Three-dimensional fracture network fractal dimension value calculation and correction system construction method

Abstract

The invention belongs to the technical field of rock mass fracture network model analysis and correction, and particularly relates to a three-dimensional fracture network fractal dimension value calculation and correction system construction method which comprises the following specific steps: acquiring rock mass revealed surface fracture data by adopting a window measurement method, and performing statistical homogeneous region and fracture dominant group division on the acquired data; the fractal dimension is calculated by adopting a box counting mode, a program is written by utilizing MATLAB software to analyze the fracture parameters according to the data of the three-dimensional fracture network model and the fractal dimension value of a certain fracture surface of the real rock mass, and the fractal dimension value of the fracture surface of the real rock mass is calculated by utilizing the Monte Carlo random sampling technology, so that the fractal dimension value of the fracture surface of the real rock mass is analyzed, and the fractal dimension value of the fracture surface of the real rock mass is calculated. The uniquely determined fracture structural surface is obtained, the fractal dimension is calculated, and correction of the three-dimensional fracture network model is realized, so that the purpose of constructing comprehensive three-dimensional rock mass simulation evaluation is achieved, and the accuracy is high.

Description

Technical Field

[0001] This invention relates to the field of rock mass fracture network model analysis and correction technology, specifically a method for constructing a three-dimensional fracture network fractal dimension calculation and correction system. Background Technology

[0002] With the increasing demand for coal resources, the depth of coal mining in my country is also increasing at a rate of 8-10 meters per year. This increase in mining depth places higher demands on the accuracy of engineering analysis and the safety of engineering construction, requiring a deeper understanding of the properties of rock and soil. The strength and occurrence of fracture surfaces strictly control the strength of the rock mass.

[0003] Therefore, when analyzing coal-bearing rock mass engineering problems, studying the spatial distribution characteristics of rock mass fracture surfaces becomes the primary consideration. Accurately and thoroughly understanding the geometric and mechanical characteristics of rock mass fracture surfaces becomes the prerequisite and foundation for engineering geologists, civil engineers, and mining experts to conduct in-depth research and even solve rock mechanics problems.

[0004] Under normal circumstances, the determination of internal fractures in rock masses can only be obtained through a few natural outcrops, artificially exposed surfaces, and drilling, but the number of such results is very limited.

[0005] Therefore, rock mass fracture network simulation has become one of the main methods for studying the distribution of fractures inside rock masses. However, the simulation results differ significantly from the actual results. Therefore, improving the accuracy of the fracture model and coupling it with engineering practice is extremely important for the analysis and correction of rock mass fracture network models. Summary of the Invention

[0006] The purpose of this invention is to provide a method for constructing a three-dimensional fracture network fractal dimension calculation and correction system to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for constructing a three-dimensional fracture network fractal dimension calculation and correction system, the specific steps of which are as follows: Step 1: Collect fracture data of exposed rock mass surface using the window measurement method, and divide the collected data into homogeneous zones and fracture dominant groups; Step 2: Use mathematical statistics methods to evaluate the probability distribution function of fracture size, attitude, coordinates and the distribution density of dominant fracture groups, and calculate the number of samples randomly sampled from each fracture group; Step 3: Use Monte Carlo random sampling technique to obtain the fracture parameters of the simulated three-dimensional fracture network model and store them in a table; Step 4: Import the 3D fracture data into the Monte Carlo random generation program of the 3D fracture network model built on the MATLAB platform to generate a visualization model; Step 5: Optimize the model using the Nelder-Mead algorithm; Step 6: Select the two-dimensional fracture image to be operated on, and obtain the unique two-dimensional fracture network image in the simulated three-dimensional fracture model; Step 7: Calculate the fractal dimension of the two-dimensional crack image using the box-counting dimension model; Step 8: By comparing the difference between the fractal dimension of the model and the measured fractal dimension of the exposed surface, appropriate additions or deletions are made to the three-dimensional fracture plates to achieve fractal correction of the three-dimensional fracture network model. The corrected three-dimensional fracture network model is then obtained.

[0008] Preferably, the three-dimensional crack data includes the coordinates of the center point of the crack disk, the coordinates of the disk edge, and the coordinates of the normal vector. Preferably, the determination of the two-dimensional fracture image involves determining the spatial location of the fracture in the cross section to be studied. This is achieved by inputting the coordinates of the center point of the fracture surface and the direction of the normal vector or dip angle, thereby determining a unique two-dimensional fracture network image in the simulated three-dimensional fracture model. Preferably, the fractal dimension calculation of the two-dimensional crack image involves calculating the number of different cells through which the crack passes, and then fitting the data to a straight line to calculate the crack fractal dimension. Preferably, the two-dimensional crack fractal dimension correction is based on the difference between the fractal dimension calculated by the simulated crack network and the actual crack fractal dimension, and a certain number of cracks are randomly added or deleted to make the fractal dimension of the entire two-dimensional crack image close to the actual value.

[0009] Preferably, the three-dimensional fracture model correction is obtained by transposing the corrected two-dimensional fracture surface to obtain the corrected three-dimensional fracture model.

[0010] Compared with the prior art, the beneficial effects of the present invention are: 1) This invention uses box counting to calculate the fractal dimension. Based on the data of the three-dimensional fracture network model and the fractal dimension value of a certain fracture surface in the actual rock mass, a program is written using MATLAB software to analyze the fracture parameters, obtain the unique fracture structure surface and calculate the fractal dimension, thereby correcting the three-dimensional fracture network model and achieving the purpose of constructing a comprehensive three-dimensional rock mass simulation and evaluation with high accuracy. 2) This invention is simple to operate and easy to apply in practice. It provides a new method and approach for the accurate analysis and research of the internal structure of rock masses, improves analysis efficiency, reduces the labor intensity of data processing personnel, and provides effective data reference for subsequent mining and utilization of mineral resources. 3) This invention uses the fractal dimension of fractures as its basis and MATLAB editing software to build a visualization platform. The two complement each other and jointly construct a fracture network correction system, which provides certain reference value for the subsequent study of the internal structure of rock masses. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating the steps of constructing the three-dimensional fracture network fractal dimension calculation and correction system of the present invention. Figure 2 It is a three-dimensional crack simulation model diagram; Figure 3 It is a two-dimensional crack image acquisition image; Figure 4 This is a graph showing the calculation of fractal dimension; Figure 5 This is a diagram showing the calculation of the fractal dimension when the simulated fractal dimension is smaller than the actual fractal dimension. Figure 6 This is a diagram showing the calculation of fractal dimension when the simulated fractal dimension is greater than the actual fractal dimension. Figure 7 This is a fractal dimension correction diagram when the simulated fractal dimension is smaller than the actual fractal dimension; Figure 8 It is a fractal dimension correction diagram when the simulated fractal dimension is greater than the actual fractal dimension. Detailed Implementation

[0012] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0013] Please see Figure 1-8 The present invention provides a technical solution: A method for constructing a three-dimensional fracture network fractal dimension calculation and correction system, the specific steps of which are as follows: Step 1: Collect fracture data of exposed rock mass surface using the window measurement method, and divide the collected data into homogeneous zones and fracture dominant groups; Step 2: Use mathematical statistics methods to evaluate the probability distribution function of fracture size, attitude, coordinates and the distribution density of dominant fracture groups, and calculate the number of samples randomly sampled from each fracture group; 1. Probability distribution of crack length (L): Negative exponential distribution: Probability density function (PDF): Cumulative Distribution Function (CDF): in, The distribution parameter (attenuation coefficient) is estimated from the sample mean: = , (n is the number of measured crack length samples, (where is the length of the i-th crack).

[0014] Log-normal distribution (suitable for cracks with large length dispersion): If inL-N(u, Then the probability density function is: in, .

[0015] 2. Fracture orientation (dip angle α, strike β) The common distributions are uniform distribution and normal distribution, with the uniform distribution best matching the characteristics of the dominant group in a homogeneous region. Probability density function (taking tilt angle α as an example): Parameter description: (The boundary range of the statistically homogeneous region along the X-axis); the formulas for the y and z coordinates are consistent, with the boundary parameters replaced accordingly. .

[0016] The formula for calculating the distribution density of cracks in the dominant group is as follows: The distribution density is divided into surface density (number of cracks per unit area, applicable to the statistics of exposed surfaces) and volume density (number of cracks per unit volume, applicable to three-dimensional models). In the patent, step 2 needs to provide density parameters for subsequent three-dimensional modeling, and the core calculation is surface density and volume density. areal density ( (For statistical purposes only) Parameter description: The areal density of this dominant group; The average diameter (in meters) of the fractures in this dominant group is derived from the average measured trace length. Approximate substitution.

[0017] Formula for calculating the number of samples randomly selected from each group of cracks: The sample size must meet the requirement of statistical significance (to ensure the reliability of the distribution fit), and a sample size formula based on the confidence level and allowable error is used: Parameter description: n is the number of randomly sampled samples from the dominant group of fractures; These are the two-sided quantiles of the standard normal distribution; σ is the overall standard deviation of the core parameters (such as trace length L) of the fracture core in this dominant group; E represents the allowable error.

[0018] Step 3: Use Monte Carlo random sampling technique to obtain the fracture parameters of the simulated three-dimensional fracture network model and store them in a table; Step 4: Import the 3D fracture data into the Monte Carlo random generation program of the 3D fracture network model built on the MATLAB platform to generate a visualization model; Step 5: Optimize the model using the Nelder-Mead algorithm; Step 6: Select the two-dimensional fracture image to be operated on, and obtain the unique two-dimensional fracture network image in the simulated three-dimensional fracture model; Step 7: Calculate the fractal dimension of the two-dimensional crack image using the box-counting dimension model; The core formula for calculating box dimension is: The final formula for calculating the fractal dimension D is: In engineering practice, this limit is solved by double logarithmic fitting, and the core fitting formula is: Where D: the fractal dimension of the two-dimensional crack image to be determined; S: Side length of the square box (cell) covering the two-dimensional crack image (unit: m, such as 0.1m, 0.05m, 0.025m, etc., a series of decreasing side length values ​​need to be taken). N(s): The minimum number of boxes that can cover all the cracks or be passed through the cracks when the side length of the box is s; C: The intercept of the fitted line.

[0019] Formula application steps: Determine the sequence of box side lengths: Select a series of decreasing square box side lengths. This ensures coverage of the entire two-dimensional crack image area.

[0020] Calculate N(s) for each side length: For each side length The region containing the two-dimensional crack image is divided into several areas with a side length of Given a square grid, count the total number of cells that are traversed by a crack at least once, denoted as . ; Double logarithmic data transformation: for each Take the natural logarithm (or common logarithm) of each data pair to obtain... .

[0021] Solving D by linear fitting: The x-axis is... Using the ordinate as the vertical axis, a line is fitted using the least multiplication method. The absolute value of the slope of the fitted straight line is the fractal dimension D of the two-dimensional crack image.

[0022] Step 8: By comparing the difference between the fractal dimension of the model and the measured fractal dimension of the exposed surface, appropriate additions or deletions are made to the three-dimensional fracture plates to achieve fractal correction of the three-dimensional fracture network model. The corrected three-dimensional fracture network model is then obtained.

[0023] The three-dimensional fracture data includes the coordinates of the center point of the fracture disk, the coordinates of the disk edge, and the coordinates of the normal vector. The determination of the two-dimensional fracture image is to determine the spatial location of the fracture in the cross section to be studied. By inputting the coordinates of the center point of the fracture surface and the direction of the normal vector or dip angle, a unique two-dimensional fracture network image is determined in the simulated three-dimensional fracture model. The fractal dimension calculation of the two-dimensional crack image involves calculating the number of different cells through which the crack passes, and then fitting the data to a straight line to calculate the crack fractal dimension. The two-dimensional crack fractal dimension correction is based on the difference between the fractal dimension calculated by the simulated crack network and the actual crack fractal dimension. Certain cracks are randomly added or deleted to make the fractal dimension of the entire two-dimensional crack image closer to the actual value.

[0024] The three-dimensional fracture model correction is obtained by transposing the corrected two-dimensional fracture surface to obtain the corrected three-dimensional fracture model.

[0025] Example: The construction method includes the following steps: Step 1: Obtain the parameters of the three-dimensional fracture network model and store them in a table; so that the data can be imported from the local table into the MATLAB software during analysis; fill in the table according to the relevant data of the three-dimensional fracture model in the simulation, including the coordinates of the center point of each fracture disk, the coordinates of the disk edge, the coordinates of the normal vector, and other relevant data.

[0026] Step 2: Open MATLAB software, import the fracture data to be analyzed from your local machine into the calibration system; and use the visualization components and editing program to visualize the three-dimensional fracture network model (such as...). Figure 2 (As shown) is displayed on the system interface, making it convenient for users to operate and process and analyze the overall data; Step 3: In the system's pop-up visualization interface, input the coordinates of the profile center point, the profile determination method, and the spatial dip direction or normal vector as required. Click the "Trim Profile" button to determine the unique location of the rock mass fracture profile view. Click the "Profile Image" button to calculate the intersection line of the rock mass fractures on the profile and project the intersection line onto the XOY plane using a transpose matrix, as shown below. Figure 3As shown.

[0027] Step 4: Click the "Fractal Dimension" button to calculate the fractal dimension of the profile, and align the coordinate axis where the crack is located according to 1. 1, 2 2, 4 4, 8 8, 16 16, 32 32. The program divides the data into cells and counts the number of grid cells the crack passes through at different ratios. This data is displayed in the fractal dimension results panel, and the system displays a "Fractal dimension division complete" message. Clicking the "Line Graph" button again allows the user to obtain the dataset of the number of grid cells the crack passes through at different ratios. Fitting a straight line and its slope represents the crack's fractal dimension. The fractal dimension calculation result is displayed in the panel below, as shown below. Figure 4 As shown.

[0028] Step 5: The user inputs the calculated fractal dimension value and the actual fractal dimension value from Step 4 into the crack correction function interface. When the actual fractal dimension value is greater than the original fractal dimension value, the number of cracks in the two-dimensional crack image is increased to make the fractal dimension value reach the actual fractal dimension value. Figure 5 As shown; when the actual fractal dimension is less than the original fractal dimension, by comparing the crack lengths, the shortest cracks in the simulated cracks are deleted sequentially, so that the simulated fractal dimension is close to the actual fractal dimension, as shown. Figure 6 As shown.

[0029] Step 6: After clicking the "Redraw Crack Section View" button, the program sequentially displays the 2D crack image with added cracks on the coordinate axis, and transforms the 2D crack image into a 3D crack image using a rotation matrix. It then fits a linear fractal dimension image based on the number of grid cells the crack passes through at different ratios. Simultaneously, the newly calculated fractal dimension value and the number of grid cells passed through after adding the crack are displayed in the command line. The program completes the crack correction function based on the fractal dimension value, as shown below. Figure 7 , 8 As shown.

[0030] For example, the table below shows some data from a simulated three-dimensional fracture network model. We will now use this software to process and analyze the data. Open the MATLAB software and import the local fracture data (i.e., the table below).

[0031] Table 1. Summary of coordinates of the center point and normal vector of the 3D fracture network model (partial) Table 2 Summary of disk edge coordinates in the 3D fracture network model (partial) This invention utilizes the box dimension calculation method and the rotation matrix method, and based on MATLAB software, it develops a system for calculating and correcting the fractal value of a three-dimensional fracture network. This system can achieve fractal analysis of a three-dimensional fracture simulation model, which is novel. Furthermore, this invention is simple to operate and easy to apply in practice, providing a new method and approach for the simulation and correction of three-dimensional fracture networks.

[0032] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or basic characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects. The scope of the invention is defined by the appended claims rather than the foregoing description. Therefore, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0033] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a three-dimensional fracture network fractal dimension calculation and correction system, characterized in that, The specific steps of this method are as follows: Step 1: Collect fracture data of exposed rock mass surface using the window measurement method, and divide the collected data into homogeneous zones and fracture dominant groups; Step 2: Use mathematical statistics methods to evaluate the probability distribution function of fracture size, attitude, coordinates and the distribution density of dominant fracture groups, and calculate the number of samples randomly sampled from each fracture group; Step 3: Use Monte Carlo random sampling technique to obtain the fracture parameters of the simulated three-dimensional fracture network model and store them in a table; Step 4: Import the 3D fracture data into the Monte Carlo random generation program of the 3D fracture network model built on the MATLAB platform to generate a visualization model; Step 5: Optimize the model using the Nelder-Mead algorithm; Step 6: Select the two-dimensional fracture image to be operated on, and obtain the unique two-dimensional fracture network image in the simulated three-dimensional fracture model; Step 7: Calculate the fractal dimension of the two-dimensional crack image using the box-counting dimension model; Step 8: By comparing the difference between the fractal dimension of the model and the measured fractal dimension of the exposed surface, appropriate additions or deletions are made to the three-dimensional fracture plates to achieve fractal correction of the three-dimensional fracture network model. The corrected three-dimensional fracture network model is then obtained.

2. The method for constructing a three-dimensional fracture network fractal dimension calculation and correction system according to claim 1, characterized in that: The three-dimensional fracture data includes the coordinates of the center point of the fracture disk, the coordinates of the disk edge, and the coordinates of the normal vector.

3. The method for constructing a three-dimensional fracture network fractal dimension calculation and correction system according to claim 1, characterized in that: The determination of the two-dimensional fracture image is to determine the spatial location of the fracture in the cross section to be studied. By inputting the coordinates of the center point of the fracture surface and the direction of the normal vector or dip angle, a unique two-dimensional fracture network image is determined in the simulated three-dimensional fracture model.

4. The method for constructing a three-dimensional fracture network fractal dimension calculation and correction system according to claim 1, characterized in that: The fractal dimension calculation of the two-dimensional crack image involves calculating the number of different cells through which the crack passes, and then fitting the data to a straight line to calculate the crack fractal dimension.

5. The method for constructing a three-dimensional fracture network fractal dimension calculation and correction system according to claim 1, characterized in that: The two-dimensional crack fractal dimension correction is based on the difference between the fractal dimension calculated by the simulated crack network and the actual crack fractal dimension. Certain cracks are randomly added or deleted to make the fractal dimension of the entire two-dimensional crack image closer to the actual value.

6. The method for constructing a three-dimensional fracture network fractal dimension calculation and correction system according to claim 1, characterized in that: The three-dimensional fracture model correction is obtained by transposing the corrected two-dimensional fracture surface to obtain the corrected three-dimensional fracture model.

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