Snow pressing road replacement depth calculation method based on dynamic nonlinear thermal process and accumulated snow heat breaking effect

Abstract

The invention discloses a snow pressing road replacement depth calculation method based on a dynamic nonlinear thermal process and a snow accumulation heat breaking effect, and relates to the technical field of geotechnical engineering in cold regions. Key air temperature data of a target area are obtained, related physical and thermodynamic parameters of a pavement structure layer and a snow accumulation layer are detected, an improved formula is proposed to calculate the freezing depth, and when the thickness of the snow accumulation layer is not considered, the freezing depth is determined through iterative calculation, and a relation curve A is drawn; when the thickness of the snow accumulation layer is considered, the freezing depth is calculated, a relation curve B is drawn and combined with the curve A to obtain a derivation curve C, then the freezing depth is determined, and the thickness reduction amount of the anti-freezing layer is determined through comparison and subtraction. The thickness of an anti-freezing layer is replaced and reduced by coupling thermophysical property nonlinear changes of materials of meteorological conditions, an accumulated snow layer and a pavement structure layer, considering an accumulated snow heat breaking effect and optimizing and improving a freezing depth formula, so that the use amount of engineering materials and the construction cost are effectively reduced.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology in cold regions, specifically a method for calculating the replacement depth of snow-covered roads based on dynamic nonlinear thermal processes and the snow insulation effect. Background Technology

[0002] In seasonally frozen areas, roadbeds are prone to periodic frost heave and thaw settlement under the influence of external environmental temperatures, leading to uneven deformation of the roadbed and affecting driving safety and pavement structural durability. To prevent frost damage, existing road designs typically control the freezing depth of the roadbed by increasing the thickness of the antifreeze layer, but these designs often rely on static empirical parameters or historical extreme values, which have certain limitations.

[0003] Existing methods fail to reflect the dynamic nonlinear thermal processes in road systems. Key parameters such as thermal conductivity and volumetric heat capacity of various road materials exhibit significant nonlinearity with changes in temperature, moisture content, density, and phase, and current static models cannot characterize this complex physical process. In contrast, dynamic nonlinear thermal process models can more scientifically and accurately predict freezing depth, thereby rationally determining the depth of frost protection layer replacement. The meteorological and soil physical parameters required for such models are more readily available through conventional methods. Furthermore, their dynamic simulation characteristics allow them to flexibly respond to and incorporate current and future climate change trends, thereby improving the adaptability and reliability of designs in a warming and humidifying environment.

[0004] Because existing calculation methods rely solely on empirical selection without incorporating physical mechanisms, they are limited in considering the sustained thermal insulation effect of snow layers. In cold, snowy regions, low-traffic roads often form stable, compacted snow layers in winter, which effectively inhibit the freezing depth of the roadbed. Ignoring the contribution of natural thermal insulation layers during the design process will directly lead to overly conservative design of the frost-resistant layer thickness, resulting in wasted engineering materials and increased costs.

[0005] Therefore, it is necessary to propose a method for calculating the displacement depth that can simultaneously and accurately couple the snow insulation effect and the dynamic nonlinear thermal process. This is of great significance for achieving accurate design of the antifreeze layer thickness and a reasonable balance between engineering and economics. Summary of the Invention

[0006] To address the shortcomings of the prior art, this invention provides a method for calculating the replacement depth of snow-shrouded roads based on dynamic nonlinear thermal processes and the snow insulation effect. By coupling meteorological conditions, the nonlinear changes in the thermal properties of the snow layer and the materials of each layer of the road structure, and considering the snow insulation effect, the freezing depth formula is optimized and improved, thereby replacing and reducing the thickness of the antifreeze layer, effectively reducing the amount of engineering materials used and construction costs.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for calculating the snow-groomed road replacement depth based on dynamic nonlinear thermal processes and snow heat insulation effects, comprising the following steps:

[0008] Step S101: Obtain key temperature data for the target area, collect daily average temperature data and daily average snow depth data for at least one consecutive year in the target area, and calculate the annual average temperature based on the daily average temperature data. Freeze time and maximum freezing index The snow freezing index is calculated based on the daily average snow depth data and daily average temperature data. ;

[0009] Step S102: Detect the relevant physical and thermodynamic parameters of the pavement structure layer and the snow layer. The pavement structure layer includes, from top to bottom, the surface layer, the base layer, the antifreeze layer and the subgrade. The relevant physical and thermodynamic parameters include the dry density, moisture content, thermal conductivity, volumetric heat capacity, latent heat of melting and thickness of each layer.

[0010] Step S103: Calculate the freezing depth using the improved formula , means as follows:

[0011]

[0012] In the formula, The freezing index has a range of values. , Here is a dimensionless coefficient related to volumetric heat capacity. The calculation is as follows:

[0013]

[0014] In the formula, For the ideal maximum freezing depth, , The thicknesses of the snow cover layer, surface layer, base layer, frost protection layer, and roadbed are, in order. The latent heat of melting for the snow layer, surface layer, base layer, antifreeze layer, and roadbed are, in that order. The thermal conductivity of the snow layer, surface layer, base layer, antifreeze layer, and roadbed are, in order.

[0015] When the thickness of the snow layer is not considered, i.e. At that time, the freezing depth was initially determined by improving the formula. The freezing depth is obtained through iterative calculations. Equal to the ideal maximum freezing depth So far, the thickness of the antifreeze layer during the iteration process Based on the obtained data, plot curve A showing the relationship between freezing depth and freezing index under conditions of no snow cover;

[0016] Step S104: Optimize the antifreeze layer thickness considering the heat insulation effect of the snow layer. When considering the snow layer thickness, i.e. At that time, based on the final obtained freezing depth Determined antifreeze layer thickness and roadbed thickness The freezing depth under snow cover was obtained by improving the calculation formula. Based on the calculation results, curve B was plotted showing the relationship between freezing depth and freezing index under snow cover conditions. The curve B was then analyzed using the snow cover freezing index. The subsequent curve partially replaces curve A from the snow freezing index. The subsequent curve section yields curve C, which is the derivation curve of the freezing depth under snow-covered surfaces. Finally, based on the actual maximum freezing index... Substitute the curve C to determine the maximum freezing depth under the snow insulation effect. To obtain the thickness of the antifreeze layer considering the heat insulation effect of snow accumulation. The reduction in frost layer thickness due to the snow insulation effect is determined by comparing it with the frost layer thickness when the snow layer is not considered.

[0017] Furthermore, in step S101, the annual average temperature The arithmetic mean method was used to sum the collected daily average temperature data and then divide by the number of observation days; freezing time The freezing start date is defined as the date when the earliest daily average temperature drops below 0°C and remains below 0°C for two consecutive days thereafter, and the freezing end date is defined as the date with the lowest cumulative daily average temperature. The number of days between the freezing start and freezing end dates is calculated; the maximum freezing index is also calculated. By accumulating the freeze time The absolute value of sub-zero temperatures for all days with an average daily temperature below 0°C; Snow freezing index. The date on which the ground first shows continuous snow cover for ≥30 days is selected as the snow cover start date, and the absolute values ​​of negative temperatures from the start of freezing to the start of snow cover are accumulated.

[0018] Furthermore, in step S101, the daily average temperature data and daily average snow depth data are obtained from qualified meteorological agencies. If data for individual dates is missing during the collection process, the missing data for three consecutive days is supplemented by using the moving average method.

[0019] Furthermore, in step S102, the moisture content of each layer is determined by the drying method, the dry density of each layer is determined by the ring cutter method, the thermal conductivity of each layer is determined by the thermal conductivity meter, and the volumetric heat capacity and latent heat of melting of each layer are determined by the differential scanning calorimeter. The thickness of the surface layer and the base layer is determined according to the "Specifications for Design of Highway Asphalt Pavement", and the maximum value of the thickness range under the corresponding load level is selected.

[0020] Furthermore, in step S103, the dimensionless coefficient From melting parameters and heat ratio Both factors determine this, among which:

[0021] Heat ratio The calculation formula is as follows:

[0022]

[0023]

[0024] Melting parameters The calculation formula is as follows:

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, The average volumetric heat capacity, For the average latent heat of fusion, The volumetric heat capacity of the snow layer, surface layer, base layer, antifreeze layer, and roadbed are listed in that order. The moisture content of the corresponding layer. This represents the dry density of the corresponding layer.

[0030] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention aims to solve the problems of traditional cold-region road design relying on static empirical parameters and failing to consider dynamic thermal processes and the heat insulation effect of snow accumulation, resulting in excessively thick antifreeze layers and high costs. Existing formulas for calculating freezing depth lack corresponding physical mechanisms. Local temperature and humidity levels change over time, and measurement is also difficult. This invention couples meteorological conditions, snow layers, and the nonlinear changes in the thermophysical properties of each layer of the pavement structure layer. It measures physical and thermodynamic parameters such as moisture content, thermal conductivity, and latent heat of melting of the pavement structure layer and snow layer, considering the changes in the physical state of each layer, and organically integrates them into the calculation equation for freezing depth to achieve accurate simulation of road freezing depth. On this basis, a dimensionless coefficient is introduced. With effective thermal parameters By optimizing and improving the freezing depth formula to ensure that the results closely match actual working conditions, the thickness of the antifreeze layer can be reasonably reduced while meeting the requirements for frost heave resistance. This can significantly improve design accuracy and effectively reduce the amount of engineering materials and construction costs while ensuring frost resistance stability. Attached Figure Description

[0031] Figure 1 This is a flowchart of the method of the present invention;

[0032] Figure 2 This is a schematic diagram showing the relationship between the freezing depth and replacement of the pavement structure layer in the method of this invention;

[0033] Figure 3 It is the dimensionless coefficient for calculating the freezing depth in the method of this invention. Values ​​chart;

[0034] Figure 4 This is a schematic diagram of the relationship between freezing depth and freezing index under no snow cover in the method of the present invention;

[0035] Figure 5 This is a schematic diagram of the relationship between freezing depth and freezing index under snow cover in the method of the present invention. Detailed Implementation

[0036] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0037] like Figures 1-5 As shown, a method for calculating the replacement depth of snow-groomed roads based on dynamic nonlinear thermal processes and snow heat insulation effects is presented, and its process is combined with... Figure 1 As shown, it includes the following steps:

[0038] Step S101: Obtain key temperature data for the target area;

[0039] Collect at least one consecutive year of daily average temperature and daily average snow depth data for the target area. Data must be sourced from qualified meteorological agencies. The data collection period, format, and completeness requirements must be clearly defined to ensure the data is complete and free of outliers. If data is missing for any particular date during the collection process, it must be supplemented using a moving average method based on data from the adjacent three days to ensure data continuity and accuracy.

[0040] Calculate the annual average temperature The arithmetic mean method is used to sum the collected daily average temperature data and then divide by the number of observation days to obtain the annual average temperature. The unit is ℃.

[0041] Determine the freeze time The freezing period begins on the date when the earliest daily average temperature drops below 0°C and remains below 0°C for two consecutive days thereafter. The freezing ends on the date when the cumulative daily average temperature reaches its lowest point. The number of days between the freezing start and end dates is then calculated to determine the freezing duration. The unit is days.

[0042] Calculate the maximum freezing index Cumulative freeze time The maximum freezing index is calculated by taking the absolute value of the negative temperature on all days with a daily average temperature below 0°C. The unit is ℃ day.

[0043] Determine the snow freezing index The snow freezing index is calculated by selecting the date when continuous snow cover on the ground for the first time for ≥30 days as the snow accumulation start date, and summing the absolute values ​​of negative temperatures from the freezing start date to the snow accumulation start date. The unit is ℃ day.

[0044] In this step, the specific implementation method is to obtain the daily average temperature and snow depth data of the target area for at least one year by connecting with qualified meteorological agencies, calculate the annual average temperature using the arithmetic mean method, define the start and end dates of freezing according to the temperature conditions and count the freezing time, accumulate the negative temperature day by day to obtain the maximum freezing index, and after screening and determining the snow accumulation start date, accumulate the negative temperature of the corresponding period to obtain the snow freezing index, ensuring the standardization of data completion and statistical logic throughout the process.

[0045] Step S102: Detect the relevant physical and thermodynamic parameters of the road surface structure layer and the snow layer;

[0046] The freezing depth is determined by the thermal conductivity of each layer in the pavement structure. The thermal conductivity of a material is influenced not only by the properties of the parent material but also by its density and moisture content. Therefore, the thermal conductivity values ​​of asphalt mixtures and subgrade materials will differ. Consequently, even under the same meteorological conditions, the freezing depth will vary due to differences in thermal conductivity between different pavement structure layers.

[0047] Under normal circumstances, the pavement structural layers are bonded. Figure 2 As shown, from top to bottom, it consists of a surface layer, a base layer, and an antifreeze layer, with the roadbed below. The total thickness of the pavement structure layers is usually set to 80% of the average maximum freezing depth of the target area over the past ten years. When the sum of the thicknesses of the surface layer and the base layer is less than this thickness, an antifreeze layer is required to fill the thickness difference.

[0048] The testing process covers the surface layer, base layer, antifreeze layer, subgrade, and snow cover of the road in the target area, obtaining the physical and thermodynamic parameters of each layer. The moisture content of each layer is determined using the drying method, and the dry density is determined using the ring cutter method. The compacted snow density of the snow layer can be obtained through on-site sampling and laboratory testing to ensure the data reflects actual working conditions. The thermal conductivity of each layer is measured using a thermal conductivity meter, and the volumetric heat capacity and latent heat of melting are measured using a differential scanning calorimeter. The testing process must comply with the specifications for testing thermal parameters of geotechnical engineering materials. The thickness of the surface layer and base layer is calculated according to the "Specifications for Design of Highway Asphalt Pavement," determined by factors such as traffic load level and subgrade bearing capacity (e.g., CBR value). From a safety perspective, the maximum value of the surface layer and base layer thickness range corresponding to the load level can be selected. The snow layer thickness is measured on-site with a straightedge, taking the average value of different road cross-sections, or can be obtained from meteorological data, and recorded in the testing table.

[0049] Parameter compilation: Compile and archive the dry density, moisture content, thermal conductivity, volumetric heat capacity, latent heat of melting, and thickness data of each layer to provide basic parameters for subsequent freezing depth calculations.

[0050] In this step, standard testing methods such as the drying method and the ring cutter method can be used to measure the physical parameters of each layer, such as moisture content and dry density. Professional instruments such as thermal conductivity meters and differential scanning calorimeters are used to determine the thermal parameters of each layer. Based on the "Specifications for Design of Asphalt Pavement on Highways," and considering factors such as traffic load level and subgrade CBR value, the thickness of the surface layer and base layer is calculated. The snow compaction density of the snow layer is obtained through laboratory testing after on-site sampling. At least five cross-sections are evenly selected on the road, with three sampling points at each cross-section. The average value of all samples is taken to ensure data accuracy. The snow layer thickness is measured on-site with a ruler, and the average value of different road cross-sections is taken. Alternatively, snow depth data provided by meteorological agencies can be used. Finally, the parameters are categorized and compiled into an archive table containing test information, providing basic data for subsequent calculations.

[0051] Step S103: Calculate the freezing depth using the improved formula ;

[0052] Based on a comprehensive analysis of methods for determining freezing depth in industries other than railways both domestically and internationally, an improved formula for calculating freezing depth is proposed, as follows:

[0053]

[0054] In the formula, The freezing index is calculated by selecting a day between the start and end of the freezing period and summing the absolute values ​​of negative temperatures from the start of the freezing period to that day. Its range is... The unit is ℃ day, The dimensionless coefficient relating to volumetric heat capacity is derived from the melting parameter. and heat ratio Both parties jointly decide, The calculation is as follows:

[0055]

[0056] In the formula, For the ideal maximum freezing depth, , The thicknesses of the snow cover layer, surface layer, base layer, frost protection layer, and roadbed are, in order. The latent heat of melting for the snow layer, surface layer, base layer, antifreeze layer, and roadbed are, in that order. The thermal conductivity is as follows: snow layer, surface layer, base layer, antifreeze layer, and roadbed.

[0057] Heat ratio The calculation formula is as follows:

[0058]

[0059]

[0060] Melting parameters The calculation formula is as follows:

[0061]

[0062]

[0063]

[0064]

[0065] In the formula, The average volumetric heat capacity, For the average latent heat of fusion, The volumetric heat capacity of the snow layer, surface layer, base layer, antifreeze layer, and roadbed are listed in that order. The moisture content of the corresponding layer. This represents the dry density of the corresponding layer.

[0066] When the thickness of the snow layer is not considered, i.e. hour:

[0067] Calculate the melting parameters and heat ratio Afterwards, combined Figure 3 As shown, dimensionless coefficients are obtained by interpolation based on the chart. At this point, the obtained parameters from each layer are substituted into the improved formula for calculating the freezing depth to initially determine the freezing depth. Determine the depth of freezing. Is it equal to the ideal maximum freezing depth? If they are not equal, then the freezing depth will be... The new ideal maximum freezing depth is used for recalculation, and the thickness of the antifreeze layer is calculated again in this recalculation. Change to The freezing depth is obtained through iterative calculations. Equal to the ideal maximum freezing depth Up to this point. Based on the obtained data, a complete curve showing the relationship between freezing depth and freezing index under conditions of no snow cover is plotted, denoted as curve A. Combined with... Figure 4 As shown, the horizontal axis represents the freezing index, and the vertical axis represents the freezing depth.

[0068] In this step, It is a key parameter for quantifying the synergistic thermal effects of different layers, and can truly reflect the dynamic heat conduction characteristics of the multi-layered roadbed structure. Heat ratio The warming or cooling characteristics of a region's climate are quantified by the ratio of annual average temperature to average freezing temperature. The larger the value, the higher the annual average temperature is relative to the freezing period temperature (e.g., in warm winter regions), and the more significant the impact of rising external temperatures on roadbed freezing. The smaller the value, the lower the temperature during the freezing period (e.g., in frigid regions), and the greater the potential for increased freezing depth. Melting parameter. Characterizing the coupling relationship between average freezing temperature and material thermophysical properties, The smaller the value, the easier the material is to freeze, and the greater the freezing depth.

[0069] Step S104: Optimize the thickness of the antifreeze layer considering the heat insulation effect of the snow layer;

[0070] On snow-covered roads, when the compacted snow layer is thick and has a low density, the freezing depth will be correspondingly reduced.

[0071] When considering the thickness of the snow layer, i.e. hour:

[0072] Based on the final obtained freezing depth Determined antifreeze layer thickness and roadbed thickness The improved calculation formula for freezing depth, which substitutes the parameters of each layer back into the freezing depth, yields the freezing depth when covered by snow. Based on the calculation results, a complete curve showing the relationship between freezing depth and freezing index under snow cover conditions was plotted, denoted as curve B. Figure 5 As shown, the self-freezing index in curve B is... The subsequent curve partially replaces curve A from the snow freezing index. The subsequent curve section yields the derived curve of the freezing depth under snow-covered surfaces, denoted as curve C. Finally, based on the actual maximum freezing index... Substitute the curve C to determine the maximum freezing depth under the snow insulation effect. To obtain the thickness of the antifreeze layer considering the heat insulation effect of snow accumulation. The reduction in frost layer thickness due to the snow insulation effect is determined by comparing it with the frost layer thickness when the snow layer is not considered.

[0073] In this step, the thermal conductivity of the snow layer is much lower than that of the surface and base materials, making it a highly efficient thermal insulation layer. This significantly increases the overall thermal conductivity resistance, thereby reducing the design thickness of the antifreeze layer.

[0074] Example

[0075] Taking Tongliao City, Inner Mongolia Autonomous Region, China as an example, the data source is a qualified meteorological agency, which simultaneously collects daily snow depth data for the same period. The relevant data calculation results are shown in Table 1:

[0076] Table 1. Meteorological parameters for a certain area

[0077]

[0078] Based on the traffic load level of the area, the surface layer thickness is taken as 20cm, and the base layer thickness as 40cm. The average maximum freezing depth of the city over the past ten years is approximately 131.7cm, which is taken as 132cm. Calculations show that the frost protection layer thickness can be initially set at 45cm, and the roadbed thickness at 27cm. The surface layer, base layer, frost protection layer, roadbed, and snow cover layer of the target area were inspected, and the physical and thermodynamic parameters of each layer were obtained and recorded as shown in Table 2.

[0079] Table 2 Relevant parameters for each material layer

[0080]

[0081] Substitute the relevant parameters from Table 2 into The calculation formula yields:

[0082]

[0083] The formula for calculating the heat ratio is:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Calculate the melting parameters and heat ratio Next, dimensionless coefficients are obtained by interpolation based on the chart. At this point, substituting the parameters of each layer into the improved formula for calculating the freezing depth yields:

[0090]

[0091] After 3 iterations when At that time, the calculation yielded , .

[0092] Calculated at this time , .

[0093] Based on the calculation results, plot curve A showing the relationship between freezing depth and freezing index under no snow cover.

[0094] Considering the heat insulation effect of snow cover, the city has a snow cover of 20cm and a snow compaction density of 0.55g / cm³. 3 When the thermodynamic parameters of the snow are substituted into the equation, it is added as an independent layer to... The calculation formula yields:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] Based on the calculation results, curve B, showing the relationship between freezing depth and freezing index under snow cover, was plotted.

[0102] The snow freezing index for when the city's roads begin to show signs of more than 30 consecutive days of snow accumulation is: At this time, the freezing depth of roads without snow cover is as follows:

[0103]

[0104] Because the roads had already reached a freezing depth of 44.088 cm during the continuous snowfall, the freezing depth was subsequently considered based on this depth, and the snow freezing index in curve B was adjusted accordingly. The subsequent curve partially replaces curve A. The subsequent curved section (curve A in) The freezing depth at the location is 44.088 cm, from which the freezing depth curve C under the snow-covered road surface can be derived. Finally, based on the actual maximum freezing index... Substitute the curve C to determine the freezing depth under the snow insulation effect. .

[0105] The thickness of the frost protection layer under snow cover conditions can be calculated:

[0106]

[0107] Further calculations were made regarding the reduction in the thickness of the antifreeze layer:

[0108]

[0109] The above calculations show that the design thickness of the antifreeze layer for the city's roads can be reduced by 5.5 cm.

[0110] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0111] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for calculating the snow-groomed road replacement depth based on dynamic nonlinear thermal processes and snow heat insulation effects, characterized in that: Includes the following steps: Step S101: Obtain key temperature data for the target area, collect daily average temperature data and daily average snow depth data for at least one consecutive year in the target area, and calculate the annual average temperature based on the daily average temperature data. Freeze time and maximum freezing index The snow freezing index is calculated based on the daily average snow depth data and daily average temperature data. ; Step S102: Detect the relevant physical and thermodynamic parameters of the pavement structure layer and the snow layer. The pavement structure layer includes, from top to bottom, the surface layer, the base layer, the antifreeze layer and the subgrade. The relevant physical and thermodynamic parameters include the dry density, moisture content, thermal conductivity, volumetric heat capacity, latent heat of melting and thickness of each layer. Step S103: Calculate the freezing depth using the improved formula , means as follows: In the formula, The freezing index has a range of values. , Here is a dimensionless coefficient related to volumetric heat capacity. The calculation is as follows: In the formula, For the ideal maximum freezing depth, , The thicknesses of the snow cover layer, surface layer, base layer, frost protection layer, and roadbed are, in order. The latent heat of melting for the snow layer, surface layer, base layer, antifreeze layer, and roadbed are, in that order. The thermal conductivity of the snow layer, surface layer, base layer, antifreeze layer, and roadbed are, in order. When the thickness of the snow layer is not considered, i.e. At that time, the freezing depth was initially determined by improving the formula. The freezing depth is obtained through iterative calculations. Equal to the ideal maximum freezing depth So far, the thickness of the antifreeze layer during the iteration process Based on the obtained data, plot curve A showing the relationship between freezing depth and freezing index under conditions of no snow cover; Step S104: Optimize the antifreeze layer thickness considering the heat insulation effect of the snow layer. When considering the snow layer thickness, i.e. At that time, based on the final obtained freezing depth Determined antifreeze layer thickness and roadbed thickness The freezing depth under snow cover was obtained by improving the calculation formula. Based on the calculation results, curve B was plotted showing the relationship between freezing depth and freezing index under snow cover conditions. The curve B was then analyzed using the snow cover freezing index. The subsequent curve partially replaces curve A from the snow freezing index. The subsequent curve section yields curve C, which is the derivation curve of the freezing depth under snow-covered surfaces. Finally, based on the actual maximum freezing index... Substitute the curve C to determine the maximum freezing depth under the snow insulation effect. To obtain the thickness of the antifreeze layer considering the heat insulation effect of snow accumulation. The reduction in frost layer thickness due to the snow insulation effect is determined by comparing it with the frost layer thickness when the snow layer is not considered.

2. The method for calculating the snow-groomed road replacement depth based on dynamic nonlinear thermal processes and snow heat insulation effects according to claim 1, characterized in that: In step S101, the annual average temperature The arithmetic mean method was used to sum the collected daily average temperature data and then divide by the number of observation days; freezing time The freezing start date is defined as the date when the earliest daily average temperature drops below 0°C and remains below 0°C for two consecutive days thereafter, and the freezing end date is defined as the date with the lowest cumulative daily average temperature. The number of days between the freezing start and freezing end dates is calculated; the maximum freezing index is also calculated. By accumulating the freeze time The absolute value of sub-zero temperatures for all days with an average daily temperature below 0°C; Snow freezing index. The date on which the ground first shows continuous snow cover for ≥30 days is selected as the snow cover start date, and the absolute values ​​of negative temperatures from the start of freezing to the start of snow cover are accumulated.

3. The method for calculating snow-groomed road replacement depth based on dynamic nonlinear thermal processes and snow heat insulation effects according to claim 1, characterized in that: In step S101, the daily average temperature data and daily average snow depth data are obtained from qualified meteorological institutions. If data for individual dates is missing during the collection process, the missing data for three consecutive days is supplemented by using the moving average method.

4. The method for calculating the snow-groomed road replacement depth based on dynamic nonlinear thermal processes and snow heat insulation effects according to claim 1, characterized in that: In step S102, the moisture content of each layer is determined by the drying method, the dry density of each layer is determined by the ring cutter method, the thermal conductivity of each layer is determined by the thermal conductivity meter, and the volumetric heat capacity and latent heat of melting of each layer are determined by the differential scanning calorimeter. The thickness of the surface layer and the base layer is determined according to the "Specifications for Design of Highway Asphalt Pavement", and the maximum value of the thickness range under the corresponding load level is selected.

5. The method for calculating the snow-groomed road replacement depth based on dynamic nonlinear thermal processes and snow heat insulation effects according to claim 1, characterized in that: In step S103, the dimensionless coefficient From melting parameters and heat ratio Both factors determine this, among which: Heat ratio The calculation formula is as follows: Melting parameters The calculation formula is as follows: In the formula, The average volumetric heat capacity, For the average latent heat of fusion, The volumetric heat capacity of the snow layer, surface layer, base layer, antifreeze layer, and roadbed are listed in that order. The moisture content of the corresponding layer. This represents the dry density of the corresponding layer.

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