Coal rock fracture connection and expansion instability analysis method and system based on graph theory

Abstract

The invention discloses a coal rock fracture connection and expansion instability analysis method and system based on a graph theory, and the method comprises the steps: obtaining sound wave data through micro-seismic monitoring, carrying out the positioning calculation and seismic source mechanism inversion, and extracting coal rock fracture core parameters; the method comprises the following steps: comprehensively considering the geometric dimension and direction characteristics of fractures, calculating the spatial geometric relationship between the fractures, defining four topological relationships, and calculating a fracture penetration possibility index BCI; a fracture network topology model is constructed based on a graph theory method, fractures serve as graph nodes, geometric information is distributed to edges, and node types and edge directionality are defined; acquiring space-time topological attribute parameters of the fracture network, quantitatively analyzing a staged time-varying trend of the fracture network along with coal rock deformation and dynamic expansion characteristics of fracture network spatial propagation, and identifying a key mode of abrupt instability and a key stage of fracture spatial expansion; the fracture surface development form reconstruction method based on the graph neural network is provided, and a means is provided for visualizing fracture connection and expanding and penetrating to unstable cross-scale evolution space development form.

Description

Technical Field

[0001] The present invention relates to the field of fracture networks, and in particular to a method and system for analyzing the connection and expansion instability of coal and rock fractures based on graph theory. Background Art

[0002] As the depth of coal mining continues to increase, the development, expansion, nucleation, and evolution of micro-cracks within the rock mass into a cross-scale process of complex fracture networks not only affect the overall stability of the mine structure, but may also induce major engineering disasters such as large-scale collapse of the surrounding rock, rock bursts, and tunnel instability, and further lead to secondary disasters such as coal and gas outbursts, the formation of seepage channels, and groundwater surges. These problems seriously weaken the bearing capacity of the rock mass and increase the risk of chain disaster triggering, becoming a key technical bottleneck for improving the safety and efficiency of deep coal mining resources. Therefore, in-depth research on the fracture connection mechanism and the spatiotemporal dynamic expansion characteristics, revealing how discrete isolated fractures evolve into through-fracture groups, is crucial for the quantitative analysis of coal and rock disasters, risk identification, and mine optimization design, and can provide important theoretical support and engineering guidance for mine safety prevention and control and disaster prediction.

[0003] The formation and evolution of fracture networks is a complex "black box" process, making it difficult to accurately characterize their temporal and spatial development using traditional methods. Microseismic monitoring, as a non-destructive detection technology, provides an effective means of analyzing the dynamic expansion of fracture networks by capturing elastic wave signals released by coal and rock during loading.

[0004] Patent CN118884524A proposes a method for constructing a fracture network model and identifying seepage channels based on microseismic monitoring. The method uses microseismic moment tensors and source parameters to construct a seepage model and identify the main channel with the shortest flow time. However, the high complexity of the fracture network structure makes existing methods face challenges in characterizing its dynamic expansion characteristics and evolution mechanism. Current research is mostly based on probabilistic statistical analysis or fractal theory, using random simulation and numerical analysis to assess rock mass stability. However, it is difficult to accurately describe the topological structure of the fracture network under complex geological conditions, and the influence of fracture geometric parameters on the topological structure of the fracture network is ignored.

[0005] Graph theory methods provide a new research paradigm for topological structure analysis of fracture networks and have become an effective tool for revealing the evolution and dynamic expansion characteristics of fracture networks. Patent CN106991244A proposes a fracture network connectivity and seepage calculation method based on graph theory. By analyzing the trace length and fracture direction of a two-dimensional fracture network, the first-level and second-level connectivity graphs are constructed, and the seepage characteristics of the fracture network are calculated to characterize the connectivity of the fractures. Patent CN119417856A discloses a method for identifying connected damage areas in a complex fracture network. The fracture network adjacency matrix is ​​constructed based on the fracture length, Euclidean distance and width, the degree value and clustering coefficient are calculated, and the fracture connected damage area is identified through the maximum connected area algorithm based on graph theory. The graph theory method abstracts the fracture network into a graph structure, with fractures as nodes and the interaction relationships between fractures as edges. It can simplify the complex representation of the fracture network, help to quantitatively characterize the topological characteristics of the fracture network, the spatial propagation and dynamic expansion process of the fracture, reveal key mutation patterns such as fracture penetration, local fracture aggregation mutation and main fracture surface formation and their action mechanisms, provide theoretical support for the mechanistic analysis of fracture evolution during coal rock instability, and lay a scientific foundation for coal rock structural stability assessment and dynamic instability research. Summary of the Invention

[0006] In response to the problems and needs raised above, this solution proposes a graph-theory-based coal-rock fracture connection and expansion instability analysis method and system. Due to the adoption of the following technical features, it can achieve the above technical objectives and bring about multiple other technical effects.

[0007] An object of the present invention is to propose a method for analyzing the connection and expansion instability of coal and rock fractures based on graph theory, comprising the following steps:

[0008] S10: Acquire raw acoustic wave data through the microseismic monitoring system, perform positioning calculation and focal mechanism inversion on the raw acoustic wave data, and obtain the core parameters of the coal and rock fracture source directly related to the fracture;

[0009] S20: Taking into account the geometric dimensions and directional characteristics of the fracture structure surface, the spatial geometric relationship between fractures is calculated, and four topological relationships, namely, intersection, connection, embedding, and separation, are defined. The intersection equation and intersection length are further determined. The fracture penetration probability index (BCI) is calculated based on the core parameters of the coal and rock fracture source.

[0010] S30: Establish a fracture network topology model for characterizing fracture connectivity, and generalize the fracture network into a graph structure based on graph theory. Fractures are used as graph nodes, and geometric information related to the fractures is assigned to the edges connecting the nodes. The node types and edge directionality are defined and classified.

[0011] S40: Obtain the temporal topological attribute parameters of the fracture network, quantitatively analyze its stage-by-stage temporal variation trend with coal rock deformation, and determine the key mutation modes and action mechanisms of the local fracture aggregation mutation, fracture penetration mutation, and main fracture surface formation mutation of the coal rock instability fracture network;

[0012] S50: Based on the distribution characteristics of spatial topological attribute parameters, quantitatively characterize the dynamic evolution process of spatial propagation of the fracture network and identify the five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration 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, use edge convolution to construct an adjacency graph and aggregate features to capture local structure and global topology; combine density clustering with the connectivity index to identify main fracture surface fractures with high expansion potential, and use B-spline surface fitting to generate a smooth and continuous macroscopic main fracture surface, realizing the cross-scale evolution visualization of fracture connection, expansion and penetration to instability.

[0014] In addition, the graph-theory-based coal-rock fracture connection and expansion 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, performing positioning calculation and focal mechanism inversion on the original acoustic wave data to obtain the core parameters of the focal mechanism directly related to the rupture includes the following steps:

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

[0017] S12: Using the arrival time data of the first wave of the acoustic wave at different sensors in the microseismic monitoring system, the simplex positioning robust algorithm is used to calculate the spatial positioning of the acoustic emission source;

[0018] S13: Based on the constraints of the tensile-shear rupture source model, the six components M of the source rupture moment tensor are solved using the acoustic first wave amplitude data collected by sensors at different locations. pq ;

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

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

[0021] Fracture volume:

[0022]

[0023] Where ΔV is the crack volume, M1 and M3 are the moment tensors M pq The characteristic value of , μ is the Lame constant;

[0024] Orientation:

[0025]

[0026] n=(cosα,0,±sinα)

[0027]

[0028] Where α is the angle between the direction of movement of the earthquake source rupture surface and the normal direction, M1, M2, and M3 are the moment tensors M pq The eigenvalues ​​of , μ and λ are the Lame 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 geometric dimensions and directional 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 equation and intersection length are further determined, including the following steps:

[0030] S21: Assuming the crack is disk-shaped, the crack's location coordinates (x0, y0, z0), volume radius R, and crack spatial orientation (n x ,n y ,n z ), the equation of the plane where the crack is located and the equation of the sphere determined by the positioning coordinates (x0, y0, z0) and the volume radius R are 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] Assume that the plane equation of the plane where any two cracks in space are located is:

[0034]

[0035] S22: From the spatial geometric relationship, we know that the normal vector of the plane of intersection of two cracks is perpendicular to the normal vector of the plane where the two cracks are located. Therefore, the normal vector of the plane of intersection of the cracks can be calculated. Let the normal vector of the intersection plane I = (a, b, c), which satisfies the following formula:

[0036]

[0037] Right now:

[0038]

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

[0040]

[0041] S24: Simultaneously solve the spherical equation and the intersection line equation, and use the discriminant of the existence condition of the quadratic equation solution to determine whether the line and the sphere intersect. If two intersection points exist, solve for the two intersection points of the crack intersection line on the crack. Determine the spatial topological relationship between the cracks based on the positional relationship between the intersection points of the intersection line and the cracks.

[0042] S25: Since the crack intersection line is the circle of the intersection of the two crack disks in geometric space, the intersection line length L is actually the diameter of the intersection circle, which is determined by the radii R1R2 of the two crack disks, the distance d between the sphere centers, 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 rock fracture source, and the specific calculation steps are as follows:

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

[0046]

[0047] Where V i is the volume of the i-th crack, μ V is the mean of all fracture volumes, σ V is the standard deviation of all fracture volumes, Z(V i ) is the normalized value of the i-th crack volume;

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

[0049]

[0050] Where, Z(V i ) and Z(V j ) are the normalized volume values ​​of the i-th crack and the j-th crack, d ij is the Euclidean distance between the i-th crack and the j-th crack;

[0051] The total penetration index (BCI) of crack i i It should be the sum of the connectivity indexes of it and all the surrounding crack nodes that satisfy the connectivity relationship; where, assuming that there are n connected crack nodes around crack i, the total connectivity index BCI 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. Fractures are used as graph nodes, and geometric information related to the fractures is assigned to edges connecting the nodes. The types of nodes and directionality of edges are defined and classified. Specifically, the following steps are included:

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

[0055] S32: Fractures are treated as graph nodes and 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 the spatial topological attribute parameters. The specific steps are:

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

[0058] S52: Combining the temporal variation analysis and spatial distribution characteristics of the fracture network, the 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 during coal rock instability.

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

[0060] S61: A spatiotemporal topology analysis model for fracture networks is constructed based on a dynamic graph neural network. This model automatically extracts discrete isolated fracture data and treats fractures as graph nodes. Using an edge convolution mechanism, an adjacency graph is constructed based on the spatial relationships between nodes. Neighborhood features are aggregated to update node representations, capturing both local structure and global topology.

[0061] S62: The similarity between high-dimensional features of cracks is calculated based on Euclidean distance. The density clustering DBSCAN algorithm is used to cluster according to the density threshold. 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, main crack surface cracks with high expansion potential are identified.

[0062] S63: The main fracture surface is reconstructed using the B-spline surface fitting algorithm to generate a smooth and continuous macroscopic main fracture surface. The main fracture direction is determined by selecting control points using the principal component analysis method. A B-spline curve is constructed based on the fracture distribution to generate the boundary contour. The outer contour line is triangulated and meshed. The fracture surface is accurately fitted using the B-spline algorithm, combining the fracture and triangular mesh. The spatial development morphology of the fracture surface is revealed, and the cross-scale evolution of the fracture from connection to extension and penetration to instability can be visualized.

[0063] Another object of the present invention is to provide a graph theory-based coal-rock fracture connection and expansion instability analysis system, comprising:

[0064] A parameter acquisition module is configured to acquire original acoustic wave data through a microseismic monitoring system, perform positioning calculation and focal mechanism inversion on the original acoustic wave data, and obtain core parameters of the coal and rock fracture source that are directly related to the fracture;

[0065] The topological relationship 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 topological relationships: intersection, connection, embedding, and separation, and further determine the intersection equation and intersection length; calculate the fracture penetration probability index (BCI) based on the core parameters of the coal and rock fracture source;

[0066] A topological model building module is configured to establish a fracture network topological model for characterizing fracture connectivity and generalize the fracture network into a graph structure based on graph theory. Fractures are used as graph nodes, and geometric information related to the fractures is assigned to the edges connecting the nodes. The node types and edge directionality are defined and classified.

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

[0068] The fracture space analysis module is configured to quantitatively characterize the dynamic evolution of the spatial propagation of the fracture network based on the distribution characteristics of spatial topological attribute parameters, and identify the five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration, and main fracture surface formation;

[0069] The fracture surface development morphology reconstruction module is configured to construct a fracture spatiotemporal 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, and capture local structure and global topology; combine density clustering and connectivity index to identify main fracture surface fractures with high expansion potential, and use B-spline surface fitting to generate a smooth and continuous macroscopic main fracture surface, realizing the cross-scale evolution visualization of fracture connection, expansion and penetration to instability.

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

[0071] a data processing unit configured to post-process the raw acoustic wave data collected by the microseismic monitoring system and extract the first wave arrival time and amplitude information using a red-delay information criterion method;

[0072] A spatial positioning unit is configured to utilize the first wave arrival time data of acoustic waves at sensors at different positions of the microseismic monitoring system and adopt a simplex positioning robust algorithm to perform spatial positioning calculation of the acoustic emission source;

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

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

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

[0076] This technical solution uses microseismic monitoring data to invert the earthquake source mechanism, breaking through the traditional description method of fracture location points and achieving accurate characterization of the geometric characteristics and spatial orientation of the complete fracture surface from discrete fracture points. Secondly, the use of source inversion technology can accurately capture the source characteristics of the fracture and dynamically track the occurrence, expansion and penetration of the fracture. This ensures that the topology of the fracture network is more consistent with the actual evolution mechanism, providing high-precision, time-varying data for the dynamic evolution analysis of the fracture network and improving its quantitative characterization capabilities.

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

[0078] This technical solution quantitatively analyzes the spatiotemporal dynamic expansion characteristics of the fracture network by obtaining 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, and identifies the key stages of local fracture aggregation, fracture penetration mutation, and main fracture surface formation, thereby deepening the analysis of the fracture expansion mechanism.

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

[0080] Hereinafter, the best embodiment of the present invention will be described in more detail with reference to the accompanying drawings so that the features and advantages of the present invention can be easily understood. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings of the embodiments of the present invention. The drawings are only used to illustrate some embodiments of the present invention, but not to limit all embodiments of the present invention thereto.

[0082] Figure 1 Flowchart of a method for analyzing coal rock fracture connection and expansion instability based on graph theory according to an embodiment of the present invention;

[0083] Figure 2 Graph showing four types of 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 into a graph structure;

[0085] Figure 4 A node type representation diagram according to an embodiment of the present invention;

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

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

[0088] Figure 7 4 is a flow chart of density clustering and surface fitting according to an embodiment of the present invention. DETAILED DESCRIPTION

[0089] In order to make the purpose, technical solution and advantages of the technical solution of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of specific embodiments of the present invention. The same figure marks in the drawings represent the same parts. It should be noted that the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work 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 persons of ordinary skill in the field to which the invention belongs. The words "first", "second" and similar terms used in the patent application specification and claims of the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Similarly, words such as "a" or "an" do not necessarily indicate a quantity limitation. Words such as "include" or "comprising" mean that the elements or objects preceding the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connected" or "connected" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0091] According to the first aspect of the present invention, a coal rock fracture connection and expansion instability analysis method based on graph theory is as follows: Figure 1 As shown, the following steps are included:

[0092] S10: Acquire raw acoustic wave data through the microseismic monitoring system, perform positioning calculation and focal mechanism inversion on the raw acoustic wave data, and obtain the core parameters of the coal and rock fracture source directly related to the fracture;

[0093] S20: Considering the geometric size and directional characteristics of the crack structure surface, calculate the spatial geometric relationship between the cracks, which is defined as follows: Figure 2 The four topological relationships of intersection, connection, embedding and separation are shown, and the intersection equation and intersection length are further determined; the fracture penetration possibility index (BCI) is calculated based on the core parameters of the coal rock fracture source, namely the fracture volume and the source radius;

[0094] S30: Establish a fracture network topology model for characterizing fracture connectivity and generalize the fracture network into a graph structure based on graph theory. Fractures are treated as graph nodes, and geometric information related to the fractures is assigned to the edges connecting the nodes. Node types and edge directionality are defined and classified to further study the dynamic expansion and evolution of fracture network topology characteristics.

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

[0096] S50: Based on the distribution characteristics of spatial topological attribute parameters such as the permeability index, crack density, and crack volume, the spatial propagation dynamic evolution process of the fracture network is quantitatively characterized, and the five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration, and main fracture surface formation are identified, revealing the fracture evolution mechanism during the instability of coal and rock.

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

[0098] This analysis method uses microseismic monitoring data to invert the focal mechanism, breaking through the traditional description of fracture location points and achieving a precise characterization of the geometric characteristics and spatial orientation of the complete fracture surface from discrete fracture points. Secondly, the source inversion technology can accurately capture the source characteristics of the fracture and dynamically track the occurrence, expansion and penetration of the fracture, ensuring that the topology of the fracture network is more consistent with the actual evolution mechanism. This provides high-precision, time-varying data for the dynamic evolution analysis of the fracture network and improves its quantitative characterization capabilities.

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

[0100] This analysis method quantitatively analyzes the spatiotemporal dynamic expansion characteristics of the fracture network by obtaining 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 the key stages of local fracture aggregation, fracture penetration mutation, and main fracture surface formation, and deepens the analysis of the fracture expansion mechanism.

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

[0102] In one example of the present invention, in step S10, performing positioning calculation and focal mechanism inversion on the original acoustic wave data to obtain the core parameters of the focal mechanism directly related to the rupture includes the following steps:

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

[0104] S12: Using the arrival time data of the first wave of the acoustic wave at different sensors in the microseismic monitoring system, the simplex positioning robust algorithm is used to calculate the spatial positioning of the acoustic emission source;

[0105] S13: Based on the constraints of the tensile-shear rupture source model, the six components M of the source rupture moment tensor are solved using the acoustic first wave amplitude data collected by sensors at different locations. pq ;

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

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

[0108] Fracture volume:

[0109]

[0110] Where ΔV is the crack volume, M1 and M3 are the moment tensors M pq The characteristic value of , μ is the Lame constant;

[0111] Orientation:

[0112]

[0113] n=(cosα,0,±sinα)

[0114]

[0115] Where α is the angle between the direction of movement of the earthquake source rupture surface and the normal direction, M1, M2, and M3 are the moment tensors M pq The eigenvalues ​​of , μ and λ are the Lame 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 geometric dimensions and directional 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 equation and intersection length are further determined, including the following steps:

[0117] S21: Assuming the crack is disk-shaped, the crack's location coordinates (x0, y0, z0), volume radius R, and crack spatial orientation (n x ,n y ,n z ), the equation of the plane where the crack is located and the equation of the sphere determined by the positioning coordinates (x0, y0, z0) and the volume radius R are 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] Assume that the plane equation of the plane where any two cracks in space are located is:

[0121]

[0122] S22: From the spatial geometric relationship, we know that the normal vector of the plane of intersection of two cracks is perpendicular to the normal vector of the plane where the two cracks are located. Therefore, the normal vector of the plane of intersection of the cracks can be calculated. Let the normal vector of the intersection plane I = (a, b, c), which satisfies the following formula:

[0123]

[0124] Right now:

[0125]

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

[0127]

[0128] S24: Simultaneously solve the spherical equation and the intersection line equation, and use the discriminant of the existence condition of the quadratic equation solution to determine whether the line and the sphere intersect. If two intersection points exist, solve for the two intersection points of the crack intersection line on the crack. Determine the spatial topological relationship between the cracks based on the positional relationship between the intersection points of the intersection line and the cracks.

[0129] Assuming that the intersection points of the intersection line with crack 1 are Ⅰ1 and Ⅰ2, and the intersection points with crack 2 are Ⅱ1 and Ⅱ2, the spatial topological relationship between the cracks can be obtained according to the positional relationship between Ⅰ1, Ⅰ2 and Ⅱ1, Ⅱ2: when Ⅰ1 and Ⅱ1, Ⅰ2 and Ⅱ2 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 Ⅰ1 and Ⅰ2 are sandwiched between Ⅱ1 and Ⅱ2, the two cracks are embedded; 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 crack intersection line is the circle of the intersection of the two crack disks in geometric space, the intersection line length L is actually the diameter of the intersection circle, which is determined by the radii R1R2 of the two crack disks, the distance d between the sphere centers, 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 rock fracture source, and the specific calculation steps are as follows:

[0133] In order to eliminate the scale differences of different fracture volumes, the Z-score normalization method was used to convert the data into a standard normal distribution with zero mean and unit variance to standardize the fracture volume. The specific expression is as follows:

[0134]

[0135] Where V i is the volume of the i-th crack, μ V is the mean of all fracture volumes, σ V is the standard deviation of all fracture volumes, Z(V i ) is the normalized value of the i-th crack volume;

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

[0137]

[0138] Where, Z(V i ) and Z(V j ) are the normalized volume values ​​of the i-th crack and the j-th crack, d ij is the Euclidean distance between the i-th crack and the j-th crack;

[0139] In other words, according to the spatial topological relationship between the above cracks, it is judged that the three types of intersection, connection and embedding satisfy the penetration relationship, that is, the three relationships of intersection, connection and embedding are judged as the penetration relationship and then the fracture penetration possibility index is calculated.

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

[0141]

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

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

[0144] S32: Fractures are treated as graph nodes and are classified into I-nodes, T-nodes, Y-nodes, X-nodes, and D-nodes based on their topological characteristics. The total number of edges connected to a node is defined as the 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 fractures (such as spatial orientation, intersection length, aperture, and volume) is assigned to edges connecting nodes. Edges are classified into unidirectional and bidirectional edges using the fracture penetration probability index (BCI). Unidirectional edges indicate low inter-fragmentation and weak inter-fragmentation interactions; bidirectional edges indicate high inter-fragmentation and strong inter-fragmentation interactions, allowing them to interpenetrate and form stable fracture pathways. The rules for defining edge directionality are shown in Table 2.

[0148] Table 2 Edge directionality definition rules

[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 the phased temporal variation trend thereof along with the coal rock deformation is quantitatively analyzed, specifically including:

[0152] Select key temporal topological attribute parameters, calculate the temporal changes of topological parameters to obtain time series data and draw time series curves, identify the mutation points in the time series curves, determine the key mutation modes and action mechanisms of the local crack aggregation mutation, crack penetration mutation, main crack surface formation mutation, etc. of the coal rock instability crack network, and then identify the precursor signals of coal rock instability. Among them, the key topological attribute parameters are selected as follows:

[0153] ① Node type: Analyze the trend of the number and proportion of five node types, namely I-node, T-node, Y-node, X-node, and D-node (i.e., the ratio of the number of each node type to the total number of node types) in the fracture network topology analysis model as the coal and rock deformation progresses.

[0154] ②Edge type: Each edge in the fracture network topology analysis model 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, and 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 to show their stage-by-stage change trend with coal rock deformation.

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

[0156] ④ Network density: This is the ratio of the number of edges in a fracture network to the maximum number of edges it can accommodate. It describes the density of edges between nodes in the network and indicates the density of fracture distribution. As fractures expand, the network density gradually increases. When a certain threshold is reached, the fractures may become interconnected, forming a primary crack.

[0157]

[0158] Where N e is the total number of edges in the fracture network, and N is the total number of nodes.

[0159] ⑤ Clustering coefficient: The clustering coefficient is a measure of the degree of clustering between 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 compactness of the local network structure around the node. The global clustering coefficient C is the average of the local clustering coefficients of all nodes. It measures the degree of clustering of all nodes in the graph and reflects the compactness of the global structure of the fracture network. If the clustering coefficient suddenly increases within a certain period of time, it indicates that the fractures are concentrated in a local area, which may form a high stress concentration area.

[0160]

[0161] Where, E v is the actual number of edges between node v’s neighbor nodes, k v is the degree of node v, and N is the total number of nodes in the graph.

[0162] ⑥ Cumulative aperture: Analyze the stage-by-stage change trend of the sum of the apertures of all nodes in the fracture network as the coal rock deforms.

[0163] ⑦ Interpenetration Index: Analyzes the trend of the sum of the fracture and interpenetration probability indices of all nodes in the fracture network as the coal rock deforms. If the sum of the interpenetration indices increases sharply over a certain period of time, it indicates that the fracture interpenetration has suddenly increased, and the coal rock may enter the 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 the spatial topological attribute parameters. The specific steps are:

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

[0166] S52: Combining the temporal variation analysis and spatial distribution characteristics of the fracture network, the 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 during coal rock instability.

[0167] Among them, the key spatial topological attribute parameters are selected as follows:

[0168] ① Spatial distribution of the BCI: The BCI of each fracture is calculated and interpolated in three-dimensional space to generate a BCI distribution cloud map, which uses a color gradient to represent the BCI of different fracture regions. High BCI areas indicate that fractures may be connected, while low BCI areas indicate that fractures are still isolated or in the initial stage of initiation, and their contribution to overall connectivity is relatively small.

[0169] ② Spatial distribution of crack density: A three-dimensional grid-based statistical method was used to calculate the crack density distribution. The study area was divided into small volume units. The number of cracks within each unit was counted, and a crack density distribution cloud map was drawn. The color gradient indicates the density of cracks in different areas. Among them, areas with high crack density indicate areas of stress concentration or active rupture, while areas with low crack density indicate that rupture may not have extended to that area.

[0170] ③ Spatial distribution of crack volume: Calculate the volume of each crack and generate a crack volume distribution cloud map through interpolation. The color gradient represents the size distribution of the crack volume. By analyzing the spatial distribution of the crack volume, high-volume crack areas can be identified. These areas are often locations where stress is concentrated and fracture expansion is strong, and may become part of the main fracture surface; low-volume crack areas may be in the early stages of fracture or the stage where the cracks have not yet expanded. Secondly, combined with the crack density analysis, the crack expansion pattern can be judged. If the crack density is high and the volume is small, it means that the crack expansion is uniformly distributed, the fracture process is relatively slow, and no obvious penetration trend has yet formed; if the crack density is low but the volume is large, it means that the cracks mainly occur in certain local areas and the fracture scale is large, which may indicate that the cracks are about to penetrate to 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 in the figure, density clustering and penetration index are combined to identify the main fracture surface cracks with high expansion potential, and B-spline surface fitting is used to generate a smooth and continuous macroscopic main fracture surface, realizing the cross-scale evolution visualization of fracture connection, expansion and penetration to instability, including the following steps:

[0172] S61: A fracture network spatiotemporal topology analysis model is constructed based on a dynamic graph neural network (DGCNN). Discrete isolated fracture data are automatically extracted, and fractures are treated as graph nodes. Edges include spatial coordinates, connectivity index, and spatial orientation. An edge convolution mechanism is used to construct an adjacency graph based on the spatial relationship between nodes, and neighborhood features are aggregated to update node representations, capturing local structure and global topology. Parameters are optimized by minimizing the loss function, and the model outputs a high-dimensional feature vector that comprehensively reflects spatiotemporal associations, physical connectivity, and topological structure.

[0173] S62: The similarity between high-dimensional features of cracks is calculated based on Euclidean distance. The density clustering DBSCAN algorithm is used to cluster according to the density threshold. 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, main crack surface cracks with high expansion potential are identified.

[0174] S63: The main fracture surface is reconstructed using the B-spline surface fitting algorithm to generate a smooth and continuous macroscopic main fracture surface. The main fracture direction is determined by selecting control points using the principal component analysis method. A B-spline curve is constructed based on the fracture distribution to generate the boundary contour. The outer contour line is triangulated and meshed. The fracture surface is accurately fitted using the B-spline algorithm, combining the fracture and triangular mesh. The spatial development morphology of the fracture surface is revealed, and the cross-scale evolution of the fracture from connection to extension and penetration to instability can be visualized.

[0175] According to a second aspect of the present invention, a graph theory-based coal-rock fracture connection and expansion instability analysis system comprises:

[0176] A parameter acquisition module is configured to acquire original acoustic wave data through a microseismic monitoring system, perform positioning calculation and focal mechanism inversion on the original acoustic wave data, and obtain core parameters of the coal and rock fracture source that are directly related to the fracture;

[0177] The topological relationship 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 topological relationships: intersection, connection, embedding, and separation, and further determine the intersection equation and intersection length; calculate the fracture penetration probability index (BCI) based on the core parameters of the coal rock fracture source: fracture volume and source radius;

[0178] A topological model building module is configured to establish a fracture network topology model for characterizing fracture connectivity and generalize the fracture network into a graph structure based on graph theory. Fractures are represented as graph nodes, and geometric information related to the fractures is assigned to the edges connecting the nodes. Node types and edge directionality are defined and classified to further study the dynamic expansion and evolution of fracture network topological characteristics.

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

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

[0181] The fracture surface development morphology reconstruction module is configured to construct a fracture spatiotemporal 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, and capture local structure and global topology; combine density clustering and connectivity index to identify main fracture surface fractures with high expansion potential, and use B-spline surface fitting to generate a smooth and continuous macroscopic main fracture surface, realizing the cross-scale evolution visualization of fracture connection, expansion and penetration to instability.

[0182] This analysis system uses microseismic monitoring data to perform focal mechanism inversion, breaking through the traditional description of fracture location points and achieving a precise characterization of the geometric characteristics and spatial orientation of the complete fracture surface from discrete fracture points. Secondly, with the help of source inversion technology, it can accurately capture the source characteristics of the fracture and dynamically track the occurrence, expansion and penetration of the fracture, ensuring that the topology of the fracture network is more consistent with the actual evolution mechanism. This provides high-precision, time-varying data for the dynamic evolution analysis of the fracture network and improves its quantitative characterization capabilities.

[0183] This analysis system constructs a fracture network topology analysis model based on graph theory. It abstracts fractures as nodes in a graph and assigns their geometric parameters to edges. This systematically characterizes the topological relationships between fractures, thereby improving the quantitative description of fracture connectivity. By defining node types and edge directionality, it accurately depicts the connectivity and topological changes of fractures at different evolutionary stages, enabling dynamic tracking of fracture network structures from initial formation to expansion and connectivity.

[0184] This analysis system obtains temporal topological parameters of the fracture network, such as connection type, network density, clustering coefficient, and connectivity index, as well as spatial topological parameters such as fracture density and fracture volume, to quantitatively analyze the spatiotemporal dynamic expansion characteristics of the fracture network, identify the key stages of local fracture aggregation, fracture penetration mutation, and main fracture surface formation, and deepen the analysis of the fracture expansion mechanism.

[0185] This analysis system proposes a method for reconstructing the development morphology of fracture surfaces based on graph neural networks, and constructs a fracture expansion evolution identification and quantitative characterization based on a fracture network model. It can reconstruct the geometric morphology and dynamic evolution characteristics of the fracture surface with high precision, and realize the cross-scale evolution visualization of fractures from connection, expansion and penetration to instability, further revealing 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] a data processing unit configured to post-process the raw acoustic wave data collected by the microseismic monitoring system and extract the first wave arrival time and amplitude information using a red-delay information criterion method;

[0188] A spatial positioning unit is configured to utilize the first wave arrival time data of acoustic waves at sensors at different positions of the microseismic monitoring system and adopt a simplex positioning robust algorithm to perform spatial positioning calculation of the acoustic emission source;

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

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

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

[0192] The above describes in detail an exemplary implementation of the graph theory-based coal rock fracture connection and expansion instability analysis method and system proposed in the present invention with reference to the preferred embodiments. However, those skilled in the art will understand that, without departing from the concept of the present invention, various modifications and variations can be made to the above-mentioned specific embodiments, and various technical features and structures proposed in the present invention can be combined in various ways without exceeding the scope of protection of the present invention, which is determined by the appended claims.

Claims

1. A graph theory-based coal rock fracture connection and expansion instability analysis method, characterized by: The steps include: S10: Acquire raw acoustic wave data through the microseismic monitoring system, perform positioning calculation and focal mechanism inversion on the raw acoustic wave data, and obtain the core parameters of the coal and rock fracture source directly related to the fracture; S20: Taking into account the geometric dimensions and directional characteristics of the fracture structure surface, the spatial geometric relationship between fractures is calculated, and four topological relationships, namely, intersection, connection, embedding, and separation, are defined. The intersection equation and intersection length are further determined. The fracture penetration probability index (BCI) is calculated based on the core parameters of the coal and rock fracture source. S30: Establish a fracture network topology model for characterizing fracture connectivity, and generalize the fracture network into a graph structure based on graph theory. Fractures are used as graph nodes, and geometric information related to the fractures is assigned to the edges connecting the nodes. The node types and edge directionality are defined and classified. S40: Obtain the temporal topological attribute parameters of the fracture network, quantitatively analyze its stage-by-stage temporal variation trend with coal rock deformation, and determine the key mutation modes and action mechanisms of the 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 spatial topological attribute parameters, quantitatively characterize the dynamic evolution process of spatial propagation of the fracture network and identify the five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration and main fracture surface formation; S60: Construct a spatiotemporal topological model of fractures based on dynamic graph neural networks, automatically extract discrete fracture data, use edge convolution to construct an adjacency graph and aggregate features to capture local structure and global topology; combine density clustering with the connectivity index to identify main fracture surface fractures with high expansion potential, and use B-spline surface fitting to generate a smooth and continuous macroscopic main fracture surface, realizing the cross-scale evolution visualization of fracture connection, expansion and penetration to instability.

2. The graph theory-based coal-rock fracture connection and expansion instability analysis method according to claim 1, characterized in that: In step S10, positioning calculation and focal mechanism inversion are performed on the original acoustic wave data to obtain the core parameters of the focal mechanism directly related to the rupture, including the following steps: S11: Post-process the raw acoustic wave data collected by the microseismic monitoring system and extract the first wave arrival time and amplitude information using the red delay information criterion method; S12: Using the arrival time data of the first wave of the acoustic wave at different sensors in the microseismic monitoring system, the simplex positioning robust algorithm is used to calculate the spatial positioning of the acoustic emission source; S13: Based on the constraints of the tensile-shear rupture source model, the six components M of the source rupture moment tensor are solved using the acoustic first wave amplitude data collected by sensors at different locations. pq ; S14: quantitatively invert and calculate the core parameters of the coal rock fracture source based on the calculated moment tensor components, wherein the core parameters of the coal rock fracture source include fracture orientation and fracture volume.

3. The graph-theory-based coal-rock fracture connection and expansion instability analysis method according to claim 2, characterized in that: In step S14, the specific calculation formula of the core parameters of the coal rock fracture source is as follows: Fracture volume: Where ΔV is the crack volume, M1 and M3 are the moment tensors M pq The characteristic value of , μ is the Lame constant; Orientation: n=(cosα,0,±sinα) Where α is the angle between the direction of movement of the earthquake source rupture surface and the normal direction, M1, M2, and M3 are the moment tensors M pq The eigenvalues ​​of , μ and λ are the Lame constants, n is the spatial orientation, and b is the direction of motion.

4. The graph-theory-based coal-rock fracture connection and expansion instability analysis method according to claim 1, characterized in that: In step S20, the geometric dimensions and directional characteristics of the crack structure surface are comprehensively considered, the spatial geometric relationship between the cracks is calculated, four topological relationships of intersection, connection, embedding, and separation are defined, and the intersection equation and intersection length are further determined, including the following steps: S21: Assuming the crack is disk-shaped, the crack's location coordinates (x0, y0, z0), volume radius R, and crack spatial orientation (n x ,n y ,n z ), the equation of the plane where the crack is located and the equation of the sphere determined by the positioning coordinates (x0, y0, z0) and the volume radius R are as follows: n x (x-x0)+n y (y-y0)+n z (z-z0)=0 (x-x0) 2 +(y-y0) 2 +(z-z0) 2 =R 2 Assume that the plane equation of the plane where any two cracks in space are located is: S22: From the spatial geometric relationship, we know that the normal vector of the plane of intersection of two cracks is perpendicular to the normal vector of the plane where the two cracks are located. Therefore, the normal vector of the plane of intersection of the cracks can be calculated. Let the normal vector of the intersection plane I = (a, b, c), which satisfies the following formula: Right now: S23: Take any point P(x p ,y p ,z p ), then point P is expressed as a function of the variable t, that is, the intersection equation of the two cracks is: S24: Simultaneously solve the spherical equation and the intersection line equation, and use the discriminant of the existence condition of the quadratic equation solution to determine whether the line and the sphere intersect. If two intersection points exist, solve for the two intersection points of the crack intersection line on the crack. Determine the spatial topological relationship between the cracks based on the positional relationship between the intersection points of the intersection line and the cracks. S25: Since the crack intersection line is the circle of the intersection of the two crack disks in geometric space, the intersection line length L is actually the diameter of the intersection circle, which is determined by the radii R1R2 of the two crack disks, the distance d between the sphere centers, and the geometric relationship between the two spheres. Its expression is:

5. The graph theory-based coal-rock fracture connection and expansion instability analysis method according to claim 1, characterized in that: In step S20, the fracture penetration probability index BCI is calculated based on the core parameters of the coal rock fracture source. The specific calculation steps are as follows: The Z-score normalization method is used to transform the data into a standard normal distribution with zero mean and unit variance to standardize the volume of the cracks. The specific expression is as follows: Where V i is the volume of the i-th crack, μ V is the mean of all fracture volumes, σ V is the standard deviation of all fracture volumes, Z(V i ) is the normalized value of the i-th crack volume; For any fractures i and j in the fracture network, after determining that the spatial topology between the fractures has a connection relationship, the calculation formula for the fracture penetration probability index is as follows: Where, Z(V i ) and Z(V j ) are the normalized volume values ​​of the i-th crack and the j-th crack, d ij is the Euclidean distance between the i-th crack and the j-th crack; The total penetration index (BCI) of crack i i It should be the sum of the connectivity indexes of it and all the surrounding crack nodes that satisfy the connectivity relationship; where, assuming that there are n connected crack nodes around crack i, the total connectivity index BCI i The calculation formula is as follows:

6. The graph-theory-based coal-rock fracture connection and expansion instability analysis method according to claim 1, characterized in that: In step S30, the fracture network is generalized into a graph structure based on graph theory. Fractures are used as graph nodes, and geometric information related to the fractures is assigned to the edges connecting the nodes. The types of nodes and the directionality of edges are defined and classified. Specifically, the following steps are included: S31: After determining the spatial topological relationship between the cracks and identifying their connection relationship, a crack network topological model for characterizing the crack penetration is established between the crack center and the center of the intersection line between the crack and another crack, and the crack network is generalized into a graph structure based on graph theory. S32: Fractures are treated as graph nodes and 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. S33: The geometric information related to the cracks is assigned to the edges connecting the nodes, and the edges are divided into unidirectional edges and bidirectional edges through the fracture penetration probability index (BCI). Unidirectional edges indicate low penetration between cracks, indicating weak interaction between cracks; bidirectional edges represent high penetration between cracks, indicating strong interaction between cracks, which can penetrate each other and form stable crack channels.

7. The graph-theory-based coal-rock fracture connection and expansion instability analysis method according to claim 1, characterized in that: In step S50, based on the distribution characteristics of the spatial topological attribute parameters, the spatial propagation dynamic evolution process of the fracture network is quantitatively described. The specific steps are: S51: We select three key spatial topological attribute parameters, namely the spatial distribution of the connectivity index, the spatial distribution of the fracture density, and the spatial distribution of the fracture volume, and combine them with spatial cloud visualization methods to quantitatively characterize the spatial evolution characteristics of the fracture network and reveal its propagation patterns and evolution trends in different regions. S52: Combining the temporal variation analysis and spatial distribution characteristics of the fracture network, the 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 during coal rock instability.

8. The graph-theory-based coal-rock fracture connection and expansion instability analysis method according to claim 1, characterized in that: In step S60, density clustering and the penetration index are combined to identify main fracture surface cracks with high expansion potential, and B-spline surface fitting is used to generate a smooth and continuous macroscopic main fracture surface to realize the cross-scale evolution visualization of fracture connection, expansion and penetration to instability, including the following steps: S61: A spatiotemporal topology analysis model for fracture networks is constructed based on a dynamic graph neural network. This model automatically extracts discrete isolated fracture data and treats fractures as graph nodes. Using an edge convolution mechanism, an adjacency graph is constructed based on the spatial relationships between nodes. Neighborhood features are aggregated to update node representations, capturing both local structure and global topology. S62: The similarity between high-dimensional features of cracks is calculated based on Euclidean distance. The density clustering DBSCAN algorithm is used to cluster according to the density threshold. 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, main crack surface cracks with high expansion potential are identified. S63: The main fracture surface is reconstructed using the B-spline surface fitting algorithm to generate a smooth and continuous macroscopic main fracture surface. The main fracture direction is determined by selecting control points using the principal component analysis method. A B-spline curve is constructed based on the fracture distribution to generate the boundary contour. The outer contour line is triangulated and meshed. The fracture surface is accurately fitted using the B-spline algorithm, combining the fracture and triangular mesh. The spatial development morphology of the fracture surface is revealed, and the cross-scale evolution of the fracture from connection to extension and penetration to instability can be visualized.

9. A graph theory-based coal rock fracture connection and expansion instability analysis system, characterized by: include: A parameter acquisition module is configured to acquire original acoustic wave data through a microseismic monitoring system, perform positioning calculation and focal mechanism inversion on the original acoustic wave data, and obtain core parameters of the coal and rock fracture source that are directly related to the fracture; The topological relationship 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 topological relationships: intersection, connection, embedding, and separation, and further determine the intersection equation and intersection length; calculate the fracture penetration probability index (BCI) based on the core parameters of the coal and rock fracture source; A topological model building module is configured to establish a fracture network topological model for characterizing fracture connectivity and generalize the fracture network into a graph structure based on graph theory. Fractures are used as graph nodes, and geometric information related to the fractures is assigned to the edges connecting the nodes. The node types and edge directionality are defined and classified. The fracture time series analysis module is configured to obtain the time series topological attribute parameters of the fracture network, quantitatively analyze its stage-by-stage time-varying trend with coal rock deformation, and determine the key mutation modes and action mechanisms of the local fracture aggregation mutation, fracture penetration mutation, and main fracture surface formation mutation of the coal rock instability fracture network; The fracture space analysis module is configured to quantitatively characterize the dynamic evolution of the spatial propagation of the fracture network based on the distribution characteristics of spatial topological attribute parameters, and identify the five key stages of fracture initiation, local fracture aggregation, fracture expansion, fracture penetration, and main fracture surface formation; The fracture surface development morphology reconstruction module is configured to construct a fracture spatiotemporal 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, and capture local structure and global topology; combine density clustering and connectivity index to identify main fracture surface fractures with high expansion potential, and use B-spline surface fitting to generate a smooth and continuous macroscopic main fracture surface, realizing the cross-scale evolution visualization of fracture connection, expansion and penetration to instability.

10. The graph theory-based coal-rock fracture connection and expansion instability analysis system according to claim 9, characterized in that: The parameter acquisition module includes: a data processing unit configured to post-process the raw acoustic wave data collected by the microseismic monitoring system and extract the first wave arrival time and amplitude information using a red-delay information criterion method; A spatial positioning unit is configured to utilize the first wave arrival time data of acoustic waves at sensors at different positions of the microseismic monitoring system and adopt a simplex positioning robust algorithm to perform spatial positioning calculation of the acoustic emission source; The moment tensor unit is configured to solve the six components M of the source rupture moment tensor based on the acoustic first wave amplitude data collected by sensors at different positions under the constraints of the tension-shear rupture source model. pq ; The core parameter unit is configured to quantitatively inversely calculate the core parameters of the coal rock fracture source based on the calculated moment tensor components, wherein the core parameters of the coal rock fracture source include fracture orientation and fracture volume.

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