Method for calculating parameters of protective belt of wind and sand prevention and control project
By scientifically calculating the parameters of the protective belt for wind and sand control projects along railway lines, the problem of inaccurate traditional designs has been solved, achieving effective wind and sand control and improving railway safety and the ecological environment.
Patent Information
- Application Number
- CN202511016946.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-23
- Publication Date
- 2025-11-07
AI Technical Summary
Traditional wind and sand control measures lack scientific calculations, resulting in inaccurate design of the width and pattern of protective belts, which cannot effectively block wind and sand, and pose operational risks and waste resources.
By acquiring information on sand control strategies and designed sand transport volumes in wind-prone areas along railway lines, we conduct spatiotemporal analysis of sandstorms, calculate the sand-blocking and sand-fixing volumes of each fence and grid, and combine this with safety blocking analysis to determine the parameters of the protective belt and form a scientific and reasonable protection system.
It significantly enhances the scientific nature and practicality of sand control and stabilization projects, effectively curbs the encroachment of wind and sand on railway facilities, eliminates operational risks, and has good sustainable development and ecological restoration value.
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Figure CN120911348A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to the technical field of engineering protection, in particular to a wind-sand prevention and control engineering protection belt parameter calculation method and device and computer equipment. BACKGROUND
[0002] In desert and gobi areas along railways, wind-sand hazards pose a challenge to the stability of railway roadbeds and the safety of train operation. Wind-sand activities can not only erode roadbeds, causing roadbed subsidence or deformation, but also accumulate on tracks, affecting the normal operation of trains and even causing serious traffic accidents. Therefore, effective wind-sand prevention and control measures are crucial to ensuring the safety and reliability of railway transportation.
[0003] However, traditional wind-sand prevention and control measures often rely on experience rather than scientific calculation, lacking precise design of protection belt width and mode, which not only leads to unsatisfactory prevention and control effect, but also causes waste of resources. For example, excessively wide protection belts can result in unnecessary land occupation and material waste, while excessively narrow protection belts can fail to effectively block wind-sand, failing to achieve the expected protection effect, ultimately leading to operational risks along railways. SUMMARY
[0004] Therefore, it is necessary to provide a wind-sand prevention and control engineering protection belt parameter calculation method, device and computer equipment capable of eliminating operational risks along railways to solve the above technical problems.
[0005] In a first aspect, the application provides a wind-sand prevention and control engineering protection belt parameter calculation method, comprising:
[0006] obtaining wind-sand prone area corresponding blocking and solidification prevention strategy information and design sand transport capacity along a railway;
[0007] performing wind-sand space-time analysis on each sand-blocking fence and each sand-fixing square in the wind-sand prone area according to the blocking and solidification prevention strategy information and the design sand transport capacity, to obtain sand-blocking capacity of each fence and sand-fixing capacity of each square;
[0008] performing safety blocking analysis on the railway line according to the sand-blocking capacity of each fence and the sand-fixing capacity of each square, to determine fence parameters corresponding to each sand-blocking fence and square parameters corresponding to each sand-fixing square;
[0009] determining wind-sand prevention and control engineering protection belt parameters of the railway line according to the fence parameters and the square parameters.
[0010] In a second aspect, the application also provides a wind-sand prevention and control engineering protection belt parameter calculation device, comprising:
[0011] The wind-sand parameter acquisition module is configured to acquire the anti-sand prevention strategy information corresponding to the wind-sand prone area along the railway line and the designed sand transport volume.
[0012] The sand prevention parameter calculation module is configured to perform wind-sand space-time analysis on each sand barrier and each sand fixation square in the wind-sand prone area according to the anti-sand prevention strategy information and the designed sand transport volume, to obtain the sand barrier volume of each sand barrier and the sand fixation volume of each sand fixation square.
[0013] The device parameter calculation module is configured to perform safety blocking analysis on the railway line according to the sand barrier volume of each sand barrier and the sand fixation volume of each sand fixation square, to determine the barrier parameter corresponding to each sand barrier and the square parameter corresponding to each sand fixation square.
[0014] The guard parameter calculation module is configured to determine the guard parameter of the wind-sand prevention engineering guard along the railway line according to the barrier parameter of each sand barrier and the square parameter of each sand fixation square.
[0015] In a third aspect, the present application further provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements any step of the wind-sand prevention engineering guard parameter calculation method when executing the computer program.
[0016] The wind-sand prevention engineering guard parameter calculation method, device and computer device described above, by acquiring the anti-sand prevention strategy information of the wind-sand prone area along the railway line and the designed sand transport volume through the system, combining the space-time evolution characteristics of the regional wind-sand, scientifically analyzing the actual sand barrier capacity of each sand barrier and the sand fixation efficiency of each sand fixation square, and further quantifying the influence degree of the sand barriers and squares of different positions and types on the wind-sand movement and deposition. Based on the accurate sand barrier volume and sand fixation volume data, the barrier structure parameters (such as height, spacing, arrangement mode, etc.) and square arrangement parameters (such as square size, material selection, distribution density, etc.) suitable for different sections are further derived, and finally the targeted, stable and economical guard parameter configuration scheme of the wind-sand prevention engineering along the railway line is formed. Not only significantly improves the scientificity and practicability of the sand prevention and fixation engineering, effectively curbs the invasion and damage of the wind-sand to the railway line facilities, eliminates the operation risk along the railway line, but also has good sustainable development and ecological restoration value, providing strong technical support for the safe operation of the railway and the improvement of the ecological environment along the railway. BRIEF DESCRIPTION OF DRAWINGS
[0017] In order to more clearly illustrate the technical solutions in the embodiments or the related art, the drawings needed to be used in the embodiments or the related art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creating laborious work.
[0018] Figure 1 A flowchart of a parameter calculation method of a wind-sand prevention engineering protection belt in an embodiment;
[0019] Figure 2 A schematic diagram of a sand prevention system width established by simulation calculation in an embodiment;
[0020] Figure 3 A graph of the relationship between sand prevention efficiency and sand barrier porosity and wind speed in an embodiment;
[0021] Figure 4 A graph of the relationship between sand prevention efficiency and sand barrier height and wind speed in an embodiment. DETAILED DESCRIPTION
[0022] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.
[0023] In an embodiment, step 101, the sand prevention strategy information corresponding to the wind-sand prone area along the railway and the designed sand transport amount are obtained;
[0024] Step 102, according to the sand prevention strategy information and the designed sand transport amount, the wind-sand space-time analysis is performed on each sand barrier and each sand fixation grid in the wind-sand prone area, to obtain the sand barrier amount of each barrier and the sand fixation amount of each grid;
[0025] Step 103, according to the sand barrier amount of each barrier and the sand fixation amount of each grid, the safety blocking analysis is performed on the railway line, to determine the barrier parameters corresponding to each sand barrier and the grid parameters corresponding to each sand fixation grid;
[0026] Step 104, according to the barrier parameters and the grid parameters, the wind-sand prevention engineering protection belt parameters of the railway line are determined.
[0027] Specifically, first, the field investigation and wind-sand environment investigation need to be carried out on the wind-sand prone area along the railway, including the historical meteorological data (such as wind speed, wind direction, wind frequency) for many years and the measured data of the current wind-sand flow field. Through the sand accumulation instrument, laser radar scanning, unmanned aerial vehicle remote sensing and other technical means, combined with the characteristics of geomorphology, topography, geology and sand source distribution, the designed sand transport amount of the wind-sand in the transverse direction of the railway is scientifically calculated. At the same time, according to the local wind-sand type, sand source condition and damage level to the railway facilities, the most suitable prevention strategy is selected, such as sand blocking, sand fixation, combination of sand blocking and sand fixation, or combination of sand blocking and sand fixation.
[0028] After the prevention and control strategy and the design sand transport capacity are determined, the time and space variation of wind sand needs to be analyzed to simulate the transport process of wind sand under different seasons and wind speed conditions. The limiting sand blocking capacity and sand fixing capacity of each type of sand barrier per unit area / length are calculated by considering the layout mode, size, height, material and arrangement spacing of different forms of sand blocking barriers (such as high vertical sand barriers) and sand fixing grids (such as grass grids or reed grids). More accurate results can be obtained through wind tunnel tests, numerical simulations, historical engineering observation data and other means.
[0029] Based on the obtained unit sand blocking and fixing capacity of each type of sand barrier, the protection demand of the entire railway line needs to be comprehensively analyzed to ensure that it has sufficient carrying capacity for the design sand transport capacity during the service period. For this purpose, a safety factor K i should be introduced to optimize the design of the number of barrier rows, height, spacing, material, considering different railway grades, climate variations, material durability and other factors, and reasonably configure the size, exposed height and layout density of the grid to ensure that the protection system is safe and effective, and has engineering economy and ecological sustainability.
[0030] Finally, each type of protection unit (sand blocking barrier and sand fixing grid) is integrated to form a complete protection belt structure. According to the idea of "external blocking and internal fixing, functional zoning", the protection belt, sand blocking belt, transition belt, sand fixing belt and isolation belt are arranged from the outer edge of the railway subgrade outward. By calculating the width of each sub-belt and its combination relationship, the total width and spatial layout mode of the protection belt along the entire railway line are finally determined to form a scientific and reasonable protection system. This systematic parameter setting ensures the efficiency and adaptability of wind sand control and improves the reliability and sustainability of the overall sand prevention project.
[0031] In one embodiment, the wind sand space-time analysis of each sand blocking barrier and each sand fixing grid in the wind sand prone area according to the sand blocking and fixing prevention strategy information and the design sand transport capacity includes:
[0032] According to the sand blocking and fixing prevention strategy information, the corresponding protection safety factor and protection design period of the railway line are determined;
[0033] According to the protection safety factor and the protection design period, the sand blocking capacity of each barrier and the sand fixing capacity of each grid are calculated under the constraint condition of the design sand transport capacity.
[0034] Step 201, according to the sand blocking and fixing prevention strategy information, the corresponding protection safety factor and protection design period of the railway line are determined;
[0035] Step 202: Using the designed sand transport volume as a constraint, calculate the sand blocking capacity of each fence and the sand fixing capacity of each grid according to the protection safety factor and the protection design period.
[0036] Specifically, after clarifying the combined strategy of sand blocking and sand fixation, it is necessary to determine the corresponding protection safety factor K based on the railway's grade (e.g., ordinary railway, passenger dedicated line, high-speed railway) and the degree of wind and sand hazard in the surrounding environment. i and the protection design cycle T x Safety factor K i This is used to enhance the redundancy of the protection system to cope with extreme sandstorm events (e.g., 1.3 for high-speed railways and 1.1 for ordinary railways); while the protection design period T x The lifespan is set based on the durability of the sand-control materials and the expected lifespan of the project. For example, the lifespan for reeds and geotextiles is 5 to 8 years, while that for steel structures or concrete components can reach 15 years. This step ensures that each protective structure has a long-term, stable, and reliable performance basis for subsequent calculations.
[0037] In obtaining the safety factor K i and design cycle T x Then, combined with the designed sediment transport volume Q s Load matching analysis was performed on various types of protection units. Specifically, Q... s ×K i ×T x The target value for the overall sand-fixing capacity is allocated to different sand-fixing fences (such as tall vertical sand barriers) and sand-fixing grids (such as grass grids and reed grids). The sand-fixing capacity of the fence is determined by its ultimate sand-fixing capacity per unit length p, the number of rows, and the spacing. The sand-fixing capacity of the grid is determined by its sand-fixing capacity per unit area q and the area to which it is laid. This calculation process can be performed using formulas (such as Q). zmax +Q gmax ≥Q s This ensures that the overall protection system has the capacity to cover the entire amount of sand transport within the expected lifespan, thereby achieving a quantitative and precise layout for wind and sand control.
[0038] In one embodiment, the step of calculating the sand-blocking capacity of each fence and the sand-fixing capacity of each grid, based on the design sand transport capacity as a constraint, the protection safety factor, and the protection design period, includes:
[0039] Step 301: Using the designed sand transport volume as a constraint, determine the minimum sand fixation volume along the railway line;
[0040] Step 302: Multiply the designed sand transport volume, the protection safety factor, and the protection design cycle to obtain the railway cycle sand transport volume;
[0041] In step 303, according to the minimum sand-fixing capacity greater than the railway periodic sand-transporting capacity, wind tunnel simulation is performed along the railway to obtain the sand-blocking capacity of each fence and the sand-fixing capacity of each square.
[0042] Specifically, in setting the protection system, a most basic goal needs to be first determined, that is, in the entire protection system, at least sufficient sand-fixing capacity needs to be provided to cope with the accumulation of the annual design sand-transporting capacity. Therefore, the "design sand-transporting capacity Q s " needs to be taken as a constraint basis, and the overall capacity of the fence sand-blocking and the square sand-fixing is combined to set a minimum sand-fixing capacity Q min . The minimum value is usually set as the necessary sand-fixing capacity for the railway subgrade to remain stable under extreme working conditions, so as to ensure that the wind sand cannot penetrate the square system or accumulate to affect the safety of railway operation.
[0043] In order to ensure the effectiveness of the protection system during the entire design period, the annual design sand-transporting capacity Q s needs to be combined with the safety factor K i and the design period T x to calculate the total sand-transporting capacity Q stotal that needs to be resisted by the railway line during the entire service period, that is: Q stotal = Q s × K i × T x , wherein Q s is the annual average sand-transporting capacity, K i is the redundant safety factor set according to the line grade and the wind sand intensity, and T x is the service life of the protection system (usually 5-15 years). This total sand-transporting capacity will be taken as a basic value for evaluating the sand-blocking fence and sand-fixing square arrangement capacity, so as to ensure that the scheme has sufficient redundancy within the design period.
[0044] If the preliminary estimated minimum sand-fixing capacity Q min ≥ Q stotal (railway periodic sand-transporting capacity), then the next stage is entered, that is, the performance parameters of each protection structure are verified and refined through wind tunnel simulation or numerical simulation. The wind tunnel simulation combines the actual sand barrier material, arrangement height, spacing, wind speed and wind direction conditions to measure the sand-blocking capacity p of each fence per unit length and the sand-fixing capacity q of each square per unit area. These measured or simulated data are used to determine the arrangement rows, spacing and coverage area of different types of sand barriers, and finally the arrangement strategy meeting the total sand-blocking and sand-fixing requirement of the design period is back calculated to realize the closed-loop calculation from the total sand-transporting capacity to the structure configuration.
[0045] In one embodiment, the safety blocking analysis is performed on the railway line according to the sand-blocking capacity of each fence and the sand-fixing capacity of each square to determine the fence parameters corresponding to each sand-blocking fence and the square parameters corresponding to each sand-fixing square.
[0046] Step 401, according to the amount of sand blocking of each fence and the amount of sand fixation of each square, analyzing the protection demand of the railway line to obtain wind-sand protection matrix information;
[0047] Step 402, according to the wind-sand protection matrix information, calculating the fence parameters corresponding to each sand-blocking fence and the square parameters corresponding to each sand-fixing square.
[0048] Specifically, after the unit blocking and fixing capabilities of various sand-blocking fences and sand-fixing squares are determined, the wind-sand intensity, sand transport distribution, and terrain changes along the entire railway line need to be comprehensively analyzed to construct a protection demand model. Specifically, the railway line should be segmented, and the required protection capability should be matched according to the sand transport intensity and wind-sand flow state of each segment to form wind-sand protection matrix information. This matrix comprehensively reflects the required sand blocking amount and sand fixation amount distribution of each segment and maps it with the performance data of various types of sand barriers to provide a basis for subsequent structure parameter configuration. This step is a transitional link from "theoretical capability" to "field matching", ensuring that the scheme has engineering pertinence and regional adaptability.
[0049] According to the protection capability required by each segment in the protection matrix and combining the unit performance parameters of the sand barriers, the structure parameter configuration of each type of protection unit is calculated. For sand-blocking fences, their height, row number, spacing, material type, and layout position need to be determined; for sand-fixing squares, their edge length, protruding height, layout density, and coverage width need to be determined. For example, in a segment with high sand transport amount, 2-3 rows of high vertical sand barriers and dense grass square layout may be required; while in a segment with weak sand source or low wind speed, the layout density can be correspondingly reduced. This step ensures that the total blocking and fixing sand capacity of the protection system in the design period ≥ the total demand, forming a scientific, economic, and effective individualized protection parameter system.
[0050] In one embodiment, the calculation of the fence parameters corresponding to each sand-blocking fence and the square parameters corresponding to each sand-fixing square according to the wind-sand protection matrix information includes:
[0051] Step 501, determining the sand-blocking fence square information and the sand-fixing square information according to the wind-sand protection matrix information;
[0052] Step 502, calculating the fence parameters corresponding to each sand-blocking fence according to the sand-blocking fence square information, and calculating the square parameters corresponding to each sand-fixing square according to the sand-fixing square information.
[0053] Specifically, after the wind-sand protection matrix is established, the matrix information needs to be further refined into executable engineering layout units, that is, the protection requirements of each section of railway are converted into sand barrier square information and sand fixation square information. The so-called "square information" refers to the layout unit of sand barrier arranged in a row-column manner in two-dimensional space, which clearly defines the number of layout layers (such as the number of rows) in the depth direction, the lateral layout spacing, the layout range length, etc. Through spatial discretization processing, each barrier or square layout unit will correspond to a specific section and the required wind-sand interception intensity, thereby forming a layout deployment diagram, laying a foundation for subsequent parameter calculation.
[0054] After obtaining the distribution information of each square unit, the engineering parameters of each type of protection measure can be further calculated based on the sand barrier performance data and the protection target. For sand barrier, the specific height (h), number of rows (n), spacing (l), wind permeability, material category and service life, etc. These parameters match the actual unit sand blocking amount (p); for sand fixation square, according to its layout area and unit sand accumulation capacity (q), the edge length size (such as 1 × 1 m), grass head protruding height (generally 10-30 cm), laying number of layers, effective coverage area and maintenance period, etc. Indexes are determined. Finally, each parameter will be reflected in the engineering design drawing and layout scheme, forming a set of fine sand prevention layout system with reasonable structure and responding to wind-sand grade changes.
[0055] In one embodiment, the calculating, according to the sand barrier square information, the barrier parameters corresponding to each of the sand barrier; and calculating, according to the sand fixation square square information, the square parameters corresponding to each of the sand fixation square, comprises:
[0056] Step 601, calculating the barrier height corresponding to each of the sand barrier according to the sand barrier square information;
[0057] Step 602, calculating the barrier layout information corresponding to the sand barrier square information according to each of the barrier height;
[0058] Step 603, determining each of the barrier parameters according to the barrier layout information and each of the barrier height;
[0059] Step 604, calculating the basic width and sand burying width corresponding to each of the sand fixation square according to the sand fixation square square information;
[0060] Step 605, calculating the square parameters corresponding to each of the sand fixation square according to the basic width and sand burying width corresponding to each of the sand fixation square.
[0061] Specifically, according to the sand transport intensity of each section in the wind-sand protection matrix and the set design period, combined with the service life and sand trapping capacity of the sand barrier, the minimum height (h) of each sand blocking fence should have is calculated by formula to ensure that the corresponding volume of wind sand can be intercepted within the design period. The height is related to the annual sand transport volume (Q s ), service life (T), and unit sand blocking capacity (p). Generally, according to the formula: h = (Q s × T) / (p × l), where l is the sand barrier spacing, and p is the unit length sand blocking capacity. The result is the lower limit of the height of the fence required at each layout location.
[0062] After determining the height required for each fence, combined with the wind speed reduction requirement and terrain conditions, a reasonable fence layout scheme is designed, including: the number of rows of fence layout, the spacing between each row (usually 10-20 times the height of the fence), the sequence of longitudinal arrangement, and the relative position to the railway center line. In high wind areas or multi-directional wind areas, a two-way staggered layout can be used, while in low wind areas, a single row is dominant. This layout information aims to achieve the best wind speed reduction and sand accumulation shape control effect through optimal layout.
[0063] After obtaining the specific layout logic and height requirements, the complete parameter set of each sand blocking fence can be determined, including: height (h), number of rows (n), spacing (l), wind permeability (generally recommended 30%50%), structure material (such as reed bundle, steel mesh, etc.), expected service life (515 years), and the layout location. These parameters will be used for construction drawing design and material list configuration to ensure that the sand trapping system matches the actual wind sand transport capacity and has long-term stability.
[0064] For sand fixation grids, combined with the wind speed characteristics and wind sand accumulation trend of the area, first calculate the basic width (L1), which is related to the frequency of wind speed (for example: when T ≥ 17 m / s, L1 = 60-60 m). Then calculate the sand burial width (L2) according to the annual sand transport volume and unit area sand accumulation capacity (q), which represents the accumulation width formed by wind sand deposition. The calculation formula is as follows: L2 = (Q s × T) / q.
[0065] Add the basic width (L1) and sand burial width (L2) calculated to determine the total laying width of the sand fixation grid (L = L1 + L2). Then select the appropriate grid side length (such as 1 × 1 m or 1 × 2 m), sand barrier height (10-30 cm), layout density, and arrangement method according to the terrain conditions. Finally, the required grid parameter set for each section is formed, including side length, height, unit area accumulation capacity, material type (such as wheat straw, reed), service life, and maintenance period. These parameters are used to determine the construction details of the sand fixation layer and the ecological restoration strategy.
[0066] In one embodiment, the design sand transport amount corresponding to the wind-sand prone area along the railway line is obtained, comprising:
[0067] Step 701, the wind-sand prone area along the railway line is divided into zones to obtain a desert edge area and / or a gobi wind-sand flow area;
[0068] Step 702, the sand transport rate corresponding to the desert edge area and / or the sand transport rate corresponding to the gobi wind-sand flow area is calculated respectively;
[0069] Step 703, the sand transport rate corresponding to the desert edge area and / or the sand transport rate corresponding to the gobi wind-sand flow area is time-integrated respectively to obtain the design sand transport amount.
[0070] Specifically, before carrying out the wind-sand prevention and control design, the wind-sand prone area along the railway line needs to be first divided into zones, and the area is divided into a desert edge area and a gobi wind-sand flow area according to the landform type, the underlying surface characteristics and the wind-sand activity intensity. The desert edge area usually has abundant sand sources, small particle size and frequent wind-sand activities; while the gobi wind-sand flow area has sparse sand sources, the underlying surface is mainly gravel and coarse sand, and the wind-sand movement is mainly low-layer airflow near the ground. The zoning result of this step determines the difference of the subsequent sand transport rate calculation formula and the differentiated setting of the protection strategy, and is the basis for carrying out scientific protection design.
[0071] According to the characteristics of different areas, the sand transport rate is calculated by using the adaptive sand transport rate calculation formula:
[0072] For the desert edge area, the function relationship between the particle size adjustment coefficient ξ and the 10-minute average wind speed V of 10 meters is usually used for calculation, and the formula is as follows: q = ξ × f(V), wherein ξ is related to the median particle size of sand. For the gobi wind-sand flow area, since the threshold wind speed (V t ) is usually high, the empirical model based on the wind speed and the particle size distribution is used to calculate the sand transport rate, which reflects the transport capacity under the critical wind speed. The calculation of these sand transport rates is in units of sand transport mass per unit time and per unit width (t / m·h), which represents the sand transport intensity of a certain section under certain meteorological conditions.
[0073] After obtaining the sand transport rate of each area under different wind speed levels, time integration is needed in combination with historical wind speed data, that is, the sand transport rate under each level of wind speed is multiplied by the cumulative number of hours in a year, and the direction is weighted to obtain the annual design sand transport amount Q s (unit: t / m·year) of the area. The calculation formula is: Q s =∑(q i ×ΔT i ). Wherein q i is the sand transport rate corresponding to the i-th level of wind speed, and ΔT iThe annual cumulative hours of the wind speed are accumulated. If there is an angle a between the wind direction and the railway direction, the angle correction must be performed to ensure that the sand transport reflects the actual influence in the cross-section direction. The final Q s is the key input parameter for the design of the protection of the region.
[0074] In an embodiment, the design sand transport is obtained by time integration of the sand transport rate corresponding to the desert edge region and / or the sand transport rate corresponding to the gobi wind-sand flow region, respectively, including:
[0075] Step 801, time integration of the sand transport rate corresponding to the desert edge region and / or the sand transport rate corresponding to the gobi wind-sand flow region, respectively, to obtain the desert region sand transport and / or the gobi region sand transport;
[0076] Step 802, wind direction correction of the desert region sand transport and / or the gobi region sand transport, respectively, to obtain the corrected desert sand transport and the gobi corrected sand transport;
[0077] Step 803, obtaining the design sand transport according to the corrected desert sand transport and / or the gobi corrected sand transport.
[0078] Specifically, after obtaining the sand transport rate (unit: t / m·h) of the desert edge region and / or the gobi wind-sand flow region, the local annual wind speed statistical data should be combined for time integration according to the wind speed grade. The specific method is: multiplying the sand transport rate under each wind speed grade by the annual cumulative hours of the grade, and adding up to obtain the annual desert region sand transport Q s沙漠 and / or the annual gobi region sand transport Q s戈壁 . The formula is expressed as: Q s _region = ∑(qi × ΔTi), which reflects the annual average wind-sand transport intensity of different regions under natural meteorological conditions and is the basis for calculating the protection load.
[0079] Since the wind-sand transport may have an angle a with the railway direction, the wind direction correction must be performed. The correction is performed by projecting the sand transport to the railway cross-section direction to adjust the sand transport intensity actually affecting the railway. The commonly used correction formula is: Q' = Q × sin(a), wherein Q is the original sand transport, a is the angle between the wind direction and the railway direction, and Q' is the corrected sand transport. By correcting the desert region and / or the gobi region respectively, the corrected desert sand transport Q' 沙漠 and / or the corrected gobi sand transport Q' 戈壁 are obtained, which represent the actual annual sand transport load in the cross-section direction along the railway after considering the regional differences and the wind direction influence, and provide a scientific basis for the subsequent parameter configuration and layout scale of the wind-sand protection system.
[0080] A specific flow chart of a wind-sand prevention engineering protective belt parameter calculation method is shown in Figure 1 The field investigation is carried out in the wind-sand prone area along the railway, the historical meteorological data along the railway are collected, and the sand transport capacity of the desert area along the railway is determined systematically according to the sand flow field monitoring data of the current year, the sand accumulation instrument, the unmanned aerial vehicle laser scanning technology and the like, and the sand transport capacity in the transverse direction of the railway subgrade is calculated:
[0081] The sand transport rate of the desert edge area
[0082] q = ξ × 3.2 × 10 -4 × (V-5.5) 3 (1-1)
[0083] In the formula, q is the sand transport rate (t / [m﹒h]); ξ is the coefficient related to the sand source particle size; when the particle size medium value is <0.1 mm, ξ is 1.25; when the particle size medium value is 0.1-0.2 mm, ξ is 1.20-1.10; and when the particle size medium value is >0.2 mm, ξ is 1.05; and V is the 10-minute average wind speed at 10 m high (m / s).
[0084] The sand transport rate of the gobi sand flow area
[0085] When the sand source is not very rich, the particle size distribution of the sand is as follows: >0.25 mm accounts for 3.4%, 0.25-0.10 mm accounts for 80.7%, and <0.10 mm accounts for 15.9%; and the underlying surface is coarse sand and gravel. The sand transport rate is calculated by the following formula:
[0086] q = 2.69 × 10 -4 × (V-V t ) 3 (1-2)
[0087] In the formula, V t is the threshold wind speed (generally V t =5 m / s);
[0088] The sand transport capacity of the desert area
[0089] The sand amount passing through a certain place per unit width in a certain period of time is generally calculated annually:
[0090]
[0091] In the formula, Q 年 is the annual sand transport capacity (t / m); q i is the sand transport rate (t / [m﹒h]) of a certain wind speed; ΔT i is the cumulative hours of the occurrence of the certain wind speed; and the wind speed of different directions is classified, such as 6 m / s (including 5.5-<6.5 m / s) and 7 m / s.
[0092] The total sand transport volume is calculated according to the left and right sides of the railway sand prevention engineering. If there is no sand source on one side, the sand transport volume on that side can not be calculated. When the wind direction is at an angle of a with the railway sand prevention engineering, the sand transport volume should be corrected according to the following formula:
[0093]
[0094] Due to the many factors affecting the sand transport volume, it is difficult to express it with a mathematical formula. Therefore, it is appropriate to investigate the sand accumulation situation of existing buildings or terrain changes in the local area. If the difference is large, the sand transport volume can be appropriately corrected to serve as a design index.
[0095] Considering different terrains, wind conditions and wind-sand hazard characteristics, especially in combination with different types of desert areas, wind-sand flow areas and the degree of harm to railway engineering, reasonable allocation of mechanical, biological and chemical measures is made to build a stable and effective protection system. The general sand desert area is designed with a combination of sand blocking and sand fixation, and the wind-sand flow area is designed with a dominant sand blocking measure.
[0096] According to the characteristics of the line area, the degree of wind-sand hazard, combined with the service period of the sand prevention system, the railway grade and other factors, a certain safety factor K i is given to adapt to different environments and engineering needs. According to the type of the protection system, the service life of the sand barrier material, the expected value, etc., the design period T x is determined; K i is the railway grade coefficient, which is 1.1 for general passenger trains and 1.3 for passenger dedicated lines, T x is the service life of the sand barrier or the design period, and the service life of reed and geotextile material is 5-8 years, and the service life of steel structure and concrete material is 15 years.
[0097] According to the characteristics of sand transport volume and wind-sand flow, the sand blocking effect and sand blocking volume of each sand blocking fence and sand fixation reed grid are scientifically calculated to ensure that the sand blocking and fixation volume is not less than the cross-section sand transport volume.
[0098]
[0099] In the formula, Q s is the annual sand transport volume, Q zmax is the sand blocking volume of the i-th high-standing sand blocking fence, Q g max is the sand accumulation volume of the low-standing grid (grass grid or reed grid) sand fixation belt.
[0100] According to the maximum unit capacity sand blocking volume p and sand fixation volume q of the selected high-standing sand blocking fence, medium-standing grid sand barrier and low-standing grid (grass grid or reed grid), the maximum sand blocking volume Q zmax and sand fixation volume Q g max. p is the limit of sand resistance of high vertical sand resistance barrier per unit length, which is related to the wind permeability and height of sand resistance barrier. Generally, one row is set, and when the sediment discharge is large, two or three rows are set, and is usually set at the outer edge of the defense zone. It is obtained by means of field actual measurement, numerical simulation or laser scanning. q is the limit of sand accumulation per unit area of low vertical square (grass square or reed square) sand barrier. According to the actual engineering measurement results, the sediment discharge of 1x1m x 0.1m low vertical square is q = 0.074m 3 / m 2 ; the sediment discharge of 1x2m x 0.1m low vertical square is q = 0.070m 3 / m 2 , and the width of the sand prevention system established by simulation calculation is shown in Figure 2 .
[0101] Height and width of sand resistance barrier
[0102] The height h of high vertical sand resistance barrier can be calculated according to formula 1-9:
[0103]
[0104] In the formula, Q E is the annual sediment discharge (m 3 / (m·year) ) ; T is the service life of the sand barrier, which is determined according to the material properties and the defense period.
[0105] For example,
[0106] If a certain material may be damaged after 5 years, it is calculated for 5 years.
[0107] After the height of the sand barrier is obtained, the number of rows can be obtained by dividing the height by the height of the material exposed to the ground. The distance between rows should be as far as possible to play the role of reducing the wind speed of the sand resistance barrier to make its sand accumulation reach the maximum value, which is generally 10-20h. Under the condition of strong wind, the height can be appropriately reduced (not less than 1.2m finally), and the number of sand resistance barrier setting channels can be appropriately increased, and the recommended number of channels is 2-3.
[0108] Width of low vertical square (grass square or reed square) sand barrier
[0109] According to the optimal correlation analysis formula between the exposed height of grass square or reed square and the square side length, the width and height of the sand fixation reed square are calculated. Field actual experience shows that when the reed square sand barrier grass head exposed height is between 10-30cm, the grass square side length is set to 100cm, and the sand fixation effect is the best.
[0110] The sand accumulation in the strip sand barrier is high on both sides and low in the middle, and the sand accumulation in the grid sand barrier is low in the middle and high on all sides, and the profile of the sand accumulation is concave. According to the observation, the relationship between the distance L between the sand barriers and the maximum depth h of the concave surface is L / h=10-15, and the ratio increases gradually, and the sand barriers can be crossed by the sand flow. If the sand barrier is 10 cm high and the distance between the sand barriers is 1.0-1.5 m, the size of the grass square commonly used for railway sand prevention is generally 1×1 m, and the sand prevention effect is good, which is consistent with the sand accumulation form.
[0111] Laying width: if only local floating sand is fixed, the laying width is determined according to the floating sand range; if sand fixation and sand prevention are both needed, the laying width is related to the sand source and the wind conditions, and in the absence of other sand prevention measures, the laying width can be calculated according to the following formula:
[0112] L=L1+L2 (1-7)
[0113] In the formula, L1 is the basic width. The cumulative hours T of wind speed ≥17 m / s in a year, when T≤5, L1=30-60 m; when T>5, L1=60-100 m; L2 is the sand burial width (m), which can be calculated according to the following formula:
[0114]
[0115] In the formula, Q E is the sand transport rate (m 3 / year); q is the limit sand accumulation per unit area in the sand barrier, 1×1 m, sand barrier height 10 cm, q=0.074 m 3 / m 2 ; 1×2 m, sand barrier height 10 cm, q=0.070 m 3 / m 2 ; T is the service life, which is related to the sand barrier material. The service life of the wheat straw sand barrier is 3 years, the service life of the reed grid sand barrier is 5 years, the service life of the earth ridge sand barrier and the asphalt felt sand barrier is 5-6 years, the service life of the salt soil block sand barrier is 8-10 years, and the service life of the geotextile sand barrier is 15 years.
[0116] According to a wind-sand prevention engineering protection belt width and mode design calculation method, the total width D 总 of the wind-sand protection system is established, and the final sand prevention system total width is formed. The wind-sand protection system from the outside to the railway embankment slope foot (trench top) is: protection belt, sand prevention belt, transition belt, sand fixation belt, isolation belt.
[0117] D 总 =L 保护带 +L 阻沙带 +L 过渡带 +L 固沙带 +L 隔离带 (1-9) In the formula, D总 L is the total width of the protection system 保护带 L is the width of the protective belt outside the protection system, generally 0-10 m 阻沙带 L is the width of the sand-blocking belt composed of high vertical sand barriers, the spacing between single sand barriers is generally 10-20 times the height of the sand barrier 过渡带 L is the width of the transition zone between different functional measures in the sand protection system 固 L is the width of the sand belt, which is a low vertical square (grass square or reed square) sand-fixing belt, and L is the width of the isolation belt between the sand protection system and the slope foot or the top of the trench, which is generally not less than 20 m.
[0118] D 总 = L 保护带 + Q zmax · Tl / p + L 过渡带 + Q gmax · T / q + L 隔离带 (1-10)
[0119] Generally, the width of the low vertical square (grass square or reed square) can be determined first according to the type of the underlying surface in the wind-sand area, and then the number of high vertical sand barriers can be calculated; according to the total amount of sand blocking and sand fixing being not less than the designed sand transport capacity of the section, the above formula can be optimized as follows:
[0120] D 总 = L 保护带 + (Q s · K i - Q gmax )· T· l / p + L 过渡带 + Q gmax · T / q + L 隔离带 (1-11)
[0121] In the formula, p is the unit length limit sand blocking capacity of high vertical sand barrier, which is related to the porosity and height of the sand barrier, generally set to 1 row, when the sand transport capacity is large, set to 2 rows or 3 rows, usually set at the outer edge of the protection belt, and l is the spacing between sand barriers, which is generally 10-20 times the height of the sand barrier. The sand protection efficiency is related to the porosity of the sand barrier and the wind speed as shown in Figure 3 , and the sand protection efficiency is related to the height of the sand barrier and the wind speed as shown in Figure 4 .
[0122] In the implementation process, first, a detailed wind-sand environment investigation of the target area is needed. The investigation contents include: historical meteorological data (especially wind speed and direction data), distribution of sand sources on the ground, intensity of wind-sand activity, characteristics of wind erosion landforms, and surrounding infrastructure layout, etc. Meteorological station data, unmanned aerial vehicle remote sensing, laser radar scanning, sand accumulation instrument measurement, and other means can be used, combined with on-site visits and topographic interpretation, to systematically master the scale, direction and law of wind-sand transport.
[0123] After obtaining enough basic data, the protection belt structure design stage is entered. The protection belt is divided into five functional areas from outside to inside, namely, the protection belt, the sand blocking belt, the transition belt, the sand fixing belt and the isolation belt, each of which has clear functional division and structure requirements. The overall layout idea is: the peripheral protection and sand blocking function belt is set to weaken the strength of the incoming flow of sand; the middle part is set as a transition zone to buffer air flow disturbance; the inner side is set as a sand fixing belt and an isolation belt to stabilize the surface sand source and ensure the safety of the line.
[0124] The protection belt is usually located at the outermost edge of the protection belt, and its main function is to buffer long-distance sand transport and weaken the direct impact of large-scale wind flow on the protection system. Natural vegetation, low sand barriers or natural formation of high difference terrain are often used; if conditions permit, wind-resistant plants or simple wind barriers can also be planted to enhance the buffering effect, and the width is generally set to 0-10 meters.
[0125] The sand blocking belt is the core component of the entire protection system. Its main function is to block most of the sand flow and provide favorable conditions for subsequent sand fixation. The sand blocking belt is usually composed of 1 to 3 rows of high vertical sand barriers, and the materials can be selected from reed bundles, straw bundles, steel mesh or environmentally friendly composite materials. The height, spacing and number of rows of sand barriers are determined comprehensively according to wind sand intensity, spatial layout and service life. When setting, the maximum reduction of wind speed, the guidance of air flow uplift and the interception of incoming sand are given priority to; in areas with frequent strong winds or where multiple winds intersect, it is recommended to use two-way layout to improve the sand blocking capacity.
[0126] The transition belt is set between the sand blocking belt and the sand fixing belt, and its main purpose is to alleviate the sudden change of wind flow velocity gradient between the front and rear areas, and avoid the emergence of local sand accumulation or new sand sources due to flow field disorder. Natural vegetation or low vertical sand barriers with high wind permeability can be appropriately retained in the transition belt to slow down the air flow from fast to stable transition and reduce surface disturbance. The width of this area can be flexibly adjusted according to the difference between the front and rear areas, generally 1-2 meters.
[0127] The sand fixing belt is the core area of long-term ecological restoration, and low vertical square sand barriers such as grass squares or reed squares are set to fix the surface loose sand particles, promote soil structure stability and promote natural restoration of vegetation. The layout of the sand fixing belt should consider factors such as surface vegetation coverage, soil water retention capacity and terrain slope, and the size of the square can be selected as 1x1 meter, 1x2 meter or larger, and the layout density should gradually decrease with the gradient of surface sand movement intensity. In practice, the square can significantly inhibit surface sanding within one year after being set, and stable shrub vegetation communities can be restored within two to three years, forming a durable ecological barrier.
[0128] The mode design calculation method provided in the implementation process emphasizes the allocation of sand blocking and sand fixing task quantities to each functional area based on the measured total annual sediment discharge, thereby inversely deducing the required number of sand barriers and the area of the grid. At the same time, a safety factor adjustment mechanism is set for different regions, construction conditions, sand source types, and line grades. For example, the design safety factor for high-speed railway areas is 1.3, for general railways is 1.1, and for ordinary highways can be set to 1.0, thereby ensuring the applicability and stability of the design scheme.
[0129] Specific implementations have been successfully applied in typical desert railway sections such as the Hezuo-Ruoji railway and the Gangu railway. Taking the Hezuo-Ruoji railway as an example, the seven-zone integrated sand prevention system constructed using this method has clear layout and reasonable arrangement in construction. The width structure of the protection zone narrows gradually from the outside to the inside, the wind-sand interception efficiency is significantly improved, and the line operation safety is significantly enhanced. Observations after the implementation of the project show that the thickness of accumulated sand on the line has decreased by about 60%, the frequency of manual sand cleaning has decreased by about 50%, the recovery rate of ecological vegetation along the line has significantly increased, and a complete protection closed loop from "interception-stabilization-recovery" has been formed.
[0130] In one embodiment, a computer device is also provided, including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps in the above method embodiments.
[0131] In one embodiment, a computer readable storage medium is provided, storing a computer program, which is executed by a processor to implement the steps in the above method embodiments.
[0132] In one embodiment, a computer program product or computer program is provided, which includes computer instructions stored in a computer readable storage medium. The processor of the computer device reads the computer instructions from the computer readable storage medium, and the processor executes the computer instructions to make the computer device execute the steps in the above method embodiments.
[0133] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or authorized by all parties, and the collection, use, and processing of related data need to comply with relevant regulations.
[0134] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer readable storage medium, and when the computer program is executed, the processes of the above-mentioned embodiments of the methods can be included. Any reference to memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (Read-Only Memory, ROM), magnetic tape, floppy disk, flash memory, optical storage, high-density embedded non-volatile memory, resistive memory (ReRAM), magnetoresistive random access memory (Magnetoresistive Random Access Memory, MRAM), ferroelectric memory (Ferroelectric Random Access Memory, FRAM), phase change memory (Phase Change Memory, PCM), graphene memory, etc. Volatile memory can include random access memory (Random Access Memory, RAM) or external cache memory, etc. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (Static Random Access Memory, SRAM) or dynamic random access memory (Dynamic Random Access Memory, DRAM), etc. The database involved in the embodiments provided in the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a block chain, etc., without being limited thereto. The processor involved in the embodiments provided in the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., without being limited thereto.
[0135] Any combination of the technical features of the above embodiments can be made. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combination of the technical features does not exist contradictory, it should be considered as the scope of the present application.
[0136] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent of the present application. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of protection of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.
Claims
1. A method for calculating the parameters of a wind-sand control engineering protective belt, characterized in that, The method includes: Obtain information on sand control strategies and designed sand transport volumes for wind-blown sand-prone areas along the railway line; Based on the information on the sand-blocking and sand-fixing strategy and the designed sand transport volume, a wind and sand spatiotemporal analysis was performed on each sand-blocking fence and each sand-fixing grid in the wind-prone area to obtain the sand-blocking volume of each fence and the sand-fixing volume of each grid. Based on the sand-blocking capacity of each fence and the sand-fixing capacity of each grid, a safety blocking analysis is conducted along the railway line to determine the fence parameters corresponding to each sand-blocking fence and the grid parameters corresponding to each sand-fixing grid. Based on the fence parameters and the grid parameters, the parameters of the wind and sand control protection zone along the railway line are determined.
2. The method of claim 1, wherein, Based on the sand-blocking strategy information and the designed sand transport volume, a wind and sand spatiotemporal analysis is performed on each sand-blocking fence and each sand-fixing grid in the wind-prone area to obtain the sand-blocking capacity of each fence and the sand-fixing capacity of each grid, including: Based on the aforementioned solidification prevention and control strategy information, the corresponding protection safety factor and protection design cycle along the railway line are determined; Using the designed sand transport volume as a constraint, and based on the protection safety factor and the protection design period, the sand blocking capacity of each fence and the sand fixing capacity of each grid are calculated.
3. The method of claim 2, wherein, The calculation of the sand-blocking capacity of each fence and the sand-fixing capacity of each grid, based on the design sand transport capacity as a constraint, the protection safety factor, and the protection design period, includes: Using the designed sediment transport capacity as a constraint, determine the minimum amount of sediment fixation along the railway line; Multiply the designed sand transport volume, the protection safety factor, and the protection design period to obtain the railway periodic sand transport volume; Based on the fact that the minimum sand fixation amount is greater than the periodic sand transport amount of the railway, wind tunnel simulation is performed along the railway line to obtain the sand blocking amount of each fence and the sand fixation amount of each grid.
4. The method of claim 1, wherein, The process involves conducting a safety barrier analysis along the railway line based on the sand-blocking capacity of each fence and the sand-fixing capacity of each grid, determining the fence parameters corresponding to each sand-blocking fence and the grid parameters corresponding to each sand-fixing grid, including: Based on the sand-blocking capacity of each fence and the sand-fixing capacity of each grid, the protection needs of the railway line are analyzed to obtain wind and sand protection matrix information. Based on the wind and sand protection matrix information, calculate the fence parameters corresponding to each sand-blocking fence and the grid parameters corresponding to each sand-fixing grid.
5. The method of claim 4, wherein, The step of calculating the fence parameters corresponding to each sand-blocking fence and the grid parameters corresponding to each sand-fixing grid based on the wind and sand protection matrix information includes: Based on the wind and sand protection matrix information, determine the sand-blocking fence array information and the sand-fixing grid array information; Based on the sand-blocking fence array information, calculate the fence parameters corresponding to each sand-blocking fence; and based on the sand-fixing grid array information, calculate the grid parameters corresponding to each sand-fixing grid.
6. The method of claim 5, wherein, The step of calculating the fence parameters corresponding to each sand-blocking fence based on the sand-blocking fence array information; and calculating the grid parameters corresponding to each sand-fixing grid based on the sand-fixing grid array information, includes: Based on the sand-blocking fence array information, calculate the fence height corresponding to each of the sand-blocking fences; According to each of the fence height, the sand barrier fence array information corresponding to the fence layout information is calculated; According to the fence layout information and each of the fence height, each of the fence parameters is determined; According to the sand fixation square array information, the corresponding basic width and sand burial width corresponding to each of the sand fixation squares are calculated; According to the corresponding basic width and sand burial width corresponding to each of the sand fixation squares, the square parameters corresponding to each of the sand fixation squares are calculated.
7. The method of claim 1, wherein, The design sand transport amount corresponding to the wind-sand prone area along the railway line is obtained, including: The wind-sand prone area along the railway line is divided into a desert edge area and / or a gobi wind-sand flow area; The sand transport rate corresponding to the desert edge area and / or the sand transport rate corresponding to the gobi wind-sand flow area is calculated respectively; The sand transport rate corresponding to the desert edge area and / or the sand transport rate corresponding to the gobi wind-sand flow area is time-integrated respectively to obtain the design sand transport amount.
8. The method of claim 7, wherein, The sand transport rate corresponding to the desert edge area and / or the sand transport rate corresponding to the gobi wind-sand flow area is time-integrated respectively to obtain the design sand transport amount, including: The sand transport rate corresponding to the desert edge area and / or the sand transport rate corresponding to the gobi wind-sand flow area is time-integrated respectively to obtain a desert area sand transport amount and / or a gobi area sand transport amount; The desert area sand transport amount and / or the gobi area sand transport amount is wind direction corrected respectively to obtain a corrected desert sand transport amount and a gobi corrected sand transport amount; The design sand transport amount is obtained according to the corrected desert sand transport amount and / or the gobi corrected sand transport amount.
9. A wind-sand control engineering protective belt parameter calculation device, characterized in that, The device includes: A wind-sand parameter acquisition module for acquiring the sand prevention and control strategy information and the design sand transport amount corresponding to the wind-sand prone area along the railway line; A sand prevention parameter calculation module for performing wind-sand space-time analysis on each sand barrier and each sand fixation square of the wind-sand prone area according to the sand prevention and control strategy information and the design sand transport amount to obtain each barrier sand prevention amount and each square sand fixation amount; A device parameter calculation module for performing safety blocking analysis on the railway line according to each of the barrier sand prevention amount and each of the square sand fixation amount to determine the fence parameters corresponding to each sand barrier and the square parameters corresponding to each sand fixation square; A guard belt parameter calculation module for determining the wind-sand prevention engineering guard belt parameters of the railway line according to each of the fence parameters and each of the square parameters. 10.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-9. The processor executes the computer program to realize the steps of the method in any one of claims 1 to 8.