Analytical calculation method for radial temperature field of deep-buried tunnel lining structure and surrounding rock

Abstract

The application discloses a kind of deep-buried tunnel lining structure and the analytical calculation method of radial temperature field along surrounding rock, including establishing the calculation model of annual temperature amplitude and annual average temperature along radial depth of tunnel lining structure and surrounding rock;Considering the influence of the difference of thermal physical properties of different material layers on the change of tunnel temperature field, the heat storage coefficient of different material layers and the surface heat storage coefficient are calculated;The annual temperature amplitude along radial depth distribution of tunnel lining structure and surrounding rock is calculated;Determine the temperature influence boundary of tunnel surrounding rock;The annual average temperature along radial depth distribution of tunnel lining structure and surrounding rock is calculated;The annual minimum temperature along radial depth distribution of tunnel lining structure and surrounding rock is calculated.The present application is based on the principle of superposition, the principle of periodic heat transfer and the principle of steady heat transfer, and a simple and easy-to-promote method for calculating the annual average temperature, annual temperature amplitude and corresponding annual minimum temperature along radial depth of tunnel lining structure and surrounding rock is proposed, which is used to guide the design of tunnel anti-freezing and heat preservation.

Description

Technical Field

[0001] This invention belongs to the field of tunnel technology, specifically relating to an analytical calculation method for the radial temperature field of the lining structure and surrounding rock of a deep-buried tunnel. Background Technology

[0002] Tunnels in cold regions are prone to frost damage under low temperatures, including lining frost heave and cracking, ice formation, and water seepage and icing on the road surface. These problems severely affect the long-term stability of the tunnel structure and threaten traffic safety. Temperature field research is fundamental and a breakthrough point for solving the frost damage problem in tunnels in cold regions. Simple and effective methods for calculating the tunnel temperature field can provide theoretical support and guidance for the design of frost damage prevention and control in tunnels in cold regions, thus solving the frost damage problem.

[0003] The radial temperature field calculation method for tunnel lining structure and surrounding rock can effectively determine the freezing depth of tunnels, providing a basis for the design of tunnel anti-freezing insulation layer thickness and central deep-buried water ditch burial depth. The analytical calculation method has a clear principle, a straightforward calculation process, and controllable accuracy of results. Therefore, the research on the analytical calculation method for the radial temperature field of tunnel lining structure and surrounding rock is of great significance for solving the problem of tunnel freezing damage in cold regions. However, the current analytical calculation method for the temperature field of tunnel lining structure and surrounding rock is very complex in its solution process, with a large amount of calculation and high difficulty in solving, making it difficult to promote its application in engineering. For example, in the article "Xia Caichu, Zhang Guozhu, Xiao Suguang. Analytical solution of temperature field of cold region tunnel considering lining and insulation layer [J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(9): 1767-1773," Xia Caichu et al. used a method combining separation of variables and Laplace variation, and introduced Bessel function, in order to solve the radial temperature field change of tunnel lining structure and surrounding rock, which is very complex in its solution process. Furthermore, in current analytical calculations, the fundamental parameter of the temperature influence boundary of the tunnel surrounding rock is difficult to obtain in advance, and no specific method for determining it has been provided. Most related studies simply take it as 10 m or infinity for calculation. In reality, the size of the temperature influence boundary is related to the magnitude of air temperature fluctuations and the thermophysical properties of the surrounding rock. If it cannot be accurately determined, it will inevitably affect the accuracy of the tunnel temperature field calculation results.

[0004] To address the aforementioned problems, this invention establishes a multi-layer flat plate calculation model for periodic heat transfer based on the superposition principle. It treats the periodic heat transfer in the tunnel as a temperature harmonic wave propagating along its radial depth, considering the influence of differences in the thermal properties of the lining concrete and surrounding rock on the propagation of the temperature harmonic wave. An analytical solution for the annual temperature amplitude along the radial depth of the tunnel lining structure and surrounding rock is proposed. A steady-state multi-layer cylindrical calculation model for heat transfer is also established. Based on the above calculation results of the annual temperature amplitude along the radial depth of the tunnel surrounding rock, and using an annual temperature amplitude of 0.05℃ as the standard, the boundary of the surrounding rock temperature influence and its radial depth are determined. Furthermore, a simplified analytical solution for the annual average temperature along the radial depth of the tunnel lining structure and surrounding rock is proposed, using the annual average air temperature and the initial temperature of the surrounding rock as constant temperature boundary conditions. By subtracting the above analytical calculation results of the annual temperature amplitude and annual average temperature along the radial depth of the tunnel lining structure and surrounding rock, the distribution of the lowest annual temperature along the radial depth of the tunnel is obtained. Based on this, the maximum freezing depth of the tunnel surrounding rock can be effectively determined, providing a basis for the design of tunnel insulation and drainage in cold regions and solving the problem of tunnel frost damage. The above analytical calculation method for the radial temperature field of tunnel lining structure and surrounding rock is based on clear principles, is simple to calculate, highly operable, and has small errors, which is conducive to its widespread application. Summary of the Invention

[0005] To address the problems of complex calculations and ineffective determination of the boundary depth of temperature influence on surrounding rock in existing analytical methods for tunnel lining structures and surrounding rock, this invention provides an analytical calculation method for the radial temperature field of deep-buried tunnel lining structures and surrounding rock, based on a clear method for determining the boundary of temperature influence on surrounding rock. This method has the advantages of clear principles, complete steps, simple calculations, and small errors. It can provide effective support for improving the design method for preventing frost damage in cold-region tunnels, solving the problem of tunnel frost damage, and is conducive to engineering promotion and application.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: An analytical calculation method for the radial temperature field of the lining structure and surrounding rock of a deeply buried tunnel includes the following steps: S1. Establish calculation models for the annual temperature amplitude and annual average temperature along the radial depth of the tunnel lining structure and surrounding rock, respectively. S2. Obtain the thermophysical parameters of the tunnel secondary lining, initial support and surrounding rock, as well as the boundary conditions of the calculation model; S3. Calculate the heat storage coefficients of secondary lining, initial support and surrounding rock respectively; S4. Considering the impact of the differences in thermal properties of different material layers on the temperature field changes in the tunnel, distinguish between "thick" and "thin" material layers, and calculate the surface heat storage coefficient of different material layers. S5. Calculate the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock. S6. Determine the boundary depth affected by the temperature of the surrounding rock in the tunnel; S7. Calculate the radial depth distribution of the annual average temperature of the tunnel lining structure and surrounding rock. S8. Calculate the annual minimum temperature distribution along the radial depth of the tunnel.

[0007] Furthermore, the calculation model for the annual temperature amplitude of the tunnel lining structure and surrounding rock along the radial depth mentioned in step S1 refers to a multi-layer flat plate calculation model for periodic heat transfer that considers the radial propagation of temperature harmonic waves. It regards the radial heat transfer of the tunnel lining structure and surrounding rock under the annual periodic temperature boundary conditions as the radial propagation of temperature harmonic waves from the lining surface, and calculates the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock.

[0008] Furthermore, the calculation model for the annual average temperature of the tunnel lining structure and surrounding rock along the radial depth mentioned in step S1 refers to a multi-layer cylindrical steady-state heat transfer calculation model with the annual average air temperature and the initial temperature of the surrounding rock as boundary conditions, used to calculate the annual average temperature distribution of the tunnel lining structure and surrounding rock along the radial depth.

[0009] Furthermore, in step S2, the thermophysical parameters of the secondary lining, initial support, and surrounding rock are obtained, specifically including density, specific heat capacity, and thermal conductivity.

[0010] Further, step S2 involves obtaining the boundary conditions of the calculation model, specifically including air temperature boundary and surrounding rock temperature boundary. The air temperature boundary condition includes the annual average air temperature and annual temperature amplitude. The surrounding rock temperature boundary, i.e., the surrounding rock temperature influence boundary, has its temperature as the initial temperature of the surrounding rock. When the boundary of the surrounding rock temperature influence is within the formation's temperature variation zone, the annual average temperature of the formation is taken; when the boundary of the surrounding rock temperature influence is within the formation's constant temperature zone, the constant temperature zone temperature is taken; when the boundary of the surrounding rock temperature influence is within the formation's warming zone, the initial temperature of the surrounding rock can be calculated using the following formula.

[0011] ; in, The temperature at the boundary is affected by the temperature of the surrounding rock, i.e., the initial temperature of the surrounding rock, in °C. Temperature of the stratigraphic isothermal zone, in °C; The depth of the tunnel (from the tunnel arch to the ground surface) is expressed in meters (m). , These represent the depths from the surface of the isothermal zone and the depths from the surface of the boundary of the surrounding rock temperature influence at the crown location, respectively, in meters. The temperature gradient in the warming zone of the strata is generally (1~3)℃ / 100 m.

[0012] Furthermore, the heat storage coefficients of the secondary lining, initial support, and surrounding rock mentioned in step S3 are calculated according to the following formula based on the thermophysical parameter values ​​obtained in S2.

[0013] ; in: In the multi-layer flat plate model, the first i The heat storage coefficient of the layer material i =1, 2, and 3 represent secondary lining, initial support, and surrounding rock, respectively, in W / (m²). 2 ·K); , Representing the passage of the first i The heat flow amplitude and surface temperature amplitude of the layer material surface; For the first i Density of the layer material, in kg / m³ 3 ; For the first i Specific heat capacity of the layer material, in J / (kg·K); For the first i Thermal conductivity of the layer material, in W / (m·K); T The annual temperature fluctuation cycle, i.e. T =3.1536×10 7 s.

[0014] Furthermore, the consideration of the influence of differences in the thermal properties of different material layers on the temperature field change, as described in step S4, distinguishing material layers as "thick" or "thin" layers, is because the temperature field change in the tunnel is affected not only by the thermal properties of each material layer itself but also by boundary conditions. In the direction of the temperature harmonic wave propagation, if layer 2 (initial support) following layer 1 (secondary lining) is a "thick" layer, meaning there is a regular fluctuation section within layer 2, then when the heat storage coefficient S2 of layer 2 is greater than the heat storage coefficient S1 of layer 1, the temperature wave attenuation within layer 1 will increase, and vice versa. If layer 3 (surrounding rock) is a "thick" layer, its influence on layer 2 is consistent. If layer 2 is a "thin" layer, meaning the temperature harmonic wave within layer 2 is significantly affected by the boundary surface and there is no regular fluctuation section, then the temperature wave attenuation within layer 1 is not only related to the surface heat storage coefficient of the material in layer 2 but also affected by layer 3. The thinner layer 2 is, the greater this influence. If layer 3 is also a "thin" layer, the external boundary conditions of the surrounding rock will still affect the temperature wave attenuation of layers 1 and 2.

[0015] Furthermore, the distinction between "thick" and "thin" tunnel secondary lining, initial support, and surrounding rock as described in step S4, as well as the surface heat storage coefficient of each material layer, are calculated and determined using the following method.

[0016] when i The layer is a "thick" layer, that is, when D i When ≥1, ; when i The layer is a "thin" layer, that is, whenD i When <1, ; in, For the first i Surface heat storage coefficient of the layer material, in W / (m²) 2 ·K); D i For the first i Thermal inertia index of layer material ; For the flat plate model i Layer thermal resistance, Unit: K / W; For the first i The thickness of the layer material, in meters (m).

[0017] Based on the thermophysical parameters of commonly used lining concrete materials and the design thickness, the secondary lining and initial support are both "thin" layers, while the surrounding rock thickness in the deep-buried section is relatively large, which is a "thick" layer, and its surface heat storage coefficient is equal to its heat storage coefficient.

[0018] Furthermore, the calculation method for the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and the surrounding rock described in step S5 is as follows.

[0019] First, based on the multi-layer flat plate model of the tunnel established in step S1 and the calculated parameter values ​​of each material layer obtained in steps S2, S3 and S4, the attenuation factor of the annual temperature amplitude of the tunnel lining structure and the surrounding rock at different radial depths relative to air is calculated using the following formula.

[0020] ; in, The attenuation factor of the annual temperature amplitude of the lining structure and surrounding rock at different radial depths relative to air. The convective heat transfer coefficient between air and the lining surface, in W / (m²). 2 ·K); , and These are the thermal conductivity coefficients of secondary lining, initial support, and surrounding rock, respectively, in meters (m). 2 / s; , and These represent the distances from the secondary lining, the inner surface of the initial support (surrounding rock side), and the boundary of the surrounding rock temperature influence to the lining surface, respectively, in meters.

[0021] Then, the annual temperature amplitude of the tunnel lining structure and surrounding rock at different radial depths is calculated using the following formula.

[0022] ; in, Annual temperature amplitude of tunnel lining structure and surrounding rock at different radial depths, in °C; The annual air temperature amplitude is expressed in °C.

[0023] Finally, by linear interpolation, the annual temperature amplitude at different depths inside the secondary lining and initial support of the tunnel was calculated, and the complete tunnel lining structure and the radial depth distribution of the annual temperature amplitude of the surrounding rock were obtained.

[0024] Furthermore, the tunnel surrounding rock temperature influence boundary mentioned in step S6 is determined by calculating the annual temperature amplitude distribution of the surrounding rock along the radial depth in step S5, taking the position where the annual temperature amplitude is equal to 0.05℃ as the tunnel surrounding rock temperature influence boundary, and determining its radial depth.

[0025] Furthermore, the calculation method for the radial depth distribution of the annual average temperature of the tunnel lining structure and surrounding rock described in step S7 is as follows.

[0026] Based on the steady-state heat transfer calculation model of the multi-layer cylindrical tunnel established in step S1, the thermal conductivity of the tunnel lining structure and surrounding rock obtained in step S2, and the boundary depth of the surrounding rock temperature influence obtained in step S6, the annual average temperature of the tunnel lining structure and surrounding rock at different radial depths is calculated using the following formula.

[0027]

[0028] in, The annual average temperature of the tunnel lining structure and surrounding rock at different radial depths, in °C; The annual average temperature of the air is expressed in °C. , , , These are the equivalent radius of the tunnel clearance, the inner surface radius of the secondary lining and initial support, and the boundary radius of the surrounding rock temperature influence, respectively, in meters (m).

[0029] Furthermore, the method for determining the radial depth distribution of the tunnel's annual minimum temperature in step S8 is as follows.

[0030] Based on the annual temperature amplitude and annual average temperature of the tunnel lining structure and surrounding rock at different radial depths obtained from steps S5 and S7, the annual minimum temperature distribution of the tunnel lining structure and surrounding rock along the radial depth is calculated using the following formula.

[0031] ; Compared with the prior art, the beneficial effects of the present invention are: I. This invention discloses an analytical calculation method for the radial temperature field of the lining structure and surrounding rock of a deeply buried tunnel. The specific steps are as follows: Based on the superposition principle, a multi-layer flat plate calculation model is established to calculate the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock, and a multi-layer cylindrical calculation model is established to calculate the radial depth distribution of the annual average temperature of the tunnel lining structure and surrounding rock; the density, specific heat capacity, thermal conductivity, and air and surrounding rock temperature boundary conditions of the secondary lining, initial support, and surrounding rock are obtained; the heat storage coefficient and surface heat storage coefficient of the tunnel antifreeze insulation layer, secondary lining, initial support, and surrounding rock are calculated; based on the periodic heat transfer principle, the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock is calculated; the depth of influence of the tunnel surrounding rock temperature is determined with an annual temperature amplitude of 0.05 ℃ as the threshold; based on the steady-state heat transfer principle, the radial depth distribution of the annual average temperature of the tunnel lining structure and surrounding rock is calculated; the radial depth distribution of the annual minimum temperature of the tunnel lining structure and surrounding rock is calculated. The analytical calculation method for the radial temperature field of the lining structure and surrounding rock of a deep-buried tunnel with annual periodicity provided by this invention avoids the problems of complex modeling, large amount of calculation, and difficulty for general engineering technicians to master when using numerical simulation calculation. The steps are complete and the principle is clear, which can provide effective support for the design of tunnel frost damage prevention.

[0032] II. This invention discloses an analytical calculation method for the radial temperature field of the lining structure and surrounding rock of a deeply buried tunnel. The method treats the annual temperature amplitude of the tunnel lining structure and surrounding rock along the radial depth as the radial propagation of a temperature harmonic wave. It fully considers the influence of differences in the thermal properties of different material layers on the propagation of the temperature harmonic wave, distinguishing between "thick" and "thin" material layers, calculating the surface heat storage coefficient of different material layers, and thus determining the attenuation of the temperature harmonic wave at different depths along the radial direction of the tunnel. The corresponding distribution of the annual temperature amplitude of the tunnel along the radial depth is obtained. Therefore, the analytical calculation method for the radial temperature field of the lining structure and surrounding rock of a deeply buried tunnel provided by this invention considers comprehensive factors, is simple in method, and has small calculation errors, making it highly valuable for widespread application. Attached Figure Description

[0033] Figure 1 This is a flowchart of an embodiment of the present invention; Figure 2 This invention provides a periodic heat transfer multi-plate calculation model considering the propagation of temperature harmonic waves along the radial direction of the tunnel. Figure 3 This is the calculation model for steady-state heat transfer in tunnels using a multi-layered cylindrical structure, as described in this invention. Figure 4 The radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock obtained by analytical calculation in the example; Figure 5 The radial depth distribution of the annual average temperature of the tunnel lining structure and surrounding rock obtained by analytical calculation in the example; Figure 6 The radial depth distribution of the tunnel lining structure and the minimum annual temperature of the surrounding rock obtained by analytical calculation in the example; Figure 7 This is a numerical simulation model of the radial temperature field of the tunnel lining structure and surrounding rock in the embodiment. Figure 8 The example shows a comparison of the annual temperature amplitude of the tunnel lining structure and the surrounding rock along the radial depth, obtained from theoretical analysis and numerical simulation. Figure 9 The difference between the annual minimum temperature of the tunnel lining structure and the surrounding rock, obtained from theoretical analysis and numerical simulation calculations in the embodiment, is distributed along the radial depth. Detailed Implementation

[0034] To make the objectives, calculation processes, and advantages of the embodiments of the present invention clearer, the processes in implementing the present invention will be clearly and completely described below with reference to the accompanying drawings and examples. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments made by those skilled in the art without inventive step are within the scope of protection of the present invention.

[0035] Figure 1 The diagram shows a flowchart of an analytical calculation method for the radial temperature field of a deep-buried tunnel lining structure and surrounding rock, according to the present invention, which includes the following steps: S1. Based on the superposition principle, periodic heat transfer multi-layer plate models considering the radial propagation of temperature harmonic waves are established, such as... Figure 2 As shown, the radial depth heat transfer of the tunnel lining structure and surrounding rock under annual periodic temperature boundary conditions is considered as a temperature harmonic wave propagating radially from the lining surface. The annual temperature amplitude at different radial depths of the tunnel lining structure and surrounding rock is simplified and calculated. A steady-state heat transfer calculation model for a multi-layered cylindrical tunnel is established with the annual average air temperature and the initial temperature of the surrounding rock as boundary conditions, as shown below. Figure 3 As shown, based on the annual average air temperature, the initial temperature of the surrounding rock, and the determined boundary depth of the surrounding rock temperature influence, the annual average temperature of the tunnel lining structure and the surrounding rock at different radial depths can be calculated using the steady-state heat conduction principle.

[0036] S2. Obtain the thermal properties calculation parameters for the tunnel secondary lining, initial support, and surrounding rock, including density, specific heat capacity, and thermal conductivity. Obtain the annual average air temperature and annual temperature amplitude as the boundary conditions for air temperature inside the tunnel. Obtain the initial temperature of the surrounding rock as the temperature boundary condition for the surrounding rock temperature influence boundary. When the surrounding rock temperature influence boundary is within the formation's temperature variation zone, the initial temperature of the surrounding rock is taken as the formation's annual average temperature; when the surrounding rock temperature influence boundary is within the formation's constant temperature zone, the constant temperature zone temperature is taken; when the surrounding rock temperature influence boundary is within the formation's warming zone, the initial temperature of the surrounding rock can be calculated using the following formula.

[0037] ; in, The temperature at the boundary is affected by the temperature of the surrounding rock, i.e., the initial temperature of the surrounding rock, in °C. Temperature of the stratigraphic isothermal zone, in °C; The depth of the tunnel (from the tunnel arch to the ground surface) is expressed in meters (m). , These represent the depths from the surface of the isothermal zone and the depths from the surface of the boundary of the surrounding rock temperature influence at the crown location, respectively, in meters. The temperature gradient of the surrounding rocks within the warming zone of the strata is generally (1~3)℃ / 100 m.

[0038] S3. Based on the density, specific heat capacity, and thermal conductivity of the secondary lining, initial support, and surrounding rock obtained in step S2, and combined with the design of the tunnel secondary lining and initial support thickness, calculate the heat storage coefficient of the secondary lining, initial support, and surrounding rock according to the principle of periodic heat transfer using the following method.

[0039] ; in: In the multi-layer flat plate model, the first i The heat storage coefficient of the layer material i =1, 2, and 3 represent secondary lining, initial support, and surrounding rock, respectively, in W / (m²). 2 ·K); , Representing the passage of the first i The heat flow amplitude and surface temperature amplitude of the layer material surface; For the first i Density of the layer material, in kg / m³ 3 ; For the first i Specific heat capacity of the layer material, in J / (kg·K); For the first i Thermal conductivity of the layer material, in W / (m·K); T The annual temperature fluctuation period is expressed in seconds (s).

[0040] S4. In the direction of the temperature harmonic wave propagation, if layer 2 (initial support) following layer 1 (secondary lining) is a "thick" layer, meaning there is a regular fluctuation section within layer 2, then when the heat storage coefficient of layer 2 material... S The heat storage coefficient of layer 2 is greater than that of layer 1 material. SWhen layer 1 is thin, the temperature wave attenuation within layer 1 will increase, and vice versa. If layer 2 is a "thin" layer, meaning that the temperature harmonic wave within layer 2 is significantly affected by the boundary surface and lacks regular fluctuation segments, then the temperature wave attenuation within layer 1 is not only related to the surface heat storage coefficient of the layer 2 material but also affected by layer 3 (surrounding rock). The thinner layer 2 is, the greater this effect. If layer 3 is also a "thin" layer, then the outer boundary conditions of the surrounding rock will still affect the temperature wave attenuation of both layer 1 and layer 2. Therefore, to consider the impact of differences in the thermal properties of different material layers on the tunnel temperature field, based on the thermophysical parameter values ​​of the secondary lining, initial support, and surrounding rock obtained in step S2, different material layers are distinguished as "thick" or "thin" layers using the following method, and the surface heat storage coefficient of each material layer is calculated.

[0041] when i The layer is a "thick" layer, that is, when D i When ≥1, ; when i The layer is a "thin" layer, that is, when D i When <1, ; in, For the first i Surface heat storage coefficient of the layer material, in W / (m²) 2 ·K); D i For the first i Thermal inertia index of layer material ; For the flat plate model i Layer thermal resistance, Unit: K / W; For the first i The thickness of the layer material, in meters (m).

[0042] It should be noted that, based on the thermophysical parameters of commonly used lining concrete materials and the design thickness, the secondary lining and initial support are both "thin" layers, while the surrounding rock of the deep-buried section is thicker and is a "thick" layer, with its surface heat storage coefficient being equal to its heat storage coefficient.

[0043] S5. Based on the multi-layer flat plate model of periodic heat transfer in the tunnel established in step S1 and the calculated parameter values ​​of each material layer obtained in steps S2, S3, and S4, and referring to the calculation method of temperature harmonic wave propagation in multi-layer wall materials proposed by Shklov (Sklov. Heat Transfer under Periodic Heat [M]. Beijing: China Building Industry Press, 1964) and Lin Haiyan (Lin Haiyan. Evaluation of Thermal Properties of Walls under Periodic Heat [C]. Proceedings of the National Conference on Building Energy Conservation Technology and Design, 2005), calculate the attenuation factor of annual temperature amplitude relative to air at different radial depths of the tunnel lining structure and surrounding rock according to the following formula.

[0044] ; in, The attenuation factor of the annual temperature amplitude of the lining structure and surrounding rock at different radial depths relative to air. The convective heat transfer coefficient between air and the lining surface, in W / (m²). 2 ·K); , and These are the thermal conductivity coefficients of secondary lining, initial support, and surrounding rock, respectively, in meters (m). 2 / s; , and These represent the distances from the secondary lining, the inner surface of the initial support (surrounding rock side), and the boundary of the surrounding rock temperature influence to the lining surface, respectively, in meters.

[0045] Based on the above calculation results, the annual temperature amplitude of the tunnel lining structure and surrounding rock at different radial depths at the corresponding locations is calculated using the following formula.

[0046] ; in, Annual temperature amplitude of tunnel lining structure and surrounding rock at different radial depths, in °C; The annual air temperature amplitude is expressed in °C.

[0047] Finally, the annual temperature amplitude at different depths inside the secondary lining and initial support of the tunnel was calculated by linear interpolation, thus obtaining the complete tunnel lining structure and the radial depth distribution of the annual temperature amplitude of the surrounding rock.

[0048] S6. Based on step S5, the annual temperature amplitude distribution of the surrounding rock along the radial depth is calculated. Taking an annual temperature amplitude of 0.05 ℃ as the standard, the temperature influence boundary of the tunnel surrounding rock and its radial depth are determined.

[0049] S7. Based on the multi-layer cylindrical steady-state heat transfer calculation model of the tunnel established in step S1, the thermal conductivity of the tunnel lining structure and surrounding rock obtained in step S2, and the radial depth of the surrounding rock temperature influence boundary obtained in step S6, the annual average temperature of the tunnel lining structure and surrounding rock at different radial depths is calculated using the multi-layer cylindrical steady-state heat transfer principle and the following formula.

[0050]

[0051] in, The annual average temperature of the tunnel lining structure and surrounding rock at different radial depths, in °C; The annual average temperature of the air is expressed in °C. , , , These are the equivalent radius of the tunnel clearance, the inner surface radius of the secondary lining and initial support, and the boundary radius of the surrounding rock temperature influence, respectively, in meters (m).

[0052] S8. Based on the annual temperature amplitude and annual average temperature distribution along the radial depth of the tunnel lining structure and surrounding rock calculated in steps S5 and S7, the annual minimum temperature distribution along the radial depth of the tunnel lining structure and surrounding rock is calculated using the following formula. .

[0053] Example: Based on the superposition principle, multi-layer flat plate models of tunnels considering radial propagation of temperature harmonics are established, such as... Figure 2 As shown; a steady-state heat transfer calculation model for a multi-layered cylindrical tunnel with annual average air temperature and initial surrounding rock temperature as boundary conditions, as follows: Figure 3 As shown.

[0054] The values ​​of density, specific heat capacity, and thermal conductivity of the secondary tunnel lining, initial support, and surrounding rock selected in this embodiment are shown in Table 1.

[0055] Table 1 Thermophysical parameters of tunnel lining structure and surrounding rock

[0056] The average annual temperature of the air inside a tunnel in a cold region Annual temperature amplitude The initial temperatures of the surrounding rock were 1℃ and 17℃, respectively. The temperature is 7 ℃. The tunnel is a two-lane tunnel with a clearance equivalent radius of 5.55 m. The thickness of the secondary lining and the initial support are 0.50 m and 0.26 m, respectively. The convective heat transfer coefficient between the tunnel air and the outer surface of the secondary lining is... h Taken as 15 W / (m 2 ·K).

[0057] Based on the principle of periodic heat transfer, and using the aforementioned thermophysical parameters of the tunnel lining structure and surrounding rock, as well as the thicknesses of the secondary lining and initial support, the heat storage coefficients of each layer of material are calculated as follows: Heat storage coefficient of secondary lining ; Heat storage coefficient of initial support ; heat storage coefficient of surrounding rock .

[0058] The calculated thermal resistances of each material layer in the flat plate model are as follows: Secondary lining thermal resistance K / W; Initial support thermal resistance K / W.

[0059] Based on the above, the thermal inertia index of the secondary lining is calculated. Thermal inertia index of initial support Therefore, both the secondary lining and the initial support are "thin" layers. Correspondingly, the surface heat storage coefficients of the tunnel's secondary lining and initial support are calculated. , For deeply buried tunnels, the surrounding rock thickness is large, and its thermal inertia index is high. D 3 must be greater than 1, indicating a "thick" layer; therefore, the heat storage coefficient of the surrounding rock surface is...

[0060] Referring to the calculation method for the propagation of temperature harmonic waves in multi-layer wall materials proposed by Shklov (Schklov. Heat Transfer under Periodic Thermal Effects [M]. Beijing: China Building Industry Press, 1964) and Lin Haiyan (Lin Haiyan. Evaluation of Thermal Properties of Walls under Periodic Thermal Effects [C]. Proceedings of the National Conference on Building Energy Conservation Technology and Design, 2005.), and using the calculation parameters obtained above, the attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel lining structure and surrounding rock is calculated according to the following formula. in, 、 The values ​​are 0.50 m and 0.76 m, respectively, the distances from the inner surface of the secondary lining and the outer surface of the initial support to the secondary lining.

[0062] ; Based on the calculation results of the attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel lining structure and surrounding rock, the annual temperature amplitude at the corresponding location is calculated using the following formula. ; in, Annual temperature amplitude of tunnel lining structure and surrounding rock at different radial depths, in °C; The annual air temperature amplitude is expressed in °C.

[0063] By using linear interpolation, the annual temperature amplitude at different depths within the tunnel lining structure is calculated, thus yielding the complete radial depth distribution function of the annual temperature amplitude of the tunnel lining structure and surrounding rock, as detailed below. ; The final obtained annual temperature amplitude distribution of the tunnel lining structure and surrounding rock along the radial depth is as follows: Figure 4 As shown.

[0064] Based on the calculation results of the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock, and taking an annual temperature amplitude of 0.05℃ as the standard, the depth of the temperature influence boundary of the tunnel surrounding rock is determined, and the distance of its location from the lining surface is obtained. It is 20 m.

[0065] Based on the established steady-state heat transfer calculation model of a multi-layer cylindrical tunnel, and using the steady-state heat transfer principle of a multi-layer cylindrical tunnel, the heat flux density of the tunnel cross section is calculated using the following formula. q ; in, , , , The values ​​are 5.55 m, 6.05 m, 6.31 m and 25.55 m, respectively, representing the equivalent radius of the tunnel clearance, the inner surface radius of the secondary lining and initial support, and the boundary radius of the surrounding rock temperature influence.

[0066] The heat flux density was calculated. .

[0067] The annual average temperature of the tunnel lining structure and surrounding rock at different radial depths is calculated using the following formula. ; The calculated radial depth distribution functions of the annual average temperature of the tunnel lining structure and surrounding rock are as follows: The final tunnel lining structure and the annual average temperature distribution of the surrounding rock along the radial depth are as follows: Figure 5 As shown.

[0069] Based on the calculated annual average temperature of the tunnel lining structure and surrounding rock, and the radial depth distribution of the annual temperature amplitude, the radial depth distribution of the tunnel's annual minimum temperature is calculated using the following formula: Figure 6 As shown.

[0070] ; The accuracy of the theoretical analytical calculation results of the above tunnel lining structure, surrounding rock annual average temperature and annual temperature amplitude were verified by numerical simulation, as follows.

[0071] (1) Establishment of computational model This calculation adopts the design standard of a two-lane highway tunnel, taking the secondary lining thickness as 50 cm and the initial support thickness as 26 cm. A two-dimensional annular boundary numerical calculation model is established, extending outward from the cross-sectional profile as the reference, as follows: Figure 7 As shown.

[0072] The values ​​of the secondary lining, initial support, and surrounding rock thermophysical parameters are consistent with those in Table (1). The density, specific heat capacity, and thermal conductivity of the pavement concrete are 2300 kg / m³. 3 The heat transfer coefficients are 920 J / (kg·K) and 1.51 W / (m·K). Air is in direct contact with the outer surface of the lining and the road surface, forming a convective heat transfer boundary; its convective heat transfer coefficient is uniformly taken as 15 W / (m²·K). 2 The annual average temperature and annual temperature amplitude of the air inside the tunnel are 1℃ and 17℃, respectively. The surrounding rock boundary, i.e., the temperature influence boundary of the surrounding rock, is set as an isothermal boundary with a temperature equal to the initial temperature of the surrounding rock, 7℃. The method for determining the surrounding rock boundary is the same as the theoretical derivation, using the radial depth position where the annual temperature amplitude of the surrounding rock drops to 0.05℃ as the temperature influence boundary. The initial temperature of the model is taken as the initial temperature of the surrounding rock. This calculation uses FLUENT software, with a calculation step size of 6 days and a total calculation time of 10 years to ensure that the heat transfer and temperature field changes inside the tunnel reach stability. During the calculation process, the temperature calculation results at each step are saved.

[0073] The average grid length for the secondary lining and initial support in the model was 0.1 m, and for the surrounding rock, it was 1 m. To verify the influence of the model grid size on the calculation results, the average grid lengths for the lining structure and the surrounding rock were reduced to 0.05 m and 0.2 m, respectively, for calculation. The maximum difference between the calculated temperature field results for the lining structure and the surrounding rock and the actual numerical model results was only 0.13 ℃. Therefore, the grid size selection used in this numerical simulation model is reasonable and has virtually no impact on the calculation results, thus ensuring the accuracy of the numerical simulation results.

[0074] (2) Analysis of calculation results The calculation results show that after 10 years, the heat transfer within the tunnel lining structure and surrounding rock has basically stabilized, with its temperature exhibiting periodic variations over time. The calculated temperatures at different radial depths along the arch crown in the 10th year were extracted, and the corresponding annual average temperature and annual temperature amplitude were obtained. Comparison with theoretical calculations revealed that the difference in annual average temperature between the tunnel lining structure and surrounding rock obtained from the theoretical analysis is relatively small, below 0.06 ℃, while the annual temperature amplitude is relatively large, but still below 1.18 ℃. A comparison of the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock obtained from theoretical analysis and numerical simulation is shown below. Figure 8 As shown, the theoretical analytical calculations are relatively conservative, with the maximum difference occurring at a depth of approximately 3 m from the lining surface. Correspondingly, the annual minimum temperature of the tunnel lining structure and surrounding rock obtained from the theoretical analysis is also lower than that calculated by numerical simulation, with a maximum difference of approximately 1.20 ℃ (e.g., ...). Figure 9 As shown in the figure, it is also located at a depth of about 3 m from the lining surface.

[0075] Therefore, the analytical calculation method for annual periodic deep buried tunnels proposed in this invention has a clear principle, complete steps, simple calculation, and small calculation error. It can provide effective support for the design of tunnel frost damage prevention and control, and has good application value.

Claims

1. An analytical calculation method for the radial temperature field of the lining structure and surrounding rock of a deeply buried tunnel, characterized in that, Includes the following steps: S1. Establish calculation models for the annual temperature amplitude and annual average temperature along the radial depth of the tunnel lining structure and surrounding rock, respectively. S2. Obtain the secondary lining, initial support and surrounding rock thermophysical parameters of the tunnel, as well as the boundary conditions of the calculation model; S3. Calculate the heat storage coefficients of secondary lining, initial support and surrounding rock based on the thermophysical parameters of step S2. S4. Considering the impact of the differences in thermal properties of different material layers on the temperature field changes in the tunnel, distinguish between "thick" and "thin" material layers, and calculate the surface heat storage coefficient of different material layers. S5. Calculate the radial depth distribution of the annual temperature amplitude of the tunnel lining structure and surrounding rock. S6. Determine the boundary depth affected by the temperature of the surrounding rock in the tunnel; S7. Calculate the radial depth distribution of the annual average temperature of the tunnel lining structure and surrounding rock. S8. Calculate the annual minimum temperature distribution along the radial depth of the tunnel.

2. The analytical calculation method for the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that, Step S1 includes the following steps: S11. Based on the superposition principle, the heat conduction of the tunnel lining structure and surrounding rock under the annual periodic temperature boundary condition is regarded as the radial propagation of temperature harmonic waves from the lining surface. A periodic heat transfer multi-layer plate calculation model considering the radial propagation of temperature harmonic waves is established. S12. Establish a multi-layer cylindrical steady-state heat transfer calculation model with the annual average air temperature and the initial temperature of the surrounding rock as boundary conditions.

3. The analytical calculation method for the radial depth of the temperature field of the deep-buried tunnel lining structure and surrounding rock as described in claim 1, characterized in that: The thermophysical parameters of the secondary lining, initial support and surrounding rock in step S2 include density, specific heat capacity and thermal conductivity.

4. The analytical calculation method for the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that: In step S2, the temperature boundaries include the air temperature boundary inside the tunnel and the surrounding rock temperature boundary. The air temperature boundary condition includes the annual average air temperature and the annual temperature amplitude. The surrounding rock temperature boundary, i.e., the surrounding rock temperature influence boundary, has its temperature as the initial temperature of the surrounding rock. When the boundary of the surrounding rock temperature influence is within the formation's temperature variation zone, the initial temperature of the surrounding rock is taken as the formation's annual average temperature; when the boundary of the surrounding rock temperature influence is within the formation's isothermal zone, the isothermal zone temperature is taken; when the boundary of the surrounding rock temperature influence is within the formation's warming zone, the initial temperature of the surrounding rock can be calculated using the following formula: ； in, The temperature at the boundary is affected by the temperature of the surrounding rock, i.e., the initial temperature of the surrounding rock, in °C. Temperature of the stratigraphic isothermal zone, in °C; The depth of the tunnel is expressed in meters (m). , These represent the depths from the surface of the isothermal zone and the depths from the surface of the boundary of the surrounding rock temperature influence at the crown location, respectively, in meters. The temperature gradient in the warming zone of the strata is generally (1~3)℃ / 100 m.

5. The analytical calculation method for the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that, In step S3, the heat storage coefficient of each material layer is calculated according to the following formula. ; in: In the multi-layer flat plate model, the first i The heat storage coefficient of the layer material, in W / (m²) 2 ·K), i =1,2,3 represent secondary lining, initial support and surrounding rock respectively; , Representing the passage of the first i The heat flow amplitude and surface temperature amplitude of the layer material surface; For the first i Density of the layer material, in kg / m³ 3 ; For the first i Specific heat capacity of the layer material, in J / (kg·K); For the first i Thermal conductivity of the layer material, in W / (m·K); T The annual temperature fluctuation cycle, i.e. T =3.1536×10 7 s.

6. The analytical calculation method for the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that, In step S4, the method for determining whether the material layer is "thick" or "thin" and for calculating the surface heat storage coefficient is as follows: when i The layer is a "thick" layer, that is, when D i When ≥1, ; when i The layer is a "thin" layer, that is, when D i When <1, ; in, For the first i Surface heat storage coefficient of the layer material, in W / (m²) 2 ·K); D i For the first i Thermal inertia index of layer material ; For the flat plate model i Layer thermal resistance, Unit: K / W; For the first i The thickness of the layer material, in meters (m); i =1,2,3 represent the secondary lining, initial support, and surrounding rock of the tunnel, respectively.

7. The analytical calculation method for the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that, Step S5 includes the following steps: S51. Calculate the attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel lining structure and surrounding rock using the following formula. ； in, The attenuation factor of the annual temperature amplitude of the lining structure and surrounding rock at different radial depths relative to air. The convective heat transfer coefficient between air and the lining surface, in W / (m²). 2 ·K); , and These are the secondary lining, initial support, and thermal conductivity of the surrounding rock, respectively. Unit m 2 / s; , and These represent the distances from the secondary lining, the inner surface of the initial support (surrounding rock side), and the boundary of the surrounding rock temperature influence to the lining surface, respectively, in meters. S52. Based on the calculation results of the attenuation factor of the annual temperature amplitude relative to air at different depths along the radial direction of the tunnel lining structure and surrounding rock, calculate the annual temperature amplitude at the corresponding depth of the tunnel using the following formula. ； in, Annual temperature amplitude of tunnel lining structure and surrounding rock at different radial depths, in °C; The annual air temperature amplitude is expressed in °C. S53. By linearly interpolating the results of S52, the annual temperature amplitude at different depths inside the secondary lining and initial support of the tunnel is calculated.

8. The analytical calculation method for the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that, In step S6, based on the radial depth distribution of the annual temperature amplitude of the surrounding rock calculated in step S5, and taking an annual temperature amplitude of 0.05℃ as the standard, the boundary of the surrounding rock temperature influence and its radial depth are determined.

9. The analytical calculation method for the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that, In step S7, the annual average temperature of the tunnel lining structure and surrounding rock at different radial depths is calculated using the following formula. ； in, The annual average temperature of the tunnel lining structure and surrounding rock at different radial depths, in °C; The annual average temperature of the air is expressed in °C. Indicates the equivalent radius of the tunnel clearance. This indicates the radius of the inner surface of the secondary lining. Indicates the radius of the inner surface of the initial support. This indicates the radius of the boundary affected by the temperature of the surrounding rock, in meters.

10. The method for analytical calculation of the radial depth of the temperature field of the lining structure and surrounding rock of a deep-buried tunnel according to claim 1, characterized in that, In step S8, the radial depth distribution of the annual minimum temperature of the tunnel lining structure and surrounding rock is calculated using the following formula. .

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