Calculation method of equivalent annual average temperature for cold region tunnels considering non-uniform ventilation

Abstract

This invention discloses a method for calculating the equivalent annual average temperature of tunnels in cold regions considering non-uniform ventilation. It can calculate both the equivalent annual average temperature and the equivalent coldest month's average temperature considering non-uniform ventilation, providing a theoretical method for calculating these two indicators and improving the accurate characterization of coldness in tunnels. This method provides key calculation parameters for determining the thickness of insulation layers in cold-region tunnels considering non-uniform ventilation. Furthermore, the equivalent annual average temperature of tunnels in cold regions calculated using this method plays an important role in guiding the design of drainage and waterproofing systems and active ventilation control in cold-region tunnels, leading to more accurate and rational frost protection designs for these tunnels.

Description

Technical Field

[0001] This invention relates to the field of frost damage prevention and control in cold-region tunnels in transportation construction, specifically a method for calculating the equivalent annual average temperature of cold-region tunnels considering non-uniform ventilation. Background Technology

[0002] The main types of frost damage in tunnels in cold regions are categorized into frost damage to the drainage system, lining, and surrounding rock. These manifest as failure of the waterproofing system, icing and blockage of drainage facilities, water leakage and ice formation in the lining, frost heave and cracking of the sidewalls, and icing at the tunnel floor, threatening traffic safety. Tunnels severely damaged by frost damage may even be forced to abandon operation. Frost damage prevention and control has become a critical and challenging issue that urgently needs to be addressed in tunnels in cold regions, and accurately characterizing the degree of coldness within the tunnel is a crucial prerequisite for the scientific and effective prevention and control of frost damage.

[0003] The "Design Specifications for Highway Tunnels" (JTG / T D70-2010) uses only the average temperature of the coldest month to characterize the coldness of tunnels, which is not accurate enough. This is because the annual average temperature can be approximately determined by the sum of the annual temperature amplitude and the average temperature of the coldest month. In regions with relatively high average temperatures in the coldest month, the annual temperature amplitude may be small, resulting in a low annual average temperature. Considering only the average temperature of the coldest month may misjudge the coldness of tunnels, leading to inadequate anti-freezing design for tunnels in cold regions. For example, the Zhadunhe Tunnel in Hulunbuir City has an average temperature of -18.0℃ in the coldest month, an annual temperature amplitude of 17.2℃, and an annual average temperature of -0.7℃; the Ela Mountain Tunnel in Qinghai Province has an average temperature of -11.0℃ in the coldest month, an annual temperature amplitude of 6.9℃, and an annual average temperature of -4.2℃. Comparing only the average temperature of the coldest month reveals that the Zadunhe Tunnel is colder. However, comparing the annual average temperatures of the two tunnels shows that the Elashan Tunnel is colder than the Zadunhe Tunnel, and the Elashan Tunnel should have higher-level anti-freezing measures than the Zadunhe Tunnel. Therefore, to accurately characterize the coldness within a tunnel, both the average temperature of the coldest month (or annual temperature amplitude) and the annual average temperature should be considered. Furthermore, the anti-freezing measures used for the lining and surrounding rock of tunnels in cold regions mainly involve laying insulation layers. Currently, the thickness of the insulation layer is designed primarily based on numerical calculations using the average temperature of the coldest month in the first year of tunnel operation, without considering the impact of non-uniform ventilation (i.e., the ventilation speed within the tunnel varies, including both natural and artificial ventilation). Since the average temperature of the coldest month cannot accurately characterize the coldness within a tunnel, the calculation results are clearly unreasonable. On the other hand, calculating the insulation layer thickness considering non-uniform ventilation is complex and difficult to promote in practical engineering. Since non-uniform ventilation objectively exists, its impact on the coldness within the tunnel should also be considered. Furthermore, the difference between the annual average air temperature and the constant temperature layer causes a decrease in ground temperature, and this decrease increases year by year, further leading to a gradual drop in the minimum temperature. Traditional insulation layer thickness designs do not take into account the cumulative change in this decrease over the years. Therefore, the difference between the annual average air temperature and the constant temperature layer is also an important indicator of the coldness within the tunnel.

[0004] In summary, to accurately characterize the coldness in a tunnel, four indicators should be considered simultaneously: the annual average air temperature, the average air temperature of the coldest month (or the annual air temperature amplitude), the difference between the annual average air temperature and the constant ground temperature, and the varying ventilation speed. In practical applications, to reduce the number of indicators and facilitate application, the principle of equivalence is used to treat the varying ventilation speed and annual average air temperature as equivalent annual average air temperature considering non-uniform ventilation. Similarly, equivalent coldest month average air temperature and equivalent annual air temperature amplitude considering non-uniform ventilation can also be obtained. Therefore, the accurate characterization of the coldness in a tunnel should be: the equivalent annual average air temperature considering non-uniform ventilation, the equivalent coldest month average air temperature (or equivalent annual air temperature amplitude considering non-uniform ventilation), and the difference between the equivalent annual average air temperature considering non-uniform ventilation and the constant ground temperature. Of these three indicators, obtaining the annual average temperature considering non-uniform ventilation and the coldest monthly average temperature considering non-uniform ventilation is the most crucial. Although these two indicators can be calculated using theoretical formulas and equivalent principles based on the temperature and wind speed at the tunnel entrance, there are very few methods available at present. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method for calculating the equivalent annual average temperature of cold-region tunnels considering non-uniform ventilation, addressing the shortcomings of existing technologies. By changing the time interval, the method can be used to calculate the equivalent coldest month's average temperature of cold-region tunnels considering non-uniform ventilation. This helps to improve the accurate characterization of the coldness in tunnels and provides key calculation parameters for calculating the thickness of the insulation layer in cold-region tunnels considering non-uniform ventilation. In addition, the equivalent annual average temperature of cold-region tunnels considering non-uniform ventilation calculated by the method of this invention plays an important role in guiding the design of drainage and waterproofing systems and active ventilation control in cold-region tunnels, making the anti-freezing design of cold-region tunnels more accurate and reasonable.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a method for calculating the equivalent annual average temperature of cold-region tunnels considering non-uniform ventilation, comprising the following steps:

[0007] Assume the air temperature entering the tunnel is T(t), and the wind speed of the non-uniform ventilation is v(t), both of which change with time t;

[0008] According to the heat calculation formula:

[0009] dQ1=C P (T(t)-T0)dm (1)

[0010] dm=ρ a Av(t)dt (2)

[0011] In the formula, dQ1 represents the heat absorbed or released by the air in a small endothermic or exothermic process; dQ1>0 indicates endothermic process, and dQ1<0 indicates exothermic process; C P ρ is the specific heat capacity of air at constant pressure; dm is the mass of air flowing into the tunnel during time dt; a Where is the air density; A is the cross-sectional area of ​​the air flowing into the tunnel; T0 is the reference temperature;

[0012] Substituting formula (2) into formula (1), we get:

[0013] dQ1=ρ a AC P v(t)(T(t)-T0)dt (3)

[0014] Taking the time interval as [t1, t2], the total heat absorbed or released by the air entering the tunnel during this time is:

[0015]

[0016] Assuming that after a period of t2–t1, the equivalent average temperature of the air flowing into the tunnel is According to formula (4), the total heat absorbed or released by the air after the t2–t1 cycle flowing into the tunnel can be obtained as follows:

[0017]

[0018] Assuming the tunnel lining surface is insulated, we can obtain the following:

[0019] Q1 = Q2 (6)

[0020]

[0021] After simplification, we get:

[0022]

[0023] When the time interval [t1, t2] is taken as one year, the equivalent annual average temperature of the cold region tunnel considering non-uniform ventilation can be calculated according to formula (8). When the time interval [t1, t2] is taken as the coldest month, the equivalent average temperature of the coldest month of the cold region tunnel considering non-uniform ventilation can be calculated according to formula (8). Therefore, according to different engineering needs, the equivalent average temperature of the tunnel under non-uniform ventilation in different time intervals can be calculated by formula (8), providing key parameters for the anti-freezing design of cold region tunnels.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] (1) The average temperature of the coldest month cannot accurately represent the coldness in the tunnel. The accurate representation of the coldness in the tunnel should be: the equivalent annual average temperature considering non-uniform ventilation, the equivalent coldest month average temperature considering non-uniform ventilation (or the equivalent annual temperature amplitude considering non-uniform ventilation), and the difference between the equivalent annual average temperature considering non-uniform ventilation and the constant temperature layer. This invention proposes a method for calculating the equivalent annual average temperature of cold-region tunnels considering non-uniform ventilation. It can calculate the equivalent annual average temperature considering non-uniform ventilation and the equivalent coldest month average temperature considering non-uniform ventilation, and provides a theoretical method for calculating these two indicators, making the accurate representation of the coldness in the tunnel more complete.

[0026] (2) The calculation method of the present invention can provide key calculation parameters for calculating the thickness of the insulation layer of cold region tunnels when considering non-uniform ventilation. In addition, the equivalent annual average temperature of cold region tunnels considering non-uniform ventilation calculated by the method of the present invention also plays an important role in guiding the design of drainage and waterproofing systems and active ventilation control of cold region tunnels, which will make the anti-freezing design of cold region tunnels more accurate and reasonable. Attached Figure Description

[0027] Figure 1 The temperature time history curve at the tunnel entrance in a specific application case;

[0028] Figure 2 This is the wind speed time history curve at the tunnel entrance in a specific application case. Detailed Implementation

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0030] The method for calculating the equivalent annual average temperature of a cold-region tunnel considering non-uniform ventilation in Example 1 includes the following steps:

[0031] Assume the air temperature entering the tunnel is T(t), and the wind speed of non-uniform ventilation is v(t), both of which change with time t; the above T(t) and v(t) data are real-time change data of air temperature and wind speed entering the tunnel obtained from tunnel survey data for more than one year.

[0032] According to the heat calculation formula:

[0033] dQ1=C P (T(t)-T0)dm (1)

[0034] dm=ρ a Av(t)dt (2)

[0035] In the formula, dQ1 represents the heat absorbed or released by the air in a small endothermic or exothermic process; dQ1>0 indicates endothermic process, and dQ1<0 indicates exothermic process; CP ρ is the specific heat capacity of air at constant pressure; dm is the mass of air flowing into the tunnel during time dt; a Where is the air density; A is the cross-sectional area of ​​the air flowing into the tunnel; T0 is the reference temperature;

[0036] Substituting formula (2) into formula (1), we get:

[0037] dQ1=ρ a AC P v(t)(T(t)-T0)dt (3)

[0038] Taking the time interval as [t1, t2], the total heat absorbed or released by the air entering the tunnel during this time is:

[0039]

[0040] Assuming that after a period of t2–t1, the equivalent average temperature of the air flowing into the tunnel is According to formula (4), the total heat absorbed or released by the air after the t2–t1 cycle flowing into the tunnel can be obtained as follows:

[0041]

[0042] Assuming the tunnel lining surface is insulated, we can obtain the following:

[0043] Q1 = Q2 (6)

[0044]

[0045] After simplification, we get:

[0046]

[0047] When the time interval [t1,t2] is taken as one year, the equivalent annual average temperature of the cold region tunnel considering non-uniform ventilation can be calculated according to formula (8); when the time interval [t1,t2] is taken as the coldest month, the equivalent coldest month average temperature of the cold region tunnel considering non-uniform ventilation can be calculated according to formula (8).

[0048] Specific application examples:

[0049] A completed tunnel is located in the Changbai Mountains in southeastern Jilin Province. It is a single-bore, two-lane, two-way tunnel, 4825m long, at an altitude of 1400m-1500m, with a maximum burial depth of 280m and a design speed of 60km / h. The route traverses a temperate continental mountain climate with distinct vertical climate zones and is a non-permafrost tunnel. The tunnel entrance section is primarily composed of Class V surrounding rock. The tunnel employs a composite lining structure with a secondary lining thickness of 35cm. Survey data indicates the constant temperature layer is 8.2℃. Meteorological data at the tunnel entrance are as follows: Figure 1 and Figure 2 As shown, the average annual wind speed is 0.3 m / s, and the maximum wind speed is 5.0 m / s.

[0050] Using the formula (8) for calculating the equivalent annual average temperature considering non-uniform ventilation, the equivalent annual average temperature of the tunnel considering non-uniform ventilation is calculated to be 6.2℃, the equivalent coldest month average temperature considering non-uniform ventilation is -11.7℃, the amplitude of the equivalent annual temperature considering non-uniform ventilation is 17.9℃, and the difference between the equivalent annual average temperature considering non-uniform ventilation and the constant temperature layer is 2.0℃.

Claims

1. A method for calculating the equivalent annual average temperature of a cold-region tunnel considering non-uniform ventilation, characterized in that, Includes the following steps: Assume the air temperature entering the tunnel is T ( t The wind speed for non-uniform ventilation is... v ( t Both change over time. t change; According to the heat calculation formula: （1） （2） In the formula, d Q 1 represents the amount of heat absorbed or released by the air in a tiny endothermic or exothermic process, d Q 1 > 0 represents endothermic heat, d Q 1 < 0 represents exothermic reaction; C P d is the specific heat capacity of air at constant pressure; m For d t The quality of air flowing into the tunnel within a given time period; ρ a air density; A The cross-sectional area of ​​the air flowing into the tunnel; For reference temperature; Substituting formula (2) into formula (1), we get: （3） Take the time interval as [ t 1, t 2], then the total heat absorbed or released by the air entering the tunnel during this time interval is: （4） Assuming after t 2 – t After one cycle, the equivalent average temperature of the air flowing into the tunnel is According to formula (4), the inflow into the tunnel can be obtained. t 2 – t The total heat absorbed or released by the air after one cycle is: （5） Assuming the tunnel lining surface is insulated, we can obtain the following: （6） （7） After simplification, we get: （8） When the time interval [ t 1, t 2] Taking one year, the equivalent annual average temperature of the cold region tunnel considering non-uniform ventilation is calculated according to formula (8).

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