A method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm

Abstract

The present invention discloses a method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm. First, the measured coefficient of variation is calculated based on a column cross-section sketch of the columnar joints drawn on site, and then a Voronoi diagram having a consistent coefficient of variation with the columnar joints is generated using a distance control algorithm. A three-dimensional column model is obtained by stretching along the axial direction of the column according to the column inclination measured on site, and finally random transverse joints are added to the column to obtain a three-dimensional columnar joint model. Compared with the prior art, the present invention overcomes the phenomenon that the existing randomly generated seed point set is too dense or uneven, greatly reduces the number of secondary judgments on the seed point set, and significantly improves the calculation efficiency and the quality of the obtained Voronoi diagram. The present invention introduces a distance control algorithm, which has the advantages of high efficiency, low cost, and being relatively advanced. A columnar joint model that is relatively consistent with the actual situation can be established, thereby better serving related rock mechanics research and providing technical support for engineering safety evaluation.

Description

Technical Field

[0001] The present invention relates to a method for constructing a columnar joint model, specifically to a method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm. Background Art

[0002] Columnar joints are primary tensional fracture structures widely developed in basaltic lava, presenting a regularly arranged polygonal prism shape. They are formed by the condensation and shrinkage of basaltic magma in the shallow part of the earth's crust along active faults after large-scale eruption and overflow to the surface. Columnar jointed rock masses are widely distributed in the southwest hydropower development area of China. Many large-scale hydropower stations, such as Jin'anqiao, Baihetan, Xiluodu, etc., have encountered a large number of columnar jointed rock masses. The diameters of the columns range from several meters to several centimeters, and their lengths can be up to 30 meters. The number of sides of a single column surface ranges from 3 to 8, among which hexagons are the most common.

[0003] The Voronoi diagram is an important concept in computational geometry. It was initially proposed by the mathematician Dirichlet in 1850 and later improved by the Russian mathematician Voronoi in 1907 and extended to higher dimensions. Therefore, the two-dimensional Voronoi diagram is also called Dirichlet tessellation, which belongs to a spatial segmentation method and has wide applications in fields such as image processing, computer graphics, life sciences, and geotechnical engineering. For a given set of seed points, a set of Voronoi cells can be generated. The characteristic of Voronoi cells is that each Voronoi region corresponds to only one seed point inside, and the distance from any point inside this region to the seed point corresponding to this region is shorter than the distance to other seed points.

[0004] In order to more accurately simulate the column surface morphology of columnar jointed rock masses formed naturally, it is a common and reasonable method to use the Voronoi diagram to simulate columnar joints. However, since the set of seed points for generating the Voronoi diagram is randomly generated, this makes the sizes of the Voronoi region divisions different, which does not conform to the typical morphology of columnar joints. Since the Voronoi diagrams of columnar joints show different morphological characteristics in different regions, how to establish a Voronoi diagram consistent with the on-site situation is a key issue. The present invention requires that the generated Voronoi diagram be consistent with the coefficient of variation reflecting the degree of polygon discreteness, which is a main parameter of columnar joint characteristics.

[0005] The present invention precisely proposes a method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm in view of how to establish a joint model consistent with the coefficient of variation of columnar joints. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm. The technical solution adopted by the present invention is as follows:

[0007] A method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm, comprising the following steps:

[0008] (1) Draw a sketch of the cross-section of the column of typical columnar joints according to the on-site situation, and measure the dip, dip angle and length of the column.

[0009] (2) Calculate the measured coefficient of variation value according to the sketch of the cross-section of the column.

[0010] (3) Generate a Voronoi diagram with the same measured coefficient of variation based on the distance control method.

[0011] (4) Stretch the Voronoi diagram along the axial direction of the column according to the measured dip of the column.

[0012] (5) Generate random transverse joints on the column to obtain a three-dimensional columnar joint model.

[0013] Among them, the specific steps of step (2) include:

[0014] (2.1) By statistically calculating the area of each polygon in the sketch of the cross-section of the column, the measured coefficient of variation value CV R can be calculated. The calculation formula is: CV = SD / m, where CV is the coefficient of variation, SD is the standard deviation of the polygon area, and m is the mean value of the polygon area.

[0015] (2.2) Calculate and determine the representative elementary volume size REV (Representative Elementary Volume), so as to obtain the cross-section size of the column and the size in the column length direction of the numerical model.

[0016] The specific steps of the distance control method described in step (3) include:

[0017] (3.1) In the i-th iteration, set the distance control parameter L (i) ;

[0018] (3.2) Generate a set of random seed point sets Among them, the n-th random seed point needs to meet the condition that the Euclidean distance from the previously generated (n - 1) random seed points is not less than the distance control parameter L (i) .

[0019] (3.3) According to the seed point set P obtained in step (3.2) (i)Generate Voronoi diagram F (i) ;

[0020] (3.4) Calculate the coefficient of variation value CV of Voronoi diagram F (i) and its measured coefficient of variation value CV (i) of the relative error. R

[0021] (3.5) If the relative error meets the preset requirements, the iteration stops. Otherwise, repeat steps (3.1) to (3.4) until the relative error meets the requirements and then stop. Then, the obtained result is the Voronoi diagram with the same coefficient of variation as the measured one.

[0022] Compared with the prior art, the present invention introduces a distance control algorithm, overcomes the phenomenon of over-dense or uneven randomly generated seed point sets in the prior art, greatly reduces the number of secondary judgments on the seed point set, and significantly improves the calculation efficiency and the quality of the obtained Voronoi diagram. The method of the present invention is highly efficient, low-cost, and relatively advanced. Through this method, a columnar joint model more consistent with the actual situation can be established. Brief Description of the Drawings

[0023] Figure 1 is the overall flowchart of the embodiment of the present invention;

[0024] Figure 2 is a schematic diagram of columnar joint rock mass;

[0025] Figure 3 is the sketch of the joint of the typical column cross-section in the embodiment of the present invention;

[0026] Figure 4 is the centroid Voronoi diagram of the model column cross-section;

[0027] Figure 5 is the columnar joint model obtained by stretching the centroid Voronoi diagram;

[0028] Figure 6 is the columnar joint model after adding transverse random joints Detailed Embodiment

[0029] The following further clarifies the present invention in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0030] As Figure 1 shown, the present invention discloses a method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm, taking the typical columnar joint situation of a certain project (such as​Figure 3 ) For example, the implementation process of the method according to the embodiments of the present invention will be described. The following steps are included:

[0031] 1. Draw a sketch of the column cross-section of typical columnar joints according to the on-site situation, and measure the dip, dip angle and length of the column.

[0032] The sketch of the column cross-section of typical columnar joints in this area is as Figure 2 shown, and the measured dip angle of the column is 18°, the dip direction DD = 145°, and the length of the column is about 1.5 m.

[0033] 2. Calculate the measured coefficient of variation value according to the sketch of the column cross-section.

[0034] Based on the sketch of the column cross-section of typical columnar joints, 10 comprehensive sketches of the column cross-sections of typical columnar joints are calculated, and the statistical average value of the coefficient of variation is 44.18%.

[0035] Considering the size effect of inhomogeneous materials, relevant research shows that it is appropriate to adopt a REV size of 5 m for columnar joints. Therefore, the cross-sectional size of the model column is 5 m × 5 m.

[0036] 3. According to the generated set of random seed points, generate a Voronori diagram with the same statistical average value of the coefficient of variation as the measured coefficient of variation according to the distance control algorithm, as Figure 4 shown.

[0037] 4. According to the dip and dip angle of the measured column, stretch the Voronoi diagram along the axial direction of the column ( Figure 5 ), and generate random transverse joints on the column, then a three-dimensional columnar joint numerical calculation model with the same coefficient of variation as the measured columnar joint rock mass can be obtained, as Figure 6 shown.

[0038] The above are only specific implementation cases of the invention. The technical features of the present invention are not limited thereto. Any changes or modifications made by those skilled in the relevant art within the scope of the present invention are covered by the protection scope of the present invention.

Claims

1. A method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm, characterized in that It includes the following steps: (1) Draw a sketch of the cross-section of the column of typical columnar joints according to the on-site situation, and measure the dip direction, dip angle and length of the column; (2) Calculate the measured coefficient of variation value according to the sketch of the column cross-section; (3) Generate a Voronoi diagram with the same measured coefficient of variation based on the distance control algorithm; (4) Stretch the Voronoi diagram along the axial direction of the column according to the measured dip direction of the column; (5) Generate random transverse joints on the column to obtain a three-dimensional columnar joint model; The specific steps of generating a Voronoi diagram with the same measured coefficient of variation based on the distance control algorithm in step (3) include: (3.1) In the i-th iteration, set the distance control parameter L (i) ; (3.2) Generate a set of random seed point sets using the distance control algorithm where each random seed point has an Euclidean distance not less than the distance control parameter L from the previously generated (n - 1) random seed points ; (i) ; (3.3) Generate the Voronoi diagram F based on the seed point set P obtained in step (3.2). (i) Generate the Voronoi diagram F (i) ; (3.4) Calculate the Voronoi diagram F (i) 's coefficient of variation value CV (i) , and its relative error with the measured coefficient of variation value CV R ; (3.5) If the relative error meets the preset requirements, the iteration stops; otherwise, repeat steps (3.1) to (3.4) until the relative error meets the requirements and then stop; then, the obtained result is the Voronoi diagram with the same measured coefficient of variation.

2. The method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm according to claim 1, characterized in that, The specific steps of calculating the measured coefficient of variation value according to the sketch of the column cross-section in step (2) include: (2.1) By statistically calculating the area of each polygon in the column cross-section sketch, the measured coefficient of variation value CV can be obtained. R The calculation formula is: CV = SD / m, where CV is the coefficient of variation, SD is the standard deviation of the polygon area, and m is the mean value of the polygon area. (2.2) Calculate and determine the Representative Elementary Volume (REV) to obtain the cross-sectional dimension of the column and the dimension in the column length direction of the numerical model.

3. A method for constructing a joint model consistent with the coefficient of variation of columnar joints based on a distance control algorithm according to claim 1, characterized in that, In the step (3), the distance control algorithm specifically refers to presetting a distance control parameter L. Each random seed point P placed in the plane n , needs to satisfy that the Euclidean distance between this seed point and the previously generated n - 1 seed points {P1, P2, …, P n-1} is not less than the distance control parameter L.

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