A rapid sampling method for wide-graded granular materials suitable for discrete element analysis

Abstract

The present invention relates to a method for rapidly preparing samples of wide-gradation granular materials suitable for discrete element analysis. For wide-gradation granular materials, a small sample with similar geometry and meeting the requirements is pre-prepared. A simple geometric method is then used to "enlarge" the pre-prepared small sample to meet the requirements of the simulated sample required for numerical simulation. Based on a similar principle, large-sized granular material samples are rapidly prepared under specified density and specified wide-gradation conditions, thereby reducing overall sample preparation time. The present invention is not only applicable to the preparation of samples with specified larger sizes under specified density and specified wide-gradation conditions, but is also applicable to the preparation of samples requiring only a larger number of particles under the same conditions. The method is not limited to single-particle-size samples and binary mixtures, but is also applicable to multi-component mixtures and continuously graded samples.

Description

Technical Field

[0001] The present invention relates to a method for rapidly preparing samples of widely graded granular materials suitable for discrete elements, belongs to the field of discrete element (DEM) numerical analysis, and is particularly suitable for preparing samples of specified size under conditions of specified density and specified wide gradation. Background Art

[0002] The discrete element method (DEM) has become an indispensable approach for analyzing and solving geotechnical engineering problems. When using DEM to simulate laboratory tests (such as standard triaxial tests), if it is necessary to prepare a sample of granular material with a specified larger size under specified density and wide gradation conditions, and if the particle distribution of the sample is required to be random, repeated trial calculations are often required to adjust the prepared sample to meet the requirements. In this case, specifying the sample size under these conditions is equivalent to determining the number of particles, and determining the number of particles is a more complex problem.

[0003] Existing methods typically achieve size requirements by directly adjusting the number of particles generated in the desired sample and repeatedly re-preparing the sample. This size requirement must also be met while also meeting the specified density. However, this significantly reduces the computational efficiency of discrete element software for wide-graded samples. Current discrete element numerical simulation methods are still limited by computing equipment, and the debugging process required to ensure that both sample size and density meet the requirements is time-consuming. This is especially true when the sample preparation required for simulation has high material stiffness, the number of particles exceeds 10,000 (or even hundreds of thousands), and the boundary conditions are complex. This requires significantly more sample preparation time, consuming a significant amount of time and effort in preparing the numerical simulation samples.

[0004] Therefore, it is urgent to design a new rapid sample preparation method that can solve the above problems. Summary of the Invention

[0005] The present invention provides a method for rapid sample preparation of wide-gradation granular materials applicable to discrete element simulation, which accelerates the preparation of required samples for wide-gradation granular materials in discrete element numerical simulation.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] A method for rapid sampling of widely graded granular materials suitable for discrete element analysis, specifically comprising the following steps:

[0008] Step S1: Pre-prepare a small sample; specifically including:

[0009] Step S11: setting the parameters required for preparing a small sample and generating n number of sample particles;

[0010] Step S12: Set the required sliding friction coefficient and apply the required confining pressure, and after stabilization, obtain a porosity ratio of e n Small specimens;

[0011] Step S13: Determine whether the void ratio in step S12 meets the requirements. If so, proceed to step S14. If not, adjust the sliding friction coefficient and proceed to step S12.

[0012] Step S14: determining the particle size of the small sample with a void ratio meeting the conditions;

[0013] Step S2: By using the principle of geometric similarity, the prepared small sample is enlarged to obtain the required number of particles of the simulated sample;

[0014] Step S3: setting parameters and preparing the required simulation sample;

[0015] As a further preferred embodiment of the present invention, the porosity ratio of the desired simulation sample is e, if e n ≠e, the required confining pressure is reapplied after adjusting the sliding friction coefficient in the numerical simulation;

[0016] As a further preferred embodiment of the present invention, it is characterized in that the step of adjusting the sliding friction coefficient is:

[0017] If e n <e, then increase the preset sliding friction coefficient; if e n >e, then reduce the preset sliding friction coefficient;

[0018] As a further preferred embodiment of the present invention, in step S2, the particle size of the small sample is determined according to step S14 to obtain the particle size of the required simulated sample under three-dimensional conditions. The calculation formula is:

[0019]

[0020] In formula (1), n ​​is the number of particles in the small sample, N is the number of particles in the required simulated sample, and V n is the volume of the small specimen, V is the volume of the required simulated specimen;

[0021] As a further preferred embodiment of the present invention, in step S2, the particle size of the small sample is determined according to step S14 to obtain the particle size of the required simulated sample under two-dimensional conditions. The calculation formula is:

[0022]

[0023] In formula (2), n is the number of particles in the small sample, N is the number of particles in the required simulated sample, and S n is the area of ​​the small specimen, S is the area of ​​the required simulated specimen;

[0024] As a further preferred embodiment of the present invention, in step S3, after determining the particle size of the small sample according to step S2 to obtain the number of particles N of the required simulation sample, continue to apply the preset confining pressure and sliding friction coefficient, and after stabilization, obtain the required simulation sample with a porosity ratio of approximately e.

[0025] Through the above technical solution, compared with the existing technology, the present invention has the following beneficial effects:

[0026] 1. The method provided by the present invention for rapid sampling of widely graded granular materials applicable to discrete element simulation can pre-prepare small samples with similar proportions and meeting the requirements, which can greatly reduce the time cost of discrete element numerical simulation;

[0027] 2. The method for rapid sample preparation of wide-graded granular materials applicable to discrete element analysis provided by the present invention only involves general geometric operations and the calculation formula is relatively simple;

[0028] 3. The method provided by the present invention for rapid sample preparation of widely graded granular materials in discrete elements is not only applicable to the preparation of samples with a specified larger size under the conditions of a specified density and a specified wide gradation, but is also applicable to the preparation of samples requiring only a larger number of particles under the same conditions.

[0029] 4. The method for rapid sample preparation of widely graded granular materials in discrete elements provided by the present invention is not only applicable to sample preparation under three-dimensional conditions, but also to sample preparation under two-dimensional conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The present invention will be further described below with reference to the accompanying drawings and examples.

[0031] Figure 1 This is a flow chart of a method for rapid sampling of widely graded granular materials applicable to discrete elements provided by the present invention;

[0032] Figure 2 This is a geometric principle diagram of the method for rapid sampling of widely graded granular materials applicable to discrete elements provided by the present invention;

[0033] Figure 3a-Figure 3b This is a comparison diagram of the small and medium-sized sample obtained in Example 1 and the matching required simulation sample according to the method for rapid sampling of medium- and wide-graded granular materials applicable to discrete elements provided by the present invention;

[0034] Figure 4a-4b This is a comparison diagram of the small and medium-sized samples in Example 2 and the matching required simulation samples obtained according to the method for rapid sampling of wide-graded granular materials applicable to discrete elements provided by the present invention. DETAILED DESCRIPTION

[0035] The present invention will now be described in further detail with reference to the accompanying drawings. In the description of this application, it should be understood that the terms "left side", "right side", "upper", "lower", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are intended only to facilitate the description of the present invention and simplify the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. "First", "second", etc. do not indicate the importance of the components and therefore should not be understood as limiting the present invention. The specific dimensions used in this embodiment are only for illustrative purposes only and do not limit the scope of protection of the present invention.

[0036] As explained in the background technology, there are usually two disadvantages for rapid sampling of discrete element particle materials with specified large sizes, especially for wide-graded particles, under specified density and specified wide-gradation conditions. The first is that due to the large-sized wide-graded particles, the time for molding the sample is usually very long, resulting in increased time costs. The second is that due to the wide-graded particles, they need to be verified many times in the discrete element numerical simulation, and the molding time of a sample is often relatively long. When the molded sample is verified to be a failure case, the time and molding cost will be further increased.

[0037] Therefore, this application cleverly proposes a concept, which is to use the principle of geometric similarity to pre-prepare small samples with similar proportions and that meet the requirements, and by "enlarging" them, speed up the preparation of simulation samples required for discrete element numerical simulation.

[0038] Then for wide graded particles, this application Figure 1 The specific steps shown include:

[0039] Step S1: Pre-prepare a small sample; specifically including:

[0040] Step S11: Set the parameters required for preparing small samples, and generate n number of sample particles within a suitable range; wherein, n is the number of particles of the prefabricated small sample, and its value can be determined according to the equipment conditions. While ensuring the stability of the small sample, in order to reduce the burden of calculation, the smaller the better, but it should not be too small. Too small a value for the number of particles will result in a large parameter error when the small sample is "enlarged". Its value is generally set to above 1000.

[0041] Step S12: Set the required sliding friction coefficient and apply the required confining pressure, and after stabilization, obtain a porosity ratio of e n For small samples, the grading and other conditions of the small samples must meet the requirements.

[0042] Step S13: Determine whether the porosity ratio in step S12 meets the requirements. If so, proceed to step S14. If not, adjust the sliding friction coefficient and proceed to step S12. The method for determining whether the requirements are met is to set the porosity ratio of the simulated sample to be e. If e n ≠e (the two are not completely different here, as long as the difference between the two values ​​is large, that is, the difference between the two values ​​in percentile is a certain value), adjust the sliding friction coefficient in the numerical simulation and re-apply the required confining pressure; if e n <e, then increase the preset sliding friction coefficient; if e n >e, then reduce the preset sliding friction coefficient until the two values ​​are very close or even the same, and measure the size of the prepared small sample. At this time, except for the sample size (i.e., the number of particles), the other parameters of the small sample meet the requirements;

[0043] It should be noted that the above step S13 needs to be calculated twice or more.

[0044] Step S14: Determine the particle size of the small sample under the conditions of the porosity ratio; this step determines the exact parameters for preparing the required simulation sample when other variables are constant and only the number of particles in the sample is different (that is, the size of the sample is different); by "scaling" the size of the required sample so that the number of particles inside it is n, adjust the sliding friction coefficient and prepare a similar small sample to meet the requirements.

[0045] Step S2: By using the principle of geometric similarity, the prepared small sample is enlarged to obtain the required number of particles of the simulation sample; for preparing the required simulation sample with a larger specified size under the conditions of specified density and specified wide gradation, the parameters of the pre-prepared small sample and the simulation sample required for numerical simulation are the same except for the size and number of particles; here, the required number of particles of the simulation sample can be determined under three-dimensional conditions and two-dimensional conditions. Figure 2 The figure shows the relationship between the size of the small sample and the required simulation sample. The particle size of the required simulation sample under three-dimensional conditions can be calculated using the following formula:

[0046]

[0047] In formula (1), n ​​is the number of particles in the small sample (can be set freely by humans), N is the number of particles in the required simulated sample (the unknown quantity to be calculated), and V n is the volume of the small sample (obtained after the small sample is prepared), and V is the volume of the required simulation sample (specified by the required specific numerical simulation experiment);

[0048] The rationality of the above formula (1) lies in that, except for the size (number of particles), the parameters of the small sample are exactly the same as those of the required simulation sample. At this time, n is equivalent to the total volume of particles in the small sample, and N is equivalent to the total volume of particles in the required simulation sample. In addition, this method only "scales" the required simulation sample, and the internal structures of the two samples themselves are extremely similar, so the equivalent replacement at this time makes the equality of the above formula valid.

[0049] To obtain the particle size of the desired simulated sample under two-dimensional conditions, it is only necessary to make some simple changes to the above formula (1), and the calculation formula is:

[0050]

[0051] In formula (2), n is the number of particles in the small sample, N is the number of particles in the required simulated sample, and S n is the area of ​​the small specimen, S is the area of ​​the required simulated specimen;

[0052] The rationality of the above formula at this time is also similar to the three-dimensional case. The difference is that at this time n and N are no longer equivalent to the total volume of the particles, but are correspondingly equivalent to the total cross-sectional area of ​​the particles in the two-dimensional plane where the sample is located.

[0053] The applicability of formula (1) or formula (2) is not affected by the density of the sample, the applied confining pressure, and the model used. Due to the particularity of the discrete element wide-graded granular material, the boundary conditions need to be specified as periodic boundaries. The spatial distribution position of the particles inside the discrete element sample needs to be random, and there is no human intervention to specify the generation position of the particles. Except for the different sample size (i.e., the total number of particles), all other parameters of the prefabricated small sample and the parameters used in the preparation of the required simulation sample must be consistent.

[0054] Step S3: Set parameters and prepare the desired simulation sample. Determine the particle size of the small sample according to step S2. After regenerating the desired number of particles N within a suitable range, continue applying the preset confining pressure and sliding friction coefficient. Once stabilized, a simulation sample with a porosity ratio of approximately e is obtained.

[0055] Due to the randomness of particle generation distribution, the density of the prepared sample may deviate greatly from that of the small sample. In this case, it is only necessary to fine-tune the relevant friction coefficient and reload the consolidation to achieve the required density. Compared with the method of directly preparing the sample without the preparation process of the small sample, the number of trial calculations is also greatly reduced.

[0056] In addition, in step S2, whether three-dimensional or two-dimensional, it is necessary to generate a sample of a specified size in the numerical simulation. For general situations where the sample size does not need to be specified, the "prefabricated small sample" method in this method can also be applied because the number of particles is reduced, the computing efficiency of the equipment is greatly improved, and the trial calculation process of sample preparation required for simulation is reduced. In other words, "prefabricated small sample" can be used as a common sense accepted by those skilled in the art, rather than being limited to the above formula (1) or formula (2).

[0057] In order to better verify the above-mentioned rapid sample preparation method, the present application provides Example 1 and Example 2 to verify the advantages of the present application. First, prefabricate Figure 3a and Figure 4a The small samples shown correspond to Example 1 and Example 2, respectively. In the two figures, the black balls are coarse particles in the small samples, and the gray balls are fine particles in the small samples (the scale on the right side of the figure indicates the particle radius). After all other conditions of the small sample except the size meet the requirements of the desired simulation sample, the relevant parameters are substituted into the formula (1) under three-dimensional conditions to calculate the total number of particles in the desired simulation sample, and the sample is prepared again to obtain the following: Figure 3b and Figure 4b The relevant data of the required simulation samples and Example 1 and Example 2 are shown in Table 1:

[0058] Table 1 Comparison of parameters of prefabricated small specimens and simulated specimens required for numerical simulation

[0059]

[0060]

[0061] Assume that the desired simulation specimen is a cubic specimen with a coarse particle size of 5 mm and a fine particle size of 1 mm, measuring 30 mm × 30 mm × 30 mm. Furthermore, the volume ratio of coarse to fine particles is required to be 4:6. The simulation uses a periodic boundary, a confining pressure of 800 kPa, a Young's modulus of 30 GPa, and a Hertz model. The actual simulated specimens are shown in Table 1. When preparing the small specimens, due to the size relationship between the coarse and fine particles, the total number of particles is very close to an integer when the total number of particles is 2550. After adjusting the interparticle sliding friction coefficient during consolidation under confining pressure to 0.36, the porosity ratio is 0.5065. Using eight parallel computing threads, the preparation of each small specimen takes approximately 30 minutes. Substituting the sample preparation results into the above three-dimensional formula (1), the number of particles required for the numerical simulation is 20249. The other parameters are the same as those for the prefabricated small sample. Under the same number of computer threads, after a total sample preparation process of 6 hours, the required simulation sample with a size of 29.89mm×29.85mm×29.91mm and a porosity of 0.507 is obtained. The results are as follows: Figure 3b and Figure 4b As shown, the parameter error is within the allowable range. If the small specimens were not prefabricated in this example, and the parameters of the simulated specimens were simply adjusted repeatedly for debugging, it would take "6 hours" to perform trial calculations, which would obviously consume a lot of time.

[0062] In summary, the rapid sample preparation method provided by this application is particularly suitable for the preparation of samples of wide-graded granular materials. For such granular materials, the discontinuity of their particle gradation is large, and they appear as binary or even multi-component mixtures. The number of particles of different particle sizes may differ by two or three orders of magnitude. In the discrete element method, the amount of calculation per time step is large, and the time spent is correspondingly long. In other words, it is not limited to the case of single particle size samples and binary mixtures, but is also applicable to multi-component mixtures and continuously graded samples. The key lies in the prefabrication and "scale-up" of small samples ( Figure 2 As shown in the figure, when preparing samples with larger sample size under the conditions of specified density and specified wide gradation, the trial calculation of sample preparation required for simulation is skipped and the trial calculation of small sample with relatively smaller calculation amount is used instead. Then, through "zooming in", the sample preparation that requires a lot of time for trial calculation can be completed almost at one time.

[0063] The calculation formula involved in the rapid sample preparation method provided by this application can achieve good results in actual operation, but it does not mean that this formula is obtained through strict logical reasoning, but exists as an empirical formula. The actual discrete element numerical simulation software has the randomness of particle distribution when generating particles, and there may be times when large errors occur, but generally speaking, the effect of this application on accelerating the overall speed of sample preparation is significant and the sample preparation effect is also good. At the same time, this application is not a discrete element numerical simulation acceleration method in the strict sense, but skips some sample preparation trial calculation processes that can be omitted, so that it can achieve the effect of accelerating the overall sample preparation process.

[0064] It has been verified that the method of prefabricating small specimens in the rapid sample preparation method provided by this application significantly reduces the time cost of discrete element numerical simulation. The calculation formula involved is relatively simple, involving only general geometric operations, but the effect it brings is not only applicable to the preparation of samples of a specified larger size under specified density and specified wide gradation conditions, but also to the preparation of samples requiring only an order of magnitude larger number of particles under the same conditions. At the same time, the same analogy can be applied to the preparation of samples under two-dimensional conditions.

[0065] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such herein, will not be interpreted in an idealized or overly formal sense.

[0066] The meaning of "and / or" in this application means that both situations where each exists alone or both exist at the same time are included.

[0067] The term “connection” as used in this application may mean a direct connection between components or an indirect connection between components via other components.

[0068] With the above-described preferred embodiments of the present invention as a guide, and with reference to the above description, relevant personnel are fully capable of making various changes and modifications without departing from the technical scope of this invention. The technical scope of this invention is not limited to the contents of the specification and must be determined according to the scope of the claims.

Claims

1. A method for rapid sample preparation of widely graded granular materials suitable for discrete element analysis, characterized in that: The specific steps include: Step S1: Prepare a small sample in advance; include: Step S11: setting the parameters required for preparing a small sample and generating n number of sample particles; Step S12: Set the required sliding friction coefficient and apply the required confining pressure, and after stabilization, obtain a porosity ratio of e n Small specimens; Step S13: Determine whether the void ratio in step S12 meets the requirements. If so, proceed to step S14. If not, adjust the sliding friction coefficient and proceed to step S12. Step S14: determining the particle size of the small sample with a void ratio meeting the conditions; Step S2: By using the principle of geometric similarity, the prepared small sample is enlarged to obtain the required number of particles of the simulated sample; The particle size of the small sample is determined according to step S14, and the particle size of the simulated sample required under three-dimensional conditions is obtained. The calculation formula is: In formula (1), n ​​is the number of particles in the small sample, N is the number of particles in the required simulated sample, and V n is the volume of the small sample, V n is the volume of the required simulated sample; Obtain the particle size of the simulated sample required under two-dimensional conditions. The calculation formula is: In formula (2), n is the number of particles in the small sample, N is the number of particles in the required simulated sample, and S n is the area of ​​the small specimen, S is the area of ​​the required simulated specimen; Step S3: Set parameters and prepare the required simulation samples.

2. The method for rapid sample preparation of wide-graded granular materials suitable for discrete element analysis according to claim 1, characterized in that: In step S13, the porosity ratio of the simulated sample required for simulation is set to e. If e n ≠e, the required confining pressure is reapplied after adjusting the sliding friction coefficient in the numerical simulation.

3. The method for rapid sample preparation of wide-graded granular materials suitable for discrete element analysis according to claim 2, characterized in that: The steps to adjust the sliding friction coefficient are: If e n <e, then increase the preset sliding friction coefficient; if e n >e, the preset sliding friction coefficient is reduced.

4. The method for rapid sample preparation of wide-graded granular materials suitable for discrete element analysis according to claim 1, characterized in that: In step S3, after determining the particle size of the small sample according to step S2 to obtain the required number of particles N of the simulation sample, continue to apply the preset confining pressure and sliding friction coefficient, and after stabilization, obtain the required simulation sample with a porosity ratio of e.

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