Method for constructing initial packing model of three-phase composite cement microstructure based on spherical harmonics

Abstract

The application discloses a kind of based on spherical harmonic function's three-phase composite cement microstructure initial accumulation model construction method, comprising: 1 determines the basic parameter of three-phase composite cement microstructure model;2 generate the cubic of microstructure model, calculate the particle size distribution of cement, mineral powder and fly ash;3 generate to be put particle, according to particle type to carry out translation transformation and rotation transformation;4 judge whether to be put particle meets boundary condition and particle interference condition, generate the particle model of successful casting.The microstructure initial accumulation model generated by the application can accurately reproduce the real particle accumulation state in specific surface area, spatial distribution and geometric morphology, thereby can reduce the error caused by hydration rate and hydration degree in computer simulation, and has important practical significance for predicting the macroscopic performance of cement paste.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of three-phase composite cement microstructure model construction, and particularly relates to a method for constructing an initial accumulation model of a three-phase composite cement microstructure based on spherical harmonics. BACKGROUND

[0002] At present, concrete is still the most widely used building material in the modern construction industry, and improving the mechanical properties and durability of concrete is an important issue in scientific research. The microstructure of hardened cement paste directly affects the crack resistance and durability of concrete, so the problem of concrete durability requires a better understanding of the hydration process and microstructure development of cement. The cement hydration kinetics model includes two aspects: microstructure formation and cement hydration calculation, and the microstructure formation has an important influence on the accuracy of the hydration calculation results. In previous studies, the parameters of most kinetic models were based on regression analysis of experimental data. However, experimental research is not only time-consuming and labor-intensive, but also limited by experimental conditions. Using computer models to simulate the hydration process and microstructure of cement-based materials is beneficial to the research and application of cement-based materials.

[0003] Scholars at home and abroad have focused their attention on establishing corresponding micro models to simulate the hydration process in order to achieve the purpose of component optimization and performance prediction. For example, microfocus X-ray computed tomography, HYMOSTRUC3D, CEMHYD3D, mic platform, DuCOM-COM3 multi-scale coupling analysis platform, etc. The particle accumulation of the above models is to approximate the simulation object as spherical particles or ellipsoidal particles, which is easy to construct. However, under the condition of constant water-cement ratio and particle size, spherical particles have the smallest surface area, while the surface area of actual irregular particles can be several times that of spherical particles. Therefore, the hydration rate and final hydration degree will have errors, which restricts the hydration accuracy and limits the application range of the model.

[0004] Zhang Zengqi modified the BNG model by approximating the simulation object as ellipsoidal particles, and established a hydration kinetics model for cement-slag composite cementitious materials; Wu Dajiang et al. further improved the CEMHYD3D model using a two-dimensional and three-dimensional irregular particle reconstruction method; however, in most models, the particles in the microstructure are considered as simplified spheres and ellipsoids, while under SEM observation, the true shape of the particles in the cement paste microstructure is not as such, and research has shown that the morphology of particles and aggregates has an important influence on the workability and mechanical properties of cement-based materials.

[0005] Until now, there is no method for constructing a more realistic three-phase composite cement microstructure model. SUMMARY

[0006] The application is to solve the limitation of the previous research, and proposes a construction method of a three-phase composite cement microstructure initial accumulation model based on spherical harmonics, so that the generated microstructure initial accumulation model can accurately reproduce the real particle accumulation state in terms of specific surface area, spatial distribution and geometric morphology, thereby reducing the error caused by the hydration rate and hydration degree in computer simulation, and improving the hydration accuracy of the model, which has important practical significance for predicting the macroscopic performance of the cement paste.

[0007] In order to achieve the above-mentioned application purposes, the application adopts the following technical solutions:

[0008] The construction method of a three-phase composite cement microstructure initial accumulation model based on spherical harmonics has the characteristics that it comprises the following steps:

[0009] Step 1: determining the basic parameters of the three-phase composite cement microstructure model; including: the size of the microstructure model, i.e. the length L, width W and height H of the cube CUBE; the water-cement ratio wcr, the density of cement PC , the density of mineral powder BFS and the density of fly ash FA ; the particle size distribution of unit volume cement [VPC1, VPC2, …, VPC i-1 , VPC i , …, VPC max ], the particle size distribution of unit volume mineral powder [VBFS1, VBFS2, …, VBFS i-1 , VBFS i , …, VBFS max ] and the particle size distribution of unit volume fly ash [VFA1, VFA2, …, VFA i-1 , VFA i , …, VFA max ]; the mass proportion coefficient of cement K PC , the mass proportion coefficient of mineral powder K BFS and the mass proportion coefficient of fly ash K FA ; the pore sieve size [W1, W2, W3, …, W i-1 , W i , …, W max ]; wherein VPC i , VBFS i and VFA i respectively represent the volume to be put of cement, mineral powder and fly ash in the particle size range (W i-1 , W i ) per unit volume; W max represents the maximum size of the pore sieve; and W i represents the size of the i-th pore sieve.

[0010] Step 2: Establish a three-dimensional Cartesian coordinate system to generate a cube CUBE with length L, width W, and height H, wherein the lower left corner of the cube CUBE is located at the coordinate origin;

[0011] Step 2.1: Calculate the total mass M of the cementitious material composed of cement, mineral powder, and fly ash according to the volume V = L x W x H of the cube CUBE, the water-cement ratio wcr, and the density p of the cement; PC

[0012] Step 2.2: Multiply the total mass M by the corresponding mass proportion coefficient K PC , K BFS , and K FA , respectively, to obtain the total mass m PC , m BFS , and m FA of cement, mineral powder, and fly ash, respectively; divide the total mass m PC , m BFS , and m FA by the corresponding density p PC , p BFS , and p FA , respectively, to obtain the total volume V PC , V BFS , and V FA of cement, mineral powder, and fly ash, respectively;

[0013] Step 2.3: Initialize i = max; multiply the total volume V PC , V BFS , and V FA by the particle size distribution of unit volume cement, the particle size distribution of unit volume mineral powder, and the particle size distribution of unit volume fly ash, respectively, to obtain the particle size distribution of cement [SVPC1, SVPC2, …, SVPC i-1 , SVPC i , …, SVPC max ], the particle size distribution of mineral powder [SVBFS1, SVBFS2, …, SVBFS i-1 , SVBFS i , …, SVBFS max ], and the particle size distribution of fly ash [SVFA1, SVFA2, …, SVFA i-1 , SVFA i , …, SVFA max ], respectively, where SVPC i , SVBFS i , and SVFA i represent the volume to be placed of cement, mineral powder, and fly ash with particle size range (W i-1 , W i ); ​

[0014] Step 3: randomly selecting a cement or mineral powder irregular particle in the spherical harmonic coefficient table database of the irregular particle, and controlling the size of the irregular particle by scaling the coefficients in the spherical harmonic coefficient table of the irregular particle, so that the size of the irregular particle is within the corresponding particle size range, and obtaining the cement or mineral powder particle to be placed;

[0015] Randomly generating fly ash spherical particles within the particle size range as fly ash particles to be placed;

[0016] Randomly generating the center coordinates and XYZ Euler rotation angles M of the placement R , for performing translation transformation and rotation transformation on the cement or mineral powder particle to be placed to obtain a cement or mineral powder particle model; and performing translation transformation on the fly ash particle to be placed to obtain a fly ash particle model;

[0017] Step 4: judging whether the particle models within the particle size range (W i-1 , W i ) satisfy the boundary condition and the particle interference condition at the same time, if so, placing the particle models within the particle size range (W i-1 , W i ) into the cube CUBE, otherwise, returning to step 3 to reselect the particle; wherein the boundary condition is that the particle model is completely within the cube CUBE; and the particle interference condition is that the particle model to be placed and all the successfully placed particle models do not interfere with each other.

[0018] The construction method of the initial accumulation model of the three-phase composite cement microstructure based on spherical harmonics according to the application also has the following characteristics: the step 3 comprises:

[0019] Step 3.1: selecting the resampling polar angle θ and the resampling azimuth angle θ={θ k =kπ / N1|k=1,2,3,…,N1}, wherein θ k is the kth resampling polar angle, and is the kth resampling azimuth angle, and N1 is the number of resampling angles;

[0020] If the irregular particle of cement or mineral powder is to be placed, the serial number t of the cement or mineral powder particle to be placed, the equivalent particle size control parameter K t of the tth cement or mineral powder irregular particle, the spherical harmonic coefficient table b nm,t of the tth irregular particle in the spherical harmonic coefficient table database of the irregular particle are randomly generated, and step 3.2 is performed; wherein t∈(1,N), and N is the total number of particles in the spherical harmonic coefficient table database;

[0021] If fly ash spherical particles are to be placed, randomly generate a spherical particle radius within the particle size range, and execute step 3.2;

[0022] Step 3.2: For the spherical harmonic coefficient table b of the tth cement or mineral powder nm,t , obtain the polar radius value of the tth irregular particle at the resampled polar angle θ and resampled azimuth angle

[0023]

[0024] In formula (1), is the spherical harmonic basis function of order n and degree m, and K is the spherical harmonic reconstruction order;

[0025] Combine the polar radius value with the resampled polar angle θ and resampled azimuth angle to form a cement or mineral powder polar coordinate sequence, convert the cement or mineral powder polar coordinate sequence into a cement rectangular coordinate sequence Z PC or a mineral powder rectangular coordinate sequence Z BFS , and execute step 3.3;

[0026] For fly ash spherical particles, combine the randomly generated spherical particle radius with the resampled polar angle θ and resampled azimuth angle to form a fly ash polar coordinate sequence, convert the fly ash polar coordinate sequence into a fly ash rectangular coordinate sequence Z FA, , and execute step 3.5;

[0027] Step 3.3: Calculate the equivalent particle diameter w of the tth cement or mineral powder particle t If w t ∈(W i-1 ,W i ), it indicates that the cement or mineral powder particle to be placed is obtained, and step 3.5 is executed, otherwise, step 3.4 is executed;

[0028] Step 3.4: Assign to b nm,t , and return to step 3.2;

[0029] Step 3.5: For the cement or mineral powder particle to be placed, translate the center coordinates of the rectangular coordinate sequence Z PC or Z BFS to the randomly generated placement center coordinates to obtain the translated rectangular coordinate sequence Z PC1 or Z BFS1 ; multiply the rectangular coordinate sequence Z PC1 or Z BFS1 by M R to obtain the rectangular coordinate sequence Z PC2 ​or Z BFS2 , by Z PC2 or Z BFS2 The particle composed of the contour points is a cement or mineral powder particle model;

[0030] For the fly ash particle to be cast, the rectangular coordinate sequence Z FA is translated to a randomly generated casting center coordinate, to obtain a translated rectangular coordinate sequence Z FA1 , by Z FA1 The particle composed of the contour points is a fly ash particle model.

[0031] The electronic device comprises a memory and a processor, and the feature lies in that the memory is used to store a program supporting the processor to execute the construction method, and the processor is configured to execute the program stored in the memory.

[0032] The computer readable storage medium stores a computer program, and the feature lies in that the computer program is executed by the processor to execute the steps of the construction method.

[0033] Compared with the prior art, the present application has the following beneficial effects:

[0034] 1. The present application uses spherical harmonics to construct cement irregular particles and mineral powder irregular particles with complex shape contours, and forms a microstructure model with fly ash spherical particles, which is more accurate in reproducing the real particle accumulation state in specific surface area, spatial distribution and geometric morphology, and improves the authenticity and hydration accuracy of the model compared with the existing microstructure model based on spherical particles or ellipsoidal particles.

[0035] 2. The CEMHYD3D model does not contain an image processing module, and researchers need to program and adjust it according to the image characteristics, which brings many unstable factors to the simulation results. Compared with the CEMHYD3D model, the present application uses the Matlab geometric modeling method, which is simple and convenient.

[0036] 3. The present application uses the EOB particle interference algorithm to shorten the generation time of the microstructure initial accumulation model, and makes the microstructure model achieve a lower water-cement ratio, thereby improving the efficiency and practicability of the simulation. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The flow chart of the microstructure initial accumulation model of the method of the present application;

[0038] Figure 2 The appearance diagram of the cement, mineral powder and fly ash particles in the model of the present application;

[0039] Figure 3 Boundary condition determination chart for the method of the present application;

[0040] Figure 4 Appearance chart for part of irregular particles in the spherical harmonic coefficient table database of the present application;

[0041] Figure 5 Initial packing model example chart of the microstructure of the present application with water-cement ratio of 0.35 and volume placement rate of 50.4834%. DETAILED DESCRIPTION

[0042] In this embodiment, as shown in the figure, a construction method of an initial packing model of a three-phase composite cement microstructure based on spherical harmonics, comprising the following steps: Figure 1

[0043] Step 1: Determine the basic parameters of the three-phase composite cement microstructure model; including: the size of the microstructure model, i.e. the length L, width W and height H of the cube CUBE; the water-cement ratio wcr, the density of cement ρ PC , the density of slag ρ BFS and the density of fly ash ρ FA ; the particle size distribution per unit volume of cement [VPC1, VPC2, …, VPC i-1 , VPC i , …, VPC max ], the particle size distribution per unit volume of slag [VBFS1, VBFS2, …, VBFS i-1 , VBFS i , …, VBFS max ] and the particle size distribution per unit volume of fly ash [VFA1, VFA2, …, VFA i-1 , VFA i , …, VFA max ]; the mass proportion coefficient of cement K PC , the mass proportion coefficient of slag K BFS and the mass proportion coefficient of fly ash K FA ; the pore sieve size [W1, W2, W3, …, W i-1 , W i , …, W max ]; wherein VPC i , VBFS i and VFA i respectively represent the volume to be placed of cement, slag and fly ash with particle size range (W i-1 , W i ) per unit volume; W max represents the maximum size of the pore sieve; W i represents the size of the i-th pore sieve;

[0044] ​Step 2: Establish a three-dimensional Cartesian coordinate system to generate a cube CUBE with length L, width W, and height H, wherein the lower left corner of the cube CUBE is located at the coordinate origin;

[0045] Step 2.1: According to the volume V = L x W x H of the cube CUBE, the water-cement ratio wcr and the density of cement PC , the total mass M of the cementitious material composed of cement, mineral powder and fly ash is calculated by formula (1);

[0046]

[0047] Step 2.2: Multiply the total mass M by the corresponding mass proportion coefficient K PC , K BFS and K FA , respectively, to obtain the total mass m PC , m BFS and m FA of cement, mineral powder and fly ash; divide the total mass m PC , m BFS and m FA by the corresponding density PC , p BFS and p FA , respectively, to obtain the total volume V PC , V BFS and V FA of cement, mineral powder and fly ash, respectively;

[0048] Step 2.3: Initialize i = max; through formula (2), formula (3) and formula (4), obtain the to-be-discharged volumes SVPC i-1 , SVBFS i and SVFA i of cement, mineral powder and fly ash with particle size range (W i , W i ); multiply the total volume V PC , V BFS and V FA by the particle size distribution of unit volume of cement, the particle size distribution of unit volume of mineral powder and the particle size distribution of unit volume of fly ash, respectively, to obtain the particle size distribution of cement [SVPC1, SVPC2, …, SVPC i-1 , SVPC i , …, SVPC max ], the particle size distribution of mineral powder [SVBFS1, SVBFS2, …, SVBFS i-1 , SVBFS i , …, SVBFS max ] and the particle size distribution of fly ash [SVFA1, SVFA2, …, SVFA i-1 , SVFAi ..., SVFA max ], wherein SVPC i , SVBFS i and SVFA i respectively represent the volume to be put of cement, slag and fly ash whose particle size ranges in (W i-1 , W i );

[0049]

[0050]

[0051] Step 3: Scanning a plurality of irregular particles by using X-ray computed tomography technology to obtain point cloud data of surfaces of the plurality of particles; processing the point cloud data into a spherical harmonic coefficient table, and establishing a three-dimensional irregular particle spherical harmonic coefficient table database, wherein the total number of particles in the database is denoted as N; the calculation formula of the spherical harmonic coefficient table of the particle is as follows:

[0052]

[0053] In formula (5), θ and are the polar angle and azimuth angle of the spherical coordinate system respectively, b nm is the spherical harmonic coefficient table of the particle, is the spherical harmonic basis function of n order and m degree, represents the polar radius value of the particle at the polar angle θ and the azimuth angle .

[0054]

[0055] In formula (6), P n m (x) is the associated Legendre polynomial, and n and m are the order and degree of the spherical harmonic function respectively.

[0056] Randomly selecting an irregular particle of cement or slag in the irregular particle spherical harmonic coefficient table database of the cement, and controlling the size of the irregular particle by scaling the coefficients in the spherical harmonic coefficient table of the irregular particle, so that the size of the irregular particle is within the corresponding particle size range, and obtaining the cement or slag particle to be put;

[0057] Randomly generating a fly ash spherical particle within the particle size range as the fly ash particle to be put;

[0058] Randomly generating a put center coordinate and XYZ Euler rotation angle M R , which is used for performing translation transformation and rotation transformation on the cement or slag particle to be put, to obtain a cement or slag particle model; and performing translation transformation on the fly ash particle to be put, to obtain a fly ash particle model;

[0059] Through the nesting of for loop and while loop in Matlab, the particles of different particle sizes are put in turn from large to small, and the particles of the same particle size are put in turn from cement particles to mineral powder particles to fly ash particles. That is, when the particles of the ith particle size are put, the cement irregular particles of the ith particle size are put first, and when the volume reaches SVPC i , the mineral powder irregular particles of the ith particle size are put, and when the volume reaches SVBFS i , the fly ash spherical particles of the ith particle size are put, and when the volume reaches SVFA i , the particles of the i-1th particle size are continuously put, and the cycle is repeated until all the particle sizes are put; specifically, the following steps are taken:

[0060] Step 3.1: Select the resampling polar angle θ and the resampling azimuth angle θ = {θ k = kπ / N1 | k = 1, 2, 3, …, N1}, where θ k is the kth resampling polar angle, is the kth resampling azimuth angle, and N1 is the number of resampling angles.

[0061] If the irregular particles of cement or mineral powder are to be put, the sequence number t of the cement or mineral powder particles to be put is randomly generated, the equivalent particle size control parameter K t of the tth cement or mineral powder irregular particle is selected, the spherical harmonic coefficient table b nm,t of the tth irregular particle in the spherical harmonic coefficient table database is selected, and step 3.2 is performed; where t ∈ (1, N), N is the total number of particles in the spherical harmonic coefficient table database.

[0062] If fly ash spherical particles are to be put, the spherical particle radius within the particle size range is randomly generated, and step 3.2 is performed.

[0063] Step 3.2: For the tth b nm,t , the polar radius value of the tth irregular particle under the resampling polar angle θ and the resampling azimuth angle is obtained using formula (7)

[0064]

[0065] In formula (7), is the spherical harmonic basis function of order n and degree m, and K is the spherical harmonic reconstruction order.

[0066] The polar radius value is combined with the resampling polar angle θ and the resampling azimuth angle The cement or slag polar coordinate sequence is jointly combined into a cement or slag rectangular coordinate sequence Z PC or a slag rectangular coordinate sequence Z BFS , and step 3.3 is performed.

[0067] For the fly ash spherical particle, the randomly generated spherical particle radius is combined with the resampled polar angle θ and the resampled azimuth angle The fly ash polar coordinate sequence is jointly combined into a fly ash rectangular coordinate sequence Z FA, , and step 3.5 is performed.

[0068] Step 3.3: Calculate the equivalent particle diameter w of the tth cement or slag particle t If w t ∈(W i-1 , W i ), it indicates that the cement or slag particle to be cast is obtained, and step 3.5 is performed, otherwise, step 3.4 is performed.

[0069] Step 3.4: Assign to b nm,t , and then return to step 3.2.

[0070] Step 3.5: For the cement or slag particle to be cast, the center coordinates of the rectangular coordinate sequence Z PC or Z BFS are translated to the randomly generated casting center coordinates to obtain the translated rectangular coordinate sequence Z PC1 or Z BFS1 ; the rectangular coordinate sequence Z PC1 or Z BFS1 is multiplied by M R to obtain the rectangular coordinate sequence Z PC2 or Z BFS2 , and the Z PC2 or Z BFS2 is filled by using the Matlab built-in function trisurf to obtain the cement or slag particle model.

[0071] For the fly ash particle to be cast, the center coordinates of the rectangular coordinate sequence Z FA are translated to the randomly generated casting center coordinates to obtain the translated rectangular coordinate sequence Z FA1 , and the fly ash particle model is filled by using the Matlab built-in function trisurf Z FA1 .

[0072]

[0073] In formula (8), M Ris the XYZ Euler rotation matrix, a is the rotation angle of the particle around the x-axis, β is the rotation angle of the particle around the y-axis, and γ is the rotation angle of the particle around the z-axis.

[0074] Step 4: judging whether the particle model with the particle size range in (W i-1 ,W i ) satisfies the boundary condition and the particle interference condition at the same time, if so, the particle model with the particle size range in (W i-1 ,W i ) is put into the cube CUBE, otherwise, returning to step 3 to select a particle again; wherein the boundary condition is that the particle model is completely in the cube CUBE; the particle interference condition is that the particle model to be put and all the particle models put successfully do not interfere with each other;

[0075] In this embodiment, the judging method of whether the particle model satisfies the boundary condition is that the position relationship between the axis-aligned minimum circumscribed cube C t of the particle model and the cube CUBE is judged by a self-compiled function of Matlab, if C t is inside the cube CUBE, it indicates that the particle model satisfies the boundary condition, and the next step of judging whether the particle model satisfies the particle interference condition is performed, otherwise, it indicates that the particle model does not satisfy the boundary condition, and returning to step 3 to select a particle again; the judging method of whether the particle model satisfies the particle interference condition is that the EOB particle interference algorithm is used to judge; mainly including the following steps:

[0076] Step 4.1: judging whether the C t of the particle model to be put is disjoint with the C t of all the particle models put successfully, if so, it indicates that the particle interference condition is satisfied, and the putting is successful; otherwise, a set AG composed of all the particle models put successfully is recorded, and step 4.2 is performed;

[0077] Step 4.2: judging whether the maximum inscribed sphere of the particle model to be put has an intersection relationship with the maximum inscribed sphere of one of the particle models in AG, if so, it indicates that the particle interference condition is not satisfied, and returning to step 3 to select a particle again; otherwise, step 4.3 is performed;

[0078] Step 4.3: judging whether all the contour points of the particle model to be put satisfy that they are all outside any one of the particle models put successfully in the set AG, if so, it indicates that the particle interference condition is satisfied, and the putting is successful; otherwise, it indicates that the particle interference condition is not satisfied, and returning to step 3 to select a particle again.

[0079] Example demonstration: the following steps are used to construct an initial packing model of a three-phase composite cement microstructure based on spherical harmonics:

[0080] Step 1: Determine the basic parameters of the three-phase composite cement microstructure model; including: microstructure model length L = 100 pm, width W = 100 pm, and height H = 100 pm; water-cement ratio wcr = 0.35, density of cement p PC = 3.14 g / cm 2 , density of slag p BFS = 2.93 g / cm 2 , and density of fly ash p FA = 2.56 g / cm 2 ; particle size distribution per unit volume of cement [VPC1, VPC2, …, VPC i-1 , VPC i , …, VPC max ], particle size distribution per unit volume of slag [VBFS1, VBFS2, …, VBFS i-1 , VBFS i , …, VBFS max ], and particle size distribution per unit volume of fly ash [VFA1, VFA2, …, VFA i-1 , VFA i , …, VFA max ]; cement, slag, and fly ash mass ratio coefficients K PC = 0.6, K BFS = 0.2, and K FA = 0.2; pore screen size [W1, W2, W3, …, W i-1 , W i , …, W max ]; wherein VPC i , VBFS i , and VFA i represent the cement, slag, and fly ash volume to be added in the particle size range (W i-1 , W i ) per unit volume; W max represents the maximum size of the pore screen; W i represents the size of the i-th pore screen, the maximum size of the pore screen W max = 45 pm, and the minimum size of the pore screen W1 = 2 pm;

[0081] Step 2: Establish a three-dimensional Cartesian coordinate system to generate a cube CUBE with length L, width W, and height H, wherein the lower left corner of the cube CUBE is located at the coordinate origin; the volume V of the cube CUBE is L x W x H = 10 6 pm 3 ; calculate the total mass M of the cementitious material composed of cement, slag, and fly ash from formula (1); multiply the corresponding mass ratio coefficients K PC , K BFS , and KFA The total mass m of cement, mineral powder and fly ash was obtained respectively. PC m BFS and m FA ; Total mass m PC m BFS and m FA Divide by the corresponding density ρ respectively PC ρ BFS and ρ FA The total volume V of cement, mineral powder and fly ash is obtained accordingly. PC =285850.4μm 3 V BFS =102112.7μm 3 and V FA =116871.1μm 3 Initialize i = 23; using formulas (2), (3) and (4), the particle size range is obtained in (W i-1 W i The volume of cement, mineral powder and fly ash to be added (SVPC) i SVBFS i and SVFA i ;

[0082] Step 3: Using nested for and while loops in Matlab, particles of different sizes are added sequentially from largest to smallest. Within the same size class, particles are added sequentially from cement particles to mineral powder particles to fly ash particles. After the i-th size class is added, particles of the (i-1)-th size class are added, and this process is repeated until all size classes have been added. Figure 2 As shown, cement particles and mineral powder particles have irregular shapes, while fly ash particles are spherical. The total number of irregular particles in the database is denoted as N = 10000; the number of resampling angles is N1 = 2562; the particle number selected for placement is randomly generated using the Matlab built-in function randi, t = randi(1, 10000); the equivalent particle size control parameter K is randomly generated using the Matlab built-in function rand. w and the particle release center coordinates (x, y, z), K w =W i-1 +(W i-1 W i )×rand(1); x=rand(L), y=rand(W), z=rand(H); Generate the Euler rotation matrix M using the built-in Matlab function eul2rotm. RRandomly select an irregular cement or mineral powder particle from the spherical harmonic coefficient table database of irregular particles, and obtain the cement or mineral powder particle to be added by scaling down the coefficients in the spherical harmonic coefficient table of irregular particles; perform translation and rotation transformations on the cement or mineral powder particle to be added to obtain the cement or mineral powder particle model; randomly generate spherical fly ash particles within the particle size range and use them as fly ash particles to be added, and perform translation transformations on the fly ash particles to be added to obtain the fly ash particle model.

[0083] Step 4: Determine the particle size range within (W) i-1 W i Does the particle model simultaneously satisfy both boundary conditions and particle interference conditions, such as... Figure 3 As shown, the boundary condition is satisfied, meaning the particle model is completely within the cube. The method for determining whether the particle model satisfies the particle interference condition is as follows: the EOB particle interference algorithm is used for judgment. First, the C-axis of the particle model to be deployed is determined. t Is it consistent with the C of all deployed particle models? t If none of the particle models intersect, the particle interference condition is met, and the deployment is successful. Otherwise, the set of all intersecting deployed particle models is denoted as AG, and the next step is to determine whether the largest inscribed sphere of the particle model to be deployed intersects with the largest inscribed sphere of one of the particle models in AG. If so, the particle interference condition is not met, and the process returns to step 3 to reselect a particle. Otherwise, the next step is to determine whether all contour points of the particle model to be deployed are outside any deployed particle model in the set AG. If so, the particle interference condition is met, and the deployment is successful. Otherwise, the particle interference condition is not met, and the process returns to step 3 to reselect a particle. If both the boundary condition and the particle interference condition are met, the particle size range is set to (W). i-1 W i If the particle model is selected, it is placed into the cube; otherwise, return to step 3 and select a new particle. Figure 4 As shown, irregular particles with different morphologies can be selected from the spherical harmonic coefficient table database; such as Figure 5 As shown, this example uses the above method to construct an initial packing model of a three-phase composite cement microstructure based on spherical harmonic functions, where the water-cement ratio is 0.35, the total packing volume is 50.4834%, and the total number of particles is 9867; the volume of cement is 28.5850%, the particle morphology is irregular, and the number of particles is 5787; the volume of mineral powder is 10.2113%, the particle morphology is irregular, and the number of particles is 2443; the volume of fly ash is 11.6871%, the particle morphology is spherical, and the number of particles is 1637.

[0084] In this embodiment, an electronic device includes a memory for storing a program supporting a processor to execute the above method, and the processor configured to execute the program stored in the memory.

[0085] In this embodiment, a computer readable storage medium has a computer program stored thereon, and the computer program is run by a processor to perform the steps of the above method.

Claims

1. A method for constructing a three-phase composite cement microstructure initial packing model based on spherical harmonics, characterized in that, Comprising the following steps: Step 1: determining the basic parameters of the three-phase composite cement microstructure model; including: the size of the microstructure model, i.e. the length L, width W and height H of the cube CUBE; the water-cement ratio wcr, the density of cement ρ PC , the density of slag ρ BFS and the density of fly ash ρ FA ; the particle size distribution per unit volume of cement [VPC1, VPC2, …, VPC i-1 , VPC i , …, VPC max ], the particle size distribution per unit volume of slag [VBFS1, VBFS2, …, VBFS i-1 , VBFS i , …, VBFS max ] and the particle size distribution per unit volume of fly ash [VFA1, VFA2, …, VFA i-1 , VFA i , …, VFA max ]; the mass proportion coefficient of cement K PC , the mass proportion coefficient of slag K BFS and the mass proportion coefficient of fly ash K FA ; the pore screen size [W1, W2, W3, …, W i-1 , W i , …, W max ]; wherein VPC i , VBFS i and VFA i respectively represent the cement, slag and fly ash to be put in the volume per unit volume under the particle size range (W i-1 , W i ); W max represents the maximum size of the pore screen; W i represents the size of the i-th pore screen; Step 2: Establish a three-dimensional Cartesian coordinate system to generate a cube CUBE with length L, width W and height H, wherein the bottom left corner of the cube CUBE is located at the coordinate origin; Step 2.1 : Calculate the total mass M of the cementitious material consisting of cement, slag and fly ash from the volume V = L x W x H of the cube CUBE, the water-cement ratio wcr and the density p of the cement PC ; Step 2.2: multiply the total mass M by the corresponding mass proportionality coefficient K PC , K BFS , and K FA , respectively, to obtain the total mass m PC , m BFS , and m FA of cement, mineral powder, and fly ash, respectively; divide the total mass m PC , m BFS , and m FA by the corresponding density p PC , p BFS , and p FA , respectively, to obtain the total volume V PC , V BFS , and V FA of cement, mineral powder, and fly ash, respectively; Step 2.3: Initialize i = max; set the total delivery volume V. PC V BFS and V FA Multiplying by the particle size distribution per unit volume of cement, the particle size distribution per unit volume of mineral powder, and the particle size distribution per unit volume of fly ash respectively yields the corresponding particle size distribution of cement [SVPC1,SVPC2,…,SVPC]. i-1 ,SVPC i ,…,SVPC max ], Particle size distribution of mineral powder [SVBFS1,SVBFS2,…,SVBFS i-1 SVBFS i ,…,SVBFS max ] and particle size distribution of fly ash [SVFA1,SVFA2,…,SVFA i-1 ,SVFA i ,…,SVFA max ], of which SVPC i SVBFS i and SVFA i These represent the particle size range in (W) i-1 W i The volume of cement, mineral powder and fly ash to be added; Step 3: Randomly select a cement or mineral powder irregular particle in the spherical harmonic coefficient table database of the irregular particle, and control the size of the irregular particle by scaling the coefficients in the spherical harmonic coefficient table of the irregular particle, so that the size of the irregular particle is within the corresponding particle size range, and obtain the cement or mineral powder particle to be put in; Randomly generate fly ash spherical particles within the particle size range as fly ash particles to be put in; Randomly generate the delivery center coordinates and XYZ Euler rotation angles M R , for performing translation transformation and rotation transformation on the cement or slag particles to be delivered, to obtain a cement or slag particle model; performing translation transformation on the fly ash particles to be delivered, to obtain a fly ash particle model; Step 4: judging whether the particle model with the particle size range in (W i-1 ,W i ) satisfies the boundary condition and the particle interference condition at the same time, if so, putting the particle model with the particle size range in (W i-1 ,W i ) into the cube CUBE, otherwise, returning to step 3 to select the particle again; wherein the boundary condition is that the particle model is completely in the cube CUBE; the particle interference condition is that the particle model to be put and all the particle models put successfully do not interfere with each other.

2. The method of claim 1, wherein, The step 3 comprises: Step 3.1: Selecting the resampling polar angle θ and the resampling azimuth angle θ = {θ k = kπ / N1 | k = 1, 2, 3, …, N1}, where θ k is the kth resampling polar angle, is the kth resampling azimuth angle, and N1 is the number of resampling angles. If the irregular particles of cement or mineral powder are to be put, the serial number t of the cement or mineral powder particle to be put is randomly generated, the equivalent particle diameter control parameter K of the tth cement or mineral powder irregular particle is determined t , the spherical harmonic coefficient table b of the tth irregular particle in the spherical harmonic coefficient table database of irregular particles is selected nm,t , and step 3.2 is executed; wherein t∈(1,N), N is the total number of particles in the spherical harmonic coefficient table database. If the fly ash spherical particle is to be put in, a spherical particle radius within the particle size range is randomly generated, and step 3.2 is executed; Step 3.2: For the t-th cement or slag, the spherical harmonic table b nm,t The polar radius value of the t-th irregular particle at the resampled polar angle θ and resampled azimuthal angle is obtained using equation (1) In formula (1), is an n-th order m-th spherical harmonic basis function, and K is a spherical harmonic reconstruction order. combining the polar radius values with the resampled polar angle θ, the resampled azimuth angle φ into a cement or slag polar coordinate sequence, transforming the cement or slag polar coordinate sequence into a cement rectangular coordinate sequence Z PC or a slag rectangular coordinate sequence Z BFS and performing step 3.3; For fly ash spherical particles, randomly generated spherical particle radius is combined with the resampled polar angle θ, resampled azimuth angle φ into a fly ash polar coordinate sequence, converting the fly ash polar coordinate sequence into a fly ash rectangular coordinate sequence Z FA and performing step 3.5; Step 3.3: Calculate the equivalent diameter w of the tth cement or slag particle t , if w t ∈(W i-1 ,W i ), then a cement or slag particle is obtained to be cast and step 3.5 is performed, otherwise step 3.4 is performed; Step 3.4: Assigning to b b = a nm,t After that, go back to step 3.2; Step 3.5: For the cement or slag particle to be cast, translate the center coordinates of the Cartesian coordinate sequence Z PC or Z BFS to the randomly generated cast center coordinates to obtain the translated Cartesian coordinate sequence Z PC1 or Z BFS1 ; multiply the Cartesian coordinate sequence Z PC1 or Z BFS1 by M R to obtain the Cartesian coordinate sequence Z PC2 or Z BFS2 , and the particle composed of the contour points Z PC2 or Z BFS2 is the cement or slag particle model; For the fly ash particle to be cast, the center coordinates of the Cartesian coordinate sequence Z FA are translated to the randomly generated casting center coordinates, obtaining the translated Cartesian coordinate sequence Z FA1 , and the particle composed of the contour points of Z FA1 is the fly ash particle model.

3. An electronic device comprising a memory and a processor, characterized in that The memory is used to store a program supporting the processor to execute the construction method of claim 1 or 2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to execute the steps of the construction method of claim 1 or 2.

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