Rock mass fracture three-dimensional fractal dimension calculation method

Abstract

The invention discloses a rock mass fracture three-dimensional fractal dimension calculation method, which is based on a fractal theory and is formed by self-writing by using a Python language, and comprises the following steps: (1) importing a rock mass fracture image, and if the image is colored, converting the image into a gray image or a binary image; (2) dividing the image into a plurality of rock mass box blocks and calculating the number of the rock mass box blocks according to the rock mass fracture distribution condition; (3) calculating the box dimension of the rock mass fracture image, and returning a dimension matrix and the size of a block; (4) calculating the fractal dimension of each rock body box, and storing the result in a three-dimensional matrix; and (5) drawing a fracture fractal dimension 3D curved surface cloud picture and an XOY plane projection cloud picture according to the three-dimensional data matrix data set, and performing three-dimensional fractal quantization on the rock mass fracture. According to the method, the defects of an existing fracture fractal algorithm technology are overcome, the problem of result deviation generated in engineering application of traditional fractal dimensions is solved, the distribution characteristics of rock mass fractures in the three-dimensional topological space are revealed, and then the rock mass failure law can be speculated.

Description

Technical Field

[0001] The invention relates to the technical field of rock mass engineering fracture, and in particular to a method for calculating three-dimensional fractal dimension of rock mass cracks based on fractal geometry. Background Art

[0002] Under the influence of engineering construction such as tunneling, coal mining, and foundation pit excavation, rock mass produces a large number of defects such as pores, joints, and cracks. These damage defects are the main pathways for the migration of water, oil, and gas, determine the integrity of the rock mass, and are important factors causing accidents such as water inrush, gas leakage, and rock collapse. Therefore, in recent decades, the development and expansion of rock mass cracks have gradually become the focus of attention. Since the cracks are randomly distributed in the rock mass, and the shape and size of these cracks cannot be described by traditional geometric paintings, this brings great difficulties to the quantification of rock mass cracks. A large number of studies have shown that the cracks in the rock mass meet self-similarity, which means that fractal theory can be used to solve this problem. When looking for a method to quantify the fracture network, scholars have gradually widely used the fractal description method. The calculation results show that the larger the fractal dimension, the more developed the fracture network is, which is in line with engineering practice, making the fractal dimension an indispensable quantitative indicator for the quantification of rock mass fractures. However, in current projects, two-dimensional fractal dimension calculation is used. The calculation formula uses the least squares method to perform linear regression on the double logarithmic curve. The approximate result of the fractal dimension is affected by the selection of regression points. If different numbers of nodes are selected, numerical disturbances will occur. This will not only cause deviations in the quantitative results, but also reduce the accuracy of using fractal dimension to predict the results of related problems.

[0003] Therefore, the existing fracture fractal calculation method has poor stability and large deviation. It is crucial to find a three-dimensional fractal dimension algorithm that is simple and efficient and can intuitively display the calculation results to solve the problem of rock engineering failure. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of existing fracture fractal algorithm technology, solve the problem of result deviation caused by traditional fractal dimension in engineering application, and provide a three-dimensional fractal dimension calculation method for rock fractures. The method can characterize the surface roughness and influence range of rock fractures, better quantify the complex rock fracture network, intuitively display the calculation results in the form of cloud maps, and analyze the stability of the rock mass.

[0005] In order to achieve the above object, the present invention mainly provides the following technical solutions:

[0006] The present invention provides a method for calculating the three-dimensional fractal dimension of rock mass fractures, the method comprising the following steps:

[0007] S1. Import the rock mass fracture image. If the image is in color, it needs to be converted into a grayscale image or a binary image.

[0008] S2, according to the distribution of rock mass cracks, divide the image into multiple rock mass box blocks and calculate their number;

[0009] S3, calculate the box dimension of the rock mass fracture image, and return the dimension matrix and the size of the block;

[0010] S4, calculating the fractal dimension of each rock mass box and storing the result in a three-dimensional matrix;

[0011] S5. Based on the three-dimensional data matrix data set, draw the 3D surface cloud map and XOY plane projection cloud map of the fracture fractal dimension to perform three-dimensional fractal quantification of rock mass fractures.

[0012] Furthermore, in the above method, as described in step S1, the size of the imported rock fracture grayscale image is most suitable for an aspect ratio of 1:1, 1:2, 1:3, or 1:4; the image type is a pixel image, and the image format is JPG, PNG, TIF, etc., and cannot be an SVG vector image format.

[0013] Furthermore, in the above method, as described in step S2, if the cracks in the rock mass area are dense, the algorithm automatically divides the box blocks into more blocks; if the cracks in the rock mass area are scattered, the algorithm automatically divides the box blocks into fewer blocks; and the number of blocks containing pixel values ​​in the rock mass crack image is counted as the box count.

[0014] Furthermore, in the above method, as described in step S3, the built-in algorithm of the present invention is the box dimension method, which is used as a theoretical basis to calculate the fractal dimension of the binary image; in each R×R grid divided, the maximum pixel value u and the minimum pixel value b are found, and the output is sorted from the maximum value to the minimum value. How many boxes are needed to cover it, and the number of boxes is recorded as n(i,j) - assuming that there are currently (i,j) grids, that is, n(i,j) = [(u-b+R-1) / R], where [] is a rounding symbol; the fractal dimension of each rock box is calculated, and the box dimension data is returned in the form of a matrix.

[0015] Furthermore, in the above method, as described in step S4, the box counts are performed on rock box blocks of different sizes, and the fracture fractal dimension of each rock box block in the image is calculated. The fractal dimension of the image is estimated by taking the logarithm of these numbers and performing linear fitting, and the result is stored in a three-dimensional matrix.

[0016] Furthermore, in the above method, as described in step S5, for an L×W rock mass fracture pixel map, the algorithm finally outputs it as a three-dimensional space surface cloud map with a length of L, a width of W, and a height of F, where F is the fractal dimension of the image.

[0017] On the basis of the above technical scheme, compared with the prior art, the technical effect achieved by the present invention is as follows: the method for calculating the three-dimensional fractal dimension of rock mass cracks provided by the present invention realizes the visual description of crack distribution characteristics, clearly describes the surface roughness and influence range of rock mass cracks, and more intuitively determines the internal structure of the rock mass. The three-dimensional fractal distribution cloud map of cracks obtained based on this method can be used to infer the law of rock mass failure. It can be widely used in engineering and technical fields such as tunneling, coal mining, and foundation pit excavation. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions for implementing the present invention, the accompanying drawings required for use in the embodiments will be briefly introduced below. The accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0019] Figure 1 This is a flow chart of a method for calculating three-dimensional fractal dimension of rock mass fractures according to the present invention;

[0020] Figure 2 The example diagram of Python code for calculating the number of rock mass boxes in the present invention;

[0021] Figure 3 An example diagram of Python code for calculating the fractal dimension of each rock mass box in the present invention;

[0022] Figure 4 An example diagram of Python code for calculating the three-dimensional fractal dimension of the entire rock mass fracture in the present invention;

[0023] Figure 5 The Python code example diagram for drawing the 3D surface cloud map and XOY plane projection cloud map of the fracture fractal dimension of the present invention;

[0024] Figure 6 In order to verify the correctness of the method for calculating the three-dimensional fractal dimension of rock mass fractures of the present invention, the 3D surface diagram and XOY plane projection diagram of the fractal dimension of a single longitudinal fracture of the rock mass are provided;

[0025] Figure 7 In order to verify the correctness of the three-dimensional fractal dimension calculation method of rock mass fractures of the present invention, the 3D surface diagram and XOY plane projection diagram of the fractal dimension of a single transverse fracture of the rock mass are provided;

[0026] Figure 8 It is the 3D surface cloud map and XOY plane projection cloud map of the fractal dimension of multi-directional and multi-type fractures in the rock mass of the present invention. DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0028] The present invention provides a method for calculating the three-dimensional fractal dimension of rock mass fractures, and the specific steps are as follows:

[0029] S1. Import the rock mass crack image. If the image is in color, it needs to be converted into a grayscale image or a binary image.

[0030] The size of the imported rock fracture grayscale image should be in an aspect ratio of 1:1, 1:2, 1:3, or 1:4. The image type should be a pixel image, and the image format should be JPG, PNG, TIF, etc. It cannot be in the SVG vector image format.

[0031] The present invention can accurately identify the length, width and roughness of rock cracks in the pixel map; whereas the length, width and roughness of rock cracks in the vector map cannot be identified.

[0032] S2. According to the distribution of rock mass cracks, the image is divided into multiple rock mass box blocks and their number is calculated.

[0033] If the cracks in the rock mass area are dense, this algorithm automatically divides more box blocks; if the cracks in the rock mass area are scattered, this algorithm automatically divides fewer box blocks; the number of blocks containing pixel values ​​in the rock mass crack image is counted as the box count.

[0034] The present invention divides the layout of the rock mass fracture box blocks into dense and sparse ones, which not only improves the calculation speed, but also conforms to the engineering practice and demonstrates the rationality of the algorithm.

[0035] S3. Calculate the box dimension of the rock mass fracture image and return the dimension matrix and the size of the block.

[0036] The built-in algorithm of the present invention is the box dimension method, which is used as the theoretical basis to calculate the box dimension of the binary image; in each R×R grid divided, the maximum pixel value u and the minimum pixel value b are found, and the output is sorted from the maximum value to the minimum value. How many boxes are needed to cover it, and the number of boxes is recorded as n(i,j) - assuming that there are (i,j) grids at present, that is, n(i,j)=[(u-b+R-1) / R], where [] is the rounding symbol; and the box dimension data is returned in the form of a matrix.

[0037] This step adds a check for counts being zero or negative, because the logarithmic function cannot handle non-positive values; at the same time, it ensures that the lengths of box_sizes and counts are consistent. If the two are inconsistent or contain data that is not suitable for fitting, an error will be raised.

[0038] S4. Calculate the fractal dimension of each rock mass box and store the result in a three-dimensional matrix.

[0039] The box counts of rock box blocks of different sizes are performed, and the fracture fractal dimension of each rock box block in the image is calculated. The fractal dimension of the image is estimated by taking the logarithm of these numbers and performing linear fitting, and the results are stored in a three-dimensional matrix.

[0040] This step realizes the batch calculation of the fractal dimension of each rock box block area in the image, and establishes a rich database for the next step of drawing the 3D surface cloud map and XOY plane projection cloud map of the fracture fractal dimension.

[0041] S5. Based on the three-dimensional data matrix data set, draw the 3D surface cloud map and XOY plane projection cloud map of the fracture fractal dimension to perform three-dimensional fractal quantification of rock mass fractures.

[0042] For an L×W rock mass fracture pixel image, the algorithm finally outputs a three-dimensional space surface cloud image with a length of L, a width of W, and a height of F, where F is the fractal dimension of the image.

[0043] In order to verify the correctness of the present invention, the pixel images of a single longitudinal crack and a transverse crack in the rock mass were specially selected for import, and the obtained Figure 6 and Figure 7 ;from Figure 6 and Figure 7 It can be seen that the three-dimensional fractal dimension value has obvious changes within the range of a single, unidirectional rock mass fracture, while the three-dimensional fractal dimension value does not change in other areas without rock mass fractures; this shows that the calculation results of the present invention are correct.

[0044] Figure 8 The calculation results are intuitively displayed in the form of cloud maps, which quantify the complex rock fracture network, characterize the surface roughness and impact range of rock fractures, and better analyze the rock stability.

[0045] The embodiments described above are only descriptions of the preferred modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for calculating the three-dimensional fractal dimension of rock mass fractures, which effectively combines the two different fields of complex rock mass fracture networks and fractal geometry, is characterized by: The following steps are involved: S1. Import the rock mass fracture image. If the image is in color, it needs to be converted into a grayscale image or a binary image. S2, according to the distribution of rock mass cracks, divide the image into multiple rock mass box blocks and calculate their number; S3, calculate the box dimension of the rock mass fracture image, and return the dimension matrix and the size of the block; S4, calculating the fractal dimension of each rock mass box and storing the result in a three-dimensional matrix; S5. Based on the three-dimensional data matrix data set, draw the 3D surface cloud map and XOY plane projection cloud map of the fracture fractal dimension to perform three-dimensional fractal quantification of rock mass fractures.

2. The method for calculating the three-dimensional fractal dimension of rock mass fractures according to claim 1, characterized in that: As described in step S1, the size of the imported rock mass fracture grayscale image is most suitable for an aspect ratio of 1:1, 1:2, 1:3, or 1:4; the image type is a pixel image, and the image format is JPG, PNG, TIF, etc., and cannot be an SVG vector image format.

3. The method for calculating the three-dimensional fractal dimension of rock mass fractures according to claim 1, characterized in that: As described in step S2, if the cracks in the rock mass area are dense, the algorithm automatically divides more box blocks; if the cracks in the rock mass area are scattered, the algorithm automatically divides fewer box blocks; the number of blocks containing pixel values ​​in the rock mass crack image is counted as the box count.

4. The method for calculating the three-dimensional fractal dimension of rock mass fractures according to claim 1, characterized in that: As described in step S3, the built-in algorithm of the present invention is the box dimension method, which is used as a theoretical basis to calculate the fractal dimension of the binary image; in each R×R grid divided, the maximum pixel value u and the minimum pixel value b are found, and the output is sorted from the maximum value to the minimum value. How many boxes are needed to cover it, and the number of boxes is recorded as n(i,j) - assuming that there are currently (i,j) grids, that is, n(i,j) = [(u-b+R-1) / R], where [] is a rounding symbol; and the box dimension data is returned in the form of a matrix.

5. The method for calculating the three-dimensional fractal dimension of rock mass fractures according to claim 1, characterized in that: As described in step S4, the box counts are performed on the rock box blocks of different sizes, and the fracture fractal dimension of each rock box block in the image is calculated. By taking the logarithm of these numbers and performing linear fitting, the fractal dimension of the image is estimated, and the result is stored in a three-dimensional matrix.

6. The method for calculating the three-dimensional fractal dimension of rock mass fractures according to claim 1, characterized in that: As described in step S5, for an L×W rock mass fracture pixel image, the algorithm finally outputs a three-dimensional space surface cloud image with a length of L, a width of W, and a height of F, where F is the fractal dimension of the image.

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