CN112380736B - Discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution - Google Patents
Discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution Download PDFInfo
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Abstract
The invention discloses a discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution, which comprises the following steps:step one, measuring the crushing strength of single particles and counting the strength characteristic value sigma of weibull distribution0And weibull modulus m; step two, measuring the size effect of the particle strength; step three, determining the corresponding relation of macro and microscopic intensity: f (sigma)micro) σ; step four, determining the corresponding relation between the particle size and the macroscopic strength: (d) ═ σ; step five, generating a particle discrete element model; assigning values to corresponding BCM particle models; and seventhly, circulating the step six, and assigning values to the particles contained in the N groups of each particle size group until all the parameters are assigned successfully. Has the advantages that: the particle crushing strength distribution of the constructed discrete element model is consistent with the actual situation. The calculation principle is simple, the calculation program is simple and efficient, and the actual particle crushing strength characteristics can be effectively reflected. Provides an effective technical means for further understanding the mechanical behavior of the breakable particle material.
Description
Technical Field
The invention relates to a discrete element model construction method, in particular to a discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution.
Background
At present, brittle granular materials are widely used in the geotechnical engineering fields including rockfill dams, dykes and dams, highways, railways and the like. The particles break up after the external load on the particles exceeds the strength of the particles themselves. Typically, single particle compression crushing laboratory experiments are used to indirectly measure particle strength σ (σ ═ F/d)2) Where F is the peak force recorded for the top plate throughout the loading process and d is the particle size. The internal structure of the brittle particles is subject to large variability due to the complex external environmental conditions during particle formation. Therefore, even if the particles are similar in shape and have similar particle sizes, the crushing strength of the particles shows significant statistical variability. For a certain lithologic particle material in a certain particle size interval, the crushing strength value accords with a certain random distribution. Scholars at home and abroad generally adopt weibull function to describe randomness of particle strength in splittingThe survival probability Ps of the particles under the action of tensile stress is as follows:
in the formula: sigma0The intensity characteristic value represents that the sample with 1/e (e is a natural constant, and 1/e is approximately equal to 37%) can survive under the stress; m is the weibull modulus, the strength dispersion is described quantitatively, and the larger m is, the lower the strength dispersion is; ps is the probability of survival of a particle under a particular stress, defined as:
in the formula, N is the number of particles used in the compression crushing experiment; i is the order corresponding to the ascending order of the particle crushing strength. In addition, the size effect of the crushing strength of the particles is obvious, and the relationship between the strength characteristic value and the particle size can be expressed as sigma by a power function0∝db. For a particular particle lithology, the value of b is constant and is generally taken to be
Since Cundall and Strack proposed the concept of discrete elements in 1979, discrete element simulation gradually became an effective means for researching the initial structure of the particle material, the crushing characteristics under complex stress loading conditions, the size effect of the discrete material, the crushing macro-micro constitutive model and the like. Generally, the BCM (bound cell model) method is widely used to simulate particle crushing. The method is to stick a plurality of units (generally coplanar polyhedrons or tangent spheres) together by adhesive force to simulate particles, wherein when external load is larger than the adhesive force between the units, the inner part of the particles is damaged, and when the damage is accumulated and penetrated, the particles are subjected to macroscopic crushing. However, in the discrete element modeling stage, how to realize the weibull distribution of the particle crushing strength and the size effect in the particle material is always a difficult problem. Although Mcdowell et al suggest that the weibull distribution of particle crush strength is achieved empirically by methods that remove 0-25% of the units. However, this method has the following drawbacks: one is that the particles exhibit a porous character when the particles remove too many units (e.g., 20%), which is not in accordance with practice. In addition, although this method can achieve weibull distribution, the strength characteristic value, weibull modulus and size effect of the particles are difficult to control. That is, it is extremely difficult to completely reflect the discreteness of the experimental results of the particle crushing strength in the discrete meta-model construction. Based on the above technical current situation, it is necessary to provide a solution to realize accurate control of single-particle crushing strength weibull distribution during discrete element model construction.
Disclosure of Invention
The invention aims to provide a discrete element model construction method for realizing the accurate control of single-particle crushing strength weibull distribution during the construction of a discrete element model.
The invention provides a discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution, which comprises the following steps:
step one, selecting a set number N of equal-particle-size particles to perform a single-particle compression crushing indoor experiment, measuring the crushing strength of single particles, and counting the strength characteristic value sigma of weibull distribution0And weibull modulus m;
step two, similar to the step one, selecting a set number N of equal-particle-size particles with different particle sizes from the step one again to perform a single-particle compression crushing indoor experiment, and measuring the size effect of the particle strength;
step three, calibrating the corresponding relation of macro and microscopic intensity parameters: establishing a single-particle discrete element model, and continuously performing a single-particle compression crushing simulation experiment on the basis of continuously modifying the microscopic intensity to determine the corresponding relation of the macroscopic intensity: f (sigma)micro)＝σ；
Step four, the particle size of the single-particle discrete element model is zoomed under the condition that other parameters are kept unchanged, and a single-particle compression crushing simulation experiment is carried out to determine the corresponding relation between the particle size and the macroscopic strength: (d) ═ σ;
step five, under the condition that the particle grading generated in the discrete element program is basically consistent with the target grading, generating a particle body discrete element model, ensuring that the number of particles with various particle diameters is a multiple of the number of the particles used in the test in the step one, and dividing the particles into M groups based on M particle diameter particles, wherein the groups are respectively named as 1, 2, … …, (M-1) and M; on the premise of not covering the former naming, dividing the granules with each particle size into N groups, respectively naming the N groups as 1, 2, … …, (N-1), wherein N and N are the number of the granules used in the testing in the step one;
step six, calculating the strength characteristic value sigma of particle crushing corresponding to a certain particle size based on the results of the step one and the step two0Calculating the Ps value of each particle group in the particle size range based on the fifth step, and calculating the intensity characteristic value sigma based on the intensity characteristic value0And determining the macroscopic strength parameters of each group in the particles with a certain particle size according to the Weibull function, the Ps value and the modulus m, deducing the microscopic strength parameter value according to the results of the third step and the fourth step, and assigning the microscopic strength parameter value to a corresponding BCM particle model. Here, the BCM particle model refers to a breakable discrete elementary particle model composed of several coplanar polyhedrons or tangent spheres stuck together;
and seventhly, circulating the step six, and assigning values to the particles contained in the N groups of each particle size group until all the parameters are assigned successfully.
And (3) setting the number of the particles with the equal particle size tested in the step one as 30, so as to reflect the statistical variability of the crushing strength of the particles with the equal particle size. In addition, it is necessary to ensure that the selected particles come from the same place of production and have the same lithology.
And in the second step, selecting a plurality of groups of particles with equal particle size to carry out indoor experiments so as to accurately determine the size effect of the particle strength and obtain a quantitative relational expression of the strength characteristic value and the particle size. In addition, it is necessary to ensure that the selected particles are the same as the particles used in step one in origin and lithology.
In the third step, the single-particle discrete element model is a simplified spherical model or a complex irregular model which is the same as the experiment, the units forming the single-particle model are polyhedrons or spheres, and the number of the units needs to be predetermined to ensure that the number of the units hardly influences the crushing strength of the particles.
In the fourth step, attention is paid to control variables, and it is required to ensure that the geometric parameters and the microscopic parameters are consistent except for different particle sizes, such as the number of units forming a single particle, and the microscopic rigidity values and microscopic strength values among the units.
In step five, the particle materials are required to be ensured to be randomly generated in the discrete element program. The grouping designations relating to particle size and the grouping designations of particulate material of a certain particle size are not mutually overrideable.
When the particle crushing strength characteristic value is calculated in the sixth step, the particle size corresponding to each particle size group needs to be input in the array of the discrete element program in advance, and the ordering of the particle sizes in the array is ensured to be the same as the naming of the particle groups. For example, when the array a (2) is 10, particles having a particle size of 10mm are all named "2".
The invention has the beneficial effects that:
the invention provides a discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution. The method is characterized in that on the basis of obtaining various macro intensity parameters of indoor experiments, the macro intensity parameters and the micro intensity parameters are converted into target micro intensity parameters of particles in a discrete element model according to the corresponding relation of the macro intensity parameters and the micro intensity parameters. And two levels of grouping naming are carried out on the basis of the generated particle model, wherein the first level corresponds to the particle size, and the second level corresponds to the weibull distribution under the equal particle size. Assignment of the mesoscopic intensity parameters to the target particles is achieved based on grouping and naming. The particle crushing strength distribution of the discrete element model constructed by the method is very consistent with the actual situation. The calculation principle is simple, the calculation program is simple and efficient, and the actual particle crushing strength characteristics can be effectively reflected. Provides an effective technical means for further understanding the mechanical behavior of the breakable particle material. And when the single particle crushing strength meets other types of distribution, such as normal distribution, chi-square distribution and the like, the method can still be applied.
Drawings
FIG. 1 is a schematic flow chart of a method for accurately controlling the single-particle crushing strength weibull distribution.
FIG. 2 is a schematic diagram of the experimental method of the present invention for counting the distribution of the particle crushing strength weibull.
FIG. 3 is a schematic diagram of a simulation experiment for single particle compression crushing according to the present invention.
FIG. 4 is a schematic diagram of the particle fracture macro-meso-intensity relationship corresponding to the discrete element simulation of the present invention.
FIG. 5 is a schematic diagram illustrating the particle size effect corresponding to discrete element simulation according to the present invention.
FIG. 6 is a schematic diagram of the particle size distribution and the spatial distribution of the particles of the present invention.
FIG. 7 is a flowchart illustrating a method for determining and assigning a value to a particle meso-scale intensity in a discrete meta-model according to the present invention.
FIG. 8 is a schematic diagram showing the distribution of the crushing strength weibull of the particles with different particle sizes simulated by the invention.
FIG. 9 is a graphical representation of simulated particle intensity characteristic versus particle size in accordance with the present invention.
Detailed Description
Please refer to fig. 1 to 9:
the invention provides a discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution, which comprises the following steps:
step one, selecting a plurality of particles with equal particle sizes to perform a single particle crushing indoor experiment, and measuring the single particle crushing strength. Selecting 30 calcium sand particles with the particle size of 20mm and the shape similar to a sphere to carry out single particle crushing experiment, and counting to obtain the crushing strength value sigma of the calcium sand particles0And weibull modulus m. The weibull distribution is shown in figure 2: weibull modulus m is 3, strength characteristic value sigma0The product shows good weibull distribution rule (R2 is 0.98) under 9 MPa.
Step two, continuously selecting the equal-particle-size particles with different particle sizes from the step one to perform a single-particle compression crushing indoor experiment, and determining the size effect of the particle strength, namely the strength characteristic value sigma0The particle size d of the particles. The slope of the linear relationship of the two logarithms is set to-3/m. I.e. the characteristic value σ of the particle strength0The following formula is satisfied between (unit: MPa) and the particle diameter d (unit: mm):
step three, establishing a single-particle discrete element model: the particle model is constructed mathematically (e.g., spherical harmonics) or a real particle model is acquired by a 3D scanner, then the particle model is divided into several coplanar polyhedrons or the model is filled with tangent spheres, and then mesoscopic intensity values are assigned between the cells. Under the action of gravity, the single-particle model is made to stand still on the fixed bottom plate, and a top plate for pressurization is generated at the highest point of the particle model. The top plate is moved downward at a very small and constant speed, with the bottom plate stationary, until the particles are broken. In the process, the stress condition of the top plate is recorded in real time. The shape of the constructed discrete element value sample is spherical, the particle size value d is 20mm, and each particle model is divided into 100 coplanar Thiessen polyhedron units by adopting a Neper open source program package, which is shown in figure 3. And (3) assigning a microscopic strength parameter to the single-particle model, and then carrying out a single-particle compression crushing simulation experiment to obtain a corresponding macroscopic strength value. And continuously modifying the microscopic intensity parameter to obtain a corresponding macroscopic intensity value so as to determine the quantitative relation between the microscopic intensity parameter and the macroscopic intensity value. Both showed good linear correlation as shown in fig. 4 (R2 ═ 0.997).
And step four, modifying the particle size d of the particles on the basis of ensuring that the shape parameters and the microscopic parameters of the particle model are not changed, so as to obtain the correlation between the particle size d of the particles and the macroscopic strength sigma. Particle sizes contemplated include: 20.0mm, 17.5mm, 15.0mm, 12.5mm, 10.0mm and 7.5 mm. The correlation results are shown in fig. 5, and the macroscopic strength value of the particles is basically kept unchanged with the increase of the particle size, which shows that the macroscopic strength is closely related to the microscopic strength and is basically not influenced by the particle size of the particle model.
And step five, generating a plurality of particles in a certain space range according to the target gradation. And to ensure that the number of particles per particle size is a multiple of the number of particles used in the step one test. The granular materials are named in groups according to the following naming rules: the particles with M particle sizes are respectively divided into groups and named as 1, 2, … …, (M-1), M, and M groups are named for the first layer; on the basis, the number N of the particles adopted in the step one for each group of particles is further divided into N groups and named as 1, 2, … …, (N-1) and N respectively. As shown in fig. 6, the particle size distribution and the spatial distribution have 6 kinds of particle sizes in total, and thus, the particle size distribution and the spatial distribution are divided into 6 groups (M: 6) and each group is divided into 30 groups (N: 30). The particle size of each group of the first level is input into the array of the discrete element program. For example, if the array a (3) is 15.0, then the first level of nomenclature is that particles having a particle size equal to 15mm are all named "3".
Step six, performing double circulation in a discrete element program according to the graph shown in fig. 7, wherein the external circulation is 1-M, mainly aiming at particles with different particle sizes, and M is the grouping number based on the particle sizes in the step 5; the internal circulation is 1-N, mainly aiming at the statistical variability of the strength of the particles with the equal particle size, and the value of N is the number of the particles used in the first step. Extracting corresponding particle diameter in each external circulation and calculating intensity characteristic value sigma corresponding to the particle diameter0. An inner loop is then performed, assigning a mesoscopic intensity to the particles contained in a certain group at a certain particle size. And circulating M times by N times. For example, in the present invention, the particle diameter dj corresponding to the array a (j) is extracted in the jth pass of the external circulation, and the intensity characteristic value σ corresponding to the particle diameter dj is obtained from the relational expression between the particle diameter and the intensity characteristic value0Taking the ith group of particles with the particle size, and calculating the Ps value (P)s1-i/(N + 1)); based on known intensity characteristic values sigma0And calculating a macroscopic intensity value corresponding to the ith group of particles according to a weibull function, and then converting the obtained relational expression of the macroscopic intensity value and the microscopic intensity value to obtain the size of the microscopic intensity value to be assigned to the particles contained in the ith group of particle sizes.
And seventhly, repeating the steps in the same way and continuously circulating. Finally, assignment of the used particle size particles is realized. And (3) performing single-particle compression crushing simulation on the particles with different particle sizes according to the steps from one step to six, and obtaining the statistics of macroscopic strength values shown in figure 8. As can be seen from the figure, the particle strength corresponding to each particle size is well in accordance with the weibull distribution (R2 is more than or equal to 0.99). The weibull modulus m is between 2.8 and 3.0, which is very close to the experimental result (m is 3.0). In addition, fig. 9 shows a particle strength characteristic value σ0Size effect plot of (1). As can be seen from the graph, the relationship between the characteristic intensity value and the particle size is very goodThe predetermined relational expression (R2 ═ 0.95) is satisfied. The results of fig. 8 and 9 demonstrate that the method can realize accurate control of the particle crushing strength weibull distribution.
Claims (5)
1. A discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution is characterized by comprising the following steps: the method comprises the following steps:
step one, selecting a set number N of equal-particle-size particles to perform a single-particle compression crushing indoor experiment, measuring the crushing strength of single particles, and counting the strength characteristic value sigma of weibull distribution0And weibull modulus m;
step two, similar to the step one, selecting a set number N of equal-particle-size particles with different particle sizes from the step one again to perform a single-particle compression crushing indoor experiment, and measuring the size effect of the particle strength;
step three, calibrating the corresponding relation of macro and microscopic intensity parameters: establishing a single-particle discrete element model, and continuously performing a single-particle compression crushing simulation experiment on the basis of continuously modifying the microscopic intensity to determine the corresponding relation of the macroscopic intensity: f (sigma)micro)＝σ；
Step four, the particle size of the single-particle discrete element model is zoomed under the condition that other parameters are kept unchanged, and a single-particle compression crushing simulation experiment is carried out to determine the corresponding relation between the particle size and the macroscopic strength: (d) ═ σ;
step five, under the condition that the particle grading generated in the discrete element program is basically consistent with the target grading, generating a particle body discrete element model, ensuring that the number of particles with various particle diameters is a multiple of the number of the particles used in the test in the step one, and dividing the particles into M groups based on M particle diameter particles, wherein the groups are respectively named as 1, 2, … …, (M-1) and M; on the premise of not covering the former naming, dividing the granules with each particle size into N groups, respectively naming the N groups as 1, 2, … …, (N-1), wherein N and N are the number of the granules used in the testing in the step one;
step six, calculating the strength characteristic value sigma of particle crushing corresponding to a certain particle size based on the results of the step one and the step two0Calculating the Ps value (P) of all particle groups corresponding to the particle size based on the fifth steps1-i/(N + 1)); and based on the intensity characteristic value sigma0Determining the macroscopic strength parameters of each group in the particles with a certain particle size according to the Weibull function, the Ps value and the modulus m, deducing the microscopic strength parameter value according to the results of the third step and the fourth step, and assigning the microscopic strength parameter value to a corresponding BCM particle model; here, the BCM particle model refers to a breakable discrete elementary particle model composed of several coplanar polyhedrons or tangent spheres stuck together;
and seventhly, circulating the step six, and assigning values to the particles contained in the N groups of each particle size group until all the parameters are assigned successfully.
2. The discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution according to claim 1, characterized in that: the statistical variability of the crushing strength of the equal-particle-diameter particles can be reflected by setting the number of the equal-particle-diameter particles experimentally tested in the step one to be 30, and the particles need to be from the same producing area and have the same lithology.
3. The discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution according to claim 1, characterized in that: selecting a plurality of groups of particles with equal particle size in the second step to carry out an indoor experiment so as to accurately determine the size effect of the particle strength and obtain a quantitative relation between the strength characteristic value and the particle size; the origin and lithology of the particles used were identical to those of the particles used in step one.
4. The discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution according to claim 1, characterized in that: in the third step, the single-particle discrete element model is a simplified spherical model or a complex irregular model which is the same as the experiment, the units forming the single-particle model are polyhedrons or spheres, and the number of the units needs to be predetermined to ensure that the number of the units hardly influences the crushing strength of the particles.
5. The discrete element model construction method for realizing accurate control of single-particle crushing strength weibull distribution according to claim 1, characterized in that: when the particle crushing strength characteristic value is calculated in the sixth step, the particle size corresponding to each particle size group needs to be input in the array of the discrete element program in advance, and the ordering of the particle sizes in the array is ensured to be the same as the naming of the particle groups.
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