A particle breakage coupling simulation method based on dynamic regulation of interface contact parameters

Abstract

The application discloses a kind of particle crushing coupling simulation method based on interface contact parameter dynamic regulation, belong to geotechnical engineering technical field.The method real-time monitoring the size distribution curve difference and interface contact quantity difference between external FRM particle and internal BPM particle, according to this, dynamically adjusts interface normal stiffness, tangential stiffness, friction coefficient, rolling resistance and five parameters of external sphere fragment replacement crushing threshold value.The external sphere fragment replacement crushing threshold value is in reverse linkage with other four parameters.The application establishes comprehensive control quantity, realizes the signed direction discrimination of interface force transmission state and parameter adaptive update, so that external particle can provide force transmission environment matched with real particle contact state with internal particle.Using the method of the application, the simulation reality of BPM internal particle crushing path and fragment morphology can be significantly improved while maintaining the high computational efficiency of FRM.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering technology, specifically relating to a particle breakage coupling simulation method based on dynamic control of interface contact parameters. Background Technology

[0002] Particulate materials are widely used in geotechnical engineering (roadbeds, ballast, earth-rock dams), energy extraction (hydraulic fracturing proppant), and other fields. Under compression, shear, impact, or cyclic loading conditions, particles break down, leading to significant changes in particle size distribution, particle morphology, contact network, and macroscopic mechanical properties. Realistically and accurately simulating the particle breakage process is crucial for revealing breakage mechanisms, predicting gradation evolution, evaluating material breakage resistance, and optimizing engineering design.

[0003] Existing numerical simulation methods for particle breakage mainly include particle bonding and fragmentation substitution methods. Particle bonding methods can realistically reflect the internal fragmentation, bonding failure, and natural fragmentation processes of particles; however, if the entire sample particle is simulated using this method, the number of computational units and contacts is enormous, resulting in low computational efficiency. Fragmentation substitution methods have higher computational efficiency and are suitable for simulating the breakage, refinement, and gradation evolution of large numbers of particles; however, the number, size, and spatial distribution of its sub-particles largely depend on preset rules, making it difficult to realistically reflect the natural breakage path and fragment morphology of the target particle.

[0004] Therefore, combining the fragment replacement method (FRM) with the particle bonding method (BPM)—that is, using FRM for the external spherical system to ensure computational efficiency and BPM for the internal target particles to ensure fragmentation accuracy—is an effective approach that balances computational efficiency and simulation realism. However, existing hybrid simulation methods typically only specify different fragmentation methods for external and internal particles, lacking mechanisms for determining and dynamically controlling parameters at their interface. Inappropriate settings for parameters such as interface normal stiffness, interface tangential stiffness, interface friction coefficient, interface rolling resistance, and the fragment replacement fragmentation threshold of the external spherical system can lead to distortion in force transmission between the external fragment replacement particles and the internal particle bonding model, causing problems such as premature or insufficient fragmentation of the internal target particles, or deviations in fragment morphology. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a particle crushing coupling simulation method based on dynamic control of interface contact parameters. By establishing a dual feedback mechanism of consistency of particle size distribution curve and consistency of interface contact quantity, the interface contact parameters between external FRM particles and internal BPM particles are dynamically adjusted, so that external particles can provide internal particles with a force transmission environment that matches the actual particle contact state, thereby improving the accuracy and stability of coupling simulation.

[0006] Therefore, the present invention provides a particle breakage coupling simulation method based on dynamic control of interface contact parameters, comprising the following steps:

[0007] Step 1: Establish a breakable model of irregularly shaped particles using the particle bonding method, and verify its microscopic parameters through single-particle breakage tests;

[0008] Step 2: Establish a breakable model of the external sphere system using the fragment substitution method, and verify its contact parameters through a low confining pressure overall test. Determine the fragment substitution breakage threshold F of the external sphere through a high confining pressure overall test. lim ;

[0009] Step 3: Construct a mixed fragmentation numerical model; wherein, the outer spherical system adopts the spherical particle and fragment substitution method, and the internal irregular particles adopt a particle bonding model based on the reconstruction of the real contour;

[0010] Step 4: During the loading simulation, monitor the differences in particle size distribution curves and the number of interfacial contacts between the external sphere system and the internal particles in real time, and dynamically adjust the interfacial contact parameters based on the double consistency feedback index.

[0011] The interface contact parameters include: interface normal stiffness, interface tangential stiffness, interface friction coefficient, interface rolling resistance coefficient, and external spherical fragment replacement breakage threshold F. lim ;

[0012] Step 5: Continue the loading simulation based on the dynamically adjusted interface contact parameters until the preset termination condition is reached.

[0013] Specifically, the method for quantifying the differences in the particle size distribution curves is as follows:

[0014] Calculate the signed particle size deviation ;

[0015] Among them, P in,k (d i () represents the irregular particle fragments within the k-th stage with a particle size d i Cumulative pass rate at point P out,k (d i For the k-stage external spherical system with particle size d i Cumulative pass rate at location d i Let be the i-th particle size sampling point, and m be the number of particle size sampling points;

[0016] when When the value is greater than 0, it indicates that the force transmission effect at the interface needs to be enhanced. When the value is less than 0, it indicates that the force transmission effect at the interface needs to be weakened.

[0017] Specifically, the method for quantifying the difference in the number of interface contacts is as follows:

[0018] Define the deviation of the number of signed contacts. ;

[0019] Among them, Z in (k) represents the average coordination number of the fragment system formed after the irregular particles inside the k-th stage break up, Z I (k) represents the average coordination number at the interface between irregular particle fragments and the external sphere at the contact interface in stage k. Specifically, Z in (k) is obtained by averaging the number of contacts between each fragment of the irregular internal particle and other internal fragments; Z I (k) is obtained by averaging the number of contacts between irregular particle fragments at the contact interface and with external spherical particles. This is achieved by comparing Z... in (k) and Z I (k) Determine whether the interface contact environment provided by the external FRM particles is consistent with the contact configuration of the internal BPM particles after their own breakage.

[0020] When e z When (k)>0, it means Z in (k)>Z I (k), meaning the average coordination number of the interface is less than the average coordination number of the internal fragment system itself, indicates insufficient fragmentation of the external spheres and a low number of interfacial spheres. In this case, it is necessary to enhance the interfacial contact and reduce F. lim (k) makes it easier for the outer sphere to undergo fragment replacement and breakage.

[0021] When e z When (k) < 0, it means Z in (k) <Z I (k), meaning the average coordination number of the interface is greater than the average coordination number of the internal fragment system itself, indicates that the external spheres are excessively fragmented or the number of interfacial spheres is too high. In this case, it is necessary to weaken the interfacial contact effect and increase F. lim (k) inhibits further breakage of the outer sphere.

[0022] Specifically, the decision-making basis for the dynamic regulation is the comprehensive regulation quantity S(k):

[0023] ;

[0024] Where a and b are weighting coefficients, and a + b = 1.

[0025] Specifically, the interface contact parameter vector for the k-th loading stage is:

[0026]

[0027] Where: k n I(k) represents the interface normal stiffness at stage k; k s I (k) represents the interface tangential stiffness at stage k; μ I (k) is the interfacial friction coefficient at stage k; μ r I (k) is the interfacial rolling resistance coefficient in the k-th stage; F lim (k) is the fragment replacement and breakage threshold for determining whether the external sphere has broken in the fragment replacement method of the k-th stage.

[0028] The above five parameters collectively regulate the interfacial force transmission state between the external FRM particles and the internal BPM particles, as well as the degree of fragmentation of the external spheres. Among them, the interfacial normal stiffness, interfacial tangential stiffness, interfacial friction coefficient, and interfacial rolling resistance mainly affect the strength of load transmission from the external spheres to the internal irregular particles; F lim (k) mainly affects the ease with which the external sphere is fragmented and replaced, thus affecting the number of small spheres at the interface and the coordination number of the interface.

[0029] The method for updating the interface contact parameters is as follows:

[0030] ;

[0031] Where, θ I (k+1) is the interface contact parameter vector for the (k+1)th loading stage; θ I (k) is the interface contact parameter vector for the kth loading stage; This indicates that the corresponding components are multiplied, where η is the update step size vector for each interface parameter, and q is the update direction vector, q = [1, 1, 1, 1, -1].

[0032] , , , and Adjust in the same direction; with Reverse adjustment.

[0033] Specifically, when If the interface force transmission or the number of interface contacts is too weak, then increase the interface normal stiffness, interface tangential stiffness, interface friction coefficient, and interface rolling resistance, while reducing... This makes the outer sphere more prone to fragmentation and breakage, thereby increasing the number of outer spheres and the number of interfacial contacts. When When this occurs, it indicates that the interface force transmission or the number of interface contacts is too strong. In this case, reduce the interface normal stiffness, interface tangential stiffness, interface friction coefficient, and interface rolling resistance, while increasing... This makes it more difficult for the outer sphere to undergo fragment replacement and breakage, thereby reducing the excessive number of interfacial contacts caused by excessive fragmentation of the outer sphere.

[0034] Specifically, the particle bonding model of the internal irregular particles is formed by obtaining the real particle external contour through CT scanning or three-dimensional laser scanning, and then discretizing the contour into sub-units and bonding them together.

[0035] Specifically, the fragment replacement method for the external spherical system adopts a fragmentation criterion based on the maximum normal contact force: when the maximum normal contact force F max >F lim During this process, the particles break apart, and the broken particles are replaced by several sub-spheres. lim This is the fragment replacement breakage threshold for determining whether an external sphere is broken in the fragment replacement method.

[0036] Specifically, the convergence condition for the dynamic adjustment of the interface contact parameters is as follows: when |S(k)| is less than the preset adjustment threshold of 0.05, the current interface contact parameters remain unchanged; when |S(k)| is less than 0.05 within 10 consecutive detection cycles, the interface contact parameter adjustment process is determined to have converged, and the subsequent dynamic update of the interface contact parameters is stopped.

[0037] Specifically, in the discrete element program, the interface contact parameters are detected and updated once every preset number of steps, where the preset number of steps is 100 time steps.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. This invention proposes for the first time a dual feedback control mechanism based on the consistency of particle size distribution and the consistency of contact quantity, which realizes the automatic and adaptive adjustment of interface parameters and overcomes the technical problem of relying on experience to determine parameters.

[0040] 2. This invention proposes F lim The strategy of inverse linkage between S(k) and S(k) is as follows: when it is necessary to enhance interface fragmentation, the threshold is lowered and the number of interface contacts is increased; when it is necessary to reduce interface fragmentation, the threshold is raised. This strategy makes the control of interface contact state more precise and efficient.

[0041] 3. Definition of this invention and e z (k) Two signed deviation indicators can not only determine whether the force transmission at the interface is out of balance, but also determine the direction of the imbalance (too strong or too weak), thereby guiding the direction of parameter adjustment (to enhance or weaken), which provides a clear logical basis for the adaptive control of parameters.

[0042] 4. By adopting a partitioned modeling strategy of external FRM and internal BPM, a large number of external particles adopt a high-efficiency spherical FRM model, while a small number of key internal particles adopt a high-precision BPM model. This ensures both overall computational efficiency and the realism of the simulation of the breaking behavior of key particles. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart of the dynamic update process of the interface parameters of this invention;

[0045] Figure 2 This is a peak diagram of the crushing force of a single particle;

[0046] Figure 3 It is a fracture strength-survival probability curve from indoor experiments and numerical simulations;

[0047] Figure 4 This is a graph showing the match between the simulated deviatoric stress-axial strain curve under low confining pressure and the indoor test results.

[0048] Figure 5 This is a graph showing the match between the simulated deviatoric stress-axial strain curve under high confining pressure and the indoor test results.

[0049] Figure 6 This is a schematic diagram of the external sphere and the internal irregular particles before loading;

[0050] Figure 7 This is a schematic diagram of the external sphere and the internal irregular particles after loading. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] A particle breakage coupling simulation method based on dynamic adjustment of interface contact parameters is proposed. This method does not simply combine external particles using a fragment substitution method and internal target particles using a particle bonding method in parallel. Instead, it establishes a feedback coupling relationship at the interface: by real-time monitoring of the difference in particle size distribution curves between the external spheres and the internal irregular particles, as well as the difference between the number of interface contacts and the reference number of internal irregular particles, the normal stiffness, tangential stiffness, friction coefficient, rolling resistance, and breakage strength threshold of the external sphere particles are dynamically adjusted. This allows the external fragment substitute particles to provide the internal particle bonding model with a force transmission environment that matches the actual particle contact state. Thus, while maintaining the high computational efficiency of the fragment substitution method, the simulation realism of the breakage path, breakage degree, and fragment morphology evolution of the internal target particles is improved.

[0053] See Figure 1 The present invention adopts the overall technical concept of internal target particle parameter verification → external spherical system parameter verification → mixed crushing model construction → dynamic control of interface contact parameters → particle crushing process simulation. The specific technical solution is as follows:

[0054] Step 1: Verification of particle bonding parameters for irregularly shaped internal particles

[0055] The external contours of the target irregular particles were obtained using non-contact measurement techniques such as 3D laser scanning and CT scanning. The obtained point cloud data was reconstructed into a 3D surface mesh, which was then discretized into multiple sub-units or block units. A breakable irregular particle bonding model was formed using a particle bonding method. Subsequently, single-particle crushing tests under plate loading were conducted to obtain test results such as single-particle contact force-displacement curves and crushing modes. Based on the test results, the microscopic parameters such as bonding strength, bonding stiffness, contact stiffness, and friction coefficient in the internal irregular particle bonding model were verified using inverse analysis methods to ensure that the crushing behavior of the internal particle bonding model was consistent with the test results.

[0056] Step 2: Verification of contact parameters and fragment substitution parameters of the external spherical system

[0057] The outer spherical particles are used to represent the surrounding particle system. Spherical particles are used for modeling, and the fragmentation and refinement of the outer particles and their gradation evolution are simulated using the fragmentation replacement method (FRM). The particle fragmentation criterion and sub-particle replacement mode adopt the method proposed by Ciantia et al. (Ciantia MO, Arroyo M, Calvetti F, et al. An approach to enhance efficiency of DEM modelling of soils with crushable grains[J]. Géotechnique,2015, 65(2): 91–110.): when the maximum normal contact force F on a particle... max Exceeding the breakage threshold F lim At that time, the particle broke apart and was replaced by 14 equal-volume subspheres.

[0058] The contact parameters of the external spherical system were verified through indoor triaxial drained shear tests of the same material under low confining pressure. Since particle breakage is weak under low confining pressure, the test results mainly reflect the basic contact, friction, and deformation characteristics of the material, and can be used to verify the normal stiffness, tangential stiffness, friction coefficient, and damping parameters of the external spherical system. Further triaxial drained shear tests under high confining pressure were conducted, and the breakage threshold F of the particles was adjusted based on the contact parameters determined under low confining pressure. lim This approach ensures that the overall stress-strain curve of the sample under high confining pressure closely approximates that of the experimental specimen, and also the particle size distribution curve. Therefore, the replacement fragmentation threshold F for external spherical fragments is determined. lim .

[0059] Step 3: Establish a hybrid crushing numerical model combining FRM and BPM.

[0060] Establish a numerical computation model, in which:

[0061] External spherical system: The spherical particle and fragmentation replacement method (FRM) is used to efficiently simulate the load transfer, fragmentation and refining of surrounding particles;

[0062] Internal target particles: A particle bonding model (BPM) reconstructed from the real external contour is used to simulate the natural breakage law of the target irregular particles.

[0063] This hybrid modeling approach, combining external FRM and internal BPM, enables external spherical particles to perform efficient contact environment simulation and internal irregular particles to perform high-precision crushing response simulation, thus balancing computational efficiency and the realism of the crushing process.

[0064] Step 4: Introduce a dynamic adjustment mechanism for interface contact parameters

[0065] In the simulation of mixed crushing, the interface contact parameters between external FRM particles and internal BPM particles are monitored and dynamically adjusted in real time. This is the core innovative step of this invention. In the discrete element method program, during the loading process, the particle contact is traversed once every 100 steps, and the interface contact parameters are dynamically adjusted according to the following criteria.

[0066] (4.1) Define the interface contact parameter vector

[0067] Define the interface contact parameter vector for the k-th loading stage as:

[0068] ;

[0069] Where: k n I (k): Interface normal stiffness at stage k; k s I (k): Interface tangential stiffness at stage k; μ I (k): The interfacial friction coefficient at stage k; μ r I (k): Interfacial rolling resistance coefficient at stage k; F lim (k): The fragment replacement fracture threshold for determining whether the outer sphere is fractured in the fragment replacement method of the k-th stage. These five parameters together determine the transmission of forces from the outer sphere to the irregular particles inside, shear constraints, rotational constraints, and the degree of fracture of the outer sphere.

[0070] (4.2) Monitoring the consistency of particle size distribution curves

[0071] In the k-th loading stage, the particle size distribution curves after the replacement of the external spherical fragments and the fragment particle size distribution curves after the internal irregular particles were broken were statistically analyzed.

[0072] Define the difference in particle size distribution curves as:

[0073] ;

[0074] in:

[0075] P out,k (d i ): In the k-th stage, the external spherical system has a particle size d i Cumulative pass rate at the location;

[0076] P in,k (d i ): Irregular particle fragments within the k-th stage with a particle size d i Cumulative pass rate at the location;

[0077] d i : The i-th particle size sampling point;

[0078] m: Number of particle size sampling points;

[0079] D P (k): The difference in particle size distribution curves between the outer spheres and the inner irregular particles.

[0080] When D P The smaller (k) is, the closer the crushing progress of the outer sphere is to the crushing progress of the inner irregular particles.

[0081] To determine the direction of regulation, a signed particle size deviation can be defined:

[0082] ;

[0083] when A value >0 indicates that the cumulative throughput of internal BPM particle fragments is higher than that of external FRM spheres. This means that the internal particle fragments are generally finer, while the external spheres are relatively less fragmented. Therefore, it is necessary to enhance the interfacial coupling and reduce the fragmentation threshold F of the external spheres. lim (k) causes the outer sphere to break further. When When the value is less than 0, it indicates that the external FRM sphere is relatively fragmented, requiring weakening of the interface coupling and increasing the F... lim (k) inhibits the outer sphere from continuing to break.

[0084] (4.3) Monitoring of consistent contact quantity

[0085] Contact quantity consistency means that the number of interfacial contacts between the external FRM particles and the internal BPM particles should be as close as possible to the number of contacts (i.e., coordination number) of the internal BPM particles themselves in the corresponding state.

[0086] First, the coordination number of the fragments at the contact interface is calculated in real time:

[0087] ;

[0088] in:

[0089] Z I (k): The average coordination number of the fragments at the contact interface in the kth stage;

[0090] C i in (k): The number of internal fragments that come into contact with other internal fragments at the contact interface;

[0091] C i out (k): The number of internal fragments that come into contact with external spherical particles at the contact interface;

[0092] N I(k): The number of fragments at the contact interface in stage k.

[0093] Then, count the number of contacts between the irregular particles inside:

[0094] ;

[0095] in:

[0096] Z in (k): The average coordination number of the fragment system formed after the irregular particles inside the k-th stage break apart;

[0097] N in (k): The number of fragments formed after the irregular particles inside the k-th stage break apart;

[0098] To determine the direction of control, a signed contact quantity deviation is defined:

[0099] ;

[0100] When e z When (k)>0, it indicates that the average coordination number of the interface is less than the average coordination number of the internal fragment system itself, suggesting insufficient fragmentation of the external spheres or a low number of interfacial contacts. Therefore, it is necessary to enhance interfacial contact and reduce the external sphere fragment substitution fragmentation threshold F. lim (k) causes the outer sphere to break further. When e z When (k) < 0, it indicates that the average coordination number of the interface is greater than the average coordination number of the internal fragment system itself, suggesting that the external sphere is excessively fragmented or that there is too much interfacial contact. It is necessary to weaken the interfacial contact effect and increase the external sphere fragment substitution fragmentation threshold F. lim (k) inhibits the outer sphere from continuing to break.

[0101] (4.4) Calculation of comprehensive regulation and control quantity

[0102] Whether the interface coupling contact parameters are reasonable is judged by the combined error of the particle size distribution curve and the error of the number of contacts:

[0103] ;

[0104] Where: S(k): the comprehensive control amount of interface parameters in the k-th stage;

[0105] e p (k): Signed particle size deviation;

[0106] e z (k): Signed contact quantity deviation;

[0107] a, b: Weighting coefficients, a + b = 1. Parameters a and b represent the influence weights of differences in particle size distribution curves and differences in contact quantity. A value of 0.5 is recommended, but can be adjusted according to actual conditions.

[0108] When S(k) > 0, it indicates that the interface force transmission or effective contact is weak, and the interface contact parameters need to be strengthened. When S(k) < 0, it indicates that the interface force transmission or effective contact is strong, and the interface contact parameters need to be weakened.

[0109] (4.5) Interface parameter update

[0110] The interface parameters are updated uniformly according to the following formula.

[0111] ;

[0112] ;

[0113] in, This indicates that the corresponding components are multiplied, and η is the update step vector of each interface parameter; , , , and These correspond to the update steps for interface normal stiffness, interface tangential stiffness, interface friction coefficient, interface rolling resistance coefficient, and external spherical fragment replacement breakage threshold, respectively.

[0114] q is the update direction vector:

[0115] q = [1, 1, 1, 1, -1];

[0116] That is: k n I (k), k s I (k), μ I (k), μ r I (k) is adjusted in the same direction as S(k); F lim S(k) is adjusted inversely to S(k). When S(k)>0, the interface stiffness, friction coefficient and rolling resistance are increased, while the external sphere breakage threshold is reduced, thus enhancing the interface effect and increasing the number of contacts; when S(k)<0, the opposite is true.

[0117] Step 5: Perform loading simulation and iteration

[0118] The above control process is executed iteratively step-by-step in the discrete element method (DEM) program until loading is complete or a preset termination condition is met. The preset termination condition can be designed as follows: when |S(k)| is less than a preset control threshold of 0.05, the current interface contact parameters remain unchanged; when |S(k)| is less than 0.05 for 10 consecutive detection cycles, the interface contact parameter control process is considered converged, and subsequent dynamic updates of the interface contact parameters are stopped. In the DEM program, the interface contact parameters are detected and updated once every preset number of steps, where the preset number of steps is 100 time steps.

[0119] The implementation steps of this invention will be further explained below with reference to specific examples.

[0120] 1. Simulation of single-particle crushing of calcareous sand in the South China Sea, and verification of BPM parameters.

[0121] Internal target particles: Irregular particles with an equivalent diameter of 3-4 mm (taking South China Sea calcareous sand particles as an example).

[0122] The external contours of realistic particles were obtained using 3D laser scanning. A curvature-based mesh simplification method was then used to reduce the particle surface to approximately 1500 triangular faces, improving modeling efficiency while preserving angular and local topographic features. Subsequently, the simplified particle contours were imported into a discrete element method (DEM) program, and an improved particle bonding method was employed to divide the particles into coplanar Voronoi polyhedral elements with an equivalent particle size of approximately 0.3 mm. The number of sub-elements within a single realistically shaped particle is approximately 1000.

[0123] The single-particle crushing simulation employed a rigid plate loading method with upper and lower plates. The particle density was 2830 kg / m³, and the local damping coefficient was 0.7. A linear parallel bonding model was used, with a normal stiffness of 4.12 × 10⁻⁶. 6 N / m, tangential stiffness is 3.10 × 10 N / m 6 The coefficient of friction is 0.5, and the cohesive strength and tensile strength are both 6.1 × 10 N / m. 6 Pa, friction angle is 45°. The loading rate can be 0.01 m / s to meet the quasi-static loading requirements.

[0124] Single-particle crushing and compression tests were conducted through simultaneous indoor experiments and numerical simulations. Firstly, based on... Figure 2 Obtain the peak crushing force of a single particle, and calculate the crushing strength σ of the particle based on the peak value. f Secondly, by comparing the fracture strength-survival probability curves from indoor experiments and numerical simulations, such as... Figure 3 As shown, the contact parameters of irregular particles are checked.

[0125] 2. Triaxial drained shear simulation, external FRM parameter verification

[0126] The contact parameters of the outer spherical particles were obtained through simultaneous triaxial drained shear tests and simulation verification under low confining pressure. A rolling resistance linear contact model was used for the outer spherical particles. The verification test used calcareous sand samples with a particle size of 3-4 mm, a relative density of 90%, and a confining pressure of 50 kPa; under these conditions, particle breakage has a weak effect and can be used to reflect the basic contact, friction, and deformation characteristics of the material. The deviatoric stress-axial strain curves obtained from DEM simulation were matched with the laboratory test results, such as... Figure 4 As shown, the parameters of the external spherical particles are determined as follows: particle density 2830 kg / m³. 3 The local damping coefficient is 0.7; the normal stiffness is 3.8 × 10⁻⁶. 6 N / m, tangential stiffness is 2.4 × 10 N / m 6 N / m, friction coefficient is 0.5, rolling friction coefficient is 0.7.

[0127] Based on the aforementioned contact parameters, further experiments and simulations of triaxial drained shear under high confining pressure (800 kPa) were conducted. The crushing strength threshold F of the spherical particles was continuously adjusted. lim To ensure that the stress-strain curves and particle size distribution curves obtained in the simulation are as consistent as possible with those obtained in the experiment, such as... Figure 5 As shown. This allows for the preliminary determination of the F-value of spherical particles with a diameter of 3-4 mm. lim The value is 83N.

[0128] 3. Lateral compression simulation of coupled BPM and FRM particle swarms

[0129] A coupled fracture model of an outer sphere and internal irregular particles was established. The fracture of the outer sphere was simulated using the Fracture-Replacement Method (FRM) for high computational efficiency, while the fracture of the internal irregular particles was realistically represented using the Brush-Particle Mixing (BPM) method. In the lateral confinement compression simulation, an outer spherical particle system was first established as the overall sample skeleton, with a sample size of 40mm × 40mm × 40mm. Rigid sidewalls were set around the perimeter to restrict lateral deformation, and the upper and lower walls were used to apply vertical compressive loads. The fracture of the outer spherical particles was simulated using the FRM fragmentation method, with an initial particle size range of 3-4 mm, responsible for the main load transfer, particle rearrangement, and gradation evolution. Several internal irregular particles were embedded in the central region of the sample, with an area of ​​approximately 18mm × 18mm × 18mm. The particle morphology was reconstructed from the scanned contours of real particles, and a fractured model was established using the BPM particle bonding method. During lateral compression, the external FRM spheres and the internal BPM irregular particles are subjected to pressure together. The coupling between the two types of particle breakage models is achieved through a dynamic control mechanism of interface contact parameters, so that the breakage and refinement of the external spherical particles and the bonding and destruction of the internal irregular particles are coordinated in terms of particle size distribution and contact quantity.

[0130] (1) Initialization of interface parameters

[0131] In the lateral compression model, the parameters of the external FRM spherical particles and the parameters of the internal irregular particles are consistent with the aforementioned verification parameters.

[0132] The initial values ​​of the interface coupling control parameters are taken as the average values ​​of the corresponding parameters of the external FRM particles and the internal BPM particles, as follows:

[0133] ;

[0134] The first two parameters are the interface normal stiffness and interface tangential stiffness, respectively, in N / m; the third parameter is the interface friction coefficient; the fourth parameter is the interface rolling resistance coefficient; and the fifth parameter is the external spherical fragment replacement and breakage threshold F. lim (0), the unit is N.

[0135] (2) Setting of control parameters

[0136] The particle size distribution weight is set to a=0.5, and the contact quantity weight is set to b=0.5, meaning that particle size distribution consistency and contact quantity consistency have equal weight. Based on experiments, the interface parameter update step size vector is set as follows:

[0137] η = [0.05, 0.05, 0.03, 0.03, 0.02];

[0138] Update direction vector:

[0139] q = [1, 1, 1, 1, -1];

[0140] The update step size is checked and the interface parameters are updated every 100 time steps.

[0141] That is, the interface normal stiffness, interface tangential stiffness, interface friction coefficient, and interface rolling resistance coefficient, and the comprehensive control amount. Adjusting in the same direction, the outer sphere breakage threshold and Reverse adjustment. Particle size distribution differences and contact number differences are detected every 100 time steps, and based on... Update interface parameters. When, keep the current interface parameters unchanged; when within 10 consecutive detection cycles At that time, it is considered that the interface parameter adjustment process has converged.

[0142] (3) Simulation results

[0143] like Figure 6 and Figure 7As shown, the fragmentation and refinement process of the external FRM spherical particles gradually coordinates with the fragmentation evolution process of the internal BPM irregular particles, and the average coordination number of the interface gradually approaches the average coordination number of the internal BPM fragment system. After dynamic adjustment:

[0144] The interface normal stiffness eventually converges to approximately 4.3 × 10⁻⁶. 6 N / m;

[0145] The tangential stiffness of the interface eventually converges to approximately 2.95 × 10⁻⁶. 6 N / m;

[0146] The interfacial friction coefficient converges to approximately 0.52;

[0147] The interface rolling resistance coefficient converges to approximately 0.72;

[0148] External spherical fragments replace the fragmentation threshold F lim It converges to approximately 65 N;

[0149] At this point, the difference in particle size distribution between the external FRM particles and the internal BPM particle fragments is D. P <0.05, the deviation between the average coordination number of the interface and the average coordination number of the internal BPM fragment system is less than 5%, and the simulation time is reduced by more than 70% compared with the full BPM particle swarm model.

[0150] The above embodiments are merely illustrative examples to clearly illustrate the present invention and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A particle breakage coupling simulation method based on dynamic control of interface contact parameters, characterized in that, Includes the following steps: Step 1: Establish a breakable model of irregularly shaped particles using the particle bonding method, and verify its microscopic parameters through single-particle breakage tests; Step 2: Establish a breakable model of the external sphere system using the fragment substitution method. Verify its contact parameters through a low confining pressure overall test, and determine the fragment substitution breakage threshold F of the external sphere through a high confining pressure overall test. lim ; Step 3: Based on the model and contact parameters of the internal irregular particles and the external spheres determined in Step 1 and Step 2, construct a mixed crushing numerical model; wherein, the external sphere system adopts the spherical particle and fragment substitution method, and the internal irregular particles adopt a particle bonding model based on the reconstruction of the real contour. Step 4: During the loading simulation, monitor the differences in particle size distribution curves and the number of interfacial contacts between the external sphere system and the internal particles in real time, and dynamically adjust the interfacial contact parameters based on the double consistency feedback index. The interface contact parameters include: interface normal stiffness, interface tangential stiffness, interface friction coefficient, interface rolling resistance coefficient, and external spherical fragment replacement breakage threshold F. lim ; Step 5: Continue the loading simulation based on the dynamically adjusted interface contact parameters until the preset termination condition is reached.

2. The particle breakage coupling simulation method according to claim 1, characterized in that, The method for quantifying the differences in the particle size distribution curves is as follows: Calculate the signed particle size deviation ; Among them, P out,k (d i For the k-th stage, the external spherical system has a particle size d. i Cumulative pass rate at point P in,k (d i () represents the irregular particle fragments within the k-th stage with a particle size d i Cumulative pass rate at location d i Let be the i-th particle size sampling point, and m be the number of particle size sampling points; when When the value is greater than 0, it indicates that the outer sphere is not sufficiently broken, and the interface coupling needs to be enhanced. When the value is less than 0, it indicates that the external sphere is breaking too strongly, and the interface coupling effect needs to be weakened.

3. The particle breakage coupling simulation method according to claim 2, characterized in that, The method for quantifying the difference in the number of interface contacts is as follows: Define the deviation of the number of signed contacts. ; Among them, Z in (k) represents the average coordination number of the fragment system formed after the irregular particles inside the k-th stage break up; Z I (k) represents the average coordination number of the fragments at the contact interface in the kth stage; When e z When (k)>0, it indicates that the interface contact needs to be enhanced; when e z When (k) < 0, it indicates that the interface contact effect needs to be weakened.

4. The particle breakage coupling simulation method according to claim 3, characterized in that, The decision-making basis for the dynamic regulation is the comprehensive regulation amount S(k): ， Where a and b are weighting coefficients, and a + b = 1.

5. The particle breakage coupling simulation method according to claim 4, characterized in that, The interface contact parameter vector for the k-th loading phase is: ； Where: k n I (k) represents the interface normal stiffness at stage k; k s I (k) represents the interface tangential stiffness at stage k; μ I (k) is the interfacial friction coefficient at stage k; μ r I (k) is the interfacial rolling resistance coefficient in the k-th stage; F lim (k) is the fragment replacement and breakage threshold for determining whether the external sphere is broken in the fragment replacement method of the k-th stage; then the update method of the interface contact parameters is: ； Where, θ I (k+1) is the interface contact parameter vector for the (k+1)th loading stage; θ I (k) is the interface contact parameter vector for the kth loading stage; This indicates that the corresponding components are multiplied, where η is the update step size vector for each interface parameter, and q is the update direction vector, q = [1, 1, 1, 1, -1].

6. The particle breakage coupling simulation method according to claim 5, characterized in that, External spherical fragments replace the fragmentation threshold F lim (k) has an inverse adjustment relationship with the comprehensive control quantity S(k), and the interface normal stiffness k n I (k) Interface tangential stiffness k s I (k), interfacial friction coefficient μ I (k), interfacial rolling resistance coefficient μ r I (k) has a positive adjustment relationship with the comprehensive control quantity S(k), that is, when S(k) > 0, it increases the interface stiffness, friction coefficient and rolling resistance, while reducing F. lim (k) makes the outer sphere more prone to fragment replacement and breakage, thereby increasing the number of outer spheres and the number of interfacial contacts; when S(k) < 0, it reduces the interfacial stiffness, interfacial friction coefficient and interfacial rolling resistance, while increasing F lim (k) makes it more difficult for the outer sphere to undergo fragment replacement and breakage, thereby reducing the excessive number of interfacial contacts caused by excessive fragmentation.

7. The particle breakage coupling simulation method according to any one of claims 1-6, characterized in that, The particle bonding model of the internal irregular particles is formed by obtaining the real external contour of the particles through CT scanning or three-dimensional laser scanning, and then discretizing the contour into sub-units and bonding them together.

8. The particle breakage coupling simulation method according to any one of claims 1-6, characterized in that, The fragmentation replacement method for the external spherical system adopts a fragmentation criterion based on the maximum normal contact force: when the maximum normal contact force F max External spherical fragments replace the breakage threshold F lim It breaks down, and the broken particles are replaced by several sub-spheres.

9. The particle breakage coupling simulation method according to any one of claims 4-6, characterized in that, The convergence condition for the dynamic adjustment of the interface contact parameters is: when |S(k)| is less than the preset adjustment threshold of 0.05, the current interface contact parameters remain unchanged; When |S(k)| is less than 0.05 within 10 consecutive detection cycles, the interface contact parameter adjustment process is determined to have converged, and the dynamic update of the interface contact parameters is stopped.

10. The particle breakage coupling simulation method according to claim 9, characterized in that, In the discrete element method, the interface contact parameters are detected and updated once every preset number of steps, where the preset number of steps is 100 time steps.

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