Fracture network reconstruction method based on two-dimensional measurement window

Abstract

The application discloses a fracture network reconstruction method based on two-dimensional measurement window, which comprises the following steps: obtaining fracture information of a fracture development area in a region to be studied, and grouping the occurrence of the fracture information; selecting a group of fractures, correcting the occurrence weight of the group of fractures, and updating the direction cosine of the normal of the fractures by using the corrected occurrence weight; calculating the Fisher parameter and volume density of the fractures; fitting a trace length fitting curve by using the trace length, and determining the distribution rule of the fitting curve; according to the distribution rule, selecting an axial probability density model of the major axis of an elliptical fracture and a ratio probability density model of the major and minor axis ratio of the elliptical fracture to calculate the distribution range of the major axis and the major and minor axis ratio of the elliptical fracture; inputting all the obtained parameters into RJNS 3D A tool box is obtained, and the fracture distribution of the current fracture group is obtained; when the fracture distribution of all the fracture groups is obtained, the fracture distribution of all the fracture groups is superimposed, and a three-dimensional fracture network model of the rock mass is generated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geotechnical engineering, and particularly relates to a fracture network reconstruction method based on a two-dimensional measurement window. BACKGROUND

[0002] After a long geological process, the originally single lithology and structure of the rock mass becomes complex, and this complexity is reflected in various scale structural planes existing in the rock mass. According to the scale of the structural plane, Gu Dezhen classifies the structural plane into five levels: I, II and III level structural planes, which are called deterministic structural planes; and IV and V level structural planes or below, which are called non-deterministic structural planes, i.e. joints, bedding and fractures. Such structural planes are relatively uniformly distributed in the rock mass and have a large number, directly control the mechanical properties of the rock mass, and are directly related to the safety of the rock mass. Such structural planes are currently the concern of engineering design and rock mechanics research.

[0003] At present, in the safety protection of rock mass engineering, the rock mass joint network model is constructed, the fractal value of the joint network model is calculated to judge the quality of the rock mass or analyze the connectivity characteristics of the rock quality slope engineering to perform risk assessment. In the construction of the common rock mass joint network model, the fractures are simplified into circles and ellipses for easy calculation. The circle is too simplified and has a large difference from the actual situation, so that the constructed rock mass joint network model has a large deviation from the actual situation.

[0004] Although the ellipse is close to the actual fracture, the solving of the size distribution of the elliptical fracture mostly adopts a numerical solution method and a method of assuming a classic distribution function to solve the trace length and size distribution relationship formula. However, the trace length distribution obtained by different geological conditions cannot be fully summarized by the classic distribution, which makes the long axis and the long-short axis ratio of the solved ellipse inaccurate, so that the finally constructed rock mass joint network model has a deviation from the actual situation, and the subsequent rock mass stability evaluation has a deviation, and finally it is difficult to develop an accurate rock mass stability safety protection scheme. SUMMARY

[0005] In view of the above problems in the prior art, the fracture network reconstruction method based on the two-dimensional measurement window provided by the present application solves the problem that the long axis and the long-short axis ratio of the ellipse obtained by the existing reconstruction method have a large deviation, and the reconstructed fracture network has a large deviation from the actual situation.

[0006] In order to achieve the above-mentioned application purposes, the technical scheme adopted by the present application is as follows:

[0007] A fracture network reconstruction method based on a two-dimensional measurement window is provided, which comprises the following steps:

[0008] S1, obtain the fracture information of a fracture development section in a region to be studied, and group the fracture development section according to the fracture information to obtain a plurality of fracture groups;

[0009] S2, select a group of unselected fracture groups, correct the occurrence weight of the fractures by using a vector correction method, and update the direction cosine of the normal direction of the fractures by using the corrected occurrence weight;

[0010] S3, calculate the Fisher parameter and the volume density of the fractures according to the fracture information of the fracture groups;

[0011] S4, fit the trace length according to the fracture information of the fracture groups to obtain a fitting curve of the trace length, and determine the distribution rule of the fitting curve according to the shape of the fitting curve;

[0012] S5, select an ellipse fracture long axis probability density model and an ellipse fracture long and short axis ratio probability density model according to the distribution rule to calculate the distribution range of the ellipse fracture long axis and the long and short axis ratio;

[0013] S6, input the average occurrence, the Fisher parameter, the volume density, the distribution rule of the trace length, and the distribution range of the long axis and the long and short axis ratio into the RJNS 3D tool box to obtain the fracture distribution of the current fracture group;

[0014] S7, judge whether the fracture distribution of the plurality of fracture groups has been obtained, if yes, go to step S8, otherwise return to step S2;

[0015] S8, superimpose the fracture distribution of all fracture groups according to the additivity of the homogeneous Poisson process to generate a rock mass three-dimensional fracture network model.

[0016] The beneficial effects of the present application are that the present application groups the fractures according to the dominant occurrence, effectively corrects the spatial fracture sampling deviation, and obtains the fracture spatial distribution closer to the actual situation; through fitting all the rock mass fracture trace lengths, the fitting curve of the trace length can be obtained, and the distribution rule of the trace length can be intuitively seen through the shape of the curve, the distribution rule of the fitting curve is taken as the distribution rule of the trace length, the two selected probability density models are more consistent with the trace length of the distribution, so that the distribution range of the ellipse long axis and the long and short axis ratio is obtained more accurately, and the accuracy of the constructed fracture network is further increased by selecting other fracture parameters in the present application, thereby ensuring the accuracy of the subsequent determination of the stability of the rock mass. From geological exploration to numerical simulation system, an elliptical fracture network reconstruction method suitable for engineering rock mass is proposed, which can facilitate the accurate acquisition of the strength and deformation of the rock mass, REV, fracture seepage, and surrounding rock stability in subsequent geotechnical engineering.

[0017] Compared with existing technologies, this scheme solves the problems of complex elliptical fracture parameters and difficult theoretical derivation. It establishes a fracture network reconstruction process that approximates the actual fracture shape. Since the probability density model is constructed based on specific distribution patterns, Monte Carlo numerical simulations have verified that the probability density function of the major axis of the elliptical fracture constructed by this scheme 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 scheme, thereby ensuring the accuracy of subsequent determination of rock mass stability. Attached Figure Description

[0018] Figure 1 This is a flowchart of a fracture network reconstruction method based on two-dimensional windowing.

[0019] Figure 2 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.

[0020] Figure 3 To obtain the trace length distribution of the first group of joints, (a) is the statistical histogram of the unpruned trace length of the first group of joints, and (b) is the trace length distribution of the first group of joints under the defined scale.

[0021] Figure 4 To obtain the trace length distribution of the second group of joints, (a) is the statistical histogram of the unpruned trace length of the second group of joints, and (b) is the trace length distribution of the second group of joints under the infinite window.

[0022] Figure 5 To generate a random stratification distribution.

[0023] Figure 6 This is a statistical simulation and window position display for the first group of joints.

[0024] Figure 7 The figures show a comparison between statistical simulation and actual measurement of the first group of joints; (a) shows the first group of joints on the left wall of the No. 3 test tunnel, and (b) shows the first group of joints on the right wall of the No. 3 test tunnel.

[0025] Figure 8 This is a statistical simulation and window position display for the second group of joints.

[0026] Figure 9 The following are comparison diagrams of statistical simulation and actual measurement of the second group of joints; (a) shows the second group of joints on the left wall of the No. 3 test tunnel; (b) shows the second group of joints on the right wall of the No. 3 test tunnel.

[0027] Figure 10 This is a model of the deep rock mass structure of Jinping. Detailed Implementation

[0028] 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.

[0029] refer to Figure 1 , Figure 1 A flowchart of a fracture network reconstruction method based on two-dimensional windowing is shown; as follows: Figure 1 As shown, the method S includes steps S1 to S8.

[0030] In step S1, fracture information of the more developed fracture areas in the study area is obtained. The fracture information in this scheme includes the distribution of all fractures within the two-dimensional measurement window of the rock mass, the length of each fracture (i.e., trace length), the orientation of the fracture, the surface density of the fracture, etc.

[0031] Subsequently, based on the fracture information, the fractured areas were grouped by attitude, resulting in several fracture groups; specifically, this scheme uses Dips software and adopts hemispherical projection to group the fractures by attitude.

[0032] In step S2, a group of unselected fracture groups is selected, and the orientation weights of the fractures are corrected using the vector correction method:

[0033]

[0034] Among them, W i V represents the corrected attitude weights; i The moving intersection volume; ω is a constant;

[0035] Then, the corrected attitude weights are used to update the direction cosine of the fracture normal as the average attitude. The formula for calculating the direction cosine is:

[0036]

[0037]

[0038] in, and These are the direction cosines of the average direction of the corrected crack along the normal direction on the x, y, and z axes, respectively; i m i and n i , where are the direction cosines of the normal direction of each crack on the x, y, and z axes before correction; n is the number of cracks.

[0039] Since the observed two-dimensional fracture directional frequencies do not represent the true three-dimensional frequencies, there is a directional sampling bias. This scheme uses a vector correction method to correct the directional sampling bias and is applicable to measurement window planes of any direction. Since the actual fracture and measurement window plane dimensions are finite, this scheme is applicable to the intersection traces of measurement window planes of finite size and fracture surfaces of any shape.

[0040] In step S3, the Fisher parameters and bulk density of the fractures are calculated based on the fracture information of the fracture groups; wherein, the formula for calculating the bulk density is:

[0041]

[0042] Among them, P 30 P is the volume density of the fracture. 20 The surface density of the fracture; Mean of equivalent diameter of elliptical crack a is the major axis of the ellipse, k is the ratio of the major axis to the minor axis of the ellipse, and α is the relative angle between the crack and the two-dimensional measuring window plane.

[0043] Since the internal fissures of the rock mass are invisible and intangible, this method can accurately infer the volume density of the fissures in three-dimensional space based on the statistical data of the traces within the two-dimensional measurement window (including the number of traces, the angle of the fissure direction, etc.).

[0044] In implementation, the preferred methods for calculating the Fisher parameters of the crack in this scheme include:

[0045] Select multiple Fisher parameter estimation formulas and calculate the estimated values. and

[0046]

[0047] Where n is the number of cracks; c i The transformation parameters represent the fracture tendency.

[0048] Using Pearson χ 2 Test, based on the estimated value and Select the smallest χ 2 The estimated value corresponding to the value is used as the final Fisher parameter.

[0049] Using the Fisher distribution function to describe fracture attitude is currently the most commonly used method. This scheme, based on hypothesis testing and comparative screening, uses the χ² distribution function to determine the fracture orientation. 2 Using quantity as the selected indicator avoids the cumbersome process of performing bivariate fit tests, while ensuring a high fit to the Fisher distribution, thus obtaining the Fisher parameters. The optimal solution value is obtained, thereby more accurately describing the orientation and distribution of spatial fractures.

[0050] In step S4, the trace length is fitted according to the fracture information of the fracture group to obtain the fitted curve of the trace length, and the distribution law of the fitted curve is determined according to the shape of the fitted curve. The fitting of this scheme can be performed by least squares fitting using Matlab software or Excel software.

[0051] In step S5, based on the distribution pattern, 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 selected to calculate the distribution range of the major axis and the ratio of the major and minor axes of the elliptical crack.

[0052] This scheme divides the distribution pattern in detail and constructs corresponding major axis probability density models and ratio probability density models to ensure the accuracy of the range of rock mass fracture parameters obtained subsequently.

[0053] 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.

[0054] When based on probability density functions, the multinomial distribution can be used as a general calculation method to calculate 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.

[0055] In step S6, the distribution patterns of average attitude, Fisher parameters, bulk density, trace length, and the distribution range of major axis and major-minor axis ratio are input into RJNS. 3D Toolbox: Obtain the fracture distribution of the current fracture group;

[0056] In step S7, it is determined whether the fracture distribution has been obtained for several fracture groups. If so, proceed to step S8; otherwise, return to step S2.

[0057] In step S8, based on the additivity of the homogeneous Poisson process, the fracture distributions of all fracture groups are superimposed to generate a three-dimensional fracture network model of the rock mass.

[0058] In one embodiment of the present invention, when the distribution is uniform, the probability density function f(l) of the trace length is:

[0059]

[0060] Where B0 and B are the lower and upper limits of the trace length, respectively; l is the trace length.

[0061] The formula for calculating the major axis probability density model g(a) is as follows:

[0062]

[0063] Where ξ0 and ζ are the lower and upper limits of the major axis, respectively; a is the major axis of the ellipse;

[0064] The formula for calculating the ratio probability density model u(k) is as follows:

[0065]

[0066] 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.

[0067] This method is suitable for situations where the field survey data of rock mass outcrops are uniformly distributed. It can directly obtain the analytical solution of the probability density function of the characteristic size of elliptical fractures, thereby obtaining the fracture distribution law of the real rock mass with higher accuracy.

[0068] When the distribution follows a fractal pattern, the probability density function f(l) of the trace length is:

[0069]

[0070] Where B0 is the lower limit of the trace length; l is the trace length; and D is the fractal dimension.

[0071] The formula for calculating the major axis probability density model g(a) is as follows:

[0072]

[0073] Where ξ0 is the lower limit of the major axis; a is the major axis of the ellipse;

[0074] The formula for calculating the ratio probability density model u(k) is as follows:

[0075]

[0076] 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.

[0077] When the sampling trace length in some study areas can be fitted to a fractal distribution, this scheme can directly obtain the analytical solution of the probability density function of the characteristic size of elliptical fractures, thus ensuring the accuracy of obtaining the fracture distribution in the real rock mass.

[0078] In one embodiment of the present invention, when the distribution law is a multinomial distribution, the probability density function f(l) of the trace length is:

[0079]

[0080] 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.

[0081] The formula for calculating the major axis probability density model g(a) is as follows:

[0082]

[0083] Where ξ0 and ζ are the lower and upper limits of the major axis, respectively; a is the major axis of the ellipse; 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.

[0084] The formula for calculating the ratio probability density model u(k) is as follows:

[0085]

[0086] 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; This is the second negative sequence. When m is odd, Q... m and P m The calculation formulas are as follows:

[0087]

[0088] Among them, the double factorial symbol represents

[0089] When m is even, Q m and P m The calculation formulas are as follows:

[0090]

[0091]

[0092] Among them, the double factorial symbol represents

[0093] When m = 1:

[0094] When m = 2:

[0095] When m ≥ 3, and m is an odd number:

[0096]

[0097]

[0098] Among them, the double factorial symbol represents

[0099] When m ≥ 3, and m is an even number:

[0100]

[0101]

[0102] Among them, the double factorial symbol represents

[0103] Since the polynomial function itself can fit the continuous distribution of trace lengths with a certain degree of accuracy, and the probability density function represented by the polynomial can be obtained by fitting the frequency distribution histogram of the trace length, the above scheme is the general solution for various complex trace length distributions, has good applicability, and also ensures the practical application effect of this scheme.

[0104] 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:

[0105] f(l)=θe -θl , l>0

[0106] 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:

[0107]

[0108] 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;

[0109] When the distribution follows a Gamma distribution, the probability density function f(l) of the trace length is:

[0110]

[0111]

[0112] 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:

[0113]

[0114] Where α and β are the Gamma distribution parameters, and α > 1, β > 0;

[0115] When the distribution pattern is chi-square χ 2 When distributed, the probability density function f(l) of the trace length is:

[0116]

[0117] 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:

[0118]

[0119] Where q is the chi-square distribution parameter, and q > 2;

[0120] When the distribution follows a log-normal distribution, the probability density function f(l) of the trace length is:

[0121]

[0122]

[0123]

[0124] 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:

[0125]

[0126] Where u and σ are the parameters of the log-normal distribution, and σ > 0.

[0127] This scheme is designed for complex distributions of trace length, such as negative exponential distribution, Gamma distribution, chi-square distribution, and log-normal distribution. It can more conveniently and directly calculate the statistical characteristic values ​​of elliptical crack size parameters, thereby allowing for a rough assessment of the average size and distribution of cracks in rock outcrops or tunnel walls on-site.

[0128] 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:

[0129] Rock joint network simulation using existing technology RJNS 3DThe (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.

[0130] This embodiment performed Monte Carlo simulations for three examples, using RJNS. 3D The toolbox generates a spatial elliptical fracture network by inputting preset parameters (parameters include the distribution of the major axis, the ratio of the major to minor axis, the rotation angle, the attitude, etc.). The simulation parameters for the example are shown in Table 1.

[0131] Table 1 RJNS 3D Toolbox Simulation Parameter Table

[0132]

[0133] 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 2 As shown.

[0134] 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.

[0135] The following examples illustrate the effectiveness of this solution and its feasibility in practical engineering applications:

[0136] A detailed geological survey was conducted at Jinping No. 3 test tunnel, which is located at chainage AK 8+750 within my country’s deepest dark matter laboratory. The tunnel is buried at a depth of approximately 2370m and consists of marble from the Baishan Formation of the T2b strata.

[0137] Survey results from sections with well-developed random joints in the 2-12m range were selected. Using Dips software and a hemispherical projection, the attitudes of each group were grouped. The dominant attitudes for each group were then determined using Dips software.

[0138] Table 2. Dominant attitude of joints in each group (fracture group).

[0139]

[0140] Determination of the trace length distribution of the first group of fracture groups:

[0141] In the investigation of Jinping No. 3 test tunnel, due to the deep rock mass and blasting construction, there were fewer joints and small-scale joints were destroyed. A total of 37 unpruned trace lengths were found on the left and right sidewalls of the first joint group. The Kaplan-Meier method was used to estimate the empirical distribution, and a histogram of the unpruned trace lengths was given based on the empirical distribution. The corresponding data were obtained by calling the corresponding functions in MATLAB. Due to the small sample size, a high-precision cubic spline function was used for fitting, followed by an approximation using a 16th-order orthogonal polynomial to obtain the trace length distribution at the corresponding scale. See [link to MATLAB function]. Figure 3 .

[0142] from Figure 3 It can be seen that the trace length distribution does not conform to a uniform or fractal distribution. Using an orthogonal polynomial approximation method, and assuming the trace length distribution function remains positive, a maximum trace length of 2.06 m is chosen. The trace length distribution of the first joint group is as follows:

[0143] f(l)=-2.340l 16 +37.93l 15 -277.43l 14 +1210.4l 13 -3507.5l 12 +7115.9l 11 -10383l 10 +11025l 9 -8531.1l 8 +4773.9l 7 -1900.4l 6 +523.93l 5 -96.068l 4 12.676l 3 -5.6099l 2 +3.9188l

[0144] Major axis probability density function distribution curve:

[0145]

[0146] Determination of the trace length distribution of the second group of fracture groups:

[0147] The Kaplan-Meier method is used to estimate the empirical distribution. Based on the empirical distribution, a histogram of the unpruned trace length is given. The histogram of the second group of unpruned trace lengths and the trace length distribution at the corresponding scale are shown below. Figure 4 .

[0148] The maximum trace length was selected as 2.06 m, and the trace length distribution was determined by the second group of joints:

[0149] f(l)=-8.467l 16 +136.97l 15 -999.67l 14 +4349.9l 13 -12564l 12 +25383l 11 -36837l 10 +38843l 9 -29776l 8 +16450l 7 -6432.2l 6 +1723.3l 5 -305.03l 4 36.309l 3 -9.502l 2 +4.6704l

[0150] Major axis probability density function distribution curve:

[0151]

[0152] Based on the weight update formula and combined with geological survey data, the weights corresponding to each occurrence were calculated, as shown in Tables 3 and 4.

[0153] Table 3. Calculation table for joint orientation frequency correction in Group 1.

[0154]

[0155] Table 4. Calculation table for joint orientation frequency correction in Group 2.

[0156]

[0157] Based on geological survey data, the Fisher distribution is proposed for joint attitude distribution, and the direction cosine of the joint normal is calculated using direction cosine. According to the weight calculation results listed in Table 3, the corrected average attitude of the first group of joints is calculated as 166.4882°∠72.7948°; according to the weight calculation results listed in Table 4, the corrected average attitude of the second group of joints is calculated as 81.4492°∠74.0101°.

[0158] In the method for calculating the Fisher parameter of the crack, the number of histogram groups was set to 5, and the significance level was set to 0.05. The value was 7.8147, and it was ultimately selected. The corresponding values ​​are used as Fisher parameters for the first and second group of fractures.

[0159] The bulk density at the midpoint of the joint is calculated based on the formula for joint bulk density and the average orientation in Table 5.

[0160] Table 5. Estimation of bulk density at the midpoint of joints.

[0161]

[0162] Leveraging RJNS 3D In the toolbox, set the simulation area size to 16m × 8m × 8m, specifying the X-direction as N32E, with the positive direction pointing from inside the tunnel to the entrance. First, generate parallel bedding planes, see... Figure 5 For the first group of fractures, bedding with negative exponential spacing was generated using a method for generating random numbers with a negative exponential distribution, see [link to be inserted here]. Figure 6 The statistical simulation comparison diagram of the first group of joints, in which... Figure 7 (a) is the joint in the statistical simulation. Figure 7 (b) refers to the actual joints recorded.

[0163] For the second group of fractures, bedding with negative exponential spacing was generated using a method for generating random numbers with a negative exponential distribution, see [link to be inserted here]. Figure 8 The statistical simulation comparison diagram of the first group of joints, in which... Figure 9 (a) is the joint in the statistical simulation. Figure 9 (b) refers to the actual joints recorded.

[0164] Based on the additivity of the homogeneous Poisson process, the obtained bedding distributions and the distributions of the first and second joint groups are superimposed to generate a deep rock mass structure model of Jinping. (Refer to...) Figure 10 .

[0165] As can be seen from the above examples, by cutting the three-dimensional fracture network generated by statistical simulation into sections, the intersection results of the statistical simulation window and the spatial fracture are obtained. By comparing the fracture traces measured on the tunnel wall in the field with the fracture traces generated by statistical simulation, it is found that the fracture network model conforms to the actual geological conditions and the error is controlled within the allowable error range. This shows that the fracture network reconstruction parameters obtained by this scheme can truly reflect the geometric characteristics of the fracture and the mechanical properties of the rock mass.

[0166] Based on the geological conditions of the Jinping deep test tunnel, the case study considered the distribution of bedding and reconstructed the deep rock mass structure model from a statistical perspective. This model can provide a geometric model containing geological information for the study of deep rock mechanics and seepage characteristics, and further carry out surrounding rock stability analysis and tunnel surrounding rock support scheme design.

Claims

1. A method for reconstructing a fracture network based on a two-dimensional window, characterized in that, Including the following steps: S1. Obtain fracture information of fractured areas in the area to be studied, and group the fractured areas by attitude based on the fracture information to obtain several fracture groups. S2. Select a group of unselected fracture groups, use the vector correction method to correct the fracture attitude weights, and use the corrected attitude weights to update the direction cosine of the fracture normal as the average attitude. S3. Calculate the Fisher parameter and bulk density of the fractures based on the fracture information of the fracture group; S4. Based on the fracture information of the fracture group, fit the trace length to obtain the trace length fitting curve, and determine the distribution law of the fitting curve based on the shape of the fitting curve. S5. Based on the distribution pattern, select 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 to calculate the distribution range of the major axis and the ratio of the major and minor axes of the elliptical crack. S6. Input the distribution patterns of average attitude, Fisher parameters, bulk density, trace length, and the distribution range of major axis and major-minor axis ratio into RJNS. 3D Toolbox: Obtain the fracture distribution of the current fracture group; S7. Determine whether the fracture distribution has been obtained for several fracture groups. If yes, proceed to step S8; otherwise, return to step S2. S8. Based on the additivity of the homogeneous Poisson process, the fracture distributions of all fracture groups are superimposed to generate a three-dimensional fracture network model of the rock mass.

2. The method for reconstructing a fracture network based on a two-dimensional window as described in claim 1, characterized in that, The formula for correcting the fracture orientation weight using the vector correction method is as follows: Among them, W i V represents the corrected attitude weights; i The moving intersection volume; ω is a constant; The formula for calculating the direction cosine is: in, and These are the direction cosines of the average direction of the corrected crack along the normal direction on the x, y, and z axes, respectively; i m i and n i , where are the direction cosines of the normal direction of each crack on the x, y, and z axes before correction; n is the number of cracks.

3. The method for reconstructing a fracture network based on a two-dimensional window as described in claim 1, characterized in that, Methods for calculating Fisher parameters of cracks include: Select multiple Fisher parameter estimation formulas and calculate the estimated values. and Where n is the number of cracks; c i These are transformation parameters representing the fracture tendency; Using Pearson χ 2 Test, based on the estimated value and Select the smallest χ 2 The estimated value corresponding to the value is used as the final Fisher parameter.

4. The method for reconstructing a fracture network based on a two-dimensional window as described in claim 1, characterized in that, The formula for calculating the bulk density is: Among them, P 30 P is the volume density of the fracture. 20 The surface density of the fracture; Mean of equivalent diameter of elliptical crack a is the major axis of the ellipse, k is the ratio of the major axis to the minor axis of the ellipse, and α is the relative angle between the crack and the two-dimensional measuring window plane.

5. The method for reconstructing a fracture network based on a two-dimensional window according to any one of claims 1-4, 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; a is the major axis of the ellipse; 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.

6. The method for reconstructing a fracture network based on a two-dimensional window according to any one of claims 1-4, 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 major axis of the ellipse; 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.

7. The method for reconstructing a fracture network based on a two-dimensional window according to any one of claims 1-4, 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 major axis of the ellipse; 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.

8. The method for reconstructing a fracture network based on a two-dimensional window according to claim 7, 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 9. The method for reconstructing a fracture network based on a two-dimensional window according to claim 7, 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 10. The method for reconstructing a fracture network based on a two-dimensional window according to any one of claims 1-4, 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: 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 q is the chi-square distribution parameter, and q > 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.

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