Rapid stacking method of DDA model of railway ballast sample ball unit and stacking model

Abstract

The invention relates to a rapid stacking method for a DDA model of a railway ballast sample ball unit. According to the method, when stacking simulation is carried out on newly-input railway ballast particles, railway ballast particles located on the lower layer are temporarily deleted, and only one layer of railway ballast particles, possibly making contact with the newly-input railway ballast particles, on the surface is used for contact judgment; then, a random iteration method is used for narrowing the range and finding the drop point of the railway ballast particles; according to the method disclosed by the invention, the existing particles are simplified, so that the time required by particle contact judgment is shortened, and the contact judgment efficiency is improved; the particle potential energy is calculated by using a dichotomy, so that a basis is provided for reasonable positions of particles in a sample; random iteration is used for gradually reducing the range, and the positions of the railway ballast particles are repeatedly and finely adjusted, so that the positions of the railway ballast particles can reach specified precision. By integrating the steps of the method, the speed is high when the railway ballast particle model is stacked, and the stacking efficiency is greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of railway numerical simulation, and in particular to a fast stacking method and a stacking model of a ballast sample ball unit DDA model. Background Art

[0002] Discontinuous deformation analysis (DDA) is a discontinuum numerical analysis method based on the principle of minimum potential energy. [1 ], compared with other non-continuum numerical analysis methods such as discrete element method, a key difference is that its solution adopts implicit calculation method, that is, the unknown variables are not obtained by direct explicit calculation, but by solving the overall equilibrium equation. The DDA simulation of particle shape mainly uses blocks as calculation units, but the calculation of contact between different blocks is very complicated, and it is difficult to form a stable and efficient contact algorithm. Huang [2] The block calculation unit in DDA is further simplified into spherical unit, and a three-dimensional spherical unit DDA software is developed. The contact type of spherical unit DDA is simpler, so the calculation efficiency is higher.

[0003] In the actual application of ballast, ballast is placed between other ballasts to form a ballast pile. It is subject to the interaction force transmitted by adjacent ballasts. If numerical simulation is used to study the crushing of ballast in the pile, it is necessary to restore the real shape of the pile in the modeling process. There are currently two main modeling methods for particle piles with real shapes: [3,4] :(1) Falling stacking method (rainfall method), arranging the particles in a larger space, allowing the particles to move downward and stack together; (2) Servo plate loading method, using several movable servo plates to compress a larger range of particles together. Figure 1 shown.

[0004] In previous numerical experiments, although the servo plate loading method is simpler to operate, it cannot present the natural stacking state of the sample. Therefore, the gravity drop method is often used for the natural stacking of ballast deposits. This method requires the reasonable arrangement of the initial position of the particles before falling. Usually, the space is divided by a bounding box or a bounding sphere, and then the shaped particles are replaced into the position of the bounding box, and then mechanical calculations are performed until the particles are accumulated in the container. The reason why many scholars use this method is that on the one hand, the natural falling accumulation conforms to the actual situation of ballast accumulation. On the other hand, for irregular particles, it is more difficult to reasonably arrange the spatial position of these particles, and it is relatively intuitive and convenient to let them spontaneously stack and arrange under the action of their own weight. However, this method also has its problems, that is, it consumes a lot of computing time. In the accumulation calculation, all irregular ballast particles are involved in the calculation, which consumes the same computing resources as the loading calculation. When the loading process is not complicated, the accumulation calculation occupies a larger part of the calculation time.

[0005] The present invention develops a fast stacking method for a ballast sample ball unit DDA model, which can improve stacking efficiency and concentrate more computing resources on loading calculations.

[0006] [1]SHI,GEN-HUA.Discontinuous Deformation Analysis:A New NumericalModel for the Statics and Dynamics of Deformable Block Structures[J].Engineering Computations,1992,9(2):157-168.

[0007] [2] YuYong J, GangHai H, ZhiYe Z, Fei Z, Long W, et al. An improved three-dimensional spherical DDA model for simulating rock failure[J], Science China-technological Sciences, 2015, 58(9): 1533-1541.

[0008] [3] Lu Lijin. Refined modeling and discrete element analysis of railway ballast particle crushing[D]. Nanjing: Southeast University, 2021.

[0009] [4] Lin Sihan. Research on ballast morphological characteristics and its application in discrete element model[D]. Kunming: Kunming University of Science and Technology, 2019. Summary of the invention

[0010] In order to solve the above problems, the present invention provides a rapid stacking method of a ballast sample ball unit DDA model, comprising the following steps:

[0011] Step (1) Simplify existing particles

[0012] When simulating the accumulation of newly added ballast particles, temporarily delete the ballast particles in the lower layer, and only use the ballast particles on the surface that may contact with the newly added ballast particles for contact judgment;

[0013] Step (2) uses a random iteration method to narrow the range and find the landing point of the ballast particles.

[0014] Based on the above scheme, the Monte Carlo method is used to simplify the existing particles in step (1).

[0015] Based on the above scheme, the specific steps of using the Monte Carlo method to simplify existing particles are as follows:

[0016] The Monte Carlo method can be used to indirectly calculate the projection area. 100 random points are taken from the ball. The random number generator random() function can obtain uniform random numbers in the interval [0, 1]. The formula for random points is:

[0017] θ=random()×2π

[0018]

[0019] x=r×cosθ+x1

[0020] y=r×sinθ+y1

[0021] Where: x1, y1 are the coordinates of the center of the sphere; R is the radius of the sphere.

[0022] Traverse all ball units. If the point (x, y) is within the projection range of other balls and the z coordinate of the ball is larger, the point is blocked. Randomly generate 100 random points within the ball units. If most of the points are blocked, the ball should be simplified. After all ball units are simplified, only a layer of ball unit particles above the ballast accumulation body is retained for contact judgment during accumulation simulation.

[0023] On the basis of the above scheme, most of the points are blocked, which means that more than 80% of the random points are blocked. All ball units are traversed to determine whether more than 80% of the points are blocked. If so, the ball unit is simplified.

[0024] Based on the above scheme, the specific process of step (2) is as follows:

[0025] (2-1) When iterating, we need to first determine the initial value. We use the random() function to randomly select 1000 sets of α, β, x, and y. The range of α and β is (0, 2π). x and y are within the container range. We use the binary search method to calculate the result of z. We take the set of α, β, x, and y corresponding to the smallest z as the initial value of the iteration, denoted as α0, β0, x0, and y0. This smallest z value is defined as the current optimal z value, denoted as z0.

[0026] (2-2) Randomly fine-tune the optimized spatial position parameters α, β, x, y based on the initial values ​​obtained in step (2-1);

[0027] The random fine-tuning range of α and β is The random fine-tuning range of x and y is (-0.005, 0.005);

[0028] (2-3) Based on the optimized spatial position parameters α, β, x, y obtained in step (2-2), the z value corresponding to the fine-tuned α, β, x, y is calculated using the dichotomy method, and the z value is compared with the initial z value:

[0029] When the z value is greater than or equal to the initial z value, return to step (2-2) and continue to perform random fine-tuning on the basis of α0, β0, x0, y0 to obtain the optimized spatial position parameters α, β, x, y;

[0030] When the z value is less than the initial z value, the current optimal z value has completed an iteration. At this time, the z value replaces the original optimal z value (i.e., z0), and the initial position parameters (α0, β0, x0, y0) are iterated to generate the corresponding α, β, x, y of the minimum z value;

[0031] (2-4) Based on the new α0, β0, x0, y0 obtained in step (2-3), range α and range β Multiply the last iteration by 0.95 to get the range α1 and range β1 , set range x and range y Multiply the last iteration by 0.8 to get the range x1 and range y1 , randomly fine-tune in the reduced range to obtain new optimized spatial position parameters α, β, x, y;

[0032] (2-5) Based on the new optimized spatial position parameters α, β, x, y obtained in step (2-4), the z value corresponding to the fine-tuned α, β, x, y is calculated using the dichotomy method, and the z value is compared with the optimal z value iterated in step (2-3);

[0033] When the z value is greater than or equal to the optimal z value iterated from step (2-3), return to step (2-4), and on the basis of the new α0, β0, x0, y0 obtained in step (2-3), randomly fine-tune in the reduced range to obtain new optimized spatial position parameters α, β, x, y;

[0034] When the z value is less than the optimal z value iterated from step (2-3), another iteration is completed. At this time, the z value iteratively replaces the optimal z value iterated from step (2-3), and the initial position parameters are iterated to generate the corresponding α, β, x, y of the minimum z value;

[0035] (2-6) After each iteration, the corresponding α, β, x, y of the new minimum z value is used to repeat steps (2-4)-(2-5) continuously; finally, the ballast placement coordinates α, β, x, y, z with sufficient accuracy are obtained, the ballast is placed at this coordinate position, and the next ballast is placed.

[0036] Based on the above scheme, the method for generating random numbers by optimizing the spatial position parameters α, β, x, y in step (2-2) is:

[0037] α=α0+(random()-0.5)×range α

[0038] β=β0+(random()-0.5)×range β

[0039] x=x0+(random()-0.5)×range x

[0040] y=y0+(random()-0.5)×range y

[0041] Among them: random() is a random number generator in the range of [0,1]; range α 、range β for range x 、range y is 0.01; α0, β0, x0, y0 are the initial values ​​of the iterative calculation.

[0042] Based on the above scheme, the method for generating random numbers for the newly optimized spatial position parameters α, β, x, y in step (2-4) is:

[0043] α=α0+(random()-0.5)×range α1

[0044] β=β0+(random()-0.5)×range β1

[0045] x=x0+(random()-0.5)×range x1

[0046] y=y0+(random()-0.5)×range y1

[0047] Where: range α1 、range β1The range in the formula for generating the optimized spatial position parameter random number before iteration α 、range β Multiply the value by 0.95, range x1 、range y1 The range in the formula for generating the optimized spatial position parameter random number before iteration x 、range y The value is multiplied by 0.8; random() is a random number generator in the range of [0,1]; α0, β0, x0, y0 are the new initial values ​​obtained in step (2-3);

[0048] Based on the above scheme, the specific process of dichotomy is:

[0049] First set the upper boundary z of the falling ballast particles max , the lower boundary z min , move the ballast particle to the midpoint between the upper boundary and the lower boundary to determine whether it is in contact with the simplified existing particle;

[0050] If it is determined that there is no contact, the upper boundary is updated to the midpoint of the original upper boundary and the lower boundary; then, the ballast particle is moved to the midpoint of the new upper boundary and the lower boundary; and then it is re-determined whether it is in contact with the existing particle;

[0051] If contact is determined, the lower boundary is updated to the midpoint of the original upper boundary and the lower boundary, and the ballast particle is moved to the midpoint of the upper boundary and the new lower boundary to re-determine whether it is in contact with the existing particle;

[0052] By repeatedly contacting and updating the upper and lower boundaries, when the upper boundary z max -Lower boundary z min When it is less than the set threshold, the output z max , at this time the upper boundary z max is the minimum z value at which the falling ballast particles do not contact the existing particles. max -z min The threshold value ensures that z max The z value that makes the ballast particles touch the existing particles is infinitely close.

[0053] Based on the above scheme, the threshold is set to 1.5e-5.

[0054] In the method of the present invention, by simplifying the existing particles, the time required for particle contact judgment is reduced, and the efficiency of contact judgment is improved; the particle potential energy is calculated by using the dichotomy method, which provides a basis for determining the reasonable position of the particles in the sample; the range is gradually narrowed by using random iteration, and the position of the ballast particles is repeatedly fine-tuned so that the position of the ballast particles can reach the specified accuracy. Combining the various steps of the present invention, the method of the present invention is faster in the accumulation of the ballast particle model, and the accumulation efficiency is greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0056] Figure 1 A schematic diagram of a ballast accumulation modeling method in the prior art;

[0057] Figure 2 A simplified schematic diagram of existing particles in the method of this application;

[0058] Figure 3 Schematic diagram of generating random points in a circle using different methods; a is a random circle point with non-uniform distribution; b is a random circle point with uniform distribution;

[0059] Figure 4 This is a schematic diagram of the principle of particle simplification in the method of this application;

[0060] Figure 5 This is a result diagram of particle simplification in the method of this application;

[0061] Figure 6 Schematic diagram of the spatial transformation of ballast particles in step (2) of the method of the present application;

[0062] Figure 7 The figure is a comparison chart of the efficiency of ballast accumulation using the method of the present invention and the rain-falling method of the prior art. DETAILED DESCRIPTION

[0063] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0064] Example 1

[0065] In order to improve the calculation efficiency and concentrate more calculation resources on the loading calculation, this application proposes a fast stacking method for ballast specimen model. The specific method is as follows:

[0066] Step (1) Simplify existing particles

[0067] Since contact judgment of particles is widely used in the position calculation of ballast particles, in order to reduce the time required for contact judgment, the existing particles can be simplified. Note that when the ballast is placed, it will only contact the particles on the top layer and not the particles on the bottom layer. Therefore, this method temporarily deletes the particles on the bottom layer and only retains the particles on the top layer, reducing the complexity of contact calculation and speeding up calculation efficiency.

[0068] The placement of each particle is calculated in turn, and the existing particles are simplified after calculation, using only the surface layer for contact judgment. The simplified effect is as follows Figure 2 As shown, green particles participate in the calculation, while blue ones do not.

[0069] The simplified judgment criterion is the occlusion relationship between particles, that is, the particles on the surface of the particle accumulation body are retained. If the particles are simply divided according to the z-direction coordinates, the upper surface shape of the ballast accumulation body is more complex, and a larger z-coordinate range needs to be retained. This paper uses the method of judging whether to retain according to the projection area on the xoy plane. If a particle is blocked by the particles above for multiple times, its projection area on the xoy plane will be reduced, such as Figure 2 As shown in the figure, when the projection area is smaller than a set threshold, the particle will be temporarily deleted.

[0070] It is difficult to directly calculate the projected area, and the Monte Carlo method in this application simplifies the existing particles.

[0071] The Monte Carlo method can be used to indirectly calculate the projection area. 100 random points are taken from the ball. The random number generator random() function can obtain uniform random numbers in the interval [0, 1]. The formula for random points is:

[0072] θ=random()×2π

[0073]

[0074] x=r×cosθ+x1

[0075] y=r×sinθ+y1

[0076] Where: x1, y1 are the coordinates of the center of the sphere; R is the radius of the sphere.

[0077] It should be noted that if the radius r is uniformly distributed r = random() × R, the generated points will be concentrated near the center of the circle rather than uniformly distributed, such as Figure 3 a. Let the radius be The distribution can generate uniform points within the circle, such as Figure 3 b.

[0078] Simplified principle Figure 4 As shown. Traverse all ball units. If the point (x, y) is within the projection range of other balls and the z coordinate of the ball is larger, then this point is blocked. Randomly generate random points in 100 ball units. If most of the points are blocked, the ball should be simplified. In the present invention, after trial calculation, this judgment threshold is set to 80%. Traverse all ball units to determine whether more than 80% of the points are blocked. If so, they should be simplified.

[0079] like Figure 5 As shown in the figure, after the ballast accumulation body is simplified, only a layer of green particles on the top of the ballast is retained for contact judgment during accumulation, and other blue particles will not come into contact with the newly added ballast. Therefore, the efficiency of ballast contact judgment is greatly improved by simplifying the existing particles through the Monte Carlo method.

[0080] Step (2) Use random iteration to narrow the range and find the point where the ballast particles fall

[0081] The position of a particle with a real shape in space can be uniquely determined by five parameters α, β, x, y, and z. α and β are the rotation angles, and x, y, and z are the positions of the center of gravity. The center of gravity of the particle is initially located at the origin, so the following can be done: Figure 6 The 5 ways shown are for space transformation. Figure 6 The reason why the rotation around the z axis is not included is that the rotation around the z axis can be compounded by the rotation around the x and y axes. If you want to place the particle at the spatial position (α, β, x, y, z), first rotate it around the y axis by an angle of β, then rotate it around the x axis by an angle of α, and finally translate the center of gravity to (x, y, z).

[0082] The specific process of narrowing the scope is as follows:

[0083] (2-1) When iterating, you must first determine the initial value. Use the random() function to randomly select 1000 groups of α, β, x, and y; the range of α and β is (0, 2π); x and y are within the container range; use the binary search method to calculate the result of z, and take the group of α, β, x, and y corresponding to the smallest z as the initial value of the iteration (denoted as α0, β0, x0, y0). This smallest z value is defined as the current optimal z value (denoted as z0).

[0084] (2-2) Based on the initial values ​​(i.e., α0, β0, x0, y0) obtained in step (2-1), random fine-tuning is performed to obtain optimized spatial position parameters α, β, x, y;

[0085] The formula for generating random numbers using the optimized spatial position parameters α, β, x, and y is:

[0086] α=α0+(random()-0.5)×range α

[0087] β=β0+(random()-0.5)×range β

[0088] x=x0+(random()-0.5)×range x

[0089] y=y0+(random()-0.5)×range y

[0090] Among them: random() is a random number generator in the range of [0,1]; range α 、range β for range x 、range y is 0.01; α0, β0, x0, y0 are the initial values ​​of iterative calculation;

[0091] At this time, the random fine-tuning range of α and β is The random fine-tuning range of x and y is (-0.005, 0.005);

[0092] (2-3) Based on the optimized spatial position parameters α, β, x, y obtained in step (2-2), the z value corresponding to the fine-tuned α, β, x, y is calculated using the dichotomy method, and the z value is compared with the initial z value (the optimal z value obtained in step (2-1), i.e., z0):

[0093] When the z value is greater than or equal to the initial z value, return to step (2-2) and continue to perform random fine-tuning on the basis of α0, β0, x0, y0 to obtain the optimized spatial position parameters α, β, x, y;

[0094] When the z value is less than the initial z value, the current optimal z value has completed the first iteration, which is defined as the initial iteration. At this time, the z value replaces the original optimal z value (i.e., z0), and the initial position parameters (α0, β0, x0, y0) are iterated to generate the corresponding α, β, x, y of the minimum z value (i.e., the newly generated α, β, x, y replace the original α0, β0, x0, y0);

[0095] (2-4) Based on the new α0, β0, x0, y0 (new α0, β0, x0, y0 after iteration) obtained in step (2-3), range α and range β Multiply the last iteration by 0.95 to get the range α1 and range β1 , set range x and range y Multiply the last iteration by 0.8 to get the range x1 and range y1 , randomly fine-tune in the reduced range to obtain new optimized spatial position parameters α, β, x, y;

[0096] The formula for generating random numbers using the new optimized spatial position parameters α, β, x, and y is:

[0097] α=α0+(random()-0.5)×range α1

[0098] β=β0+(random()-0.5)×range β1

[0099] x=x0+(random()-0.5)×range x1

[0100] y=y0+(random()-0.5)×range y1

[0101] Where: range α1 、range β1 The range in the formula for generating the optimized spatial position parameter random number before iteration α 、range β Multiply the value by 0.95, range x1 、range y1 The range in the formula for generating the optimized spatial position parameter random number before iteration x 、range y The value is multiplied by 0.8; random() is a random number generator in the range of [0,1]; α0, β0, x0, y0 are the new initial values ​​obtained in step (2-3) or step (2-5);

[0102] (2-5) Based on the new optimized spatial position parameters α, β, x, y obtained in step (2-4), the z value corresponding to the fine-tuned α, β, x, y is calculated using the dichotomy method, and the z value is compared with the optimal z value (the smaller z value after iteration) iterated in step (2-3);

[0103] When the z value is greater than or equal to the optimal z value iterated from step (2-3), return to step (2-4). At this time, based on the new α0, β0, x0, y0 obtained in step (2-3), randomly fine-tune in the reduced range to obtain new optimized spatial position parameters α, β, x, y;

[0104] When the z value is less than the optimal z value iterated from step (2-3), another iteration is completed. At this time, the z value iteratively replaces the optimal z value iterated from step (2-3), and the initial position parameters (α0, β0, x0, y0) are iterated to generate the corresponding α, β, x, y of the minimum z value (that is, the newly generated α, β, x, y replace the original α0, β0, x0, y0 in step (2-3);

[0105] (2-6) After each iteration, the new minimum z value and the corresponding α, β, x, y are used to repeat steps (2-4)-(2-5) to perform the next iteration; eventually, the ballast placement coordinates α, β, x, y, z with sufficient accuracy are obtained, the ballast is placed at this coordinate position, and the next ballast is placed.

[0106] The above steps need to be further clarified: after each iteration, range α and range β Multiply by 0.95 based on the previous iteration; range x and range y Multiply the last iteration by 0.8. α For example, the initial range α for After the initial iteration in step 2-3, the range is reduced in step 2-4 α for After iterating the optimal z value in steps 2-5, return to steps 2-4 to narrow the range α for Then iterate the steps 2-5 to find the optimal z value, and then return to steps 2-4 to narrow the range. α for range β 、range x 、range y And so on.

[0107] The specific steps of the dichotomy in the above steps are as follows:

[0108] For a ballast particle, if the rain method is used for accumulation, the ballast particle falls under the action of gravity. After the fall is completed, the ballast particle is in a spatial position where the gravitational potential energy reaches a minimum. Therefore, if you want to speed up the calculation efficiency of the fall, you can start from this point and obtain the ballast spatial position corresponding to the minimum value of the gravitational potential energy. After obtaining the result, move the ballast particle directly to the corresponding spatial position to speed up the calculation of the rain method. In this way, the calculation result obtained is similar to that of the rain method, but because the mechanical calculation process of each time step is omitted, the ballast is directly placed in the spatial position of the minimum potential energy, which greatly improves the calculation efficiency.

[0109] Among the five parameters describing the spatial position of ballast (α, β, x, y, z), z is the parameter that determines the potential energy. According to the principle of minimum potential energy, when the other four spatial position parameters are determined, z can be uniquely determined. The four spatial position parameters of ballast are known, and ballast can only move up and down. In the process of moving from top to bottom, the new ballast has no contact with the simplified existing particles at first, and contacts with the existing particles after continuing to move downward.

[0110] First set the upper boundary z of the falling ballast particles max , the lower boundary z min , move the ballast particle to the midpoint between the upper boundary and the lower boundary to determine whether it is in contact with the simplified existing particle;

[0111] If it is determined that there is no contact, the upper boundary is updated to the midpoint of the original upper boundary and the lower boundary; then, the ballast particle is moved to the midpoint of the new upper boundary and the lower boundary; and then it is re-determined whether it is in contact with the existing particle;

[0112] If contact is determined, the lower boundary is updated to the midpoint of the original upper boundary and the lower boundary, and the ballast particle is moved to the midpoint of the upper boundary and the new lower boundary to re-determine whether it is in contact with the existing particle;

[0113] By repeatedly contacting and updating the upper and lower boundaries, when the upper boundary z max -Lower boundary z min When it is less than 1.5e-5, output z max , at this time the upper boundary z max is the minimum z value at which the falling ballast particles do not contact the existing particles. max -z min The threshold value ensures that z max The z value that makes the ballast particles touch the existing particles is infinitely close.

[0114] The present invention uses the method in the embodiment and the raining method in the prior art to pile up 80 ballast particles. The results are as follows: Figure 7 As shown, by comparison, it can be found that the method of the present invention greatly improves the efficiency of ballast accumulation.

[0115] Using the method of the present invention, after 54 minutes, all 80 ballast particles have been stacked by the rapid stacking method, while the ballast stacked by the falling stacking method has only fallen a certain distance in the container at 54 minutes, and most of the ballast has not yet touched the bottom of the container.

[0116] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A fast stacking method for a ballast sample ball unit DDA model, characterized in that: The steps include: Step (1) Simplify existing particles When simulating the accumulation of newly added ballast particles, temporarily delete the ballast particles in the lower layer, and only use the ballast particles on the surface that may contact with the newly added ballast particles for contact judgment; Step (2) uses a random iteration method to narrow the range and find the landing point of the ballast particles.

2. The rapid stacking method of a ballast sample ball unit DDA model according to claim 1 is characterized in that: The Monte Carlo method is used to simplify the existing particles in step (1).

3. The rapid stacking method of the ballast sample ball unit DDA model according to claim 2 is characterized in that: The specific steps to simplify existing particles using the Monte Carlo method are as follows: The Monte Carlo method can be used to indirectly calculate the projection area. 100 random points are taken from the ball. The random number generator random() function can obtain uniform random numbers in the interval [0, 1]. The formula for random points is: θ=random()×2π x=r×cosθ+x1 y=r×sinθ+y1 Where: x1, y1 are the coordinates of the center of the sphere; R is the radius of the sphere. Traverse all ball units. If the point (x, y) is within the projection range of other balls and the z coordinate of the ball is larger, the point is blocked. Randomly generate 100 random points within the ball units. If most of the points are blocked, the ball should be simplified. After all ball units are simplified, only a layer of ball unit particles above the ballast accumulation body is retained for contact judgment during accumulation simulation.

4. The rapid stacking method of the ballast sample ball unit DDA model according to claim 3 is characterized in that: Most of the points are blocked, which means that more than 80% of the random points are blocked. All ball units are traversed to determine whether more than 80% of the points are blocked. If so, the ball unit is simplified.

5. The rapid stacking method of a ballast sample ball unit DDA model according to claim 1 is characterized in that: The specific process of step (2) is as follows: (2-1) When iterating, we need to first determine the initial value. We use the random() function to randomly select 1000 sets of α, β, x, and y. The range of α and β is (0, 2π). x and y are within the container range. We use the binary search method to calculate the result of z. We take the set of α, β, x, and y corresponding to the smallest z as the initial value of the iteration, denoted as α0, β0, x0, and y0. This smallest z value is defined as the current optimal z value, denoted as z0. (2-2) Randomly fine-tune the optimized spatial position parameters α, β, x, y based on the initial values ​​obtained in step (2-1); The random fine-tuning range of α and β is The random fine-tuning range of x and y is (-0.005, 0.005); (2-3) Based on the optimized spatial position parameters α, β, x, y obtained in step (2-2), the z value corresponding to the fine-tuned α, β, x, y is calculated using the dichotomy method, and the z value is compared with the initial z value: When the z value is greater than or equal to the initial z value, return to step (2-2) and continue to perform random fine-tuning on the basis of α0, β0, x0, y0 to obtain the optimized spatial position parameters α, β, x, y; When the z value is less than the initial z value, the current optimal z value has completed an iteration, which is defined as the initial iteration. At this time, the z value replaces the original optimal z value (i.e., z0), and the initial position parameters are iterated to generate the corresponding α, β, x, and y of the minimum z value. (2-4) Based on the new α0, β0, x0, y0 obtained in step (2-3), range α and range β Multiply the last iteration by 0.95 to get the range α1 and range β1 , set range x and range y Multiply the last iteration by 0.8 to get the range x1 and range y1 , randomly fine-tune in the reduced range to obtain new optimized spatial position parameters α, β, x, y; (2-5) Based on the new optimized spatial position parameters α, β, x, y obtained in step (2-4), the z value corresponding to the fine-tuned α, β, x, y is calculated using the dichotomy method, and the z value is compared with the optimal z value iterated in step (2-3); When the z value is greater than or equal to the optimal z value iterated from step (2-3), return to step (2-4), and on the basis of the new α0, β0, x0, y0 obtained in step (2-3), randomly fine-tune in the reduced range to obtain new optimized spatial position parameters α, β, x, y; When the z value is less than the optimal z value iterated from step (2-3), another iteration is completed. At this time, the z value iteratively replaces the optimal z value iterated from step (2-3), and the initial position parameters are iterated to generate the corresponding α, β, x, y of the minimum z value; (2-6) After each iteration is completed, the corresponding α, β, x, y of the new minimum z value is used to repeat steps (2-4)-(2-5) to perform the next iteration; eventually, the ballast placement coordinates α, β, x, y, z with sufficient accuracy are obtained, the ballast is placed at this coordinate position, and the next ballast is placed.

6. The rapid stacking method of the ballast sample ball unit DDA model according to claim 5 is characterized in that: The method for generating random numbers using the optimized spatial position parameters α, β, x, y in step (2-2) is: α=α0+(random()-0.5)×range α β=β0+(random()-0.5)×range β x=x0+(random()-0.5)×range x y=y0+(random()-0.5)×range y Among them: random() is a random number generator in the range of [0,1]; range α 、range β for range x 、range y is 0.01; α0, β0, x0, y0 are the initial values ​​of the iterative calculation.

7. The rapid stacking method of the ballast sample ball unit DDA model according to claim 6 is characterized in that: The formula for generating random numbers from the newly optimized spatial position parameters α, β, x, y in step (2-4) is: α=α0+(random()-0.5)×range α1 β=β0+(random()-0.5)×range β1 x=x0+(random()-0.5)×range x1 y=y0+(random()-0.5)×range y1 Where: range α1 、range β1 The range in the formula for generating the optimized spatial position parameter random number before iteration α 、range β Multiply the value by 0.95, range x1 、range y1 The range in the formula for generating the optimized spatial position parameter random number before iteration x 、range y The value is multiplied by 0.8; random() is a random number generator in the range [0,1].

8. The rapid stacking method of the ballast sample ball unit DDA model according to claim 5 is characterized in that: The specific process of dichotomy is: First set the upper boundary z of the falling ballast particles max , the lower boundary z min , move the ballast particle to the midpoint between the upper boundary and the lower boundary to determine whether it is in contact with the simplified existing particle; If it is determined that there is no contact, the upper boundary is updated to the midpoint of the original upper boundary and the lower boundary; then, the ballast particle is moved to the midpoint of the new upper boundary and the lower boundary; and then it is re-determined whether it is in contact with the existing particle; If contact is determined, the lower boundary is updated to the midpoint of the original upper boundary and the lower boundary, and the ballast particle is moved to the midpoint of the upper boundary and the new lower boundary to re-determine whether it is in contact with the existing particle; By repeatedly contacting and updating the upper and lower boundaries, when the upper boundary z max -Lower boundary z min When it is less than the set threshold, the output z max , at this time the upper boundary z max is the minimum z value at which the falling ballast particles do not contact the existing particles. max -z min The threshold value ensures that z max The z value that makes the ballast particles touch the existing particles is infinitely close.

9. The rapid stacking method of the ballast sample ball unit DDA model according to claim 8, characterized in that: The threshold is set to 1.5e-5.

10. A ballast sample ball unit DDA model, characterized in that: It is quickly stacked using the method described in any one of claims 1 to 9.

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