A design method for ventilation pipe foundation in permafrost regions based on heat budget balance

Abstract

The application provides a design method of a ventilation pipe foundation in permafrost regions based on the principle of heat balance, aiming to maintain the heat balance of the lower permafrost under the foundation and ensure its long-term thermal stability. The method involves collecting meteorological data, soil physical parameters, and permafrost upper limit and ground temperature distribution information to assess whether additional protection measures are needed and to determine the burial height of the ventilation pipe foundation. Based on the selected ventilation pipe configuration, the corresponding wind speed calculation formula is used to calculate the wind speed in the pipe, and the convective heat transfer coefficient is determined. Combined with the convective heat transfer coefficient and economy, the pipe diameter is determined. Further determine the cooling radius and the best operation mode of the ventilation pipe foundation to ensure the heat balance of the foundation bottom and effectively protect the lower permafrost under the foundation. The design method is simple, fast and accurate, and has important engineering application value and wide applicability.

Description

Technical Field

[0001] This invention relates to the field of foundation thermal protection design technology in permafrost regions, specifically to a method for designing ventilation pipe foundations in permafrost regions based on heat balance. Technical Background

[0002] As global warming occurs, permafrost is gradually degrading. The core reason is that the annual heat absorption of permafrost exceeds the heat release, leading to a net heat accumulation and transfer to the permafrost layer, which in turn causes permafrost thawing. Permafrost is widely distributed, and numerous buildings, roads, and pipeline projects have been constructed in these areas. These construction activities disrupt the thermal balance between the surface and the atmosphere and remove vegetation, increasing the heat transfer to the permafrost layer. This additional heat accelerates permafrost degradation, exposing projects in permafrost regions to the risk of thaw settlement, manifested as uneven settlement and cracking of buildings, longitudinal cracks and uneven slope settlement in roads, and deformation, uneven settlement, and misalignment of airport runways, as well as road surface frost heave during the warm season. [3] Disasters such as these result in high maintenance costs.

[0003] Ventilation pipe foundation in permafrost regions [4-5] Ventilation duct foundations can effectively reduce the temperature of the permafrost beneath the foundation, preventing or slowing down permafrost degradation, thereby mitigating or eliminating foundation settlement deformation caused by permafrost thaw. To achieve this effect, from a heat balance perspective, the annual net heat of the ventilation duct foundation must remain negative. If the annual net heat of the ventilation duct foundation is positive, the permafrost beneath the foundation will continue to degrade, making it impossible to effectively control foundation settlement deformation. In road and building projects in permafrost regions, ventilation duct foundations have already been used to protect the permafrost beneath the foundation. Although ventilation duct foundations have a good cooling effect, existing specifications only provide minimum design requirements, and practical applications often rely on past engineering experience and field tests, resulting in limited applicability and time-consuming processes. To address these shortcomings, there is an urgent need to propose a simple, accurate, and rapid design method for ventilation duct foundations. Summary of the Invention

[0004] To overcome the shortcomings of existing ventilation pipe foundation design methods in permafrost regions, which are time-consuming and lack specificity, this invention aims to propose a simple, accurate, and rapid ventilation pipe foundation design method to mitigate or eliminate settlement deformation caused by the degradation of permafrost beneath the foundation, thereby ensuring the thermal stability of the foundation.

[0005] To achieve the above objectives, the technical solution of this invention is to design a method to ensure that the annual net heat load of the ventilation pipe foundation in permafrost regions is below 0 KJ / m². The core lies in the rational design of the ventilation pipe and its configuration, and the accurate calculation of the foundation's annual net heat load. The specific steps are as follows:

[0006] 1) Data Collection: Collect meteorological data such as temperature, wind speed, wind direction, sandstorms, and snowfall at the project site. Determine the cross-sectional dimensions of the foundation (width, height, slope) and obtain the physical parameters of the foundation fill material to calculate its thermal conductivity and specific heat capacity. Simultaneously, collect geothermal data of the natural soil, the upper limit of permafrost, and its physical parameters, and calculate the thermal conductivity and specific heat capacity.

[0007] 2) Determine whether sand and snow protection devices are needed based on snowfall, snow accumulation, and sandstorm data. Consider adding inlet and outlet ducts to ventilation pipes to prevent sand and snow blockage. The inlet should face the prevailing winter wind direction, and its height should not exceed the foundation height. The inlet duct should be higher than the outlet duct to increase the airflow velocity within the duct.

[0008] 3) According to the literature [1-2] The burial height of ventilation ducts should exceed the natural ground surface by 0.5m.

[0009] 4) Wind speed calculation: In winter, wind speed affects the convective heat transfer between the air inside the ventilation duct and the foundation, which in turn affects the temperature distribution of the foundation and the frozen soil below. The higher the wind speed, the higher the convective heat transfer efficiency and the better the cooling effect in winter.

[0010] According to fluid dynamics theory, gas flow within a ventilation duct must overcome frictional resistance and local resistance. Frictional resistance is the resistance generated by internal friction of air as it flows through the duct, and its expression is as follows:

[0011] (1)

[0012] In the formula: L This refers to the length of the pipe. D This refers to the inner diameter of the pipe. u The average flow velocity across the pipe cross-section; This refers to the friction coefficient along the pipeline. The fluid density is given.

[0013] The friction coefficient of airflow along the ventilation duct is calculated using the Colebrook-White formula:

[0014] (2)

[0015] In the formula: The Reynolds number is... v The dynamic viscosity coefficient of airflow; k This is the equivalent roughness of the pipe.

[0016] The local resistance loss of ventilation ducts mainly includes the local resistance loss at the duct inlet, duct bends, and duct outlet. The calculation formula is as follows:

[0017] (3)

[0018] In the formula: This is the local resistance loss coefficient of the pipeline.

[0019] For horizontal ventilation ducts, only the friction loss along the duct needs to be considered. The formula for calculating the air velocity inside the duct is as follows:

[0020] (4)

[0021] In the formula: K 1 , K 2 The aerodynamic coefficients at the air inlet and outlet; L This refers to the length of the pipe. D This refers to the pipe diameter.

[0022] For ventilation ducts with added inlet and outlet ducts, the friction loss along the duct and local resistance loss must be considered. The formula for calculating the air velocity inside the duct is as follows:

[0023] (5)

[0024] In the formula: For gravity; H This refers to the height of the air inlet.

[0025] According to the design in 2), the wind speed calculation formula is selected based on the wind speed data collected in 1) to calculate the wind speed distribution for different pipe diameters.

[0026] 5) Calculation of convective heat transfer coefficient: Based on the air velocity inside the duct obtained in 4), the convective heat transfer coefficient of the ventilation duct is calculated using the following formula:

[0027] (6)

[0028] In the formula: Air velocity inside the ventilation duct.

[0029] 6) Based on the calculation results of the convective heat transfer coefficient and economic considerations, determine the optimal diameter of the ventilation duct.

[0030] 7) Cooling radius calculation: The cooling radius refers to the area in which the ventilation duct can effectively reduce the temperature when cooling the frozen soil layer. This radius has no fixed value and is affected by various factors such as diameter, burial height, extension length, and ambient wind speed.

[0031] The cooling radius of the ventilation duct foundation can be approximated as a cylindrical region centered on the ventilation duct. Using the meteorological parameters, foundation parameters, and ventilation duct design parameters collected in step 1), a numerical model is established, and the cooling radius is determined through simulation. To ensure fluid uniformity in the computational domain when constructing the numerical model of the ventilation duct foundation's cooling radius, the distance between the top of the computational domain and the ground is set to 6H, the distance between the inlet boundary and the foundation is at least 5H, and the distance between the outlet boundary and the bottom of the foundation is greater than 15H. This model only requires constructing the foundation region and the fluid region. After the model is established, the temperature of the computational domain is set based on the data collected in step 1), and the temperature in the middle of the foundation is monitored. The experiment ends when the temperature data stabilizes and reaches its lowest point.

[0032] 8) Based on the cooling radius calculated in 7), determine the laying spacing of the ventilation duct foundation pipes.

[0033] 9) Combining the established design parameters with local meteorological and geological data and design documents, perform numerical calculations and monitor the annual net heat at the bottom of the foundation ( Q The formula for calculating annual net heat is as follows:

[0034] (7)

[0035] In the formula: Q Net heat (KJ / m³) 2 ) ; q Soil heat flux density (W / m³) 2 ); A The base area (m2); t For time (days); and The interval is 1 year.

[0036] If within the design service life Q A value less than 0 indicates that the permafrost beneath the foundation is effectively protected and has not degraded. If... Q If the value is greater than 0, the operation mode of the ventilation duct foundation should be adjusted, and the annual net heat should be recalculated to ensure that the annual net heat is negative within the design service life. When constructing the numerical model of the annual net heat, the upper region is constructed according to the settings in 7), the lower soil is constructed according to the geological data in 1), and the model width is set according to the laying spacing in 8). The numerical calculation is divided into two steps: First, the temperature field distribution of the natural soil is calculated under no heating conditions, and the data on the upper limit of permafrost and ground temperature distribution collected in 1) are used for verification to ensure accuracy. After the initial temperature field calculation is completed, the normal operation of the ventilation duct foundation within the design service life is calculated under heating conditions.

[0037] This invention presents a simple, accurate, and rapid design method for ventilation duct foundations based on the heat balance of the foundation system. The core principle is to ensure that the annual net heat at the foundation bottom is negative throughout the design service life. This method provides a theoretical basis for the design and calculation of ventilation duct foundations and has significant application value in engineering. By collecting meteorological, geological, and foundation dimension data, the type and location of ventilation ducts are scientifically designed, wind speed and convective heat transfer coefficients are calculated, and the optimal diameter is determined. The cooling radius is calculated to determine the laying spacing, and the operating mode is determined based on the principle of heat balance. This method is simple, scientific, and accurate, effectively controlling settlement and deformation caused by permafrost degradation.

[0038] Compared with existing technologies, this invention has the following advantages: it provides a clear design process for ventilation duct foundations, abandoning methods that rely on engineering experience and field tests, shortening the design cycle, improving engineering efficiency, and offering strong specificity. Furthermore, this invention considers the impact of temperature changes on the design and uses actual data to verify the numerical model, ensuring the accuracy of calculation results under different environmental conditions. Attached Figure Description

[0039] Figure 1 A flowchart illustrating a method for designing ventilation duct foundations in permafrost regions based on heat balance.

[0040] Figure 2 Changes in annual net heat at the base of ventilation duct foundation

[0041] Figure 3 Changes in annual net heat load at the base of the ventilation duct foundation after the installation of temperature-controlled dampers Detailed implementation method:

[0042] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0043] This embodiment selects a section of a secondary highway in the permafrost region of the Qinghai-Tibet Plateau for design calculations. The road surface of this section is a black, high-heat-absorbing pavement. This high heat-absorbing characteristic exacerbates the thawing and settlement of the permafrost beneath the roadbed, leading to severe roadbed settlement and longitudinal cracks in the pavement. To solve this problem, we adopted a ventilation pipe foundation to protect the permafrost and achieve the goal of controlling roadbed settlement and deformation.

[0044] This embodiment uses a highway section in a permafrost region of the Qinghai-Tibet Plateau as an example for design calculations. The asphalt pavement of this section has high heat absorption, which accelerates the melting of the permafrost beneath the roadbed, leading to roadbed settlement and longitudinal cracks in the pavement. To solve these problems, this embodiment uses a ventilation pipe foundation to protect the permafrost and control roadbed settlement and deformation.

[0045] The specific implementation steps are as follows:

[0046] Step 1: Data Collection

[0047] The roadbed cross-sectional dimensions obtained from on-site measurements are: road width 13m, slope ratio 1:1.5, and fill height 3m. The design documents and geological survey results provide parameters for the roadbed soil and natural soil (see Table 1). Additionally, wind speed and snowfall data were collected based on local meteorological station data (see Tables 2 and 3).

[0048] Table 1 Physical parameters of roadbed and natural soil

[0049]

[0050] Table 2. Monthly Average Wind Speed ​​(m / s)

[0051]

[0052] Table 3 Snowfall (mm) over the past decade

[0053]

[0054] Step 2: Analyzing the snowfall data for the past ten years provided in Table 3, we determined that the snowfall in this area would not clog the pipes. Therefore, no additional snow protection measures are needed, and horizontal ventilation pipes can be used directly.

[0055] Step 3: Calculate the wind speed inside the ventilation duct using formula (4). In this case, the ventilation duct is located 0.5m above the natural ground, where K1 is 0.3 and K2 is -0.2. According to the specifications, three ventilation ducts with different inner diameters (0.4m, 0.5m, and 0.6m) are selected for calculation, with a duct length of 21m. The calculated wind speed data are detailed in Table 4.

[0056] Table 4. Average wind speed (m / s) in ventilation ducts of different diameters

[0057]

[0058] Step 4: Use formula (6) to obtain the convective heat transfer coefficient. The calculation results are shown in Table 5.

[0059] Table 5 Convection heat transfer coefficients (m) of ventilation ducts with different diameters 2 / k)

[0060]

[0061] Step 5: Table 5 shows that the convective heat transfer coefficients of 0.5m and 0.6m diameter ventilation ducts are similar. Considering economic factors, a 0.5m inner diameter ventilation duct is selected.

[0062] Step 6: Using the collected basic parameters, a numerical model with dimensions of 30m (height) × 10m (width) × 221m (length) was established. Two ventilation pipes with a centerline spacing of 5m were arranged within the model to reduce errors. Considering a 2.6℃ temperature rise over 50 years, the cooling radius of the ventilation pipes was calculated. It was found that the cooling effect was optimal within 2m on both sides of the pipe's centerline. Therefore, the optimal spacing was 4m.

[0063] Step 7: Based on the previous ventilation duct design parameters and the data in Table 1, a numerical model with a depth of 30m and a width of 4m was constructed, with the remaining dimensions the same as in Step 6. After obtaining a stable temperature field that matches the ground temperature and the upper limit of permafrost, a service life of 30 years was set. The heat at the bottom of the foundation was calculated using the warming boundary condition, and the annual net heat was calculated using formula (7). The results are shown in [Figure 7]. Figure 2 .

[0064] Step 8: Figure 2 The data shows that within the designed service life of 30 years, the net heat output of the ventilation duct foundation is negative in the first two years and positive in the third year. According to the principle of heat balance, the ventilation duct operating year-round leads to soil degradation, which does not meet the design requirements. Therefore, a temperature-controlled damper is installed to adjust the operation mode, automatically activating when the outside temperature drops below zero degrees Celsius. Figure 3 The data shows that after installing the damper, the annual net heat output remains negative throughout the entire service life.

[0065] In this specific embodiment, the ventilation pipe foundation, which is equipped with a temperature-controlled damper and has a burial height of 0.5m, a laying spacing of 4m, and a pipe diameter of 0.5m, can ensure that the permafrost under the foundation is stable and does not degrade or thaw.

[0066] The embodiments are intended to illustrate the invention and not to limit its application. Those skilled in the art can make adjustments, substitutions, or improvements without departing from the core concepts and spirit of the invention, and such modifications are all within the scope of protection of the invention.

[0067] [1] China Communications First Highway Survey and Design Institute Co., Ltd. (ed.). Technical Specifications for Highway Design and Construction in Permafrost Regions [M]. Beijing: China Communications Press, 2023;

[0068] [2] JGJ 118-2011; Code for Design of Building Foundations in Frozen Soil Areas [S]; 2011.08.29;

[0069] [3] Liu Weibao, Yu Wenbing, Chen Lin, Yi Xin, Han Fenglei, Hu Da. Current status of airport runway construction technology in permafrost areas [J]. Glacier and Permafrost, 2015, 37(6): 1599-1610;

[0070] [4] Su Wanxin, Xu Xueyan, Qiu Mingguo. Calculation of ventilation area of ​​ventilation duct foundation under heating conditions [J]; Low Temperature Building Technology, 2004, (5): 74-76;

[0071] [5] Cheng Guodong, Wu Qingbai, Ma Wei; Engineering effect of active cooling subgrade of Qinghai-Tibet Railway [J]; Science in China (Series E: Technological Sciences), 2009, 39(1): 16-22.

Claims

1. A method for designing ventilation duct foundations in permafrost regions based on heat balance, characterized as follows: 1) Collect data on temperature, wind speed, snowfall, sandstorms, wind direction, and foundation dimensions at the project site; at the same time, collect physical parameters of the backfill soil and natural soil, as well as data on the natural upper limit depth of permafrost and ground temperature distribution. 2) Based on the wind and snow data collected in 1), determine whether sand and snow prevention measures are needed; 3) Based on the wind speed information in 1), determine the laying height of the ventilation duct foundation. The laying height should be 0.5m higher than the natural ground level. 4) Use the wind speed calculation formula that takes into account duct resistance loss to calculate the wind speed inside the ventilation duct. The wind speed calculation formula for horizontal ventilation ducts is as follows: ； In the formula: K 1 , K 2 The aerodynamic coefficients at the air inlet and outlet; L This refers to the length of the pipe. D The diameter of the pipe; λ This refers to the friction coefficient along the pipeline. For ventilation ducts with added inlet and outlet ducts, the formula for calculating wind speed is as follows: ； In the formula: g For gravity; H This refers to the height of the air inlet. ξ This is the local resistance loss coefficient of the pipeline; 5) Based on the wind speed results calculated in 4), calculate the convective heat transfer coefficient and select an appropriate ventilation duct diameter; 6) Based on the results in 5), determine the cooling radius of the ventilation duct; 7) Based on the previous design results, determine the operating mode of the ventilation duct foundation to ensure a balance between heat input and output.

2. The method as described in claim 1, characterized in that: If the sand and snow prevention measure involves installing air inlet and outlet ducts, the air inlet should face the direction of higher winter wind speeds and its height should not exceed the foundation height. At the same time, the air inlet duct should be higher than the air outlet duct.

3. The method as described in claim 1, characterized in that: The convective heat transfer coefficient is calculated based on the air velocity inside the ventilation duct.

4. The method as described in claim 1, characterized in that: The cooling radius of the ventilation duct was determined through numerical simulation, taking into account a variety of factors, including the diameter of the ventilation duct, the burial height, and the ambient wind speed.

5. The method as described in claim 1, characterized in that: The operation mode of the ventilation duct foundation is determined through numerical simulation to ensure that the annual net heat at the bottom of the foundation is negative within the design service life. When the annual net heat at the bottom of the ventilation duct foundation is positive, the operation mode of the ventilation duct can be adjusted to ensure that its annual net heat is negative within the design service life.

6. The method as described in claim 1, characterized in that: The effect of temperature change is considered in the numerical calculation, and the rate of temperature change is determined based on the data collected in 1).

7. The method as described in claim 1, characterized in that: When calculating the annual net heat at the bottom of the foundation, this method uses the permafrost upper limit and ground temperature distribution data collected in 1) to verify the numerical model and ensure the accuracy of the calculation.

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