下的热传导系数,uf

u分别为冻、融状态下的体积热容量，,t为冻、融相变界面,To为岩石冻结临界温度(里具体计算时取

C)，L为水的相变潜热h2求解过程由方程(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和求导，经整理化简，我们得到关于压力P如下椭圆型方程:于是，对方程(1)中的连续性方程和动量方程的求解，我们按如下步骤进行:设定速U

0

,

0

;(U入方程并求解，得P0联立方程(的第一个和第二个方程，解得一组U1,1联立方程((1)的第一个和第三个方程，解得一组U

2

,

2

;对((3)得到的速度进行动量平均,得新U

0

,

0

返回(2);按上述方法进行迭代到前后两次的速度值之差足够小.0,U,V0为本时段的解,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度场的边界壁面的温度值难以确定我们无法分别独立地求解隧道内的气体温度场和围岩温度为克服这一困难，我们利用在洞壁表面上，固体温度等于气体温度这一事实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[相同2.3参数及初边值的确定热参数的确定方法用计算出海拔高度为的隧道现场的大气压强，再

P

计算出现场空气密度，其中T现场大气的年平均绝对温度为空气的气体常数记定压比热C,导热系数，空气的动力粘性系数P为ａ

CP

和

计算空气的导温系数和运动粘性系数.围岩的热物理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，主导风出口的气压则取为pkL/d

2

/2

[5]

，这里k隧道内的沿程阻力系数，L为隧道长度，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计算实例按以上所述的模型及计算方法们对大兴安岭西罗奇号隧道内气温随洞曰外气温变化的规律进行了模拟计算验证，所得结果与实测值[6]相比较基本规律一致.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1160,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.洞口海拔高度约为700月平均最高风速约为低风速约为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-5

0

和-

0

变化振幅分别为

0

和

0

的正弦曲

线.道的当量直径为5.8沿程阻力系数取为由于围岩的热物理参数对计算洞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.图1出了洞口及洞内年平均气温的计算值与观测值比较的情况从进口到出口，两值之差都小于0.2

0

图出了洞内(距进出口l00m以上月平均气温的计算值与观测值比较的情况可以看出温度变化的基本规律完全一致造成两值之差的主要原因是洞口气温年变化规律之正弦曲线的拟合误差，特别是年隧道现场月平均最高气温不是在7份，而是在8月份.4对大坂山隧道洞内壁温及围岩冻结状况的分析预测4.1参数及初边值按大坂山隧道的高度值3800m和年平均气

0

，我们算得空气密度

0.774kg/3比[7]kJ/m导热系数