CN112347647B - High-stone-content soil-stone mixture model construction method based on Voronoi diagram - Google Patents
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Abstract
The invention provides a construction method of a high-stone-content soil-stone mixture model based on a Voronoi diagram, which solves the problems that the existing random block generation and delivery method has higher algorithm complexity and cannot generate the high-stone-content model. 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, and obtaining the 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 reference points on each side of the particle; 5) Sequentially connecting the reference points to generate a corner particle model, or making elliptical arcs tangent to the corresponding sides by passing through two adjacent reference points, and generating a rounding particle model by connecting the elliptical arcs end to end. According to the method, initial particles are generated by using the Voronoi diagram, particle reconstruction is performed by using a method of randomly selecting reference points on each side of the particles, and a soil-stone mixture model with higher stone content and considering roundness is constructed.
Description
Technical Field
The invention belongs to the field of numerical simulation research of mechanical properties of geological materials, and particularly relates to a construction method of a high-stone-content soil-stone mixture model based on a Voronoi diagram.
Background
With the development of large-scale engineering construction and modern rock-soil mechanics at home and abroad, the concept of a soil-stone mixture is proposed, so that the engineering geologic body is further refined into a rock mass, a soil mass and a soil-stone mixture from two major categories of rock mass and soil mass in terms of material composition. The soil-stone mixture not only comprises natural crushed stone soil formed by rock weathering, carrying and stacking, but also comprises an artificially synthesized soil-stone dam, a soil-stone mixture roadbed in traffic engineering, a crushed stone soil foundation in construction engineering and the like. Therefore, the research on the mechanical properties of the soil-stone mixture has higher engineering significance and urgent practical requirements.
For the mechanical properties of the soil-stone mixture, besides experimental study, numerical simulation is an effective study means. Because of the extremely heterogeneous systematic nature of the earth-rock mixture, establishing a microscopic numerical model is a necessary means to study its mechanical properties. At present, two methods for generating a microscopic structural model of a soil-stone mixture are mainly adopted, namely an image processing method; and secondly, a random block generation and delivery method. The image processing method distinguishes soil and stone areas and establishes a model by carrying out image recognition on the cross section of the sample, but a sample model with representativeness in the statistical sense is difficult to find due to the randomness of the model, and the method has limited established model areas and certain limitation; in the random block generation and release method, random blocks are firstly generated, and then the blocks are 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 delivery method has higher algorithm complexity and cannot generate a high-stone-content model, and provides a high-stone-content soil-stone mixture model construction method based on a Voronoi diagram. The method comprises the steps of generating preliminary stone particles by utilizing a Voronoi diagram, and generating a high-stone-content soil-stone mixture by randomly selecting reference points on each side of the particles to reconstruct the particles; by adopting different reference point connection modes, corner particles with clear corners and round particles with good roundness can be generated; in addition, the volume fraction of the stone block 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-stone mixture model based on a Voronoi diagram comprises the following steps:
step one, setting a target area as a rectangle with a length and a height, wherein the total particle number is s, randomly generating s seed points in the target area, and storing seed point coordinates;
step two, performing Voronoi configuration dispersion on the target area based on the seed point coordinates obtained in the step one, wherein each obtained polygon is an initial stone particle model, and the vertex coordinates of each seed point coordinate and corresponding particles are stored as a particle data file;
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 particles in the second particle data file in the step to shrink towards the corresponding seed points, and updating the particle data file;
step four, traversing each particle in the particle data file, randomly selecting a reference point on each side of the particle, and storing coordinates of the reference points;
step five, generating a particle model;
if the angular particles are generated, sequentially connecting all the reference points in the step four, wherein the formed polygons are the angular particle models;
if the rounding particles are generated, for each reference point in the step four, making ellipses tangent to the corresponding sides by passing through two adjacent reference points, replacing polygonal sharp angles between the two reference points with elliptical arcs between the two reference points, and forming a graph by connecting the elliptical arcs end to end, namely the rounding particle model.
Further, in the third step, the process of randomly selecting m% of particles in the particle data file to shrink toward their corresponding seed points is as follows: traversing the particle data file, and generating a random number q which is uniformly distributed in (0, 100) for each particle; if q < m, the particles are contracted.
In the fifth step, the process of making an elliptical arc tangent to the corresponding edge by passing two adjacent reference points is as follows:
a) Traversing each vertex of the particle, marking the vertex as A, respectively extending a line segment formed by the vertex A and two adjacent reference points M, N to the point B, C by one time, constructing a reference triangle ABC, and taking the reference triangle ABC as a height AD and a center line AE on a bottom line BC;
b) Obtaining vectorThe included angle lambda between the positive direction of the X axis is as follows:
in the method, in the process of the invention,the positive direction unit vector of the X axis is the length direction of the target area;
c) Construction of a coordinate rotation transformation matrixCoordinate translation transformation matrix t= [ x ] B y B ]，(x B 、y B ) The coordinates are B point coordinates;
d) The length of the bottom line BC is recorded asConstruction of the normal delta A 1 B 1 C 1 Wherein B is 1 Coordinates are (0, 0), C 1 Coordinates areMake DeltaA 1 B 1 C 1 Inscribed circle O of (2) 1 Then the reference ΔABC can be defined by the positive ΔA 1 B 1 C 1 Obtained by one expansion transformation, one miscut transformation and one rotation translation transformation, delta A 1 B 1 C 1 Inscribed circle O of (2) 1 Then transformed into an ellipse tangential to delta ABC at the midpoint of three sides, wherein the scaling factor +.>The shear-shift angle gamma is the angle from AD to AE around the A point, and the anticlockwise direction is positive, and the parameter equation (x, y) of the elliptical arc to be solved is:
wherein r is DeltaA 1 B 1 C 1 Inscribed circle O of (2) 1 And θ is an angular parameter in a polar coordinate system, and (α, β) is ΔA 1 B 1 C 1 Inscribed circle O 1 Through extension of the channelThe parameter equation after the down-conversion and the miscut conversion.
Further, in the third step, the shrinkage algorithm is:
in (x) 0 ,y 0 ) Is the seed point coordinates, (x) i ,y i ) For each vertex coordinates of the particle before shrinkage, (x) i ',y i ') is the coordinates of each vertex of the particles after shrinkage, and k is the coefficient of shrinkage.
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 high-stone-content soil-stone mixture model based on a Voronoi diagram, which overcomes the defect that a traditional block stone random generation and delivery algorithm cannot generate a high-stone-content model, the volume stone content of the generated corner granular soil can reach more than 78%, and the volume stone content of the round grinding granular soil can reach more than 85%.
2. The method for constructing the soil-stone mixture model can generate two soil-stone mixture models of angular granular soil and rounding granular soil, and provides convenience for researching stone roundness influence; meanwhile, the method can flexibly adjust the volume fraction of the particles through particle shrinkage so as to generate soil-stone mixtures with different stone contents.
3. The time complexity of the earth-rock mixture model construction method depends on the time complexity of generating the Voronoi configuration, the technical level of the Voronoi configuration is nearly linear, the efficiency is high, and the method is suitable for large-scale fine scale model construction.
4. The method for constructing the soil-stone mixture model not only can be used for constructing the soil-stone mixture model, but also can 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 microscopic numerical modeling.
Drawings
FIG. 1 is a flow chart of a method for constructing a high stone content soil-stone mixture model based on a Voronoi diagram;
FIG. 2 is a plot of randomly distributed seeds generated in step one of embodiments of the present invention;
FIG. 3 is a Voronoi configuration diagram generated in step two in an embodiment of the present invention;
FIG. 4 is a schematic drawing showing a step three of randomly selecting a portion of particles for shrinkage in accordance with an embodiment of the present invention;
FIG. 5 is a diagram illustrating reference points selected in step four according to an embodiment of the present invention;
FIG. 6 is a schematic view of a corner particle model generated in step five in an embodiment of the present invention;
FIG. 7 is a schematic diagram showing the derivation of the step five tangent elliptical arc parameter equation according to the embodiment of the present invention;
FIG. 8 is a schematic diagram of a method for solving a tangent elliptical arc parameter equation of two adjacent reference points in step five according to an embodiment of the present invention;
FIG. 9 is a schematic view of a model of rounding particles generated in step five in an embodiment of the present invention;
FIG. 10 is a schematic view of a model of a soil-stone mixture having a volumetric stone content of about 60% produced in the comparative example;
FIG. 11 is a schematic view of a model of angular particles with a volume stone content of 78% produced when the particles are not shrunk in an embodiment of the present invention;
FIG. 12 is a schematic view of a model of rounded particles with a volume stone content of 85% produced when the particles are not shrunk in an example of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention provides a method for constructing a soil-stone mixture model with high stone content based on a Voronoi diagram.
As shown in fig. 1, the method for constructing the high-stone-content soil-stone mixture model based on the Voronoi diagram provided by the invention comprises the following steps:
step one, setting a target area as a rectangle with length (x direction) and height (y direction), wherein the total particle number is s, randomly generating s seed points in the target area, and storing seed point coordinates;
performing Voronoi configuration dispersion on the target area based on the seed point coordinates obtained in the step one, wherein each obtained polygon is an initial stone particle model, and each seed point and the corresponding particle geometric information are stored as a particle data file, namely each particle vertex coordinate and the corresponding seed point coordinate which are sequentially arranged to form the particle data file; the algorithm reference here is: victor.J.D.Tsai.Fast topological construction of delaunay triangulations and voronoi diagrams [ 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 is required to be adjusted, part of particles in the particle data file in the second step are randomly selected to shrink towards the corresponding seed points, and the particle data file is updated;
at this time, the shrinkage algorithm is:
in (x) 0 ,y 0 ) Is the seed point coordinates, (x) i ,y i ) For each vertex coordinates of the particles before shrinkage, (x' i ,y′ i ) The coordinates of each vertex of the particles after shrinkage are given, and k is the shrinkage coefficient;
in the step, the selection method for randomly selecting m% of particles in the particle data file comprises the following steps: traversing the particle data file, and generating a random number q which is uniformly distributed in (0, 100) for each particle; if q < m, shrinking the particles;
the method only selects partial particles to shrink, so as to ensure that certain contact exists among the particles, simulate a skeleton effect formed by the mutual contact of the particles under the condition of high stone content, and flexibly adjust the stone content and the contact condition of the particles 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 side of the particle, storing reference point coordinates, and calculating a formula of the reference point coordinates as follows:
in (x) 1 ，y 1 )、(x 2 ，y 2 ) Corresponding two vertex coordinates for each edge, (x) r ，y r ) N is a random number between (0, 1) for the selected reference point coordinates;
step five, generating a particle model
If the generation of the angular particles is planned, sequentially connecting all the reference points in the step four, and forming a new polygon which is the angular particle model;
if the generation of the rounding particles is planned, for each reference point in the step four, making ellipses tangent to the corresponding sides by passing through two adjacent reference points, replacing polygonal sharp angles between the two reference points with elliptical arcs, and forming a graph by connecting the elliptical arcs end to end, namely the 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, and respectively extending a line segment formed by the vertex A and two adjacent reference points M, N to a point B, C by one time as shown in FIG. 7 to construct a reference triangle ABC, and taking the reference triangle ABC as a height AD and a center line AE on a base BC;
b) Obtaining vectorAnd an included angle lambda between the positive direction of the X axis and the positive direction of the X axis is calculated according to the following formula:
in the method, in the process of the invention,is the positive direction unit vector of the x axis, and the x axis direction is the targetThe length direction of the region;
c) Construction of a coordinate rotation transformation matrixCoordinate translation transformation matrix t= [ x ] B y B ]，(x B 、y B ) The coordinates are B point coordinates;
d) The length of the bottom line BC is recorded asAs shown in FIG. 8, a plus DeltaA is constructed 1 B 1 C 1 Wherein B is 1 Coordinates are (0, 0), C 1 Coordinates areMake DeltaA 1 B 1 C 1 Inscribed circle O of (2) 1 Then the reference ΔABC can be defined by the positive ΔA 1 B 1 C 1 Obtained by one expansion transformation, one miscut transformation and one rotation translation transformation, delta A 1 B 1 C 1 Inscribed circle O of (2) 1 Then transformed into an ellipse tangential to delta ABC at the midpoint of three sides, wherein the scaling factor +.>The shear-shift angle gamma is the angle from AD to AE around the A point, and the anticlockwise direction is positive, and the parameter equation (x, y) of the elliptical arc to be solved is:
wherein r is DeltaA 1 B 1 C 1 Inscribed circle O of (2) 1 And θ is an angular parameter in a polar coordinate system, and (α, β) is ΔA 1 B 1 C 1 Inscribed circle O 1 And parameter equations after the expansion transformation and the miscut transformation.
Term interpretation:
voronoi diagram: also called Thiessen polygons or Dirichlet figures, are continuous polygons made up of perpendicular bisectors of the lines connecting adjacent points in the figure. In the present invention, each polygon constitutes an initial stone particle.
2 affine transformation: also called affine mapping, in geometry, one vector space is transformed into another vector space by linear transformation and translation, including expansion transformation (a coordinate value is enlarged or reduced by x times), shear transformation (a coordinate value is fixed, another coordinate value is linearly transformed with respect to the fixed coordinate value), rotation transformation, translation transformation, and the like. The affine transformation has the characteristics of unchanged collinear characteristics of points before and after transformation, unchanged ratio of lengths of parallel line segments and the like, and can be utilized to transform a circle into an ellipse, so that the difficulty of solving an equation is reduced.
3. Rounding particles, corner particles: according to the designation of gravels and earths in the building foundation design Specification GB50007-2011, the gravels and earths are distinguished by the content of grain groups, and the particles with the particle shapes of round and sub-round are respectively defined as boulders, pebbles and round gravels, and the particles with the shapes of square are respectively defined as boulders, gravels and gravels, wherein the particle sizes d are larger than 200mm, 20mm and 2mm, and the particle contents exceed 50% of the total weight. For convenience of description, the invention refers to the boulders, pebbles and round gravels as round particles, and the boulders, gravels and the corner gravels as corner particles.
The method of the present invention will be described in more detail with reference to the following examples, and the model constructed by the method of the present invention will be compared with the model constructed by the conventional method.
The method for constructing the high-stone-content soil-stone mixture model based on the Voronoi diagram comprises the following steps:
step one, as shown in fig. 2, setting a soil-stone mixture model to be square with the length of 30cm and the width of 30cm, setting the total stone particle number to be 100, randomly generating 100 seed points in a square target area with the length of 30 multiplied by 30cm, and storing seed point coordinates;
step two, as shown in fig. 3, based on the coordinates of the seed points in the step one, performing Voronoi configuration dispersion on the target area, wherein each obtained polygon is an initial stone particle model, and the geometric information of each seed point and corresponding particles is stored;
step three, stone content adjustment: as shown in fig. 4, in the step two, m% of the particles in the particle data file shrink toward the seed point, the shrinkage coefficient is k, and then the particle data file is updated, where in this embodiment, the value of m is 40, and the value of 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 side of the particle, and storing coordinates of the reference points;
step five, generating a particle model
Generating angular particles, as shown in fig. 6, sequentially connecting all the reference points in the fourth step, wherein the formed new polygon is the angular particle model;
generating rounding particles, for each reference point in the fourth step, making ellipses tangent to the corresponding sides by passing through two adjacent reference points, replacing polygonal sharp angles between the two reference points with elliptical arcs, and forming a figure by connecting the elliptical arcs end to end, namely a rounding particle model, wherein the generated rounding particle soil model is shown in figure 9.
The following references: chen Li, zhang Peng and Zheng Hong. The two-dimensional microscopic structural model of the soil-stone mixture is established and simulated by a numerical manifold method. The method in the method of rock-soil mechanics, 38 (8) and P2402-10 and 2017.08 is the existing method, and the effect of the method is compared with that of the embodiment of the invention.
As shown in fig. 10, the stone particles produced by the conventional method are entirely convex polygons, the influence of the roundness of the particles cannot be considered, the volume stone content is about 60%, and it is difficult to achieve higher. Meanwhile, in the existing method, a random throwing method is adopted, a large number of contact judgment needs to be carried out, and the more difficult and time-consuming to throw the block stones in the later stage is, the more difficult and time-consuming is.
Compared with the prior art, the soil-stone mixture model construction method based on the Voronoi diagram can generate corner granular soil and rounding granular soil so as to consider the influence of the rounding degree; if the particle shrinkage in the third step is not carried out, the maximum stone content of the volume of the generated corner particle soil can reach 78%, the maximum stone content of the volume of the round-ground particle soil can reach 85%, as shown in fig. 11 and 12, the stone content is far higher than that in the comparative example, and the invention does not need to use a contact judgment algorithm, so that the algorithm efficiency is higher.
Claims (4)
1. The construction method of the high-stone-content soil-stone mixture model based on the Voronoi diagram is characterized by comprising the following steps of:
step one, setting a target area as a rectangle with a length and a height, wherein the total particle number is s, randomly generating s seed points in the target area, and storing seed point coordinates;
step two, performing Voronoi configuration dispersion on the target area based on the seed point coordinates obtained in the step one, wherein each obtained polygon is an initial stone particle model, and the vertex coordinates of each seed point coordinate and corresponding particles are stored as a particle data file;
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 particles in the second particle data file in the step to shrink towards the corresponding seed points, and updating the particle data file;
step four, traversing each particle in the particle data file, randomly selecting a reference point on each side of the particle, and storing coordinates of the reference points;
step five, generating a particle model;
if the angular particles are generated, sequentially connecting all the reference points in the step four, wherein the formed polygons are the angular particle models;
if the rounding particles are generated, for each reference point in the step four, making ellipses tangent to the corresponding sides by passing through two adjacent reference points, replacing polygonal sharp angles between the two reference points with elliptical arcs between the two reference points, and forming a graph by connecting the elliptical arcs end to end, namely the rounding particle model.
2. The method for constructing the high-stone-content soil-stone mixture model 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 towards the corresponding seed points is as follows: traversing the particle data file, and generating a random number q which is uniformly distributed in (0, 100) for each particle; if q < m, the particles are contracted.
3. The method for constructing the high-stone-content soil-stone mixture model based on the Voronoi diagram according to claim 1 or 2, wherein in the fifth step, the process of making an elliptical arc tangent to the corresponding side by passing two adjacent reference points is as follows:
a) Traversing each vertex of the particle, marking the vertex as A, respectively extending a line segment formed by the vertex A and two adjacent reference points M, N to the point B, C by one time, constructing a reference triangle ABC, and taking the reference triangle ABC as a height AD and a center line AE on a bottom line BC;
b) Obtaining vectorThe included angle lambda between the positive direction of the X axis is as follows:
in the method, in the process of the invention,the positive direction unit vector of the X axis is the length direction of the target area;
c) Construction of a coordinate rotation transformation matrixCoordinate translation transformation matrix t= [ x ] B y B ]，(x B 、y B ) The coordinates are B point coordinates;
d) The length of the bottom line BC is recorded asConstruction of the normal delta A 1 B 1 C 1 Wherein B is 1 Coordinates are (0, 0), C 1 Coordinates of->Make DeltaA 1 B 1 C 1 Inscribed circle O of (2) 1 Then the reference ΔABC can be defined by the positive ΔA 1 B 1 C 1 Obtained by one expansion transformation, one miscut transformation and one rotation translation transformation, delta A 1 B 1 C 1 Inscribed circle O of (2) 1 Then transformed into an ellipse tangential to delta ABC at the midpoint of three sides, wherein the scaling factor +.>The shear-shift angle gamma is the angle from AD to AE around the A point, and the anticlockwise direction is positive, and the parameter equation (x, y) of the elliptical arc to be solved is:
wherein r is DeltaA 1 B 1 C 1 Inscribed circle O of (2) 1 And θ is an angular parameter in a polar coordinate system, and (α, β) is ΔA 1 B 1 C 1 Inscribed circle O 1 And parameter equations after the expansion transformation and the miscut transformation.
4. A Voronoi diagram-based high-stone-content earth-stone mixture model construction method according to claim 3, wherein in step three, the shrinkage algorithm is:
in (x) 0 ,y 0 ) Is the seed point coordinates, (x) i ,y i ) For each vertex coordinates of the particle before shrinkage, (x) i ',y i ') is the coordinates of each vertex of the particles after shrinkage, and k is the coefficient of shrinkage.
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| 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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Patent Citations (4)
| 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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