工程方面的外文文獻翻譯--嚴寒地區(qū)隧道圍巖凍融狀況分析的導(dǎo)熱與對流換熱模型

1、<p><b>　　中文3990字</b></p><p>　　A convection-conduction model for analysis of the freeze-thaw</p><p>　　conditions in the surrounding rock wall of a</p><p>　　tunnel in

2、 permafrost regions</p><p>　　HE Chunxiong(何春雄)，</p><p>　　(State Key Laboratory of Frozen Soil Engineering, Lanzhou Institute of Glaciology and Geocryology,</p><p>　　Chinese Academy

3、of Sciences, Lanzhou 730000, China; Department of Applied Mathematics,</p><p>　　South China University of Technology, Guangzhou 510640, China)</p><p>　　WU Ziwang(吳紫汪)and ZHU Linnan(朱林楠)</p>

4、;<p>　　(State key Laboratory of Frozen Soil Engineering, Lanzhou Institute of Glaciology and Geocryology</p><p>　　Chinese Academy of Sciences, Lanzhou 730000, China)</p><p>　　Received Feb

5、ruary 8, 1999</p><p><b>　　Abstract</b></p><p>　　Based on the analyses of fundamental meteorological and hydrogeological conditions at the site of a tunnel in the cold regions, a comb

6、ined convection-conduction model for air flow in the tunnel and temperature field in the surrounding has been constructed. Using the model, the air temperature distribution in the Xiluoqi No. 2 Tunnel has been simulate

7、d numerically. The simulated results are in agreement with the data observed. Then, based on the in situ conditions of sir temperature, atmospheri</p><p>　　Keywords: tunnel in cold regions, convective heat

8、exchange and conduction, freeze-thaw.</p><p>　　A number of highway and railway tunnels have been constructed in the permafrost regions and their neighboring areas in China. Since the hydrological and therma

9、l conditions changed after a tunnel was excavated，the surrounding wall rock materials often froze, the frost heaving caused damage to the liner layers and seeping water froze into ice diamonds，which seriously interfered

10、 with the communication and transportation. Similar problems of the freezing damage in the tunnels also appeared in other</p><p>　　Many tunnels，constructed in cold regions or their neighbouring areas，pass th

11、rough the part beneath the permafrost base .After a tunnel is excavated，the original thermodynamical conditions in the surroundings are and thaw destroyed and replaced mainly by the air connections without the heat radi

12、ation, the conditions determined principally by the temperature and velocity of air flow in the tunnel，the coefficients of convective heat transfer on the tunnel wall，and the geothermal heat. In order to</p><

13、p>　　Mathematical model</p><p>　　In order to construct an appropriate model, we need the in situ fundamental conditions as a ba-sis .Here we use the conditions at the scene of the Dabanshan Tunnel. The Da

14、banshan Tunnel is lo-toted on the highway from Xining to Zhangye, south of the Datong River, at an elevation of 3754.78-3 801.23 m, with a length of 1 530 m and an alignment from southwest to northeast. The tunnel runs

15、from the southwest to the northeast.</p><p>　　Since the monthly-average air temperature is beneath 0`}C for eight months at the tunnel site each year and the construction would last for several years，the sur

16、rounding rock materials would become cooler during the construction .We conclude that, after excavation, the pattern of air flow would depend mainly on the dominant wind speed at the entry and exit，and the effects of the

17、 temperature difference between the inside and outside of the tunnel would be very small .Since the dominant wind direc</p><p>　　Based on the reasons mentioned，we simplify the tunnel to a round tube，and cons

18、ider that the</p><p>　　air flow and temperature are symmetrical about the axis of the tunnel，Ignoring the influence of the air temperature on the speed of air flow, we obtain the following equation:</p>

19、;<p>　　where t，x，r are the time，axial and radial coordinates; U，V are axial and radial wind speeds; T is temperature; p is the effective pressure(that is，air pressure divided by air density); v is the kinematic vi

20、scosity of air; a is the thermal conductivity of air; L is the length of the tunnel; R is the equivalent radius of the tunnel section; D is the length of time after the tunnel construction;，</p><p>　　(t), (t

21、) are frozen and thawed parts in the surrounding rock materials respectively; ,and , are thermal conductivities and volumetric thermal capacities in frozen and thawed parts respectively; X= (x , r)，(t) is phase change fr

22、ont; Lh is heat latent of freezing water; and To is critical freezing temperature of rock ( here we assume To= -0.1℃).</p><p>　　used for solving the model</p><p>　　Equation(1)shows flow. We fir

23、st solve those concerning temperature at that the temperature of the surrounding rock does not affect the speed of air equations concerning the speed of air flow, and then solve those equations every time elapse.</p&g

24、t;<p>　　2. 1 Procedure used for solving the continuity and momentum equations</p><p>　　Since the first three equations in(1) are not independent we derive the second equation by x</p><p&g

25、t;　　and the third equation by r. After preliminary calculation we obtain the following elliptic equation concerning the effective pressure p:</p><p>　　Then we solve equations in(1) using the following proce

26、dures:</p><p>　　(i ) Assume the values for U0，V0;</p><p>　　( ii ) substituting U0，V0 into eq. (2)，and solving (2)，we obtain p0;</p><p>　　(iii) solving the first and second equations

27、 of(1)，we obtain U0，V1;</p><p>　　(iv) solving the first and third equations of(1)，we obtain U2，V2;</p><p>　　(v) calculating the momentum-average of U1，v1 and U2，v2，we obtain the new U0，V0;</p

28、><p>　　then return to (ii);</p><p>　　(vi) iterating as above until the disparity of those solutions in two consecutive iterations is sufficiently small or is satisfied，we then take those values of

29、p0，U0 and V0 as the initial values for the next elapse and solve those equations concerning the temperature..</p><p>　　2 .2 Entire method used for solving the energy equations</p><p>　　As menti

30、oned previously，the temperature field of the surrounding rock and the air flow affect each other. Thus the surface of the tunnel wall is both the boundary of the temperature field in the surrounding rock and the boundary

31、 of the temperature field in air flow .Therefore， it is difficult to separately identify the temperature on the tunnel wall surface，and we cannot independently solve those equations concerning the temperature of air flow

32、 and those equations concerning the temperature of t</p><p>　　Determination of thermal parameters and initial and boundary conditions</p><p>　　2.3.1 Determination of the thermal parameters. Us

33、ing p= 1013.25-0.1088 H，we calculate</p><p>　　air pressure p at elevation H and calculate the air density using formula , where T is the yearly-average absolute air temperature，and G is the humidity consta

34、nt of air. Letting be the thermal capacity with fixed pressure, the thermal conductivity，</p><p>　　and the dynamic viscosity of air flow, we calculate the thermal conductivity and kinematic viscosity usin

35、g the formulas and. The thermal parameters of the surrounding rock are determined from the tunnel site.</p><p>　　2 .3.2 Determination of the initial and boundary conditions .Choose the observed monthly ave

36、rage wind speed at the entry and exit as boundary conditions of wind speed，and choose the relative effective pressure p=0 at the exit ( that is，the entry of the dominant wind trend) and on the section of entry ( that is

37、，the exit of the dominant wind trend )，where k is the coefficient of resistance along the tunnel wall, d = 2R，and v is the axial average speed. We approximate T varying by the sine law ac</p><p>　　A simulate

38、d example</p><p>　　Using the model and the solving method mentioned above，we simulate the varying law of the air temperature in the tunnel along with the temperature at the entry and exit of the Xiluoqi No.2

39、 Tunnel .We observe that the simulated results are close to the data observed[6].</p><p>　　The Xiluoqi No .2 Tunnel is located on the Nongling railway in northeastern China and passes through the part beneat

40、h the permafrost base .It has a length of 1 160 m running from the northwest to the southeast, with the entry of the tunnel in the northwest，and the elevation is about 700 m. The dominant wind direction in the tunnel is

41、from northwest to southeast, with a maximum monthly-average speed of 3 m/s and a minimum monthly-average speed of 1 .7 m/s . Based on the data observed，we approxima</p><p>　　Figure 1 shows the simulated year

42、ly-average air temperature inside and at the entry and exit of the tunnel compared with the data observed .We observe that the difference is less than 0 .2 `C from the entry to exit.</p><p>　　Figure 2 shows

43、a comparison of the simulated and observed monthly-average air temperature in-side (distance greater than 100 m from the entry and exit) the tunnel. We observe that the principal law is almost the same，and the main reaso

44、n for the difference is the errors that came from approximating the varying sine law at the entry and exit; especially , the maximum monthly-average air temperature of 1979 was not for July but for August.</p><

45、;p>　　Prediction of the freeze-thaw conditions for the Dabanshan Tunnel</p><p>　　4 .1 Thermal parameter and initial and boundary conditions</p><p>　　Using the elevation of 3 800 m and the ye

46、arly-average air temperature of -3℃, we calculate the air density p=0 .774 kg/m.Since steam exists In the air, we choose the thermal capacity with a fixed pressure of air heat conductivity and the dynamic viscosity Af

47、ter calculation we obtain the thermal diffusivity a= 1 .3788 and the kinematic viscosity， .</p><p>　　Considering that the section of automobiles is much smaller than that of the tunnel and the auto-mobiles

48、pass through the tunnel at a low speed，we ignore the piston effects，coming from the movement of automobiles，in the diffusion of the air. </p><p>　　We consider the rock as a whole component and choose the dry

49、 volumetric cavity ,content of water and unfrozen water W=3% and W=1%, and the thermal conductivity ,,heat capacity and ,</p><p>　　According to the data observed at the tunnel site，the maximum monthly-avera

50、ge wind speed is about 3 .5 m/s，and the minimum monthly-average wind speed is about 2 .5 m/s .We approximate the wind speed at the entry and exit as , where t is in month. The initial wind speed in the tunnel is set to

51、be </p><p>　　The initial and boundary values of temperature T are set to be</p><p>　　where f(x) is the distance from the vault to the permafrost base，and R0=25 m is the radius of do-main of sol

52、ution T. We assume that the geothermal gradient is 3%，the yearly-average air temperature outside tunnel the is A=-3，and the amplitude is B=12.</p><p>　　As for the boundary of R=Ro，we first solve the equatio

53、ns considering R=Ro as the first type of boundary; that is we assume that T=f(x)3%on R=Ro. We find that, after one year, the heat flow trend will have changed in the range of radius between 5 and 25m in the surrounding r

54、ock.. Considering that the rock will be cooler hereafter and it will be affected yet by geothermal heat, we appoximately assume that the boundary R=Ro is the second type of boundary; that is，we assume that the gradient v

55、alue，</p><p>　　Considering the surrounding rock to be cooler during the period of construction，we calculatefrom January and iterate some elapses of time under the same boundary. Then we let the boundary valu

56、es vary and solve the equations step by step(it can be proved that the solution will not depend on the choice of initial values after many time elapses ).</p><p>　　4 .2 Calculated results</p><p&

57、gt;　　Figures 3 and 4 show the variations of the monthly-average temperatures on the surface of the tunnel wall along with the variations at the entry and exit .Figs .5 and 6 show the year when permafrost begins to form a

58、nd the maximum thawed depth after permafrost formed in different surrounding sections.</p><p>　　4 .3 Preliminary conclusion</p><p>　　Based on the initial-boundary conditions and thermal parame

59、ters mentioned above, we obtain the following preliminary conclusions:</p><p>　　1)The yearly-average temperature on the surface wall of the tunnel is approximately equal to the air temperature at the entry a

60、nd exit. It is warmer during the cold season and cooler during the warm season in the internal part (more than 100 m from the entry and exit) of the tunnel than at the entry and exit . Fig .1 shows that the internal mont

61、hly-average temperature on the surface of the tunnel wall is 1.2℃ higher in January, February and December, 1℃higher in March and October, and 1 .6℃ lowe</p><p>　　2) Since it is affected by the geothermal he

62、at in the internal surrounding section，especially in the central part, the internal amplitude of the yearly-average temperature on the surface of the tunnel wall decreases and is 1 .6℃ lower than that at the entry and ex

63、it.</p><p>　　3 ) Under the conditions that the surrounding rock is compact , without a great amount of under-ground water, and using a thermal insulating layer(as designed PU with depth of 0.05 m and heat co

64、nductivity =0.0216 W/m℃，F(xiàn)BT with depth of 0.085 m and heat conductivity =0.0517W/m℃)，in the third year after tunnel construction，the surrounding rock will begin to form permafrost in the range of 200 m from the entry and

65、 exit .In the first and the second year after construction, the surrounding rock will </p><p>　　4) If permafrost forms entirely in the surrounding rock，the permafrost will provide a water-isolating layer and

66、 be favourable for communication and transportation .However, in the process of construction，we found a lot of underground water in some sections of the surrounding rock .It will permanently exist in those sections，seepi

67、ng out water and resulting in freezing damage to the liner layer. Further work will be reported elsewhere.</p><p>　　嚴寒地區(qū)隧道圍巖凍融狀況分析的導(dǎo)熱與對流換熱模型</p><p>　　何春雄 吳紫汪 朱林楠</p><p>　　（中國科學(xué)院寒區(qū)旱區(qū)

68、環(huán)境與工程研究所凍土工程國家重點實驗室） </p><p>　　（華南理工大學(xué)應(yīng)用數(shù)學(xué)系）</p><p><b>　　摘 要</b></p><p>　　通過對嚴寒地區(qū)隧道現(xiàn)場基本氣象條件的分析，建立了隧道內(nèi)空氣與圍巖對流換熱及固體導(dǎo)熱的綜合模型。用此模型對大興安嶺西羅奇2號隧道的洞內(nèi)氣溫分布進行了模擬計算，結(jié)果與實測值基本一致。分析預(yù)

69、報了正在開鑿的祁連山區(qū)大坂山隧道開通運營后洞內(nèi)溫度及圍巖凍結(jié)、融化狀況。</p><p>　　關(guān)鍵詞 嚴寒地區(qū)隧道 導(dǎo)熱與對流換熱 凍結(jié)與融化</p><p>　　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)，造成對襯砌層的凍脹破壞以及洞內(nèi)滲水凍結(jié)成冰凌等，嚴重影響了正常交通。類似隧道凍害問題同樣出現(xiàn)在其他國家

70、（蘇聯(lián)、挪威、日本等)的寒冷地區(qū)。如何預(yù)測分析隧道開挖后圍巖的凍結(jié)狀況，為嚴寒地區(qū)隧道建設(shè)的設(shè)計、施工及維護提供依據(jù)，這是一個亟待解決的重要課題。</p><p>　　在多年凍土及其臨近地區(qū)修筑的隧道，多數(shù)除進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)對流為特征的新的熱力系統(tǒng).隧道開通運營后，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—

71、固交界面的換熱以及地?zé)崽荻人_定。為分析預(yù)測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，分析計算了隧道圍巖的溫度場[3]。但實際情況下，圍巖與氣體的溫度場相互作用，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)上很難測定，從而由氣溫的變化確定壁面溫度的變化難以實現(xiàn).本文通過氣一固禍

72、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)，計算出圍巖的溫度場。</p><p><b>　　1數(shù)學(xué)模型</b></p><p>　　為確定合適的數(shù)學(xué)模型，須以現(xiàn)場的基本情況為依據(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

73、.78~3801.23 m，全長1530 m ,隧道近西南—東北走向。</p><p>　　由于大坂山地區(qū)隧道施工現(xiàn)場平均氣溫為負溫的時間每年約長8個月，加之施工時間持續(xù)數(shù)年，圍巖在施土過程中己經(jīng)預(yù)冷，所以隧道開通運營后，洞內(nèi)氣體流動的形態(tài)主要由進出口的主導(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小。冬季祁連山區(qū)盛行西北風(fēng)，氣流將從隧道出曰流向進口端，夏季雖然祁連山區(qū)盛行東偏南風(fēng)，但考慮到洞口兩端

74、氣壓差、溫度壓差以及進出口地形等因素，洞內(nèi)氣流仍將由出口北端流向進口端。另外，由于現(xiàn)場年平均風(fēng)速不大，可以認為洞內(nèi)氣體將以層流為主。</p><p>　　基于以上基本情況，我們將隧道簡化成圓筒，并認為氣流、溫度等關(guān)十隧道中心線軸對稱，忽略氣體溫度的變化對其流速的影響，可有如下的方程：</p><p>　　其中t為時間，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

75、效壓力(即空氣壓力與空氣密度之比少，V為空氣運動粘性系數(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為時間長度， 分別為圍巖的凍、融區(qū)域。,分別為凍、融狀態(tài)下的熱傳導(dǎo)系數(shù)，，分別為凍、融狀態(tài)下的體積熱容量，X=(x,r) ， 為凍、融相變界面，To為巖石凍結(jié)臨界溫度(這里具體計算時取To=-0.10)，為水的相變潛熱。</p><p><b>　　2 求解過程</b></

76、p><p>　　由方程(1)知，圍巖的溫度的高低不影響氣體的流動速度，所以我們可先解出速度，再解溫度。</p><p>　　2.1 連續(xù)性方程和動量方程的求解</p><p>　　由于方程((1)的前3個方程不是相互獨立的，通過將動量方程分別對x和r求導(dǎo)，經(jīng)整理化簡，我們得到關(guān)于壓力P的如下橢圓型方程：</p><p>　　于是，對方程(1)中的

77、連續(xù)性方程和動量方程的求解，我們按如下步驟進行：</p><p><b>　　(1)設(shè)定速度，；</b></p><p>　　( 2)將，代入方程并求解，得；</p><p>　　(3)聯(lián)立方程(1)的第一個和第二個方程，解得一組解，；</p><p>　　(4)聯(lián)立方程((1)的第一個和第三個方程，解得一組解，；<

78、;/p><p>　　(5)對((3) ，(4)得到的速度進行動量平均，得新的，返回(2) ；</p><p>　　(6)按上述方法進行迭代，直到前后兩次的速度值之差足夠小。以，，作為本時段的解，下一時段求解時以此作為迭代初值。</p><p>　　2. 2 能量方程的整體解法</p><p>　　如前所述，圍巖與空氣的溫度場相互作用，壁面既是氣體

79、溫度場的邊界，又是固體溫度場的邊界，壁面的溫度值難以確定，我們無法分別獨立地求解隧道內(nèi)的氣體溫度場和圍巖溫度場。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，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：解流體溫度場時不考慮相變和解固體溫度時沒有對流項；在洞壁表面上方程系數(shù)的光滑化。另外，帶相變的溫度場的算法與文獻[3]相同。</p><p

80、>　　2. 3熱參數(shù)及初邊值的確定</p><p>　　熱參數(shù)的確定方法： 用p=1013.25-0.1088H計算出海拔高度為H的隧道現(xiàn)場的大氣壓強，再由計算出現(xiàn)場空氣密度，其中T為現(xiàn)場大氣的年平均絕對溫度，G為空氣的氣體常數(shù)。記定壓比熱為，導(dǎo)熱系數(shù)為，空氣的動力粘性系數(shù)為。按 和 計算空氣的導(dǎo)溫系數(shù)和運動粘性系數(shù)，圍巖的熱物理參數(shù)則由現(xiàn)場采樣測定。</p><p>　　初邊值的確

81、定方法:洞曰風(fēng)速取為現(xiàn)場觀測的各月平均風(fēng)速.取卞導(dǎo)風(fēng)進曰的相對有效氣壓為0，主導(dǎo)風(fēng)出口的氣壓則取為，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，為進口端面軸向平均速度。進出口氣溫年變化規(guī)律由現(xiàn)場觀測資料，用正弦曲線擬合，圍巖內(nèi)計算區(qū)域的邊界按現(xiàn)場多年凍土下限和地?zé)崽荻却_定出適當(dāng)?shù)臏囟戎祷驕囟忍荻取?lt;/p><p><b>　　3 計算實例</b></p>

82、<p>　　按以上所述的模型及計算方法，我們對大興安嶺西羅奇2號隧道內(nèi)氣溫隨洞曰外氣溫變化的規(guī)律進行了模擬計算驗證，所得結(jié)果與實測值[6]相比較，基本規(guī)律一致。 西羅奇2號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1160 m ，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)向為西北風(fēng)。洞口海拔高度約為700 m，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)場觀測資料，我們將進出口氣溫擬合為

83、年平均分別為-5和-6.4，年變化振幅分別為18.9和17.6的正弦曲線.隧道的當(dāng)量直徑為5.8 m，沿程阻力系數(shù)取為0.025.由于圍巖的熱物理參數(shù)對計算洞內(nèi)氣溫的影響遠比洞口的風(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。</p><p>　　圖1給出了洞口及洞內(nèi)年平均氣溫的計算值與觀測值比較的情況，從進口到出口，兩值之差都小于0.2。 </p><p>　　圖2

84、給出了洞內(nèi) (距進出口l00m以上)月平均氣溫的計算值與觀測值比較的情況，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)場月平均最高氣溫不是在7月份，而是在8月份。</p><p>　　4 對大坂山隧道洞內(nèi)壁溫及圍巖凍結(jié)狀況的分析預(yù)測</p><p>　　4. 1熱參數(shù)及初邊值</p><p&

85、gt;　　按大坂山隧道的高度值3 800 m和年平均氣溫-3，我們算得空氣密度；由于大氣中含有水汽，我們將空氣的定壓比熱取為[7] 導(dǎo)熱系數(shù)，空氣的動力粘性系數(shù)取為。經(jīng)計算，得出空氣的導(dǎo)溫系數(shù)和運動粘性系數(shù)。</p><p>　　考慮到車體迎風(fēng)面與隧道端面相比較小、車輛在隧道內(nèi)行駛速度較慢等因素，我們這里忽略了車輛運行時所形成的活塞效應(yīng)對氣體擴散性能的影響。</p><p>　　巖體的導(dǎo)熱

86、系數(shù)皆按完好致密巖石的情況處理，取巖石的干容重時，含水量和末凍水含量分別為W=3%和W=1 %，，巖石的比熱取為，,。</p><p>　　另外，據(jù)有關(guān)資料，大坂山地區(qū)月平均最大風(fēng)速約為3.5 m/s，月平均最小大風(fēng)速約為2.5m/s;我們將洞口風(fēng)速擬合為，這里t為月份。</p><p>　　洞內(nèi)風(fēng)速初值為：這里取.而將溫度的初邊值取為：</p><p>　　這里記

87、f (x)為多年凍土下限到隧道拱頂?shù)木嚯x，Ro = 25m為求解區(qū)域的半徑.地?zé)崽荻热?%，洞外天然年平均氣溫A=-3，年氣溫變化振幅B=12。</p><p>　　對于邊界R = Ro，我們先按第一類邊值(到多年凍土下限的距離乘以3 %)計算，發(fā)現(xiàn)一年后，在半徑為5m到25m范圍內(nèi)圍巖的熱流方向己經(jīng)發(fā)生轉(zhuǎn)向?？紤]到此后圍巖會繼續(xù)冷卻，但在邊界R=上又受地?zé)崽荻鹊淖饔?，我們近似地將邊界R= Ro作為第二類邊界處

88、理，即把由定邊值計算一年后R=R上的溫度梯度作為該邊界上的梯度值?？紤]到圍巖在施土過程中己經(jīng)預(yù)冷，我們這里從幾月份算起，在同一邊值下進行迭代，直到該邊值下的溫度場基本穩(wěn)定后，再令邊值依正弦規(guī)律變化，逐時段進行求解(可以證明，很多時段后的解，將不依賴于初值的選擇)。</p><p><b>　　4. 2 計算結(jié)果</b></p><p>　　圖3和圖4給出了我們預(yù)測的隧

89、道壁溫隨洞口氣溫變化的情況，圖5和圖6給出了我們預(yù)測的不同部位圍巖開始形成多年凍土的起始年份和多年凍土形成后圍巖的年最大融化深度。</p><p><b>　　4. 3初步結(jié)論</b></p><p>　　對于大坂山隧道，按如上選取的參數(shù)及初邊值進行計算，我們得出如下初步結(jié)論：</p><p>　　（1）洞內(nèi)（距進出口100 m以上）年平均壁溫

90、與洞外年平均氣溫基本相同，但洞內(nèi)寒季較暖、暖季較涼。從圖1可以看出，洞內(nèi)壁溫與洞外氣溫相比較：1、2 、12月份高約1. 2 ；3 、11月份高約1；4 、5 、9和10月份基本相同；6月份和8月份低約1.6 ；7月份低約2。</p><p>　?。?）由于隧道內(nèi)部（距進出口100 m以上，特別是靠中心地段）受地?zé)嶙饔幂^強，洞內(nèi)平均壁溫的年變化振幅降低。年平均壁面溫度約為-3，振幅約為10.4。</p&g

91、t;<p>　　（3）就我們所考慮的完好致密巖石、沒有大量地下水流動的情況，按現(xiàn)有設(shè)計鋪設(shè)保溫材料(PU厚0.05m，導(dǎo)熱系數(shù)，F(xiàn)BT厚0.085 m，導(dǎo)熱系數(shù)后，在距進出曰200 m的范圍內(nèi)，開通運營后第3年就開始形成多年凍土，其中40 m以內(nèi)和100 m以內(nèi)在第一年和第二年就開始形成多年凍土;在距進出曰200 m以上的中間段，開通運營8年后開始形成多年凍土，其中在距洞中心200 m的范圍內(nèi)，14—15年后開始形成多年凍

92、土。多年凍土形成后的一兩年內(nèi)，年最大融化深度較大(尤其是中間段)，以后逐年減小，至19—20年后融化深度基本達到穩(wěn)定，洞口段及中間段的融化深度都在2—3 m的范圍內(nèi)。</p><p>　　(4)洞內(nèi)若整體性形成多年凍土，這將成為一道隔水屏障，有利于車輛運行的安全，但在目前的施土中己發(fā)現(xiàn)有些部位有較豐富的地下水，因此很有可能在地下水溢出帶中出現(xiàn)永久性融區(qū)，造成洞內(nèi)滲水結(jié)冰病害，這個問題我們將在以后詳細討論。<