A three-dimensional morphology simulation method of sand particles based on spherical harmonic reconstruction and 3D printing technology
Through spherical harmony reconstruction and 3D printing technology, the limitations of sand and soil particle morphology simulation in the existing technology are solved, and the random generation and efficient simulation of three-dimensional morphology of natural sand particles are realized. It is suitable for the study of the mechanical properties of sand and soil, and provides a kind of Low-cost and efficient simulation method.
Patent Information
- Application Number
- CN202210560576.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-05-23
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2042-05-23
AI Technical Summary
The prior art is difficult to effectively simulate the morphology of real sand soil particles, especially in controlling the morphological characteristics of particles and efficient simulation, resulting in poor simulation results, and methods based on X-CT scanning and 3D printing are costly and inefficient.
Using spherical harmonic reconstruction and 3D printing technology, the CT images of sand particles are obtained, the three-dimensional coordinates are extracted, and the spherical harmonic coefficients are fitted to spherical coordinates to generate spherical harmonic characterization factors. The multiple Gaussian distribution model is used to generate random sequences and reconstruct sand particles. morphology and efficient simulation through 3D printing technology.
The random generation and high simulation of three-dimensional morphology of natural sand particles are realized, and a low-cost and efficient particle morphology simulation method is provided, suitable for the study of the mechanical properties and seepage characteristics of sand soil, filling the simulation gap of the existing technology.
Smart Images
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Abstract
Description
Technical Field
[0001] The invention relates to a three-dimensional morphology simulation method for sand grains, and in particular to a three-dimensional morphology simulation method for sand grains based on spherical harmonic reconstruction and 3D printing technology. Background Art
[0002] Particle morphology is one of the most important characteristics of sand, and its correlation with macroscopic mechanical properties has received increasing attention. Particle morphology has a particularly significant effect on the basic mechanical properties and particle crushing characteristics of sand, including the compression characteristics, shear strength, dilatancy effect and critical state behavior of sand under low stress conditions, as well as particle crushing behavior under high stress conditions. The main methods for studying the mechanism of the influence of sand particle morphology are usually numerical simulation and physical experiments. In terms of numerical simulation research, the numerical simulation of particles of different shapes based on discrete elements has developed relatively maturely, but due to the large gap between the simulated shape and the real particles, it has not been widely used. In terms of physical experimental research, there are still the following deficiencies:
[0003] (1) Due to the limitations of test equipment and methods, test materials are often limited to natural or artificial substitute materials with different morphological characteristics. Different natural materials have differences in basic properties such as density, elastic modulus, and single-particle shear strength, making it difficult to control a single variable based on particle morphology; artificial substitute materials, such as steel balls and glass beads, have a single and uncontrollable particle morphology, making it difficult to simulate real sand to the same degree.
[0004] (2) Although the natural sand simulation method based on X-CT scanning and 3D printing technology has the ability to completely replicate the three-dimensional shape of real sand, each physical experiment requires scanning and printing a large number of sand particles, which has the problems of high scanning cost and low production efficiency. Summary of the invention
[0005] Purpose of the invention: The purpose of the present invention is to provide a method for simulating the three-dimensional morphology of sand grains based on spherical harmonic reconstruction and 3D printing technology, which can realize the random generation and high simulation of the three-dimensional morphology of natural sand grains.
[0006] Technical solution: The present invention comprises the following steps:
[0007] (1) Obtaining a CT image of the sample sand grains, performing image processing and analysis on the CT image, extracting the boundary voxels of each sand grain, and converting the resolution of the boundary pixels to obtain the three-dimensional coordinates of each vertex constituting the surface of the sand grains;
[0008] (2) introducing spherical harmonics, converting the three-dimensional coordinates in step (1) into spherical coordinates as the input values of the spherical harmonics, and fitting to obtain the spherical harmonic coefficients corresponding to each sand particle;
[0009] (3) Based on the spherical harmonic coefficients in step (2), define and obtain the spherical harmonic characterization factor of each sample sand particle, and use the spherical harmonic characterization factor as a digital representation of the sand particle morphology in each frequency space;
[0010] (4) Statistical analysis is performed on the spherical harmonic characterization factor sequence of the sample sand particles, and a multivariate Gaussian distribution model is used to generate a random sequence of spherical harmonic characterization factors;
[0011] (5) restoring a random spherical harmonic coefficient sequence according to the random sequence of spherical harmonic characterization factors generated in step (4), and reconstructing the three-dimensional shape of the sand grains through spherical harmonic functions, thereby generating virtual sand grains;
[0012] (6) performing 3D printing modeling on the generated virtual sand particles, constructing a support system for the virtual sand particles, and then dividing the constructed 3D model into layer-by-layer slices to guide the printer to print layer by layer;
[0013] (7) After printing is completed, the support is removed, the printed sand is cleaned and cured, and the production of simulated sand particles is completed.
[0014] The spherical harmonic function in step (2) is expressed as follows:
[0015]
[0016]
[0017]
[0018] where g(θ,φ) is the distance from the center of the sand grain to the vertex of the surface, θ∈[0,π] and φ∈[0,2π] are the zenith angle and azimuth angle in the spherical coordinate system, respectively, and d n,m are the spherical harmonic coefficients, u n,m is a spherical harmonic sequence, p n,m (x) is the Legendre polynomial corresponding to the nth order and mth degree terms, and i is the imaginary unit.
[0019] The spherical harmonic characterization factor in step (3) is expressed as follows:
[0020]
[0021] D n =A n / A 0
[0022] Among them, A n represents the amplitude of the nth frequency space, D n represents the spherical harmonic characterization factor of the nth frequency space, D 0 =1,D 1 =0.
[0023] The multivariate Gaussian distribution model in step (4) adopts the following expression:
[0024]
[0025] Where P(D) is the probability density distribution function, D = [D 2 ,...,D n ] T is the spherical harmonic characterization factor sequence, μ=[μ 2 ,...,μ n ] T is the average value sequence of D, The covariance matrix of D is (n-1)×(n-1).
[0026] The random spherical harmonic coefficient sequence expression in step (5) is:
[0027] d′ n =D′ n ·h n
[0028]
[0029] Where d′ n and D′ n are the spherical harmonic coefficients and spherical harmonic characterization factors randomly generated according to the multivariate Gaussian distribution model, h n is a unit random sequence, r n,m and t n,m They are all random natural numbers in the range of -1 to 1.
[0030] The 3D printing modeling in step (6) includes a sand particle morphology main body model and a support system.
[0031] The main sand grain morphology model includes multiple triangular facets, each of which includes the three-dimensional coordinates of each vertex of the triangle and the normal vector of the triangular facet. The surface simulation accuracy of the printed sand grains is adjusted by the number of triangular facets. The more triangular facets there are, the higher the accuracy.
[0032] The support system includes main supports and auxiliary supports. The main supports are located at the local lowest point of the main model. The auxiliary supports are arranged around the main supports to fill the larger gaps between the main supports. The arrangement spacing should not be higher than 20% of the diameter of the main model.
[0033] The thickness of the slice in step (6) should be less than 5‰ of the height of the main model.
[0034] Beneficial effect: The simulated sand with different particle morphology characteristics prepared by the present invention fills the gap in the production of real sand morphology characteristics in actual research, can realize the random generation and high simulation of the three-dimensional morphology of natural sand particles, and provides a sand micromechanical simulation test method that fully considers the particle morphology. The random generation of the three-dimensional morphology of natural sand particles is achieved through spherical harmonic analysis, and then the 3D printing technology is introduced to realize the efficient simulation of natural sand. It is suitable for related experimental research on the macro and micro mechanical properties of sand, and then to carry out related research on mechanical properties, seepage properties, and rheological properties considering the influence of sand particle morphology. The materials used are simple, the cost is low, and the operation is simple. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 The sand grain CT scan and spherical harmonic reconstruction image constructed according to the preferred embodiment of the present invention;
[0036] Figure 2 The spherical harmonic characterization factor of a certain sand grain constructed according to the preferred embodiment of the present invention and its visualization image;
[0037] Figure 3 The random virtual sand grains are constructed according to the preferred embodiment of the present invention;
[0038] Figure 4 An example of 3D printing modeling constructed according to a preferred embodiment of the present invention;
[0039] Figure 5 Printing sand particles produced according to the preferred embodiment of the present invention;
[0040] Figure 6 The present invention is an example of a consolidated drained triaxial test performed on printed sand particles according to a preferred embodiment of the present invention. DETAILED DESCRIPTION
[0041] The present invention will be further described below in conjunction with the accompanying drawings.
[0042] The sand grain three-dimensional morphology simulation method of the present invention comprises the following steps:
[0043] Step 1: Select a limited number of natural sand grains as scanning samples, use X-ray computer tomography to obtain CT images of the sample sand grains, construct the three-dimensional morphology of the sand grains after image processing and analysis of the CT images, then extract the boundary voxels of each sand grain, and convert the coordinates of each vertex that makes up the sand grain surface in the three-dimensional coordinate system of space according to the resolution of the boundary pixels.
[0044] Step 2: Introduce spherical harmonics, convert the three-dimensional coordinates in step 1 into spherical coordinates as the input value of the spherical harmonics, and set the maximum value n of the spherical harmonic reconstruction order n max=15, that is, corresponding to 15 frequency spaces, the spherical harmonic coefficients corresponding to each sand grain are obtained by least squares fitting, and the spherical harmonic reconstruction of the three-dimensional morphology of the sand grains is completed, such as Figure 1 shown.
[0045] Among them, spherical harmonics are expressed as follows:
[0046]
[0047]
[0048]
[0049] where g(θ,φ) is the distance from the center of the sand grain to the vertex of the surface, θ∈[0,π] and φ∈[0,2π] are the zenith angle and azimuth angle in the spherical coordinate system, respectively, and d n,m are the spherical harmonic coefficients, u n,m is a spherical harmonic sequence, p n,m (x) is the Legendre polynomial corresponding to the nth order and mth degree term, i is the imaginary unit. The maximum value of n (n max ) determines the fitting accuracy of spherical harmonic reconstruction and the total number of frequency spaces involved in the reconstruction, n max The larger the value, the higher the accuracy. max =15, corresponding to 15 frequency spaces.
[0050] Step 3: Based on the spherical harmonic coefficients obtained in step 2, define and obtain the spherical harmonic characterization factor of each sample sand grain, and use the spherical harmonic characterization factor as a digital representation of the complex three-dimensional morphology of the sand grain in each frequency space. The spherical harmonic characterization factor uses the following expression:
[0051]
[0052] D n =A n / A 0
[0053] Among them, A n represents the amplitude of the nth frequency space, D n represents the spherical harmonic characterization factor of the nth frequency space. It should be noted that D 0 =1,D 1 =0; Each sample sand particle corresponds to a set of spherical harmonic characterization factors, which is called a spherical harmonic characterization factor sequence D = [D 2 ,...,D n ] T .
[0054] Step 4: Figure 2The figure shows the constructed spherical harmonic characterization factor of a certain sand grain and its visualization image. It can be seen that for a certain reconstructed sand grain, the intensity of its morphology in different frequency spaces varies, and the sum of the morphologies in each frequency space is the true reconstructed morphology of the sand grain. Therefore, the spherical harmonic characterization factor sequence of the selected sample sand grains is statistically analyzed as the morphological characteristic data of a certain type of natural sand. The multivariate Gaussian distribution model is used to generate a random sequence of spherical harmonic characterization factors. The multivariate Gaussian distribution model uses the following expression:
[0055]
[0056] Where P(D) is the probability density distribution function, D = [D 2 ,...,D n ] T is the spherical harmonic characterization factor sequence, μ=[μ 2 ,...,μ n ] T is the average value sequence of D, The covariance matrix of D is (n-1)×(n-1).
[0057] Step 5: restore the random spherical harmonic coefficient sequence according to the random sequence of spherical harmonic characterization factors generated in step 4, and reconstruct the three-dimensional shape of the sand grains through spherical harmonic functions, thereby generating an infinite number of virtual sand grains with given natural sand grain morphological characteristics, such as Figure 3 For the random virtual sand grains constructed according to the method of the present invention, the random spherical harmonic coefficient sequence restored from the spherical harmonic characterization factor sequence is expressed as:
[0058] d′ n =D′ n ·h n
[0059]
[0060] Where d′ n and D′ n are the spherical harmonic coefficients and spherical harmonic characterization factors randomly generated according to the multivariate Gaussian distribution model, h n is a unit random sequence, r n,m and t n,m They are all random natural numbers in the range of -1 to 1.
[0061] Step 6: Use computer modeling software to perform 3D printing modeling on the generated virtual sand particles and build a support system for the virtual sand particles. Figure 5This is an example of the constructed 3D printing modeling. The constructed 3D model is then divided into slices layer by layer. The thickness of the slices should be less than 5‰ of the height of the main model, so as to guide the printer to print layer by layer. Among them, the 3D printing modeling is divided into a sand grain morphology main model and a support system. The sand grain morphology main model is composed of multiple triangular facets. Each triangular facet includes the three-dimensional coordinates of each vertex of the triangle and the normal vector of the triangular facet. The surface simulation accuracy of the printed sand grains is adjusted by the number of triangular facets. The more triangular facets, the higher the accuracy. The support system includes at least one main support and a limited number of auxiliary supports. The main support is located at the local lowest point of the main model. The auxiliary supports are arranged around the main support to fill the larger gaps between the main supports. The arrangement spacing should not be higher than 20% of the diameter of the main model.
[0062] Step 7: After printing, remove the support and clean and maintain the printed sand, including soaking it in anhydrous alcohol to clean the residual liquid resin on the surface of the printed sand, and then irradiate the printed sand with a 405-nanometer ultraviolet light source at 60°C until the printed sand reaches the preset strength, completing the production of simulated sand. Figure 5 The printed sand produced is shown in Figure 2. The printed sand is applied to relevant physical experiments and research, and the mechanical mechanism of the complex three-dimensional morphology of the sand can be studied. Figure 6 This is an example of a consolidated drained triaxial test on printed sand. The figure shows that the printed sand exhibits obvious shear expansion and stress softening under shear, and presents an X-shaped shear band as the shear develops, showing the unique physical and mechanical properties of medium-dense natural sand.
Claims
1. A sand grain three-dimensional morphology simulation method based on spherical harmonic reconstruction and 3D printing technology, characterized in that: The following steps are involved: (1) Obtaining a CT image of the sample sand grains, performing image processing and analysis on the CT image, extracting the boundary voxels of each sand grain, and converting the resolution of the boundary voxels to obtain the three-dimensional coordinates of each vertex constituting the surface of the sand grains; (2) Introducing the spherical harmonic function, converting the three-dimensional coordinates in step (1) into spherical coordinates as the input value of the spherical harmonic function, and fitting to obtain the spherical harmonic coefficients corresponding to each sand particle; the spherical harmonic function adopts the following expression: where g(θ,φ) is the distance from the center of the sand grain to the vertex of the surface, θ∈[0,π] and φ∈[0,2π] are the zenith angle and azimuth angle in the spherical coordinate system, respectively, and d n,m are the spherical harmonic coefficients, u n,m is a spherical harmonic sequence, p n,m (x) is the Legendre polynomial corresponding to the nth order and mth degree terms, and i is the imaginary unit; (3) Based on the spherical harmonic coefficients in step (2), define and obtain the spherical harmonic characterization factor of each sample sand particle, and use the spherical harmonic characterization factor as a digital characterization of the sand particle morphology in each frequency space; the spherical harmonic characterization factor adopts the following expression: D n =A n / A0 Among them, A n represents the amplitude of the nth frequency space, D n Represents the spherical harmonic characterization factor of the nth frequency space, D0=1, D1=0; (4) Statistical analysis is performed on the spherical harmonic characterization factor sequence of the sample sand particles, and a multivariate Gaussian distribution model is used to generate a random sequence of spherical harmonic characterization factors; the multivariate Gaussian distribution model uses the following expression: Where P(D) is the probability density distribution function, D=[D2,...,D n ] T is the spherical harmonic characterization factor sequence, μ=[μ2,…,μ n ] T is the average value sequence of D, The covariance matrix of D is (n-1)×(n-1); (5) According to the random sequence of spherical harmonic characterization factors generated in step (4), a random spherical harmonic coefficient sequence is restored, and the three-dimensional shape of the sand grains is reconstructed by spherical harmonic functions, thereby generating virtual sand grains; the random spherical harmonic coefficient sequence is expressed as: d′ n =D′ n ·h n Where d′ n and D′ n are the spherical harmonic coefficients and spherical harmonic characterization factors randomly generated according to the multivariate Gaussian distribution model, h n is a unit random sequence, r n,m and t n,m They are all random natural numbers between -1 and 1; (6) performing 3D printing modeling on the generated virtual sand particles, constructing a support system for the virtual sand particles, and then dividing the constructed 3D model into layer-by-layer slices to guide the printer to print layer by layer; (7) After printing is completed, the support is removed, the printed sand is cleaned and cured, and the production of simulated sand particles is completed.
2. The method for simulating the three-dimensional morphology of sand particles based on spherical harmonic reconstruction and 3D printing technology according to claim 1, characterized in that: The 3D printing modeling in step (6) includes a sand particle morphology main body model and a support system.
3. The method for simulating the three-dimensional morphology of sand particles based on spherical harmonic reconstruction and 3D printing technology according to claim 2, characterized in that: The sand grain morphology main body model comprises a plurality of triangular facets, each of which comprises the three-dimensional coordinates of each vertex of the triangle and the normal vector of the triangular facet.
4. The method for simulating the three-dimensional morphology of sand particles based on spherical harmonic reconstruction and 3D printing technology according to claim 2, characterized in that: The support system includes a main support and auxiliary supports. The main support is located at the local lowest point of the main model, and the auxiliary supports are arranged around the main support.
5. The method for simulating the three-dimensional morphology of sand particles based on spherical harmonic reconstruction and 3D printing technology according to claim 1, characterized in that: The thickness of the slice in step (6) should be less than 5‰ of the height of the main model.