1. A method for calculating the pore size distribution of a cement-based material particle stacking system is characterized by comprising the following steps: the sphere stacking system pore size distribution calculation method comprises the steps of firstly establishing a sphere particle stacking geometric model, secondly performing Delaunay tetrahedron subdivision on a sphere center point set to divide the stacking model into a set consisting of a plurality of tetrahedrons, then acquiring the pore diameters and pore volumes of the tetrahedrons in the set one by one, and finally performing information statistics and computational analysis to obtain the pore size distribution information of the stacking system pore structure.

2. The method for calculating the pore size distribution of the cement-based material particle stacking system according to claim 1, wherein the method comprises the following steps: the process of establishing the spherical particle stacking geometric model comprises the following steps:

for a system with specified spherical particle size distribution and porosity, firstly determining the size of a cubic filling space, then sequentially putting spherical particles into the cubic filling space from large to small according to the size, wherein the coordinate of each spherical particle is randomly generated by a Monte Carlo method until all the spherical particles are put in, and forming a spherical particle stacking geometric model.

3. The method for calculating the pore size distribution of the cement-based material particle stacking system according to claim 2, wherein the method comprises the following steps: in the process of establishing a spherical particle stacking geometric model, when a stacking system does not allow particle overlapping, sphere intersection detection needs to be performed, that is, when the ith sphere is put into, any j smaller than i needs to satisfy a formula one:

|(X_i,Y_i,Z_i)–(X_j,Y_j,Z_j)|>R_i+R_j (1)

in the above formula, (Xi, Yi, Zi) is the cartesian coordinate of the ith input sphere, (Xj, Yj, Zj) is the cartesian coordinate of the jth input sphere, Ri is the radius of the ith input sphere, and Rj is the radius of the jth input sphere;

when the accumulation system allows the particle overlapping condition to exist, the intersection of spheres does not need to be detected, and all sphere particles are directly and randomly thrown into the area.

4. The method for calculating the pore size distribution of the cement-based material particle stacking system according to claim 3, wherein the method comprises the following steps: when the spherical particle stacking geometric model is a low-porosity non-overlapping spherical stacking system, a compression movement strategy is adopted to ensure that all spherical particles are in a non-overlapping accommodating state in a cubic filling space, so that the calculation requirement of a formula I is met, and the operation process of the compression movement strategy is as follows:

firstly, spherical particles are put into an expanded cubic space, the expansion of the cubic space can be realized by amplifying the side length of the cubic space to two times, the volume of the cubic space is eight times of the volume of the original cubic space, the filling density in the expanded cubic space is only one eighth of the target filling density under the condition that the spherical particles are put into the expanded cubic space, and after all the spherical particles are put into the expanded cubic space, the spherical particles are randomly moved, and each moved particle is prevented from colliding with other particles during movement; then, determining the shortest surface distance between every two particles, dividing the surface distance by the center distance of the two nearest particles to be used as a compression ratio, and compressing the cubic filling area by the compression ratio, wherein the radius of all spherical particles is unchanged and the coordinate is reduced in an equivalent manner during compression; and finally, repeatedly executing the two steps of moving the spherical particles and compressing the filling space until the expanded cubic space is compressed to the initial set size, thereby completing the establishment process of the target low-porosity non-overlapping spherical accumulation model.

5. The method for calculating the pore size distribution of the cement-based material particle packing system according to claim 1, 2, 3 or 4, wherein the method comprises the following steps: based on the sphere particle accumulation geometric model, the operation process of performing Delaunay tetrahedron subdivision on the sphere center point set is as follows:

according to the information of the spherical particle stacking geometric model, coordinates of the centers of all spheres are arranged to form a two-dimensional matrix, the two-dimensional matrix has three rows which are respectively an abscissa, an ordinate and a column coordinate of the center of the sphere, each row in the matrix represents the sphere coordinate of one sphere, and the two-dimensional matrix is acted by a Delaunay Triangulation function in MATLAB, namely Delaunay tetrahedron subdivision of the sphere center point set is realized; in the two-dimensional case, the matrix has only two columns, respectively set of abscissas and sets of column coordinates of the circle, on which the Delaunay Triangulation function is applied to perform a Delaunay Triangulation of a set of circle center points.

6. The method for calculating the pore size distribution of the cement-based material particle stacking system according to claim 5, wherein the method comprises the following steps: after the Delaunay tetrahedron subdivision is performed on the sphere center point set, the stacking model is divided into a set consisting of a plurality of tetrahedrons, and the process of determining the pore aperture and the pore volume of the tetrahedrons in the set one by one is as follows:

the particle stacking system after being subdivided by the Delaunay tetrahedron is composed of a plurality of mutually independent and non-overlapping tetrahedrons, wherein each tetrahedron is composed of a solid phase occupied by the vertex angle spherical particles and a pore phase, the pore phase is the residual phase of the solid phase occupied by the tetrahedron minus the four vertex angle spherical particles, the pore phase of the tetrahedron is the tetrahedral pore, and the volume corresponding to the pore is the pore volume of the tetrahedron;

the tetrahedron is provided with four triangular surfaces, each triangular surface consists of a solid phase and a pore phase, wherein the surface solid phase is the sum of sector areas intersected by particles with three angular points on the surface, and the surface pore phase is the residual phase of the tetrahedron surface minus the corresponding solid phase; the surface pore phase is the cross section of the narrowest part of a channel connecting the tetrahedral pore and the adjacent tetrahedral pore, namely the throat cross section; the radius of an inscribed circle corresponding to the cross section of the throat is the roar of a tetrahedron pore, and because one tetrahedron has four surfaces, namely one tetrahedron pore corresponds to four cross sections of the throat and four roar corresponding to the four cross sections of the throat one by one; when a tetrahedral pore is considered to be a spherical whole, the corresponding size of the spherical whole is the pore size of the tetrahedral pore.

7. The method for calculating the pore size distribution of the cement-based material particle stacking system according to claim 6, wherein the method comprises the following steps: the process of obtaining the pore diameter and pore volume of each tetrahedral pore is as follows:

the tetrahedral aperture has a plurality of characteristic apertures, wherein the size of the throat cross section on the surface of the tetrahedron is the roar diameter, the size of the internal aperture of the tetrahedron is the pore size of the pore body, the roar diameter is calculated by determining an inscribed circle for each triangular surface in the tetrahedron according to the geometrical relationship, the inscribed circle is not only in a tangent state with the spheres at the three angular points, but also has the same distance from the center of the inscribed circle to each angular point, the radius value of the inscribed circle is a roar of a tetrahedral pore, the maximum value of the four roar of the tetrahedral pore is determined to be the maximum roar, the minimum value of the four roar is the minimum roar, the calculation process of the pore radius is that according to the geometric relationship, the distances from the center of an inscribed sphere of four angular point spheres to each angular point sphere are equal, and the inscribed sphere in the tetrahedral pore is determined, wherein the radius value of the sphere is the pore radius of the tetrahedral pore;

the pore volume of tetrahedral pores is calculated by calculating the volume V of tetrahedron for non-overlapping sphere stacking system_tAnd the volume V of the intersection of the four vertex spherical particles with the tetrahedron₁、V₂、V₃And V₄Volume of tetrahedral pores V_pCalculating by the formula two:

V_p＝V_t–(V₁+V₂+V₃+V₄) (2)

for the sphere stacking system allowing overlapping existence, the following scheme is adopted for calculation due to the more complicated structure:

randomly putting N particles into a tetrahedron, generating the particle coordinates by a Monte Carlo method, counting the number N of the particles falling in the pores, and determining the volume V of the pores in the tetrahedron_pCan be calculated by the formula three:

V_p＝(n/N)*V_t (3)。

8. the method for calculating the pore size distribution of the cement-based material particle stacking system according to claim 7, wherein the method comprises the following steps: the particle stacking system after being subdivided by the Delaunay tetrahedrons is composed of a plurality of mutually independent and non-overlapping tetrahedrons, all the tetrahedrons are traversed to obtain the pore diameter and the pore volume corresponding to each tetrahedron, the pore diameter of the pore is taken as an independent variable, the sum of the pore volumes of all the tetrahedron pores smaller than or equal to the pore diameter is taken as a dependent variable, a cumulative distribution function curve of the pore diameter distribution is obtained, and finally, the cumulative distribution function of the pore diameter distribution is subjected to difference or derivation, so that a probability density function curve of the pore diameter distribution of the spherical particle stacking system is obtained.

Background

The cement-based material is a heterogeneous dispersion system with multiple phases, particles with multiple particle sizes stacked and multiple pore sizes contained inside. For example, the aggregate in concrete is required to have good particle grading, so that the stacking porosity is reduced to reduce the consumption of cement, and the particle close-stacking effect of a cement system is very important for the rheological property of fresh slurry and the strength development of hardened slurry, so that the research on the method for improving the compactness (porosity and pore size distribution) of the stacking system of the cement-based material particles is always a research hotspot in the field. The existing method for determining the pore size distribution of a particle-packed porous material system comprises the following steps: experimental and numerical simulations.

The methods commonly used in the traditional experimental method are mercury pressure method and gas adsorption method: the method has the defects of obvious time consumption, small size and poor representativeness of a required sample, and a plurality of hours are required in one experiment; in addition, limited by the experimental principle, only pore information in a specified pore size range can be analyzed, for example, the pore analysis range of the mercury intrusion method is only 440 micrometers to 3.6 nanometers, and all information of the microscopic three-dimensional pore structure cannot be comprehensively represented.

Due to the rapidly developed digital modeling technology, the microscopic three-dimensional pore structure in the porous medium material is simulated and characterized. The emerging numerical simulation method mainly depends on a computer image analysis technology, and the technology divides a three-dimensional model of a porous material into a plurality of congruent cubic pixels by pixelation, wherein the pixels are solid if the central points of the pixels are solid, and the pixels are pores if the central points of the pixels are pores, and then performs subsequent pore size distribution calculation on the processed three-dimensional model of the porous material. The three-dimensional model of the numerical simulation method is reconstructed according to the structure of the scanning electron microscope or reconstructed according to the structure of the material.

The smallest pore that can be identified by the pixelized material model is related to the size of the selected pixel: the smaller the selected pixel is, the smaller the minimum pore which can be analyzed is, and the finer the established porous material three-dimensional model is, but at the same time, the total pixel quantity of the material model is increased, the more the content which needs to be processed when the pore size distribution calculation is subsequently carried out is, and the overall operation efficiency is reduced; the larger the selected pixel is, the larger the minimum pore size that can be analyzed is, the coarser the porous material three-dimensional model is, although the operation speed is high, the distribution information of some finer pores can be ignored, and it is difficult to comprehensively and accurately represent all the information of the microscopic three-dimensional pore structure.

In summary, the existing pore size distribution evaluation algorithm mainly implements the calculation of the pore size distribution by performing different types of pixelation processing on the particle-packed porous material three-dimensional model, which is limited by the resolution, and the pore size distribution evaluation algorithm based on the pixelation processing cannot have both high calculation accuracy and high operation efficiency. For a sphere accumulation system with a special geometric structure, the requirements of high accuracy of a calculation result and high efficiency of an operation process cannot be met simultaneously by adopting a pixel processing-based aperture distribution analysis method.

Disclosure of Invention

The invention aims to provide a method for calculating the pore size distribution of a cement-based material particle stacking system.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a method for calculating the pore size distribution of a cement-based material particle stacking system comprises the steps of firstly establishing a spherical particle stacking geometric model, secondly performing Delaunay tetrahedron subdivision on a spherical center point set to divide the stacking model into a set consisting of a plurality of tetrahedrons, then acquiring the pore diameters and pore volumes of the tetrahedrons in the set one by one, and finally performing information statistics and calculation analysis to further acquire the pore size distribution information of the whole pore structure.

As a preferable scheme: the process of establishing the spherical particle stacking geometric model comprises the following steps:

for a system with specified spherical particle size distribution and porosity, firstly determining the size of a cubic filling space, then sequentially putting spherical particles into the cubic filling space from large to small according to the size, wherein the coordinate of each spherical particle is randomly generated by a Monte Carlo method until all the spherical particles are put in, and forming a spherical particle stacking geometric model.

As a preferable scheme: in the process of establishing a spherical particle stacking geometric model, when a stacking system which does not allow particles to overlap is adopted, sphere intersection detection needs to be performed, that is, when the ith sphere is put into use, any j smaller than i needs to satisfy the formula one:

|(X_i,Y_i,Z_i)–(X_j,Y_j,Z_j)|>R_i+R_j(1)

in the above formula, (Xi, Yi, Zi) is the cartesian coordinate of the ith input sphere, (Xj, Yj, Zj) is the cartesian coordinate of the jth input sphere, Ri is the radius of the ith input sphere, and Rj is the radius of the jth input sphere;

when the particle stacking system is a stacking system allowing particles to be overlapped, the intersection of spheres does not need to be detected, and all spherical particles are directly randomly put into an area.

As a preferable scheme: when the spherical particle stacking geometric model is a low-porosity non-overlapping spherical stacking system, a compression movement strategy is adopted to ensure that all spherical particles are in a non-overlapping accommodating state in a cubic filling space, so that the calculation requirement of a formula I is met, and the operation process of the compression movement strategy is as follows:

firstly, spherical particles are put into an expanded cubic space, the expansion of the cubic space can be realized by amplifying the side length of the cubic space to two times, the volume of the cubic space is eight times of the volume of the original cubic space, the filling density in the expanded cubic space is only one eighth of the target filling density under the condition that the spherical particles are put into the expanded cubic space, and the spherical particles are randomly moved after all the spherical particles are put into the expanded cubic space, so that each moved particle is prevented from colliding with other particles during movement; then, determining the shortest surface distance between every two particles, dividing the surface distance by the center distance of the two nearest particles to be used as a compression ratio, and compressing the cubic filling area by the compression ratio, wherein the radius of all spherical particles is unchanged and the coordinate is reduced in an equivalent manner during compression; and finally, repeatedly executing the two steps of moving the spherical particles and compressing the filling space until the expanded cubic space is compressed to the initial set size, thereby completing the establishment process of the target low-porosity non-overlapping spherical accumulation model.

As a preferable scheme: based on the sphere particle accumulation geometric model, the operation process of performing Delaunay tetrahedron subdivision on the sphere center point set is as follows:

according to the information of the spherical particle stacking geometric model, coordinates of the centers of all spheres are arranged to form a two-dimensional matrix, the two-dimensional matrix has three rows which are respectively an abscissa, an ordinate and a column coordinate of the center of the sphere, each row in the matrix represents the sphere coordinate of one sphere, and the two-dimensional matrix is acted by a Delaunay Triangulation function in MATLAB, namely Delaunay tetrahedron subdivision of the sphere center point set is realized; in the two-dimensional situation, the matrix has only two columns which are respectively an abscissa set and a column coordinate set of the circle, and a Delaunay Triangulation function is acted on the matrix to execute Delaunay Triangulation on a circle center point set;

as a preferable scheme: after the Delaunay tetrahedron subdivision is performed on the sphere center point set, the stacking model is divided into a set consisting of a plurality of tetrahedrons, and the process of determining the pore aperture and the pore volume of the tetrahedrons in the set one by one is as follows:

the particle stacking system after being subdivided by the Delaunay tetrahedron is composed of a plurality of mutually independent and non-overlapping tetrahedrons, wherein each tetrahedron is composed of a solid phase occupied by the vertex angle spherical particles and a pore phase, the pore phase is the residual phase of the solid phase occupied by the tetrahedron minus the four vertex angle spherical particles, the pore phase of the tetrahedron is the tetrahedral pore, and the volume corresponding to the pore is the pore volume of the tetrahedron;

the tetrahedron is provided with four triangular surfaces, each triangular surface consists of a solid phase and a pore phase, wherein the surface solid phase is the sum of sector areas intersected by particles with three angular points on the surface, and the surface pore phase is the residual phase of the tetrahedron surface minus the corresponding solid phase; the surface pore phase is the cross section of the narrowest part of a channel connecting the tetrahedral pore and the adjacent tetrahedral pore, namely the throat cross section; the size of the corresponding inscribed circle of the cross section of the throat is the roar of the tetrahedral pore, and because one tetrahedron has four surfaces, namely one tetrahedron pore corresponds to four cross sections of the throat and four roars corresponding to the four cross sections of the throat one by one; when the tetrahedral internal pore is regarded as a spherical whole, the corresponding size of the spherical whole is the pore volume pore diameter of the tetrahedral pore.

As a preferable scheme: the process of obtaining the pore diameter and pore volume of each tetrahedral pore is as follows:

the tetrahedral aperture has a plurality of characteristic apertures, wherein the size of the throat cross section on the surface of the tetrahedron is the roar diameter, the size of the whole of the internal aperture of the tetrahedron is the pore size of the pore body, the roar diameter is calculated by determining an inscribed circle for each triangular surface in the tetrahedron according to the geometrical relationship, the inscribed circle is not only in a tangent state with the spheres at the three angular points, but also has the same distance from the center of the inscribed circle to each angular point, the radius value of the inscribed circle is a roar of a tetrahedral pore, the maximum value of the four roar of the tetrahedral pore is determined to be the maximum roar, the minimum value of the four roar is the minimum roar, the calculation process of the pore radius is that according to the geometric relationship, the distances from the center of an inscribed sphere of four angular point spheres to each angular point sphere are equal, and the inscribed sphere in the tetrahedral pore is determined, wherein the radius value of the sphere is the pore radius of the tetrahedral pore;

the pore volume of tetrahedral pores is calculated by calculating the volume V of tetrahedron for non-overlapping sphere stacking system_tAnd the volume V of the intersection of the four vertex spherical particles with the tetrahedron₁、V₂、V₃And V₄Volume of tetrahedral pores V_pCalculating by the formula two:

V_p＝V_t–(V₁+V₂+V₃+V₄) (2)

for the sphere stacking system allowing overlapping existence, the following scheme is adopted for calculation due to the more complicated structure:

randomly putting N particles into a tetrahedron, generating the particle coordinates by a Monte Carlo method, counting the number N of the particles falling in the pores, and determining the volume V of the pores in the tetrahedron_pCan be calculated by the formula three:

V_p＝(n/N)*V_t (3)。

as a preferable scheme: the particle stacking system after being subdivided by the Delaunay tetrahedrons is composed of a plurality of mutually independent and non-overlapping tetrahedrons, all the tetrahedrons are traversed to obtain the pore diameter and the pore volume corresponding to each tetrahedron, the pore diameter of the pore is taken as an independent variable, the sum of the pore volumes of all the tetrahedron pores smaller than or equal to the pore diameter is taken as a dependent variable, a cumulative distribution function curve of the pore diameter distribution is obtained, and finally, the cumulative distribution function of the pore diameter distribution is subjected to difference or derivation, so that a probability density function curve of the pore diameter distribution of the spherical particle stacking system is obtained.

Compared with the prior art, the invention has the following beneficial effects:

the invention relates to an aperture distribution evaluation method based on Delaunay triangulation, which has the advantages of scientific and reasonable calculation principle, simple steps, no requirement on operation experience of operators, quick, stable and accurate obtained result aging.

Based on the intrinsic geometric relationship of spherical particle accumulation, the method avoids the method of obtaining high precision by means of high resolution in a pixelation processing method, does not introduce additional errors, and can extract real and accurate aperture distribution information.

The method can accurately acquire the maximum roar diameter distribution, the minimum roar diameter distribution and the pore radius distribution of the accumulation system, and provides an effective acquisition method of related data for further research of a subsequent multi-level unequal-diameter sphere accumulation system.

The method is suitable for calculating the accumulation conditions of multiple particles which are closely accumulated or not closely irregularly accumulated, the calculation principle is reasonable and comprehensive, the calculation result is accurate, and the actual requirements are met better.

The method can be further expanded to the calculation of the pore size distribution of an irregular polyhedral particle stacking system, and has wide application scenes and potential space for future development and optimization.

Drawings

The invention will be further described with reference to the accompanying drawings

FIG. 1 is a schematic flow diagram of a non-overlapping random sphere distribution model generation algorithm;

FIG. 2 is a schematic diagram of a two-dimensional Delaunay triangulation;

FIG. 3 is a schematic representation of the tetrahedral pore throat and the radius of the pore body;

FIG. 3a is a schematic structural view of a first surface of a tetrahedron;

FIG. 3b is a schematic structural view of a second surface of the tetrahedron;

FIG. 3c is a schematic structural view of the third surface of the tetrahedron;

FIG. 3d is a schematic structural diagram of a front view of a fourth surface of a tetrahedron;

FIG. 4 is a schematic diagram of modeling results of a non-overlapping single-particle-diameter sphere stacking system;

FIG. 5 is a diagram showing the calculation results of pore size distribution of a non-overlapping single-particle-size sphere stacking system;

FIG. 6 is a schematic diagram of modeling results of a non-overlapping multi-particle-size sphere stacking system;

FIG. 7 is a diagram showing the calculation results of pore size distribution of a non-overlapping multi-particle-size sphere stacking system;

fig. 8 is a block flow diagram of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiment is only one specific embodiment of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the processing steps closely related to the solution of the present invention are shown in the drawings, and the minor details not related to the present invention are omitted.

The first embodiment is as follows: the present embodiment is described with reference to fig. 1, fig. 2, fig. 3a, fig. 3b, fig. 3c, fig. 3d, fig. 4, fig. 5, fig. 6, fig. 7, and fig. 8, in which the method for calculating pore size distribution of a sphere stacking system according to the present embodiment first establishes a geometric model of sphere particle stacking, then performs Delaunay tetrahedron subdivision on a sphere center point set to divide the stacking model into sets consisting of independent tetrahedrons, then determines pore sizes and pore volumes of the tetrahedrons in the sets one by one, and finally performs information statistics and computational analysis, thereby obtaining comprehensive information of pore size distribution of the whole pore structure.

The sphere stacking system pore size distribution calculation method specifically comprises the following five steps:

s1, establishing a three-dimensional geometric model of random sphere accumulation;

s2, performing Delaunay tetrahedron subdivision on the spherical center point set;

s3, traversing and calculating the pore aperture of the split tetrahedral pore;

s4, traversing and calculating the pore volume of the split tetrahedral pore;

and S5, obtaining pore size distribution information of the stacking system through statistical analysis.

Further, step S1 is to realize the random distribution modeling of the spherical particles by the monte carlo algorithm according to the known spherical particle size distribution information; and for a system with a close packing requirement, implementing a compression moving iteration strategy to realize modeling.

Further, in step S2, based on the built sphere stacking model, Delaunay tetrahedron splitting is performed on the sphere center point set, and the split stacking model becomes a set composed of mutually independent tetrahedrons, each tetrahedron in the set being composed of sphere particles at four corner points and tetrahedral pores between four spheres.

Further, step S3 finds inscribed circles at the cross sections of the four throats of the tetrahedral pore and an inscribed sphere inside the pore according to the geometric relationship, and determines the four pore throat pore diameters and the pore body radius of the tetrahedral pore.

Further, step S4 calculates the total volume of the tetrahedron and the volume of the intersection of the four corner spherical particles and the tetrahedron, and subtracts the two volumes to find the volume of the pore phase of the tetrahedron.

Further, for a sphere stacking system allowing overlapping existence, random particles are placed in a tetrahedron, particle coordinates are generated by a Monte Carlo method, and then the number of the particles falling in the pores is counted to calculate the pore volume in the tetrahedron.

Further, steps S3 and S4 need to solve the pore diameter and pore volume of each tetrahedron in the tetrahedron set formed by the sphere stacking system after Delaunay subdivision.

Further, step S5 is to use all tetrahedrons with the calculated pore information as research objects, perform statistical analysis calculation, obtain the pore volume ratio in the specified pore interval, and finally obtain the pore size distribution information of the real pore structure.

The second embodiment is as follows: the embodiment is further limited by the first embodiment, and the process of establishing the sphere particle stacking geometric model in the sphere stacking system pore size distribution calculation method is as follows:

for a system with specified spherical particle size distribution and porosity, firstly determining the size of a cubic filling space, then sequentially putting the spherical particles into the cubic filling space from large to small according to the size of the spherical particles, and randomly generating coordinates of each spherical particle by a Monte Carlo method until all the spherical particles are put into the cubic filling space to form a spherical particle stacking geometric model.

In the process of establishing a spherical particle stacking geometric model, when a stacking system which does not allow particles to overlap is adopted, sphere intersection detection needs to be performed, that is, when the ith sphere is put into use, any j smaller than i needs to satisfy the formula one:

|(X_i,Y_i,Z_i)–(X_j,Y_j,Z_j)|>R_i+R_j(1)

in the above formula, (Xi, Yi, Zi) is the cartesian coordinate of the ith input sphere, (Xj, Yj, Zj) is the cartesian coordinate of the jth input sphere, Ri is the radius of the ith input sphere, and Rj is the radius of the jth input sphere;

when the particle stacking system is a stacking system allowing particles to be overlapped, the intersection of spheres does not need to be detected, and all spherical particles are directly randomly put into an area.

When the sphere particle accumulation geometric model is a low-porosity non-overlapping sphere accumulation system, a compression movement strategy is adopted to ensure that all sphere particles can be effectively accommodated in a cube filling space, and the effectively accommodated state is just the non-overlapping part, so that the calculation requirement of a formula I is met, and the operation process of the compression movement strategy is as follows:

firstly, spherical particles are put into an expanded cubic space, the expansion of the cubic space can be realized by amplifying the side length of the cubic space to two times, the volume of the cubic space is eight times of the volume of the original cubic space, the filling density in the expanded cubic space is only one eighth of the target filling density under the condition that the spherical particles are put into the expanded cubic space, and the spherical particles are randomly moved after all the spherical particles are put into the expanded cubic space, so that each moved particle is prevented from colliding with other particles during movement; then, determining the shortest surface distance between every two particles, dividing the surface distance by the center distance of the two nearest particles to be used as a compression ratio, and compressing the cubic filling area by the compression ratio, wherein the radius of all spherical particles is unchanged and the coordinate is reduced in an equivalent manner during compression; and finally, repeatedly executing the two steps of moving the spherical particles and compressing the filling space until the expanded cubic space is compressed to the initial set size, and thus, establishing a target low-porosity non-overlapping spherical stacking model.

The third concrete implementation mode: the present embodiment is further limited to the first specific embodiment, a process of arranging coordinates of centers of all spheres to form a two-dimensional matrix in the present embodiment is an existing calculation method, and a processing principle of the Delaunay tetrahedron subdivision is the same as that of the existing Delaunay tetrahedron subdivision.

The specific process of step S1, which is to realize the random distribution modeling of non-overlapping spherical particles by using the monte carlo algorithm according to the known spherical particle size distribution information, is described with reference to fig. 1: the method comprises the steps of sorting N spheres to be generated from large to small according to the radius, randomly generating an ith sphere when the i is detected, detecting whether the spheres are in an intersecting state, randomly generating the ith sphere again when the spheres are detected to be in the intersecting state, re-detecting, carrying out the next operation when the spheres are detected not to be in the intersecting state, namely i is i +1, randomly generating the ith sphere again when the i is smaller than or equal to the N, repeating the detection operation, and finishing the generation of all the spheres when the i is larger than the N.

The fourth concrete implementation mode: the present embodiment is further limited to the first, second, or third embodiment, and based on the sphere particle stacking geometry model, the operation process of performing Delaunay tetrahedron subdivision on the sphere center point set is as follows:

according to the information of the spherical particle stacking geometric model, coordinates of the centers of all spheres are arranged to form a two-dimensional matrix, the two-dimensional matrix has three rows which are respectively an abscissa, an ordinate and a column coordinate of the sphere center, each row in the matrix represents the sphere coordinate of one sphere, and the two-dimensional matrix is acted by a Delaunay Triangulation function in MATLAB, namely Delaunay tetrahedron subdivision is executed on a sphere center point set; in the two-dimensional case, the matrix has only two columns, respectively set of abscissas and sets of column coordinates of the circle, on which the Delaunay Triangulation function is applied to perform a Delaunay Triangulation of a set of circle center points.

In the present embodiment, the set of spherical center points is a set in which the spherical coordinates of all spherical particles are combined.

The result of the two-dimensional Delaunay triangulation in this embodiment is schematically shown in fig. 2, where a circle represents a particle, and a straight line segment set is a division result of a circle center point set.

The fifth concrete implementation mode: the embodiment is further defined as the first, second, third or fourth embodiment, and the step of determining the pore diameter and pore volume corresponding to each tetrahedron after performing Delaunay tetrahedron subdivision on the sphere center point set is as follows:

the particle stacking system after being subdivided by the Delaunay tetrahedron is composed of a plurality of mutually independent and non-overlapping tetrahedrons, wherein each tetrahedron is composed of two parts: the solid phase portion occupied by the apex angle spherical particles and the pore phase other than the solid phase portion. The tetrahedral mesoporosity may be referred to as tetrahedral porosity, and the corresponding volume is the pore volume of the tetrahedron.

Each tetrahedron is provided with four surfaces, each surface is a triangular surface, correspondingly, each triangular surface is also composed of two parts, namely a solid phase occupied by the vertex angle spherical particles and a pore phase except the solid phase, the solid phase is a surface solid phase, and the surface solid phase is the sum of sector areas intersected by the particles with three corner points on the surface. The pore phase is the surface pore phase, which is the residual phase of the tetrahedral surface minus the corresponding solid phase, and is also the cross section of the tetrahedral pore throat. The throat is a channel connecting the tetrahedral pore with adjacent tetrahedral pores, the size of an inscribed circle in the cross section of the throat is the roar path of the tetrahedral pore, and because the tetrahedron has four surfaces, the tetrahedral pore also has the cross sections of four throats and four roars corresponding to the cross sections. Furthermore, regarding the tetrahedral internal pores as a whole, the corresponding size is the pore volume pore diameter of the tetrahedral pores.

The sixth specific implementation mode: the embodiment is further defined by the first, second, third, fourth or fifth embodiment, and the process of obtaining the pore diameter and pore volume of a single tetrahedron is as follows:

the calculation process of the pore diameter of the tetrahedron is as follows: the tetrahedral pores have a plurality of characteristic pore diameters including a pore body pore diameter and a pore throat pore diameter, wherein the cross-sectional dimension of the throat is the pore throat pore diameter, also known as the roar diameter, and the dimension of the interior pores as a whole is the pore body pore diameter. The roar path affects the ease with which the transport medium can enter and exit the pore, and the radius of the pore body can characterize the environment in which the internal medium is located in the pore structure. The process of calculating the roar is that according to the geometric relationship, an inscribed circle is determined on each triangular surface in the tetrahedron, the inscribed circle is not only in a tangent state with three angular point spheres simultaneously, but also the distance from the center of the inscribed circle to each angular point is equal, and the radius value of the inscribed circle is the roar of the tetrahedral aperture. The maximum value of the four roar paths of the tetrahedral pore is determined to be the maximum roar path, and the minimum value is the minimum roar path. The calculation process of the hole radius is that according to the geometric relationship, the distances from the center of an inscribed sphere of four corner point spheres to each corner point sphere are equal, the inscribed sphere in a tetrahedral hole is determined, and the radius value of the sphere is the hole radius of the tetrahedral hole.

The process of finding and determining the inscribed sphere inside the tetrahedral pore in this embodiment is prior art.

Referring to fig. 3, 3a, 3b, 3c and 3d, the tetrahedral shape formed by the first spherical particle 1, the second spherical particle 2, the third spherical particle 3 and the fourth spherical particle 4 and the pore throat aperture and the pore radius of the corresponding pore phase, the fifth spherical particle 5 in fig. 3 represents the inner tangent sphere of the tetrahedral pore, the first spherical particle 1, the second spherical particle 2, the third spherical particle 3 and the fourth spherical particle 4 are respectively tangent to the fifth spherical particle 5, and the radius R of the fifth spherical particle 5₁₂₃₄The triangle in fig. 3a, 3b, 3c and 3d is composed of any three of four spherical particles, i.e. a first spherical particle 1, a second spherical particle 2, a third spherical particle 3 and a fourth spherical particle 4, and represents a surface of the tetrahedron, the pore phase of the surface is a throat cross section, and an inscribed circle of the throat cross section corresponds to the radius R₁₂₃、R₁₂₄、R₁₃₄And R₂₃₄The four roar paths representing the tetrahedral aperture, by comparison of the radii R₁₂₃、R₁₂₄、R₁₃₄And R₂₃₄The maximum roar path and the minimum roar path can be obtained by the length of the rotary shaft, namely the maximum value R₁₂₄The maximum throat diameter, minimum value R, of the tetrahedral pore₁₃₄The smallest throat of the tetrahedral pore.

The tetrahedral pore volume calculation process is to calculate the tetrahedral volume V for the non-overlapping sphere stacking system_tAnd the volume V of the intersection of the four vertex spherical particles with the tetrahedron₁、V₂、V₃And V₄Volume of tetrahedral pores V_pCalculating by the formula two:

V_p＝V_t–(V₁+V₂+V₃+V₄) (2)

for the sphere stacking system allowing overlapping existence, the following scheme is adopted for calculation due to the more complicated structure:

randomly putting N particles into tetrahedron, generating the particle coordinates by Monte Carlo method, counting the number N of particles falling in the pore space, and obtaining the volume V of the pore space of the tetrahedron_pCan be calculated by the formula three:

V_p＝(n/N)*V_t (3)。

the seventh embodiment: the embodiment is further defined as the first, second, third, fourth, fifth or sixth embodiment, each tetrahedron in the tetrahedron set formed after the Delaunay subdivision is traversed, the pore diameter corresponding to each tetrahedron and the pore volume corresponding to each tetrahedron are obtained and calculated, and finally, statistical analysis is performed, so that all pore diameter distribution information of the spherical particle stacking geometric model is obtained.

The specific process of statistical analysis in this embodiment is as follows:

and finally, carrying out difference or derivation on the pore size distribution cumulative distribution function to obtain a probability density function curve of the pore size distribution of the sphere particle stacking system.

The particle accumulation in the cement-based material is assumed to be spherical particle accumulation, the existing various non-uniform particle close accumulation models are also assumed to be spherical particles, irregular particles are generally simplified into spherical particles for processing, and the purpose of doing so is to achieve simple and efficient calculation.

The following embodiments are described in conjunction with the advantageous effects of the present invention and the accompanying drawings 1 to 8 of the specification:

the first embodiment is as follows:

selecting a non-overlapping single-particle-diameter sphere accumulation system with the porosity of 0.5, wherein the sphere radius is 1, firstly establishing a three-dimensional model of the non-overlapping sphere accumulation system by adopting a Monte Carlo method, then carrying out Delaunay tetrahedron division on the established accumulation system, then traversing and calculating the pore diameter and pore volume of each tetrahedron, and statistically acquiring the pore diameter distribution information of the corresponding system to display the operation and calculation results of the algorithm:

the built packing model is shown in fig. 4, although the porosity is only 0.5, the model shows that the packing degree is very tight; the calculated pore size distribution is shown in fig. 5, and the four curves in fig. 5 respectively show probability density distribution conditions of the minimum roar diameter, the maximum roar diameter, the average roar diameter and the pore body radius of the stacking system; the probability density curves of the four pore size distributions are in quasi-normal distribution, wherein the distribution range of the smallest roar diameter is 0.00-0.85, the distribution range of the largest roar diameter is 0.15-0.92, the distribution range of the average roar diameter is 0.10-0.90, and the distribution range of the radius of a pore body is 0.22-0.94; the probability density peak value of the minimum roar path distribution is maximum and reaches 3.0, and the probability density peak value of the average roar path distribution is minimum and is only 2.5; the distribution ranges of the maximum roar diameter and the radius of the hole body are approximately equal to the peak value of the probability density curve, and the probability density curves of the maximum roar diameter and the radius of the hole body are found to have consistent and highly consistent overall variation trends.

Example two:

selecting a non-overlapping multi-particle-size sphere accumulation system with the porosity of 0.5, wherein spherical particles with two particle sizes exist in the system, the particle sizes of the two kinds of spherical particles are respectively 0.5 and 2, and the total volume ratio of the two kinds of spherical particles is 1: firstly, establishing a three-dimensional model of a non-overlapping sphere accumulation system by adopting a Monte Carlo method, then performing Delaunay tetrahedron division on the established accumulation system, then traversing and calculating the pore aperture and pore volume of each tetrahedron, and statistically acquiring the pore aperture distribution information of a corresponding system to display the operation and calculation results of an algorithm:

the built accumulation model is shown in fig. 6, and the system accumulation rule is that small particles are filled in gaps where large particles are accumulated; the calculated pore size distribution is shown in fig. 7, and the four curves in fig. 7 respectively show probability density distribution conditions of the minimum roar diameter, the maximum roar diameter, the average roar diameter and the pore body radius of the stacking system; the probability density curves of the four pore size distributions are in quasi-normal distribution, wherein the distribution range of the smallest roar diameter is 0.00-1.40, the distribution range of the largest roar diameter is 0.20-1.65, the distribution range of the average roar diameter is 0.10-1.50, and the distribution range of the radius of a pore body is 0.20-1.65; the probability density peak of the minimum roar distribution is the largest and reaches 2.0, and the probability density peak of the maximum roar distribution and the radius distribution of the hole body is the smallest and is only 1.5; the distribution range of the maximum roar diameter and the radius of the hole body is almost completely consistent with the peak value of the probability density curve, and the probability density curves of the maximum roar diameter and the radius of the hole body are highly consistent with each other overall.

In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.