A graph-based method and system for analyzing coal and rock fracture connectivity and propagation instability.

Abstract

This invention discloses a graph theory-based method and system for analyzing the connection, expansion, and instability of coal and rock fractures. The method includes: acquiring acoustic data through microseismic monitoring, performing location calculations and source mechanism inversion, and extracting core parameters of coal and rock fractures; comprehensively considering the geometric dimensions and directional characteristics of fractures, calculating the spatial geometric relationships between fractures, defining four topological relationships, and calculating the fracture penetration probability index (BCI); constructing a fracture network topological model based on graph theory, with fractures as graph nodes and geometric information allocated to edges, defining node types and edge directions; acquiring spatiotemporal topological attribute parameters of the fracture network, quantitatively analyzing its stage-specific time-varying trends with coal and rock deformation and the dynamic expansion characteristics of fracture network spatial propagation, identifying key modes of abrupt instability and key stages of fracture spatial expansion; and proposing a graph neural network-based fracture surface development morphology reconstruction method, providing a means to visualize the cross-scale evolution and spatial development morphology of fracture connections, expansion, and instability.

Description

Technical Field

[0001] This invention relates to the field of fracture networks, and more particularly to a graph theory-based method and system for analyzing the connection, propagation, and instability of coal and rock fractures. Background Technology

[0002] With the increasing depth of coal mining, the development, expansion, nucleation, and evolution of microfractures within the rock mass into complex fracture networks—a multi-scale process—not only affects the overall stability of the mine structure but may also induce major engineering disasters such as large-scale surrounding rock collapses, rockbursts, and roadway instability. Furthermore, it can lead to secondary disasters such as coal and gas outbursts, seepage channel formation, and groundwater inrush. These problems severely weaken the bearing capacity of the rock mass and increase the risk of chain-reaction disasters, becoming a key technical bottleneck for improving the safety and efficiency of deep coal mining. Therefore, in-depth research into fracture connection mechanisms and spatiotemporal dynamic expansion characteristics, revealing how discrete, isolated fractures evolve into interconnected fracture clusters, is crucial for the quantitative analysis, risk identification, and optimal mine design of coal and rock hazards. It can provide important theoretical support and engineering guidance for mine safety control and disaster prediction.

[0003] The formation and evolution of fracture networks is a complex "black box" process, and traditional methods struggle to accurately characterize its spatiotemporal development. Microseismic monitoring, as a non-destructive detection technique, captures elastic wave signals released during coal and rock loading, providing an effective means to analyze the dynamic expansion of fracture networks.

[0004] Patent CN118884524A proposes a method for constructing a fracture network model and identifying seepage channels based on microseismic monitoring. It utilizes the microseismic moment tensor and source parameters to construct a seepage model and identify the main channels with the shortest flow time. However, the high complexity of fracture network structures poses challenges to existing methods in characterizing their dynamic expansion features and evolution mechanisms. Current research largely relies on probabilistic statistical analysis or fractal theory, employing stochastic simulation and numerical analysis to assess rock mass stability. However, under complex geological conditions, it is difficult to accurately describe the topological structure of fracture networks, neglecting the influence of fracture geometric parameters on the fracture network topology.

[0005] Graph theory methods offer a novel research paradigm for the topological analysis of fracture networks, becoming an effective tool for revealing the evolution and dynamic expansion characteristics of fracture networks. Patent CN106991244A proposes a graph theory-based method for calculating the connectivity and seepage of fracture networks. By analyzing the trace length and fracture direction of a two-dimensional fracture network, it constructs first- and second-level connectivity graphs and calculates the seepage characteristics of the fracture network, thereby characterizing the connectivity of the fractures. Patent CN119417856A discloses a method for identifying connectivity impairment regions in complex fracture networks. It constructs an adjacency matrix of the fracture network based on fracture length, Euclidean distance, and width, calculates the degree value and clustering coefficient, and identifies connectivity impairment regions of the fractures using a graph theory-based maximum connectivity algorithm. Graph theory methods abstract fracture networks into graph structures, with fractures as nodes and the interactions between fractures as edges. This simplifies the complex characterization of fracture networks and helps to quantitatively describe the topological features of fracture networks, the spatial propagation and dynamic expansion processes of fractures. It also reveals key mutation modes and their mechanisms, such as fracture connection, local fracture aggregation and abrupt changes, and the formation of the main fracture surface. This provides theoretical support for the analysis of the mechanism of fracture evolution during coal and rock instability and lays a scientific foundation for the stability assessment and dynamic instability research of coal and rock structures. Summary of the Invention

[0006] This solution addresses the problems and needs raised above by proposing a graph theory-based method and system for analyzing coal and rock fracture connections and propagation instability. The method achieves the aforementioned technical objectives and brings about several other technical benefits by adopting the following technical features.

[0007] One objective of this invention is to propose a graph-based method for analyzing coal and rock fracture connections and propagation instability, comprising the following steps:

[0008] S10: Raw acoustic wave data is acquired through a microseismic monitoring system. The raw acoustic wave data is used for location calculation and source mechanism inversion to obtain the core parameters of the coal and rock fracture source that are directly related to the fracture.

[0009] S20: Taking into account the geometric dimensions and directional characteristics of the fracture structure surface, calculate the spatial geometric relationship between fractures, define four topological relationships: intersecting, connected, embedded, and separated, and further determine the intersection line equation and intersection line length; calculate the fracture penetration probability index BCI based on the core parameters of the coal and rock fracture source.

[0010] S30: Establish a topological model of a fracture network to characterize fracture penetration, and generalize the fracture network into a graph structure based on graph theory; wherein the fracture is a graph node, the geometric information related to the fracture is assigned to the edges connecting the nodes, and the types of nodes and the directionality of edges are defined and classified.

[0011] S40: Obtain the temporal topological attribute parameters of the fracture network, quantitatively analyze its stage-wise time-varying trend with coal and rock deformation, and determine the key mutation modes and mechanisms of local fracture aggregation mutation, fracture connection mutation, and main fracture surface formation mutation in the coal and rock instability fracture network.

[0012] S50: Based on the distribution characteristics of spatial topological attribute parameters, it quantitatively characterizes the spatial propagation dynamic evolution process of fracture networks and identifies five key stages: fracture initiation, local fracture aggregation, fracture propagation, fracture connection, and main fracture surface formation.

[0013] S60: Construct a spatiotemporal topological model of fractures based on dynamic graph neural networks, automatically extract discrete fracture data, construct an adjacency graph using edge convolution and aggregate features to capture local structure and global topology; combine density clustering and connectivity index to identify main fracture surfaces with high expansion potential, and use B-spline surface fitting to generate smooth and continuous macroscopic main fracture surfaces, realizing the visualization of cross-scale evolution from fracture connection, expansion and connectivity to instability.

[0014] Furthermore, the graph-based coal and rock fracture connection and propagation instability analysis method and system according to the present invention may also have the following technical features:

[0015] In one example of the present invention, in step S10, the original acoustic data is used to perform localization calculations and focal mechanism inversion to obtain core parameters of the focal mechanism directly related to the rupture, including the following steps:

[0016] S11: Post-process the raw acoustic data acquired by the microseismic monitoring system, and use the red-delay information criterion method to extract the arrival time and amplitude information of the first wave;

[0017] S12: Using the arrival time data of the first wave of sound waves at different locations of sensors in the microseismic monitoring system, a simplex localization robust algorithm is used to calculate the spatial location of the acoustic emission source.

[0018] S13: Solving for the six components M of the source rupture moment tensor based on the acoustic first-wave amplitude data collected by sensors at different locations under the constraint of the tension-shear rupture source model. pq ;

[0019] S14: Based on the calculated moment tensor components, quantitatively invert and calculate the core parameters of the coal and rock fracture source, including the fracture orientation and fracture volume.

[0020] In one example of the present invention, in step S14, the specific calculation formula for the core parameters of the coal and rock fracturing source is as follows:

[0021] Crack volume:

[0022]

[0023] In the formula, ΔV is the fracture volume, and M1 and M3 are the moment tensors M. pq eigenvalues, where μ is the Lamé constant;

[0024] Orientation and direction:

[0025]

[0026] n=(cosα,0,±sinα)

[0027]

[0028] In the formula, α is the angle between the direction of motion of the earthquake source rupture surface and the normal direction, and M1, M2, and M3 are the moment tensors M. pq The eigenvalues ​​are μ and λ, which are Lamé constants, n is the spatial orientation, and b is the direction of motion.

[0029] In one example of the present invention, in step S20, the spatial geometric relationship between cracks is calculated by comprehensively considering the geometric dimensions and directional characteristics of the crack structure surface, defining four topological relationships: intersecting, connected, embedded, and separated, and further determining the intersection line equation and intersection line length, including the following steps:

[0030] S21: Assuming the fracture is disk-shaped, its location coordinates (x0, y0, z0), volume radius R, and spatial orientation (n) are given. x ,n y ,n z From this, we can obtain the equation of the plane containing the crack and its location coordinates (x0, y0, z0), and the equation of the sphere determined by the volume radius R, as follows:

[0031] n x (x-x0)+n y (y-y0)+n z (z-z0)=0

[0032] (x-x0) 2 +(y-y0) 2 +(z-z0) 2 =R 2

[0033] Let the plane equations of any two cracks in space be:

[0034]

[0035] S22: From spatial geometric relationships, we know that the normal vector of the plane where the two fractures intersect is perpendicular to the normal vectors of the planes containing the two fractures. Therefore, the normal vector of the plane where the fractures intersect can be obtained. Let the normal vector of the plane where the fractures intersect be I = (a, b, c), satisfying the following equation:

[0036]

[0037] Right now:

[0038]

[0039] S23: Take any point P(x) on the intersection line of the fracture. p ,y p ,z p If point P is expressed as a function of the variable t, then the equation of the intersection line of the two cracks is:

[0040]

[0041] S24: Solve the equations of the sphere and the line of intersection simultaneously, and use the discriminant of the existence condition of the solution of the quadratic equation to determine whether the line and the sphere have an intersection point. If there are two intersection points, solve for the two intersection points of the line of intersection on the crack. Determine the spatial topological relationship between the cracks based on the positional relationship between the intersection points of the line of intersection and the crack.

[0042] S25: Since the intersection line of the fissures is the circle of the intersection of the two fissure disks in geometric space, the length L of the intersection line is actually the diameter of the intersection circle, which is determined by the radii R1R2 of the two fissure disks, the distance d between the centers of the spheres, and the geometric relationship between the two spheres. Its expression is:

[0043]

[0044] In one example of the present invention, in step S20, the fracture penetration probability index (BCI) is calculated based on the core parameters of the coal and rock fracture source. The specific calculation steps are as follows:

[0045] The Z-score standardization method is used to transform the data into a standard normal distribution with zero mean and unit variance to standardize the fracture volume. The specific expression is as follows:

[0046]

[0047] In the formula, V i Let μ be the volume of the i-th crack. V σ is the mean of all fracture volumes. V Z(V) represents the standard deviation of all fracture volumes. i ) represents the standardized value of the volume of the i-th fracture.

[0048] For any fractures i and j in a fracture network, after determining that the spatial topology between the fractures has a connection relationship, the formula for calculating their fracture penetration probability index is as follows:

[0049]

[0050] In the formula, Z(V) i ) and Z(V j ) are the normalized volume values ​​of the i-th and j-th fractures, respectively, and d ij Let be the Euclidean distance between the i-th fracture and the j-th fracture;

[0051] The total penetration index (BCI) of crack i i It should be the sum of the connectivity indices of the fracture i and all surrounding fracture nodes that satisfy the connectivity relationship; where, assuming there are n connected fracture nodes around fracture i, the total connectivity index BCI is... i The calculation formula is as follows:

[0052]

[0053] In one example of the present invention, in step S30, the fracture network is generalized into a graph structure based on graph theory; wherein the fractures are graph nodes, and the geometric information related to the fractures is assigned to the edges connecting the nodes. The types of nodes and the directionality of the edges are defined and classified, specifically including the following steps:

[0054] S31: After determining the spatial topological relationship between the cracks and identifying their connection relationship, a crack network topological model is established between the crack center and the center of the intersection line between the crack and another crack to characterize the crack connection, and the crack network is generalized into a graph structure based on graph theory.

[0055] S32: Cracks are treated as graph nodes and are divided into I nodes, T nodes, Y nodes, X nodes and D nodes according to their topological characteristics. The total number of edges connected to a node is defined as the degree.

[0056] In one example of the present invention, in step S50, the spatial propagation dynamic evolution process of the fracture network is quantitatively characterized based on the distribution characteristics of spatial topological attribute parameters. The specific steps are as follows:

[0057] S51: Select three key spatial topological attribute parameters—spatial distribution of connectivity index, spatial distribution of fracture density, and spatial distribution of fracture volume—and combine them with spatial cloud map visualization methods to quantitatively characterize the spatial evolution characteristics of fracture networks and reveal their propagation patterns and evolution trends in different regions.

[0058] S52: By combining temporal variation analysis and spatial distribution characteristics of fracture networks, five key stages are identified: fracture initiation, local fracture aggregation, fracture propagation, fracture connection, and formation of the main fracture surface, in order to reveal the fracture evolution mechanism during coal and rock instability.

[0059] In one example of the present invention, in step S60, density clustering and connectivity index are combined to identify main fracture surfaces with high propagation potential, and B-spline surface fitting is used to generate smooth and continuous macroscopic main fracture surfaces, thereby realizing the visualization of cross-scale evolution from fracture connection and propagation to instability, including the following steps:

[0060] S61: Based on dynamic graph neural network, construct spatiotemporal topology analysis model of fracture network, automatically extract discrete isolated fracture data, and treat fractures as graph nodes; use edge convolution mechanism to construct adjacency graph through spatial relationship between nodes, and aggregate neighborhood features to update node representation, capturing local structure and global topology;

[0061] S62: Based on Euclidean distance, the similarity between high-dimensional features of cracks is calculated. The density clustering DBSCAN algorithm is used to cluster cracks according to the density threshold, and cracks with similar features are grouped into the same cluster. Each cluster represents a crack surface and is assigned a unique number. Noise points are excluded to reduce interference. Combined with the optimization results of the penetration index, cracks with high propagation potential are identified.

[0062] S63: The main fracture surface is reconstructed using a B-spline surface fitting algorithm to generate a smooth and continuous macroscopic main fracture surface. The main direction of the fracture is determined by selecting control points through principal component analysis. Based on the fracture distribution, a B-spline curve is constructed to generate the boundary contour. The outer contour line is triangulated and meshed. Combining the fracture and the triangular mesh, the B-spline algorithm is used to accurately fit the fracture surface, revealing the spatial development morphology of the fracture surface and realizing the visualization of the cross-scale evolution from fracture connection, expansion and penetration to instability.

[0063] Another objective of this invention is to propose a graph-based system for analyzing coal and rock fracture connectivity and propagation instability, comprising:

[0064] The parameter acquisition module is configured to acquire raw acoustic wave data through the microseismic monitoring system, perform location calculations and source mechanism inversion on the raw acoustic wave data, and obtain the core parameters of the coal and rock fracture source that are directly related to the fracture.

[0065] The topology calculation module is configured to comprehensively consider the geometric dimensions and directional characteristics of fracture structure surfaces, calculate the spatial geometric relationships between fractures, define four types of topology relationships: intersecting, connected, embedded, and separated, and further determine the intersection line equation and intersection line length; and calculate the fracture penetration probability index (BCI) based on the core parameters of the coal and rock fracture source.

[0066] The topology model building module is configured to build a topology model of a fracture network to characterize fracture connectivity, and generalize the fracture network into a graph structure based on graph theory. The fracture is treated as a graph node, and the geometric information related to the fracture is assigned to the edges connecting the nodes. The types of nodes and the directionality of the edges are defined and classified.

[0067] The fracture time series analysis module is configured to acquire the time series topological attribute parameters of the fracture network, quantitatively analyze its stage-wise time-varying trend with coal and rock deformation, and determine the key mutation modes and mechanisms of local fracture aggregation mutation, fracture connection mutation, and main fracture surface formation mutation in the coal and rock instability fracture network.

[0068] The fracture spatial analysis module is configured to quantitatively characterize the spatial propagation dynamic evolution process of fracture networks based on the distribution characteristics of spatial topological attribute parameters, and identify five key stages: fracture initiation, local fracture aggregation, fracture propagation, fracture connection, and main fracture surface formation.

[0069] The fracture surface development morphology reconstruction module is configured to construct a fracture spatiotemporal topology model based on a dynamic graph neural network. It automatically extracts discrete fracture data, uses edge convolution to construct an adjacency graph and aggregates features to capture local structure and global topology. It combines density clustering and connectivity index to identify main fracture surfaces with high expansion potential, and uses B-spline surface fitting to generate smooth and continuous macroscopic main fracture surfaces, realizing the visualization of cross-scale evolution from fracture connection, expansion and connectivity to instability.

[0070] In one example of the present invention, the parameter acquisition module includes:

[0071] The data processing unit is configured to perform post-processing on the raw acoustic data acquired by the microseismic monitoring system, and to extract the arrival time and amplitude information of the first wave using the red-delay information criterion method.

[0072] The spatial positioning unit is configured to use the arrival time data of the first wave of sound waves at different locations of sensors in the microseismic monitoring system to perform spatial positioning calculations on the acoustic emission source using a simplex positioning robust algorithm.

[0073] The moment tensor element is configured to solve for the six components M of the source rupture moment tensor based on the acoustic first-wave amplitude data collected by sensors at different locations under the constraints of a tension-shear rupture source model. pq ;

[0074] The core parameter unit is configured to quantitatively invert and calculate the core parameters of the coal and rock fracture source based on the calculated moment tensor components. The core parameters of the coal and rock fracture source include the fracture orientation and fracture volume.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] This technical solution utilizes microseismic monitoring data for focal mechanism inversion, breaking through the traditional method of describing fracture location points and achieving a precise characterization of the geometric features and spatial orientation of the complete fracture surface from discrete fracture points. Secondly, focal inversion technology can accurately capture the source characteristics of fractures, dynamically tracking the occurrence, expansion, and penetration of fractures, ensuring that the fracture network topology more closely matches the actual evolution mechanism. This provides high-precision, time-varying data for the dynamic evolution analysis of fracture networks, enhancing its quantitative characterization capabilities.

[0077] This technical solution constructs a topological analysis model of a fracture network based on graph theory. Fractures are abstracted as nodes in a graph, and their geometric parameters are assigned to edges, systematically characterizing the topological relationships between fractures and thus improving the quantitative description of fracture connectivity. By defining node types and edge directionality, the connection relationships and topological changes of fractures at different evolutionary stages are accurately depicted, enabling dynamic tracking of the fracture network structure from its initial formation to its expansion and connectivity.

[0078] This technical solution quantitatively analyzes the spatiotemporal dynamic expansion characteristics of fracture networks by acquiring temporal topological parameters such as connection type, network density, clustering coefficient, and connectivity index, as well as spatial topological parameters such as fracture density and fracture volume. It identifies key stages such as local fracture aggregation, abrupt fracture connectivity changes, and the formation of the main fracture surface, thus deepening the analysis of fracture expansion mechanisms.

[0079] This technical solution proposes a method for reconstructing the development morphology of fracture surfaces based on graph neural networks. It constructs a fracture expansion and evolution identification and quantitative characterization based on a fracture network model, which can reconstruct the geometric morphology and dynamic evolution characteristics of fracture surfaces with high accuracy. It realizes the visualization of cross-scale evolution of fractures from connection, expansion and connection to instability, and further reveals the intrinsic mechanism between the connection relationship of complex fracture networks and the formation of macroscopic fracture surfaces.

[0080] The preferred embodiments of the invention will be described in more detail below with reference to the accompanying drawings, so as to facilitate an understanding of the features and advantages of the invention. Attached Figure Description

[0081] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly described below. The drawings are merely illustrative of some embodiments of the present invention and are not intended to limit the scope of the present invention to all embodiments.

[0082] Figure 1 This is a flowchart of a graph theory-based method for analyzing coal and rock fracture connections and propagation instability according to an embodiment of the present invention.

[0083] Figure 2 This is a diagram showing four spatial topological relationships between cracks according to an embodiment of the present invention;

[0084] Figure 3 The fracture network according to an embodiment of the present invention is generalized as a graph structure;

[0085] Figure 4 This is a diagram representing the node types according to an embodiment of the present invention;

[0086] Figure 5 This is a flowchart of the crack surface development morphology reconstruction based on graph neural networks according to an embodiment of the present invention;

[0087] Figure 6 This is a schematic diagram of a dynamic graph neural network according to an embodiment of the present invention;

[0088] Figure 7 This is a flowchart of density clustering and surface fitting according to an embodiment of the present invention. Detailed Implementation

[0089] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The same reference numerals in the drawings represent the same components. It should be noted that the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0090] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms “first,” “second,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, “an” or “a” and similar terms do not necessarily indicate a quantity limitation. Terms such as “comprising” or “including” mean that the element or object preceding the word encompasses the element or object listed following the word and its equivalents, without excluding other elements or objects. Terms such as “connected” or “linked” are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as “upper,” “lower,” “left,” and “right” are used only to indicate relative positional relationships; these relative positional relationships may change accordingly when the absolute position of the described object changes.

[0091] According to a first aspect of the present invention, a graph-based method for analyzing coal and rock fracture connectivity and propagation instability is provided, such as... Figure 1 As shown, it includes the following steps:

[0092] S10: Raw acoustic wave data is acquired through a microseismic monitoring system. The raw acoustic wave data is used for location calculation and source mechanism inversion to obtain the core parameters of the coal and rock fracture source that are directly related to the fracture.

[0093] S20: Taking into account the geometric dimensions and orientation characteristics of the fracture structure surface, calculate the spatial geometric relationship between fractures, defined as follows: Figure 2 The four topological relationships of intersecting, connected, embedded, and separated are shown, and the intersection line equation and intersection line length are further determined; the fracture penetration probability index (BCI) is calculated based on the core parameters of coal and rock fracture source, fracture volume and source radius.

[0094] S30: Establish a topological model of a fracture network to characterize fracture penetration, and generalize the fracture network into a graph structure based on graph theory; where fractures are graph nodes, and geometric information related to fractures is assigned to the edges connecting nodes. Define and classify the types of nodes and the directionality of edges to study the dynamic expansion and evolution of fracture network topological features in depth.

[0095] S40: Obtain temporal topological attribute parameters such as fracture network connection type, network density, clustering coefficient, cumulative aperture and penetration index, quantify and analyze their stage-wise time-varying trends with coal and rock deformation, and determine the key mutation modes and mechanisms of local fracture aggregation mutation, fracture penetration mutation, and main fracture surface formation mutation in the coal and rock instability fracture network.

[0096] S50: Based on the distribution characteristics of spatial topological attribute parameters such as connectivity index, fracture density, and fracture volume, this study quantitatively characterizes the spatial propagation dynamic evolution process of fracture networks, identifies five key stages: fracture initiation, local fracture aggregation, fracture expansion, fracture connectivity, and main fracture surface formation, and reveals the fracture evolution mechanism during coal and rock instability.

[0097] S60: Construct a spatiotemporal topological model of fractures based on dynamic graph neural networks, automatically extract discrete fracture data, construct an adjacency graph using edge convolution and aggregate features to capture local structure and global topology; combine density clustering and connectivity index to identify main fracture surfaces with high expansion potential, and use B-spline surface fitting to generate smooth and continuous macroscopic main fracture surfaces, realizing the visualization of cross-scale evolution from fracture connection, expansion and connectivity to instability.

[0098] This analytical method utilizes microseismic monitoring data for focal mechanism inversion, breaking through the traditional method of describing fracture location points and achieving a precise characterization of the geometric features and spatial orientation of the complete fracture surface from discrete fracture points. Secondly, by leveraging focal inversion technology, it can accurately capture the source characteristics of fractures, dynamically track the occurrence, expansion, and penetration of fractures, ensuring that the fracture network topology more closely matches the actual evolution mechanism. This provides high-precision, time-varying data for the dynamic evolution analysis of fracture networks, enhancing its quantitative characterization capabilities.

[0099] This analytical method constructs a topological analysis model of the fracture network based on graph theory. Fractures are abstracted as nodes in a graph, and their geometric parameters are assigned to edges, systematically characterizing the topological relationships between fractures and thus improving the quantitative description of fracture connectivity. By defining node types and edge directionality, the method accurately depicts the connection relationships and topological changes of fractures at different evolutionary stages, enabling dynamic tracking of the fracture network structure from its initial formation to its expansion and connectivity.

[0100] This analytical method quantitatively analyzes the spatiotemporal dynamic expansion characteristics of fracture networks by acquiring temporal topological parameters such as connection type, network density, clustering coefficient, and connectivity index, as well as spatial topological parameters such as fracture density and fracture volume. It identifies key stages such as local fracture aggregation, abrupt fracture connectivity changes, and the formation of the main fracture surface, thus deepening the analysis of fracture expansion mechanisms.

[0101] This analytical method proposes a fracture surface development morphology reconstruction method based on graph neural networks. It constructs a fracture expansion evolution identification and quantitative characterization based on a fracture network model, which can reconstruct the geometric morphology and dynamic evolution characteristics of fracture surfaces with high accuracy. It realizes the visualization of cross-scale evolution of fractures from connection, expansion and connection to instability, and further reveals the intrinsic mechanism between the connection relationship of complex fracture networks and the formation of macroscopic fracture surfaces.

[0102] In one example of the present invention, in step S10, the original acoustic data is used to perform localization calculations and focal mechanism inversion to obtain core parameters of the focal mechanism directly related to the rupture, including the following steps:

[0103] S11: Post-process the raw acoustic data acquired by the microseismic monitoring system, and use the red-delay information criterion method to extract the arrival time and amplitude information of the first wave;

[0104] S12: Using the arrival time data of the first wave of sound waves at different locations of sensors in the microseismic monitoring system, a simplex localization robust algorithm is used to calculate the spatial location of the acoustic emission source.

[0105] S13: Solving for the six components M of the source rupture moment tensor based on the acoustic first-wave amplitude data collected by sensors at different locations under the constraint of the tension-shear rupture source model. pq ;

[0106] S14: Based on the calculated moment tensor components, quantitatively invert and calculate the core parameters of the coal and rock fracture source, including the fracture orientation and fracture volume.

[0107] In one example of the present invention, in step S14, the specific calculation formula for the core parameters of the coal and rock fracturing source is as follows:

[0108] Crack volume:

[0109]

[0110] In the formula, ΔV is the fracture volume, and M1 and M3 are the moment tensors M. pq eigenvalues, where μ is the Lamé constant;

[0111] Orientation and direction:

[0112]

[0113] n=(cosα,0,±sinα)

[0114]

[0115] In the formula, α is the angle between the direction of motion of the earthquake source rupture surface and the normal direction, and M1, M2, and M3 are the moment tensors M. pq The eigenvalues ​​are μ and λ, which are Lamé constants, n is the spatial orientation, and b is the direction of motion.

[0116] In one example of the present invention, in step S20, the spatial geometric relationship between cracks is calculated by comprehensively considering the geometric dimensions and directional characteristics of the crack structure surface, defining four topological relationships: intersecting, connected, embedded, and separated, and further determining the intersection line equation and intersection line length, including the following steps:

[0117] S21: Assuming the fracture is disk-shaped, its location coordinates (x0, y0, z0), volume radius R, and spatial orientation (n) are given. x ,n y ,n z From this, we can obtain the equation of the plane containing the crack and its location coordinates (x0, y0, z0), and the equation of the sphere determined by the volume radius R, as follows:

[0118] n x (x-x0)+n y (y-y0)+n z (z-z0)=0

[0119] (x-x0) 2 +(y-y0) 2 +(z-z0) 2 =R 2

[0120] Let the plane equations of any two cracks in space be:

[0121]

[0122] S22: From spatial geometric relationships, we know that the normal vector of the plane where the two fractures intersect is perpendicular to the normal vectors of the planes containing the two fractures. Therefore, the normal vector of the plane where the fractures intersect can be obtained. Let the normal vector of the plane where the fractures intersect be I = (a, b, c), satisfying the following equation:

[0123]

[0124] Right now:

[0125]

[0126] S23: Take any point P(x) on the intersection line of the fracture. p ,y p ,z p If point P can be expressed as a function of the variable t, then the equation of the intersection line of the two cracks is:

[0127]

[0128] S24: Solve the equations of the sphere and the line of intersection simultaneously, and use the discriminant of the existence condition of the solution of the quadratic equation to determine whether the line and the sphere have an intersection point. If there are two intersection points, solve for the two intersection points of the line of intersection on the crack. Determine the spatial topological relationship between the cracks based on the positional relationship between the intersection points of the line of intersection and the crack.

[0129] Assuming the intersection points of the line of intersection with crack 1 are I1 and I2, and the intersection points of the line of intersection with crack 2 are II1 and II2, the spatial topological relationship between the cracks can be obtained based on the positional relationship between I1 and I2 and II1 and II2: when I1 and II1, and I2 and II2 both coincide, the two cracks intersect; when I1, I2, II1 and II2 are arranged alternately, the two cracks are connected; when II1 and II2 are sandwiched between I1 and I2, or when I1 and I2 are sandwiched between II1 and II2, the two cracks are interlocked; when I1, I2, II1 and II2 are arranged in sequence, and the distance between I1 and II1 is greater than the distance between I1 and I2, the two cracks are separated.

[0130] S25: Since the intersection line of the fissures is the circle of the intersection of the two fissure disks in geometric space, the length L of the intersection line is actually the diameter of the intersection circle, which is determined by the radii R1R2 of the two fissure disks, the distance d between the centers of the spheres, and the geometric relationship between the two spheres. Its expression is:

[0131]

[0132] In one example of the present invention, in step S20, the fracture penetration probability index (BCI) is calculated based on the core parameters of the coal and rock fracture source. The specific calculation steps are as follows:

[0133] To eliminate the scale differences in fracture volumes, the Z-score standardization method is used to transform the data into a standard normal distribution with zero mean and unit variance, thereby standardizing the fracture volume. The specific expression is as follows:

[0134]

[0135] In the formula, V i Let μ be the volume of the i-th crack. V σ is the mean of all fracture volumes. V Z(V) represents the standard deviation of all fracture volumes. i ) represents the standardized value of the volume of the i-th fracture.

[0136] For any fractures i and j in a fracture network, after determining that the spatial topology between the fractures has a connection relationship, the formula for calculating their fracture penetration probability index is as follows:

[0137]

[0138] In the formula, Z(V) i ) and Z(V j ) are the normalized volume values ​​of the i-th and j-th fractures, respectively, and d ij Let be the Euclidean distance between the i-th fracture and the j-th fracture;

[0139] In other words, based on the spatial topological relationship between the fractures above, the three types of intersecting, connected, and embedded relationships are determined to satisfy the continuity relationship. That is, the relationship that satisfies the three types of intersecting, connected, and embedded relationships is determined to be a continuity relationship, and then the fracture continuity probability index is calculated.

[0140] The total penetration index (BCI) of crack i i It should be the sum of the connectivity indices of the fracture i and all surrounding fracture nodes that satisfy the connectivity relationship; where, assuming there are n connected fracture nodes around fracture i, the total connectivity index BCI is... i The calculation formula is as follows:

[0141]

[0142] In one example of the present invention, such as Figure 3 , Figure 4 As shown, in step S30, the fracture network is generalized into a graph structure based on graph theory; wherein the fractures are graph nodes, and the geometric information related to the fractures is assigned to the edges connecting the nodes. The types of nodes and the directionality of the edges are defined and classified, specifically including the following steps:

[0143] S31: After determining the spatial topological relationship between the cracks and identifying their connection relationship, a crack network topological model is established between the crack center and the center of the intersection line between the crack and another crack to characterize the crack connection, and the crack network is generalized into a graph structure based on graph theory.

[0144] S32: Cracks are treated as graph nodes and classified into I, T, Y, X, and D nodes based on their topological characteristics. The total number of edges connected to a node is defined as its degree, denoted by deg. The node type definition rules are shown in Table 1.

[0145] Table 1 Node Type Definition Rules

[0146]

[0147] S33: Geometric information related to the fracture (such as spatial orientation, intersection length, aperture, volume, etc.) is assigned to the edges connecting the nodes. The edges are classified as unidirectional or bidirectional edges using the fracture penetration probability index (BCI). Unidirectional edges indicate lower penetration between fractures, suggesting weaker interaction between them; bidirectional edges represent higher penetration between fractures, indicating stronger interaction and the ability to penetrate each other and form stable fracture channels. The rules for defining the directionality of edges are shown in Table 2.

[0148] Table 2 Rules for Defining the Directionality of Sides

[0149]

[0150]

[0151] In one example of the present invention, in step S40, the temporal topological attribute parameters of the fracture network are obtained, and their phased time-varying trend with coal and rock deformation is quantitatively analyzed, specifically including:

[0152] Key temporal topological attribute parameters were selected, and the temporal changes of these parameters were calculated to obtain time-series data and plotted as time-series curves. Abrupt points in the time-series curves were identified to determine key abrupt change patterns and mechanisms in the coal and rock instability fracture network, including local fracture aggregation abrupt changes, fracture connection abrupt changes, and main fracture surface formation abrupt changes. This process was then used to identify precursor signals of coal and rock instability. The key topological attribute parameters selected are as follows:

[0153] ① Node Types: Analyze the trends of the number and proportion of five node types (I, T, Y, X, and D nodes) in the fracture network topology analysis model as the coal and rock deformation changes in stages.

[0154] ② Edge types: In the fracture network topology analysis model, each edge connects two nodes. Different edge types are formed according to the combination of the types of these two nodes, including 15 types: II, IT, IY, IX, ID, TT, TY, TX, TD, YY, YX, YD, XX, XD, DD. The number and proportion of each edge type (i.e., the ratio of the number of each edge type to the total number of edges) are analyzed as the coal and rock deformation stages change.

[0155] ③ Directionality of edges: Analyze the trend of the total number of edges and the number and ratio of unidirectional and bidirectional edges (i.e., the ratio of the number of unidirectional or bidirectional edges to the total number of edges) in the fracture network topology analysis model as the coal and rock deformation changes in stages.

[0156] ④ Network density: The ratio of the number of edges in a fractured network to the maximum number of edges it can accommodate. It describes the edge density between nodes in the network and represents the density of the fracture distribution. As the fractures expand, the network density gradually increases. When a certain threshold is reached, the fractures may connect, forming a main crack.

[0157]

[0158] In the formula, N e Let N be the total number of edges in the fracture network, and N be the total number of nodes.

[0159] ⑤ Clustering Coefficient: The clustering coefficient is an indicator that measures the degree of clustering among nodes in a fracture network. It is divided into the local clustering coefficient C(v) and the global clustering coefficient C. The local clustering coefficient C(v) is the ratio of the actual number of edges between the neighboring nodes of a node v to the total number of possible edges between the neighboring nodes of that node, reflecting the density of the local network structure around that node. The global clustering coefficient C is the average of the local clustering coefficients of all nodes, measuring the degree of clustering among all nodes in the graph, reflecting the density of the global structure of the fracture network. If the clustering coefficient suddenly increases over a certain period of time, it indicates that the fractures are concentrated in a local area, which may form a high stress concentration zone.

[0160]

[0161] In the formula, E v k is the actual number of edges between the neighboring nodes of node v. v Let v be the degree of node v, and N be the total number of nodes in the graph.

[0162] ⑥ Cumulative aperture: Analyze the trend of the sum of apertures of all nodes in the fracture network as a function of coal and rock deformation.

[0163] ⑦ Connectivity Index: This analyzes the trend of the sum of the fracture connectivity probability indices of all nodes in the fracture network as the coal and rock deformation progresses through different stages. If the sum of the connectivity indices rises sharply over a certain period, it indicates a sudden increase in fracture connectivity, and the coal and rock may be entering a stage of instability and failure.

[0164] In one example of the present invention, in step S50, the spatial propagation dynamic evolution process of the fracture network is quantitatively characterized based on the distribution characteristics of spatial topological attribute parameters. The specific steps are as follows:

[0165] S51: Select three key spatial topological attribute parameters—spatial distribution of connectivity index, spatial distribution of fracture density, and spatial distribution of fracture volume—and combine them with spatial cloud map visualization methods to quantitatively characterize the spatial evolution characteristics of fracture networks and reveal their propagation patterns and evolution trends in different regions.

[0166] S52: By combining temporal variation analysis and spatial distribution characteristics of fracture networks, five key stages are identified: fracture initiation, local fracture aggregation, fracture propagation, fracture connection, and formation of the main fracture surface, in order to reveal the fracture evolution mechanism during coal and rock instability.

[0167] The key spatial topology attribute parameters are selected as follows:

[0168] ① Spatial distribution of the continuity index: The continuity index of each fracture is calculated, and a continuity index distribution cloud map is generated by interpolation in three-dimensional space. The continuity of fractures in different regions is represented by color gradient. Among them, the high BCI region indicates that the fracture may be connected; the low BCI region indicates that the fracture is still isolated or in the initial stage and contributes little to the overall continuity.

[0169] ② Spatial distribution of fracture density: A three-dimensional gridded statistical method was used to calculate the fracture density. The study area was divided into small volume units, the number of fractures in each unit was counted, and a fracture density distribution cloud map was plotted. The color gradient represents the degree of fracture density in different regions. Among them, high fracture density areas indicate areas of stress concentration or active fracture; low fracture density areas indicate areas where fracture may not have yet extended to.

[0170] ③ Spatial Distribution of Crack Volume: The volume of each crack is calculated, and a crack volume distribution cloud map is generated using interpolation. The color gradient represents the size distribution of the crack volume. By analyzing the spatial distribution of crack volume, high-volume crack areas can be identified. These areas are often locations of stress concentration and strong fracture propagation, and may become part of the main fracture surface. Low-volume crack areas may be in the early stage of fracture or before the crack has propagated. Secondly, combined with crack density analysis, the crack propagation pattern can be determined. If the crack density is high and the volume is small, it indicates that the crack propagation is uniformly distributed, the fracture process is relatively slow, and no obvious through-crack trend has yet formed. If the crack density is low but the volume is large, it indicates that the crack mainly occurs in certain local areas and the fracture scale is large, which may indicate that the crack is about to penetrate and form the main fracture surface.

[0171] In one example of the present invention, in step S60, as Figure 5 , Figure 6 , Figure 7 As shown, density clustering and connectivity index are combined to identify high-expansion-potential main fracture surfaces, and B-spline surface fitting is used to generate smooth and continuous macroscopic main fracture surfaces, realizing the visualization of cross-scale evolution from fracture connection and expansion to instability. The process includes the following steps:

[0172] S61: A spatiotemporal topology analysis model for fracture networks is constructed based on Dynamic Graph Neural Network (DGCNN). It automatically extracts discrete isolated fracture data, treats fractures as graph nodes, and includes spatial coordinates, connectivity index, and spatial orientation on edges. Using edge convolution mechanism, an adjacency graph is constructed through the spatial relationships between nodes, and neighborhood features are aggregated to update node representations, capturing local structure and global topology. By minimizing the loss function to optimize parameters, the model outputs a high-dimensional feature vector that comprehensively reflects spatiotemporal correlation, physical connectivity, and topological structure.

[0173] S62: Based on Euclidean distance, the similarity between high-dimensional features of cracks is calculated. The density clustering DBSCAN algorithm is used to cluster cracks according to the density threshold, and cracks with similar features are grouped into the same cluster. Each cluster represents a crack surface and is assigned a unique number. Noise points are excluded to reduce interference. Combined with the optimization results of the penetration index, cracks with high propagation potential are identified.

[0174] S63: The main fracture surface is reconstructed using a B-spline surface fitting algorithm to generate a smooth and continuous macroscopic main fracture surface. The main direction of the fracture is determined by selecting control points through principal component analysis. Based on the fracture distribution, a B-spline curve is constructed to generate the boundary contour. The outer contour line is triangulated and meshed. Combining the fracture and the triangular mesh, the B-spline algorithm is used to accurately fit the fracture surface, revealing the spatial development morphology of the fracture surface and realizing the visualization of the cross-scale evolution from fracture connection, expansion and penetration to instability.

[0175] According to a second aspect of the present invention, a graph-based system for analyzing coal and rock fracture connections and propagation instability includes:

[0176] The parameter acquisition module is configured to acquire raw acoustic wave data through the microseismic monitoring system, perform location calculations and source mechanism inversion on the raw acoustic wave data, and obtain the core parameters of the coal and rock fracture source that are directly related to the fracture.

[0177] The topology calculation module is configured to comprehensively consider the geometric dimensions and directional characteristics of the fracture structure surface, calculate the spatial geometric relationship between fractures, define four types of topology relationships: intersecting, connected, embedded, and separated, and further determine the intersection line equation and intersection line length; and calculate the fracture penetration probability index (BCI) based on the core parameters of the coal and rock fracture source: fracture volume and source radius.

[0178] The topology model building module is configured to establish a topology model of a fracture network to characterize fracture connectivity, and generalizes the fracture network into a graph structure based on graph theory. The fracture is treated as a graph node, and the geometric information related to the fracture is assigned to the edges connecting the nodes. The types of nodes and the directionality of edges are defined and classified to study the dynamic expansion and evolution of the topological characteristics of the fracture network in depth.

[0179] The fracture time series analysis module is configured to acquire time series topological attribute parameters such as fracture network connection type, network density, clustering coefficient, cumulative opening degree and penetration index, quantitatively analyze their stage time-varying trend with coal and rock deformation, and determine the key mutation modes and mechanisms of local fracture aggregation mutation, fracture penetration mutation, and main fracture surface formation mutation in the coal and rock instability fracture network.

[0180] The fracture space analysis module is configured to quantitatively characterize the spatial propagation dynamic evolution process of fracture networks based on the distribution characteristics of spatial topological attribute parameters such as connectivity index, fracture density, and fracture volume. It identifies five key stages: fracture initiation, local fracture aggregation, fracture expansion, fracture connectivity, and main fracture surface formation, revealing the fracture evolution mechanism during coal and rock instability.

[0181] The fracture surface development morphology reconstruction module is configured to construct a fracture spatiotemporal topology model based on a dynamic graph neural network. It automatically extracts discrete fracture data, uses edge convolution to construct an adjacency graph and aggregates features to capture local structure and global topology. It combines density clustering and connectivity index to identify main fracture surfaces with high expansion potential, and uses B-spline surface fitting to generate smooth and continuous macroscopic main fracture surfaces, realizing the visualization of cross-scale evolution from fracture connection, expansion and connectivity to instability.

[0182] This analysis system utilizes microseismic monitoring data for focal mechanism inversion, breaking through the traditional method of describing fracture locations and achieving a precise characterization of the geometric features and spatial orientation of the complete fracture surface from discrete fracture points. Secondly, by leveraging focal inversion technology, it can accurately capture the source characteristics of fractures, dynamically track the occurrence, expansion, and penetration of fractures, ensuring that the fracture network topology more closely matches the actual evolution mechanism. This provides high-precision, time-varying data for the dynamic evolution analysis of fracture networks, enhancing its quantitative characterization capabilities.

[0183] This analysis system constructs a topological analysis model of the fracture network based on graph theory. Fractures are abstracted as nodes in a graph, and their geometric parameters are assigned to edges, systematically characterizing the topological relationships between fractures and thus improving the quantitative description of fracture connectivity. By defining node types and edge directionality, the system accurately depicts the connection relationships and topological changes of fractures at different evolutionary stages, enabling dynamic tracking of the fracture network structure from its initial formation to its expansion and connectivity.

[0184] This analysis system quantitatively analyzes the spatiotemporal dynamic expansion characteristics of fracture networks by acquiring temporal topological parameters such as connection type, network density, clustering coefficient, and connectivity index, as well as spatial topological parameters such as fracture density and fracture volume. It identifies key stages such as local fracture aggregation, abrupt fracture connectivity changes, and the formation of the main fracture surface, thus deepening the analysis of fracture expansion mechanisms.

[0185] This analysis system proposes a method for reconstructing the development morphology of fracture surfaces based on graph neural networks. It constructs a fracture expansion and evolution identification and quantitative characterization based on a fracture network model, which can reconstruct the geometric morphology and dynamic evolution characteristics of fracture surfaces with high accuracy. It realizes the visualization of cross-scale evolution of fractures from connection, expansion and connection to instability, and further reveals the intrinsic mechanism between the connection relationship of complex fracture networks and the formation of macroscopic fracture surfaces.

[0186] In one example of the present invention, the parameter acquisition module includes:

[0187] The data processing unit is configured to perform post-processing on the raw acoustic data acquired by the microseismic monitoring system, and to extract the arrival time and amplitude information of the first wave using the red-delay information criterion method.

[0188] The spatial positioning unit is configured to use the arrival time data of the first wave of sound waves at different locations of sensors in the microseismic monitoring system to perform spatial positioning calculations on the acoustic emission source using a simplex positioning robust algorithm.

[0189] The moment tensor element is configured to solve for the six components M of the source rupture moment tensor based on the acoustic first-wave amplitude data collected by sensors at different locations under the constraints of a tension-shear rupture source model. pq ;

[0190] The core parameter unit is configured to quantitatively invert and calculate the core parameters of the coal and rock fracture source based on the calculated moment tensor components. The core parameters of the coal and rock fracture source include the fracture orientation and fracture volume.

[0191] It should be noted that the graph theory-based coal and rock fracture connection and propagation instability analysis system of the present invention can also perform any of the processing described in the graph theory-based coal and rock fracture connection and propagation instability analysis method previously described, and the specific details are not repeated here.

[0192] The foregoing description, with reference to preferred embodiments, details the exemplary implementation of the graph theory-based coal and rock fracture connection and propagation instability analysis method and system proposed in this invention. However, those skilled in the art will understand that various modifications and alterations can be made to the above specific embodiments without departing from the concept of this invention, and various combinations can be made to the various technical features and structures proposed in this invention without exceeding the protection scope of this invention, which is determined by the appended claims.

Claims

1. A coal rock fracture connection and extension instability analysis method based on graph theory, characterized in that, Comprising the following steps: S10: Obtain original acoustic wave data by microseismic monitoring system, perform positioning calculation and source mechanism inversion on the original acoustic wave data, and obtain coal rock rupture source core parameters directly related to rupture; S20: Considering the geometric size and direction characteristics of the fracture structure, calculate the spatial geometric relationship between the fractures, define four topological relationships of intersection, connection, embedding and separation, and further determine the intersection line equation and intersection line length; calculate the rupture breakthrough possibility index BCI based on the coal rock rupture source core parameters; S30: Establish a fracture network topology model for representing fracture penetration, and generalize the fracture network into a graph structure based on graph theory; wherein the fractures are graph nodes, and the geometric information related to the fractures is distributed to the edges connecting the nodes, the types of nodes and the directionality of edges are defined and classified; S40: Obtain the timing topological attribute parameters of the fracture network, quantitatively analyze the stage-wise time-varying trend thereof with coal rock deformation, and determine the mutation key mode and mechanism of local fracture aggregation mutation, fracture penetration mutation and main fracture surface formation mutation of the coal rock instability fracture network; S50: Based on the distribution characteristics of the spatial topological attribute parameters, quantitatively depict the spatial propagation dynamic evolution process of the fracture network, and identify five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration and main fracture surface formation; S60: Construct a fracture spatio-temporal topology model based on a dynamic graph neural network, automatically extract discrete fracture data, use edge convolution to construct an adjacency graph and aggregate features, capture local structure and global topology; combine density clustering and penetrability index to identify main fracture surface fractures with high expansion potential, and use B-spline surface fitting to generate a smooth and continuous macro main fracture surface, realizing visualization of the cross-scale evolution of fracture connection, expansion and penetration to instability.

2. The coal rock fracture connection and expansion instability analysis method based on graph theory according to claim 1, characterized in that, In the step S10, the original acoustic wave data is subjected to positioning calculation and source mechanism inversion to obtain source mechanism core parameters directly related to rupture, comprising the following steps: S11: Post-process the original acoustic wave data collected by the microseismic monitoring system, and use the Akaike information criterion method to extract first arrival time and amplitude information; S12: Use the first arrival time data of acoustic waves at different positions of the sensor of the microseismic monitoring system, and use the simplex positioning robust algorithm to calculate the spatial positioning of the acoustic emission source; S13: Based on the shear crack source model constraint condition, the amplitude data of the first wave of the sound wave collected by the sensors at different positions are used to solve the 6 components of the source rupture moment tensor ; S14: Quantitatively invert and calculate the coal rock rupture source core parameters according to the calculated moment tensor components, wherein the coal rock rupture source core parameters include fracture orientation and fracture volume.

3. The coal rock fracture connection and expansion instability analysis method based on graph theory according to claim 2, characterized in that, In the step S14, the specific calculation formula of the coal rock rupture source core parameters is as follows: Fracture volume: wherein is the crack volume, , is the eigenvalue of the tensor , is the Lame constant; Orientation: wherein is the angle between the direction of the fault plane motion and the normal direction, , , is the eigenvalue of the moment tensor , and are the Lame constants, n is the spatial orientation, and b is the direction of motion.

4. The coal rock fracture connection and expansion instability analysis method based on graph theory according to claim 1, characterized in that, In the step S20, the geometric size and direction characteristics of the fracture structure surface are comprehensively considered, the spatial geometric relationship between the fractures is calculated, four topological relationships of intersection, connection, embedding and separation are defined, and the intersection line equation and the intersection line length are further determined, including the following steps: S21: Assuming that the fissure is discoid, the plane equation and the positioning coordinates of the fissure can be obtained from the positioning coordinates of the fissure, the volume radius R and the spatial orientation of the fissure The spherical equation determined by the plane equation, the positioning coordinates and the volume radius R is as follows:​​ Suppose that the plane equation of any two fractures in the space is: S22: From the spatial geometric relationship, the normal vector of the intersection line plane of the two fractures is perpendicular to the normal vector of the plane where the two fractures are located, so the normal vector of the intersection line plane of the two fractures can be obtained; let the normal vector of the intersection line plane of the two fractures be , which satisfies the following formula: That is: S23: Take any point on the intersection line of the two cracks Then the point P is expressed as a function of the variable t, i.e. the equation of the intersection line of the two cracks is: S24: The spherical equation and the intersection line equation are solved together, and the existence condition discriminant of the quadratic equation solution is used to determine whether the straight line and the spherical surface have intersection points. If there are two intersection points, the two intersection points of the fracture intersection line on the fracture are solved, and the spatial topological relationship between the fractures is determined according to the position relationship between the intersection points of the intersection line and the fracture; S25: Since the fracture intersection line is the intersection part of the intersection of the two fracture discs in the geometric space, the intersection line length L is actually the diameter of the intersection line circle, which is determined by the radii R1R2 of the two fracture discs, the distance d between the centers of the two spheres and the geometric relationship of the two spheres, and the expression is: 。 5. The coal rock fracture connection and extension instability analysis method based on graph theory according to claim 1, characterized in that, In the step S20, the fracture breakthrough possibility index BCI is calculated based on the core parameters of the coal rock fracture source, and the specific calculation steps are as follows: The Z-score standardization method is used to convert the data into a standard normal distribution with zero mean and unit variance to standardize the volume of the fracture, and the specific expression is as follows: wherein V is the volume of the i-th fissure, is the mean of all fissure volumes, is the standard deviation of all fissure volumes, is the normalized value of the i-th fissure volume; For any fracture i and j in the fracture network, after determining the spatial topological relationship between the fractures, the fracture breakthrough possibility index calculation formula is as follows: wherein and is the normalized volume value of the i-th fissure and j-th fissure, respectively, is the Euclidean distance between the i-th fissure and j-th fissure; Total transmissibility index of fracture i It should be the sum of the transmissibility indices of all fracture nodes around it that satisfy the transmissibility relationship; where, assuming that there are n transmissive fracture nodes around fracture i, the total transmissibility index of fracture i is The calculation formula is as follows: 。 6. The coal rock fracture connection and extension instability analysis method based on graph theory according to claim 1, characterized in that, In the step S30, the fracture network is generalized into a graph structure based on graph theory; wherein the fracture is taken as a graph node, and the geometric information related to the fracture is distributed to the edge connecting the nodes, the type of the node and the directionality of the edge are defined and classified, and the specific steps include the following steps: S31: After determining the spatial topological relationship between the fractures and identifying the connection relationship, a fracture network topological model for representing the fracture breakthrough is established between the fracture center and the intersection center of the fracture and another fracture, and the fracture network is generalized into a graph structure based on graph theory; S32: The fracture is taken as a graph node, and is divided into I node, T node, Y node, X node and D node according to its topological characteristics, and the total number of edges connected to a node is defined as the degree; S33: The geometric information related to the fracture is distributed to the edge connecting the nodes, and the edge is divided into one-way edge and two-way edge through the fracture breakthrough possibility index BCI, wherein the one-way edge represents that the breakthrough between the fractures is low, indicating that the interaction between the fractures is weak; the two-way edge represents that the breakthrough between the fractures is high, indicating that there is strong interaction between the fractures, which can penetrate each other and form a stable fracture channel.

7. The coal rock fracture connection and extension instability analysis method based on graph theory according to claim 1, characterized in that, In the step S50, the spatial propagation dynamic evolution process of the fracture network is quantitatively described based on the distribution characteristics of the spatial topological attribute parameters, and the specific steps are as follows: S51: Select the three key spatial topological attribute parameters of the spatial distribution of the connectivity index, the spatial distribution of the fracture density and the spatial distribution of the fracture volume, combine the spatial cloud map visualization method, quantitatively depict the spatial evolution characteristics of the fracture network, and reveal the propagation law and evolution trend thereof in different regions; S52: In combination with the time sequence change analysis and the spatial distribution characteristics of the fracture network, five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration and main fracture surface formation are identified to reveal the fracture evolution mechanism in the coal rock instability process.

8. The coal rock fracture connection and expansion instability analysis method based on graph theory according to claim 1, characterized in that, In the step S60, the main fracture surface fracture with high expansion potential is identified in combination with the density clustering and the connectivity index, and a smooth and continuous macro main fracture surface is generated by using a B-spline surface fitting to realize the visualization of the cross-scale evolution of the fracture connection, expansion and penetration to instability, including the following steps: S61: Based on the dynamic graph neural network, a fracture network space-time topological analysis model is constructed to automatically extract discrete isolated fracture data, and the fracture is taken as a graph node; an adjacency graph is constructed by using an edge convolution mechanism through the spatial relationship between nodes, and the node representation is updated by aggregating the neighborhood features to capture the local structure and global topology; S62: Based on the Euclidean distance, the similarity between high-dimensional features of the fracture is calculated, and the DBSCAN algorithm is used for clustering according to the density threshold to classify the fractures with similar features into the same cluster, each cluster represents a crack surface, and a unique number is assigned, and noise points are excluded to reduce interference; in combination with the optimization result of the connectivity index, the main crack surface fracture with high expansion potential is identified; S63: A B-spline surface fitting algorithm is used to reconstruct the main fracture surface to generate a smooth and continuous macro main fracture surface; the principal component analysis method is used to select control points to determine the main direction of the fracture, a B-spline curve is constructed based on the fracture distribution to generate a boundary contour, the external contour line is triangulated and divided into grids, and in combination with the fracture and the triangular grid, the B-spline algorithm is used to accurately fit the fracture surface to reveal the spatial development form of the fracture surface, and realize the visualization of the cross-scale evolution of the fracture connection, expansion and penetration to instability.

9. A coal rock fracture connection and extension instability analysis system based on graph theory, characterized in that, It comprises: A parameter acquisition module configured to acquire original acoustic wave data through a microseismic monitoring system, perform positioning calculation and source mechanism inversion on the original acoustic wave data, and obtain coal rock rupture source core parameters directly related to the rupture; A topological relationship calculation module configured to comprehensively consider the geometric size and direction characteristics of the fracture surface, calculate the spatial geometric relationship between the fractures, define four topological relationships of intersection, connection, embedding and separation, and further determine the intersection line equation and intersection line length; calculate the rupture penetration possibility index BCI based on the coal rock rupture source core parameters; A topological model construction module configured to establish a fracture network topological model for representing the fracture penetration, and generalize the fracture network into a graph structure based on the graph theory; wherein the fracture is taken as a graph node, and the geometric information related to the fracture is distributed to the edge connected to the node, and the type of the node and the directionality of the edge are defined and classified. A fracture time sequence analysis module is configured to obtain fracture network time sequence topological property parameters, quantitatively analyze the stage time-varying trend with coal rock deformation, and determine the mutation key mode and mechanism of local fracture aggregation mutation, fracture penetration mutation, and main fracture surface formation mutation of the coal rock instability fracture network. A fracture space analysis module is configured to quantitatively describe the spatial propagation dynamic evolution process of the fracture network based on the distribution characteristics of the spatial topological property parameters, and identify five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration, and main fracture surface formation. A fracture surface development morphology reconstruction module is configured to construct a fracture space-time topological model based on a dynamic graph neural network, automatically extract discrete fracture data, use edge convolution to construct an adjacency graph and aggregate features, capture local structure and global topology, identify main fracture surfaces with high expansion potential by combining density clustering and penetrability index, and generate a smooth and continuous macro main fracture surface by using B-spline surface fitting, thereby realizing visualization of the cross-scale evolution of fracture connection, expansion and penetration to instability.

10. The coal rock fracture connection and expansion instability analysis system based on graph theory according to claim 9, characterized in that: The parameter acquisition and obtaining module comprises: A data processing unit is configured to post-process the original acoustic wave data collected by the microseismic monitoring system, and extract the first arrival time and amplitude information by using the Akaike information criterion method. A spatial positioning unit is configured to use the first arrival time data of acoustic waves at different position sensors of the microseismic monitoring system, and calculate the spatial positioning of the acoustic emission source by using a simplex positioning robust algorithm. A moment tensor unit is configured to solve 6 components of a seismic source rupture moment tensor based on amplitude data of the first arrival of acoustic waves collected by different position sensors under the constraint of a shear crack rupture source model ; A core parameter unit is configured to quantitatively inverse calculate the coal rock fracture source core parameters, including fracture orientation azimuth and fracture volume, according to the calculated moment tensor components.

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