【正文】 of the entry and exit， the air flow in the tunnel would also be from the exit to entry .Additionally，since the wind speed at the tunnel site is low， we could consider that the air flow would be principally laminar. Based on the reasons mentioned， we simplify the tunnel to a round tube，and consider that the 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: 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 4 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 viscosity 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。， fS (t), uS (t) are frozen and thawed parts in the surrounding rock materials respectively。 f? , u? and fC , uC are thermal conductivities and volumetric thermal capacities in frozen and thawed parts respectively。 X= (x , r)， ? (t) is phase change front。 Lh is heat latent of freezing water。 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。 ( ii ) substituting U0， V0 into eq. (2)， and solving (2)， we obtain p0。 (iii) solving the first and second equations of(1)， we obtain U0，V1。 (iv) solving the first and third equations of(1)， we obtain U2， V2。 (v) calculating the momentumaverage of U1， v1 and U2， v2， we obtain the new U0， V0。 then return to (ii)。 (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 p0， U0 and V0 as the initial values for the next elapse and solve those equations concerning the temperature.. 2 .2 Entire method used for solving the energy equations As mentioned 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 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 and those equations concerning the temperature of the surrounding rock .In order to cope with this problem ， we simultaneously solve the two groups of equations based on the fact that at the tunnel wall surface both temperatures are equal .We should bear 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 6 in mind the phase change while solving those equations concerning the temperature of the surrounding rock， and the convection while solving those equations concerning the temperature of the air flow, and we only need to smooth those relative parameters at the tunnel wall surface .The solving methods for the equations with the phase change are the same as in reference [3]. Determination of thermal parameters and initial and boundary conditions Determination of the thermal parameters. Using p= H， we calculate air pressure p at elevation H and calculate the air density ? using formula GTP?? , where T is the yearlyaverage absolute air temperature，and G is the humidity constant of air. Letting PC be the thermal capacity with fixed pressure, ? the thermal conductivity， and ? the dynamic viscosity of air flow, we calculate the thermal conductivity and kinematic viscosity using the formulas ??PC?ａ and????. The thermal parameters of the surrounding rock are determined from the tunnel site. 2 . Determination of the initial and boundary conditions .Choose the observed monthly average 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 ]5[2 2/)/1( vdkLp ??? on the section of entry ( that is， 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