A method for constructing a particle characteristic breakage strength prediction model, and a model constructed thereby

Abstract

The present application relates to a kind of granule characteristic breaking strength prediction model construction method, model constructed by it.The method of the present application does not rely on spherical assumption, but the contact mechanics mechanism of real granule topography is established prediction model.In prediction model, particle size d0, sphericity S V And roundness R are three independent variables, each corresponds to explicit physical meaning;When the shape of particle changes, directly input new topography parameter can obtain differentiated prediction result.The present application provides a kind of granule characteristic breaking strength prediction model for calcareous sand particles, can directly carry out the prediction of unknown calcareous sand particle characteristic breaking strength during construction.When facing quartz sand, artificial aggregate, rockfill material and other granular materials, only need to use the method of the present application, combine the indoor or numerical test results corresponding to material, reconstruct the prediction model of granule characteristic breaking strength.

Description

Technical Field

[0001] This invention belongs to the technical field of rock and soil granular materials research, specifically involving a method for constructing a particle characteristic fracture strength prediction model, the constructed model, and the particle characteristic fracture strength prediction method. Background Technology

[0002] Particulate materials (such as calcareous sand, quartz sand, riprap, and ballast) are widely used in hydraulic engineering, geotechnical engineering, and transportation engineering. The shape characteristics of particles at different scales (including overall morphology at a large scale, roundness of edges and corners at a medium scale, and surface roughness at a small scale) significantly affect the contact mechanical behavior between particles (including particle slippage and interlocking), thus influencing the macroscopic mechanical response characteristics of particles, including crushing behavior, compressibility, shear strength, expansion, internal friction angle, and permeability. Therefore, accurately characterizing and quantifying the influence of particle morphology on its mechanical behavior, especially crushing strength, has significant engineering implications and scientific value.

[0003] Chinese invention patent CN121637939A discloses "A method and system for simulating particle breakage size effect based on discrete element method". This method has the following shortcomings: (1) The particle shape is simplified to spherical. All simulations are based on spherical aggregates, while in actual engineering, a large number of particles have irregular angular or needle-like shapes. (2) The fitting formula only contains one independent variable, particle size, and does not involve multi-scale characterization and quantitative analysis of particle morphology. The method cannot separate the independent contributions of each factor, nor can it distinguish the differential effects of different scale morphological characteristics (overall sphericity, angular roundness, etc.) on breakage behavior. When the particle shape changes, it cannot give differential predictions. Chinese invention patent CN 118329591 A discloses "a method for determining the crushing strength of calcareous soil particles of different sizes and shapes". This patent method has the following defects: (1) The patent uses a single-scale shape factor, which uses a simple shape factor based on length, width and height, and confuses all shape characteristics of particles; (2) When modeling, the patent uses manual selection of macroscopic shapes (block, sheet, rod), which cannot obtain continuous quantitative values ​​and cannot control the individual changes of single shape indicators. In addition, in this patent method, the shape factor only affects the overall strength as a multiplicative term. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a method for constructing a particle characteristic fracture intensity prediction model, comprising the following steps: S1 selects particle samples of the same material type, obtains their three-dimensional morphology data, and obtains the following three parameters: equivalent particle size d0, sphericity S V and roundness R; S2 uses the same type of granular material with the same sphericity obtained in step S1.V For multiple groups of particle samples with the same roundness R but different equivalent particle sizes d0, the functional relationship between the size effect index α and roundness R was obtained as α=f(R). S3 uses the same type of particulate material obtained in step S1, with the same roundness R and the same equivalent particle size d0, but different sphericity S. V Multiple sets of particle samples were used to obtain the material constant χ and the sphericity effect index β. S4 Substitutes the α obtained in step S2, the χ and β obtained in step S3 into the prediction model formula to obtain the prediction model of the particle characteristic crushing strength of this type of material. The prediction model is as follows: In the formula, d0 is the equivalent particle size, and S V Let α be the sphericity of the particles, and α be the size effect index of the particles. χ is the particle size parameter, β is the material constant, and β is the sphericity effect exponent.

[0005] Based on the above scheme, the specific method of step S2 is as follows: The crushing strength σ is obtained through single-particle flat plate compression numerical tests or laboratory tests until total failure. f and representative value The maximum contact force when the particle breaks down as a whole is denoted as F. f ,according to Calculate the crushing strength; take the average of 5 samples at each particle size level as the representative value for that particle size. ; Using α as the feature intensity in double logarithmic coordinates By fitting the slope of the straight line with the equivalent particle size d0, multiple (R, α) data pairs are obtained. By fitting the data pairs, a functional relationship α=f(R) between α and R is established.

[0006] Based on the above scheme, the specific method of step S3 is as follows: The characteristic breaking strength σ0 under various sphericities was obtained through single-particle flat plate compression numerical tests or indoor tests; the α value corresponding to the sphericity R was calculated using the functional relationship α=f(R) determined in step S2, and the values ​​of each group (S) were then compared. V Substituting the data (σ0) into the prediction model, the material constant χ and the sphericity effect index β are obtained by joint fitting using the least squares method.

[0007] Based on the above scheme, the specific method for obtaining the three-dimensional morphology data of the particles in step S1 is as follows: A coarse-grained triangular mesh model database is obtained through methods such as CT scanning or 3D laser scanning. Using the models in this database as the basic geometry, multi-view image reconstruction of particles is performed.

[0008] Based on the above scheme, a noise superposition algorithm is used when reconstructing multi-view images of particles.

[0009] This invention also provides a method for predicting the characteristic fracture intensity of particles, using the model constructed by the above-described method for predicting the characteristic fracture intensity of particles. Specifically, it includes the following steps: (1) Obtain the three morphological parameters of the particle to be predicted: equivalent particle size d0, sphericity S V and roundness R; (2) The size effect index α of the particle is determined by the roundness R; (3) Calculate the characteristic crushing strength; The equivalent particle size d0 and sphericity S obtained in step (1) are used to... V The size effect index α obtained in step (2), and the calibrated constants. Substituting χ and β into the prediction model formula, we obtain the characteristic crushing strength σ0 of the predicted particles.

[0010] The beneficial effects of this invention are: The model and method of this invention do not rely on the sphericity assumption, but instead establish a predictive model based on the contact mechanics mechanism of real particle morphology. In the predictive model, particle size d0 and sphericity S are... V The roundness R (entered into the formula via α=f(R)) are three independent variables, each with a clear physical meaning; when the particle shape changes, the differential prediction results can be obtained by directly inputting the new morphology parameters. This invention addresses the roundness S... V And roundness R as an independent explicit variable, S V By controlling the intensity level (as the base) and R (which controls the strength of the size effect via α as the exponent), differentiated prediction results can be obtained for particles of different shapes. The model of this invention quantifies the differentiated control laws of morphology at different scales.

[0011] This invention provides a predictive model for the characteristic crushing strength of calcareous sand particles, allowing for direct prediction of the unknown characteristic crushing strength of calcareous sand particles during construction. When dealing with other granular materials such as quartz sand, artificial aggregates, and riprap, the method of this invention, combined with the results of corresponding indoor or numerical tests, can be used to reconstruct the predictive model for the characteristic crushing strength of the particles.

[0012] In practical engineering applications, this invention only requires calibration of the coefficients in the prediction formula using a small number of representative particles through plate compression tests to complete model adaptation. There is no need to conduct mechanical tests on each particle individually, which significantly shortens the field test cycle and reduces testing costs. Furthermore, the formula structure is universal and applicable to various granular materials such as quartz sand, calcareous sand, artificial aggregate, and riprap. Attached Figure Description

[0013] Figure 1 Comparison of the size effect strength of crushing strength of particles with the same roundness but different sphericity; Figure 2 Comparison of the size effect strength of crushing strength of particles with the same sphericity but different roundness; Figure 3 This is a fitting curve of parameter α in Example 2; Figure 4 Survival probability curves for particles with different sphericity; Figure 5 Normalized curves for the generation probability of particles with different roundness; Figure 6 The characteristic intensity and Weibull parameter variation of particles with different sphericity; Figure 7 The fitted curves for parameters χ and β; Figure 8 The model validation results are for sample A; Figure 9 The model validation results are for sample B; Figure 10 The model validation results are for sample C; Figure 11 The model validation results are for sample D. Detailed Implementation

[0014] The terminology used in this invention, unless otherwise specified, generally has the meanings commonly understood by those skilled in the art. The invention is further described in detail below with reference to specific embodiments and data. The following embodiments are merely illustrative and are not intended to limit the scope of the invention in any way.

[0015] Unless otherwise specified, the experimental methods used in the following embodiments are conventional methods, performed according to the techniques or conditions described in the literature in this field or according to the product instructions. Unless otherwise specified, the experimental materials, reagents, and chemicals used in the following embodiments can be obtained through general channels.

[0016] Example 1

[0017] This invention provides a particle breakage strength prediction model that considers multi-scale morphology and size effects. The model is constructed by the following method: Step S1: Obtain three morphological parameters of the particle sample group. A group of particle samples of the same material type was selected, and a coarse-grained triangular mesh model database was obtained through CT scanning or 3D laser scanning. Using the models in this database as the basic geometry, multi-view image reconstruction of the particles was performed to obtain their 3D morphology data and calculate the following three parameters: (a) Equivalent particle size d0: d0 = (d1 + d2 + d3) / 3, where d1, d2, and d3 are the lengths of the major axis, median axis, and minor axis of the particle, respectively. This definition method has been verified by research to better reflect the influence of particle shape on crushing strength than other methods such as the spacing between loading plates.

[0018] (b) Sphericity S V S is defined as the ratio of the surface area of ​​a sphere with the same volume as the particle to the actual surface area of ​​the particle. V The closer the value is to 1, the closer the overall shape of the particle is to a sphere. Sphericity is a large-scale morphological parameter.

[0019] (c) Roundness R: Defined as the arithmetic mean of the ratio of the radius of curvature at each corner of the particle to the radius of the inscribed sphere of the particle. The closer R is to 1, the smoother the corners of the particle. Roundness is a mesoscale morphological parameter.

[0020] Step S2: Determine the functional relationship between the size effect index α and roundness R: α = f(R) Select the same sphericity S from the particle sample group V The failure strength σ of multiple groups of particles with the same roundness R but different equivalent particle size d0 was obtained through single-particle plate compression numerical tests or laboratory tests until overall failure. f and representative value The specific calculation method is as follows: The maximum contact force when the particles break apart as a whole is denoted as F. f According to Hiramatsu's research, it can be arranged as follows: Calculate the crushing strength. Take the average value for each particle size level as the representative value for that particle size. .

[0021] Lee proposed that the relationship between particle size and representative characteristic intensity values ​​can be described by a power-law relationship: (where α is the representative value of feature intensity in double logarithmic coordinates) The slope of the straight line fitted to the equivalent particle size d0 can be used to fit and obtain the size effect index α corresponding to the roundness R.

[0022] Keeping other material conditions constant, only changing the roundness R of the selected particle samples, the above process is repeated to obtain multiple (R, α) data pairs. Fitting these data pairs establishes a functional relationship between α and R: α = f(R). This functional relationship is approximately linear: α = a·Rb, where a and b are fitting constants related to the particle material. The physical meaning of the function is: the lower the roundness R (the sharper the particle edges), the larger |α|, and the stronger the size effect; the higher the roundness R (the smoother the particles), the smaller |α|, and the weaker the size effect.

[0023] For a particle with a certain size effect index α to be measured, the roundness R obtained in step S1 can be substituted into the functional relationship α=f(R) to calculate the size effect index α corresponding to the particle.

[0024] Step S3: Establishing the prediction formula The prediction formula of this invention is constructed according to the following logic: (a) Following the framework of the power law function, the basic form is tentatively defined as the characteristic fracture intensity. , where C and α are parameters to be determined.

[0025] (b) From S1, we know that α is a function of roundness R: α = f(R). The basic form is then updated to... .

[0026] (c) The constant term C is not a fixed value, but varies with the sphericity S. V It increases significantly, and σ0 is related to... Since they are directly proportional, C should include a term reflecting the contribution of sphericity.

[0027] (d) Sphericity S V The effect on the absolute value of strength is much greater than that on roundness R. Therefore, sphericity S V The roundness R should be directly entered into the formula as an independent variable controlling the absolute level of intensity (as the base term), while the roundness R is only used as an adjustment variable controlling the strength of the size effect (entering the exponential position through α). This allocation of physical roles is the core feature of the formula structure of this invention.

[0028] Based on the above analysis, C can be decomposed into a constant χ reflecting the inherent properties of the material and a factor reflecting the contribution of sphericity. For the purpose of dimensional normalization, this invention takes d. ref =1mm, which is only used as a reference length for dimension normalization and does not represent a specific physical scale, nor does it need to be recalibrated under different modeling or material conditions. The complete prediction formula is as follows: In the formula: d0 is the equivalent particle size; S V α represents the sphericity of the particles; α is the size effect index of the particles. χ is the particle size parameter, taken as 1 mm; χ is the material constant; β is the sphericity effect index.

[0029] Step S4: Calibrate the material constant χ and the sphericity effect index β Select particle sample groups with the same roundness R and the same equivalent particle size d0, but different sphericity S V Multiple groups of particle samples were subjected to single-particle plate compression numerical tests or indoor tests until overall failure to obtain the fracture strength σ. f Because the fragmentation strength data of a single particle has strong dispersion, even particles with identical shape and size will exhibit random fluctuations in their fragmentation strength. Therefore, the fragmentation strength of a single particle cannot be directly used to represent the overall mechanical properties of the morphology group. Instead, statistical methods are needed to extract representative indicators from a set of experimental data. The fragmentation strength is processed using statistical methods to obtain its characteristic fragmentation strength σ0. The specific processing method is as follows: This invention uses the Weibull distribution to describe the statistical law of particle crushing intensity. The Weibull distribution is a widely used statistical model in particle crushing research, and its form is as follows: In the formula, P represents the crushing strength of the particles. s In stress The probability that the next particle will not break (i.e., the survival probability); For characteristic intensity (corresponding to P) s (The breaking strength is approximately 37%); m is the Weibull modulus, used to characterize the dispersion of breaking strength. The larger the value of m, the smaller the dispersion of breaking strength.

[0030] For a set of particles with known crushing strength data, the following procedure is followed to determine... and m: (a) Crushing strength of 30 particles Sort by size from smallest to largest.

[0031] (b) The survival probability of each particle is estimated using the average ranking method: Where i is the index sorted by crushing strength from smallest to largest, and N t This represents the total number of particles tested.

[0032] (c) For the formula Taking the natural logarithm twice on both sides, we get: This formula shows that, With ln(σ f The relationship between the two is linear, and the slope of the straight line is the Weibull modulus m.

[0033] (d) ln(σ) f Using π as the x-axis and ln[ln(1 / Ps)] as the y-axis, plot 30 data points on a coordinate system and perform linear regression. The slope of the regression line is the Weibull modulus m. The σ corresponding to the point ln[ln(1 / Ps)]=0 is... f The value is the characteristic strength. .

[0034] The above method can be used to calculate different sphericities S. V The characteristic strength σ0 of the particles. Using the functional relationship α=f(R) determined in step S2, calculate the α value corresponding to the roundness R of this group of particles, and then assign the (S) value of this group of particles to the α value. V Substituting the data (σ0) into the prediction model formula, the material constant χ and the sphericity effect index β are obtained by joint fitting using the least squares method.

[0035] Step S5: Calculate the characteristic crushing strength For a particle in the particle sample group whose characteristic crushing strength is to be tested, the equivalent particle size d0 and sphericity S obtained in step S1 are used as the basis for determining the particle size. V The size effect index α obtained in step S2, and the calibrated constants. Substituting χ and β into the prediction model formula, the predicted characteristic fracture strength σ0 of the particle can be obtained.

[0036] Example 2

[0037] Based on the method in Example 1, this invention uses calcareous sand particles as an example to construct and apply a model.

[0038] (1) Generation of particle model Three-dimensional laser scanning was performed on a group of real calcareous sand particles to obtain a database of coarse-grained triangular mesh models. Using the models in this database as the basic geometry, noise parameters were superimposed to generate a series of models with the target sphericity S. V The three-dimensional particle model with roundness R (as shown in Table 2) specifically uses the noise superposition algorithm provided by the inventor's team's existing patent CN118797998A. This method can independently adjust the sphericity and roundness levels while preserving the real particle morphology characteristics, and generate a statistically significant sample size.

[0039] (2) Discrete Element Numerical Experiment Setup Numerical tests on single-particle flat plate compression were conducted using the Discrete Element Method (DEM). A linear parallel bonding model was employed between sub-particles within the particle. This model can simultaneously transmit force and torque; when the stress exceeds the bond strength, the bond fails, simulating the particle fracture process. The mesoscopic parameters used in the numerical calculations of this invention referenced those used in Dong's simulation of single-particle breakage and were calibrated based on the results of single-particle compression chamber tests. The mesoscopic parameters are shown in Table 1.

[0040] Table 1. Mesoscopic parameters of single-particle plate compression numerical test The particles were placed between two rigid plates, with the upper plate loading downwards at a rate of 0.01 m / s. Sensitivity analysis of the loading rate showed that the loading curve and crushing energy remained relatively stable at this rate. The coefficient of friction between the particles and the loading plates was set to 0.1 to reduce the influence of relative slippage.

[0041] (3) Determine the functional relationship between the calibrated size effect index α and roundness R. The experimental plan is shown in Table 2: Table 2 Sample Particle Parameter Design Table Each particle was subjected to flat plate compression simulation until overall failure. The maximum contact force at which the particle fails is denoted as F. f ,according to Calculate the crushing strength. Take the average value for each particle size level as the representative value for that particle size. Figure 1 and Figure 2 The average crushing strength of the particles is given. The relationship between α and equivalent particle size d0 is shown. The smaller the absolute value of α, the weaker the size effect on crushing strength. The results indicate that sphericity has little effect on the change in crushing strength with decreasing particle size, while roundness has a more significant effect. As roundness increases, the absolute value of α decreases rapidly; for particles with R=0.2, the absolute value of α is approximately five times that of particles with R=0.8. These results suggest that the crushing strength of irregular particles is more sensitive to mesoscale roundness.

[0042] Perform a linear fit between α and R in the results (e.g.) Figure 3 As shown in the figure, we get: α = 0.55R - 0.52 (4) Calibrate the material constant χ and the sphericity effect index β Under the conditions of maintaining roundness R=0.6, equivalent particle size d0=3.5mm, and no internal pores, the sphericity S is set. V The sample consisted of four groups: 0.2, 0.4, 0.6, and 0.8 μm, with 30 particles in each group, for a total of 120 particles. The sample design scheme is shown in Table 3. Table 3. Sample Design Table for the Same Roundness and Particle Size but Different Sphericity Flat plate compression simulations were performed on each group of particles to obtain the crushing strength σ of each particle. f Through data processing, the characteristic fracture strength σ0 of each group was obtained, as detailed in [link to data]. Figure 4 , Figure 5 and Figure 6 .

[0043] from Figure 4 , Figure 5 and Figure 6 As can be seen, when the sphericity increases from 0.2 to 0.8, the characteristic strength increases from 8.77 MPa to 14.15 MPa, an increase of about 61%, which is significantly higher than the strength fluctuation caused by the change in roundness (when the roundness increases from 0.2 to 0.8, the strength change is only about 16%). This indicates that sphericity is the main morphological parameter controlling the absolute level of crushing strength.

[0044] Based on the calibration results from step (4), R=0.6 corresponds to α=-0.19. Figure 3 Group 4 (S) V Substitute the data (σ0) into the prediction model formula Fitting was performed using χ and β as undetermined parameters (results are shown below). Figure 7 As shown in the figure, χ = 19.4 MPa and β = 0.34 were obtained.

[0045] Therefore, the complete prediction model for calcareous sand particles is as follows: (5) Model validation To verify the model's prediction accuracy, four groups of samples were randomly selected from the numerical experimental dataset under different morphological and particle size conditions for validation. The samples are shown in Table 4, and the validation results are as follows: Figure 8 , Figure 9 , Figure 10 and Figure 11 As shown.

[0046] Table 4 shows the random sampling data used to validate the model. The four sets of samples mentioned above cover different combinations of sphericity, roundness, and particle size, with a maximum prediction deviation of no more than 6.2%. The verification results demonstrate that the model of this invention has good predictive reliability.

[0047] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for constructing a particle characteristic crushing strength prediction model, characterized in that, Includes the following steps: S1 selects particle samples of the same material type, obtains their three-dimensional morphology data, and obtains the following three parameters: equivalent particle size d0, sphericity S V and roundness R; S2 uses the same type of particulate material with the same sphericity obtained in step S1. V For multiple groups of particle samples with the same roundness R but different equivalent particle sizes d0, the functional relationship between the size effect index α and roundness R was obtained as α=f(R). S3 uses the same type of particulate material obtained in step S1, with the same roundness R and the same equivalent particle size d0, but different sphericity S. V Multiple sets of particle samples were used to obtain the material constant χ and the sphericity effect index β. S4 Substitutes the α obtained in step S2, the χ and β obtained in step S3 into the prediction model formula to obtain the prediction model of the particle characteristic crushing strength of this type of material. The prediction model is as follows: In the formula, d0 is the equivalent particle size, and S V Let α be the sphericity of the particles, and α be the size effect index of the particles. χ is the particle size parameter, β is the material constant, and β is the sphericity effect exponent.

2. The method for constructing the particle characteristic crushing intensity prediction model according to claim 1, characterized in that, The specific method for step S2 is as follows: The crushing strength σ is obtained through single-particle flat plate compression numerical tests or laboratory tests until total failure. f and representative value The maximum contact force when the particle breaks down as a whole is denoted as F. f ,according to Calculate the crushing strength; take the average of 5 samples at each particle size level as the representative value for that particle size. ; Using α as the feature intensity in double logarithmic coordinates By fitting the slope of the straight line with the equivalent particle size d0, multiple (R, α) data pairs are obtained. By fitting the data pairs, a functional relationship α=f(R) between α and R is established.

3. The method for constructing the particle characteristic crushing strength prediction model according to claim 1, characterized in that, The specific method for step S3 is as follows: The characteristic breaking strength σ0 under various sphericities was obtained through single-particle flat plate compression numerical tests or indoor tests; the α value corresponding to the sphericity R was calculated using the functional relationship α=f(R) determined in step S2, and the values ​​of each group (S) were then compared. V Substituting the data (σ0) into the prediction model, the material constant χ and the sphericity effect index β are obtained by joint fitting using the least squares method.

4. The method for constructing the particle characteristic crushing intensity prediction model according to claim 1, characterized in that, The specific method for obtaining the three-dimensional morphology data of the particles in step S1 is as follows: A coarse-grained triangular mesh model database is obtained through methods such as CT scanning or 3D laser scanning. Using the models in this database as the basic geometry, multi-view image reconstruction of particles is performed.

5. The method for constructing the particle characteristic crushing strength prediction model according to claim 4, characterized in that, When reconstructing multi-view images of particles, a noise superposition algorithm is used.

6. A particle characteristic crushing intensity prediction model constructed by any one of claims 1-5.

7. A method for predicting the characteristic crushing strength of particles, characterized in that, The model constructed using the method for constructing the particle characteristic crushing intensity prediction model according to any one of claims 1-5.

8. The method for predicting the characteristic crushing strength of particles according to claim 7, characterized in that, Includes the following steps: (1) Obtain the three morphological parameters of the particle to be predicted: equivalent particle size d0, sphericity S V and roundness R; (2) The size effect index α of the particle is determined by the roundness R; (3) Calculate the characteristic crushing strength; The equivalent particle size d0 and sphericity S obtained in step (1) V The size effect index α obtained in step (2), and the calibrated constants. Substituting χ and β into the prediction model formula, we obtain the characteristic crushing strength σ0 of the predicted particles.

Images