A method for calculating the thickness of a surface laid anti-freezing and heat preserving layer of a deep buried tunnel in a cold region

Abstract

The application discloses a kind of analytical calculation method for the surface laying thickness of antifreeze insulation layer of deep-buried tunnel in cold region, comprising the following steps: establishing tunnel antifreeze insulation layer, lining structure, annual temperature amplitude and annual average temperature along the radial depth analytical calculation model of surrounding rock;Considering the influence of the thermal physical property difference of different material layers on the change of tunnel temperature field, calculate the heat storage coefficient and surface heat storage coefficient of each material layer;Calculate the annual temperature amplitude distribution along the radial depth of tunnel;Determine the temperature influence boundary and its depth of tunnel surrounding rock;Calculate the annual average temperature of waterproof plate position between tunnel secondary lining and primary support;Calculate the annual minimum temperature of waterproof plate position, determine the required antifreeze insulation layer thickness.The application is based on superposition principle, steady-state heat transfer principle and periodic heat transfer principle for theoretical derivation, obtain a simple, easy-to-promote analytical calculation method for the surface laying thickness of antifreeze insulation layer of deep-buried tunnel in cold region, for guiding tunnel antifreeze insulation layer design.

Description

Technical Field

[0001] This invention belongs to the field of tunnel technology, specifically relating to an analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep buried tunnels in cold regions. 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. Laying an anti-freeze insulation layer is the most widely used method for preventing frost damage in tunnels in cold regions. It ensures that the back of the tunnel's waterproofing liner does not reach sub-zero temperatures, prevents groundwater in the surrounding rock from freezing, and allows it to drain smoothly out of the tunnel, thus avoiding frost damage.

[0003] A thicker antifreeze insulation layer results in higher thermal resistance and better insulation performance. However, increased thickness also raises construction costs. Therefore, to achieve tunnel antifreeze while maintaining economic efficiency, the minimum thickness needs to be calculated. Methods for calculating the thickness of the antifreeze insulation layer mainly fall into two categories: theoretical analytical methods and numerical simulation methods. Theoretical analytical methods include the equivalent thickness method and the temperature analytical method. The equivalent thickness method is based on the steady-state heat transfer principle and assumes that the heat flux density of the cross-section is the same before and after the antifreeze insulation layer is laid. It is widely used due to its simplicity and ease of application. However, the air temperature inside the tunnel changes periodically over time, and transient heat transfer occurs within the tunnel structure, which contradicts the steady-state heat transfer calculation principle of the equivalent thickness method. Furthermore, the thermophysical properties of the antifreeze insulation layer differ significantly from those of the lining structure and surrounding rock. Whether the heat flow from the tunnel lining structure and surrounding rock to the air remains unchanged before and after the antifreeze insulation layer is laid, and whether the heat transfer state before and after laying the antifreeze insulation layer can be equated, lacks valid evidence. Temperature analysis involves analytically calculating the temperature field of the tunnel lining structure and surrounding rock after the antifreeze insulation layer is laid, using the absence of negative temperature on the back of the waterproof membrane as a standard to determine the thickness of the antifreeze insulation layer. However, current analytical calculation methods are very complex, and the boundary of the surrounding rock temperature influence cannot be determined in advance, often relying on simple assumptions. For example, in the article "Feng Qiang, Jiang Binsong. An analytical method for calculating the thickness of insulation layer in multi-layer medium cold-region highway tunnels [J]. Chinese Journal of Geotechnical Engineering, 2014, 36(10): 1879-1887", Feng Qiang et al. assumed the boundary of the surrounding rock temperature influence to be an infinite boundary and calculated the thickness of the antifreeze insulation layer to be 27 cm using the inverse Laplace transform, which cannot be widely applied in actual engineering. Numerical simulation calculation methods have clear theories and principles, but the outer boundary of the model, i.e., the boundary of the surrounding rock temperature influence, cannot be determined in advance and can only be determined through experience, which easily leads to calculation errors. At the same time, numerical calculation modeling is complex and computationally intensive, making it difficult for general technical personnel to master.

[0004] To address the aforementioned problems, this invention, based on the superposition principle, establishes a multi-layer flat plate calculation model for periodic heat transfer considering the frost-resistant insulation layer. The periodic heat transfer in the tunnel is viewed as a temperature harmonic wave propagating radially along the frost-resistant insulation layer, lining structure, and surrounding rock. The influence of differences in the thermal properties of the frost-resistant insulation layer, lining concrete, and surrounding rock on the propagation of the temperature harmonic wave is considered. The annual temperature amplitude distribution along the radial depth of the tunnel lining structure and surrounding rock with a certain thickness of frost-resistant insulation layer is calculated. A steady-state heat transfer multi-layer cylindrical calculation model considering the frost-resistant insulation layer is also established. Based on the calculation results of the annual temperature amplitude along the radial depth of the surrounding rock, and using an annual temperature amplitude of 0.05℃ as a standard, the boundary of the surrounding rock temperature influence and its radial depth are determined. Furthermore, a constant temperature boundary condition is proposed, using the annual average air temperature and the initial temperature of the surrounding rock, to calculate the annual average temperature at the location of the tunnel waterproofing slab with a certain thickness of frost-resistant insulation layer. Based on the analytical calculation results of the annual temperature amplitude and annual average temperature at the location of the tunnel waterproofing membrane, the difference between the two yields the annual minimum temperature at the location of the tunnel waterproofing membrane where a certain thickness of antifreeze insulation layer is laid. If the temperature is 0 ℃, it indicates that the thickness of the antifreeze insulation layer is reasonable; if the temperature is not equal to 0 ℃, it indicates that the thickness of the antifreeze insulation layer is too large or too small, and the thickness of the antifreeze insulation layer needs to be adjusted and recalculated until the annual minimum temperature at the location of the waterproofing membrane is equal to 0 ℃. The above analytical calculation method for the surface thickness of the antifreeze insulation layer in tunnels in cold regions has a clear principle, is simple to calculate, is highly operable, and has small errors, which is conducive to its widespread application. Summary of the Invention

[0005] The existing calculation principle of the equivalent thickness method for anti-freezing insulation layers in cold-region tunnels does not match the actual heat transfer characteristics of tunnels. Furthermore, the depth of the boundary influencing surrounding rock temperature cannot be determined in advance in theoretical analysis and numerical simulation methods, which often rely on simple assumptions and empirical selection, making it difficult to guarantee calculation accuracy. Theoretical analysis is complex, and numerical simulation modeling is difficult and computationally intensive, hindering its widespread application. This invention, based on a clear method for determining the boundary influencing surrounding rock temperature, provides an analytical calculation method for the thickness of anti-freezing insulation layers in deeply buried tunnels, specifically for surface paving of anti-freezing insulation layers in cold-region tunnels. This method has advantages such as a clear principle, complete steps, and simple calculation, with small errors. It can provide effective support for improving the design method for preventing frost damage in cold-region tunnels, solving tunnel frost damage problems, and is conducive to engineering application.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: An analytical calculation method for the thickness of the surface frost-resistant insulation layer in deeply buried tunnels in cold regions includes the following steps: S1. Assuming the thickness of the anti-freeze insulation layer, establish analytical calculation models for the annual temperature amplitude and annual average temperature of the tunnel anti-freeze insulation layer, lining structure, and surrounding rock along the radial depth when the anti-freeze insulation layer is laid on the surface. S2. Obtain the thermophysical parameters of the tunnel's anti-freezing insulation layer, secondary lining, initial support, and surrounding rock, as well as the temperature boundary conditions of the calculation model; S3. Calculate the heat storage coefficients of the tunnel anti-freeze insulation layer, 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 each material layer as a "thick" layer or a "thin" layer, and calculate the surface heat storage coefficient of different material layers. S5. Calculate the radial depth distribution of the annual temperature amplitude of the antifreeze insulation layer, lining structure and surrounding rock. S6. Using an annual temperature amplitude of 0.05 ℃ as the standard, determine the boundary of the temperature influence of the surrounding rock of the tunnel and its radial depth; S7. Calculate the annual average temperature at the location of the waterproof membrane between the secondary lining and the initial support of the tunnel. S8. Calculate the minimum annual temperature at the location of the waterproof membrane between the secondary lining and the initial support of the tunnel. S9. Determine whether the assumed thickness of the antifreeze insulation layer is reasonable, and determine the required thickness of the antifreeze insulation layer for the tunnel.

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

[0008] Furthermore, the calculation model for the annual average temperature of the tunnel antifreeze insulation layer, 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 temperature of the air and the initial temperature of the surrounding rock as boundary conditions, used to calculate the annual average temperature at the location of the tunnel waterproofing membrane.

[0009] Furthermore, in step S2, the thermophysical parameters of the tunnel antifreeze insulation layer, 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 conditions and surrounding rock boundary (surrounding rock temperature-affected boundary) temperature conditions. The air temperature boundary conditions include the annual average air temperature and annual temperature amplitude, while the surrounding rock boundary temperature conditions are 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 temperature constant zone, the temperature of the temperature constant zone is taken; when the boundary of the surrounding rock temperature influence is within the formation's temperature increase 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 of the isothermal zone and the depths of the boundary between the temperature-affected surrounding rock 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 tunnel antifreeze insulation layer, 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, 3, 4 represent the frost-resistant insulation layer, 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).

[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 (secondary lining) following layer 1 (anti-freeze and insulation layer) is a "thick" layer, meaning there is a regular fluctuation segment 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 layers 3 (initial support) and 4 (surrounding rock) are also "thick" layers, their influence on the layer above 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 segment, 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, then the heat storage coefficient of the material surface of layer 4 will also affect the temperature wave attenuation of layers 1 and 2.

[0015] Furthermore, the distinction between "thick" and "thin" layers of tunnel antifreeze insulation layer, 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 according to 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, 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).

[0017] Furthermore, the calculation method for the radial depth distribution of the annual temperature amplitude of the inner lining structure of the tunnel antifreeze and insulation layer and the surrounding rock as described in step S5 is as follows.

[0018] 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 relative to air at different radial depths of the tunnel's anti-freezing and heat-insulating layer, lining structure, and surrounding rock is calculated using the following formula. ; in, The attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel's antifreeze insulation layer, lining structure, and surrounding rock. The convective heat transfer coefficient between air and the antifreeze insulation layer, in W / (m²). 2 ·K); , , and These are respectively the antifreeze insulation layer, secondary lining, initial support, and the thermal conductivity of the surrounding rock. Unit m 2 ·s -1 ; , , and These are the distances from the antifreeze insulation layer, the secondary lining, the inner surface of the initial support (surrounding rock side), and the boundary of the surrounding rock temperature influence from the outer surface of the antifreeze insulation layer, respectively, in meters.

[0019] Then, the annual temperature amplitude of the tunnel's anti-freezing and insulation layer, lining structure, and surrounding rock at the corresponding radial depth is calculated using the following formula. ; in, Annual temperature amplitude at different radial depths of tunnel antifreeze insulation layer, lining structure and surrounding rock, in °C; The annual air temperature amplitude is expressed in °C.

[0020] 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 S4, 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.

[0021] Furthermore, the method for calculating the annual average temperature at the location of the waterproofing membrane between the secondary lining and the initial support of the tunnel in step S7 is as follows.

[0022] Based on the tunnel multi-layer cylindrical steady-state heat transfer calculation model established in step S1, and the thermal conductivity of the tunnel anti-freeze insulation layer, lining structure, and surrounding rock obtained in step S2, and the boundary depth of the surrounding rock temperature influence obtained in step S5, the annual average temperature at the location of the tunnel waterproofing membrane is calculated using the following formula. .

[0023] ; ; in, The annual average temperature of the air is expressed in °C. The equivalent radius of the tunnel clearance. , , and These are the radii of the inner surfaces of the antifreeze and insulation layer, the secondary lining and the initial support, and the radius of the boundary affected by the temperature of the surrounding rock, respectively, in meters (m).

[0024] Furthermore, the method for determining the annual minimum temperature at the location of the tunnel waterproofing membrane in step S8 is as follows.

[0025] Based on the annual temperature amplitude and annual average temperature at the location of the tunnel waterproofing membrane obtained from steps S5 and S7, the annual minimum temperature is calculated using the following formula.

[0026] ; Furthermore, the method for determining whether the assumed antifreeze insulation layer thickness is reasonable in step S9 and for determining the required antifreeze insulation layer thickness for the tunnel is as follows.

[0027] Based on the annual minimum temperature at the location of the tunnel waterproofing membrane calculated in step S8, determine whether the assumed thickness of the anti-freeze insulation layer is reasonable. t min =0 ℃, then the assumed thickness of the antifreeze insulation layer meets the requirements, and this value is taken as the calculated value of the antifreeze insulation layer thickness; if t min If the temperature is not equal to 0℃, the assumed thickness of the antifreeze insulation layer is either too thick or too thin. The thickness of the antifreeze insulation layer needs to be adjusted and recalculated until the desired temperature is reached. t min Up to 0 ℃, take the corresponding antifreeze insulation layer thickness as the calculated value.

[0028] Compared with the prior art, the beneficial effects of the present invention are: I. This invention discloses an analytical calculation method for the surface thickness of the antifreeze insulation layer in deeply buried tunnels in cold regions. The specific steps are as follows: Assuming the thickness of the antifreeze insulation layer, based on the superposition principle, calculation models are established for the annual temperature amplitude and annual average temperature along the radial direction of the tunnel antifreeze insulation layer, secondary lining, initial support, and surrounding rock. The density, specific heat capacity, thermal conductivity, and temperature boundary conditions of the tunnel antifreeze insulation layer, secondary lining, initial support, and surrounding rock are obtained. The heat storage coefficient and surface heat storage coefficient of the tunnel secondary lining, antifreeze insulation layer, initial support, and surrounding rock are calculated. The radial depth distribution of the annual temperature amplitude of the tunnel antifreeze insulation layer, secondary lining, initial support, and surrounding rock is calculated. Using an annual temperature amplitude of 0.05 ℃ as a standard, the temperature influence boundary and its radial depth of the tunnel surrounding rock are determined. The annual average temperature at the location of the waterproofing membrane between the secondary lining and initial support is calculated. Based on the calculation results of the annual temperature amplitude and annual average temperature at the location of the tunnel waterproofing membrane, the annual minimum temperature at the location of the tunnel waterproofing membrane is calculated. t min ;by t min Whether the assumed antifreeze insulation layer is reasonable is determined by whether it equals 0℃ as the standard. t min =0 ℃, then the assumed thickness of the antifreeze insulation layer meets the requirements, and this value is taken as the calculated value of the antifreeze insulation layer thickness. If t min If the temperature is ≠ 0℃, the thickness of the antifreeze insulation layer needs to be adjusted and recalculated until the temperature reaches 0℃. t min The thickness of the antifreeze insulation layer is taken as the calculated value up to 0℃. The simplified analytical calculation method for the required thickness of the antifreeze insulation layer surface laying in the deep buried section of cold-region tunnels 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 antifreeze insulation layers.

[0029] II. This invention discloses an analytical calculation method for the surface thickness of the antifreeze insulation layer in deeply buried tunnels. It treats the annual temperature amplitude of the tunnel's antifreeze insulation layer, secondary lining, initial support, and surrounding rock along the radial depth as a 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, distinguishes between "thick" and "thin" material layers, calculates the surface heat storage coefficient of different material layers, and then determines the attenuation of the temperature harmonic wave at different depths along the tunnel's radial direction, thus obtaining the corresponding distribution of the tunnel's annual temperature amplitude along the radial depth. Therefore, the analytical calculation method for the surface thickness of the antifreeze insulation layer in deeply buried tunnels provided by this invention is comprehensive in its considerations, simple in its method, and has small calculation errors, making it highly valuable for widespread application. Attached Figure Description

[0030] Figure 1This is a flowchart of an embodiment of the present invention; Figure 2 This invention provides a periodic heat transfer multi-layer flat plate calculation model that considers the radial propagation of temperature harmonic waves along the tunnel's antifreeze insulation layer, lining structure, and surrounding rock. Figure 3 This invention provides a calculation model for the tunnel anti-freezing and heat insulation layer, lining structure, and surrounding rock steady-state heat transfer multi-layer cylindrical structure. Figure 4 The radial depth distribution of the annual temperature amplitude of the tunnel antifreeze insulation layer, lining structure, and surrounding rock obtained by analytical calculation in the example; Figure 5 The embodiment uses a numerical calculation model of the radial temperature field of the tunnel antifreeze insulation layer, lining structure, and surrounding rock. Detailed Implementation

[0031] 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.

[0032] Figure 1 The diagram shows a flowchart of an analytical calculation method for the surface thickness of an antifreeze and insulation layer in a deep-buried tunnel according to the present invention, which includes the following steps: S1. Assuming the thickness of the antifreeze insulation layer, based on the superposition principle, establish periodic heat transfer multi-layer plate models considering the radial propagation of temperature harmonic waves, such as... Figure 2 As shown, the radial depth heat transfer of the tunnel's anti-freezing insulation layer, lining structure, and surrounding rock under annual periodic temperature boundary conditions is considered as a temperature harmonic wave propagating radially from the surface of the anti-freezing insulation layer. The annual temperature amplitude at different radial depths in the tunnel's anti-freezing insulation layer, lining structure, and surrounding rock can be 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 at the location of the tunnel waterproofing membrane can be calculated using the steady-state heat conduction principle.

[0033] S2. Obtain the calculation parameters for the tunnel's anti-freezing and insulation layer, secondary lining, initial support, and surrounding rock thermal properties, including density, specific heat capacity, and thermal conductivity. Obtain the annual average air temperature and annual temperature amplitude as boundary conditions for air temperature inside the tunnel. Obtain the initial temperature of the surrounding rock as the temperature 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 surrounding rock temperature 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 surrounding rock temperature can be calculated using the following formula.

[0034] ; 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 of the isothermal zone and the depths of the boundary between the temperature-affected surrounding rock at the crown location, respectively, in meters. The temperature gradient in the warming zone of the strata is generally (1~3)℃ / 100 m.

[0035] S3. Based on the density, specific heat capacity, and thermal conductivity of the antifreeze insulation layer, 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 antifreeze insulation layer, secondary lining, initial support, and surrounding rock according to the principle of periodic heat transfer using the following method.

[0036] ; in: In the multi-layer flat plate model, the first i The heat storage coefficient of the layer material i =1, 2, 3, 4 represent the frost-resistant insulation layer, 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).

[0037] S4. In the direction of the temperature harmonic wave, if layer 2 (secondary lining) following layer 1 (anti-freeze insulation layer) is a "thick" layer, meaning there is a regular fluctuation segment 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. S At time 1, the temperature wave attenuation within layer 1 will increase, and vice versa. If layers 3 (initial support) and 4 (surrounding rock) are also "thick" layers, their influence on the layer above will be consistent. 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 is also affected by layer 3. The thinner layer 2 is, the greater this influence. If layer 3 is also a "thin" layer, then the surface heat storage coefficient of the layer 4 material will also affect the temperature wave attenuation of layers 1 and 2. Therefore, to consider the influence of the 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.

[0038] The surface heat storage coefficients of tunnel antifreeze insulation, secondary lining, initial support, and surrounding rock are calculated using the following method.

[0039] 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).

[0040] It should be noted that, based on the commonly used thermophysical parameters of antifreeze insulation layers and lining concrete materials, as well as the design thickness, the antifreeze insulation layer, secondary lining, and initial support are all "thin" layers, while the surrounding rock thickness in deep-buried sections is relatively large, making it a "thick" layer, and its surface heat storage coefficient is equal to its heat storage coefficient.

[0041] 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 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 Characteristics of Walls under Periodic Heat [C]. Proceedings of the National Conference on Building Energy Conservation Technology and Design, 2005), calculate the attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel antifreeze insulation layer, lining structure, and surrounding rock according to the following formula. ; in, The attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel's antifreeze insulation layer, lining structure, and surrounding rock. The convective heat transfer coefficient between air and the antifreeze insulation layer, in W / (m²). 2 ·K); , , and These are respectively the antifreeze insulation layer, secondary lining, initial support, and the thermal conductivity of the surrounding rock. Unit m 2 ·s -1 ; , , and These are the distances from the antifreeze insulation layer, the secondary lining, the inner surface of the initial support (surrounding rock side), and the boundary of the surrounding rock temperature influence from the outer surface of the antifreeze insulation layer, respectively, in meters.

[0042] Based on the above calculation results, the annual temperature amplitude at the corresponding radial depth of the tunnel anti-freeze insulation layer, lining structure, and surrounding rock is calculated using the following formula. ; in, Annual temperature amplitude at different radial depths of tunnel antifreeze insulation layer, lining structure and surrounding rock, in °C; The annual air temperature amplitude is expressed in °C.

[0043] S6. Based on the calculation of the annual temperature amplitude distribution of the surrounding rock along the radial depth in step S4, and taking the annual temperature amplitude of 0.05 ℃ as the standard, determine the temperature influence boundary of the tunnel surrounding rock and its radial depth.

[0044] S7. Based on the multi-layer cylindrical tunnel steady-state heat transfer calculation model established in step S1, the thermal conductivity of the tunnel anti-freeze insulation layer, lining structure, and surrounding rock obtained in step S2, and the radial depth of the surrounding rock temperature influence boundary obtained in step S5, the annual average temperature at the location of the waterproofing membrane between the secondary lining and the initial support of the tunnel is calculated using the multi-layer cylindrical steady-state heat transfer principle according to the following formula. .

[0045] ; ; in, The annual average temperature of the air is expressed in °C. The equivalent radius of the tunnel clearance. , , and These are the radii of the inner surfaces of the antifreeze and insulation layer, the secondary lining and the initial support, and the radius of the boundary affected by the temperature of the surrounding rock, respectively, in meters (m).

[0046] S8. Based on the annual temperature amplitude and annual average temperature at the location of the tunnel waterproofing membrane calculated in steps S5 and S7, the annual minimum temperature at the location of the waterproofing membrane is calculated using the following formula.

[0047] ; S9. Based on the annual minimum temperature at the location of the tunnel waterproofing membrane calculated in step S8, determine whether the assumed thickness of the anti-freeze insulation layer is reasonable. t min =0 ℃, then the assumed thickness of the antifreeze insulation layer meets the requirements, and this value is taken as the calculated value of the antifreeze insulation layer thickness; if t min If the temperature is not equal to 0℃, the assumed thickness of the antifreeze insulation layer is either too thick or too thin. The thickness of the antifreeze insulation layer needs to be adjusted and recalculated until the desired temperature is reached. t min Up to 0 ℃, take the corresponding antifreeze insulation layer thickness as the calculated value.

[0048] Example: Assuming the required antifreeze insulation layer thickness is 5 cm, based on the superposition principle, multi-layer flat tunnel models considering harmonic radial temperature propagation 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.

[0049] The values ​​of density, specific heat capacity, and thermal conductivity of the tunnel antifreeze insulation layer, secondary lining, initial support, and surrounding rock selected in this embodiment are shown in Table 1.

[0050] Table 1 Thermophysical parameters of tunnel lining structure and surrounding rock 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 3℃ and 17℃, respectively. The temperature is 7°C. The tunnel is a two-lane tunnel with a clearance equivalent radius of 5.55 m. The secondary lining and initial support thicknesses are 0.50 m and 0.26 m, respectively. The convective heat transfer coefficient between the tunnel air and the outer surface of the antifreeze insulation layer is... h 15 W / (m 2 ·K).

[0051] Based on the principle of periodic heat transfer, and using the aforementioned thermophysical parameters of the tunnel antifreeze insulation layer, lining structure, and surrounding rock, as well as the corresponding thickness values, the heat storage coefficients of each layer are calculated as follows: The heat storage coefficient of the antifreeze insulation layer ; Heat storage coefficient of secondary lining ; Heat storage coefficient of initial support ; heat storage coefficient of surrounding rock .

[0052] The calculated thermal resistances of each material layer in the flat plate model are as follows: Thermal resistance of antifreeze insulation layer K / W; Secondary lining thermal resistance K / W; Initial support thermal resistance K / W.

[0053] Based on the above, the thermal inertia index of the antifreeze insulation layer was calculated. Thermal inertia index of secondary lining Thermal inertia index of initial support Therefore, both the secondary lining and the initial support are "thin" layers. Correspondingly, the surface heat storage coefficient of the tunnel's anti-freezing and insulation layer is calculated. The heat storage coefficient of the secondary lining surface Initial support surface heat storage coefficient For deeply buried tunnels, the surrounding rock thickness is large, and its thermal inertia index is high. D 4 must be greater than 1, indicating a "thick" layer; therefore, the heat storage coefficient of the surrounding rock surface is... Referring to the calculation method for the propagation of temperature harmonic waves in multilayer 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 antifreeze insulation layer, lining structure, and surrounding rock is calculated according to the following formula. ; in, , 、 and The values ​​are 0.05 m, 0.55 m, and 0.81 m, respectively, representing the distances from the outer surface of the antifreeze insulation layer, the secondary lining, the inner surface of the initial support, and the boundary of the surrounding rock temperature influence.

[0054] Based on the calculation results of the attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel anti-freeze insulation layer, lining structure, and surrounding rock, the annual temperature amplitude at the corresponding radial depth is calculated using the following formula. ; in, Annual temperature amplitude at different radial depths of tunnel antifreeze insulation layer, lining structure and surrounding rock, in °C; The annual average temperature of the air is expressed in °C.

[0055] The final obtained annual temperature amplitude distribution along the radial depth of the tunnel anti-freeze insulation layer, lining structure, and surrounding rock is as follows: Figure 4 As shown, the annual temperature amplitude at the waterproofing membrane between the secondary lining and the initial support of the tunnel is 4.23 ℃.

[0056] 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 temperature influence boundary of the tunnel surrounding rock is determined, and the distance of its location from the outer surface of the antifreeze insulation layer is obtained. It is 16.40 m.

[0057] Based on the established steady-state heat transfer calculation model of the multi-layer cylindrical tunnel, and using the steady-state heat transfer principle of the multi-layer cylindrical tunnel, the heat flux density is calculated according to the following formula. q ; in, , , , and The values ​​are 5.55 m, 5.60 m, 6.10 m, 6.36 m and 21.95 m, respectively, representing the equivalent radius of the tunnel clearance, the inner surface radius of the antifreeze insulation layer, the secondary lining and the initial support, and the boundary radius of the surrounding rock temperature influence.

[0058] The heat flux density was calculated. .

[0059] The annual average temperature at the waterproofing membrane between the secondary lining and the initial support of the tunnel is calculated to be 5.06℃ using the following formula.

[0060] ; Based on the calculated annual temperature amplitude and annual average temperature at the location of the tunnel waterproofing membrane, the annual minimum temperature at the location of the tunnel waterproofing membrane is calculated using the following formula. t min =0.83 ℃.

[0061] ; Therefore, assuming the thickness of the antifreeze insulation layer is 5 cm, t min If the temperature exceeds 0℃, the thickness is too large, requiring a reduction in the thickness of the antifreeze insulation layer and recalculation. Finally, the calculation shows that when the antifreeze insulation layer thickness is 4 cm, the boundary of the surrounding rock temperature influence is 17.0 m from the outer surface of the antifreeze insulation layer, and the annual minimum temperature at the waterproofing membrane is... t min =0 ℃, therefore, the thickness of the antifreeze insulation layer is taken as 4 cm as the final calculated value.

[0062] The accuracy of the calculated thickness of the tunnel antifreeze insulation layer was verified using numerical simulation methods, as detailed below.

[0063] (1) Establishment of computational model This calculation adopts the design standard for 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 inner contour of the cross-section. The anti-freeze insulation layer is set on the outer surface of the secondary lining. By calculating the tunnel lining structure and surrounding rock temperature with different thicknesses of anti-freeze insulation layer, and taking the absence of negative temperature on the waterproof membrane as the standard, the required thickness of the anti-freeze insulation layer is determined.

[0064] The values ​​for the antifreeze insulation layer, 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). The air is in direct contact with the inner surface of the antifreeze insulation layer 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 3 ℃ 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 of 7 ℃. The method for determining the depth of the surrounding rock boundary is the same as the theoretical derivation, taking the radial depth position when the annual temperature amplitude of the surrounding rock drops to 0.05 ℃ as the temperature influence boundary of the surrounding rock. Therefore, when determining the outer boundary of the model, it is necessary to first perform a trial calculation of the tunnel temperature field to determine the depth of the temperature influence boundary of the surrounding rock. The initial temperature of the model is taken as the initial temperature of the surrounding rock. The average grid lengths of the anti-freezing insulation layer, lining structure, and surrounding rock are taken as 0.01 m, 0.1 m, and 1 m, respectively. This calculation uses FLUENT software with a calculation step 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.

[0065] The calculation results show that when the tunnel uses a 3.1 cm anti-freeze insulation layer, the temperature influence boundary of the surrounding rock is approximately 13 m, and the annual minimum temperature at the corresponding waterproofing membrane location is approximately 0 ℃. Therefore, the required anti-freeze insulation layer thickness for the tunnel calculated by numerical simulation is 3.1 cm, which is 0.9 cm smaller than the thickness calculated theoretically by this patent. This indicates that the analytical calculation method for the surface thickness of the anti-freeze insulation layer in the deep-buried tunnel section proposed in this patent is relatively conservative, with the calculated result slightly larger than that calculated by numerical simulation, and the difference between the two is within 1 cm.

[0066] Based on the above, the simplified analytical calculation method for the required thickness of the surface of the antifreeze and heat insulation layer for deep buried tunnels in cold regions proposed in this invention has a clear principle, complete steps, simple and conservative calculation, and small calculation error. It can provide effective support for the design of tunnel frost damage prevention and control, and has good promotion and application value.

Claims

1. A method for analytically calculating the thickness of the surface layer for frost-resistant insulation in deeply buried tunnels in cold regions, characterized in that... Includes the following steps: S1. Assuming the thickness of the anti-freeze insulation layer, establish calculation models for the tunnel anti-freeze insulation layer, secondary lining, initial support, annual temperature amplitude of surrounding rock and annual average temperature along radial depth when the surface of the anti-freeze insulation layer is laid. S2. Obtain the thermophysical parameters of the tunnel's anti-freezing insulation layer, secondary lining, initial support, and surrounding rock, as well as the temperature boundary conditions of the calculation model; S3. Calculate the heat storage coefficients of the tunnel anti-freeze insulation layer, 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 anti-freeze insulation layer, secondary lining, initial support and surrounding rock. S6. Using an annual temperature amplitude of 0.05 ℃ as the standard, determine the boundary of the temperature influence of the surrounding rock of the tunnel and its radial depth; S7. Calculate the annual average temperature at the location of the waterproof membrane between the secondary lining and the initial support of the tunnel. S8. Calculate the minimum annual temperature at the location of the waterproof membrane between the secondary lining and the initial support of the tunnel. S9. Determine whether the assumed thickness of the antifreeze insulation layer is reasonable, and determine the required thickness of the antifreeze insulation layer for the tunnel.

2. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions according to claim 1, characterized in that, Step S1 includes the following steps: S11. Based on the superposition principle, the radial depth heat transfer of the tunnel under the annual periodic temperature boundary condition is regarded as the radial propagation of temperature harmonic waves. A multi-plate calculation model for periodic heat transfer considering the radial propagation of temperature harmonic waves along the anti-freeze insulation layer, lining structure and surrounding rock 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 surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions 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 temperature variation zone, the initial temperature of the surrounding rock is taken as the annual average temperature of the formation; when the boundary of the surrounding rock temperature influence is within the formation temperature constant zone, the temperature of the constant zone is taken; when the boundary of the surrounding rock temperature influence is within the formation temperature increase zone, the initial temperature of the surrounding rock can be calculated by 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 (from the tunnel arch to the ground surface) is expressed in meters (m). , These represent the depths of the isothermal zone and the depths of the boundary between the temperature-affected surrounding rock at the crown location, respectively, in meters. The temperature gradient in the warming zone of the strata is generally (1~3)℃ / 100 m.

4. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions according to claim 1, characterized in that, In step S3, the heat storage system 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 i =1, 2, 3, 4 represent the frost-resistant insulation layer, 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.

5. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions 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 =1,2,3,4 represent the antifreeze insulation layer, secondary lining, initial support, and surrounding rock, respectively.

6. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions 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's anti-freezing insulation layer, secondary lining, initial support, and surrounding rock. ； in, The attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel's antifreeze insulation layer, lining structure, and surrounding rock. The convective heat transfer coefficient between air and the antifreeze insulation layer, in W / (m²). 2 ·K); , , and These are respectively the antifreeze insulation layer, secondary lining, initial support, and the thermal conductivity of the surrounding rock. Unit m 2 ·s -1 ; , , and These are the distances from the antifreeze insulation layer, the secondary lining, the inner surface of the initial support (surrounding rock side), and the boundary of the surrounding rock temperature influence from the outer surface of the antifreeze insulation layer, respectively, in meters; S52. Based on the calculation results of the attenuation factor of the annual temperature amplitude relative to air at different radial depths of the tunnel's anti-freezing insulation layer, secondary lining, initial support, and surrounding rock, calculate the annual temperature amplitude at the corresponding radial depth of the tunnel using the following formula. ； in, Annual temperature amplitude at different radial depths of tunnel antifreeze insulation layer, lining structure and surrounding rock, in °C; The annual air temperature amplitude is expressed in °C.

7. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions according to claim 1, characterized in that, In step S6, the radial depth distribution of the annual temperature amplitude of the surrounding rock is calculated based on step S5. The boundary of the surrounding rock temperature influence and its radial depth are determined with an annual temperature amplitude of 0.05 ℃ as the standard.

8. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions according to claim 1, characterized in that, In step S6, the annual average temperature at the location of the waterproofing membrane between the secondary lining and the initial support of the tunnel is calculated using the following formula. ； ； in, The annual average temperature of the air is expressed in °C. The equivalent radius of the tunnel clearance. , , and The radius of the inner surface of the antifreeze insulation layer, secondary lining, and initial support, as well as the radius of the boundary affected by the temperature of the surrounding rock, are measured in meters (m).

9. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions according to claim 1, characterized in that, In step S8, the annual minimum temperature at the location of the tunnel waterproofing membrane is calculated using the following formula. t min 。 10. The analytical calculation method for the surface thickness of the antifreeze and insulation layer in deep-buried tunnels in cold regions according to claim 1, characterized in that, In step S9, the annual minimum temperature at the location of the tunnel waterproofing membrane, calculated according to step S8, is determined. t min Determine whether the assumed thickness of the antifreeze insulation layer is reasonable. t min If the temperature is 0℃, then the assumed thickness of the antifreeze insulation layer meets the requirements, and this value is taken as the calculated value of the antifreeze insulation layer thickness. like t min If the temperature is not equal to 0℃, the assumed thickness of the antifreeze insulation layer is either too thick or too thin. The thickness of the antifreeze insulation layer needs to be adjusted and recalculated until the desired temperature is reached. t min Up to 0 ℃, take the corresponding antifreeze insulation layer thickness as the calculated value.

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