A method for predicting axial temperature distribution in cold-region tunnels considering diurnal variation

Abstract

The invention discloses a method for predicting the axial temperature distribution of a tunnel in a cold region taking into account the daily variation process, comprising the following steps: step 1, solving the axial distribution of the annual average temperature in the tunnel, the axial distribution of the annual amplitude of the temperature in the tunnel, the axial distribution of the annual phase of the temperature in the tunnel, the axial distribution of the daily amplitude of the temperature in the tunnel and the axial distribution of the daily phase of the temperature in the tunnel; step 2, establishing an expression for the axial temperature distribution of the tunnel in the cold region. The prediction method of the invention has small calculation amount and high calculation efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of cold region tunnel engineering, and in particular to a method for predicting axial temperature distribution in cold region tunnels taking into account a daily variation process. Background Art

[0002] At present, in order to meet the needs of economic development in high-latitude regions such as Northeast my country, Northwest China, and North China, as well as high-altitude regions such as the Qinghai-Tibet Plateau, the construction of local transportation infrastructure has been rapidly promoted, and many highway tunnels and railway tunnels have been built. However, tunnel projects in these cold climate regions often face a series of frost damage problems, such as lining cracking, material degradation, freezing of drainage systems, ice accumulation in tunnels, etc., which seriously threaten the safety and comfort of driving and have a very adverse impact on the normal operation of tunnels. Temperature conditions are a necessary factor leading to frost damage. Current frost damage prevention and control measures mainly start from the temperature perspective, such as laying insulation layers, setting cold-proof doors, heating drainage ditches, etc., but the adoption of specific measures needs to be based on the known temperature distribution. Therefore, predicting and obtaining the temperature distribution in cold-region tunnels is a prerequisite for evaluating the frost damage situation and taking corresponding prevention and control measures.

[0003] In response to the problem of longitudinal distribution of temperature in cold region tunnels, many scholars have proposed corresponding analytical solutions. In 2008, TAKUMI et al. from Japan published an article titled "An estimation of inner temperatures at cold region tunnel for heat insulator design" in the Proceedings of Structural Engineering Symposium, applying the superposition principle and the energy conservation principle to obtain an analytical solution to the distribution of temperature in cold region tunnels along the depth direction, and proved the accuracy of the solution by comparing with the measured values. In 2010, Zhang Guozhu et al. published an article titled "Theoretical Solution of Axial and Radial Temperature Distribution in Cold Region Tunnels" in the Journal of Tongji University (Natural Science Edition), applying the superposition principle and the orthogonality and expansion theorem of Bessel characteristic functions, and obtained the axial and radial analytical solutions of the temperature field in cold region tunnels when only the tunnel structure is considered as the surrounding rock medium. In 2010, Xia Caichu et al. published an article titled "Analytical Solution of Temperature Field in Cold Region Tunnels Considering Lining and Insulation Layer" in the Chinese Journal of Rock Mechanics and Engineering. They applied the superposition principle and divided the cold region tunnel into a steady-state temperature field and a transient temperature field. They also used Laplace transform and inverse convolution transform methods to solve the transient temperature field. They obtained the analytical solution of the radial temperature field in the cold region tunnel considering the lining and insulation layer, and brought the radial solution result into the air energy equation in the tunnel to obtain the analytical solution of the axial distribution of temperature in the tunnel.

[0004] Although current theoretical research has achieved many results, the proposed theoretical analytical calculation method does not take into account the daily variation of temperature, which may ignore the frost damage in the tunnel caused by extreme low temperature weather outside. On the one hand, not considering the daily variation of temperature will overestimate the lowest temperature at different locations in the tunnel. On the other hand, it may underestimate the length of the low-temperature air outside the tunnel invading the tunnel, resulting in inadequate prevention and control engineering measures. Therefore, considering the daily variation of temperature is of positive significance for the prediction and early warning of frost damage in the tunnel and the adoption of corresponding prevention and control measures. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting axial air temperature distribution in cold-region tunnels taking into account diurnal variation processes in order to address the technical defects existing in the prior art.

[0006] The technical solution adopted to achieve the purpose of the present invention is:

[0007] A method for predicting axial temperature distribution in cold-region tunnels taking into account daily variation processes comprises the following steps:

[0008] Step 1: Solve the axial distribution of the annual average temperature in the tunnel , Axial distribution of annual amplitude of temperature in tunnel , Axial distribution of annual phase of temperature in tunnel , Axial distribution of daily amplitude of temperature in the tunnel Axial distribution of daily phase of temperature in the tunnel , is the depth, in m;

[0009] Step s1, solve the axial distribution of the annual average temperature in the tunnel :

[0010] (I);

[0011] In formula (I), is the convective heat transfer coefficient between the tunnel structure and the air in the tunnel, in units of , is the air density in the tunnel, in kg·m -3 , is the specific heat capacity of air, in J·kg -1 ℃ -1 , is the inner surface radius of the insulation layer, in m, is the wind speed in the tunnel, in m·s -1 , is the annual average temperature at the cave entrance, in °C;

[0012] In formula (I), For the intermediate parameters:

[0013] (II);

[0014] In formula (II), To go deeper The tunnel depth at is in meters. is an independent variable, For the general middle z Replace with y The value obtained later, The temperature of the surrounding rock in 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 influence depth of the tunnel surrounding rock temperature field, in m, is the burial depth of the isothermal layer, in m, is the geothermal gradient, in ℃×m -1 ;

[0015] In formula (I) and formula (II) and All are intermediate parameters. , , , , and All are intermediate parameters;

[0016] ;

[0017] Steady-state matrix as follows:

[0018] ;

[0019] Steady-state matrix , , , as follows:

[0020] ;

[0021] , , They are the thermal conductivity of the insulation layer, lining concrete, and surrounding rock, in units of W×m -1 ×℃ -1 ; , , They are the inner radius of the lining concrete, the inner radius of 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, that is, the outer boundary radius of the tunnel, in meters;

[0022] Step s2, solve the axial distribution of the annual amplitude of the temperature in the tunnel :

[0023] (III);

[0024] In formula (III), is the annual amplitude of the temperature at the tunnel entrance, in °C, is the real part of the complex number, is an intermediate parameter, when hour, , s is the intermediate parameter, is an imaginary unit, is the annual frequency of temperature, ;

[0025] (IV);

[0026] In formula (IV), , , is the intermediate parameter, , ;

[0027] Transient Matrix as follows:

[0028] ;

[0029] Transient Matrix as follows: ;

[0030] Transient Matrix as follows:

[0031] ;

[0032] , , are the densities of the insulation layer, lining concrete, and surrounding rock, in kg·m -3 , are the specific heat capacities of the insulation layer, lining concrete, and surrounding rock, in J·kg -1 ℃ -1 , and The first category w Class II wThe Bessel function of the order imaginary quantity, w= 0 or 1;

[0033] Step s3, solve the axial distribution of the annual phase of temperature in the tunnel :

[0034] (V);

[0035] In formula (V), is the imaginary part of the complex number, is the annual phase of temperature at the cave entrance;

[0036] Step s4, solve the axial distribution of the daily amplitude of the temperature in the tunnel :

[0037] (VI);

[0038] In formula (VI), is the daily amplitude of the temperature at the tunnel entrance, in °C; is the real part of a complex number, when hour, , is the daily frequency of temperature, ;

[0039] Step s5, solve the axial distribution of the daily phase of the temperature in the tunnel :

[0040] (VII);

[0041] In formula (VII), is the daily phase of temperature at the cave entrance;

[0042] Step 2: Establish the axial temperature distribution of cold-region tunnels The expression is:

[0043] (VIII);

[0044] In formula (VIII), , , , and All obtained from step 1.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. The present invention takes into account the effect of daily temperature changes and gives the axial distribution of the annual average temperature in the tunnel. , Axial distribution of annual amplitude of temperature in tunnel , Axial distribution of annual phase of temperature in tunnel , Axial distribution of daily amplitude of temperature in the tunnel Axial distribution of daily phase of temperature in the tunnel The calculation method can obtain a complete analytical solution for the temperature distribution;

[0047] 2. The present invention proposes a prediction method for the influence of daily temperature changes on the axial distribution of temperature in the tunnel, that is, adding the fluctuation of a sinusoidal function with a daily period to the boundary conditions, and the daily variation of the temperature in the tunnel under this influence can be obtained by quantitative calculation, thereby calculating the instantaneous minimum temperature in the tunnel during the year, the maximum freezing intrusion length and other data, providing a basis for the prediction and early warning of freezing damage and the adoption of prevention and control measures;

[0048] 3. The present invention introduces the calculation method of Laplace transform and inverse convolution transform into the solution process of radial transient temperature field, which greatly reduces the amount of calculation and improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a theoretical derivation flow chart of the present invention.

[0050] Figure 2 It is a schematic diagram of the radial structure of the cold region tunnel in the present invention.

[0051] Figure 3 It is a schematic diagram of the heat exchange process between the tunnel structure and the air in the axial direction of the cold region tunnel in the present invention.

[0052] Figure 4 This is a comparison chart between the actual measured value and the analytical value of the annual average axial temperature of cold-region tunnels selected in the present invention.

[0053] Figure 5 This is a comparison chart between the measured values ​​and the analytical values ​​of the annual amplitude of the axial temperature in cold-region tunnels selected in the present invention.

[0054] Figure 6 This is a comparison chart between the measured values ​​and the analytical values ​​of the daily amplitude of the annual average temperature in the axial direction of cold-region tunnels selected in the present invention. DETAILED DESCRIPTION

[0055] 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.

[0056] Example 1

[0057] A method for predicting axial temperature distribution in cold-region tunnels taking into account daily variation processes comprises the following steps:

[0058] Step S1, obtaining the required calculation parameters in the tunnel. The corresponding parameters include: the annual average temperature at the tunnel entrance , annual amplitude of temperature , annual phase of temperature , daily amplitude of temperature Daily phase of temperature , the convection heat transfer coefficient between the tunnel structure and the air in the tunnel , the density of the insulation layer , density of lining concrete , the density of surrounding rock , thermal conductivity of the insulation layer , Thermal conductivity of lining concrete Thermal conductivity of surrounding rock Specific heat capacity of the insulation layer Specific heat capacity of lining concrete Specific heat capacity of surrounding rock , the inner surface radius of the insulation layer , inner radius of lining concrete , inner radius of surrounding rock , Tunnel outer boundary radius , wind speed in the tunnel , the air density in the tunnel , specific heat capacity of air , tunnel depth , the surrounding rock temperature of the isothermal layer , the tunnel surrounding rock temperature field affects the depth , constant temperature layer burial depth , geothermal gradient ;

[0059] Step S2, decompose the radial temperature field of the tunnel. The radial structure of the tunnel is as follows: Figure 2 As shown in the figure, the radial temperature field of the cold zone tunnel is decomposed into the steady-state temperature field under the influence of the annual average temperature in the tunnel and the temperature at the radius of the outer boundary of the tunnel. , Transient temperature field under the influence of annual temperature changes Transient temperature field under the influence of daily temperature changes , a total of three temperature fields are solved and calculated separately, and the expression of the surface temperature inside the tunnel is obtained. z is the depth, in m, is the radius in m, is time, unit is s;

[0060] Step S3, first solve the depth under steady-state conditions z、 Inner surface radius of insulation layer Temperature .

[0061] According to Fourier's law of heat conduction, the steady-state heat transfer differential equation in cylindrical coordinates is as follows:

[0062] (1);

[0063] In formula (1): Represents the number of layers of tunnel structural materials. When the values ​​are 1, 2, and 3, they represent insulation layer, lining concrete, and surrounding rock. is the thermal conductivity of the material, when 1, 2, and 3 respectively. They are the thermal conductivity of the insulation layer, lining concrete, and surrounding rock, in units of W×m -1 ×℃ -1 ; For the The density of the layer material is 1, 2, and 3 respectively. They are the densities of the insulation layer, lining concrete, and surrounding rock, in kg×m -3 ; For the The specific heat capacity of the layer material is 1, 2, and 3 respectively. They are the specific heat capacities of the insulation layer, lining concrete, and surrounding rock, in J×kg -1 ×℃ -1 .

[0064] The boundary conditions are as follows:

[0065] (2);

[0066] (3);

[0067] (4);

[0068] (5);

[0069] In formulas (2) to (5): is the convective heat transfer coefficient between the tunnel structure and the air in the tunnel, in units of W×m -2 ×℃ -1 ; They are the inner surface radius of the insulation layer, the inner radius of the lining concrete, the inner radius of 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, that is, the outer boundary radius of the tunnel, in meters; To go deeper , Tunnel outer boundary radius The temperature at the tunnel outer boundary is in °C; represents the axial distribution of the annual average temperature in the tunnel, that is, the depth is The annual average temperature at the location is in °C.

[0070] It is easy to get the solution of formula (1):

[0071] (6);

[0072] Where: and are the coefficients used in the solution process.

[0073] Substituting equation (6) into the boundary conditions equations (2) to (5) and writing the resulting system of equations in matrix form, we can obtain:

[0074] (7);

[0075] In formula (7): , , , , , are coefficients in the solution process.

[0076] Steady-state matrix S as follows:

[0077] (8);

[0078] Intermediate parameters , , and as follows:

[0079] ;

[0080] Steady-state matrix , , , as follows:

[0081]

[0082] Intermediate parameters and The calculation formula is as follows:

[0083] (13);

[0084] (14);

[0085] Therefore, the depth under steady-state conditions is , Inner surface radius of insulation layer Temperature As shown in formula (15):

[0086] (15);

[0087] Step S4, solving the depth under transient conditions affected by annual temperature changes: , Inner surface radius of insulation layer Temperature The depth under transient conditions affected by daily temperature changes is , Inner surface radius of insulation layer Temperature .

[0088] For convenience of representation, the transient temperature field is expressed as ,in According to Fourier's law of heat conduction, the transient heat transfer differential equation in cylindrical coordinates is as follows:

[0089] (16);

[0090] The boundary conditions are as follows:

[0091] (17);

[0092] (18);

[0093] (19);

[0094] (20);

[0095] In formula (17): is an intermediate parameter and is calculated as follows:

[0096] (twenty one);

[0097] In formula (21): x =2, To go deeper The annual amplitude of the temperature at the location is in °C. x =3, To go deeper The daily amplitude of the temperature at the location is in °C; x =2, is the annual change frequency, when x =3, is the daily change frequency, when x =2, To go deeper The axial distribution of the annual phase of temperature at x =3, To go deeper Axial distribution of daily phase of temperature at ;

[0098] when x=2, (twenty two);

[0099] when x =3, (twenty three);

[0100] In formulas (22) and (23): The depth of the tunnel is The axial distribution of the annual phase of temperature at The depth of the tunnel is The axial distribution of the daily phase of temperature at is the annual frequency of change, is the daily variation frequency, , The depth of the tunnel is Axial distribution of annual amplitude of temperature at , in °C, The tunnel depth is Axial distribution of the daily amplitude of air temperature at , in ℃.

[0101] Assume that the initial moment is When the transient temperature field .by As the independent variable, Laplace transform is performed on equations (16) to (20), and we get:

[0102] (twenty four);

[0103] (25);

[0104] (26);

[0105] (27);

[0106] (28);

[0107] In formulas (24) to (28): , and They are , and The transformed function and independent variables; is the intermediate parameter, or , i is an imaginary unit, is the annual frequency of temperature, is the daily frequency of temperature.

[0108] The solution of formula (24) is:

[0109] (29);

[0110] In formula (29): and is the coefficient in the solution process; and The first category w Class II w The Bessel function of the order imaginary quantity, w= 0 or 1.

[0111] Substituting equation (29) into the boundary conditions equations (25) to (28) and writing them in matrix form, we can obtain:

[0112] (30);

[0113] In formula (30): , , , , , are coefficients in the solution process.

[0114] Transient Matrix as follows:

[0115] (31);

[0116] Using the determinant reduction method and Cramer's rule to solve, the calculation method of the intermediate parameters is as follows:

[0117] (32);

[0118] (33);

[0119] In formulas (32) and (33): , is the intermediate parameter;

[0120] Transient Matrix as follows:

[0121] ;

[0122] Transient Matrix as follows:

[0123] ;

[0124] Intermediate parameters The calculation method is as follows:

[0125] (34);

[0126] In formula (34): is the intermediate parameter.

[0127] Therefore, the depth under transient conditions after Laplace transformation is z Inner surface radius of insulation layer Temperature The solution is:

[0128] (35);

[0129] In formula (35): The depth under transient conditions after Laplace transformation is z Inner surface radius of insulation layer Place temperature.

[0130] Using the inverse convolution transform method, we perform inverse Laplace transform on equation (35), and we get:

[0131] (36);

[0132] In formula (36): represents the form after inverse Laplace transformation, represents convolution, express The original function of for Lieutenant General s Replace with The value after is an independent variable, is the modulus of a complex number, and are the imaginary and real parts of the complex number, respectively.

[0133] Applying the auxiliary angle formula, the depth under transient conditions is Inner surface radius of insulation layer Temperature The solution is:

[0134] (37);

[0135] In formula (37): The depth under transient conditions is z Inner surface radius of insulation layer The temperature in °C.

[0136] Therefore, the depth under transient conditions affected by annual temperature changes is z , Inner surface radius of insulation layer Temperature The depth under transient conditions affected by daily temperature changes isz、 Inner surface radius of insulation layer Temperature for:

[0137] (38);

[0138] (39);

[0139] In formulas (38) and (39): The depth under transient conditions affected by annual temperature changes is z , Inner surface radius of insulation layer The temperature in °C, The depth under transient conditions affected by daily temperature changes is z、 Inner surface radius of insulation layer The temperature in °C, and Respectively middle s Replace with and The value calculated later.

[0140] Step S5, superimposing to obtain the temperature value expression of the inner surface of the tunnel in the cold region in the radial direction.

[0141] According to equations (15), (38) and (39), the temperature distributions obtained above are superimposed to obtain , Inner surface radius of insulation layer Temperature , which is expressed as follows:

[0142] (40);

[0143] In formula (40): is the inner surface radius of the insulation layer The axial distribution of temperature, i.e. the depth is , Inner surface radius of insulation layer The temperature in °C.

[0144] Step S6, the heat exchange process between the air and the tunnel structure in the axial direction of the tunnel is as follows: Figure 3 As shown in the figure, the energy equation of the microelement air in the tunnel is as follows:

[0145] (41);

[0146] In formula (41): is the wind speed in the tunnel, in m·s -1 ; is the density of the air in the tunnel, in kg·m-3 ; is the specific heat capacity of air, in J·kg -1 ℃ -1 ; represents the axial distribution of temperature in the tunnel, that is, the depth is The temperature at the location is expressed in °C and is as follows:

[0147] (42);

[0148] Substitute equations (40) and (42) into the energy equation (41) of the microelement air in the tunnel and decompose it into three equations as follows:

[0149] (43);

[0150] (44);

[0151] (45);

[0152] Step S7, solving to obtain the axial distribution of the annual average temperature in the tunnel.

[0153] Deep , Tunnel outer boundary radius Temperature The approximate calculation formula is:

[0154] (46);

[0155] In formula (46): is the temperature of the surrounding rock in the isothermal layer, in °C, is the influence depth of the tunnel surrounding rock temperature field, in m; is the burial depth of the isothermal layer, in m, is the geothermal gradient, in ℃× m -1 , To go deeper The tunnel burial depth at is in meters.

[0156] The boundary condition corresponding to formula (43) is:

[0157] (47);

[0158] In formula (47): is the annual average temperature at the cave entrance, in ℃.

[0159] Solving equation (43), we can obtain the axial distribution of the annual average temperature in the tunnel: :

[0160] (48);

[0161] In formula (48): is an intermediate parameter, and its calculation formula is shown in formula (49):

[0162] (49);

[0163] In formula (49): is an independent variable.

[0164] Step S8, solve the axial distribution of the annual amplitude and annual phase of the temperature in the tunnel. Rearranging equation (44) yields equation (50):

[0165] (50);

[0166] Therefore, we can get equations (51) and (52):

[0167] (51);

[0168] (52);

[0169] The boundary condition corresponding to formula (51) is:

[0170] (53);

[0171] In formula (53): is the annual phase of temperature at the cave entrance.

[0172] The boundary condition corresponding to formula (52) is:

[0173] (54);

[0174] In formula (54): is the annual amplitude of air temperature at the tunnel entrance, in °C.

[0175] Solving equation (51), we can obtain the axial distribution of the annual phase of the temperature in the tunnel: :

[0176] (55);

[0177] Solving equation (52), we can obtain the axial distribution of the annual amplitude of the temperature in the tunnel: :

[0178] (56);

[0179] In formula (56): is the annual amplitude of air temperature at the tunnel entrance, in °C.

[0180] Step S9, solve equation (45) to obtain the axial distribution of the daily amplitude and daily phase of the temperature in the tunnel. Similarly, the axial distribution of the daily phase of the temperature in the tunnel can be obtained: :

[0181] (57);

[0182] In formula (57): It is the daily phase of temperature at the cave entrance.

[0183] Axial distribution of daily amplitude of air temperature in tunnel as follows:

[0184] (58);

[0185] In formula (58): is the daily amplitude of air temperature at the tunnel entrance, in °C.

[0186] Step S10, superimpose the three temperature fields obtained. According to the solution results of equations (48), (55) to (58), the axial distribution of the temperature in the tunnel can be obtained: As shown in formula (42).

[0187] Example 2

[0188] The observation tunnel is located in the northeastern edge of the Qinghai-Tibet Plateau, in a seasonally frozen soil zone. The tunnel is a double-hole, one-way separated tunnel with a designed speed of 80 km×h. -1 The length is 7527 m, the inlet and outlet altitudes are 3213 m and 3360 m respectively, the single slope gradient is 1.95%, and the maximum burial depth is 530 m.

[0189] Data from the nearby municipal meteorological station show that the average annual temperature is 3.1 °C, the average temperature of the coldest month is -13.1 °C, the average annual precipitation is 127 mm, and the maximum seasonal freezing depth is about 2.3 m. The mountains in the tunnel site area generally extend from east to west, with a relative height difference of 560 m. The rock types passed through by the tunnel body are mainly quartz schist, marble and granite, and the groundwater is mainly bedrock fissure water and pore water in the Quaternary loose accumulation layer. The tunnel was started in June 2016, completed in July 2021, and opened for operation in March 2022.

[0190] Data from May 2022 to April 2023 were selected for analysis. Monitoring data show that the average annual temperature at the tunnel entrance is The annual fluctuation of the temperature at the tunnel entrance is 1.2℃. The daily fluctuation of the temperature at the tunnel entrance is 11.2℃. is 11.0°C. In the calculation, the inner surface radius of the insulation layer , inner radius of lining concrete , inner radius of surrounding rock The outer boundary radius of the tunnel is 5.38 m, 5.43 m and 6.19 m respectively. Take 10 m, the thermal conductivity of the insulation layer Take 0.04 W·m -1 ℃ -1 , thermal conductivity of lining concrete Take 1.60 W·m -1 ℃ -1 , thermal conductivity of surrounding rock Take 2.70 W·m -1 °C -1 , the density of the insulation layer 55 kg·m -3 , density of lining concrete 2500kg·m -3 , the density of surrounding rock 2400 kg·m -3 , the specific heat capacity of the insulation layer 1200 J·kg -1 ℃ -1 Specific heat capacity of lining concrete 970 J·kg -1 ℃ -1 , the specific heat capacity of the surrounding rock 1200 J·kg -1 ℃ -1 , the convective heat transfer coefficient between the tunnel structure and the air in the tunnel Take 13.7 W·m -2 ℃ -1 , geothermal gradient Take 0.02℃·m -1 , constant temperature layer burial depth and the influence depth of tunnel surrounding rock temperature field The temperature of the surrounding rock in the isothermal layer is 10 m. Take 1 ℃, the air density in the tunnel Take 0.8 kg·m -3 , specific heat capacity of air Take 950 J·kg -1 ℃ -1 , wind speed in the tunnel Take 2.2 m·s -1 Calculations were performed under the condition of laying a 1000 m insulation layer at the tunnel entrance. The axial distributions of the annual average temperature, annual temperature amplitude, and daily temperature amplitude in the tunnel are as follows: Figures 4 to 6 As shown, it can be seen that the corresponding analytical results are close to the measured values ​​to a certain extent, thus verifying the accuracy of the analytical solution.

[0191] 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 axial temperature distribution in cold-region tunnels considering daily variation, characterized in that: The following steps are involved: Step 1: Solve the axial distribution of the annual average temperature in the tunnel , Axial distribution of annual amplitude of temperature in tunnel , Axial distribution of annual phase of temperature in tunnel , Axial distribution of daily amplitude of temperature in the tunnel Axial distribution of daily phase of temperature in the tunnel , is the depth, in m; Step s1, solve the axial distribution of the annual average temperature in the tunnel : （I）； In formula (I), is the convective heat transfer coefficient between the tunnel structure and the air in the tunnel, in units of , is the air density in the tunnel, in kg·m -3 , is the specific heat capacity of air, in J·kg -1 ℃ -1 , is the inner surface radius of the insulation layer, in m, is the wind speed in the tunnel, in m·s -1 , is the annual average temperature at the cave entrance, in °C; In formula (I), For the intermediate parameters: (II); In formula (II), To go deeper The tunnel depth at is in meters. is an independent variable, For the general middle z Replace with y The value obtained later, The temperature of the surrounding rock in 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 influence depth of the tunnel surrounding rock temperature field, in m, is the burial depth of the isothermal layer, in m, is the geothermal gradient, in ℃×m -1 ; In formula (I) and formula (II) and These are all intermediate parameters. , , , , and All are intermediate parameters; ； Steady-state matrix as follows: ； Steady-state matrix , , , as follows: ； , , They are the thermal conductivity of the insulation layer, lining concrete, and surrounding rock, in units of W×m -1 ×℃ -1 ; , , They are the inner radius of the lining concrete, the inner radius of 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, that is, the outer boundary radius of the tunnel, in meters; Step s2, solve the axial distribution of the annual amplitude of the temperature in the tunnel : (III); In formula (III), is the annual amplitude of the temperature at the tunnel entrance, in °C, is the real part of the complex number, is an intermediate parameter, when hour, , s is the intermediate parameter, is an imaginary unit, is the annual frequency of temperature, ; (IV); In formula (IV), , , is the intermediate parameter, , ; Transient Matrix as follows: ； Transient Matrix as follows: ； Transient Matrix as follows: ； , , are the densities of the insulation layer, lining concrete, and surrounding rock, in kg·m -3 , are the specific heat capacities of the insulation layer, lining concrete, and surrounding rock, in J·kg -1 ℃ -1 , and The first category w Class II w The Bessel function of the order imaginary quantity, w= 0 or 1; Step s3, solve the axial distribution of the annual phase of temperature in the tunnel : （V）； In formula (V), is the imaginary part of the complex number, is the annual phase of temperature at the cave entrance; Step s4, solve the axial distribution of the daily amplitude of the temperature in the tunnel : (WE); In formula (VI), is the daily amplitude of the temperature at the tunnel entrance, in °C; is the real part of a complex number, when hour, , is the daily frequency of temperature, ; Step s5, solve the axial distribution of the daily phase of the temperature in the tunnel : (VII); In formula (VII), is the daily phase of temperature at the cave entrance; Step 2: Establish the axial temperature distribution of cold-region tunnels The expression is: (VIII); In formula (VIII), , , , and All obtained from step 1.

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