A method, device and medium for calculating temperature change of critical fortification of cold region tunnel

Abstract

The application discloses a kind of cold region tunnel critical fortification temperature change calculation method, belong to cold region tunnel engineering technical field.Firstly based on steady-state heat conduction and multilayer flat wall thermal resistance theory, the theoretical calculation model of critical fortification temperature of cold region tunnel is constructed.Through establishing tunnel longitudinal temperature field heat flow solid coupling calculation model, variable separation method is used to derive the analytical expression of wall temperature distribution and combined with surrounding rock-lining temperature heat conduction model, obtain the temperature prediction formula of each structure layer interface of tunnel under the condition of no insulation layer and with insulation layer;Based on the requirements of anti-freezing fortification temperature, temperature prediction formula and critical condition, the critical fortification temperature in tunnel hole is calculated back and the anti-freezing fortification length of cold region tunnel is determined.The application can simplify the calculation process of cold region tunnel temperature field, reduce the dependence on field monitoring data, accurately determine the critical fortification temperature and fortification length under different environmental conditions, and provide scientific basis for anti-freezing design and insulation layer setting of cold region tunnel.

Description

Technical Field

[0001] This invention relates to a method, equipment, and medium for calculating temperature changes, specifically to a method, equipment, and medium for calculating the critical design temperature changes of tunnels in cold regions, belonging to the technical field of tunnel engineering in cold regions. Background Technology

[0002] During operation, tunnels in cold regions experience significant changes in their internal temperature field due to the intrusion of cold air currents in winter. When the temperature of the surrounding rock drops below freezing, it can cause frost heave in the lining and freeze-thaw cycles in the surrounding rock, severely impacting the long-term stability and operational safety of the tunnel structure. Therefore, accurately predicting the temperature field distribution patterns inside tunnels in cold regions and rationally determining the length of frost protection measures are of great importance for the frost-resistant design and insulation measures for tunnels in cold regions.

[0003] Existing research has laid a good foundation for predicting the temperature field inside tunnels in cold regions. However, in determining and selecting the design length, most existing methods simply use negative temperature as the dividing line, that is, only consider whether the air temperature inside the tunnel is below 0℃, while ignoring the thermal conductivity characteristics of the surrounding rock-lining structure system and lacking in-depth discussion on its selection criteria. This results in the design length being determined too roughly, making it difficult to meet the actual needs of engineering.

[0004] In solving temperature fields, existing methods are mainly divided into two categories: numerical simulation and field monitoring. While numerical simulation can accurately simulate the evolution of the temperature field, the calculation process is complex, requiring the establishment of a refined thermo-fluid-structure interaction model, which places high demands on computational resources. Field monitoring methods, on the other hand, rely on long-term monitoring data, are costly, and are limited by field conditions, making them difficult to apply under different environmental conditions. Furthermore, most existing theoretical analytical methods are designed for specific working conditions and lack simplified calculation methods for temperature fields in cold-region tunnels applicable to different environmental factors such as external wind speed, ambient temperature, lining thickness, and surrounding rock temperature. Summary of the Invention

[0005] The purpose of this invention is to provide a simple calculation method for the critical design temperature change of tunnels in cold regions, which is highly applicable and can comprehensively consider various environmental factors. By establishing an air domain convection-conduction coupling model and a surrounding rock-lining multilayer heat conduction model, the invention solves the problems of complex calculation process and difficulty in applying to different environmental conditions, and achieves accurate prediction of longitudinal temperature distribution in tunnels, providing a theoretical basis for the thermal insulation design of tunnels in cold regions.

[0006] To achieve the above-mentioned objectives, this invention proposes a method for calculating the critical design temperature variation of tunnels in cold regions, comprising the following steps:

[0007] Step 1: Establish a thermal-fluid-structure interaction calculation model for the longitudinal temperature field of the tunnel. By using the variable separation method and the principal mode approximation, obtain the expression for the longitudinal temperature distribution of the tunnel wall.

[0008] Step 2: Based on the temperature heat conduction calculation model of surrounding rock-lining, combined with the multi-layer flat wall approximation and the thermal resistance series principle, the temperature prediction formula of the interface of each structural layer of the tunnel under the conditions of no insulation layer and with insulation layer is obtained.

[0009] Step 3: Use the longitudinal temperature distribution expression of the tunnel wall obtained in Step 1 as the inner boundary temperature of the surrounding rock-lining temperature heat conduction calculation model in Step 2. Calculate the critical design temperature when the temperature of the secondary lining-primary lining contact surface or the temperature of the primary lining-surrounding rock interface is 0℃ at different axial positions. Substitute the critical design temperature into the longitudinal temperature distribution expression of the tunnel wall to obtain the critical axial position, thereby determining the anti-freezing design length of the tunnel in the cold region.

[0010] Furthermore, in step 1, the expression for the tunnel heat transfer control equation in the longitudinal temperature field thermo-fluid-structure interaction calculation model is as follows: ,

[0011] in, The tunnel axial position The air temperature there Indicates the position along the tunnel axis The distance traveled at that location; Air velocity; The thermal conductivity of air; air density; The specific heat capacity of air at constant pressure;

[0012] Set boundary conditions, including tunnel entrance boundary, tunnel central axis symmetry boundary, and tunnel inner wall heat transfer boundary;

[0013] The expression for the tunnel entrance boundary is: ,

[0014] The expression for the symmetrical boundary of the tunnel's central axis is: ,

[0015] The expression for the heat transfer boundary of the tunnel inner wall is: ,

[0016] in, Indicates the air temperature at the tunnel entrance; The tunnel wall in axial position Temperature at that location; The convective heat transfer coefficient between the air and the wall.

[0017] Furthermore, in step 1, the process of deriving the expression for the longitudinal temperature distribution of the tunnel wall through the variable separation method and principal mode approximation includes:

[0018] Let the temperature field be separated into the following variables: After substituting the data into the longitudinal temperature field thermo-fluid-structure interaction calculation model of the tunnel, the axial part was separated. With radial portion ;

[0019] in, For eigenvalues, It is a zeroth-order Bessel function of the first kind. The attenuation coefficient;

[0020] Combining the axial and radial components, the expression for the temperature field, expanded using modal series, is as follows: ,

[0021] in, , and The first The amplitude coefficients, eigenvalues, and attenuation coefficients of the first mode are taken as follows: The approximate expression for the tunnel wall temperature is as follows: ;

[0022] Introducing surrounding rock geothermal temperature and the temperature at the tunnel entrance The expression for tunnel wall temperature is reconstructed, and the tunnel wall temperature is further expressed as: ;

[0023] The energy equation along the tunnel axis is expressed as: A is the cross-sectional area of ​​the tunnel;

[0024] For a circular tunnel in a cold region, the circumference is... The area is , The total height of the tunnel cross-section is expressed as... Let the radius of the tunnel be denoted as , and substituting it into the energy equation, we get: ;

[0025] make and If is a constant, then: Substituting into the above equation, we get: And solve for the parameters Finally, the expression for the longitudinal temperature distribution on the tunnel wall was derived as follows: .

[0026] Furthermore, in step 2, the thermal resistance of the primary lining, secondary lining, and surrounding rock required for deriving the temperature prediction formula under conditions without insulation is expressed as follows: ;

[0027] in, For the thermal conductivity of the surrounding rock, The effective thickness of the surrounding rock, Represents the initial lining thermal resistance. Represents the thermal resistance of the secondary lining. Represents the thermal resistance of the surrounding rock. For the initial lining thickness, For the thickness of the secondary lining, The thermal conductivity of the initial lining concrete is related to the concrete grade. Related, The thermal conductivity of the secondary lining concrete is related to the concrete grade. Related;

[0028] The total thermal resistance from the tunnel wall to the surrounding rock is: .

[0029] Furthermore, in step 2, the derivation process of the temperature prediction formula for each interface under the condition of no insulation layer includes:

[0030] The thermal resistance from the tunnel inner wall to the secondary lining-primary lining contact surface is given by the secondary lining thermal resistance. ,therefore: Overall heat flux density for ,Right now: From the above and It can be deduced that the temperature at the contact surface between the secondary lining and the primary lining is... for: ;

[0031] Similarly, the thermal resistance from the tunnel inner wall to the interface between the primary lining and the surrounding rock is the thermal resistance of the primary lining. The thermal resistance of the secondary lining is ,therefore: ,Right now: From the above , and It can be deduced that the temperature at the interface between the primary lining and the surrounding rock is... for: .

[0032] Furthermore, in step 2, with the existing insulation layer, an insulation layer is added to the inner wall of the tunnel, and the insulation layer has a thermal resistance... The calculation formula is: ;

[0033] in, For the thickness of the insulation layer, The thermal conductivity of the insulation layer material;

[0034] The total thermal resistance is the sum of the thermal resistances of the primary lining, insulation layer, surrounding rock, and secondary lining, expressed as:

[0035] ;

[0036] The overall heat flux density when heat flows through multiple layers of material with an insulation layer is: ;

[0037] The contact surface temperature between the secondary lining and the primary lining is: Substitute Sorted as:

[0038] ;

[0039] The interface temperature between the surrounding rock and the lining structure is Substitute Sorted as: ; .

[0040] Furthermore, in step 3, under the condition of no insulation layer, when the temperature at the interface between the surrounding rock and the lining is required to be 0℃, ,at this time , Assuming a critical design temperature, substitute the interface temperature between the initial lining and the surrounding rock. From the expression, the formula for the critical protection temperature can be obtained as follows: ;

[0041] Similarly, when the temperature requirement for the contact surface between the secondary lining and the primary lining is 0℃, ,at this time , Assuming the critical design temperature, substitute the contact temperature between the secondary lining and the primary lining. From the expression, the formula for the critical protection temperature can be obtained as follows: .

[0042] Furthermore, in step 3, the derivation process of the prediction formula for the critical temperature of the inner surface of the insulation layer under the condition of having an insulation layer includes:

[0043] When the interface temperature between the surrounding rock and the lining structure is required to be 0℃. ,at this time , Let be the critical design temperature of the inner surface of the insulation layer. Substituting this into the expression for the interface temperature between the surrounding rock and the lining structure under the condition of having an insulation layer, we obtain... Therefore, the critical protection temperature of the inner surface of the insulation layer is:

[0044] ;

[0045] When the contact surface temperature between the secondary lining and the primary lining is required to be 0℃. ,at this time , Let be the critical protection temperature of the inner surface of the insulation layer. Substituting this into the expression for the contact surface temperature between the secondary lining and the primary lining under the condition of having an insulation layer, the critical protection temperature of the inner surface of the insulation layer is: .

[0046] The present invention also provides an electronic device, including a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method.

[0047] The present invention also provides a storage medium storing a computer program or instructions that, when the computer program or instructions are run on a computer, execute the steps of the method described.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] This invention establishes a thermo-fluid-structure interaction calculation model for the longitudinal temperature field of a tunnel, and derives an explicit analytical expression for the longitudinal temperature distribution of the tunnel wall by using the variable separation method and principal mode approximation. This avoids the complex numerical simulation calculation process, eliminates the need to rely on long-term on-site monitoring data, significantly simplifies the solution method for the temperature field of tunnels in cold regions, has high computational efficiency, and is convenient for practical engineering applications.

[0050] This invention changes the traditional approach of simply using the negative temperature of the air inside the tunnel as the basis for determining the design length. It explores in depth the selection criteria for the design length and uses the critical freezing temperature of the surrounding rock-lining structure system (i.e., the temperature at the interface between the surrounding rock and the lining reaches 0℃ or the temperature at the contact surface between the secondary lining and the primary lining reaches 0℃) as the design criterion. This is more in line with the actual physical mechanism of frost damage in tunnels in cold regions, and the determination of the design length is more scientific and reasonable.

[0051] Based on steady-state heat conduction theory and the principle of multi-layer flat wall thermal resistance series connection, this invention establishes a calculation model for the temperature heat conduction of surrounding rock and lining. It comprehensively considers the material properties and heat transfer characteristics of the primary lining, secondary lining, insulation layer and surrounding rock. By accurately calculating the temperature distribution at the interface of each structural layer through the thermal resistance distribution law, it can determine the corresponding critical protection temperature for different lining structures and insulation layer settings.

[0052] This invention comprehensively considers the influence of various environmental factors and structural parameters, such as external wind speed, external air temperature, lining thickness, and surrounding rock temperature, on the temperature field and design length of tunnels in cold regions. It can adapt to tunnels in cold regions with different climatic conditions, geological conditions, and structural forms, and has a wide range of applications and strong versatility. It provides a theoretical basis for the differentiated anti-freezing design of tunnels in cold regions. Attached Figure Description

[0053] Figure 1 This is a flowchart of the calculation method for the critical design temperature change of tunnels in cold regions proposed in this invention;

[0054] Figure 2 This invention presents a convection-conduction coupling model for the temperature field of tunnels in cold regions.

[0055] Figure 3 This invention presents a cross-sectional model of a tunnel in a cold region.

[0056] Figure 4 This is a comparison diagram of the theoretical and measured temperature field distribution inside the tunnel. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0058] Example 1:

[0059] like Figure 1 As shown, this paper specifically relates to a method for calculating the temperature field and critical design temperature changes inside a tunnel in a cold region, including the following steps:

[0060] Step 1: Obtain tunnel geometric parameters (inlet and outlet radii, length, burial depth), external environmental parameters (external wind speed, external temperature), surrounding rock temperature, and other physical parameters.

[0061] Step 2: Based on the steady-state heat conduction and multi-layer flat wall thermal resistance theory, construct a theoretical calculation model for the critical design temperature of tunnels in cold regions, and comprehensively consider the influence of external wind speed, external air temperature, lining thickness and surrounding rock ground temperature on the frost-resistant design length of tunnels in cold regions.

[0062] Step 3: Establish a thermal-fluid-structure interaction calculation model for the longitudinal temperature field of the tunnel. Using the variable separation method and principal mode approximation, derive an explicit analytical expression for the longitudinal temperature distribution on the tunnel wall.

[0063] Step 4: Based on the temperature and heat conduction calculation model of the surrounding rock-lining, combined with the multi-layer flat wall approximation and the thermal resistance series principle, determine the temperature prediction formula of the interface between each structural layer of the tunnel under the conditions of no insulation layer and with insulation layer.

[0064] Step 5: Use the longitudinal temperature distribution expression of the tunnel wall obtained in Step 3 as the inner boundary temperature of the transverse heat conduction model of the surrounding rock-lining in Step 4. Calculate the contact surface temperature of the secondary lining-primary lining and the interface temperature of the primary lining-surrounding rock at different axial positions. Take the temperature of the secondary lining-primary lining contact surface or the interface temperature of the primary lining-surrounding rock reaching (0℃) as the freezing critical condition. Back-calculate the corresponding tunnel wall temperature, which is the critical protection temperature of the tunnel wall. Substitute the critical protection temperature of the tunnel into the longitudinal temperature distribution expression of the tunnel wall to obtain the corresponding critical axial position, thereby determining the anti-freezing protection length of the tunnel in the cold region.

[0065] Specifically, the thermal-fluid-structure interaction calculation model for the longitudinal temperature field of the tunnel is established based on the following basic assumptions, which can be simplified as follows: Figure 2 As shown:

[0066] (1) The tunnel cross-section is simplified to a circle;

[0067] (2) Air and the wall exchange heat through convection, cooling the tunnel wall;

[0068] (3) In the axial direction, heat transfer is dominated by convection, while in the radial direction, heat transfer is dominated by conduction.

[0069] (4) The surrounding rock geothermal temperature is equivalent to an isothermal boundary, according to the geothermal gradient formula calculate, The temperature of the Earth's surface isothermal layer. The geothermal gradient in China averages approximately 0.03℃ / m. This refers to the tunnel's burial depth.

[0070] (5) The axial velocity of air in the tunnel is constant.

[0071] Specifically, the tunnel heat transfer control equations are established, including the air domain heat conduction-convection equations: ;

[0072] in, Air temperature; Indicates the position along the tunnel axis The distance traveled at that location; Air velocity; The thermal conductivity of air; air density; The specific heat capacity of air at constant pressure;

[0073] Setting boundary conditions includes:

[0074] (1) Tunnel entrance boundary: ;

[0075] in, This represents the air temperature at the tunnel entrance, typically taken from the average temperature of the coldest month. Since airflow is stable and the entrance temperature is approximately uniform, it is assumed to be constant in the radial direction.

[0076] (2) Symmetrical boundary of the tunnel's central axis: ;

[0077] (3) Heat transfer boundary of tunnel inner wall: ;

[0078] in, The tunnel wall in axial position Temperature at that location; The air temperature at the tunnel entrance serves as a convective cold source; The convective heat transfer coefficient between air and the wall is affected by wind speed. The influence, the numerical value of which is usually expressed using independent semi-empirical relationships. Characterization (independent of the current temperature difference; once this coefficient is determined, it is substituted into the boundary conditions) (Calculation of heat transfer heat flux density). The diameter of the tunnel. and It is an empirical constant. This reflects the sensitivity of wind speed V to the enhancing effect of the convective heat transfer coefficient h. This reflects the influence of fluid properties (such as thermal conductivity, viscosity, density, specific heat capacity, etc.) and factors such as the roughness and shape of the tunnel wall on convective heat transfer. In permafrost and cold-region geotechnical engineering, empirical constants are used. The value range is from 15 to 40, and the index The value ranges from 0.75 to 0.8.

[0079] Specifically, the process of deriving the analytical solution for the wall temperature distribution using the method of separation of variables includes:

[0080] Set temperature field Let the separable variable be the temperature field. ;

[0081] Substitute into the main control equation Separating the variables, the axial portion yields:

[0082] The radial portion yields: ;

[0083] in: These eigenvalues ​​determine the modal decay rate. It is a zeroth-order Bessel function of the first kind. The attenuation coefficient represents the rate at which the temperature decreases along the tunnel axis.

[0084] Combining the two parts, the expression for the temperature field is a modal series expansion: ;

[0085] in: , and The first The amplitude coefficients, eigenvalues, and attenuation coefficients of the first mode are considered, taking the dominant role of the principal mode in the temperature recovery process as an example. Approximately, the temperature at the wall surface can be obtained as: ;

[0086] Specifically, introducing surrounding rock geothermal temperature and the temperature at the tunnel entrance The temperature expression is reconstructed to express the wall temperature as:

[0087] ;

[0088] The energy equation along the tunnel axis is expressed as: A is the cross-sectional area of ​​the tunnel;

[0089] For a circular tunnel in a cold region, the circumference is... The area is , The total height of the tunnel cross-section is expressed as... Let the radius of the tunnel be denoted, and then substituting it into the energy equation: ;

[0090] make ,and If is a constant, then: Substituting, we get: ;

[0091] First-order linear homogeneous equations: , thus obtaining parameters Substituting the relationship between wall temperature and air temperature, the expression for the longitudinal temperature distribution of the tunnel wall is finally derived as follows: ;

[0092] Engineering practice shows that, since the critical temperature for frost damage deviates from the traditional experience-based 0°C benchmark for tunnel walls, the current anti-freezing design standards face the risk of deviating from reality. Therefore, the critical protection temperature point is often selected when the interface between the primary lining and the surrounding rock or the contact surface between the secondary lining and the primary lining is 0°C.

[0093] Specifically, the calculation model for transverse heat conduction between the surrounding rock and the lining is based on the following assumptions, and the specific details of the tunnel's internal cross-section are as follows: Figure 3 As shown:

[0094] (1) The heat transfer inside the tunnel wall is in a steady state;

[0095] (2) The normal heat flow along the lining thickness direction is dominant, and the circumferential heat flow is ignored;

[0096] (3) The different material layers are in close contact with each other, with no contact thermal resistance;

[0097] (4) The thermal conductivity of each layer of material is constant.

[0098] Specifically, under conditions without insulation, the thermal resistance between the primary lining, secondary lining, and surrounding rock is expressed as:

[0099] ;

[0100] in, For the thermal conductivity of the surrounding rock, The effective thickness of the surrounding rock, Represents the initial lining thermal resistance. Represents the thermal resistance of the secondary lining. Represents the thermal resistance of the surrounding rock. For the initial lining thickness, For the thickness of the secondary lining, For heat flux density, The thermal conductivity of the initial lining concrete is related to the concrete grade. Related, The thermal conductivity of the secondary lining concrete is related to the concrete grade. Related;

[0101] The thermal conductivity of concrete of different grades is as follows: ;

[0102] The total thermal resistance from the tunnel wall to the surrounding rock is: ;

[0103] Specifically, heat flux density The derivation process includes:

[0104] The heat flux density from the surrounding rock to the interface is expressed as: , The temperature of the tunnel wall;

[0105] The heat flow through the secondary lining, primary lining, and interface to the surrounding rock is continuous. The heat flow density for the secondary lining is expressed as: , This refers to the temperature at the contact surface between the secondary lining and the primary lining of the tunnel.

[0106] For the initial lining (thickness) ): , This refers to the temperature between the initial lining and the surrounding rock.

[0107] The overall heat flow from the tunnel wall to the surrounding rock is represented as: ;

[0108] It should be noted that in the formula , and This does not act independently on different final calculation formulas, but rather describes the layered heat transfer state when heat flows sequentially through the secondary lining, primary lining, and equivalent surrounding rock layers under conditions without insulation. Since this model assumes steady-state heat transfer within the tunnel wall and tight contact with no contact thermal resistance between material layers, the heat flow remains continuous in each layer; that is, the heat flux density of the secondary lining, primary lining, and surrounding rock side is equal to the overall heat flux density. Based on this continuity condition, the overall heat flux density is used in subsequent derivations. A unified representation of heat flow in each layer is used, and the temperature drop is distributed through the thermal resistance of each layer, thereby obtaining a temperature prediction formula for the interface between each structural layer.

[0109] Specifically, the derivation process of the prediction formulas for the temperatures of each interface under conditions without insulation includes:

[0110] The thermal resistance from the tunnel inner wall to the secondary lining-primary lining contact surface is given by the secondary lining thermal resistance. ,therefore: ,Right now: Rearranging the terms, we get From the above and It can be deduced that the temperature at the contact surface between the secondary lining and the primary lining is... for: ;

[0111] Similarly, the thermal resistance from the tunnel inner wall to the interface between the primary lining and the surrounding rock is the thermal resistance of the primary lining. The thermal resistance of the secondary lining is ,therefore: ,Right now: Transpose to get From the above , and It can be deduced that the temperature at the interface between the primary lining and the surrounding rock is... for: .

[0112] Specifically, under conditions without insulation, when the temperature requirement at the interface between the surrounding rock and the lining is 0℃, ,at this time , Substituting the critical protection temperature into the equation: , can be obtained ,therefore: The wall surface boundary protection temperature is calculated as follows: From the above , and The formula for the critical design temperature can be derived as follows: ;

[0113] Similarly, when the temperature requirement for the contact surface between the secondary lining and the primary lining is 0℃, ,at this time , Substituting the critical protection temperature into the equation: , can be obtained ,therefore: The wall surface boundary protection temperature obtained by reverse calculation is: From the above , and The formula for the critical design temperature can be derived as follows: ;

[0114] Specifically, in the case of an existing insulation layer, an insulation layer is installed on the inner wall of the tunnel. The thermal resistance of the insulation layer... The calculation formula is: , For the thickness of the insulation layer, The thermal conductivity of the insulation layer material;

[0115] The total thermal resistance is the sum of the thermal resistances of the primary lining, insulation layer, surrounding rock, and secondary lining, expressed as:

[0116] ;

[0117] When heat flows through multiple layers of material with insulation, the total temperature difference is proportional to the total thermal resistance, and the overall heat flux density is: ;

[0118] Specifically, with an insulation layer, the inner surface temperature of the insulation layer... The derivation process of the prediction formula includes:

[0119] The interface temperature between the surrounding rock and the lining structure is Substitute Sorted as: ;

[0120] When the interface temperature between the surrounding rock and the lining structure is required to be 0℃. ,at this time , Let the critical protection temperature of the inner surface of the insulation layer be: ,therefore: Therefore, the critical protection temperature of the inner surface of the insulation layer is: From the above , , and The mathematical formula for the critical design temperature of the inner surface of the insulation layer can be derived as follows: ;

[0121] The contact surface temperature between the secondary lining and the primary lining is Substitute Sorted as:

[0122] ;

[0123] When the contact surface temperature between the secondary lining and the primary lining is required to be 0℃. ,at this time , Let the critical protection temperature of the inner surface of the insulation layer be: ,therefore: Therefore, the critical protection temperature of the inner surface of the insulation layer is: From the above , , and The mathematical formula for the critical design temperature of the inner surface of the insulation layer can be derived as follows: .

[0124] This invention relates to a method for calculating the critical design temperature variation of tunnels in cold regions. Based on the theory of steady-state heat conduction and multi-layer flat wall thermal resistance, this method constructs a theoretical calculation model for the critical design temperature of tunnels in cold regions. It comprehensively considers factors such as external wind speed, external air temperature, lining thickness, and surrounding rock temperature. By establishing a longitudinal temperature field thermal-fluid-structure interaction calculation model and a surrounding rock-lining temperature heat conduction calculation model, the method determines the temperature distribution at the interfaces of various structural layers of the tunnel under conditions with and without insulation, so as to meet the scientific requirements for determining the anti-freezing design length of tunnels in cold regions.

[0125] This invention constructs a calculation model applicable to temperature field prediction and critical design temperature determination for tunnels in cold regions. By deeply studying the longitudinal temperature field distribution law of tunnels and the multi-layer heat conduction characteristics of lining structures, it helps to solve the technical problems of fuzzy standards for determining the anti-freezing design length of tunnels in cold regions, complex temperature field solution process, and reliance on field monitoring data. It simplifies the temperature field calculation process for tunnels in cold regions and provides a scientific basis for anti-freezing design and insulation layer setting of tunnels in cold regions.

[0126] The following example demonstrates the application of the method for calculating the critical design temperature variation of tunnels in cold regions proposed in this invention:

[0127] Taking the Yushuchuan Tunnel as an example, its entrance radius is 5.4m, the maximum relative elevation difference is about 132m, the overall burial depth is relatively shallow, the extreme minimum temperature recorded over the years is -37.1℃, the average temperature of the coldest month is -15.2℃, and the annual average temperature is 4.6℃. Its primary lining is C30 grade concrete with a thickness of 25cm, and the secondary lining is C40 grade concrete with a thickness of 35cm. The thermal conductivity of the surrounding rock is 2.5W / m·K. According to on-site measurements, when the wind speed at the entrance is 4.3m / s, the surrounding rock temperature is 5℃, and the outside air temperature is -10.29℃, the convective heat transfer coefficient can be derived from the prediction model as 7.1. Under the condition of no insulation layer, the predicted critical design temperature of the tunnel wall is -2.22℃, which is close to the measured value of -2.21℃. If a 5cm thick polyurethane insulation board is installed, the predicted critical design temperature is -9.56℃, which is close to the measured value of -9.67℃.

[0128] Based on the above derivation, it can be seen that without an insulation layer, when the temperature of the tunnel secondary lining-primary lining contact surface is 0℃, the corresponding critical protection temperature of the wall surface is -2.22℃. The critical protection temperature point predicted by the model is located approximately 1440m from the tunnel entrance. This predicted value is close to the measured distance of 1444m, and the difference is within the allowable error range for engineering, verifying the effectiveness and engineering applicability of the model. Further calculations based on the model show that without an insulation layer, the distance from the tunnel entrance is 848m when the tunnel surrounding rock-lining interface is at a negative temperature; with an insulation layer, the distance from the tunnel entrance is 59m when the tunnel secondary lining-primary lining contact surface is at a negative temperature, and the entire surrounding rock-lining interface is in a non-frozen state.

[0129] This invention, based on the physical mechanism of axial convection and radial heat conduction dominance, derives an explicit analytical expression for the exponential decay of tunnel wall temperature along the longitudinal direction through variable separation and principal mode approximation. This aligns with the observed law of rapid temperature decrease from the tunnel entrance and gradual convergence to the surrounding rock temperature. Simultaneously, the model directly couples key parameters such as external wind speed, air temperature, lining thickness, and surrounding rock temperature into the decay coefficient. The input parameters for the Yushuchuan Tunnel precisely match the theoretical decay rate with the measured gradient. This invention uses 0℃ at the secondary lining-primary lining contact surface or the surrounding rock-lining interface as the critical criterion. Through multi-layer flat wall thermal resistance series calculation, the temperature difference between the wall surface and the internal temperature of the structural layers is accurately determined. The calculated critical design temperature and design length are consistent with the measured height, enabling the model to accurately reproduce the actual temperature distribution trend without relying on complex numerical simulations and long-term monitoring. Specific results are as follows: Figure 4 As shown.

[0130] Example 2:

[0131] This invention provides an electronic device, including a processor and a memory. The memory stores program instructions for implementing the method for calculating the critical design temperature change of tunnels in cold regions according to Embodiment 1. The processor executes the program instructions stored in the memory to calculate the critical design temperature change of tunnels in cold regions.

[0132] The processor can also be called a Central Processing Unit (CPU). A processor may be an integrated circuit chip with signal processing capabilities. A processor can also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. A general-purpose processor can be a microprocessor or any conventional processor.

[0133] The methods described in Embodiment 1 of this invention are applicable to this electronic device embodiment. The specific functions implemented by this electronic device embodiment are the same as those in the above method embodiment, and the beneficial effects achieved are also the same as those achieved by the above methods.

[0134] Example 3:

[0135] This embodiment provides a storage medium storing a computer program or instructions capable of implementing the above-described method for calculating the critical design temperature change of tunnels in cold regions. When the computer program or instructions are run on a computer, the steps of the above-described method for calculating the critical design temperature change of tunnels in cold regions are executed.

[0136] The computer program or instructions can be stored in the aforementioned storage medium in the form of a software product, including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods of various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks, or terminal devices such as computers, servers, mobile phones, and tablets.

[0137] The methods described in Embodiment 1 of this invention are all applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above methods.

[0138] This invention provides a method, equipment, and medium for calculating the critical design temperature change of tunnels in cold regions. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A method for calculating the critical design temperature variation of tunnels in cold regions, characterized in that, Includes the following steps: Step 1: Establish a thermal-fluid-structure interaction calculation model for the longitudinal temperature field of the tunnel. By using the variable separation method and the principal mode approximation, obtain the expression for the longitudinal temperature distribution of the tunnel wall. Step 2: Based on the temperature heat conduction calculation model of surrounding rock-lining, combined with the multi-layer flat wall approximation and the thermal resistance series principle, the temperature prediction formula of the interface of each structural layer of the tunnel under the conditions of no insulation layer and with insulation layer is obtained. Step 3: Use the longitudinal temperature distribution expression of the tunnel wall obtained in Step 1 as the inner boundary temperature of the surrounding rock-lining temperature heat conduction calculation model in Step 2. Calculate the critical design temperature when the temperature of the secondary lining-primary lining contact surface or the temperature of the primary lining-surrounding rock interface is 0℃ at different axial positions. Substitute the critical design temperature into the longitudinal temperature distribution expression of the tunnel wall to obtain the critical axial position, thereby determining the anti-freezing design length of the tunnel in the cold region.

2. The method for calculating the critical design temperature change of tunnels in cold regions according to claim 1, characterized in that, In step 1, the expression for the tunnel heat transfer control equation in the longitudinal temperature field thermo-fluid-structure interaction calculation model is as follows: ， in, The tunnel axial position The air temperature there Indicates the position along the tunnel axis The distance traveled at that location; Air velocity; The thermal conductivity of air; air density; The specific heat capacity of air at constant pressure; Set boundary conditions, including tunnel entrance boundary, tunnel central axis symmetry boundary, and tunnel inner wall heat transfer boundary; The expression for the tunnel entrance boundary is: , The expression for the symmetrical boundary of the tunnel's central axis is: , The expression for the heat transfer boundary of the tunnel inner wall is: , in, Indicates the air temperature at the tunnel entrance; The tunnel wall in axial position Temperature at that location; The convective heat transfer coefficient between the air and the wall.

3. The method for calculating the critical design temperature change of tunnels in cold regions according to claim 1, characterized in that, In step 1, the process of deriving the expression for the longitudinal temperature distribution of the tunnel wall through the variable separation method and principal mode approximation includes: Let the temperature field be separated into the following variables: After substituting the data into the longitudinal temperature field thermo-fluid-structure interaction calculation model of the tunnel, the axial part was separated. With radial portion ; in, For eigenvalues, It is a zeroth-order Bessel function of the first kind. The attenuation coefficient; Combining the axial and radial components, the expression for the temperature field, expanded using modal series, is as follows: , in, , and The first The amplitude coefficients, eigenvalues, and attenuation coefficients of the first mode are taken as follows: The approximate expression for the tunnel wall temperature is as follows: ; Introducing surrounding rock geothermal temperature and the temperature at the tunnel entrance The expression for tunnel wall temperature is reconstructed, and the tunnel wall temperature is further expressed as: ; The energy equation along the tunnel axis is expressed as: Let A be the cross-sectional area of ​​the tunnel and P be the perimeter of the tunnel, which can be further expressed as: , Indicates the tunnel radius; make and If is a constant, then: Substituting into the above equation, we get: Solving for the parameters Finally, the expression for the longitudinal temperature distribution on the tunnel wall was derived as follows: .

4. The method for calculating the critical design temperature change of tunnels in cold regions according to claim 1, characterized in that, In step 2, the thermal resistance of the primary lining, secondary lining, and surrounding rock required for deriving the temperature prediction formula under conditions without insulation is expressed as follows: ； in, For the thermal conductivity of the surrounding rock, The effective thickness of the surrounding rock, Represents the initial lining thermal resistance. Represents the thermal resistance of the secondary lining. Represents the thermal resistance of the surrounding rock. For the initial lining thickness, The thickness of the secondary lining is... The thermal conductivity of the initial lining concrete is related to the concrete grade. Related, The thermal conductivity of the secondary lining concrete is related to the concrete grade. Related; The total thermal resistance from the tunnel wall to the surrounding rock is: .

5. The method for calculating the critical design temperature change of tunnels in cold regions according to claim 1, characterized in that, In step 2, the derivation process of the temperature prediction formula for each interface under the condition of no insulation layer includes: The thermal resistance from the tunnel inner wall to the secondary lining-primary lining contact surface is given by the secondary lining thermal resistance. ,therefore Overall heat flux density for ,Right now: From the above and It can be deduced that the temperature at the contact surface between the secondary lining and the primary lining is... for: ; Similarly, the thermal resistance from the tunnel inner wall to the interface between the primary lining and the surrounding rock is the thermal resistance of the primary lining. The thermal resistance of the secondary lining is ,therefore: ,Right now: From the above , and It can be deduced that the temperature at the interface between the primary lining and the surrounding rock is... for: .

6. The method for calculating the critical design temperature change of tunnels in cold regions according to claim 1, characterized in that, In step 2, with an existing insulation layer, an insulation layer is added to the inner wall of the tunnel. The insulation layer has a thermal resistance... The calculation formula is: , For the thickness of the insulation layer, The thermal conductivity of the insulation layer material; The total thermal resistance is the sum of the thermal resistances of the primary lining, insulation layer, surrounding rock, and secondary lining, expressed as: ； The overall heat flux density when heat flows through a multi-layered material with an insulation layer is: ; The contact surface temperature between the secondary lining and the primary lining is Substitute Sorted as: ； The interface temperature between the surrounding rock and the lining structure is Substitute Sorted as: .

7. The method for calculating the critical design temperature change of tunnels in cold regions according to claim 1, characterized in that, In step 3, without an insulation layer, when the temperature at the interface between the surrounding rock and the lining is required to be 0℃... ,at this time , Assuming a critical design temperature, substitute the interface temperature between the initial lining and the surrounding rock. From the expression, the formula for the critical protection temperature can be obtained as follows: ; Similarly, when the temperature requirement for the contact surface between the secondary lining and the primary lining is 0℃, ,at this time , Assuming the critical design temperature, substitute the contact temperature between the secondary lining and the primary lining. From the expression, the formula for the critical protection temperature can be obtained as follows: .

8. The method for calculating the critical design temperature change of tunnels in cold regions according to claim 1, characterized in that, In step 3, the derivation process of the prediction formula for the critical temperature of the inner surface of the insulation layer under the condition of having an insulation layer includes: When the interface temperature between the surrounding rock and the lining structure is required to be 0℃. ,at this time , Let be the critical design temperature of the inner surface of the insulation layer. Substituting this into the expression for the interface temperature between the surrounding rock and the lining structure under the condition of having an insulation layer, we obtain... Therefore, the critical protection temperature of the inner surface of the insulation layer is: ； When the contact surface temperature between the secondary lining and the primary lining is required to be 0℃. ,at this time , Let be the critical protection temperature of the inner surface of the insulation layer. Substituting this into the expression for the contact surface temperature between the secondary lining and the primary lining under the condition of having an insulation layer, the critical protection temperature of the inner surface of the insulation layer is: .

9. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program code that, when executed by the processor, causes the processor to perform the steps of the method for calculating the critical design temperature change of cold-region tunnels as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, The system stores a computer program or instructions that, when run on a computer, execute the steps of the method for calculating the critical design temperature change of tunnels in cold regions as described in any one of claims 1 to 8.

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