Method for obtaining rock mass fracture parameters based on elliptical model

Abstract

The application discloses a kind of rock mass fracture parameter acquisition methods based on elliptical model, it includes obtaining the fracture image of the rock mass surface to be studied, and it is carried out image segmentation and enhancement processing;Enhanced fracture image is identified using neural network after processing, and the trace length of the identification result and rock mass fracture of rock mass fracture is obtained;All trace length data of the rock mass to be studied are counted, and the frequency distribution histogram of trace length is drawn, so that the distribution curve of trace length is fitted, and the distribution law of fitting curve is determined;According to the distribution law of fitting curve, the probability density function of trace length is selected;According to the probability density function of trace length, the long axis probability density model of the long axis of elliptical fracture and the ratio probability density model of the ratio of long and short axis of elliptical fracture are respectively constructed;The distribution range of the long axis of elliptical fracture is obtained using long axis probability density model, and the distribution range of the ratio of long and short axis is obtained using ratio probability density model.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering safety technology, specifically to a method for obtaining rock mass fracture parameters based on an elliptical model. Background Technology

[0002] The complex distribution of fractures in rock masses disrupts their integrity and controls their stress patterns and stability. Using a discrete fracture network (DFN) to simulate an equivalent real fractured rock mass allows for the determination of rock mass stability and seepage field. Among these parameters, fracture characteristic size is a crucial parameter for constructing the fracture network model. Therefore, the rock mass fracture parameters (major axis, major-minor axis ratio, etc.) must first be obtained during the DFN construction process.

[0003] When acquiring rock mass fracture parameters, completely excavating and dissecting the rock mass to observe the various dimensional parameters of elliptical fractures is difficult because external disturbances can cause the fractures to extend and expand further, or even form new fractures. Currently, researchers generally infer estimated fracture sizes by fitting trace length distributions, which serve as important parameters for reconstructing discrete fracture networks.

[0004] Due to different assumptions about the shape of the fractures, the characteristic dimensions and derivation methods of the fractures also differ. Currently, when constructing fracture networks, there are assumptions that the fractures are planar circles, parallelograms, and ellipses. However, regardless of the method used to obtain rock mass fracture parameters, the distribution of fractures in the rock mass is randomly assumed, and then the corresponding function of rock mass fracture parameters is constructed.

[0005] Although this method can predict the parameter range, since the fracture distribution is randomly selected, if the assumption happens to match the fracture distribution, the obtained parameters will be close to the true values. If the assumption is wrong, the obtained fracture parameters will be very inaccurate, resulting in a particularly large error in determining the subsequent rock mass stability and making it difficult to guarantee an accurate rock mass stability safety protection plan. Summary of the Invention

[0006] To address the aforementioned shortcomings in the existing technology, this invention provides a method for obtaining rock mass fracture parameters based on an elliptical model. This method solves the problem that the obtained rock mass fracture parameters deviate from the true values ​​due to the difficulty in accurately determining the fracture distribution pattern in the existing technology.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0008] A method for obtaining rock mass fracture parameters based on an elliptical model is provided, which includes the following steps:

[0009] Acquire images of cracks on the surface of the rock mass under study, and perform image segmentation and enhancement processing;

[0010] A neural network was used to identify the enhanced fracture images to obtain the identification results of rock mass fractures and the trace length of rock mass fractures;

[0011] Based on all trace length data of the rock mass under study, a frequency distribution histogram of trace length is plotted, a distribution curve of trace length is obtained by fitting, and the distribution law of the fitted curve is determined.

[0012] Based on the distribution pattern of the fitted curve, select the probability density function of the trace length;

[0013] Based on the probability density function of the trace length, the probability density model of the major axis of the elliptical crack and the probability density model of the ratio of the major and minor axes of the elliptical crack are constructed respectively.

[0014] The distribution range of the major axis of the elliptical crack is obtained by using the major axis probability density model, and the distribution range of the ratio of the major and minor axes is obtained by using the ratio probability density model.

[0015] The beneficial effects of this invention are as follows: This solution can amplify the difference between the fracture and the rock wall in the fracture image through image enhancement, and combined with the neural network, it can quickly identify the fracture in the image, ensuring the accuracy of fracture extraction and further ensuring the accuracy of the obtained fracture trace length.

[0016] By fitting the lengths of all rock mass fracture traces, a fitted curve for the trace length can be obtained. The shape of the curve can intuitively show the distribution pattern of the trace length. This scheme takes the distribution pattern of the fitted curve as the distribution pattern of the trace length. Combining this with the two probability density models constructed in this scheme, a relatively accurate distribution pattern of the major axis and the ratio of the major axis to the minor axis can be obtained.

[0017] Compared to existing technologies, this approach constructs a probability density model based on specific distribution patterns. Through Monte Carlo numerical simulation, it was found that the probability density function of the major axis of the elliptical fracture constructed by this approach has a high degree of overlap with the theoretical distribution curve of the original input. This verifies the high reliability of the data obtained by this approach, thereby ensuring the accuracy of subsequent determination of rock mass stability.

[0018] Furthermore, when the distribution pattern is uniform, the probability density function f(l) of the trace length is:

[0019]

[0020] Where B0 and B are the lower and upper limits of the trace length, respectively; l is the trace length.

[0021] The formula for calculating the major axis probability density model g(a) is as follows:

[0022]

[0023] Where ξ0 and ζ are the lower and upper limits of the major axis, respectively; and a is the length of the major axis.

[0024] The formula for calculating the probability density model u(k) of the major-minor axis ratio is:

[0025]

[0026] Where k is the ratio of the major axis to the minor axis; ξ k This represents the upper limit of the ratio of the major axis to the minor axis; s = B / a is an intermediate parameter.

[0027] The beneficial effects of the above technical solution are as follows: When the field survey data of the rock mass outcrop length is uniformly distributed, this solution can directly obtain the analytical solution of the probability density function of the characteristic size of the elliptical fracture, thereby obtaining the fracture distribution law of the real rock mass with higher accuracy.

[0028] Furthermore, when the distribution pattern is fractal, the probability density function f(l) of the trace length is:

[0029]

[0030] Where B0 is the lower limit of the trace length; l is the trace length; and D is the fractal dimension.

[0031] The formula for calculating the major axis probability density model g(a) is as follows:

[0032]

[0033] Where ξ0 is the lower limit of the major axis; a is the length of the major axis;

[0034] The formula for calculating the ratio probability density model u(k) is as follows:

[0035]

[0036] Where k is the ratio of the major axis to the minor axis; ξ k This represents the upper limit of the ratio of the major axis to the minor axis.

[0037] The beneficial effects of the above technical solution are as follows: if the sampling trace length of some study areas can be fitted with a fractal distribution, this solution can directly obtain the analytical solution of the probability density function of the characteristic size of elliptical fractures, thereby ensuring the accuracy of obtaining the fracture distribution in the real rock mass.

[0038] Furthermore, when the distribution pattern is a multinomial distribution, the probability density function f(l) of the trace length is:

[0039]

[0040] Among them, C mHere, B represents the coefficients of each order; l represents the trace length; and m represents the degree of the polynomial.

[0041] The formula for calculating the major axis probability density model g(a) is as follows:

[0042]

[0043] Where ξ0 and ζ are the lower and upper limits of the major axis, respectively; a is the length of the major axis; Q m P is the first positive sequence; m This is the first negative sequence; k is the ratio of the major axis to the minor axis.

[0044] The formula for calculating the ratio probability density model u(k) is as follows:

[0045]

[0046] Where, ξ k This represents the upper limit of the ratio of the major axis to the minor axis. It is the second positive sequence; It is the second negative sequence.

[0047] Furthermore, when m is odd, Q m and P m The calculation formulas are as follows:

[0048]

[0049] Among them, the double factorial symbol represents

[0050] When m is even, Q m and P m The calculation formulas are as follows:

[0051]

[0052] Among them, the double factorial symbol represents

[0053] Furthermore, when m = 1:

[0054] When m = 2:

[0055] When m ≥ 3, and m is an odd number:

[0056]

[0057] Among them, the double factorial symbol represents

[0058] When m ≥ 3, and m is an even number:

[0059]

[0060] Among them, the double factorial symbol represents

[0061] The beneficial effects of the above technical solution are as follows: since the polynomial function itself can fit the continuous distribution of trace lengths with a certain accuracy, and the probability density function represented by the polynomial is obtained by fitting the frequency distribution histogram of the trace length, the above solution is a general solution for various complex trace length distributions, has good applicability, and also ensures the practical application effect of the solution.

[0062] Furthermore, when the distribution follows a negative exponential distribution, the probability density function f(l) of the trace length is:

[0063] f(l)=θe -θl , l>0

[0064] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0065]

[0066] Where k is the ratio of the major and minor axes of the elliptical crack; θ is the negative exponential distribution parameter θ > 0, and the mean trace length u l and standard deviation σ l The value is 1 / θ;

[0067] When the distribution follows a Gamma distribution, the probability density function f(l) of the trace length is:

[0068]

[0069]

[0070] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0071]

[0072] Where α and β are the Gamma distribution parameters, and α > 1, β > 0;

[0073] When the distribution pattern is chi-square χ 2 When distributed, the probability density function f(l) of the trace length is:

[0074] u l =n; σ l =2n;

[0075] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0076]

[0077] Where n is the chi-square distribution parameter, and n > 2;

[0078] When the distribution follows a log-normal distribution, the probability density function f(l) of the trace length is:

[0079]

[0080]

[0081]

[0082] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0083]

[0084] Where u and σ are the parameters of the log-normal distribution, and σ > 0.

[0085] The beneficial effects of the above technical solution are as follows: This solution can more conveniently calculate the statistical characteristic values ​​of the elliptical crack size parameters directly when the trace length follows a complex distribution such as negative exponential distribution, Gamma distribution, chi-square distribution, and log-normal distribution. Thus, the average size and distribution of cracks in rock outcrops or tunnel walls can be roughly assessed on site.

[0086] Furthermore, the neural network uses U-net as its basic architecture and adds upsampling and downsampling as well as skip connections that connect the feature maps between the encoder and decoder.

[0087] The beneficial effects of the above technical solution are as follows: This solution uses skip connections between the encoder and decoder, which can link corresponding feature maps of the same size. This means that the pre-compressed spatial information is used to improve the resolution during upsampling, thereby improving the accuracy of extracting the actual gaps. When the neural network is trained, this feature can also propagate gradients to the front of the neural network through direct connection paths, which can alleviate the gradient vanishing / exploding problem that worsens as the network deepens. Attached Figure Description

[0088] Figure 1 This is a flowchart of a method for obtaining rock mass fracture parameters based on an elliptical model.

[0089] Figure 2 This is a schematic diagram of the parameters of the elliptical crack.

[0090] Figure 3 Probability density function of the major axis of the elliptical crack calculated by Monte Carlo simulation: (a) Example 1, (b) Example 2, (c) Example 3. Detailed Implementation

[0091] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0092] Analysis revealed that the rock mass fracture parameters of the elliptical model defined in this scheme are related to five variables: the relative angle α between the elliptical fracture surface and the sampling surface, the rotation angle β of the elliptical fracture relative to the sampling surface, the distance H from the center point of the elliptical fracture to the sampling surface, the length a of the major axis of the elliptical fracture, and the ratio k of the major and minor axes of the elliptical fracture.

[0093] like Figure 2 As shown, five variable parameters are used to represent the size of the elliptical fracture and its relative position to the sampling surface (sampling window). The relative angle α between the elliptical fracture surface and the sampling surface is ignored because their relative orientation only affects the orientation of the intersecting traces and not the trace length distribution. The distance H from the center point of the elliptical fracture to the sampling surface is not used in the subsequent construction of the rock mass fracture model using the software, so it is also not considered when obtaining the rock mass fracture parameters.

[0094] The rotation angle of the elliptical fracture relative to the sampling surface is β. Since this angle is difficult to obtain through calculation, it is generally determined based on empirical values ​​from actual surveys, taking into account the characteristics of the rock mass. Through analysis, it is found that the fracture model is mainly related to the major axis length a and the major-minor axis ratio k. Therefore, this scheme focuses on obtaining the major-minor axis ratio k and the major axis length a when acquiring fracture parameters.

[0095] refer to Figure 1 , Figure 1 A flowchart illustrating a method for obtaining rock mass fracture parameters based on an elliptical model is shown; for example... Figure 1 As shown, the method 100 includes steps 101 to 106.

[0096] In step 101, a fracture image of the surface of the rock mass to be studied is acquired, and the image is segmented and enhanced. The purpose of image enhancement is to highlight the fractures of interest in the fracture image, thereby improving the accuracy of subsequent neural network recognition.

[0097] In step 102, a neural network is used to identify the enhanced fracture image to obtain the identification result of rock mass fracture and the trace length of rock mass fracture; wherein, the neural network uses U-net as the basic architecture, and adds upsampling and downsampling as well as skip connections for feature mapping between encoder and decoder on the basic architecture.

[0098] In step 103, based on all trace length data of the rock mass to be studied, a frequency distribution histogram of trace length is plotted, the distribution curve of trace length is fitted, and the distribution law of the fitted curve is determined. The fitting of this scheme can be performed by least squares fitting using Matlab software or Excel software.

[0099] In step 104, the probability density function of the trace length is selected according to the distribution law of the fitted curve. This scheme divides the distribution law in detail and constructs the corresponding major axis probability density model and ratio probability density model respectively to ensure the accuracy of the range of rock mass fracture parameters obtained later.

[0100] The distribution patterns of this scheme encompass uniform distribution, fractal distribution, multinomial distribution, negative exponential distribution, Gamma distribution, and chi-square distribution. 2 Distributions include the log-normal distribution, etc.; among them, the uniform distribution, fractal distribution, and multinomial distribution are based on the probability density function to obtain the range of values ​​for the major axis 'a' and the ratio of the major axis to the minor axis 'k'; negative exponential distribution, Gamma distribution, chi-square distribution, and χ² distribution are also included. 2 The log-normal distribution is based on statistical characteristics to determine the expected values ​​of the ratio of the major axis to the minor axis k and the length of the major axis a.

[0101] When based on probability density functions, the multinomial distribution can be used as a general calculation method, which can realize the range of values ​​for the ratio of major axis to minor axis k and the length of major axis a for uniform and fractal distributions. Relatively speaking, when the distribution pattern conforms to uniform and fractal distributions, using the corresponding functions to obtain the range of values ​​for the ratio of major axis to minor axis k and the length of major axis a has higher accuracy.

[0102] In step 105, based on the probability density function of the trace length, the probability density model of the major axis of the elliptical crack and the probability density model of the ratio of the major and minor axes of the elliptical crack are constructed respectively.

[0103] In step 106, the distribution range of the major axis of the elliptical crack is obtained by using the major axis probability density model, and the distribution range of the major-minor axis ratio is obtained by using the ratio probability density model.

[0104] In one embodiment of the present invention, when the distribution pattern is fractal, the probability density function f(l) of the trace length is:

[0105]

[0106] Where B0 is the lower limit of the trace length; l is the trace length; and D is the fractal dimension.

[0107] The formula for calculating the major axis probability density model g(a) is as follows:

[0108]

[0109] Where ζ0 is the lower limit of the major axis; a is the length of the major axis;

[0110] The formula for calculating the ratio probability density model u(k) is as follows:

[0111]

[0112] Where k is the ratio of the major axis to the minor axis; ξ k This represents the upper limit of the ratio of the major axis to the minor axis; s = B / a is an intermediate parameter.

[0113] When the distribution follows a fractal pattern, the probability density function f(l) of the trace length is:

[0114]

[0115] Where B0 is the lower limit of the trace length; l is the trace length; and D is the fractal dimension.

[0116] The formula for calculating the major axis probability density model g(a) is as follows:

[0117]

[0118] Where ζ0 is the lower limit of the major axis; a is the length of the major axis;

[0119] The formula for calculating the ratio probability density model u(k) is as follows:

[0120]

[0121] Where k is the ratio of the major axis to the minor axis; ξ k This represents the upper limit of the ratio of the major axis to the minor axis.

[0122] The uniform and fractal distributions in this scheme can be directly determined by fitting the trace length curve. When the distribution pattern satisfies either of these two conditions, the range of the major axis and the ratio of the major and minor axes can be accurately obtained by directly using the corresponding formula.

[0123] In one embodiment of the present invention, when the distribution follows a multinomial distribution, the probability density function f(l) of the trace length is:

[0124]

[0125] Among them, C mHere, B represents the coefficients of each order; l represents the trace length; and m represents the degree of the polynomial.

[0126] The formula for calculating the major axis probability density model g(a) is as follows:

[0127]

[0128] Where ξ0 and ζ are the lower and upper limits of the major axis, respectively; a is the length of the major axis; Q m This is the first positive sequence; households m This is the first negative sequence; k is the ratio of the major axis to the minor axis.

[0129] When m is odd, Q m and P m The calculation formulas are as follows:

[0130]

[0131] Among them, the double factorial symbol represents

[0132] When m is even, Q m and P m The calculation formulas are as follows:

[0133]

[0134] Among them, the double factorial symbol represents

[0135] The formula for calculating the ratio probability density model u(k) is as follows:

[0136]

[0137] Where, ξ k This represents the upper limit of the ratio of the major axis to the minor axis. It is the second positive sequence; It is the second negative sequence.

[0138] When m = 1:

[0139] When m = 2:

[0140] When m ≥ 3, and m is an odd number:

[0141]

[0142] Among them, the double factorial symbol represents

[0143] When m ≥ 3, and m is an even number:

[0144]

[0145] Among them, the double factorial symbol represents

[0146] The multinomial distribution in this scheme is mainly used for cases where the distribution pattern is non-uniform and fractal. Of course, the multinomial distribution can also be used for uniform and fractal distributions, but the accuracy will be reduced.

[0147] In one embodiment of the present invention, when the distribution follows a negative exponential distribution, the probability density function f(l) of the trace length is:

[0148] f(l)=θe -θl , l>0

[0149] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0150]

[0151] Where k is the ratio of the major and minor axes of the elliptical crack; θ is the negative exponential distribution parameter θ > 0, and the mean trace length u l and standard deviation σ l The value is 1 / θ;

[0152] When the distribution follows a Gamma distribution, the probability density function f(l) of the trace length is:

[0153]

[0154]

[0155] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0156]

[0157] Where α and β are the Gamma distribution parameters, and α > 1, β > 0;

[0158] When the distribution pattern is chi-square χ 2 When distributed, the probability density function f(l) of the trace length is:

[0159]

[0160] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0161]

[0162] Where n is the chi-square distribution parameter, and n > 2;

[0163] When the distribution follows a log-normal distribution, the probability density function f(l) of the trace length is:

[0164]

[0165]

[0166]

[0167] The formulas for calculating the major axis probability density model E(a) and the ratio probability density model E(k) are as follows:

[0168]

[0169] Where u and σ are the parameters of the log-normal distribution, and σ > 0.

[0170] The accuracy of the range of the major axis and major-minor axis ratio obtained from the multinomial distribution function model constructed in this scheme is verified by Monte Carlo numerical simulation:

[0171] Rock joint network simulation using existing technology RJNS 3D The (3D Rock-mass Joint Network Simulation) toolbox is used to simulate and verify the model constructed in this scheme. It is a Matlab toolbox developed using the Monte Carlo method, a classic algorithm based on computational geometry, and many graphics functions written in Matlab.

[0172] This embodiment performed Monte Carlo simulations for three examples. The RJNS3D toolbox was used to generate a spatial elliptical fracture network by inputting preset parameters (parameters included the distribution of the major axis, the ratio of the major to minor axis, the rotation angle, and the orientation). The simulation parameters for the examples are shown in Table 1.

[0173] Table 1 RJNS 3D Toolbox Simulation Parameter Table

[0174]

[0175] Then, assuming an arbitrary sampling surface (measuring window), intersects with the fracture network to generate traces and calculates the trace length; a statistical histogram is then created using the trace length, and the probability density function of the unpruned trace length at both ends is obtained by fitting it; through trace length processing, the probability density function of the true trace length under an infinite plane is generalized from a finite measuring window and fitted as a multinomial distribution function; substituting the previously derived formula for the characteristic size of an elliptical fracture based on stereochemistry, the analytical expression of the probability density function of the major axis a is deduced, and finally plotted as a curve, as shown below. Figure 3 As shown.

[0176] By comparing the curves, it was found that the probability density function of the major axis of the elliptical fracture calculated using simulated data had a high degree of overlap with the theoretical distribution curve of the original input, thus verifying the correctness of the probability function model of the major axis of the elliptical fracture derived from the polynomial function of the trace length distribution.

Claims

1. A method for obtaining rock mass fracture parameters based on an elliptical model, characterized in that, Including the following steps: Acquire images of cracks on the surface of the rock mass under study, and perform image segmentation and enhancement processing; A neural network was used to identify the enhanced fracture images to obtain the identification results of rock mass fractures and the trace length of rock mass fractures; Based on all trace length data of the rock mass under study, a frequency distribution histogram of trace length is plotted, a distribution curve of trace length is obtained by fitting, and the distribution law of the fitted curve is determined. Based on the distribution pattern of the fitted curve, select the probability density function of the trace length; Based on the probability density function of the trace length, the probability density model of the major axis of the elliptical crack and the probability density model of the ratio of the major and minor axes of the elliptical crack are constructed respectively. The distribution range of the major axis of the elliptical crack is obtained by using the major axis probability density model, and the distribution range of the ratio of the major and minor axes is obtained by using the ratio probability density model.

2. The method for obtaining rock mass fracture parameters based on an elliptical model according to claim 1, characterized in that, When the distribution pattern is uniform, the probability density function f(l) of the trace length is: Where B0 and B are the lower and upper limits of the trace length, respectively; l is the trace length. The formula for calculating the major axis probability density model g(a) is as follows: Where ξ0 and ζ are the lower and upper limits of the major axis, respectively; and a is the length of the major axis. The formula for calculating the ratio probability density model u(k) is as follows: Where k is the ratio of the major axis to the minor axis; ξ k This represents the upper limit of the ratio of the major axis to the minor axis; s = B / a is an intermediate parameter.

3. The method for obtaining rock mass fracture parameters based on an elliptical model according to claim 1, characterized in that, When the distribution pattern is a fractal distribution, the probability density function f(l) of the trace length is: Where B0 is the lower limit of the trace length; l is the trace length; and D is the fractal dimension. The formula for calculating the major axis probability density model g(a) is as follows: Where ξ0 is the lower limit of the major axis; a is the length of the major axis; The formula for calculating the ratio probability density model u(k) is as follows: Where k is the ratio of the major axis to the minor axis; ξ k This represents the upper limit of the ratio of the major axis to the minor axis.

4. The method for obtaining rock mass fracture parameters based on an elliptical model according to claim 1, characterized in that, When the distribution follows a multinomial distribution, the probability density function f(l) of the trace length is: Among them, C m Here, B represents the coefficients of each order; l represents the trace length; and m represents the degree of the polynomial. The formula for calculating the major axis probability density model g(a) is as follows: Where ξ0 and ζ are the lower and upper limits of the major axis, respectively; a is the length of the major axis; Q m P is the first positive sequence; m This is the first negative sequence; k is the ratio of the major axis to the minor axis. The formula for calculating the ratio probability density model u(k) is as follows: Where, ξ k This represents the upper limit of the ratio of the major axis to the minor axis. It is the second positive sequence; It is the second negative sequence.

5. The method for obtaining rock mass fracture parameters based on an elliptical model according to claim 4, characterized in that, When m is odd, Q m and P m The calculation formulas are as follows: Among them, the double factorial symbol represents When m is even, Q m and P m The calculation formulas are as follows: Among them, the double factorial symbol represents 6. The method for obtaining rock mass fracture parameters based on an elliptical model according to claim 4, characterized in that, When m = 1: When m = 2: When m ≥ 3, and m is an odd number: Among them, the double factorial symbol represents When m ≥ 3, and m is an even number: Among them, the double factorial symbol represents 7. The method for obtaining rock mass fracture parameters based on an elliptical model according to claim 4, characterized in that, When the distribution follows a negative exponential distribution, the probability density function f(l) of the trace length is: f(l)=θe -θl ,l>0 The formulas for calculating the major axis probability density model E(a) and the major-minor axis ratio probability density model E(k) are as follows: Where k is the ratio of the major and minor axes of the elliptical crack; θ is the negative exponential distribution parameter, θ > 0, and the mean trace length u l and standard deviation σ l The value is 1 / θ; When the distribution follows a Gamma distribution, the probability density function f(l) of the trace length is: u l ＝αβ， The formulas for calculating the major axis probability density model E(a) and the major-minor axis ratio probability density model E(k) are as follows: Where α and β are the Gamma distribution parameters, and α > 1, β > 0; When the distribution pattern is chi-square χ 2 When distributed, the probability density function f(l) of the trace length is: you l =n;σ l =2n; The formulas for calculating the major axis probability density model E(a) and the major-minor axis ratio probability density model E(k) are as follows: Where n is the chi-square distribution parameter, and n > 2; When the distribution follows a log-normal distribution, the probability density function f(l) of the trace length is: The formulas for calculating the major axis probability density model E(a) and the major-minor axis ratio probability density model E(k) are as follows: Where u and σ are the parameters of the log-normal distribution, and σ > 0.

8. The method for obtaining rock mass fracture parameters based on an elliptical model according to any one of claims 1-7, characterized in that, The neural network uses U-net as its basic architecture, and adds upsampling and downsampling as well as skip connections for feature maps between the encoder and decoder.

Images