Modeling method of two-dimensional ballast particle discrete element model and two-dimensional sleeper-track bed-subgrade discrete element model containing sand
By using a two-dimensional discrete element model of ballast particles and the particle coordinate accumulation method, the contradiction between model accuracy and cost after sand particles intrude into the ballast bed was resolved. This enabled the rapid filling of sand particles in the ballast bed and the simulation of particle contact state, thereby improving the simulation accuracy and efficiency of the model.
Patent Information
- Application Number
- CN202311605835.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-28
- Publication Date
- 2026-08-25
- Estimated Expiration
- 2043-11-28
AI Technical Summary
Existing technologies suffer from high computational costs, difficulty in balancing model accuracy, and difficulty in visually displaying the contact state between ballast particles and sand particles when simulating the impact of sand particles on the mechanical properties of the ballast bed. Two-dimensional ballast particle modeling has limitations in simulating particle breakage and wear.
A two-dimensional discrete element model of ballast particles was adopted. By extracting the outer contour of the ballast particles, determining the inner contour and filling the inscribed disk, a periodic boundary was established. Combined with particle coordinate accumulation and contact cycle monitoring method to fill sand particles, a two-dimensional discrete element model of sand-containing sleeper-ballast bed-matrix was constructed.
It achieves a balance between model accuracy and computational cost, and can quickly build track bed models with different dirt rates to simulate particle wear and breakage, and intuitively display the particle contact state.
Smart Images
Figure CN117592345B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a modeling method for a two-dimensional discrete element model of ballast particles and a two-dimensional discrete element model of sand-containing sleeper-ballast bed-matrix, belonging to the field of railway particle flow numerical simulation technology. Background Technology
[0002] During the service of desert railways, due to the gaps between ballast particles in the ballasted track bed, sand particles continuously infiltrate and settle under the coupled effects of wind force and train load. This sand intrusion alters the contact state between the ballast particles, reducing the track bed's stiffness, drainage performance, and shear resistance, significantly impacting its service performance and lifespan, and threatening safe train operation. Therefore, studying the impact of sand intrusion on the mechanical properties of the track bed is of great significance. Current indoor model tests and finite element track bed models have significant limitations.
[0003] When analyzing the micromechanical properties and macroscopic energy changes of ballast tracks, the computational cost of three-dimensional discrete element ballast models, which contain hundreds of millions of particles, is prohibitively high. This makes it difficult to quickly construct ballast track models with varying levels of contamination, and traversing loops during model analysis is challenging. More importantly, it is difficult to visually represent the direct contact between ballast particles and sand particles. Furthermore, current two-dimensional ballast particle modeling primarily uses combinations of disks of similar or varying sizes, making it difficult to balance model accuracy with computational cost, and it also has limitations in simulating ballast particle breakage and wear. Summary of the Invention
[0004] This invention provides a modeling method for a two-dimensional ballast particle discrete element model and a sand-containing two-dimensional sleeper-ballast-matrix discrete element model. On the one hand, it is used to establish a template for the ballast particle discrete element model. On the other hand, it is used to establish an initial discrete element model of a sand-containing two-dimensional sleeper-ballast-matrix with different ballast contamination rates based on the established template for the ballast particle discrete element model.
[0005] The technical solution of this invention is:
[0006] According to a first aspect of the present invention, a modeling method for a two-dimensional discrete element model of ballast particles is provided, comprising: extracting the outer contour of the ballast particles; determining the inner contour of the ballast particles based on the outer contour; filling the inner contour of the ballast particles with the largest inscribed disk until a preset standard is reached; filling the inner contour of the ballast particles with a ring of inscribed disks between the inner contour and the outer contour; exporting the radius and position coordinates of each disk after filling; establishing a periodic boundary, and establishing a discrete element model template for the ballast particles based on the radius and coordinates of each disk.
[0007] The method of determining the inner contour of ballast particles based on the outer contour is as follows: set a scaling factor r, and use a scaling command to shrink the outer contour using the center of the outer contour as the scaling center to obtain the inner contour of the ballast particles.
[0008] According to a second aspect of the present invention, a modeling method for a two-dimensional discrete element model of a sand-containing sleeper-ballast-matrix includes:
[0009] Establish a periodic boundary, arbitrarily set the position coordinates of matrix particles within the periodic boundary, set the radius of matrix particles, and generate a matrix particle model template;
[0010] Establish a sleeper geometry model, obtain the coordinates and radius of the ball element in the sleeper geometry model, and use them to generate a sleeper model template;
[0011] Establish a boundary wall, generate a preset number of matrix particles according to the gradation range based on the matrix particle model template, assign contact parameters, set equilibrium conditions and cycle to equilibrium, delete excess matrix particles according to the required height of the matrix layer, and obtain the matrix layer model.
[0012] Based on the matrix layer model, a preset number of ballast particles are generated on top of it according to the ballast particle discrete element model template as described above, according to the set gradation range. Contact parameters are assigned, equilibrium conditions are set and the process is repeated until equilibrium is reached. Excess ballast particles are deleted according to the required height of the ballast layer to generate the initial model of the track bed.
[0013] In the initial model of the track bed, a geometric model of the sleeper is established at the corresponding position of each sleeper, and the ballast particles inside the sleeper geometric model are deleted. Based on the sleeper model template, the sleeper is generated at the specified position, the equilibrium conditions are set, and a discrete element model of sleeper-track bed-matrix without sand particles is generated.
[0014] Based on the aforementioned discrete element model of sleeper-ballast-matrix without sand particles, sand particles are gradually filled into the gaps between ballast particles using the particle coordinate accumulation method and the contact cycle monitoring deletion method to obtain the first initial discrete element model of sleeper-ballast-matrix containing sand.
[0015] Based on the initial discrete element model of the first sand-laden sleeper-track bed-matrix, excess sand particles were removed by the interval deletion method to construct two-dimensional initial discrete element models of sand-laden sleeper-track bed-matrix with different track bed contamination rates.
[0016] The method of filling sand particles into the voids of ballast particles one by one using the particle coordinate accumulation method and the contact cycle monitoring and deletion method to obtain the initial discrete element model of the first sand-containing sleeper-ballast bed-matrix is as follows: the sand particle radius is set to r, the ballast bed width to X, the height to Y, and the position coordinates of the first sand particle to (x, y) are set to r. i ,y i If the coordinates of the next sand grain generated are (x, y), then the coordinates of the position where the next sand grain is generated are (x, y). i +2r,y iThe model is generated in a loop. After each loop, the horizontal coordinate is accumulated, the vertical coordinate is accumulated, and the horizontal coordinate is accumulated again until the standard width and height of the track bed are reached. After each grain of sand is generated, the loop is executed once. If the sand grain comes into contact with the ballast particles, it is deleted. This is how the initial discrete element model of the first sand-containing sleeper-track bed-matrix is obtained.
[0017] The interval deletion method is as follows: by traversing the sand grain IDs, the sand grains are deleted in intervals by taking the remainder of the sand grain ID. If every other grain is deleted, the sand grains whose IDs have a remainder when divided by 2 are deleted. If every two grains are deleted, the sand grains whose IDs have a remainder when divided by 3 are deleted, and so on.
[0018] The beneficial effects of this invention are: the two-dimensional ballast particle discrete element model provided by this invention solves the contradiction between model accuracy and computational cost, and can better simulate particle wear and breakage; the modeling method of the sand-laden two-dimensional sleeper-ballast-matrix discrete element model for sand intrusion in railway track bed can realize the rapid filling of fine particles in the gaps of track bed ballast, and the model filled by fine particles can quickly establish track beds with other dirt rates. Attached Figure Description
[0019] Figure 1 This is a schematic diagram of the model construction process in the two-dimensional ballast particle discrete element model modeling method provided in this invention;
[0020] Figure 2 The outlines of different types of ballast and schematic diagrams after construction are shown in the two-dimensional ballast particle discrete element modeling method provided in this invention.
[0021] Figure 3 This is a schematic diagram of the track bed boundary wall and matrix layer model in the modeling method of the two-dimensional discrete element model of sand-containing sleeper-track bed-matrix provided in this invention;
[0022] Figure 4 This is a schematic diagram of the initial model of the track bed without sand particles in the modeling method of the two-dimensional discrete element model of sand-containing sleeper-track bed-matrix provided in this invention;
[0023] Figure 5 This is a schematic diagram of sleeper installation in the initial model of the track bed without sand particles in the modeling method of the two-dimensional sleeper-track bed-matrix discrete element model containing sand provided in this invention;
[0024] Figure 6 This is a schematic diagram of a sleeper in the modeling method of the two-dimensional sleeper-track bed-matrix discrete element model containing sand provided in this invention;
[0025] Figure 7 This is a schematic diagram of the sand-free sleeper-track-matrix layer in the modeling method of the two-dimensional discrete element model of sand-containing sleeper-track-matrix provided in this invention.
[0026] Figure 8 Figure 1 is a schematic diagram of the initial discrete element model of the two-dimensional sleeper-ballast-matrix layer containing sand in the modeling method of the two-dimensional sleeper-ballast-matrix layer containing sand provided in this invention; wherein Figure (a) is an overall schematic diagram of the unbalanced sleeper-ballast-matrix layer containing sand after sand filling, Figure (b) is a partial schematic diagram of the unbalanced sleeper-ballast-matrix layer containing sand after sand filling, and Figure (c) is a partial schematic diagram of the sleeper-ballast-matrix layer containing sand after sand filling and balancing.
[0027] Figure 9 This is a flowchart illustrating the modeling methods for the two-dimensional ballast particle discrete element model and the sand-containing two-dimensional sleeper-ballast bed-matrix discrete element model provided in this invention. Detailed Implementation
[0028] The invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of the invention is not limited to the description.
[0029] Example 1: As Figure 1-9 As shown, according to a first aspect of the present invention, a modeling method for a two-dimensional discrete element model of ballast particles is provided, comprising: extracting the outer contour of the ballast particles; determining the inner contour of the ballast particles based on the outer contour; filling the inner contour of the ballast particles with the largest inscribed disk until a preset standard is reached; filling the inner contour of the ballast particles with a ring of inscribed disks between the inner contour and the outer contour; exporting the radius and position coordinates of each disk after filling; establishing a periodic boundary, and establishing a discrete element model template for the ballast particles based on the radius and coordinates of each disk.
[0030] Furthermore, determining the inner contour of ballast particles based on the outer contour specifically involves setting a scaling factor r and using a scaling command to shrink the outer contour using the center of the outer contour as the scaling center, thereby obtaining the inner contour of the ballast particles.
[0031] According to a second aspect of the present invention, a modeling method for a two-dimensional discrete element model of a sand-containing sleeper-ballast-matrix railway includes: establishing a periodic boundary; arbitrarily setting the position coordinates of matrix particles within the periodic boundary; setting the radius of matrix particles; and generating a matrix particle model template; establishing a sleeper geometry model; obtaining the coordinates and radii of ball elements in the sleeper geometry model for generating a sleeper model template; establishing a boundary wall; generating a preset number of matrix particles according to a gradation range based on the matrix particle model template; assigning contact parameters; setting equilibrium conditions and cycling to equilibrium; deleting excess matrix particles according to the required height of the matrix layer; and obtaining a matrix layer model; based on the matrix layer model, generating a preset number of ballast particles on its upper part according to a set gradation range based on the generated ballast particle discrete element model template as described in any one of the above methods; and assigning contact parameters. The process involves setting equilibrium conditions and iterating until equilibrium is reached. Excess ballast particles are removed based on the required height of the ballast layer, generating an initial ballast bed model. A sleeper geometry model is then established at the corresponding position of each sleeper in the initial ballast bed model, and ballast particles inside the sleeper geometry model are removed. Sleepers are generated at designated positions based on the sleeper model template, equilibrium conditions are set, and a sand-free sleeper-ballast-matrix discrete element model is generated. Based on the sand-free sleeper-ballast-matrix discrete element model, sand particles are gradually filled into the gaps between ballast particles using a particle coordinate accumulation method and a contact cycle monitoring deletion method to obtain a first sand-containing sleeper-ballast-matrix initial discrete element model. Based on the first sand-containing sleeper-ballast-matrix initial discrete element model, excess sand particles are removed using an interval deletion method to construct sand-containing two-dimensional sleeper-ballast-matrix initial discrete element models with different ballast bed contamination rates.
[0032] Furthermore, the method of filling sand particles one by one into the voids of ballast particles using the particle coordinate accumulation method and the contact cycle monitoring and deletion method to obtain the initial discrete element model of the first sand-containing sleeper-ballast bed-matrix is as follows: the sand particle radius is set to r, the ballast bed width to X, the height to Y, and the position coordinates of the first sand particle to (x, y) are given. i ,y i If the coordinates of the next sand grain generated are (x, y), then the coordinates of the position where the next sand grain is generated are (x, y). i +2r,y i The model is generated in a loop. After each loop, the horizontal coordinate is accumulated, the vertical coordinate is accumulated, and the horizontal coordinate is accumulated again until the standard width and height of the track bed are reached. After each grain of sand is generated, the loop is executed once. If the sand grain comes into contact with the ballast particles, it is deleted. This is how the initial discrete element model of the first sand-containing sleeper-track bed-matrix is obtained.
[0033] Furthermore, the interval deletion method is specifically as follows: by traversing the sand grain IDs, the sand grains are deleted in intervals by taking the remainder of the sand grain ID. If every other grain is deleted, the sand grains whose IDs have a remainder when divided by 2 are deleted. If every two grains are deleted, the sand grains whose IDs have a remainder when divided by 3 are deleted, and so on.
[0034] Example 2: The following describes some specific embodiments of the present invention with reference to the accompanying drawings:
[0035] According to a first aspect of the present invention, a modeling method for a two-dimensional discrete element model of ballast particles is provided, comprising: extracting the outer contour of the ballast particles; determining the inner contour of the ballast particles based on the outer contour, specifically: extracting the geometric features of the ballast particles using laser scanning technology, obtaining the outer contour of the ballast particles through MATLAB; and using a scaling command, setting a scaling factor r according to the required accuracy of the model, and scaling the outer contour by using the center of the outer contour as the scaling center to obtain the inner contour of the ballast particles; it should be noted that 0.7 < r < 1, and the closer to 1, the higher the accuracy of the model. Figure 1 As shown, the value is 0.75.
[0036] See Figure 1 The process involves continuously filling the inner contour of the ballast particles with the maximum inscribed circle using AutoCAD (e.g., using the "Create circle tangent to three objects" function) until a preset standard is reached. Between the inner and outer contours of the ballast particles, an inscribed circle is filled using AutoCAD. After filling, the radius and position coordinates of each circle are exported. The preset standard is achieved when the maximum inscribed circle covers the area with approximately no gaps. Specifically, in this embodiment, the minimum radius of the maximum inscribed circle for filling the inner contour is 1 mm. The first inscribed circle between the inner and outer contours of the ballast particles is filled using the "Create circle tangent to two objects" function, followed by the "Create circle tangent to three objects" function, until a complete inscribed circle is formed.
[0037] A periodic boundary is established, and a discrete element model template for ballast particles is created based on the radius and coordinates of each disk. Specifically, PFC is used for modeling. The random number seed is set using the `model random` command, the periodic boundary of the model is set using the `domain extent` command, the discrete element model template for ballast particles is created using the `clump template create` command based on the radius and position coordinates of each disk, and the volume and inertia tensor of the discrete element model for ballast particles are calculated using the `pebcalculate` command.
[0038] According to a second aspect of the present invention, a modeling method for a two-dimensional discrete element model of a sand-containing sleeper-ballast-matrix is provided, comprising:
[0039] 1. Establish a periodic boundary, arbitrarily set the position coordinates of matrix particles within the periodic boundary, set the radius of matrix particles, and generate a matrix particle model template; specifically, set the periodic boundary of the model by using domain extent, create a matrix particle model template by using the clump template create command, and calculate the volume and inertia tensor of the model by using the pebcalculate command.
[0040] 2. Establish the sleeper geometry model and obtain the coordinates and radii of the ball elements in the sleeper geometry model for generating the sleeper model template. Specifically, the sleeper geometry model is created using the geometry edge create command, and densely packed disk ball elements are generated in the geometry using generate hexagonal. The position coordinates and radii of each ball element are exported using the first Fish language programming, and the sleeper model template is created using the clump template command.
[0041] 3. Establish the boundary wall. Based on the matrix particle model template, generate a preset number of matrix particles according to the gradation range, assign contact parameters, set equilibrium conditions and cycle to equilibrium, delete excess matrix particles according to the required height of the matrix layer, and obtain the matrix layer model.
[0042] Based on the matrix layer model, a preset number of ballast particles are generated on top of it according to the generated ballast particle discrete element model template and the set gradation range. Contact parameters are assigned, equilibrium conditions are set and the process is repeated until equilibrium is reached. Excess ballast particles are deleted according to the required height of the ballast layer to generate the initial model of the track bed.
[0043] See Figure 3 , 4 5. Specifically, three boundary walls are constructed using the `wall create vertices` command. Then, the `clump generate` command generates a preset number of matrix particles, and the `gauss` command controls the particle size distribution. The magnitude and direction of gravity, density, contact parameters, and equilibrium conditions of the matrix particles are set. After equilibrium is achieved, excess particles in the Y direction are deleted based on the matrix layer height (i.e.,...). Figure 5 (as shown in the vertical direction); The `clump generate` command generates a preset number of ballast particles, controlling the particle size using `diameter size` and the particle generation range using `box`. The gravity and direction, density, contact parameters, and equilibrium conditions of the ballast particles are set. After equilibrium is achieved, excess ballast particles in the Y direction are deleted according to the required ballast layer height (i.e.,...). Figure 5 (as shown in the vertical direction).
[0044] Considering the scaling effect, a linear contact model is adopted to improve model accuracy. The contact parameters include the normal contact stiffness k. n Tangential contact stiffness k s Friction coefficient fric, normal damping coefficient dp_nratio.
[0045] 4. Establish the sleeper geometry model at the corresponding position of each sleeper in the initial model of the track bed, and after enlarging the sleeper geometry model, delete the ballast particles inside it. Generate sleepers at the specified position based on the sleeper model template, set the equilibrium conditions, and generate a sleeper-track bed-matrix discrete element model without sand particles.
[0046] See Figure 6 , 7 Specifically, the geometry is generated at the corresponding position of the sleeper using the geometry edge create command, the ballast particles contained inside the geometry are deleted using the clump delete command, and finally the sleeper is generated using the clump generate command. The magnitude and direction of gravity, density, contact parameters and equilibrium conditions of the ballast particles are set, and the sleeper is fixed to not rotate using the clumpspin fix command and the clump spin attribute command, thus forming a discrete element model of sleeper-ballast bed-matrix without sand particles.
[0047] V. Based on the aforementioned discrete element model of sleeper-ballast-matrix without sand particles, sand particles are gradually filled into the gaps between ballast particles using the particle coordinate accumulation method and the contact cycle monitoring deletion method to obtain the first initial discrete element model of sleeper-ballast-matrix containing sand.
[0048] See Figure 8 Specifically, the generated sand grains are kept stationary using the ball attribute and ball fix command, and the ballast particles are kept stationary during sand grain generation using the clump attribute and clump fix command. Sand grain generation is controlled using a second fish language. If the sand grain radius is set to r, the ballast width to X, and the height to Y (in this embodiment, X is 1800mm and Y is 400mm + 350mm), the position coordinates of the first sand grain are (x...). i ,y i The coordinates of the location where the next sand grain will be generated are (x...). i +2r,y i The data is generated sequentially and cyclically. The number of cycles for accumulating the horizontal coordinate is determined by the width of the track bed, X / 2r. After each cycle of horizontal coordinate accumulation, the vertical coordinate is accumulated once (for example, the coordinate of the first sand grain in the second horizontal row is (x...). i ,y i+2r), the coordinates of the location where the second sand grain was generated are (x i +2r,y i +2r), and so on), the horizontal axis is added again until the standard width and height of the track bed is reached, and the number of times the vertical axis is added is determined according to Y / 2r; the second fish language is used to determine whether the sand particles are retained after they are generated: after each sand particle is generated, the contact loop is executed once. If the sand particle comes into contact with the ballast particles (if it is within the contact detection distance rgap, it is considered to be in contact), it is deleted, thus obtaining the first sand-containing sleeper-track bed-matrix initial discrete element model;
[0049] Set the volumetric dirtiness rate f v V is an indicator for evaluating the dirt and grime status of roadbeds. f V represents the volume of sand particles in the track bed. b Given the volume of ballast, the volumetric contamination rate of the first discrete element model of the sand-laden sleeper-ballast bed-matrix is established. In the formula, m b The total mass of ballast particles is m. f ρ is the total weight of the sand grains. b ρ is the density of ballast particles. f n is the density of sand grains. f n represents the total number of sand grains. b V represents the total number of ballast particles. if Let V be the volume of the i-th sand grain. jb Let be the volume of the j-th ballast particle;
[0050] Through function V f =ball.vol(bp) and V b =clump.vol(bp) calculates the volume of sand and ballast particles separately. For cases where uniform-sized sand is used for filling, the formula can be used directly. Calculation. By statistically analyzing the volumes of sand and ballast particles, the volumetric fouling rate of the first sand-containing sleeper-ballast-matrix initial discrete element model can be obtained. The fouling rate of the established ballast can be changed by altering the sand particle size r.
[0051] VI. Based on the initial discrete element model of the first sand-laden sleeper-ballast-matrix, excess sand particles were removed by the interval deletion method to construct two-dimensional initial discrete element models of sand-laden sleeper-ballast-matrix with different ballast contamination rates.
[0052] When establishing the next sand content model based on the initial discrete element model of the first sand-containing sleeper-ballast-matrix, the interval deletion method of the third language (Fish) is used to delete the generated sand particles. Specifically, the interval deletion method involves iterating through the sand particle IDs and deleting them at intervals by taking the remainder of the ID. If every other ID is deleted, sand particles with a remainder after dividing by 2 are deleted; if every two IDs are deleted, sand particles with a remainder after dividing by 3 are deleted, and so on. The interval for deleting sand particles is set according to the required ballast contamination rate. For example, if the ballast contamination rate of the initial discrete element model of the first sand-containing sleeper-ballast-matrix is 100%, and a ballast contamination rate of 50% needs to be established, then sand particles with a remainder after dividing by 2 are deleted.
[0053] The goal is to determine whether the track bed contamination rate of the established initial discrete element model of sand-containing two-dimensional sleeper-track bed-matrix with different track bed contamination rates meets the expected standard.
[0054] VII. Based on the initial discrete element model of sand-containing two-dimensional sleeper-track bed-matrix with different track bed dirt rates, set the equilibrium conditions and cycle to equilibrium. After cyclic equilibrium, the discrete element model of sand-containing two-dimensional sleeper-track bed-matrix with different track bed dirt rates is established.
[0055] In the embodiments provided by this invention, the contact parameters mentioned in the above steps include those between particles, between particles and the wall, and the properties of the particles themselves. Contact between particles mainly includes ball-ball, ball-pebble, and pebble-pebble; contact between particles and the wall includes ball-facet and pebble-facet. The contact parameters of the linear contact model used include contact stiffness, friction coefficient, and normal damping coefficient. Particle properties include density, particle size, and the overall model's gravity setting. During the cyclic sand filling step, the contact detection distance rgap can be reduced to ensure denser sand filling. The method provided by this invention is not only applicable to the construction of multi-scale models of sand intrusion into railway track beds, but also to the modeling of other contaminant particle intrusion into track beds, such as coal ash and soil particles. In this embodiment of the invention, rgap is set to 0.
[0056] In the embodiments provided by this invention, the radius and position coordinate information of one of the discrete element models of ballast particles are as follows:
[0057]
[0058]
[0059] In the embodiments provided by this invention, the fish function is written as follows: First, the fish language, code for exporting particle coordinate information.
[0060]
[0061] The second code uses the Fish language to establish a method for accumulating particle coordinates.
[0062]
[0063]
[0064] Thirdly, the Fish language code for particle contact loop detection and deletion:
[0065]
[0066] In this embodiment, there is also a process to verify the model construction effect, specifically, to construct an initial discrete element model of a sand-laden railway track bed with a sand volume contamination rate of 80% that meets the following parameter conditions, and to perform microstructure modeling:
[0067] The model is 1.8m long and 0.75m high. The sleeper cross-sectional dimensions are based on the new Type II concrete sleeper, and it contains three sleepers.
[0068] Wall-related parameters: Normal contact stiffness (Kn) 4×10 8 N / m, tangential contact stiffness (Ks) 4×10 8 N / m, coefficient of friction (fric) 0.38;
[0069] Sand grain (ball) related parameters: Normal contact stiffness (Kn) 3×10 8 N / m, tangential contact stiffness (Ks) 2.6×10 8 N / m, coefficient of friction (fric) 0.68, sand density 2650 kg / m³ 3 ;
[0070] Ballast (clump) related parameters: Normal contact stiffness (Kn) 3×10 8 N / m, tangential contact stiffness (Ks) 2.8×10 8 N / m, coefficient of friction (fric) 0.75, sand density 2700 kg / m³ 3 .
[0071] The operational steps for modeling its microstructure using PFC2D based on the present invention are as follows:
[0072] (1) Construct a discrete element model template for ballast particles, such as Figure 1 and Figure 2 .
[0073] (2) Construct the longitudinal section wall of the track bed, fill the disks according to the specified gradation, assign contact parameters and particle properties, set the equilibrium condition to 1e-4, and complete the matrix layer model construction, such as... Figure 3 .
[0074] (3) Based on the established discrete element model template for ballast particles, fill the ballast according to the first-order gradation standard, assign contact parameters and particle properties, set the equilibrium condition to 1e-4, and complete the initial model establishment of the ballast bed. Figure 4 .
[0075] (4) Based on the relative position standard between the track bed sleepers, establish geometry at the corresponding positions in the initial track bed model, and use the clump delete command combined with range geometry cout odd to delete the internal clumps, such as... Figure 5 .
[0076] (5) Establish the geometry based on the cross-sectional dimensions of the new Type II concrete sleeper, and use the ball generate and hexagonal commands to complete the filling, export the ball information, and use the information to create a sleeper model template, see Figure 6 .
[0077] (6) Based on the established sleeper model template, install the sleepers. During sleeper balancing, use the clump attribute and clump fix commands to prevent the sleepers from rotating and ensure they fall vertically to achieve balance. The generated sleeper-track bed-matrix discrete element model without sand particles is as follows: Figure 7 As shown.
[0078] (7) The sand particle radius was set to 0.8 mm. Using the particle coordinate accumulation method, contact cycle monitoring deletion method, and interval deletion method, an initial discrete element model of sand-containing two-dimensional sleeper-track bed-matrix with a track bed dirt rate of 80% was generated.
[0079] (8) Balance model, adjust the track bed cross-section, and complete the discrete element model of sand-containing two-dimensional sleeper-track bed-matrix with a dirt rate of 80%, such as Figure 8 .
[0080] In summary, the two-dimensional ballast particle discrete element model of this invention is based on the two-dimensional contour of real ballast particles. The contour region is divided into inner and outer parts. Inside the contour region, the maximum inscribed circle method of AutoCAD is used to continuously fill the maximum inscribed circle in the partition until the disk covers approximately no gaps. Outside the contour region, a dense ring of inscribed disks is filled with AutoCAD to depict the contour shape. After the disks in both parts are filled, the radius and position coordinates of each disk are exported. Finally, the two-dimensional ballast particle discrete element model is established. The establishment of the sand-containing two-dimensional sleeper-ballast bed-matrix discrete element model involves setting the model boundary wall and using the two-dimensional ballast particle discrete element model combination method to generate a sleeper-ballast bed-matrix discrete element model without sand particles according to the gradation. The sand particle model is represented by disks. The initial discrete element model of sand-containing two-dimensional sleeper-ballast bed-matrix with different ballast bed dirt rates is generated by using the particle coordinate accumulation method and the contact cycle detection and deletion method. This invention constructs a two-dimensional ballast particle discrete element model with low computational cost and high model accuracy. Using this model, rapid modeling of sand-containing two-dimensional railway track beds is achieved through fish language functions. Compared with existing methods, the provided two-dimensional ballast particle discrete element model resolves the contradiction between model accuracy and computational cost, and can better simulate particle wear and breakage. The modeling method for sand-infiltrated two-dimensional sleeper-ballast-matrix discrete element model of railway track beds enables rapid filling of fine particles into the ballast voids, and the model filled with fine particles can quickly establish track beds with other dirt levels.
[0081] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.
Claims
1. A modeling method for a two-dimensional discrete element model of ballast particles, characterized in that, include: Extract the outer contour of ballast particles; Determine the inner contour of the ballast particles based on the outer contour; The maximum inscribed disk is continuously filled within the inner contour partition of the ballast particles until a preset standard is reached; the preset standard is achieved when the maximum inscribed disk covers the area with approximately no gaps; a ring of inscribed disks is filled between the inner and outer contours of the ballast particles; after filling, the radius and position coordinates of each disk are exported. Establish periodic boundaries and create a discrete element model template for ballast particles based on the radius and coordinates of each disk; The method of determining the inner contour of ballast particles based on the outer contour is as follows: set a scaling factor r, and use a scaling command to shrink the outer contour using the center of the outer contour as the scaling center to obtain the inner contour of the ballast particles.
2. A modeling method for a two-dimensional discrete element model of a sand-containing sleeper-track bed-matrix, characterized in that, include: Establish a periodic boundary, arbitrarily set the position coordinates of matrix particles within the periodic boundary, set the radius of matrix particles, and generate a matrix particle model template; Establish a sleeper geometry model, obtain the coordinates and radius of the ball element in the sleeper geometry model, and use them to generate a sleeper model template; Establish a boundary wall, generate a preset number of matrix particles according to the gradation range based on the matrix particle model template, assign contact parameters, set equilibrium conditions and cycle to equilibrium, delete excess matrix particles according to the required height of the matrix layer, and obtain the matrix layer model. Based on the matrix layer model, a preset number of ballast particles are generated on its upper part according to the ballast particle discrete element model template of claim 1 and the set gradation range. Contact parameters are assigned, equilibrium conditions are set and the cycle is repeated until equilibrium is reached. Excess ballast particles are deleted according to the required height of the ballast layer to generate the initial model of the track bed. In the initial model of the track bed, a geometric model of the sleeper is established at the corresponding position of each sleeper, and the ballast particles inside the sleeper geometric model are deleted. Based on the sleeper model template, the sleeper is generated at the specified position, the equilibrium conditions are set, and a discrete element model of sleeper-track bed-matrix without sand particles is generated. Based on the aforementioned discrete element model of sleeper-ballast-matrix without sand particles, sand particles are gradually filled into the gaps between ballast particles using the particle coordinate accumulation method and the contact cycle monitoring deletion method to obtain the first initial discrete element model of sleeper-ballast-matrix containing sand. Based on the first initial discrete element model of sand-laden sleeper-ballast-matrix, excess sand particles were removed by the interval deletion method to construct two-dimensional initial discrete element models of sand-laden sleeper-ballast-matrix with different ballast contamination rates. Based on the initial discrete element model of sand-containing two-dimensional sleeper-track bed-matrix with different track bed dirt rates, equilibrium conditions are set and the model is iterated until equilibrium is reached. After the cyclic equilibrium is reached, the discrete element model of sand-containing two-dimensional sleeper-track bed-matrix with different track bed dirt rates is established.
3. The modeling method for the two-dimensional discrete element model of sand-containing sleeper-track bed-matrix as described in claim 2, characterized in that, The method of filling sand particles into the voids of ballast particles one by one using the particle coordinate accumulation method and the contact cycle monitoring and deletion method to obtain the initial discrete element model of the first sand-containing sleeper-ballast bed-matrix is as follows: the radius of the sand particle is set to r, the width of the ballast bed is X, the height is Y, and the position coordinates of the first sand particle are ( , Then the coordinates of the location where the next sand grain will be generated are ( +2r, The process is repeated cyclically. After each iteration of the horizontal axis accumulation, the vertical axis is accumulated once, and the horizontal axis is accumulated again until the standard width and height of the track bed are reached. After each grain of sand is generated, the process is repeated once. If the sand grain comes into contact with the ballast particles, it is deleted. This is how the initial discrete element model of the first sand-containing sleeper-track bed-matrix is obtained.
4. The modeling method for the two-dimensional discrete element model of sand-containing sleeper-track bed-matrix as described in claim 2, characterized in that, The interval deletion method is as follows: by traversing the sand grain IDs, the sand grains are deleted in intervals by taking the remainder of the sand grain ID. If every other grain is deleted, the sand grains whose IDs have a remainder when divided by 2 are deleted. If every two grains are deleted, the sand grains whose IDs have a remainder when divided by 3 are deleted, and so on.