【正文】 ions of the surrounding wall rock of a tunnel， presuming the axial variations of air flow temperature and the coefficients of convective heat transfer, Lunardini discussed the freeze and thaw conditions by the approximate formulae obtained by Shamsundar in study of freezing outside a circular tube with axial variations of coolant temperature .We simulated the temperature conditions on the surface of a tunnel wall varying similarly to the periodic changes of the outside air temperature .In fact， the temperatures of the air and the surrounding wall rock material affect each other so we cannot find the temperature variations of the air flow in advance。 R is the equivalent radius of the tunnel section。 (iii) solving the first and second equations of(1)， we obtain U0，V1。 that is we assume that T=f(x)? 3%C0 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 rock.. 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。 (4)聯(lián)立方程 ((1)的第一個和第三個方程，解得一組解 2U , 2V 。上的溫度梯度作為該邊界上的梯度值 考慮到圍巖在施土過程中己經(jīng)預冷，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 ). 4. 2 計算結果 圖 3 和圖 4給出了我們預測的隧道壁溫隨洞口氣溫變化的情況，圖 5 和圖 6給出了我們 預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 . 重慶交通大學土木工程專 業(yè)（隧道與城市軌道交通工程方向）畢業(yè)設計外文翻譯 19 圖 圖 度。觀測值 4 對大坂山隧道洞內(nèi)壁溫及圍巖凍結狀況的分析預測 4. 1 熱參數(shù)及初邊值 按大坂山隧道的高度值 3 800 m 和年平均氣溫 3 C0 ，我們算得空氣密度3/ mkg?? ；由于大氣中含有水汽，我們將空氣的定壓比熱取為 [7] smkJC p ?? / 導熱系數(shù) CmW 02 / ??? ?? ，空氣的動力粘性系數(shù)取為smkg ??? ? / 6? ,經(jīng)計算，得出空氣的導溫系數(shù) sma /103 7 8 25??? 和運動粘性系數(shù) sm / 25???? . 考慮到車體迎風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對氣體擴散性能的影響 . 巖體的導熱系數(shù)皆按完好致密巖石的情況處理，取巖石的干容重3/2400 mkgd ?? 時 ， 含 水 量 和 末 凍 水 含 量 分 別 為 W=3% 和 W=1 % ，cmW ou ./?? , cmW of ./?? 巖 石 的 比 熱 取 為 CkgkJCV 0./? ，重慶交通大學土木工程專 業(yè)（隧道與城市軌道交通工程方向）畢業(yè)設計外文翻譯 18 duf W wC ????? 1 )(,duu W wC ????? 1 )(. 另外，據(jù)有關資料，大坂山地區(qū)月平均最大風速約為 m/s，月平均最小大風速約為 。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為空氣運動 粘性系數(shù)，a為空氣的導溫系數(shù)， L 為隧道長度， R為隧道的當量半徑， D為時間長度 )(tSf , )(tSu 分別為圍巖的凍、融區(qū)域 . f? , u? 分別為凍、融狀態(tài)下的熱傳導系數(shù)，fC , uC 分別為凍、融狀態(tài)下的體積熱容量， X=(x,r) , )(t? 為凍、融相變界面 ,To 為巖石凍結臨界溫度 (這里具體計算時取To= )， hL 為水的相變潛熱 . 重慶交通大學土木工程專 業(yè)（隧道與城市軌道交通工程方向）畢業(yè)設計外文翻譯 15 2 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速度，所以我們可先解出速度，再解溫度 . 連續(xù)性方程和動量方程的求解 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，經(jīng)整理 化簡，我們得到關于壓力 P 的如下橢圓型方程 : 于是，對方程 (1)中的連續(xù)性方程和動量方 程的求解，我們按如下步驟進行 : (1)設定速度 0U , 0V 。2,observed values parison of simulated and observed air temperature inside The Xiluoqi Tunnel in ,simulated values。 and To is critical freezing temperature of rock ( here we assume To= ℃ ). 2 used for solving the model Equation(1)shows flow. We first 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. 2. 1 Procedure used for solving the continuity and momentum equations 重慶交通大學土木工程專 業(yè)（隧道與城市軌道交通工程方向）畢業(yè)設計外文翻譯 5 Since the first three equations in(1) are not independent we derive the second equation by x and the third equation by r. After preliminary calculation we obtain the following elliptic equation concerning the effective pressure p: Then we solve equations in(1) using the following procedures: (i ) Assume the values for U0， V0。 a is the thermal conductivity of air。 furthermore， it is difficult to quantify the coefficient of convective heat exchange at the surface of the tunnel wall .Therefore it is not practicable to define the temperature on the surface of the tunnel wall according to the outside air temperature .In this paper, we bine the air flow convective heat exchange and heat conduction in the surrounding rock material into one model， and simulate the freezethaw conditions of the surrounding rock material based on the in situ conditions of air temperature， atmospheric pressure， wind force at the entry and exit of the tunnel， and the conditions of hydrogeology and engineering geology. 重慶交通大學土木工程專 業(yè)（隧道與城市軌道交通工程方向）畢業(yè)設計外文翻譯 3 Mathematical model In order to construct an appropriate model, we need the in situ fundamental conditions as a basis .Here we use the conditions at the scene of the Dabanshan Tunnel. The Dabanshan Tunnel is lototed on the highway from Xining to Zhangye, south of the Datong River, at an elevation of m, with a length of 1 530 m and an alignment from southwest to northeast. The tunnel runs from the southwest to the northeast. Since the monthlyaverage air temperature is beneath 0`}C for eight months at the tunnel site each year and the construction would last for several years， the surrounding rock materials would bee cooler during the construction .We conclude that, after