Wind speed-considered coldest month air temperature axial distribution prediction method in cold region tunnel

Abstract

The invention discloses a cold region tunnel coldest month air temperature axial distribution prediction method considering wind speed, which comprises the following steps: firstly solving a cold region tunnel axial temperature field, then solving coldest month air temperature axial distribution in a cold region tunnel, then solving the wind speed in the tunnel, and carrying out iterative calculation solution on the wind speed in the tunnel and the coldest month air temperature axial distribution in the cold region tunnel. The axial distribution of the coldest month air temperature in the cold region tunnel is predicted, a predicted value is close to an actually measured value, and the method has a good engineering application prospect.

Description

Technical Field

[0001] The invention relates to the technical field of cold region tunnel engineering, and in particular to a method for predicting the axial distribution of the coldest month's air temperature in a cold region tunnel taking wind speed into consideration. Background Art

[0002] The temperature environment in cold-region tunnels has a significant impact on the occurrence and development of frost damage. Regulating the temperature distribution in tunnels by various means is an important idea for the current prevention and control of tunnel frost damage. There is a coupling effect between the temperature in cold-region tunnels and the air flow in tunnels. On the one hand, the air temperature distribution in tunnels affects the thermal potential difference in tunnels, which in turn affects the wind speed. On the other hand, the wind speed determines the intensity of convective heat exchange between air and tunnel structure, and the flow rate of low-temperature air entering the tunnel in cold seasons, which in turn has a significant impact on the temperature environment in tunnels. Therefore, if the temperature distribution in tunnels is to be accurately obtained, the influence of ventilation cannot be ignored.

[0003] In the current research on the influence of cold-region tunnel ventilation on temperature distribution, many scholars have achieved a series of results. In the "Analytical Solution of Temperature Field in Cold-Region Tunnels Considering Lining and Insulation Layer" published in the "Journal of Rock Mechanics and Engineering" in 2010, Xia Caichu et al. assumed that the wind speed in the tunnel was a constant, and under this condition, obtained the analytical solution of the temperature distribution in the cold-region tunnel. In the article "Research on Temperature Field in Cold-Region Tunnels Influenced by Thermal Potential Difference and Net Pressure Difference at the Tunnel Portal" published in "Science, Technology and Engineering" in 2021, Zhang Chenxi et al. pointed out the three pressure difference factors that cause ventilation in the tunnel, and pointed out the significant influence of thermal potential difference on ventilation and temperature in cold-region tunnels. In 2016, Jia Hui of Southwest Jiaotong University summarized the various factors that cause ventilation in the tunnel in his master's thesis "Research on the Influence of Meteorological Elements on Temperature Field in Cold-Region Tunnels and Longitudinal Zoning", and conducted on-site measurements of the temperature distribution of a cold-region tunnel in Northeast China, and analyzed the ventilation principle and the mechanism affecting temperature in the tunnel. In the article "Anovelindicator for equivalent mean air temperature within the tunnel considering time-varying ventilation wind speeds: Calculation and application" published in the International Journal of Thermal Sciences in 2024, Xia Caichu pointed out the coupling effect between air temperature and wind speed in the tunnel, and proposed a method to determine the optimal antifreeze axis and insulation layer thickness design of the tunnel under the influence of ventilation.

[0004] In the above studies on the influence of ventilation on temperature in cold-region tunnels, the flow field and temperature field in cold-region tunnels are analyzed from a theoretical perspective, and numerical simulation methods are used to verify and predict the influence of ventilation on temperature distribution, or the temperature field distribution is analytically calculated under the condition of assumed wind speed. However, there is still a lack of corresponding research on the analytical calculation method and computational mechanics of the coupling of wind speed and air temperature in tunnels.

[0005] Based on this, the present invention proposes a method for predicting the axial distribution of the coldest monthly air temperature in cold zone tunnels taking into account wind speed, so as to quantify the influence of the ventilation process in the tunnel on the temperature distribution, so as to solve the temperature distribution in the tunnel more accurately and reasonably. Summary of the invention

[0006] The purpose of the present invention is to provide a method for predicting the axial distribution of the coldest monthly temperature in a cold zone tunnel taking into account wind speed, in view of the fact that in the prior art, the temperature field is solved only under the assumption of wind speed, and the selection of wind speed is very blind and artificial, resulting in unreasonable and inaccurate calculation results.

[0007] The technical solution adopted to achieve the purpose of the present invention is:

[0008] A method for predicting the axial distribution of the coldest monthly temperature in a tunnel in a cold region taking into account wind speed comprises the following steps:

[0009] Step 1: Solve for intermediate parameters and intermediate parameters α 11 , α 21 , α 31 and α 41 All are intermediate parameters, among which:

[0010]

[0011] The matrix S is:

[0012]

[0013] Matrix S 11 , S 21 , S 31 , S 41 They are:

[0014]

[0015]

[0016] Where: h is the convection heat transfer coefficient between the tunnel structure and the air, in W·m -2 ℃ -1; λ1, λ2, λ3 are the thermal conductivity of the insulation layer, lining concrete, and surrounding rock, respectively, and the unit is W·m -1 ℃ -1 ; r0, r1, r2, r3 are respectively the inner radius of the insulation layer, the interface radius between the insulation layer and the lining concrete, the interface radius between the lining concrete and the surrounding rock, and the radius of the surrounding rock whose temperature does not change with time when the radial depth reaches a certain value, i.e. the outer boundary radius of the tunnel structure, all in m;

[0017] Solve the intermediate parameters F1(r0,s,h), k1 is the thermal diffusion coefficient of the insulation layer, in m 2 ·s -1 ; I0(·) and K0(·) are the first and second type 0th order imaginary Bessel functions, respectively; s is the intermediate parameter, s = iω, ω is the annual variation frequency, unit is s -1 ; i is the imaginary unit; β 11 (r0,s,h) and β 21 (r0,s,h) are intermediate parameters, where:

[0018]

[0019] The matrix S' is:

[0020]

[0021] Matrix S' 11 , S' 21 They are as follows:

[0022]

[0023] Where: I1(·) and K1(·) are the first-order and second-order Bessel functions of imaginary variables of the first kind, respectively; k2 and k3 are the thermal diffusion coefficients of lining concrete and surrounding rock, respectively, in m 2 ·s -1 ;

[0024] Step 2, solving the axial temperature field of the cold region tunnel;

[0025] Solve the process value of the annual average temperature in the tunnel at depth z (unit is °C), where z is the depth (unit is m):

[0026]

[0027] Where: L Mis the process value of the annual average temperature in the tunnel, the depth of the boundary between the inlet and outlet sections, in meters; h1 and h2 are the convection heat transfer coefficients between the tunnel structure and the air at the inlet and outlet sections of the tunnel, in W·m -2 ℃ -1 , where h1=3.36v1+6.32, h2=3.36v2+6.32; v1 and v2 are the wind speeds at the entrance and exit of the tunnel, respectively, in m·s -1 ; T M,0 and T M,L are the annual average temperatures of the tunnel entrance and exit, respectively, in °C; L is the tunnel length, in m; ρ is the air density in the tunnel, in kg·m -3 ; c is the specific heat capacity of air, in J·kg -1 ℃ -1 ; are all intermediate parameters. When h=h1, When h=h2, T s is the outer boundary temperature of the tunnel structure, that is, the temperature at the outer boundary radius r3 of the tunnel structure, in °C, which can be calculated by the following formula:

[0028]

[0029] Where: T c The temperature of the surrounding rock of the isothermal layer, in degrees Celsius. The isothermal layer refers to the area where the temperature no longer changes with time and remains unchanged all year round when reaching a certain depth from the surface. is the average burial depth of the whole tunnel, in m; R0 is the influence depth of the tunnel surrounding rock temperature field, in m; R1 is the burial depth of the isothermal layer, in m; K is the geothermal gradient, in ℃·m -1 ;

[0030] L M Determined by the following formula:

[0031]

[0032] Solve the annual amplitude value T of the temperature in the tunnel at depth z A (z)(unit: °C):

[0033]

[0034] Where: L A T is the annual amplitude of the temperature in the tunnel, and the depth of the boundary between the inlet and outlet sections, in meters; A,0 and T A,Lare the annual amplitude values ​​of the air temperature at the tunnel entrance and exit, respectively, in °C; Re(·) is the real part of the imaginary number; F1(r0,iω,h1) and F1(r0,iω,h2) are intermediate parameters. When h=h1 and s=iω, F1(r0,iω,h1)=F1(r0,s,h); when h=h2 and s=iω, F1(r0,iω,h2)=F1(r0,s,h);

[0035] L A Determined by the following formula:

[0036]

[0037] Step 3: Calculate the process value T of the axial distribution of the coldest month temperature in the cold zone tunnel cm (z)(unit: °C):

[0038]

[0039] Among them: τ is an independent variable;

[0040] Step 4, iterative calculation and solution of the axial distribution of wind speed in the tunnel and the coldest month temperature in the cold zone tunnel:

[0041] Initially assume that the wind speeds v1 and v2 in the tunnel entrance and exit are unknown. When the air density ρ in the tunnel is unknown, use steps 1 to 3 to solve the process value T of the axial distribution of the coldest month temperature in the cold region tunnel. cm (z); where the air density ρ in the tunnel at this time is taken as the air density ρ0 in the tunnel in the coldest month (in kg·m 3 ), that is, ρ=ρ0; in solving L M and L A When ρ0=ρ' avg , ρ' avg is the annual average air density in the tunnel site, in kg·m -3 , and its calculation formula is ρ' in and ρ' out are the annual average air density at the tunnel entrance and exit, in kg·m -3 ;

[0042] Solve for T cm (z), the equivalent coldest monthly temperature in the tunnel is calculated using the following formula (Unit: °C):

[0043]

[0044] Then the equivalent coldest monthly temperature in the tunnel, which finally contains only one unknown number ρ0, is Substitute the following formula and combine it with other parameter values ​​to calculate the air density ρ0 in the tunnel in the coldest month. The calculation result is accurate to 0.001 kg·m -3 :

[0045]

[0046] Where: T m,in is the coldest monthly temperature in the tunnel site, in °C; ΔT is the difference between Kelvin and Celsius, which is 273 °C; ρ avg is the air density of the tunnel site in the coldest month, in kg·m -3 , and its calculation formula is Among them, ρ in and ρ out are the air densities at the tunnel entrance and exit in the coldest month, in kg·m -3 , and the calculation formulas are and Among them, T m,0 and T m,L are the coldest monthly temperatures at the tunnel entrance and exit, respectively, in °C;

[0047] After ρ0 is obtained, the equivalent wind speeds v1' and v2' (in m·s) at the inlet and outlet of the tunnel after iteration are solved by using the ultra-clean pressure difference, thermal potential difference, and wind wall pressure difference. -1 ), the specific steps are as follows:

[0048] The calculation formulas for the ultra-clean pressure difference ΔP1 at the tunnel inlet section and the ultra-clean pressure difference ΔP'1 (both in Pa) at the outlet section are ΔP1 = 0.6ρ avg v a 2 and ΔP'1=0.6ρ avg v b 2 ;

[0049] The calculation formulas for the thermal potential difference ΔP2 at the tunnel entrance and the thermal potential difference ΔP'2 at the tunnel exit (both in Pa) are: and

[0050] The calculation formulas for the wind wall pressure difference ΔP3 at the tunnel entrance section and the wind wall pressure difference ΔP'3 at the exit section (both in Pa) are: and

[0051] Where: v a and v b The natural wind speed from the outside of the tunnel to the entrance and exit, respectively, in m·s -1 ; g is the acceleration due to gravity, unit is m·s -2; ΔH and ΔH' are the differences between the highest point in the tunnel and the entrance and exit of the tunnel, respectively, in meters;

[0052] according to and Calculate v'1 and v'2 with an accuracy of 0.1 m·s -1 ; Among them, λ r is the friction loss coefficient of the tunnel wall; ζ e is the tunnel portal loss coefficient; D is the tunnel hydraulic diameter, in m;

[0053] At this time, the solved v1' and v2' are used as the new v1 and v2, and T is solved again. cm (z), and this process is repeated until v1'=v1, v2'=v2, at which point the iterated v1, v2 and ρ0 are obtained;

[0054] Step 5: Based on the v1, v2 and ρ0 obtained after continuous iteration in step 4, the final value T of the axial distribution of the coldest month temperature in the cold zone tunnel is solved based on this value. cm '(z)(unit: °C). At this time, ρ=ρ0 is still used, and the tunnel depth is no longer the average depth of the entire tunnel length. Instead, we take the tunnel depth H(z) (in meters) at the depth z and calculate T s Replaced by the outer boundary temperature of the tunnel structure at a depth of z, that is, the temperature T at the radius r3 of the outer boundary of the tunnel structure at a depth of z s (z) (unit: °C), the calculation formula is as follows:

[0055] T s (z) = T c +[H(z)-R0-R1]K

[0056] At this time, the final value of the annual average temperature in the tunnel at depth z is T M The calculation formula of '(z) (unit: °C) is as follows:

[0057]

[0058] Where: L' M The final value of the annual average temperature in the tunnel is the depth L' of the boundary between the inlet and outlet sections. M , unit is m;

[0059] L' M The calculation formula is:

[0060]

[0061] Wherein: x is an independent variable, H(x) is the value after z in H(z) is replaced by x, H(Lx) is the value after z in H(z) is replaced by Lx; H'(z) is the tunnel depth at the depth z in the reverse direction from the exit to the entrance, in meters, and its calculation formula is H'(z) = H(Lz). When z is replaced by x, H'(x) = H(Lx);

[0062] The final value of the axial distribution of the coldest month temperature in the cold zone tunnel is obtained by solving the following formula: cm '(z):

[0063]

[0064] In the above technical solution, Where: ρ1, ρ2, ρ3 are the densities of the insulation layer, lining concrete, and surrounding rock, respectively, in kg·m -3 ; c1, c2, c3 are the specific heat capacities of the insulation layer, lining concrete, and surrounding rock, respectively, in J·kg -1 ℃ -1 .

[0065] In the above technical solution,

[0066] In the above technical solution, in step S5, T m,in Obtained through actual measurement.

[0067] In the above technical solution, in step S5, ρ' in and ρ' out Obtained by actual measurement or by empirical formula ρ' in =1.25e -0.0001H ',ρ' out =1.25e -0.0001H "Approximate calculation, H' and H" are the altitudes of the tunnel entrance and exit respectively, in meters. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a schematic diagram of the radial structure of the cold region tunnel in the present invention.

[0069] Figure 2 It is a schematic diagram of axial heat transfer in a cold region tunnel according to the present invention.

[0070] Figure 3 The present invention is a flow chart of the coupled calculation method of the temperature field in a cold region tunnel and the wind speed in the tunnel.

[0071] Figure 4 The actual value and the fitted value of the tunnel burial depth of the cold region tunnel selected in the present invention vary with the depth.

[0072] Figure 5 This is a comparison chart between the analytical calculation results and the measured values ​​of the coldest month axial air temperature in a cold region tunnel selected in the present invention. DETAILED DESCRIPTION

[0073] The present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0074] The present invention is based on the following assumptions:

[0075] (1) The cross section of the tunnel is circular;

[0076] (2) The tunnel is a straight line;

[0077] (3) The contact between the various structural layers of the tunnel is good, and the contact thermal resistance between the layers is ignored;

[0078] (4) In the tunnel structure, heat is transferred only in the radial direction, and the heat transferred in the axial direction is negligible;

[0079] (5) The air velocity in the tunnel remains constant;

[0080] (6) The temperature in the tunnel only changes along the axial direction of the tunnel, and the temperature difference in the radial direction is negligible.

[0081] Example 1

[0082] A method for predicting the axial distribution of the coldest monthly temperature in a tunnel in a cold region taking into account wind speed comprises the following steps:

[0083] Step S1, solving the radial temperature field of the cold region tunnel:

[0084] Step s11, taking a three-layer tunnel structure consisting of an insulation layer, lining concrete, and surrounding rock as an example, its schematic diagram is as follows Figure 1 As shown. The heat transfer differential equation in the radial direction is:

[0085]

[0086] In formula (1), r is the radius, in m; t is the time, in s; z is the depth, i.e., the distance between a certain point in the tunnel and the tunnel entrance, in m; j is the number of layers of the tunnel radial structure from the inside to the outside, when j is 1, 2, and 3, it represents the insulation layer, lining concrete, and surrounding rock, respectively; T j (r, t, z) is the radial temperature field of the cold zone tunnel, in °C; k j is the thermal diffusion coefficient of the jth layer material. When j is equal to 1, 2, and 3, k1, k2, and k3 are the thermal diffusion coefficients of the insulation layer, lining concrete, and surrounding rock, respectively, in m 2 ·s -1 .

[0087] The thermal diffusion coefficient k of the jth layer of material j The calculation formula is as follows:

[0088]

[0089] In formula (2): j is the thermal conductivity of the jth layer material. When j is equal to 1, 2, and 3, λ1, λ2, and λ3 are the thermal conductivity of the insulation layer, lining concrete, and surrounding rock, respectively, in W·m -1 ℃ -1 ρ j is the density of the jth layer of material. When j is equal to 1, 2, and 3, ρ1, ρ2, and ρ3 are the densities of the insulation layer, lining concrete, and surrounding rock, respectively, in kg·m -3 ;c j is the specific heat capacity of the jth layer material. When j is equal to 1, 2, and 3, c1, c2, and c3 are the specific heat capacities of the insulation layer, lining concrete, and surrounding rock, respectively. The unit is J·kg -1 ℃ -1 .

[0090] The boundary conditions are:

[0091]

[0092] T j (r,t,z)=T j+1 (r,t,z),r=r j ,j=1,2(4)

[0093]

[0094] T3(r,t,z)=T s ,r=r3(6)

[0095] In formulas (3) to (6), h is the convection heat transfer coefficient between the tunnel structure and the air, in W·m -2 ℃ -1 ; T air (t,z) is the temperature at the depth z in the tunnel at time t, in °C; r0, r1, r2, and r3 are the inner radius of the insulation layer, the interface radius between the insulation layer and the lining concrete, the interface radius between the lining concrete and the surrounding rock, and the radius of the surrounding rock where the temperature does not change with time when the radial depth reaches a certain value, that is, the outer boundary radius of the tunnel structure, all in m; T s is the outer boundary temperature of the tunnel structure at a depth of z, that is, the temperature at the radius r3 of the outer boundary of the tunnel structure, in °C;

[0096] T air The calculation formula for (t,z) is:

[0097]

[0098] In formula (7): T M (z) and T A (z) are the annual average and annual amplitude of the temperature in the tunnel at depth z, respectively, in °C; ω is the annual variation frequency, in s -1 , is the annual phase at depth z.

[0099] In order to facilitate calculation and improve calculation efficiency, the solution is performed under the condition that the tunnel burial depth is equivalent to the average burial depth of the entire tunnel. s The calculation formula is:

[0100]

[0101] In formula (8): T c is the temperature of the surrounding rock of the isothermal layer, in °C; is the average burial depth of the whole tunnel, in m; R0 is the influence depth of the tunnel surrounding rock temperature field, in m; R1 is the burial depth of the isothermal layer, in m; K is the geothermal gradient, in ℃·m -1 .

[0102] Step s12, using the superposition principle, the radial temperature field T j (r, t, z) is decomposed into the annual average temperature in the tunnel and the steady-state temperature field T under the influence of the temperature of the outer boundary of the tunnel structure. 1j (r, z) and transient temperature field T under the influence of annual temperature change 2j (r,t,z).

[0103] Step s13, solving the steady-state temperature field T 1j Steady-state temperature T at radius r0 inside the insulation layer (r,z) 11 (r0,z). Steady-state temperature field T 1j The heat transfer differential equation for (r,z) is as follows:

[0104]

[0105] The boundary conditions are shown in equations (10) to (13):

[0106]

[0107] T 1j (r,z)=T 1(j+1) (r,z),r=r j ,j=1,2 (11)

[0108]

[0109] T 13 (r,z)=T s ,r=r3 (13)

[0110] It is easy to get the solution of formula (9):

[0111] T 1j (r,z)=A 1j lnr+B 1j (14)

[0112] In formula (14): A 1j To B 1j are the coefficients used in the solution process.

[0113] Substituting equation (14) into the boundary conditions equations (10) to (13), and writing the resulting system of equations in matrix form, we can obtain:

[0114]

[0115] In formula (15): A 11 , B 11 , A 12 , B 12 , A 13 , B 13 are coefficients in the solution process;

[0116] Define the steady-state matrix S as formula (16):

[0117]

[0118] Applying the determinant reduction method and Cramer's rule, the intermediate parameter values ​​​​for calculation are shown in equations (17) to (20):

[0119]

[0120] Matrix S 11 , S 21 , S 31 , S 41 See equations (17) to (20):

[0121]

[0122]

[0123] Intermediate parameters of the calculation The calculation method of is shown in equations (25) and (26):

[0124]

[0125] Therefore, T 11 The calculation formula of (r0,z) is shown in formula (27):

[0126]

[0127] Step s14, solving the transient temperature field T 2j Transient temperature T at radius r0 inside the insulation layer in (r, t, z) 21 (r0,t,z). Transient temperature field T 2j The heat transfer differential equation of (r, t, z) is shown in equation (28):

[0128]

[0129] The boundary conditions are shown in equations (29) to (32):

[0130]

[0131] T 2j (r,t,z)=T 2(j+1) (r,t,z),r=r j ,j=1,2 (30)

[0132]

[0133] T 23 (r, t, z) = 0, r = r3 (32)

[0134] In formula (29): T v (t,z) is the annual variation of the temperature in the tunnel at depth z, and its expression is as follows:

[0135]

[0136] Assume that at the initial time t = 0, there is T 2j (r, t, z) = 0. Taking t as the independent variable, Laplace transform is performed on equations (29) to (32), and we get:

[0137]

[0138] U 2j (r,s,z)=U 2(j+1) (r,s,z),r=r j ,j=1,2(36)

[0139]

[0140] U 23 (r,s,z)=0,r=r3(38)

[0141] In formulas (34) to (38): U 2j (r,s,z),U v (s,z) and s are T 2j (r,t,z),T v (s,z) and t are the transformed functions and independent variables.

[0142] The solution of formula (34) is:

[0143]

[0144] In formula (39): A 2j To B 2j are the coefficients in the solution process; I0(·) and K0(·) are the first-kind 0th-order and second-kind 0th-order imaginary Bessel functions, respectively.

[0145] Substituting equation (39) into the boundary conditions equations (35) to (38), and writing the resulting equations in matrix form, we can obtain:

[0146]

[0147] In formula (40): A 21 , B 21 , A 22 , B 22 , A 23 , B 23 are coefficients in the solution process;

[0148] The definition of transient matrix S' is shown in formula (41):

[0149]

[0150] Using the determinant reduction method and Cramer's rule to solve, the intermediate parameter β 11 (r0,s,h),β 21 The calculation method of (r0,s,h) is shown in equations (42) and (43):

[0151]

[0152] Matrix S' 11 , S' 21 See equations (44) and (45):

[0153]

[0154] The calculation method of the intermediate parameter F1(r0,s,h) is shown in formula (46):

[0155]

[0156] Therefore, the transient temperature field U after Laplace transformation can be obtained: 2j Transient temperature U at radius r0 inside the insulation layer in (r, t, z) 21 The solution of (r0,t,z) is:

[0157] U 21 (r0,s,z)=F1(r0,s,h)U v (s,z)(47)

[0158] Using the inverse convolution transform method, we perform the Laplace inverse transform on equation (47), and we have:

[0159]

[0160] In formula (48): L -1 [·] represents the form after inverse Laplace transform, * represents convolution, f1(r0,t,h) represents the original function of F1(r0,s,h), F1(r0,iω,h) is the value after s in F1(r0,s,h) is replaced by iω; τ is an independent variable; Re(·) is the real part of the complex number.

[0161] Therefore, the transient temperature field T 2j Transient temperature T at radius r0 inside the insulation layer in (r, t, z) 21 The solution of (r0,t,z) is:

[0162]

[0163] Step s15, according to equations (27) and (49), the radial temperature field T of the cold region tunnel j The solution formula for the temperature T1(r0,t,z) at the inner radius r0 of the insulation layer at the time t with a depth of z is:

[0164]

[0165] Step S2, solving the axial temperature distribution of cold region tunnels:

[0166] Schematic diagram of axial heat transfer in tunnel Figure 2 In the figure, T0 is the temperature of the hole, T1(r0,t) is the temperature at the radius r0 inside the insulation layer, and q z It is the heat transferred between the surrounding rock and the gas in the tunnel.

[0167] The energy conservation equation of the microelement dz per unit length of air in the tunnel is as follows:

[0168]

[0169] In formula (51), ρ is the air density in the tunnel, in kg·m -3 ; c is the specific heat capacity of air, in J·kg -1 ℃ -1 ; v is the wind speed in the tunnel, in m·s -1 .

[0170] The temperature expression in the tunnel is written in complex form. According to formula (7), we have:

[0171]

[0172] Substituting equations (50) and (52) into equation (51), we have:

[0173]

[0174] Decomposing formula (53), we can get:

[0175]

[0176] After analysis and collation, we can get:

[0177]

[0178]

[0179] The boundary conditions are:

[0180] T M (z=0)=T M,in (58)

[0181] T A (z=0)=T A,in (59)

[0182] In formula (59): T M,in and T A,in They are the annual average and annual amplitude of the temperature at the tunnel entrance, in ℃.

[0183] Solving equations (56) and (57) yields:

[0184]

[0185] Therefore, according to formula (60), the process value of the annual average temperature in the tunnel at depth z is for:

[0186]

[0187] In formula (62): L M is the process value of the annual average temperature in the tunnel, the depth of the boundary between the inlet and outlet sections, in meters; TM,0 and T M,L are the annual average temperatures at the tunnel entrance and exit, respectively, in °C; h1 and h2 are the convection heat transfer coefficients between the tunnel structure and air at the tunnel entrance and exit, respectively, in W·m -2 ℃ -1 ; v1 and v2 are the wind speeds at the entrance and exit of the tunnel, respectively, in m·s -1 ; L is the tunnel length, in meters; when h = h1, When h=h2,

[0188] L M According to formula (63),

[0189]

[0190] According to formula (64), the annual amplitude value of the temperature in the tunnel at depth z is T A (z) is:

[0191]

[0192] In formula (64): T A (z) is the annual amplitude of the temperature in the tunnel at depth z, in °C; T A,0 and T A,L are the annual amplitudes of the temperatures at the tunnel entrance and exit, respectively, in °C; when h=h1 and s=iω, F1(r0,iω,h1)=F1(r0,s,h); when h=h2 and s=iω, F1(r0,iω,h2)=F1(r0,s,h); L A The depth of the boundary between the inlet and outlet sections of the annual temperature amplitude, in meters;

[0193] L A Determined by formula (65):

[0194]

[0195] Step S3, solving the axial distribution of the coldest month temperature in the cold region tunnel:

[0196] In current engineering practice, tunnels in seasonally frozen soil areas are mostly designed to resist freezing using the coldest month’s temperature. Therefore, without considering the phase change of the temperature distribution at different depths of the tunnel, the process value T of the axial distribution of the coldest month’s temperature in the cold region tunnel is cm (z) is:

[0197]

[0198] Step S4, solving the wind speed v'1 and v'2 of the inlet and outlet sections in the equivalent tunnel

[0199] In the calculation, it is necessary to obtain the air density value at the entrance and exit of the tunnel. If there are meteorological observation stations at both ends of the tunnel, the air density data obtained by on-site monitoring can be directly used for calculation. If there is no measured data, only when the altitude of the tunnel entrance and exit is known, the corresponding air density can be approximately calculated according to equations (67) and (68):

[0200] ρ' in =1.25e -0.0001H' (67)

[0201] ρ' out =1.25e -0.0001H” (68)

[0202] In formulas (61) and (62): ρ' in and ρ' out are the annual average air density at the tunnel entrance and exit, in kg·m -3 ; H' and H" are the altitudes of the tunnel entrance and exit, respectively, in meters. According to equations (63) and (64), the air density ρ at the tunnel entrance and exit in the coldest month is obtained: in and ρ out :

[0203]

[0204]

[0205] In formulas (63) and (64): T m,0 and T m,L are the coldest monthly temperatures at the tunnel entrance and exit, respectively, in °C; ΔT is the difference between Kelvin and Celsius, and its value is 273 °C.

[0206] Define ρ avg is the air density of the tunnel site in the coldest month, in kg·m -3 , and its calculation formula is:

[0207]

[0208] definition is the equivalent coldest monthly temperature in the tunnel, in °C, and its calculation formula is as follows:

[0209]

[0210] Assume that the air density ρ in the tunnel at each position is a constant. The air density ρ in the tunnel takes the value of the air density ρ0 in the tunnel in the coldest month, that is, ρ=ρ0, then in the coldest month:

[0211]

[0212] In formula (73): T m,in It is the coldest monthly temperature in the tunnel site area, in ℃, which can be obtained based on the measured value.

[0213] For tunnels without inclined shafts and vertical shafts, under the condition of natural ventilation, the reason for the air flow at the tunnel entrance is the atmospheric pressure difference, thermal potential difference and wind wall pressure difference at the tunnel entrances at both ends. The ultra-clean pressure difference and wind wall pressure difference can both be calculated using the natural wind speed outside the tunnel flowing towards the inlet and outlet.

[0214] Under the action of natural wind, the positive pressure formed in front of the mountain is or The negative pressure behind the mountain is or The calculation formulas for the ultra-clean pressure difference between the tunnel inlet and outlet are:

[0215] ΔP1=0.6ρ avg v a 2 (74)

[0216] ΔP'1=0.6ρ avg v b 2 (75)

[0217] The calculation formulas for the thermal potential difference between the tunnel entrance and exit sections are:

[0218]

[0219] The calculation formulas for the wind wall pressure difference between the tunnel entrance and exit sections are:

[0220]

[0221]

[0222] In formulas (74) to (79), ΔP1 and ΔP'1 are the ultra-clean pressure differences between the inlet and outlet sections of the tunnel, in Pa; ΔP2 and ΔP'2 are the thermal potential differences between the inlet and outlet sections of the tunnel, in Pa; ΔP3 and ΔP'3 are the wind wall pressure differences between the inlet and outlet sections of the tunnel, in Pa; v a and v b The natural wind speed from the outside of the tunnel to the entrance and exit, respectively, in m·s -1 ; g is the acceleration due to gravity, unit is m·s -2; ΔH and ΔH' are the differences between the highest point in the tunnel and the entrance and exit of the tunnel. When the tunnel entrance is the highest point in the tunnel, the value is 0. The unit is m. In the coldest month, the temperature in the tunnel is often higher than the ambient temperature. Therefore, the air density ρ0 in the tunnel in the coldest month is often less than the air density ρ in the tunnel area in the coldest month. avg , at this time, a "floating effect" will occur, and ΔP2 and ΔP'2 of the uphill section are greater than 0, while ΔP2 and ΔP'2 of the downhill section are 0.

[0223] According to the wind resistance formula, we have:

[0224]

[0225] In formulas (80) and (81): r is the friction loss coefficient of the tunnel wall; ζ e is the tunnel portal loss coefficient; D is the tunnel hydraulic diameter, in m; v'1 and v'2 are the equivalent inlet and outlet wind speeds in the tunnel after iterative update, in m·s -1 .

[0226] Step S5, iterative calculation and solution of the axial distribution of wind speed in the tunnel and the coldest month temperature in the cold zone tunnel:

[0227] The flowchart of iterative solution is as follows Figure 3 As shown. In the solution, it is first assumed that the wind speeds v1 and v2 at the entrance and exit of the tunnel are unknown. When the air density ρ0 in the tunnel in the coldest month is unknown, the steps S1 to S3 of the present invention are used to solve the axial distribution of the air temperature in the coldest month. In the calculation, in order to ensure the convenience of the calculation, L is solved by equations (63) and (65). M and L A When the air density changes slightly, the influence on the solution is very limited. At this time, the air density ρ in the tunnel can be taken as the annual average value of the air density in the tunnel site area ρ' avg (Unit: kg·m 3 ) is calculated, and the calculation formula is shown in formula (82); in addition, according to formula (83), h1 and h2 can be calculated using v1 and v2.

[0228]

[0229] h1=3.36v1+6.32, h2=3.36v2+6.32(83)

[0230] After that, the calculation steps of equations (67) to (73) in step S4 are executed, and the terms that finally contain only one unknown variable, namely ρ0, are substituted into equation (73) to calculate the air density ρ0 in the tunnel in the coldest month, and the result is accurate to 0.001 kg·m -3After obtaining the value of ρ0, the thermal potential difference in the tunnel is calculated by using equations (76) and (77) in step S4. The atmospheric pressure difference and wind wall pressure difference obtained by equations (74), (75), (78) and (79) are combined to solve v1' and v2' according to equations (80) and (81). The results are accurate to 0.1 m·s -1 . Use the solved v1', v2' and ρ0 as the new v1, v2 and ρ0, and solve T again. cm (z), and this process is repeated until v1'=v1, v2'=v2, at which point the iterative wind speeds v1 and v2 of the inlet and outlet sections and the air density ρ0 in the tunnel in the coldest month are obtained;

[0231] Step S6, based on v1, v2 and ρ iteratively calculated in step S5, and according to the steps in S2 and S3, the final value T of the axial distribution of the coldest month temperature in the cold zone tunnel is solved. cm '(z). The tunnel depth is no longer the average depth of the entire tunnel length. Instead, the tunnel burial depth H(z) at depth z is taken, and the outer boundary temperature of the tunnel structure is calculated using formula (84):

[0232] T s (z) = T c +[H(z)-R0-R1]K (84)

[0233] In formula (84): T s (z) is the outer boundary temperature of the tunnel structure at a depth of z, that is, the temperature at a radius r3 of the outer boundary of the tunnel structure at a depth of z, in °C.

[0234] At this time, in steps S1 to S3, T s Replace with T s (z), then equation (56) becomes:

[0235]

[0236] Solve equation (85) and substitute equation (84) to obtain:

[0237]

[0238] In formula (86): T M '(z) is the final value of the annual average temperature in the tunnel at a depth of z, in °C; x is an independent variable; H(x) is the value after z in H(z) is replaced by x.

[0239] T M '(z) is shown in the following formula:

[0240]

[0241] In formula (87): L' M To finally solve the depth of the demarcation point between the inlet and outlet sections of the mid-year average temperature, the unit is m; the tunnel burial depth H'(x) at the reverse depth z from the outlet to the inlet is defined as follows:

[0242] H'(x)=H(Lx)(88)

[0243] In formula (88), H(Lx) is the value obtained by replacing z in H(z) with Lx.

[0244] At this time, L' M The calculation formula is:

[0245]

[0246] Therefore, the final value of the annual average temperature in the cold zone tunnel T is solved by equations (87) and (64) respectively: M '(z) and annual amplitude value T A (z), and then use formula (90) to calculate the final value of the axial distribution of the coldest month temperature in the cold region tunnel T cm '(z):

[0247]

[0248] Example 2

[0249] The Altun Mountain Highway Tunnel is located in Aksai Kazakh Autonomous County, Jiuquan City, Gansu Province. It is a key project on the Liuyuan to Golmud National Highway. The lengths of the left and right lines of the tunnel are 7525m and 7527m respectively. The tunnel length is 7527m. The altitudes of the entrance and exit are 3201m and 3347m respectively. The tunnel is a single slope uphill section with a slope of 1.95% from the entrance to the exit. During the solution process, the calculation was performed with 1000m and 1200m of insulation layers laid at the entrance and exit respectively. The geothermal gradient K is taken as 0.015℃·m -1 The burial depth of the isothermal layer R1 and the influence depth of the temperature field of the tunnel surrounding rock R0 are both taken as 10m. The inner radius of the insulation layer r0, the interface radius of the insulation layer and the lining concrete r1, the interface radius of the lining concrete and the surrounding rock r2 and the outer boundary radius of the tunnel structure r3 are taken as 5.38m, 5.43m, 5.83m and 13m respectively. The hydraulic diameter of the tunnel D is taken as 10.76m. The temperature of the surrounding rock of the isothermal layer T c Take 1℃, and the specific heat capacity c of air as 1000J·kg -1 ℃ -1 ; Annual average temperature at tunnel inlet T M,0 Take 1.6℃ as the annual average temperature at the tunnel exit T M,L Take 1.2℃, the annual amplitude value of the tunnel inlet temperature is TA,0 Take 10.6℃, the annual amplitude value of the tunnel exit temperature T A,L Take 7.1℃; the coldest monthly temperature at the tunnel entrance is T m,0 The coldest monthly temperature at the outlet is T m,L is -5.8℃; the natural wind speed v from the outside of the tunnel to the inlet and outlet a and v b 0.6m·s -1 and 0.5 m·s -1 .

[0250] The tunnel structure consists of three layers from the inside to the outside: insulation layer, lining concrete, and surrounding rock. The thermal conductivity coefficients λ1, λ2, and λ3 of the three layers are 0.04 W·m -1 ℃ -1 , 1.80W·m -1 ℃ -1 and 2.70W·m -1 ℃ -1 The densities ρ1, ρ2, and ρ3 of the three are 55 kg·m -3 , 2500kg·m -3 and 2400kg·m -3 The specific heat capacities c1, c2, and c3 of the three are 1200 J·kg -1 ℃ -1 、970J·kg -1 ℃ -1 and 1200 J·kg -1 ℃ -1 In the wind resistance formula, the tunnel wall friction loss coefficient λ r Take 0.02, tunnel opening loss coefficient ζ e Take 0.6.

[0251] The variation of the buried depth along the Altun Mountain Tunnel and the fitting function are shown in the figure below. Figure 4 As shown, it can be seen that the average burial depth of the Altun Mountain highway tunnel is 290m. In addition, the fitting function of the tunnel burial depth H(z) changing with the depth z is:

[0252] H(z)=-5.5256×10 -13 z 4 +9.7117×10 -9 z 3 -8.6709×10 -5 z 2 +0.3390z-24.4309

[0253] The method proposed in the present invention is used for calculation. Initially, the wind speed at the entrance and exit of the tunnel is 2 m·s -1The number of iterative calculations and the results obtained each time are as follows:

[0254] In the first calculation, the wind speed v1 and v2 at the entrance and exit of the tunnel are both 2.0 m·s -1 , the depth L of the boundary between the annual average temperature inlet section and the outlet section M The depth L of the boundary between the inlet and outlet sections of the annual temperature fluctuation is 3123m. A The air density in the tunnel in the coldest month is ρ0, which is 0.918 kg·m -3 , equivalent coldest monthly temperature in the tunnel The equivalent wind speeds v'1 and v'2 of the tunnel entrance and exit sections after iterative update are 1.6 m·s -1 and 0.2 m·s -1 ;

[0255] In the second calculation, the wind speeds v1 and v2 at the tunnel entrance and exit are 1.6 m·s -1 and 0.2 m·s -1 , the depth L of the boundary between the annual average temperature inlet section and the outlet section M The depth L of the boundary between the inlet and outlet sections of the annual temperature fluctuation is 6189 m. A The air density in the tunnel in the coldest month is ρ0, which is 0.918 kg·m -3 , equivalent coldest monthly temperature in the tunnel The equivalent wind speeds v'1 and v'2 of the tunnel entrance and exit sections after iterative update are 1.7 m·s -1 and 0.2 m·s -1 ;

[0256] In the third calculation, the wind speeds v1 and v2 at the entrance and exit of the tunnel are 1.7 m·s -1 and 0.2 m·s -1 , the depth L of the boundary between the annual average temperature inlet section and the outlet section M The depth L of the boundary between the inlet and outlet sections of the annual temperature fluctuation is 6227 m. A The air density in the tunnel in the coldest month is ρ0, which is 0.917 kg·m -3 , equivalent coldest monthly temperature in the tunnel The equivalent wind speeds v'1 and v'2 of the tunnel entrance and exit sections after iterative update are 1.7 m·s -1 and 0.2 m·s -1 In this calculation, the iteratively updated equivalent wind speeds v'1 and v'2 of the tunnel entrance and exit sections are consistent with the wind speeds v1 and v2 of the tunnel entrance and exit sections, respectively, and the calculation ends.

[0257] The wind speeds v1 and v2 at the entrance and exit of the tunnel are 1.7 m·s -1 and 0.2 m·s -1 , the air density ρ0 in the tunnel in the coldest month is taken as 0.917 kg·m -3 , the predicted and measured values ​​of the coldest month temperature are as follows Figure 5 It can be seen that the predicted value of the axial distribution of the coldest month temperature in the cold zone tunnel is relatively close to the measured value; in addition, the air flow in the tunnel mainly flows from the inlet to the outlet, resulting in significant asymmetry in the temperature distribution in the tunnel.

[0258] The above is only a preferred embodiment of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for predicting the axial distribution of the coldest monthly temperature in a tunnel in a cold region taking into account wind speed, characterized in that: The following steps are involved: Step 1: Solve for intermediate parameters and intermediate parameters α 11 , α 21 , α 31 and α 41 All are intermediate parameters, among which: The matrix S is: Matrix S 11 , S 21 , S 31 , S 41 They are: Where: h is the convection heat transfer coefficient between the tunnel structure and the air, in W·m -2 ℃ -1 ; λ1, λ2, λ3 are the thermal conductivity of the insulation layer, lining concrete, and surrounding rock, respectively, and the unit is W·m -1 ℃ -1 ; r0, r1, r2, r3 are respectively the inner radius of the insulation layer, the interface radius between the insulation layer and the lining concrete, the interface radius between the lining concrete and the surrounding rock, and the radius of the surrounding rock whose temperature does not change with time when the radial depth reaches a certain value, i.e. the outer boundary radius of the tunnel structure, all in m; Solve the intermediate parameters F1(r0,s,h), k1 is the thermal diffusion coefficient of the insulation layer, in m 2 ·s -1 ; I0(·) and K0(·) are the first and second type 0th order imaginary Bessel functions, respectively; s is the intermediate parameter, s = iω, ω is the annual variation frequency, unit is s -1 ; i is the imaginary unit; β 11 (r0,s,h) and β 21 (r0,s,h) are intermediate parameters, where: The matrix S' is: Matrix S' 11 , S' 21 They are as follows: Where: I1(·) and K1(·) are the first-order and second-order Bessel functions of imaginary variables of the first kind, respectively; k2 and k3 are the thermal diffusion coefficients of lining concrete and surrounding rock, respectively, in m 2 ·s -1 ; Step 2, solving the axial temperature field of the cold region tunnel; Solve the process value of the annual average temperature in the tunnel at depth z The unit is °C, where z is the depth in meters: Where: L M is the process value of the annual average temperature in the tunnel, the depth of the boundary between the inlet and outlet sections, in meters; h1 and h2 are the convection heat transfer coefficients between the tunnel structure and the air at the inlet and outlet sections of the tunnel, in W·m -2 ℃ -1 , where h1=3.36v1+6.32, h2=3.36v2+6.32; v1 and v2 are the wind speeds at the entrance and exit of the tunnel, respectively, in m·s -1 ; T M,0 and T M,L are the annual average temperatures of the tunnel entrance and exit, respectively, in °C; L is the tunnel length, in m; ρ is the air density in the tunnel, in kg·m -3 ; c is the specific heat capacity of air, in J·kg -1 ℃ -1 ; are all intermediate parameters. When h=h1, When h=h2, T s is the outer boundary temperature of the tunnel structure, that is, the temperature at the outer boundary radius r3 of the tunnel structure, in °C, which can be calculated by the following formula: Where: T c The temperature of the surrounding rock of the isothermal layer, in degrees Celsius. The isothermal layer refers to the area where the temperature no longer changes with time and remains unchanged all year round when reaching a certain depth from the surface. is the average burial depth of the whole tunnel, in m; R0 is the influence depth of the tunnel surrounding rock temperature field, in m; R1 is the burial depth of the isothermal layer, in m; K is the geothermal gradient, in ℃·m -1 ; L M Determined by the following formula: Solve the annual amplitude value T of the temperature in the tunnel at depth z A (z), unit is °C: Where: L A T is the annual amplitude of the temperature in the tunnel, and the depth of the boundary between the inlet and outlet sections, in meters; A,0 and T A,L are the annual amplitude values ​​of the air temperature at the tunnel entrance and exit, respectively, in °C; Re(·) is the real part of the imaginary number; F1(r0,iω,h1) and F1(r0,iω,h2) are intermediate parameters. When h=h1 and s=iω, F1(r0,iω,h1)=F1(r0,s,h); when h=h2 and s=iω, F1(r0,iω,h2)=F1(r0,s,h); L A Determined by the following formula: Step 3: Calculate the process value T of the axial distribution of the coldest month temperature in the cold zone tunnel cm (z), unit is °C: Among them: τ is an independent variable; Step 4, iterative calculation and solution of the axial distribution of wind speed in the tunnel and the coldest month temperature in the cold zone tunnel: Initially assume that the wind speeds v1 and v2 in the tunnel entrance and exit are unknown. When the air density ρ in the tunnel is unknown, use steps 1 to 3 to solve the process value T of the axial distribution of the coldest month temperature in the cold region tunnel. cm (z); where the air density ρ in the tunnel at this time is the air density ρ0 in the tunnel in the coldest month, in kg·m 3 , that is, ρ=ρ0; in solving L M and L A When ρ0=ρ' avg , ρ' avg is the annual average air density in the tunnel site, in kg·m -3 , and its calculation formula is ρ' in and ρ' out are the annual average air density at the tunnel entrance and exit, in kg·m -3 ; Solve for T cm (z), the equivalent coldest monthly temperature in the tunnel is calculated using the following formula The unit is ℃: Then the equivalent coldest monthly temperature in the tunnel, which finally contains only one unknown number ρ0, is Substitute the following formula and combine it with other parameter values ​​to calculate the air density ρ0 in the tunnel in the coldest month. The calculation result is accurate to 0.001 kg·m -3 : Where: T m,in is the coldest monthly temperature in the tunnel site, in °C; ΔT is the difference between Kelvin and Celsius, which is 273 °C; ρ avg is the air density of the tunnel site in the coldest month, in kg·m -3 , and its calculation formula is Among them, ρ in and ρ out are the air densities at the tunnel entrance and exit in the coldest month, in kg·m -3 , and the calculation formulas are and Among them, T m,0 and T m,L are the coldest monthly temperatures at the tunnel entrance and exit, respectively, in °C; After ρ0 is obtained, the equivalent wind speeds v1' and v2' in the tunnel entrance and exit sections after iteration are solved by using the ultra-clean pressure difference, thermal potential difference and wind wall pressure difference. The unit is m·s -1 , the specific steps are as follows: The ultra-clean pressure difference ΔP1 at the tunnel inlet and the ultra-clean pressure difference ΔP'1 at the outlet are both in Pa, and the calculation formulas are ΔP1 = 0.6ρ avg v a 2 and ΔP'1=0.6ρ avg v b 2 ; The thermal potential difference ΔP2 of the tunnel entrance section and the thermal potential difference ΔP'2 of the tunnel exit section are both in Pa and are calculated by the following formulas: and The wind wall pressure difference ΔP3 at the tunnel entrance and the wind wall pressure difference ΔP'3 at the exit are both in Pa and are calculated as follows: and Where: v a and v b The natural wind speed from the outside of the tunnel to the entrance and exit, respectively, in m·s -1 ; g is the acceleration due to gravity, unit is m·s -2 ; ΔH and ΔH' are the differences between the highest point in the tunnel and the entrance and exit of the tunnel, respectively, in meters; according to and Calculate v'1 and v'2 with an accuracy of 0.1 m·s -1 ; Among them, λ r is the friction loss coefficient of the tunnel wall; ζ e is the tunnel portal loss coefficient; D is the tunnel hydraulic diameter, in m; At this time, the solved v1' and v2' are used as the new v1 and v2, and T is solved again. cm (z), and this process is repeated until v1'=v1, v2'=v2, at which point the iterated v1, v2 and ρ0 are obtained; Step 5: Based on the v1, v2 and ρ0 obtained after continuous iteration in step 4, the final value T of the axial distribution of the coldest month temperature in the cold zone tunnel is solved based on this value. cm '(z), unit is ℃, at this time, ρ=ρ0 is still taken, and the tunnel depth is no longer the average depth of the entire tunnel length Instead, we take the tunnel depth H(z) at depth z in meters and calculate T in the step s Replaced by the outer boundary temperature of the tunnel structure at a depth of z, that is, the temperature T at the radius r3 of the outer boundary of the tunnel structure at a depth of z s (z), in °C, is calculated as follows: T s (z)=T c +[H(z)-R0-R1]K At this time, the final value of the annual average temperature in the tunnel at depth z is T M The calculation formula of '(z) is as follows: Where: L' M The final value of the annual average temperature in the tunnel is the depth L' of the boundary between the inlet and outlet sections. M , unit is m; L' M The calculation formula is: Wherein: x is an independent variable, H(x) is the value after z in H(z) is replaced by x, H(Lx) is the value after z in H(z) is replaced by Lx; H'(z) is the tunnel depth at the depth z in the reverse direction from the exit to the entrance, in meters, and its calculation formula is H'(z) = H(Lz). When z is replaced by x, H'(x) = H(Lx); The final value of the axial distribution of the coldest month temperature in the cold zone tunnel is obtained by solving the following formula: cm '(z):

2. The method for predicting the axial distribution of the coldest monthly temperature in a cold region tunnel taking into account wind speed according to claim 1, characterized in that: Where: ρ1, ρ2, ρ3 are the densities of the insulation layer, lining concrete, and surrounding rock, respectively, in kg·m -3 ; c1, c2, c3 are the specific heat capacities of the insulation layer, lining concrete, and surrounding rock, respectively, in J·kg -1 ℃ -1 .

3. The method for predicting the axial distribution of the coldest monthly temperature in a cold region tunnel taking into account wind speed according to claim 1, characterized in that:

4. The method for predicting the axial distribution of the coldest monthly temperature in a cold region tunnel taking into account wind speed according to claim 1, characterized in that: In step S5, T m,in Obtained through actual measurement.

5. The method for predicting the axial distribution of the coldest monthly temperature in a cold region tunnel taking into account wind speed according to claim 1, characterized in that: In step S5, ρ' in and ρ' out Obtained by actual measurement or by empirical formula ρ' in =1.25e -0.0001H' , ρ' out =1.25e -0.0001H” Approximately calculated, H' and H" are the altitudes of the tunnel entrance and exit, respectively, in meters.

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