Sandstone strength prediction method based on multi-fracture characteristic parameters and electronic device

Abstract

The application relates to a sandstone strength prediction method based on multi-fracture characteristic parameters and an electronic device, and relates to the technical field of geotechnical engineering, and comprises the following steps: obtaining fracture measurement data of sandstone outcrops and drilling cores, extracting a fracture dip angle interval, a fracture rate, a length interval and a width interval, and constructing a fracture characteristic parameter set; the distribution law of each fracture parameter is fitted by using a Weibull distribution, and a random fracture network model is generated in combination with the fracture rate; a connectivity coefficient is extracted from the model, the strength of a complete rock block is reduced by using a negative exponential decay function, and an initial prediction value of the strength is obtained; the initial prediction value is anisotropically corrected according to the included angle between the main direction of the ground stress and the fracture dip, and a final prediction value is obtained. The application solves the technical problems that in the strength prediction of a sandstone formation, a small-scale complete rock sample cannot represent a real rock mass containing random fractures, the strength parameters are overestimated, and the traditional test method is time-consuming and difficult to cover a large range of formations.

Description

Technical Field

[0001] This application relates to the field of geotechnical engineering technology, and in particular to a method and electronic equipment for predicting the strength of sandstone based on multi-fracture characteristic parameters. Background Technology

[0002] In the construction of underground engineering projects such as tunnels and roadways, the strength parameters of sandstone strata are key bases for evaluating surrounding rock stability and designing support systems. Currently, in engineering practice, core samples are obtained by drilling in the target section. After processing the obtained rock cores into standard cylindrical specimens, indoor uniaxial or triaxial compression tests are conducted to directly determine the compressive strength and elastic modulus of the rock samples. These parameters are then appropriately reduced based on engineering experience to serve as predicted values ​​for the sandstone strata strength.

[0003] However, the aforementioned traditional methods have significant limitations. First, the rock samples used in laboratory tests are intact small pieces of rock after macroscopic fractures have been removed. In reality, sandstone strata typically contain randomly distributed fracture networks, and the strength test results of intact rock samples cannot reflect the weakening effect of fractures on the overall rock mass strength. Direct use of these samples will lead to an overestimation of strength parameters. Second, drilling and coring, as well as laboratory testing, have long cycles, making it difficult to meet the demands of rapid underground engineering construction for real-time acquisition of surrounding rock parameters. Furthermore, the number of drilling points is limited, and the test results only represent the rock strength at local locations. For large-scale, complex strata with uneven fracture distribution and significant lithological variations, data from a single point or a small number of measuring points are insufficient to comprehensively characterize the strength characteristics of the entire target section. Summary of the Invention

[0004] This application provides a sandstone strength prediction method and electronic equipment based on multi-fracture characteristic parameters, which improves the technical problem that the prediction results deviate significantly from the actual strength of fractured rock masses in the field due to relying solely on indoor rock sample tests and empirical reduction.

[0005] This application discloses the following technical solution:

[0006] In a first aspect, this application provides a method for predicting the strength of sandstone based on multi-fracture characteristic parameters, the method comprising:

[0007] Multiple sets of fracture measurement data from sandstone outcrops and borehole cores within the target section were obtained, and fracture dip angle intervals, fracture ratio, fracture length intervals, and fracture width intervals were extracted from them to construct a fracture characteristic parameter set.

[0008] Based on the set of fracture feature parameters, the distribution of fracture dip angle, fracture length and fracture width in their respective intervals is fitted using the Weber distribution probability density function to determine the Weber distribution shape parameter and scale parameter of each parameter, and a random fracture network model is generated by combining the fracture rate.

[0009] The fracture network connectivity coefficient is extracted from the random fracture network model. The standard value of the uniaxial compressive strength of the intact rock block in the target section is reduced and corrected by the negative exponential decay function to obtain the initial predicted value of the fractured rock mass strength.

[0010] Obtain the principal stress direction of the in-situ stress field within the target section, calculate the angle deviation between the dip direction of each fracture and the direction of the maximum principal stress in the random fracture network model, and perform anisotropic correction on the initial predicted value of the fractured rock mass strength to obtain the final predicted value of the fractured rock mass strength.

[0011] Secondly, this application provides an electronic device for predicting sandstone strength based on multi-fracture characteristic parameters, the electronic device comprising:

[0012] The feature extraction module is used to acquire multiple sets of fracture measurement data from sandstone outcrops and borehole cores in the target section, and extract fracture dip angle intervals, fracture ratio, fracture length intervals and fracture width intervals from them to construct a fracture feature parameter set;

[0013] The network generation module is used to fit the distribution of fracture dip angle, fracture length and fracture width in their respective intervals based on the fracture feature parameter set and the Weber distribution probability density function, to determine the Weber distribution shape parameter and scale parameter of each parameter, and to generate a random fracture network model in combination with the fracture rate.

[0014] The strength reduction module is used to extract the fracture network connectivity coefficient from the random fracture network model, and use a negative exponential decay function to reduce and correct the standard value of the uniaxial compressive strength of the intact rock block in the target section of sandstone to obtain the initial predicted value of the fractured rock mass strength.

[0015] An anisotropy correction module is used to obtain the principal stress direction of the in-situ stress field in the target section, calculate the angle deviation between the dip direction of each fracture and the maximum principal stress direction in the random fracture network model, and perform anisotropy correction on the initial predicted value of the fractured rock mass strength to obtain the final predicted value of the fractured rock mass strength.

[0016] One or more technical solutions provided in this application have at least the following technical effects or advantages:

[0017] The technical solution of this application provides a sandstone strength prediction method based on multiple fracture characteristic parameters. First, by extracting fracture dip angle intervals, fracture ratio, fracture length intervals, and fracture width intervals from multiple sets of fracture measurement data from sandstone outcrops and borehole cores in the target section, a systematic set of fracture characteristic parameters is constructed. This achieves a comprehensive quantification and standardized expression of the on-site fracture distribution characteristics, solving the problems of scattered fracture information collection and lack of unified parameter representation in traditional methods.

[0018] Furthermore, by fitting the distribution of fracture geometric parameters in each interval using the Weiber distribution probability density function and combining it with the fracture rate to generate a random fracture network model, the statistical distribution law of actual fractures is transformed into a computable two-dimensional network model, realizing the probabilistic modeling of the random distribution characteristics of fractures and solving the problem that complete rock sample tests cannot reflect the overall characteristics of the fracture network.

[0019] Furthermore, by extracting the fracture network connectivity coefficient from the random fracture network model and using a negative exponential decay function to reduce and correct the standard value of the uniaxial compressive strength of the intact rock block, the degree of connectivity between fractures is quantified and introduced into the strength calculation, thereby realizing a quantitative assessment of the weakening effect of fractures on rock mass strength and solving the problem that the traditional empirical reduction method lacks quantitative basis for fracture connectivity.

[0020] Finally, by obtaining the principal stress direction of the in-situ stress field and calculating the angle deviation between the dip direction of each fracture and the direction of the maximum principal stress, anisotropic correction is made to the initial strength prediction value. The relative relationship between the stress direction and the fracture direction is incorporated into the strength evaluation, thus realizing accurate correction of the anisotropy of the fractured rock mass strength and solving the problem that traditional methods ignore the influence of the stress direction on the strength of fractured rock mass.

[0021] In summary, this application extracts a set of characteristic parameters of in-situ fractures, uses a Weiber distribution to fit and generate a random fracture network model, extracts the fracture network connectivity coefficients and performs strength reduction correction, and then combines the in-situ stress direction for anisotropy correction to obtain the final predicted value of fractured rock mass strength. This achieves a systematic quantitative assessment from fracture statistical characteristics to rock mass strength prediction, solving the technical problem that traditional indoor tests cannot represent real fractured rock masses and have large prediction biases. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a flowchart illustrating the sandstone strength prediction method based on multi-fracture characteristic parameters provided in this application embodiment.

[0024] Figure 2 A flowchart illustrating the generation process of a random fracture network model for a sandstone strength prediction method based on multiple fracture characteristic parameters, as provided in this application embodiment.

[0025] Figure 3This is a schematic diagram of the structure of an electronic device for predicting sandstone strength based on multiple fracture characteristic parameters, provided in an embodiment of this application.

[0026] In the attached diagram, Figure 3 The components represented by each label are explained as follows: Feature extraction module 11, Network generation module 12, Intensity reduction module 13, and Anisotropy correction module 14. Detailed Implementation

[0027] This application provides a sandstone strength prediction method and electronic equipment based on multi-fracture characteristic parameters. It is used to solve the technical problem that in sandstone strata of underground engineering such as tunnels and roadways, indoor rock sample testing can only reflect the strength of local intact rock at the drilling point, while the actual rock mass has random fracture distribution, large differences in the degree of fracture network connectivity and variable geostress direction. Existing methods are difficult to efficiently and accurately predict the strength of large-scale complex fractured rock masses.

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that the numerical values ​​in the embodiments are for illustrative purposes only and do not constitute a limitation on this application.

[0029] Example 1, as shown in the appendix Figure 1 As shown, this application provides a method for predicting the strength of sandstone based on multi-fracture characteristic parameters. The method includes the following steps:

[0030] S100: Obtain multiple sets of fracture measurement data from sandstone outcrops and borehole cores within the target section, and extract fracture dip angle intervals, fracture rate, fracture length intervals, and fracture width intervals from them to construct a fracture characteristic parameter set.

[0031] In this embodiment, the sandstone strata fractures are randomly and unevenly distributed. Data obtained by traditional measurement methods are scattered and lack unified quantitative characterization, making them difficult to use directly for intensity prediction. Therefore, it is necessary to systematically extract geometric features such as fracture dip angle, length, width, and fracture ratio from outcrop scanning and borehole cores to construct a standardized set of fracture feature parameters.

[0032] Step S100 in the method provided in this application embodiment includes:

[0033] A three-dimensional laser scan was performed on the surface of the sandstone outcrop in the target section to obtain point cloud data, and a CT scan was performed on the borehole core to obtain a radial cross-sectional sequence image. Based on the point cloud data and the radial cross-sectional sequence image, the fractured area and the intact rock area were separated, and the boundary contour lines of the fractured area were extracted. For each extracted fracture boundary contour line, the direction of the maximum variance of the contour point set was calculated, and the angle between the direction of the maximum variance and the horizontal plane was taken as the fracture dip angle. The Euclidean distance between the two endpoints of the fracture boundary contour line was calculated as the fracture length, and the average value of the maximum inscribed circle diameter inside the fracture boundary contour line was calculated as the fracture width.

[0034] Collect samples of fracture dip angle, fracture length, and fracture width from all fractures, and plot cumulative frequency curves for dip angle, length, and width, respectively. Construct fracture dip angle intervals, fracture length intervals, and fracture width intervals. Calculate the area of ​​the measurement region corresponding to each set of measurement data, and extract the area enclosed by the boundary contours of all fractures within the corresponding measurement region. Based on the relative relationship between the total fracture area and the area of ​​the corresponding measurement region, determine the single-set area fracture rate for each measurement region. Merge the single-set area fracture rates from multiple sets of measurement data to determine the average fracture rate within the target segment. Combine the fracture dip angle interval, fracture length interval, fracture width interval, and the average fracture rate to form the fracture feature parameter set. Detailed explanation follows:

[0035] The fracture measurement data is a collection of fracture geometry information obtained from sandstone outcrops and borehole cores using 3D laser scanning and CT scanning, respectively. It includes parameters such as the dip angle, length, and width of each fracture. The fracture dip angle, measured in degrees (°), is the angle between the fracture surface and the horizontal plane, calculated by taking the angle between the direction of the maximum variance of the fracture boundary profile point set and the horizontal plane.

[0036] The direction of maximum variance is determined using principal component analysis. A covariance matrix is ​​constructed for the spatial coordinates of all points within the region enclosed by the fracture boundary contour. The eigenvalues ​​and eigenvectors of the covariance matrix are then solved. The direction of the eigenvector corresponding to the largest eigenvalue is taken as the direction of maximum variance for the contour point set. The angle between the direction of maximum variance and the horizontal plane is determined as the fracture dip angle, based on the fact that the direction of maximum variance for the contour point set corresponds to the principal extension direction of the narrow fracture contour. The fracture length, measured in meters (m), is the length of the trace extending from the fracture on the outcrop surface or core section. It is obtained by calculating the Euclidean distance between the two endpoints of the fracture boundary contour.

[0037] Crack width, measured in mm, is a measure of crack opening. It is obtained by averaging the maximum inscribed circle diameters at multiple locations within the crack boundary contour. This is based on the fact that crack opening is typically non-uniform along the trace, and averaging provides a more stable representation of the average crack opening. The crack dip angle interval is a statistical interval constructed based on the cumulative frequency curves of all crack dip angle samples. The dip angle value corresponding to 5% of the cumulative frequency is taken as the lower limit of the interval, and the dip angle value corresponding to 95% of the cumulative frequency is taken as the upper limit. This is based on the fact that excluding the extreme values ​​at both ends (5% at each end) effectively filters outliers caused by measurement errors or local anomalies, retaining 90% of the central sample interval, which reflects the main distribution range and has statistical robustness.

[0038] Similarly, the fracture length and fracture width intervals are constructed, each taking the range from 5% to 95% of the cumulative frequency of the corresponding samples as the interval. The single-group area fracture rate is the ratio of the total area enclosed by all fracture boundary contours within the measurement area corresponding to a single set of measurement data to the area of ​​the measurement area, reflecting the degree of fracture development in that local region. The average fracture rate is the arithmetic mean of the single-group area fracture rates of multiple sets of measurement data, serving as a representative value of the overall fracture rate of the target section. The fracture characteristic parameter set consists of the fracture dip angle interval, fracture length interval, fracture width interval, and average fracture rate.

[0039] In this step, several representative measurement areas are first selected within the target section. The surface of the sandstone outcrop is scanned using a 3D laser scanner to obtain point cloud data. At the same time, the borehole core is CT scanned to obtain radial cross-sectional sequence images.

[0040] Then, the point cloud data and cross-sectional images were used to separate the fractured region from the intact rock region, and the boundary contour line of each fracture was extracted. For each fracture boundary contour line, principal component analysis was used to calculate the direction of maximum variance and determine the fracture dip angle, the Euclidean distance between the two endpoints was calculated to determine the fracture length, and the average value of the maximum inscribed circle diameter was calculated to determine the fracture width.

[0041] All fracture dip angle, length, and width samples were collected, and cumulative frequency curves were plotted for each. The range corresponding to 5% to 95% was used to construct intervals for each feature. The area fracture rate of each measurement region was statistically analyzed, and the arithmetic mean was taken to obtain the average fracture rate. Finally, the fracture dip angle interval, fracture length interval, fracture width interval, and average fracture rate were combined to form a fracture feature parameter set.

[0042] Step S100 in the method provided in this application embodiment further includes:

[0043] Based on the point cloud data and the radial cross-sectional sequence image, the fracture region and the intact rock region are separated, and the boundary contour line of the fracture region is extracted, including: performing covariance analysis on the neighborhood of each point in the point cloud data, and separating the fracture region and the intact rock region in the point cloud by taking the spatial location where the normal vector direction changes abruptly as the boundary.

[0044] Dynamic thresholding is performed on the grayscale values ​​of each pixel in the radial cross-sectional image sequence. Pixels with grayscale values ​​lower than the neighborhood mean are selected as candidate areas for fractures, and pixels with grayscale values ​​higher than the neighborhood mean are selected as candidate areas for intact rock. The boundary position is iteratively updated to maximize the difference in grayscale statistical features on both sides of the boundary until the boundary converges, thus separating the fracture area from the intact rock area in the cross-sectional image. Using the spatial coordinates and borehole azimuth of the borehole core as the positioning reference, the fracture cross-sectional contour lines extracted from each cross-sectional image are transformed into a set of cross-sectional contour points in three-dimensional space according to the depth coordinates. The optimization objective is to minimize the sum of the squared Euclidean distances between each set of cross-sectional contour points and the fracture boundary point set within the corresponding depth interval in the point cloud data. The rotation matrix and translation vector are iteratively solved through spatial rigid body transformation to make the two sets of boundary point sets coincide in a unified spatial coordinate system. The outer edge connection line of the coincident boundary point set is used as the boundary contour line of the fracture area. Detailed explanation is as follows:

[0045] Covariance analysis constructs a covariance matrix of the spatial coordinates of all points in the local neighborhood of each point in the point cloud, calculates the eigenvalues ​​and eigenvectors of this matrix, and the eigenvector corresponding to the smallest eigenvalue is the normal vector direction of that point. The normal vector of a intact rock surface changes continuously. When a fissure exists, the point clouds on both sides of the fissure belong to different planes, and the normal vector direction changes abruptly. By detecting the rate of change of the neighborhood normal vector point by point, the fissure boundary can be accurately located, thus separating the fissure region from the intact rock region.

[0046] Dynamic thresholding segmentation compares the grayscale value of each pixel in a CT cross-sectional image with the mean of its neighborhood. Pixels with grayscale values ​​lower than the neighborhood mean are selected as candidate regions for fractures. Since fracture regions have lower grayscale values ​​due to internal voids, pixels with grayscale values ​​higher than the neighborhood mean are selected as candidate regions for intact rock. The segmentation position is iteratively updated until convergence, driven by maximizing the difference in grayscale statistical features between the two sides of the boundary, thus achieving the separation of fractures from intact rock. This adaptive segmentation method can adapt to the brightness variations of different CT images, avoiding the failure of fixed thresholds on cross-sectional images at different depths.

[0047] Spatial rigid body transformation transforms the fracture cross-sectional contour lines extracted from each cross-sectional image into a set of cross-sectional contour points in three-dimensional space according to the borehole depth coordinates. The optimization objective is to minimize the sum of the squared spatial Euclidean distances between each set of cross-sectional contour points and the set of fracture boundary points in the corresponding depth interval of the point cloud data. By iteratively solving the rotation matrix and translation vector, the two sets of boundary points are made to coincide in a unified spatial coordinate system. The outer edge connecting line of the coincident boundary point set is used as the boundary contour line of the fracture region.

[0048] In this step, neighborhood covariance analysis is performed point-by-point on the point cloud data to calculate the normal vector and detect abrupt change locations. These abrupt changes in the normal vector are used as the fracture boundary to separate the fracture from the intact rock. Dynamic thresholding is then performed pixel-by-pixel on the CT cross-section image, iteratively updating the boundary positions until convergence, thus separating the fracture from the intact rock. Then, using the borehole spatial coordinates and azimuth as a reference, the CT cross-section contour line is transformed into three-dimensional space and rigidly registered with the point cloud fracture boundary point set to solve for rotation and translation parameters, ensuring that the two point sets coincide in a unified coordinate system. The outer edge connecting line of the coincident point set is used as the final fracture boundary contour line.

[0049] In summary, this step, through the acquisition and standardization of multi-source fracture measurement data, extracts key geometric features such as fracture dip angle, length, width, and fracture rate, and constructs a systematic set of fracture feature parameters. This provides complete and reusable statistical input for subsequent Weber distribution fitting and random fracture network generation, which is beneficial for accurately characterizing the distribution pattern of fractures within the target section.

[0050] S200: Based on the set of fracture feature parameters, the distribution of fracture dip angle, fracture length and fracture width in their respective intervals is fitted using the Weber distribution probability density function to determine the Weber distribution shape parameter and scale parameter of each parameter, and a random fracture network model is generated by combining the fracture rate.

[0051] In this embodiment, based on the obtained set of fracture characteristic parameters, the statistical distribution of each fracture geometric parameter needs to be transformed into a computable two-dimensional network model. Since the distribution patterns of fracture dip angle, length, and width vary within their respective intervals, a Weiber distribution is used for fitting to determine the distribution parameters, and the fracture rate is used to control the model density to generate a random fracture network consistent with the statistical characteristics of fractures in the field, providing a model basis for subsequent connectivity analysis and strength reduction.

[0052] Step S200 in the method provided in this application embodiment includes:

[0053] From the fracture feature parameter set, extract fracture dip angle sample set, fracture length sample set, and fracture width sample set respectively. Use the fracture dip angle interval, fracture length interval, and fracture width interval as the cutoff boundary of the corresponding sample set, respectively, and remove sample points located outside the cutoff boundary to form a dip angle cutoff sample set, a length cutoff sample set, and a width cutoff sample set. Construct log-likelihood functions for the dip angle cutoff sample set, the length cutoff sample set, and the width cutoff sample set respectively. The log-likelihood function uses the shape parameter and scale parameter of the Weiber distribution as independent variables, and the sum of the logarithmic values ​​of the probability density of the Weiber distribution of all sample points in each cutoff sample set as the function value.

[0054] With the objective of maximizing the log-likelihood function, the log-likelihood functions of the dip-truncated sample set, length-truncated sample set, and width-truncated sample set are solved respectively. The convergence criterion is that the relative changes in shape and scale parameters between two adjacent iterations are all below a tolerance threshold. The optimal estimates of the Weber distribution shape and scale parameters are output. The Weber distribution shape and scale parameters corresponding to the dip-truncated, length-truncated, and width-truncated sample sets are respectively used as the Weber distribution parameters for fracture dip angle, fracture length, and fracture width. A detailed explanation follows:

[0055] The Weiber distribution probability density function describes the distribution shape of a random variable. In fracture parameter statistics, it is used to fit the distribution patterns of dip angle, length, and width. The distribution shape is controlled by two parameters: a shape parameter and a scale parameter. The shape parameter determines the skewness of the distribution curve and is dimensionless. When the shape parameter is less than 1, the distribution shows a decreasing trend; when it equals 1, it degenerates into an exponential distribution; and when it is greater than 1, it exhibits a unimodal shape. The larger the shape parameter value, the more concentrated the distribution. The scale parameter controls the lateral scale of the probability density curve and has the same dimensions as the corresponding fracture parameter. A larger scale parameter indicates that the overall fracture parameter values ​​are larger and the distribution is more dispersed. The Weiber distribution is chosen because fracture geometric parameters in nature usually exhibit skewed or unimodal distributions. The Weiber distribution combines flexible shape control with the ability to fit various distribution shapes well, and is widely used in geological engineering for statistical modeling of fracture parameters.

[0056] The truncated sample set is a subset formed by removing sample points from the original sample set that fall outside the interval boundaries, using the dip angle, length, and width intervals of the fracture feature parameter set as truncation boundaries. This subset is used for distribution fitting within the defined intervals, avoiding interference from extreme values ​​in parameter estimation. The log-likelihood function uses the shape and scale parameters of the Weiber distribution as independent variables, and the sum of the logarithmic probability densities of all sample points in the truncated sample set as the objective function. The optimal estimate of the distribution parameters is obtained by maximizing this function value.

[0057] The Newton-Raphson iterative scheme is used to solve for the maximum log-likelihood function. This scheme is a classic numerical method for solving nonlinear optimization problems, exhibiting quadratic convergence speed under the condition that the likelihood function is twice differentiable, and can efficiently and stably converge to the optimal solution. A tolerance threshold is used to determine the convergence of the iteration. Iteration stops when the relative changes in shape and scale parameters between two consecutive iterations are both below this threshold; specifically, in this scheme, it is set to 10⁻⁻⁶. 5 The basis for this is the balance between the accuracy requirements of parameter estimation and the cost of iterative calculation. The relative errors of shape parameters and scale parameters under this tolerance are much smaller than the engineering accuracy requirements.

[0058] In this step, dip angle, length, and width sample sets are first extracted from the fracture feature parameter set. Samples outside the boundaries of each interval are then removed to form a truncated sample set. For each truncated sample set, a log-likelihood function is constructed based on the Weiber probability density function. The shape and scale parameters that maximize the log-likelihood function value are solved using the Newton-Raphson iterative scheme. When the relative change of parameters in two consecutive iterations is less than 10⁻ 5 When convergence is determined, the optimal estimate is output as the Weiber distribution parameter of the corresponding fracture parameter.

[0059] Step S200 in the method provided in this application embodiment further includes:

[0060] The generation steps of the random fracture network model include: determining a two-dimensional solution domain based on the spatial range of the target segment, establishing a local coordinate system within the two-dimensional solution domain; generating fractures one by one based on the Weber distribution shape parameters and scale parameters of each parameter, wherein the fracture generation steps include: randomly sampling from the fracture dip angle Weber distribution parameters to obtain the dip angle value of the current fracture, randomly sampling from the fracture length Weber distribution parameters to obtain the trace length value of the current fracture, randomly sampling from the fracture width Weber distribution parameters to obtain the aperture value of the current fracture, randomly determining the center point coordinates of the current fracture within the two-dimensional solution domain, and determining the direction of the fracture line segment in the two-dimensional solution domain based on the dip angle value;

[0061] After each fracture is generated, the sum of the areas of all generated fractures within the current 2D solution domain is accumulated. The ratio of this sum to the total area of ​​the 2D solution domain is calculated as the current cumulative area fracture rate. This current cumulative area fracture rate is compared with the average fracture rate. If the current cumulative area fracture rate is lower than the average fracture rate, the next fracture is generated. When the current cumulative area fracture rate reaches the average fracture rate, generation stops, and the set of all generated fractures within the 2D solution domain at this point is taken as the random fracture network model. The random fracture network model generation process in this step is as follows: Figure 2 As shown. A detailed explanation follows:

[0062] The random fracture network model is a set of fracture segments randomly generated in the two-dimensional solution domain based on the statistical distribution of fracture geometric parameters. The dip angle, length and width of each fracture are randomly sampled and assigned from the corresponding Weiber distribution. The number and density of fractures are controlled by the average fracture rate, and it is used to characterize the spatial distribution characteristics of fractures in the target section.

[0063] The two-dimensional solution domain is a rectangular planar region defined by the spatial extent of the target segment. Its size is determined by the projection range of the target segment onto the horizontal plane. A local coordinate system is established within the domain for the random generation and spatial positioning of cracks.

[0064] The center point coordinates are the reference position coordinates of each fracture in the two-dimensional solution domain. The fracture line segment is formed by extending half the length of the trace line to both sides of the center point in a direction determined by a randomly sampled inclination angle. The current cumulative area fracture rate is the ratio of the sum of the areas of all generated fractures to the total area of ​​the two-dimensional solution domain. The area of ​​a single fracture is approximately calculated by the product of its trace length and aperture, that is, the fracture outline is simplified to a rectangle with the trace length as the long side and the aperture as the short side. The area of ​​this rectangle is used as an approximation of the fracture area to compare with the target average fracture rate in order to control the number of fractures generated.

[0065] In this step, the size of the two-dimensional solution domain is first determined based on the spatial range of the target section, and a local coordinate system is established. Then, a loop for generating fractures is entered: each time, the dip angle of the current fracture is randomly sampled from the Weber distribution parameters of the fracture dip angle, the trace length is randomly sampled from the Weber distribution parameters of the fracture length, and the aperture is randomly sampled from the Weber distribution parameters of the fracture width. The coordinates of the center point are randomly determined within the two-dimensional solution domain, and the fracture direction is determined based on the dip angle to generate a fracture line segment. The areas of all currently generated fractures are accumulated and the cumulative area fracture ratio is calculated and compared with the average fracture ratio. If it is lower, the next fracture is generated; if it reaches or exceeds the average fracture ratio, generation stops. All generated fractures are output as a random fracture network model.

[0066] For example, the training process of a randomized fracture network model is as follows:

[0067] The sample set was truncated at an inclination angle of 82 samples, ranging from 15° to 78°. The initial shape parameter was set to 1.5, and the scale parameter was set to (78−15)÷2=31.5. The maximum value of the log-likelihood function was solved using the Newton-Raphson iterative scheme, with a tolerance threshold of 10⁻. 5After iterative convergence, the shape parameter is 1.5 and the scale parameter is 30.0°. Similarly, the length-truncated sample set is solved, yielding a length-based Weiber distribution with a shape parameter of 1.7 and a scale parameter of 2.0m. The width-truncated sample set is solved, yielding a width-based Weiber distribution with a shape parameter of 1.4 and a scale parameter of 2.0mm. The two-dimensional solution domain is 20m × 20m, with an average fracture rate of 1.43%. Fractures are generated sequentially, with the area of ​​a single fracture approximated by multiplying the trace length by the aperture. The process stops when the cumulative area fracture rate reaches 1.43%, resulting in approximately 1430 fractures, forming a random fracture network model.

[0068] In summary, this step generates a random fracture network model by fitting the Weiber distribution and constraining the fracture rate. This transforms the statistical characteristics of the fractures in the field into a computable two-dimensional network representation, which is beneficial for objectively reflecting the spatial distribution of fractures and provides a reliable numerical model for subsequent connectivity coefficient extraction and intensity prediction.

[0069] S300: Extract the fracture network connectivity coefficient from the random fracture network model, and use a negative exponential decay function to reduce and correct the standard value of the uniaxial compressive strength of the intact rock block in the target section to obtain the initial predicted value of the fractured rock mass strength.

[0070] In this embodiment, after the random fracture network model is generated, the fractures intersect to form connected paths, and the weakening effect on the overall strength of the rock mass varies significantly depending on the degree of connectivity. To quantify the impact of fracture connectivity on rock mass strength, it is necessary to extract connectivity coefficients from the network model to characterize the degree of fracture penetration, and establish a quantitative relationship between connectivity coefficients and strength reduction, so as to achieve a reasonable reduction of the strength parameters of the intact rock block.

[0071] Step S300 in the method provided in this application embodiment includes:

[0072] Based on the center point coordinates, dip direction, and trace length of each fracture in the random fracture network model, the endpoint coordinates of each fracture in the two-dimensional solution domain are determined, and each fracture is represented as a fracture line segment bounded by its two endpoints. All fracture line segments are paired for intersection, and two fracture line segments with intersection points are marked as a connected pair. Based on all connected pairs, fracture line segments with direct or indirect connectivity are grouped into the same connected group. The connected group with the largest number of fracture line segments is counted, and the ratio of the number of fracture line segments in the largest connected group to the total number of fractures in the random fracture network model is calculated. This ratio is used as the connectivity coefficient of the fracture network. Detailed explanation follows:

[0073] The fracture network connectivity coefficient is used to quantify the degree to which fractures interconnect to form a network under the combined effects of fracture dip angle, fracture length, fracture width and fracture ratio. It is taken as the ratio of the number of fractures in the largest connected group to the total number of fractures, with a value range of 0 to 1. The closer it is to 1, the higher the degree of fracture network connectivity and the worse the rock mass integrity.

[0074] A connected pair refers to a combination of two fracture segments that intersect in the two-dimensional solution domain. The existence of the intersection indicates that the two fractures directly intersect in space, forming a direct connectivity relationship in the fracture network. The pairwise intersection determination of connected pairs employs the fast exclusion and cross-testing methods for line segment intersections in computational geometry, which can efficiently handle the intersection detection of a large number of fracture segments. A connected set refers to a set of multiple fracture segments with direct or indirect connectivity relationships. All fractures with transitive connectivity are grouped into the same set using the disjoint-set data structure (DFS) algorithm. DFS is a standard data structure for handling dynamic connectivity problems; path compression and rank-based merging can efficiently merge all connected fractures. The number of fractures in the largest connected set reflects the core connectivity scale of the fracture network.

[0075] In this step, firstly, based on the coordinates of the center point, dip direction, and trace length of each fracture in the random fracture network model, the coordinates of the two endpoints of each fracture segment are calculated, and each fracture is represented as a line segment bounded by its two endpoints. Then, all fracture segments are paired for intersection; if two segments intersect, they are marked as a connected pair. Based on all connected pairs, a disjoint-set data structure (DFS) algorithm is used to group fractures with direct or indirect connectivity into the same connected group. Finally, the number of fractures in the connected group with the largest number of fractures is counted, and divided by the total number of fractures to obtain the fracture network connectivity coefficient.

[0076] Step S300 in the method provided in this application embodiment further includes:

[0077] The target section is divided into multiple sub-regions, and the fracture network connectivity coefficient of each sub-region is obtained. Rock cores are drilled from each sub-region, and intact rock samples without macroscopic fractures are prepared. The standard value of the uniaxial compressive strength of the intact rock block in each sub-region is obtained through indoor uniaxial compression tests. For each sub-region, the uniaxial compressive strength of the fractured rock mass in each sub-region is calculated by uniaxial compression numerical simulation. The ratio of the standard value of the uniaxial compressive strength of the intact rock block to the uniaxial compressive strength of the fractured rock mass is used as the strength reduction factor for each sub-region.

[0078] Using the fracture network connectivity coefficient of each sub-region as the independent variable and the corresponding strength reduction factor as the dependent variable, a data point set is constructed and nonlinear regression is performed to fit the decay coefficient of the negative exponential decay function. The standard value of the uniaxial compressive strength of the intact rock block in the target section is substituted into the fitted negative exponential decay function to obtain the initial predicted value of the fractured rock mass strength. Detailed explanation follows:

[0079] The standard value of the uniaxial compressive strength of an intact rock block is the ultimate compressive stress at which an intact rock sample without macroscopic cracks fails under uniaxial compression conditions, measured in MPa. It is obtained through indoor uniaxial compression tests and represents the strength of the rock matrix itself. When preparing intact rock samples without macroscopic cracks, core samples are drilled from each sub-region, and the core surface is observed segment by segment indoors using a magnifying glass or industrial camera. Core segments with visible cracks are discarded.

[0080] The remaining core segments were prepared into cylindrical specimens with a height-to-diameter ratio of approximately 2:1 using a rock cutting machine. The end faces were then ground smooth to ensure the non-parallelism and non-perpendicularity of the two end faces met the requirements of the rock mechanics testing procedures. The processed specimens underwent a second visual inspection and were supplemented with ultrasonic wave velocity testing. Specimens with abnormally low wave velocities were discarded, ultimately obtaining intact rock samples without macroscopic fractures. The strength reduction factor is the ratio of the standard value of the uniaxial compressive strength of an intact rock block to the uniaxial compressive strength of fractured rock mass. It reflects the degree to which fractures weaken the rock mass strength; a larger value indicates a more significant reduction in strength due to fractures.

[0081] The uniaxial compression numerical simulation method for calculating the uniaxial compressive strength of fractured rock mass in each sub-region involves using finite element or discrete element numerical simulation software to perform uniaxial compression tests on a randomly generated fracture network model for each sub-region. The simulation applies the same boundary conditions as laboratory tests: the lower end of the specimen is fixed, and uniform displacement is applied to the upper end until failure, with the loading rate consistent with the laboratory tests. The geometric information of the fracture network model is automatically used to generate the computational mesh, which is then refined at fracture locations. Contact elements are used to simulate the opening and slip behavior at the fracture surfaces. The stress-strain curve is obtained through numerical calculation, and the peak stress is used as the uniaxial compressive strength of the fractured rock mass in that sub-region.

[0082] The negative exponential decay function describes the exponential decay of the intensity reduction factor as the fracture network connectivity coefficient increases, and is in the form y , where x is the fracture network connectivity coefficient, y is the strength reduction factor, and a and b are fitting parameters. The higher the degree of fracture connectivity, the smaller the strength reduction factor, and the closer the rock mass strength is to the fracture-controlled state. The attenuation coefficient, i.e., parameter b in the function, controls the attenuation rate of the strength reduction factor as the fracture network connectivity coefficient increases. It is obtained through nonlinear regression fitting of data points from multiple sub-regions; a larger value indicates a faster strength attenuation.

[0083] In this step, the target section is divided into multiple sub-regions. For each sub-region, a random fracture network model is generated according to the aforementioned steps, and the fracture network connectivity coefficient is extracted. Core samples are drilled from each sub-region, and intact rock samples without macroscopic fractures are prepared using the above method. Indoor uniaxial compression tests are then conducted to obtain the standard value of the uniaxial compressive strength of the intact rock mass. Uniaxial compression numerical simulations are performed on the random fracture network models of each sub-region to obtain the uniaxial compressive strength of the fractured rock mass, and the strength reduction factor for each sub-region is calculated.

[0084] A data point set was constructed using the fracture network connectivity coefficient of each sub-region as the independent variable and the strength reduction factor as the dependent variable. A nonlinear regression was performed using a negative exponential decay function to fit the decay coefficients a and b. Finally, the standard value of the uniaxial compressive strength of the intact rock block in the target section was substituted into the fitted negative exponential decay function, and the initial predicted value of fractured rock mass strength was calculated as: initial predicted value = standard value of uniaxial compressive strength of intact rock block × Calculations were performed to obtain the initial predicted value of the fractured rock mass strength.

[0085] For example, taking a sandstone strength prediction in a target section as an example, there are a total of 1430 fractures. After pairwise intersection judgment and clustering, the largest connected group contains 286 fractures, and the fracture network connectivity coefficient = 286 ÷ 1430 ≈ 0.20. The target section is divided into 5 sub-regions, and random fracture networks are generated for each sub-region, with connectivity coefficients calculated as follows: 0.12, 0.18, 0.24, 0.31, and 0.42. The standard values ​​of uniaxial compressive strength of intact rock samples in each sub-region are 68 MPa, 72 MPa, 65 MPa, 70 MPa, and 67 MPa, respectively, while the numerical simulation values ​​of uniaxial compressive strength of fractured rock mass are 52 MPa, 49 MPa, 38 MPa, 31 MPa, and 22 MPa, respectively, with strength reduction factors of 1.31, 1.47, 1.71, 2.26, and 3.05, respectively. A nonlinear regression was performed using 5 data points, yielding a = 1.02, b = 3.15, and the negative exponential decay function was y = 1.02 × The standard value of the uniaxial compressive strength of the intact rock block in the target section is taken as the average value of each sub-region, which is 68.4 MPa. The initial predicted value of the fractured rock mass strength is 68.4 × ≈68.4×0.533≈36.4MPa.

[0086] In summary, this step establishes a quantitative mapping relationship between fracture connectivity and strength reduction through connectivity coefficient extraction and negative exponential decay function fitting. This is beneficial for transforming fracture network structural characteristics into calculable strength parameters and improving the objectivity of fractured rock mass strength prediction.

[0087] S400: Obtain the principal stress direction of the in-situ geostress field within the target section, calculate the angle deviation between the dip direction of each fracture and the direction of the maximum principal stress in the random fracture network model, and perform anisotropic correction on the initial predicted value of the fractured rock mass strength to obtain the final predicted value of the fractured rock mass strength.

[0088] In this embodiment, the strength of fractured rock mass is not only affected by the degree of fracture connectivity, but also closely related to the angle of the fracture direction relative to the geostress field. When the angle between the fracture dip and the direction of the maximum principal stress is different, the combination of normal stress and shear stress on the fracture surface is different, resulting in anisotropy of rock mass strength. To reasonably assess the correction effect of geostress direction on strength, it is necessary to calculate the deviation of each fracture from the principal stress direction and perform anisotropy correction accordingly.

[0089] Step S400 in the method provided in this application embodiment further includes:

[0090] Obtain the direction of the maximum principal stress in the in-situ stress field within the target section, and transform the direction of the maximum principal stress into the local coordinate system of the two-dimensional solution domain; calculate the angle between the dip of each fracture in the random fracture network model and the direction of the maximum principal stress, and use the corresponding value of the angle difference in the range of 0° to 90° as the angle deviation of each fracture.

[0091] Anisotropy correction coefficients are determined for each fracture based on the angular deviation of each fracture. These correction coefficients monotonically increase with increasing angular deviation, reaching a minimum when the angular deviation is zero and a maximum when the angular deviation is 90 degrees. A weighted average of all fracture correction coefficients is calculated using the fracture area as the weight, yielding a comprehensive anisotropy correction coefficient. The initial predicted strength of the fractured rock mass is multiplied by this comprehensive anisotropy correction coefficient to obtain the final predicted strength of the fractured rock mass. Detailed explanation follows:

[0092] In-situ stress field refers to the natural stress state inherent in the rock mass within the target section, encompassing the magnitude and direction of the three principal stresses. It is obtained through field testing methods such as hydraulic fracturing. Hydraulic fracturing involves injecting high-pressure fluid into the borehole section to induce tensile fractures in the borehole wall. The fractures propagate along the direction perpendicular to the minimum principal stress. The direction of the maximum principal stress can be determined based on the fracture orientation recorded by the impression device. This method is recommended by the International Society for Rock Mechanics for measuring in-situ stress.

[0093] The direction of the maximum principal stress is the direction of action of the maximum principal stress in the in-situ stress field, usually expressed as an azimuth angle in degrees (°). After transformation to the local coordinate system of the two-dimensional solution domain, it is used to calculate the angle between the fracture dip direction and this direction. The angle deviation is the corresponding value of the angle between the fracture dip direction and the direction of the maximum principal stress within the range of 0° to 90°, also in degrees (°). A deviation of 0° indicates that the fracture is parallel to the maximum principal stress, while a deviation of 90° indicates that the fracture is perpendicular to the maximum principal stress.

[0094] The anisotropy correction factor is a strength correction factor determined based on the deviation of the included angle. The calculation formula is: Anisotropy Correction Factor = Minimum Correction Factor + (Maximum Correction Factor - Minimum Correction Factor) × (Angle Deviation ÷ 90°). When the deviation is 0°, the minimum value is taken. At this point, the crack is parallel to the principal stress, the normal stress on the crack surface is maximum, and the shear stress is minimum, resulting in the weakest strength weakening effect of the crack. When the deviation is 90°, the maximum value is taken. At this point, the crack is perpendicular to the principal stress, the shear stress on the crack surface is maximum, resulting in the strongest strength weakening effect of the crack.

[0095] The minimum correction factor is set at 0.85, and the maximum at 1.15. This is based on the influence of the angle between the fracture surface and the principal stress on strength in rock mechanics. Parallel fractures reduce strength by a minimum of approximately 15%, while perpendicular fractures reduce it by a maximum of approximately 15%. A weighted average is performed using the area of ​​each fracture as a weight because the fracture area is approximately calculated by multiplying the trace length by the aperture. Larger fracture areas have a greater impact on the overall strength of the rock mass, and using this weight allows for a more reasonable synthesis of the correction contributions of each fracture.

[0096] The comprehensive anisotropy correction factor is an overall correction factor obtained by area-weighted averaging of the anisotropy correction factors of all fractures. The final predicted value of fractured rock mass strength is the product of the initial predicted value of fractured rock mass strength and the comprehensive anisotropy correction factor, comprehensively reflecting the dual influence of fracture connectivity and geostress direction.

[0097] In this step, the direction of the maximum principal stress in the in-situ stress field of the target section is first obtained using the hydraulic fracturing method, and then transformed into the local coordinate system of the two-dimensional solution domain. Next, the angle between the dip direction of each fracture and the direction of the maximum principal stress is calculated for each fracture in the random fracture network model, and the corresponding value within the range of 0° to 90° is taken as the angle deviation. For each fracture, the anisotropy correction coefficient formula is substituted to calculate its correction coefficient, and all correction coefficients are weighted and averaged using the fracture area as the weight to obtain the comprehensive anisotropy correction coefficient. Finally, the initial predicted value of the fractured rock mass strength obtained in the previous steps is multiplied by the comprehensive anisotropy correction coefficient to obtain the final predicted value of the fractured rock mass strength.

[0098] Step S400 in the method provided in this application embodiment further includes:

[0099] Obtain the measured value of fractured rock mass strength at at least one verification location within the target section, wherein the verification location and the location of the fracture measurement data are spatially adjacent and do not overlap; obtain the final predicted value of fractured rock mass strength at the verification location, compare it with the measured value of fractured rock mass strength, and calculate the relative deviation between the two.

[0100] When the relative deviation exceeds the allowable deviation range, the ratio of the measured value of the fractured rock mass strength to the final predicted value of the fractured rock mass strength is used as the correction coefficient. The scale parameters in the Weber distribution parameters of the fracture dip angle, the Weber distribution parameters of the fracture length, and the Weber distribution parameters of the fracture width are multiplied by the correction coefficient to obtain the updated Weber distribution scale parameters, while keeping the shape parameters of each Weber distribution unchanged.

[0101] When the relative deviation does not exceed the allowable deviation range, the final predicted value of the fractured rock mass strength remains unchanged; based on the updated Weber distribution scale parameters and the unchanged Weber distribution shape parameters, an updated stochastic fracture network model is regenerated; the updated fracture network connectivity coefficient is extracted from the updated stochastic fracture network model, and strength reduction correction and anisotropy correction are performed to obtain the updated final predicted value of the fractured rock mass strength. Detailed explanation follows:

[0102] The verification location is a detection point within the target section used to verify the accuracy of the prediction. It is spatially adjacent to but does not overlap with the location of the fracture measurement data. The measured value of the fractured rock mass strength at this location is obtained through in-situ testing. The relative deviation is the absolute value of the ratio of the difference between the measured value and the predicted value of the fractured rock mass strength at the verification location to the measured value. It is used to evaluate the accuracy of the prediction results.

[0103] The allowable deviation range is the upper limit of the relative deviation for determining whether the prediction result is qualified. When the relative deviation exceeds this range, the feedback correction of the Weiber distribution parameters is triggered. The specific value is 15%, which is based on the engineering accuracy requirements. A deviation range of 15% can effectively filter out normal statistical fluctuations and can also identify systematic errors caused by parameter estimation deviations in a timely manner.

[0104] The correction factor is the ratio of the measured value to the predicted value of the fractured rock mass strength. When the predicted value is too low, the ratio is greater than 1, and when it is too high, the ratio is less than 1. The correction factor is multiplied by the scale parameter of each Weibull distribution because the scale parameter controls the overall scale of the distribution. Correcting the scale parameter can adjust the statistical distribution range of the fracture parameters as a whole, while keeping the shape parameter unchanged can maintain the basic morphological characteristics of the distribution.

[0105] In this step, at least one verification location adjacent to but not overlapping with the fracture measurement location is first selected within the target section. The measured strength of the fractured rock mass is obtained through in-situ testing. Following the method described earlier, the final predicted strength of the fractured rock mass at this verification location is obtained, and the relative deviation between the measured and predicted values ​​is calculated. If the relative deviation is less than or equal to 15%, the predicted value remains unchanged; if the relative deviation is greater than 15%, the ratio of the measured to the predicted value is used as a correction coefficient to scale the scale parameters of the three Weber distributions, while keeping the shape parameters unchanged. Based on the updated scale parameters and the original shape parameters, a new stochastic fracture network model is generated. The connectivity coefficients are extracted again, and strength reduction and anisotropy correction are performed to obtain the updated final predicted strength of the fractured rock mass.

[0106] For example, taking a sandstone strength prediction in a target section as an example, the direction of the maximum principal stress, measured by the hydraulic fracturing method, is NE45°, which corresponds to an angle of 45° after conversion to the local coordinate system of the two-dimensional solution domain. In the random fracture network model generated by S200, the first fracture dips at 30°, the angle deviation is |45°−30°|=15°, and the anisotropy correction coefficient is 0.85+(1.15−0.85)×(15°÷90°)=0.85+0.30×0.167≈0.90. After traversing all 1430 fractures, a weighted average is calculated using the area of ​​each fracture as the weight, resulting in a comprehensive anisotropy correction coefficient of 0.96. The initial predicted value of the fractured rock mass strength obtained by S300 is 36.4MPa, and the final predicted value of the fractured rock mass strength is 36.4×0.96≈34.9MPa.

[0107] During the verification and correction phase, an in-situ test was conducted at a selected verification location, with a measured value of 31.5 MPa. The predicted value for this verification location, calculated using the aforementioned steps, was 34.9 MPa, with a relative deviation of |31.5−34.9|÷31.5≈10.8%, which is less than the allowable deviation range of 15%. Therefore, the prediction result meets the accuracy requirements, and the final predicted value of 34.9 MPa remains unchanged. If the measured value is 24.0 MPa, the relative deviation is |24.0−34.9|÷24.0≈45.4%, exceeding 15%. Therefore, the correction factor is 24.0÷34.9≈0.688. The updated scale parameters are obtained by multiplying the scaling parameters of the three Weiber distributions by 0.688 respectively. After the update, the length scale parameter becomes 2.0m × 0.688 ≈ 1.38m, the width scale parameter becomes 2.0mm × 0.688 ≈ 1.38mm, and the dip angle scale parameter becomes 30.0° × 0.688 ≈ 20.6°. A new random fracture network model is then generated. Since the total fracture area constraint remains unchanged, the area of ​​a single fracture after the update is approximately 1.38m × 0.00138m ≈ 0.0019㎡, generating approximately 3010 fractures. The connectivity coefficient is extracted again, and strength reduction and anisotropy correction are performed to calibrate the prediction bias.

[0108] In summary, this step, by introducing the angular deviation between the direction of geostress and the fracture dip, anisotropically corrects the initial strength prediction value and performs feedback calibration by verifying the measured values. This helps to reflect the directional influence of the geostress direction on the strength of fractured rock mass and improves the consistency between the prediction results and actual engineering conditions.

[0109] The embodiments of this application, through the specific implementation methods described above, achieve the following technical effects:

[0110] This application proposes a sandstone strength prediction method based on multiple fracture characteristic parameters. By systematically extracting characteristic parameters such as fracture dip angle, length, width, and fracture ratio from sandstone outcrops and borehole cores, a standardized set of fracture characteristic parameters is constructed. The Weber distribution is used to fit each geometric parameter, and a fracture network model consistent with the field statistical characteristics is randomly generated line by line in combination with the fracture ratio.

[0111] The connectivity coefficients of the fracture network are extracted from the network model to quantify the degree of fracture penetration. A negative exponential decay function is used to reduce and correct the standard value of the uniaxial compressive strength of the intact rock block, obtaining an initial predicted strength value. Then, the angular deviation of each fracture is calculated by combining the direction of the maximum principal stress of the in-situ in-situ stress, and directional correction is performed using an anisotropy correction coefficient. Finally, verified measured values ​​are used for feedback calibration to obtain the final predicted value of the fractured rock mass strength. This achieves a systematic quantitative assessment from the statistical characteristics of fractures in the field to the prediction of fractured rock mass strength, solving the technical problem that traditional indoor rock sample tests cannot represent real rock masses containing random fractures and that the predicted results deviate significantly from the actual values.

[0112] Example 2, as shown in the appendix Figure 3 As shown, based on the same inventive concept as the sandstone strength prediction method based on multi-fracture characteristic parameters provided in Embodiment 1, this application also provides an electronic device for sandstone strength prediction based on multi-fracture characteristic parameters, specifically including:

[0113] Feature extraction module 11 is used to acquire multiple sets of fracture measurement data from sandstone outcrops and borehole cores in the target section, and extract fracture dip angle intervals, fracture ratio, fracture length intervals and fracture width intervals from them to construct a fracture feature parameter set;

[0114] The network generation module 12 is used to fit the distribution of the fracture dip angle, fracture length and fracture width in their respective intervals based on the fracture feature parameter set and the Weiber distribution probability density function, to determine the Weiber distribution shape parameter and scale parameter of each parameter, and to generate a random fracture network model in combination with the fracture rate.

[0115] The strength reduction module 13 is used to extract the fracture network connectivity coefficient from the random fracture network model, and use a negative exponential decay function to reduce and correct the standard value of the uniaxial compressive strength of the intact rock block in the target section of the sandstone to obtain the initial predicted value of the fractured rock mass strength.

[0116] Anisotropy correction module 14 is used to obtain the principal stress direction of the in-situ stress field in the target section, calculate the angle deviation between the dip direction of each fracture and the maximum principal stress direction in the random fracture network model, and perform anisotropy correction on the initial predicted value of the fractured rock mass strength to obtain the final predicted value of the fractured rock mass strength.

[0117] In one embodiment, the feature extraction module 11 is further configured to: perform three-dimensional laser scanning on the surface of the sandstone outcrop in the target section to obtain point cloud data, and perform CT scanning on the borehole core to obtain radial cross-sectional sequence images; based on the point cloud data and the radial cross-sectional sequence images, separate the fractured region from the intact rock region, and extract the boundary contour lines of the fractured region; for each extracted fracture boundary contour line, calculate the maximum variance direction of the contour point set, take the angle between the maximum variance direction and the horizontal plane as the fracture dip angle, calculate the Euclidean distance between the two endpoints of the fracture boundary contour line as the fracture length, and calculate the average value of the maximum inscribed circle diameter inside the fracture boundary contour line as the fracture width; and collect all fracture data. Samples of fracture dip angle, fracture length, and fracture width were used to plot cumulative frequency curves for dip angle, length, and width, respectively, and fracture dip angle intervals, fracture length intervals, and fracture width intervals were constructed. The area of ​​the measurement region corresponding to each set of measurement data was statistically analyzed, and the area enclosed by all fracture boundary contours within the corresponding measurement region was extracted. Based on the relative relationship between the total fracture area and the area of ​​the corresponding measurement region within each measurement region, the single-set area fracture rate of each measurement region was determined. The single-set area fracture rates of multiple sets of measurement data were merged to determine the average fracture rate within the target segment, and the fracture dip angle interval, fracture length interval, fracture width interval, and the average fracture rate were combined to form the fracture feature parameter set.

[0118] Furthermore, the feature extraction module 11 is also used to: perform covariance analysis on the neighborhood of each point in the point cloud data, and separate the fracture region from the intact rock region in the point cloud by using the spatial location where the normal vector direction changes abruptly as the boundary; perform dynamic threshold segmentation on the gray value of each pixel in the radial cross-section sequence image, using pixels with gray values ​​lower than the neighborhood mean as fracture candidate regions and pixels with gray values ​​higher than the neighborhood mean as intact rock candidate regions, and iteratively update the boundary position by maximizing the difference in gray statistical features on both sides of the boundary until the boundary converges, thus separating the fracture region from the intact rock region in the cross-section image. A complete rock region; using the spatial coordinates and borehole azimuth of the drill core as the positioning reference, the fracture cross-sectional contour lines extracted from each cross-sectional image are transformed into a set of cross-sectional contour points in three-dimensional space according to the depth coordinates; with the goal of minimizing the sum of the squared spatial Euclidean distances between each set of cross-sectional contour points and the fracture boundary point set in the corresponding depth interval of the point cloud data, the rotation matrix and translation vector are solved iteratively through spatial rigid body transformation, so that the two sets of boundary point sets coincide in a unified spatial coordinate system, and the outer edge connecting line of the coincident boundary point set is used as the boundary contour line of the fracture region.

[0119] In one embodiment, the network generation module 12 is further configured to: extract fracture dip angle sample sets, fracture length sample sets, and fracture width sample sets from the fracture feature parameter set, respectively; and use the fracture dip angle interval, fracture length interval, and fracture width interval as the cutoff boundaries of the corresponding sample sets, respectively, and remove sample points located outside the cutoff boundaries to form a dip angle cutoff sample set, a length cutoff sample set, and a width cutoff sample set; and construct log-likelihood functions for the dip angle cutoff sample set, the length cutoff sample set, and the width cutoff sample set, respectively, wherein the log-likelihood function uses the shape parameter and scale parameter of the Weiber distribution as independent variables, and the values ​​within each cutoff sample set are used as independent variables. The sum of the logarithmic probabilities of the Weiber distribution for the sample points is the function value. With the goal of maximizing the log-likelihood function value, the log-likelihood functions for the dip-truncated sample set, the length-truncated sample set, and the width-truncated sample set are solved respectively. The convergence criterion is that the relative changes in shape and scale parameters between two adjacent iterations are all below the tolerance threshold. The optimal estimates of the Weiber distribution shape and scale parameters are output. The Weiber distribution shape and scale parameters corresponding to the dip-truncated sample set, the length-truncated sample set, and the width-truncated sample set are respectively used as the Weiber distribution parameters for fracture dip angle, fracture length, and fracture width.

[0120] Furthermore, the network generation module 12 is also used to: determine a two-dimensional solution domain based on the spatial range of the target segment, establish a local coordinate system within the two-dimensional solution domain; generate fractures one by one based on the Weber distribution shape parameters and scale parameters of each parameter, wherein the fracture generation steps include: randomly sampling from the fracture dip angle Weber distribution parameters to obtain the dip angle value of the current fracture, randomly sampling from the fracture length Weber distribution parameters to obtain the trace length value of the current fracture, randomly sampling from the fracture width Weber distribution parameters to obtain the aperture value of the current fracture, randomly determining the center point coordinates of the current fracture within the two-dimensional solution domain, and based on... The orientation of the fracture line segment in the two-dimensional solution domain is determined by the tilt angle assignment. After each fracture is generated, the sum of the areas of all generated fractures in the current two-dimensional solution domain is accumulated, and the ratio of the sum of the areas to the total area of ​​the two-dimensional solution domain is calculated as the current cumulative area fracture rate. The current cumulative area fracture rate is compared with the average fracture rate. If the current cumulative area fracture rate is lower than the average fracture rate, the next fracture is generated. When the current cumulative area fracture rate reaches the average fracture rate, generation stops, and the set of all generated fractures in the two-dimensional solution domain at this time is taken as the random fracture network model.

[0121] In one embodiment, the strength reduction module 13 is further configured to: determine the endpoint coordinates of each fracture in the two-dimensional solution domain based on the center point coordinates, dip direction, and trace length of each fracture in the random fracture network model, and represent each fracture as a fracture line segment bounded by its two endpoints; perform pairwise intersection judgment on all fracture line segments, and mark two fracture line segments with intersection points as a connected pair; based on all connected pairs, merge fracture line segments with direct or indirect connectivity into the same connected group; count the connected group with the largest number of fracture line segments, calculate the ratio of the number of fracture line segments in the largest connected group to the total number of fractures in the random fracture network model, and use the ratio as the fracture network connectivity coefficient.

[0122] Furthermore, the strength reduction module 13 is also used to: divide the target section into multiple sub-regions and obtain the fracture network connectivity coefficient of each sub-region; drill rock cores for each sub-region and prepare intact rock samples without macroscopic fractures, and obtain the standard value of the uniaxial compressive strength of the intact rock blocks in each sub-region through indoor uniaxial compression tests; calculate the uniaxial compressive strength of the fractured rock mass in each sub-region using uniaxial compression numerical simulation, and use the ratio of the standard value of the uniaxial compressive strength of the intact rock blocks to the uniaxial compressive strength of the fractured rock mass as the strength reduction factor for each sub-region; construct a data point set and perform nonlinear regression using the fracture network connectivity coefficient of each sub-region as the independent variable and the corresponding strength reduction factor as the dependent variable, and fit the decay coefficient of the negative exponential decay function; substitute the standard value of the uniaxial compressive strength of the intact rock blocks in the target section into the fitted negative exponential decay function to obtain the initial predicted value of the fractured rock mass strength.

[0123] In one embodiment, the anisotropy correction module 14 is further configured to: obtain the direction of the maximum principal stress in the in-situ stress field within the target section, and transform the direction of the maximum principal stress to the local coordinate system of the two-dimensional solution domain; calculate the angle between the dip direction of each fracture in the random fracture network model and the direction of the maximum principal stress, and use the corresponding values ​​of the angle difference in the range of 0° to 90° as the angle deviation of each fracture; determine the anisotropy correction coefficient corresponding to each fracture according to the angle deviation of each fracture, wherein, the The anisotropy correction coefficient increases monotonically with the increase of the included angle deviation, and the anisotropy correction coefficient reaches its minimum value when the included angle deviation is zero and its maximum value when the included angle deviation is 90 degrees. Using the fracture area of ​​each fracture as the weight, the anisotropy correction coefficients corresponding to all fractures are weighted and averaged to obtain the comprehensive anisotropy correction coefficient. The initial predicted value of the fractured rock mass strength is multiplied by the comprehensive anisotropy correction coefficient to obtain the final predicted value of the fractured rock mass strength.

[0124] Furthermore, the anisotropy correction module 14 is also used to: obtain the measured value of fractured rock mass strength at at least one verification location within the target section, wherein the verification location and the location of the fracture measurement data are spatially adjacent and do not overlap; obtain the final predicted value of fractured rock mass strength at the verification location, compare it with the measured value of fractured rock mass strength, and calculate the relative deviation between the two; when the relative deviation exceeds the allowable deviation range, use the ratio of the measured value of fractured rock mass strength to the final predicted value of fractured rock mass strength as a correction coefficient to adjust the scale parameter in the Weber distribution parameters of fracture dip angle and the scale parameter in the Weber distribution parameters of fracture length. The scale parameters in the degree parameter and the fracture width Weber distribution parameter are multiplied by the correction coefficient to obtain the updated Weber distribution scale parameters, while keeping the shape parameters of each Weber distribution unchanged. When the relative deviation does not exceed the allowable deviation range, the final predicted value of the fractured rock mass strength remains unchanged. Based on the updated Weber distribution scale parameters and the unchanged Weber distribution shape parameters, an updated stochastic fracture network model is regenerated. The updated fracture network connectivity coefficient is extracted from the updated stochastic fracture network model, and strength reduction correction and anisotropy correction are performed to obtain the updated final predicted value of the fractured rock mass strength.

[0125] This application provides an electronic device for predicting sandstone strength based on multiple fracture characteristic parameters. This device can be applied to sandstone strata strength prediction scenarios in underground engineering projects such as tunnels and roadways. It can be integrated into geological exploration data processing platforms or geotechnical engineering analysis systems to extract fracture characteristic parameters, model random fracture networks, perform strength reduction corrections and anisotropy corrections on target sections, and automatically output the final predicted value of fractured rock mass strength. This electronic device improves the accuracy and efficiency of sandstone strata strength prediction by incorporating on-site fracture statistical characteristics and geostress direction information into the strength calculation. For specific optimization processes and implementation details of this electronic device, please refer to Embodiment 1.

[0126] It should be noted that the order of the embodiments in this application is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Specific embodiments of this specification have been described above. Furthermore, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

Claims

1. A method for predicting the strength of sandstone based on multi-fracture characteristic parameters, characterized in that, The method includes: Multiple sets of fracture measurement data from sandstone outcrops and borehole cores within the target section were obtained, and fracture dip angle intervals, fracture ratio, fracture length intervals, and fracture width intervals were extracted from them to construct a fracture characteristic parameter set. Based on the fracture feature parameter set, the distributions of fracture dip angle, fracture length, and fracture width within their respective intervals are fitted using the Weiber distribution probability density function to determine the Weiber distribution shape and scale parameters of each parameter. A random fracture network model is then generated by combining this with the fracture rate. The steps for generating the random fracture network model include: The two-dimensional solution domain is determined by the spatial range of the target segment, and a local coordinate system is established within the two-dimensional solution domain; Based on the Weber distribution shape and scale parameters of each parameter, cracks are generated one by one, wherein the crack generation steps include: The dip angle of the current fracture is randomly sampled from the Weber distribution parameters of the fracture dip angle, the trace length of the current fracture is randomly sampled from the Weber distribution parameters of the fracture length, and the aperture of the current fracture is randomly sampled from the Weber distribution parameters of the fracture width. The coordinates of the center point of the current fracture are randomly determined in the two-dimensional solution domain, and the direction of the fracture line segment in the two-dimensional solution domain is determined based on the dip angle assignment. After each crack is generated, the sum of the areas of all generated cracks in the current two-dimensional solution domain is accumulated, and the ratio of the sum of the areas to the total area of ​​the two-dimensional solution domain is calculated as the current cumulative area crack rate. The current cumulative area crack rate is compared with the average crack rate. If the current cumulative area crack rate is lower than the average crack rate, the next crack is generated. When the current cumulative area fracture rate reaches the average fracture rate, generation stops, and the set of all generated fractures in the two-dimensional solution domain at this time is taken as the random fracture network model. The fracture network connectivity coefficients are extracted from the random fracture network model. A negative exponential decay function is used to reduce and correct the standard value of the uniaxial compressive strength of the intact sandstone blocks in the target section, thereby obtaining the initial predicted value of the fractured rock mass strength. The extraction of the fracture network connectivity coefficients from the random fracture network model includes: Based on the center point coordinates, dip direction and trace length of each fracture in the random fracture network model, the endpoint coordinates of each fracture in the two-dimensional solution domain are determined, and each fracture is represented as a fracture line segment bounded by the two endpoints. Perform pairwise intersection checks on all fracture segments and mark the two fracture segments that have an intersection point as a connected pair; Based on all connected pairs, gap segments that have direct or indirect connectivity are grouped into the same connected group. The connected group with the largest number of fracture segments is counted, and the ratio of the number of fracture segments in the largest connected group to the total number of fractures in the random fracture network model is calculated. The ratio is used as the connectivity coefficient of the fracture network. Obtain the principal stress direction of the in-situ stress field within the target section, calculate the angle deviation between the dip direction of each fracture and the direction of the maximum principal stress in the random fracture network model, and perform anisotropic correction on the initial predicted value of the fractured rock mass strength to obtain the final predicted value of the fractured rock mass strength.

2. The sandstone strength prediction method based on multi-fracture characteristic parameters according to claim 1, characterized in that, Multiple sets of fracture measurement data from sandstone outcrops and borehole cores within the target section were acquired, and fracture dip angle intervals, fracture ratio intervals, fracture length intervals, and fracture width intervals were extracted from them to construct a fracture characteristic parameter set, including: Three-dimensional laser scanning was performed on the surface of the sandstone outcrop in the target section to obtain point cloud data, and CT scanning was performed on the borehole core to obtain radial cross-sectional sequence images. Based on the point cloud data and the radial cross-sectional sequence images, the fractured region and the intact rock region are separated, and the boundary contour line of the fractured region is extracted. For each extracted crack boundary contour line, calculate the direction of the maximum variance of the contour point set, take the angle between the maximum variance direction and the horizontal plane as the crack inclination angle, calculate the Euclidean distance between the two endpoints of the crack boundary contour line as the crack length, and calculate the average value of the maximum inscribed circle diameter inside the crack boundary contour line as the crack width. Collect samples of fracture dip angle, fracture length and fracture width from all fractures, plot the cumulative frequency curves of dip angle, length and width respectively, and construct fracture dip angle interval, fracture length interval and fracture width interval. The area of ​​the measurement region corresponding to each set of measurement data is statistically analyzed, and the area enclosed by all the fracture boundary contours in the corresponding measurement region is extracted. Based on the relative relationship between the total fracture area in each measurement region and the area of ​​the corresponding measurement region, the single-group area fracture rate of each measurement region is determined. The single-group area fracture rate based on multiple sets of measurement data is merged to determine the average fracture rate within the target section, and the fracture dip angle interval, fracture length interval, fracture width interval, and the average fracture rate are combined to form the fracture feature parameter set.

3. The sandstone strength prediction method based on multi-fracture characteristic parameters according to claim 2, characterized in that, Based on the point cloud data and the radial cross-sectional image sequence, the fractured region and the intact rock region are separated, and the boundary contour line of the fractured region is extracted, including: Covariance analysis was performed on the neighborhood of each point in the point cloud data, and the fractured region and the intact rock region in the point cloud were separated by the spatial location where the normal vector direction changed abruptly. Dynamic thresholding is performed on the gray values ​​of each pixel in the radial cross-section sequence image. Pixels with gray values ​​lower than the neighborhood mean are selected as crack candidate areas, and pixels with gray values ​​higher than the neighborhood mean are selected as complete rock candidate areas. The boundary position is iteratively updated with the maximization of the difference in gray statistical features on both sides of the boundary as the driving force until the boundary converges, thus separating the crack area and the complete rock area in the cross-section image. Using the spatial coordinates and borehole azimuth of the drill core as the positioning reference, the fracture profile lines extracted from each cross-section image are transformed into a set of cross-section profile points in three-dimensional space according to the depth coordinates. The optimization objective is to minimize the sum of the squared Euclidean distances between each set of cross-sectional contour points and the set of fracture boundary points in the corresponding depth interval of the point cloud data. The rotation matrix and translation vector are solved iteratively by spatial rigid body transformation so that the two sets of boundary points coincide in a unified spatial coordinate system. The outer edge connecting line of the coincident boundary point set is used as the boundary contour line of the fracture region.

4. The sandstone strength prediction method based on multi-fracture characteristic parameters according to claim 1, characterized in that, Based on the aforementioned set of fracture characteristic parameters, the distributions of fracture dip angle, fracture length, and fracture width within their respective intervals are fitted using a Weber distribution probability density function to determine the Weber distribution shape and scale parameters of each parameter, including: Extract the fracture dip angle sample set, fracture length sample set, and fracture width sample set from the fracture feature parameter set, respectively. Use the fracture dip angle interval, fracture length interval, and fracture width interval as the cutoff boundary of the corresponding sample set, respectively, and remove the sample points located outside the cutoff boundary to form the dip angle cutoff sample set, length cutoff sample set, and width cutoff sample set. Log-likelihood functions are constructed for the tilt angle truncated sample set, length truncated sample set, and width truncated sample set, respectively. The log-likelihood function uses the shape parameter and scale parameter of the Weiber distribution as independent variables and the sum of the logarithmic values ​​of the probability density of the Weiber distribution of all sample points in each truncated sample set as the function value. With the goal of maximizing the log-likelihood function value, the log-likelihood functions of the tilt-trimmed sample set, the length-trimmed sample set, and the width-trimmed sample set are solved respectively. The convergence criterion is that the relative changes of the shape parameter and the scale parameter between two adjacent iterations are all lower than the tolerance threshold. The optimal estimates of the shape parameter and the scale parameter of the Weber distribution are output. The shape and scale parameters of the Weber distribution corresponding to the truncated sample set of dip angle, the truncated sample set of length, and the truncated sample set of width are respectively used as the Weber distribution parameters of the fracture dip angle, the Weber distribution parameters of the fracture length, and the Weber distribution parameters of the fracture width.

5. The sandstone strength prediction method based on multi-fracture characteristic parameters according to claim 1, characterized in that, The standard value of the uniaxial compressive strength of intact sandstone blocks in the target section is reduced and corrected using a negative exponential decay function to obtain the initial predicted value of the fractured rock mass strength, including: The target segment is divided into multiple sub-regions, and the fracture network connectivity coefficient of each sub-region is obtained; Core samples were drilled from each sub-region and intact rock samples without macroscopic fractures were prepared. The standard values ​​of the uniaxial compressive strength of the intact rock blocks in each sub-region were obtained by indoor uniaxial compression tests. For each sub-region, the uniaxial compressive strength of the fractured rock mass in each sub-region is calculated by uniaxial compression numerical simulation. The ratio of the standard value of the uniaxial compressive strength of the intact rock block to the uniaxial compressive strength of the fractured rock mass is used as the strength reduction factor for each sub-region. Using the fracture network connectivity coefficient of each sub-region as the independent variable and the corresponding intensity reduction factor as the dependent variable, a data point set is constructed and nonlinear regression is performed to fit and obtain the decay coefficient of the negative exponential decay function. Substituting the standard value of the uniaxial compressive strength of the intact rock block in the target section into the fitted negative exponential decay function, the initial predicted value of the fractured rock mass strength is obtained.

6. The sandstone strength prediction method based on multi-fracture characteristic parameters according to claim 1, characterized in that, Obtain the principal stress directions of the in-situ in-situ stress field within the target section, calculate the angle deviation between the dip direction of each fracture and the direction of maximum principal stress in the stochastic fracture network model, and perform anisotropic correction on the initial predicted value of the fractured rock mass strength to obtain the final predicted value of the fractured rock mass strength, including: Obtain the direction of the maximum principal stress in the in-situ stress field within the target section, and transform the direction of the maximum principal stress into the local coordinate system of the two-dimensional solution domain; Calculate the angle between the inclination of each fracture in the random fracture network model and the direction of the maximum principal stress, and use the corresponding value of the angle difference in the range of 0° to 90° as the angle deviation of each fracture. The anisotropy correction coefficient corresponding to each crack is determined according to the angle deviation of each crack. The anisotropy correction coefficient increases monotonically with the increase of the angle deviation, and the anisotropy correction coefficient takes the minimum value when the angle deviation is zero and the maximum value when the angle deviation is 90 degrees. Using the fracture area of ​​each fracture as the weight, the anisotropy correction coefficients corresponding to all fractures are weighted and averaged to obtain the comprehensive anisotropy correction coefficient. The initial predicted value of the fractured rock mass strength is multiplied by the comprehensive anisotropy correction coefficient to obtain the final predicted value of the fractured rock mass strength.

7. The sandstone strength prediction method based on multi-fracture characteristic parameters according to claim 1, characterized in that, After obtaining the final predicted value of the fractured rock mass strength, the following steps are also included: Obtain the measured value of the fractured rock mass strength at at least one verification location within the target section, wherein the verification location and the location of the fracture measurement data are spatially adjacent and do not overlap; Obtain the final predicted value of the fractured rock mass strength at the verification location, compare it with the measured value of the fractured rock mass strength, and calculate the relative deviation between the two. When the relative deviation exceeds the allowable deviation range, the ratio of the measured value of the fractured rock mass strength to the final predicted value of the fractured rock mass strength is used as the correction coefficient. The scale parameters in the Weber distribution parameters of the fracture dip angle, the Weber distribution parameters of the fracture length, and the Weber distribution parameters of the fracture width are multiplied by the correction coefficient to obtain the updated Weber distribution scale parameters, while keeping the shape parameters of each Weber distribution unchanged. When the relative deviation does not exceed the allowable deviation range, the final predicted value of the fractured rock mass strength remains unchanged; Based on the updated Weber distribution scale parameters and the unchanged Weber distribution shape parameters, the updated stochastic fracture network model is regenerated. The updated fracture network connectivity coefficients are extracted from the updated random fracture network model, and strength reduction and anisotropy corrections are performed to obtain the final predicted value of the updated fractured rock mass strength.

8. An electronic device for predicting sandstone strength based on multi-fracture characteristic parameters, characterized in that, The electronic device is used to execute the sandstone strength prediction method based on multi-fracture characteristic parameters according to any one of claims 1 to 7, and the electronic device includes: The feature extraction module is used to acquire multiple sets of fracture measurement data from sandstone outcrops and borehole cores in the target section, and extract fracture dip angle intervals, fracture ratio, fracture length intervals and fracture width intervals from them to construct a fracture feature parameter set; The network generation module is used to fit the distributions of fracture dip angle, fracture length, and fracture width within their respective intervals using the Weber distribution probability density function based on the fracture feature parameter set, determine the Weber distribution shape and scale parameters of each parameter, and generate a random fracture network model in conjunction with the fracture rate. The steps for generating the random fracture network model include: The two-dimensional solution domain is determined by the spatial range of the target segment, and a local coordinate system is established within the two-dimensional solution domain; Based on the Weber distribution shape and scale parameters of each parameter, cracks are generated one by one, wherein the crack generation steps include: The dip angle of the current fracture is randomly sampled from the Weber distribution parameters of the fracture dip angle, the trace length of the current fracture is randomly sampled from the Weber distribution parameters of the fracture length, and the aperture of the current fracture is randomly sampled from the Weber distribution parameters of the fracture width. The coordinates of the center point of the current fracture are randomly determined in the two-dimensional solution domain, and the direction of the fracture line segment in the two-dimensional solution domain is determined based on the dip angle assignment. After each crack is generated, the sum of the areas of all generated cracks in the current two-dimensional solution domain is accumulated, and the ratio of the sum of the areas to the total area of ​​the two-dimensional solution domain is calculated as the current cumulative area crack rate. The current cumulative area crack rate is compared with the average crack rate. If the current cumulative area crack rate is lower than the average crack rate, the next crack is generated. When the current cumulative area fracture rate reaches the average fracture rate, generation stops, and the set of all generated fractures in the two-dimensional solution domain at this time is taken as the random fracture network model. The strength reduction module is used to extract fracture network connectivity coefficients from the random fracture network model, and to reduce and correct the standard value of the uniaxial compressive strength of intact sandstone blocks in the target section using a negative exponential decay function to obtain the initial predicted value of fractured rock mass strength. The extraction of fracture network connectivity coefficients from the random fracture network model includes: Based on the center point coordinates, dip direction and trace length of each fracture in the random fracture network model, the endpoint coordinates of each fracture in the two-dimensional solution domain are determined, and each fracture is represented as a fracture line segment bounded by the two endpoints. Perform pairwise intersection checks on all fracture segments and mark the two fracture segments that have an intersection point as a connected pair; Based on all connected pairs, gap segments that have direct or indirect connectivity are grouped into the same connected group. The connected group with the largest number of fracture segments is counted, and the ratio of the number of fracture segments in the largest connected group to the total number of fractures in the random fracture network model is calculated. The ratio is used as the connectivity coefficient of the fracture network. An anisotropy correction module is used to obtain the principal stress direction of the in-situ stress field in the target section, calculate the angle deviation between the dip direction of each fracture and the maximum principal stress direction in the random fracture network model, and perform anisotropy correction on the initial predicted value of the fractured rock mass strength to obtain the final predicted value of the fractured rock mass strength.

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