A method for predicting the axial distribution of the coldest month air temperature in cold-region tunnels considering wind speed

Abstract

The present invention discloses a method for predicting the axial distribution of the coldest month's air temperature in a cold region tunnel taking into account wind speed. The method first solves the axial temperature field of the cold region tunnel, then solves the axial distribution of the coldest month's air temperature in the cold region tunnel, and then solves the wind speed in the tunnel. The wind speed in the tunnel and the axial distribution of the coldest month's air temperature in the cold region tunnel are iteratively calculated and solved, and the axial distribution of the coldest month's air temperature in the cold region tunnel is predicted. The predicted value is relatively close to the measured value, and the method has good engineering application prospects.

Description

Technical Field

[0001] The present 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 within tunnels in cold regions significantly influences the occurrence and development of frost damage. Controlling the temperature distribution within tunnels through various means is currently a key approach to preventing and controlling frost damage in tunnels. A coupling effect exists between the temperature and air flow within tunnels in cold regions. On the one hand, the air temperature distribution within the tunnel affects the thermal potential within the tunnel, which in turn influences wind speed. On the other hand, wind speed determines the intensity of convective heat exchange between the air and the tunnel structure, as well as the flow rate of low-temperature air entering the tunnel during cold seasons, significantly impacting the temperature environment within the tunnel. Therefore, the influence of ventilation cannot be ignored if accurate temperature distribution within tunnels is to be achieved.

[0003] In the current research on the influence of ventilation on temperature distribution in cold-region tunnels, many scholars have achieved a series of results. In the article "Analytical Solution of Temperature Field in Cold-Region Tunnels Considering Lining and Insulation Layer" published in the "Chinese 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 "Study on Temperature Field in Cold-Region Tunnels Influenced by Thermal Potential Difference and Net Pressure Difference at the 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 "Study 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 in 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 airtemperature 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 calculation 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-region tunnels taking into account wind speed, so as to quantify the impact of the ventilation process in the tunnel on the temperature distribution, thereby solving the temperature distribution status 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 the wind speed, in response to the existing technology that only solves the temperature field 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 month's air temperature in a cold region tunnel 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 are all 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 coefficients of the insulation layer, lining concrete, and surrounding rock, respectively, all in W·m -1 ℃ -1 r0, r1, r2, and 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 where the 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, unit is 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 imaginary Bessel functions, respectively; k2 and k3 are the thermal diffusivities of the 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 convective heat transfer coefficients between the tunnel structure and the air at the inlet and outlet sections, respectively, 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 at 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, unit is 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 in the isothermal layer, in degrees Celsius. The isothermal layer refers to the area from the surface to a certain depth where the temperature no longer changes with time and remains unchanged throughout the year. is the average burial depth of the entire tunnel, in meters; R0 is the influence depth of the tunnel surrounding rock temperature field, in meters; R1 is the burial depth of the isothermal layer, in meters; K is the geothermal gradient, in degrees Celsius·m -1 ;

[0030] L M Determined by the following formula:

[0031]

[0032] Calculate 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, the depth of the boundary between the inlet and outlet sections, in meters; A,0 and T A,Lare the annual amplitudes 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 sections 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 (unit: 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 area, 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, respectively, in kg·m -3 ;

[0042] Solve to get 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 only contains 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 entrance and the ultra-clean pressure difference ΔP'1 at the tunnel exit (both in Pa) 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 of the tunnel entrance section and the thermal potential difference ΔP'2 of the tunnel exit section (both in Pa) are and

[0050] The calculation formulas for the wind wall pressure difference ΔP3 at the tunnel entrance and the wind wall pressure difference ΔP'3 at the tunnel exit (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 tunnel entrance and exit altitudes, 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 tunnel wall friction loss coefficient; e is the tunnel portal loss coefficient; D is the tunnel hydraulic diameter, in m;

[0053] At this time, the solved v1', v2' are used as the new v1, v2, and T is solved again. cm (z), and so on and so forth 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 is ℃). In this case, 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 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 outer boundary radius r3 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] Where x is an independent variable, H(x) is the value obtained by replacing z in H(z) with x, and H(Lx) is the value obtained by replacing z in H(z) with Lx. H'(z) is the tunnel depth at a depth of z in the reverse direction from the exit to the entrance, in meters, and is calculated as 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, and the unit is 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 This is a schematic diagram of axial heat transfer in cold region tunnels according to the present invention.

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

[0071] Figure 4 The actual value and 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 of the analytical calculation results and measured values ​​of the axial air temperature in the coldest month in a cold region tunnel selected in the present invention. DETAILED DESCRIPTION

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

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

[0075] (1) The tunnel cross section 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 negligible;

[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 changes only 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 month's air temperature in a cold region tunnel taking into account wind speed comprises the following steps:

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

[0084] Step s11, taking the three-layer tunnel structure consisting of 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 meters; t is the time, in seconds; z is the depth, i.e., the distance between a certain point in the tunnel and the tunnel entrance, in meters; j is the number of layers in the tunnel radial structure from the inside to the outside, where j is 1, 2, and 3, representing 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 diffusivity of the jth layer material. When j is equal to 1, 2, and 3, k1, k2, and k3 are the thermal diffusivity of the insulation layer, lining concrete, and surrounding rock, respectively. The unit is m 2 ·s -1 .

[0087] The thermal diffusivity k of the jth layer 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 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 meters; T s is the outer boundary temperature of the tunnel structure at a depth of z, that is, the temperature at the outer boundary radius r3 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 mean and annual amplitude values ​​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 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 entire tunnel, in meters; R0 is the influence depth of the tunnel surrounding rock temperature field, in meters; R1 is the burial depth of the isothermal layer, in meters; K is the geothermal gradient, in degrees Celsius·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 changes 2j (r,t,z).

[0103] Step s13, solve 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 at (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 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 used 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 formulas (25) and (26):

[0124]

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

[0126]

[0127] Step s14, solve 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, perform Laplace transform on equations (29) to (32) and obtain:

[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 used 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, 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 can be obtained 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 is j The solution formula for the temperature T1(r0,t,z) at the inner radius r0 of the insulation layer at 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, q z It is the heat transferred between the surrounding rock and the gas in the tunnel.

[0167] The energy conservation equation of the infinitesimal volume 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, unit is 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 are the annual mean and annual amplitude of the air temperature at the tunnel entrance, respectively, in °C.

[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 The depth of the boundary between the inlet and outlet sections of the tunnel is measured in meters.M,0 and T M,L are the annual average temperatures at the tunnel entrance and exit, respectively, in °C; h1 and h2 are the convective heat transfer coefficients between the tunnel structure and the 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 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 air temperature 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, solve the axial distribution of the coldest month temperature in the cold region tunnel:

[0196] In current engineering practice, tunnels in seasonally frozen 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 cold-region tunnels is cm (z) is:

[0197]

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

[0199] In the calculation, it is necessary to obtain the air density values ​​at the tunnel entrance and exit. 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, respectively, in kg·m -3 H' and H" are the altitudes of the tunnel entrance and exit, respectively, in meters. The air density ρ at the tunnel entrance and exit in the coldest month is obtained according to equations (63) and (64): 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, which 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 is calculated as follows:

[0209]

[0210] Assume that the air density ρ in the tunnel at each location is a constant. The air density ρ in the tunnel is taken as 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 °C, 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 super-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 exit.

[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 entrance and exit sections 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 net pressure differences between the inlet and outlet sections of the tunnel, respectively, in Pa; ΔP2 and ΔP'2 are the thermal potential differences between the inlet and outlet sections of the tunnel, respectively, in Pa; ΔP3 and ΔP'3 are the wind wall pressure differences between the inlet and outlet sections of the tunnel, respectively, 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 altitudes, respectively. When the tunnel entrance is exactly the highest point in the tunnel, the value is 0, and 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 on the uphill section are greater than 0, while ΔP2 and ΔP'2 on the downhill section are 0.

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

[0224]

[0225] In formulas (80) and (81): r is the tunnel wall friction loss coefficient; e is the tunnel portal loss coefficient; D is the tunnel hydraulic diameter, in m; v'1 and v'2 are the equivalent wind speeds at the inlet and outlet of 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 formulas (63) and (65). M and L A Since the small change of air density has a very limited impact on the solution, the air density ρ in the tunnel can be taken as the annual average value of the air density in the tunnel 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, execute the calculation steps from (67) to (73) in step S4, and substitute the terms that ultimately contain only one unknown variable, ρ0, into (73) to calculate the air density ρ0 in the tunnel in the coldest month, with the result accurate to 0.001 kg·m -3After obtaining the value of ρ0, the thermal potential difference in the tunnel is calculated 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 so on and so forth 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 obtained by iterative calculation in step S5, solve the final value T of the axial distribution of the coldest month temperature in the cold zone tunnel according to the steps in S2 and S3. cm '(z). The tunnel depth is no longer the average depth of the entire tunnel length. Instead, the tunnel depth H(z) at the 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 depth 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 after z in H(z) is replaced by 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 entrance and exit are at an altitude of 3201m and 3347m respectively. The tunnel is a single-slope uphill section with a gradient 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 depth of the isothermal layer R1 and the depth of influence 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 1000 J·kg -1 ℃ -1 ; Annual average temperature at tunnel entrance 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 TA,0 Take 10.6℃, the annual amplitude value of the tunnel outlet 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 The natural wind speed v from the outside of the tunnel to the entrance and exit is -5.8℃; a and v b 0.6 m·s -1 and 0.5 m·s -1 .

[0250] The tunnel structure consists of three layers from the inside out: 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 , 970 J·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 portal loss coefficient ζ e Take 0.6.

[0251] The variation of the buried depth along the Altun Mountain Tunnel and the fitting function are as follows: Figure 4 As shown, it can be seen that the average buried depth of the Alxa League Highway Tunnel is 290m. In addition, the fitting function of the tunnel buried 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 calculation method proposed in this invention is used. Initially, the wind speed at the entrance and exit of the tunnel is set to 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 tunnel entrance and exit are both 2.0 m·s -1 , the depth L of the boundary between the annual average temperature inlet and outlet sections M The depth L of the boundary between the inlet and outlet sections of the annual temperature amplitude is 3123m. A The air density in the tunnel in the coldest month is ρ0, which is 0.918 kg·m -3 , the equivalent coldest monthly temperature in the tunnel The equivalent wind speeds v'1 and v'2 at 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 and outlet sections M The depth L of the boundary between the inlet and outlet sections of the annual temperature amplitude is 6189m. A The air density in the tunnel in the coldest month is ρ0, which is 0.918 kg·m -3 , the equivalent coldest monthly temperature in the tunnel The equivalent wind speeds v'1 and v'2 at 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 tunnel entrance and exit are 1.7 m·s -1 and 0.2 m·s -1 , the depth L of the boundary between the annual average temperature inlet and outlet sections M The depth L of the boundary between the inlet and outlet sections of the annual temperature amplitude is 6227m. A The air density in the tunnel in the coldest month is ρ0, which is 0.917 kg·m -3 , the equivalent coldest monthly temperature in the tunnel The equivalent wind speeds v'1 and v'2 at 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 at the entrance and exit of the tunnel are consistent with the wind speeds v1 and v2 at the entrance and exit of the tunnel, 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 temperature in the coldest month in the cold region 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 a 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 principles 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 month's air temperature in a cold region tunnel 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 are all 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 coefficients of the insulation layer, lining concrete, and surrounding rock, respectively, all in W·m -1 ℃ -1 r0, r1, r2, and 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 where the 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, unit is 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 imaginary Bessel functions, respectively; k2 and k3 are the thermal diffusivities of the 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 convective heat transfer coefficients between the tunnel structure and the air at the inlet and outlet sections, respectively, 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 at 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, unit is 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 in the isothermal layer, in degrees Celsius. The isothermal layer refers to the area from the surface to a certain depth where the temperature no longer changes with time and remains unchanged throughout the year. is the average burial depth of the entire tunnel, in meters; R0 is the influence depth of the tunnel surrounding rock temperature field, in meters; R1 is the burial depth of the isothermal layer, in meters; K is the geothermal gradient, in degrees Celsius·m -1 ; L M Determined by the following formula: Calculate 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, the depth of the boundary between the inlet and outlet sections, in meters; A,0 and T A,L are the annual amplitudes 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 sections 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, and the unit is 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 area, 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, respectively, in kg·m -3 ; Solve to get T cm (z), the equivalent coldest monthly temperature in the tunnel is calculated using the following formula: Unit is ℃: Then the equivalent coldest monthly temperature in the tunnel, which only contains 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 solving for ρ0, the equivalent wind speeds v1' and v2' at the inlet and outlet of the tunnel after iterative update 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 entrance and the ultra-clean pressure difference ΔP'1 at the exit 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 as follows: and The wind wall pressure difference ΔP3 at the tunnel entrance and the wind wall pressure difference ΔP'3 at the tunnel 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 tunnel entrance and exit altitudes, 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 tunnel wall friction loss coefficient; 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 so on and so forth 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 °C, at this time we still take ρ=ρ0, and the tunnel depth is no longer the average depth of the entire tunnel length Instead, we take the tunnel depth H(z) at the depth z, in meters, and calculate T in the steps s Replaced by the outer boundary temperature of the tunnel structure at a depth of z, that is, the temperature T at the outer boundary radius r3 of the tunnel structure at a depth of z s (z), unit is °C, and its calculation formula is 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: Where x is an independent variable, H(x) is the value obtained by replacing z in H(z) with x, and H(Lx) is the value obtained by replacing z in H(z) with Lx. H'(z) is the tunnel depth at a depth of z in the reverse direction from the exit to the entrance, in meters, and is calculated as 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 month's temperature in a cold region tunnel considering 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, and the unit is 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 month's air 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 month's air temperature in a cold region tunnel taking into account wind speed according to claim 1, characterized in that: In step 5, T m,in Obtained through actual measurement.

5. The method for predicting the axial distribution of the coldest month's air temperature in a cold region tunnel taking into account wind speed according to claim 1, characterized in that: In step 5, 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.

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