A calculation method for the freezing depth of multi-layered media tunnels in cold regions

Abstract

The present invention relates to the technical field of cold-region tunnel engineering, and discloses a calculation method for the freezing depth of a multi-layer medium cold-region tunnel. This calculation method takes into account factors such as the tunnel freezing type, medium layer type, thermal conductivity, latent heat of phase change, water content, and air temperature change. The method includes the following steps: S1. Determine the freezing type of the multi-layer medium cold-region tunnel according to the tunnel operation years, local voids and defects in the lining, porosity and water content of the surrounding rock, etc.; S2. Combine the setting method of the tunnel insulation layer to determine the types and distribution forms of the cold-region tunnel media; S3. Calculate the freezing index of the cold-region tunnel; S4. Estimate the maximum freezing depth based on the statistical results of meteorological data and the engineering experience of cold-region tunnels. The calculation method for the freezing depth of the multi-layer medium cold-region tunnel provided by the present invention comprehensively considers the influence of multiple factors in the actual operation process of the multi-layer medium cold-region tunnel, can calculate the freezing depth of the multi-layer medium cold-region tunnel more accurately, can effectively prevent and reduce the occurrence of tunnel diseases, and improve the durability and safety of the tunnel structure.

Description

Technical Field

[0001] The present invention relates to the technical field of cold region tunnel engineering, and particularly to a calculation method for the freezing depth of a multi-layer medium cold region tunnel. Background Art

[0002] After the completion of tunnel construction, air flows in the tunnel. Due to the new convective heat transfer boundary at the tunnel wall, the temperature of the lining structure and the surrounding rock mass changes periodically, forming a seasonal freeze-thaw circle in the tunnel. Micro defects and cracks in the lining develop rapidly under the continuous action of freeze-thaw cycles, resulting in continuous deterioration of the lining, and even causing tunnel diseases such as lining cracks, water leakage, and spalling. In addition, the weathering effect of the surrounding rock mass is amplified by repeated freeze-thaw, the surrounding rock mass is damaged, its own bearing capacity is continuously reduced, and the frost heave occurs when the water inside the surrounding rock mass freezes, resulting in an increase in the bearing capacity received by the lining structure, threatening the durability and safety of the tunnel structure, and directly damaging the lining structure seriously in severe cases.

[0003] In view of these situations, different forms of thermal insulation materials are often used in cold region tunnels to reduce the temperature difference between the inside and outside of the tunnel and weaken the degree of heat exchange between the air flow and the surrounding rock, so as to achieve the goal of reducing the development depth and migration speed of the seasonal freeze-thaw circle. However, with the increase of the service life, the insulation layer ages continuously and the insulation efficiency gradually decreases. In view of the actual multiple factors such as the freezing type, medium layer type, air temperature change, lining deterioration, surrounding rock damage, and insulation layer aging in the actual operation process of cold region tunnels, there is currently no calculation method that can comprehensively consider the coupling effect between multiple factors to calculate the freezing depth of multi-layer medium cold region tunnels more accurately. Summary of the Invention

[0004] In view of the situation that the existing calculation formula for the freezing depth of cold region tunnels ignores the complex freezing type in the actual operation process and the actual multiple factors such as insulation layer aging, lining deterioration, and surrounding rock damage, the present invention provides a practical calculation method for the freezing depth of multi-layer medium cold region tunnels under the influence of tunnel freezing type, medium layer type, thermal conductivity, latent heat of phase change, water content, and air temperature change.

[0005] The calculation method for the freezing depth of multi-layer medium cold region tunnels provided by the present invention considers factors such as tunnel freezing type, medium layer type, thermal conductivity, latent heat of phase change, water content, and air temperature change. The method includes the following steps:

[0006] S1. Determine the freezing type of the multi-layer medium cold region tunnel according to the tunnel operation years, local cavities and defects of the lining, porosity and water content of the surrounding rock mass, etc.

[0007] S2. Determine the types and distribution forms of the cold region tunnel media in combination with the setting method of the tunnel insulation layer.

[0008] S3. Calculate the freezing index of the tunnel in cold regions;

[0009] S4. Estimate the maximum freezing depth according to the statistical results of meteorological data and the engineering experience of tunnels in cold regions;

[0010] S5. Calculate the latent heat of phase change and the thermal conductivity of each layer of medium;

[0011] S6. Select the corresponding calculation formula according to the freezing type of the tunnel and the setting method of the insulation layer;

[0012] S7. Substitute the freezing index of the tunnel in cold regions, the initial estimated value of the freezing depth, the latent heat of phase change and the thermal conductivity of each layer of medium into the selected formula to solve the calculated value of the freezing depth of the tunnel in cold regions;

[0013] S8. Compare the calculated value with the initial estimated value. If they are not equal, reselect the estimated value and recalculate until the calculated value is equal to the initial estimated value to determine the final freezing depth.

[0014] Preferably, according to the operation years of the tunnel, local cavities and defects of the lining, porosity and water content of the surrounding rock, etc., the freezing types of multi-layer medium tunnels in cold regions are divided into single-factor dominant freezing type, two-factor coupling freezing type and three-factor coupling freezing type.

[0015] Preferably, the setting methods of the tunnel insulation layer in S2 are as follows: setting a double-layer insulation layer, the insulation layer is located outside the secondary lining, the insulation layer is located between the primary support and the secondary lining, and the case where no insulation layer is set.

[0016] Preferably, in S5, the calculation of the latent heat of phase change of each layer of medium includes the calculation of the latent heat of phase change of the insulation layer, the latent heat of phase change of the lining and the latent heat of phase change of the surrounding rock, and the factors such as the dry density, total moisture content and unfrozen moisture content during freezing of the material are considered.

[0017] Preferably, in S5, the calculation of the thermal conductivity of each layer of medium includes the thermal conductivity of the insulation layer, the thermal conductivity of the lining and the thermal conductivity of the surrounding rock.

[0018] Compared with the related technology, the calculation method of the freezing depth of multi-layer medium tunnels in cold regions provided by the present invention has the following beneficial effects:

[0019] This calculation method comprehensively considers the influence of multiple factors in the actual operation process of multi-layer medium tunnels in cold regions, can calculate the freezing depth of multi-layer medium tunnels in cold regions more accurately, can effectively prevent and reduce the occurrence of tunnel diseases, and improve the durability and safety of the tunnel structure; this method can provide a scientific basis for the design, construction and operation of tunnel structures, waterproof and drainage facilities, heat insulation and preservation in cold regions, and has high practical value and popularization prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is the flow chart for solving the maximum freezing depth of a multi-layered medium cold region tunnel in the present invention. Detailed implementation manners

[0021] The present invention will be further described below in conjunction with the accompanying drawings and implementation manners.

[0022] Considering the tunnel operation life, local cavities and defects in the lining, porosity and water content of the surrounding rock, etc., the freezing types of the multi-layered medium cold region tunnel can be classified into single-factor dominant freezing type, two-factor coupling freezing type and three-factor coupling freezing type. The freezing types of different medium layers and their occurrence conditions are shown in Table 1.

[0023] Table 1 Multi-factor coupling freezing types of tunnels

[0024]

[0025] Currently, the setting methods of the tunnel insulation layer mainly include three categories. The first category is to directly set the insulation layer on the outer side of the secondary lining. The second category is to set the insulation layer between the primary support and the secondary lining. The third category is to set the insulation layer between the primary support and the secondary lining and on the outer side of the secondary lining at the same time. Therefore, combining the multi-factor coupling freezing types of the cold region tunnel, the setting method of the insulation layer, the air temperature change, and the influence of the changes in water content, thermal conductivity, and latent heat of phase change induced by insulation layer aging, lining deterioration, and surrounding rock damage, the calculation method of the maximum freezing depth of the multi-layered medium cold region tunnel includes:

[0026] Freezing depth of the three-factor coupling multi-layered medium cold region tunnel

[0027] (1) When setting a double-layer insulation layer in Type VII, the expression for the freezing depth is:

[0028]

[0029] In the formula, T y is the annual average air temperature; A y is the annual temperature amplitude; R is the maximum freezing radius of the tunnel; (R fr -R o ) is the initial freezing depth of the tunnel; R inp is the radius of the first insulation layer; R ls is the radius of the secondary lining; R ins is the radius of the second insulation layer; R lp is the radius of the primary support; R i is the radius of the local water accumulation space; R mr is the radius of the weathered layer; t inp is the thickness of the first insulation layer; t ls is the thickness of the secondary lining; t ins is the thickness of the second insulation layer; t lp is the thickness of the primary support; L inpThe latent heat of volume phase change during the freezing of the first-layer tunnel insulation layer; L ls The latent heat of volume phase change during the freezing of the secondary lining; L ins The latent heat of volume phase change during the freezing of the second-layer insulation layer; L lp The latent heat of volume phase change during the freezing of the primary support; L w The latent heat of volume phase change during the freezing of water; L mr The latent heat of volume phase change during the freezing of the weathered layer; L r The latent heat of volume phase change during the freezing of the surrounding rock; λ inp The thermal conductivity of the first-layer insulation layer; λ ls The thermal conductivity of the secondary lining; λ ins The thermal conductivity of the second-layer insulation layer; λ lp The thermal conductivity of the primary support; λ i The thermal conductivity of ice; λ mr The thermal conductivity of the weathered layer; λ r The thermal conductivity of the surrounding rock.

[0030] (2) When the Class VII insulation layer is set outside the secondary lining, the calculation formula for the freezing depth is:

[0031]

[0032] (3) When the Class VII insulation layer is set between the primary support and the secondary lining, the calculation formula for the freezing depth is:

[0033]

[0034] (4) When the Class VII insulation layer is not set, the calculation formula for the freezing depth of the tunnel is:

[0035]

[0036] Freezing depth of cold-region tunnel with multi-layer media under two-factor coupling

[0037] 1. Freezing depth of cold-region tunnel with Class VI multi-layer media

[0038] (1) When double-layer insulation layer is set, the calculation formula for the freezing depth of cold-region tunnel is:

[0039]

[0040] (2) When the insulation layer is set outside the secondary lining, the calculation formula for the freezing depth of cold-region tunnel is:

[0041]

[0042] (3) When the insulation layer is set between the primary support and the secondary lining, the calculation formula for the freezing depth of cold-region tunnel is:

[0043]

[0044] (4) When there is no insulation layer, the calculation formula for the freezing depth of tunnels in cold regions is:

[0045]

[0046] 2. Freezing depth of tunnels in cold regions with the fifth type of multi-layer media

[0047] There are two working conditions according to the actual freezing degree: When R f ≥R mr At this time, the freezing depth of the multi-layer media is R mr ; When R i <R f <R mr At this time, the freezing depth of the multi-layer media is R f Under this condition, the freezing depth can be solved according to the calculation formula for the freezing depth of tunnels in cold regions with the fourth type of frost heaving model multi-layer media.

[0048] 3. Freezing depth of tunnels in cold regions with the fourth type of multi-layer media

[0049] (1) The calculation formula for the freezing depth when a double-layer insulation layer is set is:

[0050]

[0051] (2) The calculation formula for the freezing depth of tunnels in cold regions when the insulation layer is set outside the secondary lining of the tunnel is:

[0052]

[0053] (3) The calculation formula for the freezing depth of tunnels in cold regions when the insulation layer is set between the primary support and the secondary lining is:

[0054]

[0055] (4) The calculation formula for the freezing depth of tunnels in cold regions when there is no insulation layer is:

[0056]

[0057] Freezing depth of tunnels in cold regions with multi-layer media dominated by single factors

[0058] 1. Freezing depth of tunnels in cold regions with the third type of multi-layer media

[0059] (1) The calculation formula for the freezing depth of tunnels in cold regions when a double-layer insulation layer is set is:

[0060]

[0061] (2) The calculation formula for the freezing depth of tunnels in cold regions when the insulation layer is set outside the secondary lining is:

[0062]

[0063] (3) When the insulation layer is set between the primary support and the secondary lining, the calculation formula for the freezing depth of a tunnel in a cold region is:

[0064]

[0065] (4) When there is no insulation layer, the calculation formula for the freezing depth of a tunnel in a cold region is:

[0066]

[0067] 2. When determining the freezing depth of a multi-layer medium tunnel in a cold region for the first and second types of frost heave models dominated by a single factor, the freezing radius of the tunnel is solved according to the calculation formula for the third type of freezing depth, and then the magnitudes of the calculated freezing radius, the weathered layer radius of the tunnel, and the local water accumulation radius are compared. When the calculated freezing radius is larger, the weathered layer radius of the tunnel and the local water accumulation radius are used for the next calculation; when the calculated freezing radius is smaller, the calculated freezing radius is used for the next calculation.

[0068] In view of the influence of actual multiple factors such as the aging of the insulation layer, the deterioration of the lining, and the damage of the surrounding rock on the freezing of the tunnel during the operation of the existing cold-region tunnel, considering the changes in the type, moisture content, and air temperature of the medium layer, a calculation method for the thermal conductivity and phase change latent heat of the insulation layer, lining, and surrounding rock that conforms to the actual situation is provided.

[0069] 1. Phase change latent heat of each layer of medium

[0070] (1) Phase change latent heat of the insulation layer

[0071] In the initial stage of tunnel operation, under normal maintenance conditions, the moisture content of the insulation layer is very small and can be ignored, so the phase change latent heat of the insulation layer is 0.

[0072] As the service life increases, due to the dampness of the tunnel wall, and even local water leakage in the tunnel, coupled with the fact that the insulation material generally has a relatively large porosity and strong water absorption, the water vapor retained in the pores of the insulation layer condenses to form condensate when it meets cold, causing the moisture content of the insulation layer to increase. In addition, the water inside the lining concrete will also gradually seep into the pores of the insulation layer, also causing the moisture content to increase. The influence of the phase change latent heat of the insulation layer on the freezing depth after water absorption cannot be ignored, so the calculation formula for the phase change latent heat of the insulation layer is:

[0073]

[0074] (2) Phase change latent heat of the lining

[0075] Under the influence of freeze-thaw cycles, the lining of a cold-region tunnel deteriorates continuously. Considering the continuous increase in porosity and moisture content during the deterioration process of the lining, the calculation formula for the phase change latent heat of the lining is:

[0076]

[0077] (3) Latent heat of phase change of surrounding rock:

[0078] Under the influence of freeze-thaw cycles, the surrounding rock of a tunnel in cold regions is gradually damaged. Considering the continuous increase in porosity and water content during the damage process of the surrounding rock, the calculation formula for the latent heat of phase change of the surrounding rock is:

[0079]

[0080] In the formula, ρ inpd is the dry density of the first insulation layer; w inp is the total water content of the first insulation layer; w inpu is the unfrozen water content of the first insulation layer during freezing; ρ lsd is the dry density of the secondary lining of the tunnel; w ls is the total water content of the secondary lining; w lsu is the unfrozen water content of the secondary lining during freezing; ρ insd is the dry density of the second insulation layer; w ins is the total water content of the second insulation layer; w insu is the unfrozen water content of the second insulation layer during freezing; ρ lpd is the dry density of the primary support; w lp is the total water content of the primary support; w lpu is the unfrozen water content of the primary support during freezing; ρ mrd is the dry density of the weathered layer; w mr is the total water content of the weathered layer; w mru is the unfrozen water content of the weathered layer during freezing; ρ rd is the dry density of the surrounding rock; w r is the total water content of the surrounding rock; w fru is the unfrozen water content of the surrounding rock during freezing; G ls is the specific gravity of the lining concrete; n l is the porosity of the lining concrete; χ is the ratio of the value when the unfrozen water content of the frozen surrounding rock remains unchanged to the total water content. For rock, χ = 7%; T f is the temperature when the surrounding rock begins to freeze, at which the water in the surrounding rock begins to undergo phase change; T m is the starting temperature when the unfrozen water content in the frozen surrounding rock does not change with temperature. For rock, T m = -15°C; a and b are characteristic parameters of the unfrozen water content curve, a = -1.3426, b = 0.6458.

[0081] (4) The weathered layer is also part of the surrounding rock, and the volume latent heat of phase change of the weathered layer is calculated by the above formula.

[0082] 2. Thermal conductivity of each layer of medium

[0083] (1) Thermal conductivity of the insulation layer:

[0084] As the service life of the insulation layer increases, the influence of the service environment temperature on the insulation layer becomes more and more obvious, resulting in material aging and continuous reduction of the insulation effect of the insulation layer. Considering the influence of the moisture content of the insulation layer and the change of air temperature, multiple actual factors need to be comprehensively considered to correct the thermal conductivity. Therefore, the calculation formula for the thermal conductivity of the insulation layer in the same period is:

[0085]

[0086] λ in is the average thermal conductivity of the insulation material; λ ind is the initial thermal conductivity of the insulation material; a' is the correction parameter of the thermal conductivity of the insulation material. Among them, for polyurethane in severe cold and cold regions, and hot summer and cold winter regions, it is taken as 1.15, and for phenolic aldehyde in severe cold and cold regions, and hot summer and cold winter regions, it is taken as 1.15 and 1.20 respectively; b' is the influence coefficient of the moisture content of the insulation layer. Among them, the values of polyurethane and phenolic aldehyde are 4.47e -4 and 1.47e -4 respectively; λ w is the thermal conductivity of liquid water; w in is the moisture content of the insulation material; w ini is the ice content of the insulation layer; λ i is the thermal conductivity of ice; γ' is the influence coefficient of the freezing of the insulation layer. Among them, the values of polyurethane and phenolic aldehyde are 0.34 and 0.79 respectively.

[0087] (2) Lining thermal conductivity:

[0088] Considering the influence of air temperature change on the lining thermal conductivity, the calculation formula for the lining thermal conductivity in the same period is:

[0089]

[0090] (3) Surrounding rock thermal conductivity:

[0091] Considering the influence of air temperature change on the surrounding rock thermal conductivity, the calculation formula for the surrounding rock thermal conductivity in the same period is:

[0092]

[0093] In the formula, λ rs , λ w , λ g are the thermal conductivities of the surrounding rock skeleton particles, moisture and gas; S rw is the saturation of the unfrozen surrounding rock; n r is the porosity of the surrounding rock; ρ rd is the dry density of the surrounding rock; ρ w is the density of liquid water; ρ i is the density of ice; G rs is the specific gravity of the surrounding rock; w ris the moisture content of unfrozen surrounding rock; w ri is the ice content of frozen surrounding rock.

[0094] (4) The weathered layer is also part of the surrounding rock, and the thermal conductivity of the weathered layer is calculated as described above.

[0095] Solving process for the freezing depth of tunnels in cold regions:

[0096] Based on the actual state of the tunnel in cold regions, judge the freezing type of the tunnel, consider the setting method of the tunnel insulation layer, determine the types and distribution forms of the media in the tunnel in cold regions, and then calculate the freezing index of the tunnel in cold regions. In order to obtain the sum of the thicknesses of each layer of media in the tunnel, give an initial estimate value X = R fr -R o . According to the statistical results of meteorological data and the engineering experience of tunnels in cold regions, estimate the maximum freezing depth through the average temperature of the coldest month, as shown in the following formula:

[0097] X = αT cm +β

[0098] In the formula, T cm is the average temperature of the coldest month; α and β are regression coefficients. For natural strata, α = -0.11 and β = 0.16. For tunnels in cold regions, α = -0.11 and β = 0.39.

[0099] After obtaining the initial estimated value of the freezing depth, calculate the latent heat of phase change and thermal conductivity of each layer of media, and select the corresponding calculation formula according to the freezing type of the tunnel and the setting method of the insulation layer. Finally, substitute the freezing index of the tunnel, the initial estimated value of the freezing depth, the latent heat of phase change and thermal conductivity of each layer of media into the selected formula to solve the calculated value R of the freezing depth of the tunnel in cold regions. Compare the calculated value R with the initial estimated value X. If |(R - X) / R| > 0.05, reselect the estimated value X. The new estimated value is between the calculated value and the initial estimated value, and recalculate the freezing depth according to the Figure 1 solving process until |(R - X) / R| ≤ 0.05, stop the calculation, and take the last calculated value of the freezing depth as the freezing depth of the tunnel in cold regions with multi-layer media.

[0100] 3. Technical effects

[0101] The following takes the calculation of the maximum freezing depth of the Xing'anling Highway Tunnel as an example:

[0102] For example, in the calculation of the maximum freezing depth of the Xing'anling Highway Tunnel, due to the relatively complex geological environment of the Xing'anling Highway Tunnel, the high degree of weathering of the surrounding rock, the development of joints and fissures, diseases such as local water inrush, flowing water, and seepage occurred during the construction and operation process. On-site inspection found that there were local cavities and non-dense phenomena in the Xing'anling Highway Tunnel. In addition, an insulation layer was set outside the secondary lining of the Xing'anling Highway Tunnel. The calculation was carried out using the calculation formula for the freezing depth of the tunnel in cold regions when the insulation layer was set outside the secondary lining with three-factor coupling. The calculated maximum freezing depth was 4.15 m, and the maximum measured freezing depth on-site was 4.10 m. The error between the calculated value and the measured value was less than 0.1 m, which could fully meet the actual application requirements of tunnel engineering in cold regions. This invention patent can provide reference for the structure of tunnels in cold regions, the design, construction and operation of waterproof and drainage facilities and thermal insulation.

[0103] The above are only the embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be included in the patent protection scope of the present invention by the same token.

Claims

1. A calculation method for the freezing depth of a multi-layered medium tunnel in cold regions, characterized in that The method takes into account factors such as tunnel freezing type, medium layer type, thermal conductivity, latent heat of phase change, water content, and air temperature change. The method includes the following steps: S1. Determine the freezing type of a multi-layered medium cold region tunnel based on the tunnel operation years, local voids and defects in the lining, porosity and water content of the surrounding rock; S2. Determine the types and distribution forms of the tunnel medium in the cold region in combination with the setting method of the tunnel insulation layer; S3. Calculate the freezing index of the cold region tunnel; S4. Estimate the maximum freezing depth based on the statistical results of meteorological data and the engineering experience of cold region tunnels; S5. Calculate the latent heat of phase change and thermal conductivity of each layer of the medium; S6. Select the corresponding calculation formula according to the tunnel freezing type and the setting method of the insulation layer; S7. Substitute the freezing index of the cold region tunnel, the initial estimated value of the freezing depth, the latent heat of phase change and thermal conductivity of each layer of the medium into the selected formula to solve the calculated value of the freezing depth of the cold region tunnel; S8. Compare the calculated value with the initial estimated value. If they are not equal, reselect the estimated value and recalculate until the calculated value is equal to the initial estimated value to determine the final freezing depth.

2. The calculation method of the freezing depth of the multi-layered medium cold region tunnel according to claim 1, characterized in that, According to the tunnel operation years, local voids and defects in the lining, porosity and water content of the surrounding rock, the freezing types of multi-layered medium cold region tunnels are divided into single-factor dominant freezing types, two-factor coupled freezing types, and three-factor coupled freezing types.

3. The calculation method for the freezing depth of multi-layered media in cold region tunnels according to claim 1, wherein The setting methods of the tunnel insulation layer in S2 are as follows: setting a double-layer insulation layer, the insulation layer is located outside the secondary lining, the insulation layer is located between the primary support and the secondary lining, and the case where no insulation layer is set.

4. The calculation method of the freezing depth of the multi-layered medium cold region tunnel according to claim 1, characterized in that, In S5, the calculation of the latent heat of phase change of each layer of the medium includes the calculation of the latent heat of phase change of the insulation layer, the latent heat of phase change of the lining, and the latent heat of phase change of the surrounding rock, taking into account factors such as the dry density of the material, the total water content, and the unfrozen water content during freezing.

5. The calculation method for the freezing depth of a multi-layered medium cold region tunnel according to claim 1, characterized in that, In S5, the calculation of the thermal conductivity of each layer of the medium includes the thermal conductivity of the insulation layer, the thermal conductivity of the lining, and the thermal conductivity of the surrounding rock.

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