CN112347647A - Voronoi diagram-based high-stone-content soil-rock mixture model construction method - Google Patents

Voronoi diagram-based high-stone-content soil-rock mixture model construction method Download PDF

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CN112347647A
CN112347647A CN202011232514.1A CN202011232514A CN112347647A CN 112347647 A CN112347647 A CN 112347647A CN 202011232514 A CN202011232514 A CN 202011232514A CN 112347647 A CN112347647 A CN 112347647A
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丁洋
卢强
王占江
刘赟哲
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Northwest Institute of Nuclear Technology
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Abstract

The invention provides a construction method of a soil-rock mixture model with high stone content based on a Voronoi diagram, and solves the problems that an existing random block generation and release method is high in algorithm complexity and cannot generate a model with high stone content. The method comprises the following steps: 1) randomly distributing seed points in a target area; 2) obtaining a Voronoi diagram according to the seed points to obtain geometric information of the particles; 3) if the stone content needs to be adjusted, randomly selecting particles to shrink and updating particle data, otherwise, directly entering the step 4); 4) circulating each particle, and randomly selecting a reference point on each side of each particle; 5) and sequentially connecting the reference points to generate an edge and corner particle model, or making an elliptical arc tangent to the corresponding edge through two adjacent reference points, and connecting the elliptical arcs end to generate a rounded particle model. The method generates initial particles by using the Voronoi diagram, reconstructs the particles by using a method of randomly selecting reference points on each edge of the particles, and constructs a soil-stone mixture model with higher stone content and considering roundness.

Description

Voronoi diagram-based high-stone-content soil-rock mixture model construction method
Technical Field
The invention belongs to the field of numerical simulation research on mechanical properties of geological materials, and particularly relates to a construction method of a high-stone-content soil-rock mixture model based on a Voronoi diagram.
Background
With the development of large-scale engineering construction at home and abroad and modern geotechnical mechanics, the concept of the soil-rock mixture is provided, so that the engineering geologic body is further refined from two major classes of rock bodies and soil bodies into the rock body, soil body and soil-rock mixture in terms of material composition. The soil-rock mixture not only comprises natural gravelly soil formed by weathering, carrying and stacking of rocks, but also comprises artificially synthesized soil-rock dams, soil-rock mixture roadbeds in traffic engineering, gravel soil foundations in building engineering and the like. Therefore, the method has higher engineering significance and urgent practical requirements on the research of the mechanical properties of the soil-rock mixture.
For the mechanical properties of the soil-rock mixture, besides experimental research, numerical simulation is an effective research means. Due to the extremely uneven system characteristics of the earth-rock mixture, the establishment of a mesoscopic numerical model is a necessary means for researching the mechanical characteristics of the earth-rock mixture. At present, two methods for generating a soil-rock mixture mesoscopic structure model are mainly used, namely an image processing method; the second is a random block generating and putting method. The image processing method distinguishes soil and stone areas by carrying out image recognition on sample sections and establishes a model, but because of the randomness of the model, a sample model which is representative in statistical sense is difficult to find, and the model area which can be established by the method is limited and has certain limitation; in the random block generation and release method, the random block is generated firstly, and then the block is released to a designated area by utilizing a release algorithm.
Disclosure of Invention
The invention aims to solve the problems that the existing random block generation and putting method is high in algorithm complexity and cannot generate a high-stone-content model, and provides a construction method of a high-stone-content soil-rock mixture model based on a Voronoi diagram. Generating preliminary stone particles by using a Voronoi diagram, and randomly selecting reference points on all sides of the particles to reconstruct the particles to generate a soil-stone mixture with high stone content; by adopting different reference point connection modes, edge angle particles with clear edges and rounding particles with better roundness can be generated; in addition, the volume fraction of the stone can be flexibly adjusted through particle shrinkage.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
a construction method of a high-stone-content soil-rock mixture model based on a Voronoi diagram comprises the following steps:
step one, setting a target area as a rectangle with a long length and a high height, randomly generating s seed points in the target area with a total particle number of s, and storing coordinates of the seed points;
secondly, carrying out Voronoi configuration dispersion on the target area based on the seed point coordinates obtained in the first step to obtain polygons, namely initial stone particle models, and storing the seed point coordinates and the vertex coordinates of the corresponding particles as particle data files;
step three, if the stone content does not need to be adjusted, directly executing the step four; if the stone content needs to be adjusted, randomly selecting part of the particles in the particle data file in the step two to shrink to the corresponding seed points, and updating the particle data file;
traversing each particle in the particle data file, randomly selecting a reference point on each edge of each particle, and storing the coordinates of the reference points;
step five, generating a particle model;
if the corner particles are generated, sequentially connecting all the reference points in the fourth step to form a polygon which is a corner particle model;
if rounding particles are generated, for each reference point in the fourth step, an ellipse tangent to the corresponding edge is made through two adjacent reference points, an elliptical arc between the two reference points replaces a polygonal sharp corner between the two reference points, and a graph formed by connecting the elliptical arcs end to end is a rounding particle model.
Further, in the third step, the process of randomly selecting m% of particles in the particle data file to shrink to the corresponding seed points thereof is as follows: traversing the particle data file, and generating a random number q which meets the requirement of uniform distribution in (0, 100) for each particle; if q < m, the particle is shrunk.
Further, in the fifth step, the process of making the elliptic arc tangent to the corresponding side by passing through the two adjacent reference points is as follows:
a) traversing each vertex of the particles, marking the vertex as A, respectively extending a line segment formed by the vertex A and two adjacent reference points M, N by one time to a point B, C, constructing a reference triangle ABC, and taking a height AD and a middle line AE on a bottom side BC;
b) finding a vector
Figure BDA0002765679660000031
The included angle lambda between the positive direction of the x axis is as follows:
Figure BDA0002765679660000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002765679660000033
is a unit vector in the positive direction of the x axis, and the direction of the x axis is the length direction of the target area;
c) constructing coordinate rotation transformation matrix
Figure BDA0002765679660000034
And coordinate translation transformation matrix T ═ xB yB]，(xB、yB) Is the coordinate of point B;
d) remember that the length of the base line BC is
Figure BDA0002765679660000035
Construction of Positive Delta A1B1C1In which B is1The coordinates are (0, 0), C1The coordinates are
Figure BDA0002765679660000036
As delta A1B1C1Inscribed circle O of1Then refer toDelta ABC can be calculated from positive Delta A1B1C1Is obtained by one-time expansion transformation, one-time miscut transformation and one-time rotation translation transformation, and the delta A is1B1C1Inscribed circle O of1Then transformed into an ellipse tangent to Δ ABC at the midpoint of the three sides, with scaling transform coefficients
Figure BDA0002765679660000037
The miscut transformation angle gamma is the angle from AD rotating around A point to AE, and if the anticlockwise direction is positive, the parameter equation (x, y) of the elliptic arc to be solved is as follows:
Figure BDA0002765679660000038
in the formula, r is Delta A1B1C1Inscribed circle O of1Theta is the angle parameter in the polar coordinate system, and (alpha, beta) is delta A1B1C1Inscribed circle O1And (5) performing a parameter equation after telescopic transformation and shear transformation.
Further, in step three, the contraction algorithm is:
Figure BDA0002765679660000039
in the formula (x)0,y0) As seed point coordinates, (x)i,yi) For each vertex coordinate of the particle before shrinkage, (x)i',yi') coordinates of each vertex of the particle after shrinkage, and k is the shrinkage coefficient.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
1. the invention provides a construction method of a soil-rock mixture model with high stone content based on a Voronoi diagram, which overcomes the defect that a traditional block-rock random generation and putting algorithm cannot generate a model with high stone content, the stone content of the generated edge-corner granular soil can reach more than 78%, and the stone content of the ground round granular soil can reach more than 85%.
2. The soil-stone mixture model building method provided by the invention can generate a soil-stone mixture model of angular granular soil and rounded granular soil, and provides convenience for researching the influence of stone roundness grinding; meanwhile, the method can flexibly adjust the volume fraction of the particles through particle shrinkage so as to generate soil-rock mixtures with different stone contents.
3. The time complexity of the soil-rock mixture model building method depends on the time complexity of the Voronoi configuration generation, and the technical level of the Voronoi configuration is close to linearity and high in efficiency at present, so that the method is suitable for building a large-scale mesoscale model.
4. The method for constructing the soil-rock mixture model provided by the invention can be used for constructing the soil-rock mixture model and can also be used for constructing composite material models such as filler concrete and the like, and the beneficial effects are also applicable to the field of concrete mesoscopic numerical modeling.
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FIG. 1 is a flow chart of a construction method of a soil-rock mixture model with high stone content based on a Voronoi diagram;
FIG. 2 is a random distribution seed point diagram generated in step one according to an embodiment of the present invention;
FIG. 3 is a Voronoi configuration diagram generated in step two of the present invention;
FIG. 4 is a schematic diagram of randomly selecting a portion of particles for shrinkage in step three of the present invention;
FIG. 5 is a schematic diagram of a reference point selected in step four according to the embodiment of the present invention;
FIG. 6 is a schematic diagram of an angular particle model generated in step five of the present invention;
FIG. 7 is a schematic diagram of a step five-tangent elliptic arc parametric equation derivation in the embodiment of the present invention;
FIG. 8 is a schematic diagram of a method for solving an elliptical arc parameter equation of tangents of two adjacent reference points in step five in the embodiment of the present invention;
FIG. 9 is a schematic view of a rounded grain model generated in step five of the present invention;
FIG. 10 is a schematic diagram of a model of a rock-soil mixture having a rock content of about 60% by volume produced in a comparative example;
FIG. 11 is a schematic diagram of a corner particle model with a volume stone content of 78% generated without shrinkage of the particles in an embodiment of the present invention;
FIG. 12 is a schematic diagram of a model of rounded particles with a volume stone content of 85% generated when the particles are not shrunk in the example of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
The invention provides a construction method of a soil-rock mixture model with high stone content based on a Voronoi diagram.
As shown in FIG. 1, the construction method of the soil-rock mixture model with high stone content based on the Voronoi diagram, provided by the invention, comprises the following steps:
step one, setting a target area as a rectangle with a long length (x direction) and a high height (y direction), randomly generating s seed points in the target area with a total particle number of s, and storing coordinates of the seed points;
secondly, carrying out Voronoi configuration discretization on the target area based on the seed point coordinates obtained in the first step to obtain polygons, namely initial stone particle models, and storing the seed points and the geometric information of the corresponding particles as particle data files, namely the vertex coordinates of the particles and the coordinates of the corresponding seed points which are sequentially arranged to form the particle data files; algorithmic references herein: viral.J.D.Tsai.fast topological construction of delaunay transformations and voronoi diagramems [ J ]. Computers & Geosciences, 1993, 19(10): 1463. 1474;
step three, if the stone content does not need to be adjusted, directly executing the step four; if the stone content needs to be adjusted, randomly selecting a part of particles in the particle data file in the step two to contract towards corresponding seed points, and updating the particle data file;
at this time, the contraction algorithm is:
Figure BDA0002765679660000061
in the formula (x)0,y0) As seed point coordinates, (x)i,yi) Is the coordinates of each vertex of the particle before shrinkage, (x'i,y′i) Coordinates of each vertex of the particles after shrinkage are shown, and k is a shrinkage coefficient;
in this step, the selection method for randomly selecting m% of particles in the particle data file is as follows: traversing the particle data file, and generating a random number q which meets the requirement of uniform distribution in (0, 100) for each particle; if q < m, shrinking the particle;
the method only selects partial particles for shrinkage, so as to ensure that certain contact exists between the particles, so as to simulate the skeleton effect formed by the mutual contact of the particles under the condition of high stone content, and the stone content and the particle contact condition can be flexibly adjusted by adjusting the values of k and m;
step four, traversing each particle in the particle data file, randomly selecting a reference point on each edge of each particle, and storing the coordinates of the reference points, wherein the reference point coordinate calculation formula is as follows:
Figure BDA0002765679660000062
in the formula (x)1，y1)、(x2，y2) For each edge, two vertex coordinates are assigned, (x)r，yr) N is a random number between (0, 1) for the selected reference point coordinates;
step five, generating a particle model
If the angular particles are planned to be generated, sequentially connecting all the reference points in the step four, and forming a new polygon which is an angular particle model;
if the rounding particles are planned to be generated, for each reference point in the fourth step, an ellipse tangent to the corresponding edge is made through two adjacent reference points, an elliptical arc replaces a polygonal sharp corner between the two reference points, and a graph formed by connecting the elliptical arcs end to end is a rounding particle model.
The parameter equation of the elliptic arc can be obtained by an affine transformation method in geometry, and the calculation steps are as follows:
a) traversing each vertex of each particle, marking the current vertex as A, respectively extending a line segment formed by the vertex A and two adjacent reference points M, N thereof by one time to a point B, C as shown in FIG. 7, constructing a reference triangle ABC, and taking a height AD and a middle line AE on a base BC;
b) finding a vector
Figure BDA0002765679660000071
The included angle lambda between the positive direction of the x axis and the positive direction of the x axis is calculated by the following formula:
Figure BDA0002765679660000072
in the formula (I), the compound is shown in the specification,
Figure BDA0002765679660000073
is a unit vector in the positive direction of the x axis, and the direction of the x axis is the length direction of the target area;
C) constructing coordinate rotation transformation matrix
Figure BDA0002765679660000074
And coordinate translation transformation matrix T ═ xB yB]，(xB、yB) Is the coordinate of point B;
d) remember that the length of the base line BC is
Figure BDA0002765679660000075
As shown in FIG. 8, a positive Δ A is constructed1B1C1In which B is1The coordinates are (0, 0), C1The coordinates are
Figure BDA0002765679660000076
As delta A1B1C1Inscribed circle O of1Then reference Δ ABC can be defined by positive Δ A1B1C1Is obtained by one-time expansion transformation, one-time miscut transformation and one-time rotation translation transformation, and the delta A is1B1C1Inscribed circle O of1Then transformed into an ellipse tangent to Δ ABC at the midpoint of the three sides, wherein the scaling transform coefficients
Figure BDA0002765679660000077
The miscut transformation angle gamma is the angle from AD rotating around A point to AE, and if the anticlockwise direction is positive, the parameter equation (x, y) of the elliptic arc to be solved is as follows:
Figure BDA0002765679660000078
in the formula, r is Delta A1B1C1Inscribed circle O of1Theta is the angle parameter in the polar coordinate system, and (alpha, beta) is delta A1B1C1Inscribed circle O1And (5) performing a parameter equation after telescopic transformation and shear transformation.
Interpretation of terms:
voronoi diagram: also called Thiessen polygons or Dirichlet diagrams, are continuous polygons formed by perpendicular bisectors connecting adjacent points in the diagram. In the present invention, each polygon constitutes one initial stone particle.
2, affine transformation: the affine mapping is a geometric method in which one vector space is subjected to linear transformation and translation, and transformed into another vector space, and includes scaling transformation (one coordinate value is enlarged or reduced by x times), miscut transformation (one coordinate value is fixed and the other coordinate value is linearly transformed with respect to the fixed coordinate value), rotation transformation, translation transformation, and the like. The affine transformation has the properties of unchanged collinear features of the points before and after transformation, unchanged length ratio of parallel line segments and the like, and can transform a circle into an ellipse by utilizing the affine transformation, so that the difficulty in solving an equation is reduced.
3. Rounding particles and corner particles: according to the names of broken stones and gravels in the building foundation design Specification GB50007-2011, the broken stones and the gravels are respectively defined by the particle group content, corresponding to the soil with the particle size d of more than 200mm, 20mm and 2mm and the particle content of more than 50 percent of the total weight, wherein the particle shapes mainly including round and sub-round are respectively defined as boulders, pebbles and round gravels, and the particle shapes mainly including edges are respectively defined as boulders, broken stones and corner gravels. For convenience of description, boulders, pebbles and round gravels are collectively referred to as round grinding particles, and lump stones, broken stones and round gravels are collectively referred to as corner particles.
The method of the present invention is described below in terms of specific examples, and the model constructed by the method of the present invention is compared with a model constructed by a conventional method.
The method for constructing the soil-rock mixture model with high stone content based on the Voronoi diagram comprises the following steps of:
step one, as shown in fig. 2, setting a soil-rock mixture model as a square with the length of 30cm and the width of 30cm, randomly generating 100 seed points in a target area of the square with the length of 30 multiplied by 30cm, and storing coordinates of the seed points, wherein the total number of the stone particles is 100;
step two, as shown in fig. 3, performing Voronoi configuration discretization on the target area based on the coordinates of the seed points in the step one, wherein each obtained polygon is an initial stone particle model, and storing geometric information of each seed point and particles corresponding to the seed point;
step three, adjusting the stone content: as shown in fig. 4, randomly selecting m% of the particles in the particle data file in the second step to shrink toward the seed point, where the shrinkage coefficient is k, and then updating the particle data file, where in this embodiment, m is 40, and k is 0.8;
step four, as shown in fig. 5, traversing each particle in the particle data file, randomly selecting a reference point on each edge of the particle, and storing the coordinates of the reference points;
step five, generating a particle model
Generating corner particles, as shown in fig. 6, sequentially connecting the reference points in the fourth step, and forming a new polygon, namely a corner particle model;
and (3) generating rounding particles, namely, for each reference point in the fourth step, making an ellipse tangent to the corresponding edge through two adjacent reference points, replacing a polygonal sharp corner between the two reference points with an elliptical arc, wherein a figure formed by connecting the elliptical arcs end to end is a rounding particle model, and the generated rounding particle soil model is shown in fig. 9.
The following references are made: the method in Cheng Li, Zhang Peng, Zheng hong, soil and rock mixture two-dimensional microscopic structure model and numerical value manifold method simulation, geotechnical mechanics, 38(8), P2402-10, 2017.08 is the existing method, and the effect is compared with the effect of the embodiment of the invention.
As shown in fig. 10, the stone particles produced by the conventional method are completely convex polygons, the influence of the particle roundness cannot be considered, and the volume stone content is about 60%, which is difficult to achieve higher. Meanwhile, in the existing method, a random putting method is adopted, a large amount of contact judgment needs to be carried out, and the stone blocks are difficult to put in the later period, so that the time consumption is large.
Compared with the prior art, the soil-rock mixture model construction method based on the Voronoi diagram can generate the edge-angle granular soil and the rounded granular soil so as to consider the influence of roundness grinding; if the particle shrinkage in the third step is not carried out, the stone content of the generated corner angle particle soil volume can reach 78% at most, and the stone content of the ground round particle soil volume can reach 85% at most, as shown in fig. 11 and 12, the stone content is far higher than that of the comparative example, and the algorithm efficiency is higher without using a contact judgment algorithm.

Claims (4)

1. A construction method of a soil-rock mixture model with high stone content based on a Voronoi diagram is characterized by comprising the following steps:
step one, setting a target area as a rectangle with a long length and a high height, randomly generating s seed points in the target area with a total particle number of s, and storing coordinates of the seed points;
secondly, carrying out Voronoi configuration dispersion on the target area based on the seed point coordinates obtained in the first step to obtain polygons, namely initial stone particle models, and storing the seed point coordinates and the vertex coordinates of the corresponding particles as particle data files;
step three, if the stone content does not need to be adjusted, directly executing the step four; if the stone content needs to be adjusted, randomly selecting part of the particles in the particle data file in the step two to shrink to the corresponding seed points, and updating the particle data file;
traversing each particle in the particle data file, randomly selecting a reference point on each edge of each particle, and storing the coordinates of the reference points;
step five, generating a particle model;
if the corner particles are generated, sequentially connecting all the reference points in the fourth step to form a polygon which is a corner particle model;
if rounding particles are generated, for each reference point in the fourth step, an ellipse tangent to the corresponding edge is made through two adjacent reference points, an elliptical arc between the two reference points replaces a polygonal sharp corner between the two reference points, and a graph formed by connecting the elliptical arcs end to end is a rounding particle model.
2. The method for constructing the soil and rock mixture model with the high stone content based on the Voronoi diagram according to claim 1, wherein in the third step, the process of randomly selecting m% of particles in the particle data file to shrink to the corresponding seed points comprises the following steps: traversing the particle data file, and generating a random number q which meets the requirement of uniform distribution in (0, 100) for each particle; if q < m, the particle is shrunk.
3. The construction method of the soil and rock mixture model with the high stone content based on the Voronoi diagram is characterized in that in the fifth step, the process of making the elliptic arc tangent to the corresponding side by passing through the two adjacent reference points is as follows:
a) traversing each vertex of the particles, marking the vertex as A, respectively extending a line segment formed by the vertex A and two adjacent reference points M, N by one time to a point B, C, constructing a reference triangle ABC, and taking a height AD and a middle line AE on a bottom side BC;
b) finding a vector
Figure FDA0002765679650000021
The included angle lambda between the positive direction of the x axis is as follows:
Figure FDA0002765679650000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002765679650000023
is a unit vector in the positive direction of the x axis, and the direction of the x axis is the length direction of the target area;
c) constructing coordinate rotation transformation matrix
Figure FDA0002765679650000024
And coordinate translation transformation matrix T ═ xB yB]，(xB、yB) Is the coordinate of point B;
d) remember that the length of the base line BC is
Figure FDA0002765679650000025
Construction of Positive Delta A1B1C1Wherein B is1The coordinates are (0, 0), C1The coordinates are
Figure FDA0002765679650000026
As delta A1B1C1Inscribed circle O of1Then reference Δ ABC can be defined by positive Δ A1B1C1Is obtained by one-time expansion transformation, one-time miscut transformation and one-time rotation translation transformation, and the delta A is1B1C1Inscribed circle O of1Then transformed into an ellipse tangent to Δ ABC at the midpoint of the three sides, with scaling transform coefficients
Figure FDA0002765679650000027
The miscut transformation angle gamma is the angle from AD rotating around A point to AE, and if the anticlockwise direction is positive, the parameter equation (x, y) of the elliptic arc to be solved is as follows:
Figure FDA0002765679650000028
in the formula, r is Delta A1B1C1Inscribed circle O of1Theta is the angle parameter in the polar coordinate system, and (alpha, beta) is delta A1B1C1Inscribed circle O1And (5) performing a parameter equation after telescopic transformation and shear transformation.
4. The construction method of the soil and rock mixture model with the high stone content based on the Voronoi diagram is characterized in that in the third step, a contraction algorithm is as follows:
Figure FDA0002765679650000031
in the formula (x)0,y0) As seed point coordinates, (x)i,yi) For each vertex coordinate of the particle before shrinkage, (x)i',yi') coordinates of each vertex of the particle after shrinkage, and k is the shrinkage coefficient.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH11276997A (en) * 1998-01-27 1999-10-12 Nishimura Tekkosho:Kk Soil and stone separating conveyor and soil and stone separation using the conveyor
CN109241646A (en) * 2018-09-20 2019-01-18 重庆大学 Based on the oval multifactor two-dimentional soil-rock mixture generation method stacked with random field
CN109509251A (en) * 2018-11-08 2019-03-22 重庆大学 Multifactor three-dimensional soil-rock mixture generation method
CN111428359A (en) * 2020-03-23 2020-07-17 河海大学 Anisotropic rock modeling method considering grain occlusion

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH11276997A (en) * 1998-01-27 1999-10-12 Nishimura Tekkosho:Kk Soil and stone separating conveyor and soil and stone separation using the conveyor
CN109241646A (en) * 2018-09-20 2019-01-18 重庆大学 Based on the oval multifactor two-dimentional soil-rock mixture generation method stacked with random field
CN109509251A (en) * 2018-11-08 2019-03-22 重庆大学 Multifactor three-dimensional soil-rock mixture generation method
CN111428359A (en) * 2020-03-23 2020-07-17 河海大学 Anisotropic rock modeling method considering grain occlusion

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