Method and system for analyzing progressive instability mode of rock block system based on complex network

Abstract

The invention discloses a method and a system for analyzing a progressive instability mode of a rock block system based on a complex network. The method comprises the following steps: determining an adjacent relation between rock blocks through rough detection and fine detection of a bounding box; analyzing potential instability modes of the single block, including falling instability, single-sided slippage instability and double-sided slippage instability, and calculating corresponding safety coefficients; a potential instability network of the block system is constructed, rock blocks and potential instability modes thereof are expressed as network nodes, and the influence relation between the rock blocks is expressed as directed edges; and an unstable block and adjacent rocks thereof are identified through iteration, an actual instability network is constructed, and the instability sequence and hierarchy are determined. According to the method, the progressive instability process of the rock system can be efficiently and accurately predicted through the complex network model, and the problems that a traditional method is high in calculation cost, and instability sequence and hierarchy are difficult to reflect are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of geotechnical engineering and complex system analysis, and particularly relates to a method and a system for analyzing the progressive instability mode of a rock block system based on complex network analysis. Background Art

[0002] A rock mass is a complex natural system composed of rocks and structural planes, and its stability assessment is a key issue in geological engineering projects (such as underground engineering, tunnel engineering, slope engineering, and mineral mining, etc.). The instability of a rock mass system usually shows progressive instability, also known as chain reaction, that is, after the surface rock blocks are unstable, the adjacent internal rock blocks lose support, and then larger-scale instability is triggered. Traditional rock mass stability analysis mainly focuses on the mechanical properties of individual blocks, such as precise mechanical analysis and exploration of instability modes. However, with the in-depth understanding of the failure behavior of rock masses, researchers have found that analyzing the stability of only individual rock blocks is not sufficient to comprehensively evaluate the overall stability of the rock mass system, and the connection relationship and interaction between rock blocks also need to be considered.

[0003] At present, although common methods such as the discrete element method can perform overall mechanical analysis on the block system, there are problems such as high computational cost and difficulty in reflecting the orderliness and hierarchy of instability. Therefore, there is an urgent need for an efficient and accurate method to analyze the progressive instability mode of the rock mass system to better predict and evaluate the stability of the rock mass system. Summary of the Invention

[0004] Aiming at the defects of the prior art, the present invention provides a method and a system for analyzing the progressive instability mode of a rock block system based on complex network analysis.

[0005] In order to achieve the above invention purposes, the technical solutions adopted by the present invention are as follows:

[0006] A method for analyzing the progressive instability mode of a rock block system based on complex network analysis, comprising the following steps:

[0007] Detect the adjacent relationship of the block system, and determine the adjacent relationship between rock blocks based on rough inspection of the bounding box and fine inspection of the intersecting bounding boxes;

[0008] Analyze the potential instability mode of a single block, calculate the dot product of the resultant external driving force and the unit normal vector of the non-free face, and judge the falling instability mode according to the dot product value;

[0009] For non-free faces that meet the conditions of hindering falling instability, calculate the single-sided slip and double-sided slip instability modes.

[0010] Construct a potential instability network of the block system, represent the rock blocks and their potential instability modes as network nodes, and represent the influence relationship between rock blocks through the instability mode as a directed edge.

[0011] Construct the actual instability network of the block system, and identify the unstable blocks and their adjacent rock blocks through iteration to gradually determine the order and hierarchy of instability.

[0012] Further, the calculation of the single-sided slip direction includes: calculating the cross product of the resultant external driving force and the unit normal vector of the structural plane, and calculating the potential slip direction based on the cross product vector.

[0013] Further, the nodes of the potential instability network include: nodes representing rock blocks and nodes representing the instability modes of rock blocks.

[0014] Further, extract the instability modes of each rock block from the potential instability network, sort them according to the safety factor, and gradually check whether the rock block is unstable due to this instability mode.

[0015] Further, the analysis of the potential instability mode of a single block includes: calculating the dot product of the resultant external driving force and the unit normal vector of the non-free face, and the formula is:

[0016] D i = r·n i

[0017] where i is the serial number of the non-free face, and D i represents the dot product of the driving force and the inward unit normal vector of the i-th non-free face, r is the unit vector of the resultant external driving force, and n i is the inward unit normal vector of the i-th non-free face;

[0018] When D i < 0, this face will prevent the rock block from falling and may serve as a potential slip surface for single-sided or double-sided slip.

[0019] Further, the formula for calculating the potential single-sided slip direction s i is:

[0020]

[0021] where i is the serial number of the non-free face, n i is the inward unit normal vector of the i-th structural plane, r is the unit vector of the resultant external driving force, × represents the cross product operation, and ∣·∣ represents the modulus of the vector.

[0022] Further, the formula for calculating the slip direction s ij of the potential double-sided slip is:

[0023]

[0024] where both i and j are the serial numbers of the non-free faces, n i and n jThey are the inward unit normal vectors of the $i$-th and $j$-th structural planes respectively, and $r$ is the unit vector of the resultant external driving force. $\text{sign}()$ is a sign function that satisfies:

[0025] If $x > 0$, $\text{sign}(x)=1$

[0026] If $x = 0$, $\text{sign}(x)=0$

[0027] If $x < 0$, $\text{sign}(x)= - 1$.

[0028] Furthermore, the formula for calculating the safety factor $F$ s for single-plane sliding is:

[0029]

[0030] where $i$ is the non-free-face serial number, $n$ i is the inward unit normal vector of the $i$-th plane, $r$ is the unit vector of the resultant external driving force, and $\varphi_i$

[0031] is the internal friction angle corresponding to the $i$-th plane. s Furthermore, the formula for calculating the safety factor $F$

[0032]

[0033] for double-plane sliding is: i where $i$ and $j$ are both non-free-face serial numbers, $N$ j and $N$ and are the anti-sliding force vectors corresponding to the $i$-th and $j$-th structural planes respectively,

[0034] Furthermore, the formulas for calculating $N$ i and $N$ j and $T$ are:

[0035]

[0036] where $n$ i and $n$ j are the inward unit normal vectors of the $i$-th and $j$-th structural planes respectively, and $r$ is the unit vector of the resultant external driving force.

[0037] Furthermore, the method uses the Gephi tool for network visualization and analysis to display the potential instability network and actual instability network of the block system.

[0038] The present invention also discloses a system for analyzing the progressive instability mode of a rock block system based on complex networks. This system can be used to implement the method for analyzing the progressive instability mode of a rock block system based on complex networks. Specifically, it includes:

[0039] An adjacent relationship detection module, which is used to detect the adjacent relationship of the block system. By performing a rough check using bounding boxes and a detailed check on the intersecting bounding boxes, the adjacent relationship between rock blocks is determined;

[0040] A potential instability mode analysis module, which is used to analyze the potential instability mode of a single block. Calculate the dot product of the resultant external driving force and the unit normal vector of the non-free face, and judge the falling instability according to the dot product value; for the non-free face that meets the falling instability condition, further calculate the single-sided slip and double-sided slip instability modes;

[0041] A potential instability network construction module, which is used to construct the potential instability network of the block system. Represent the rock blocks and their potential instability modes as network nodes, and represent the influence relationship between rock blocks through the instability mode as a directed edge;

[0042] An actual instability network construction module, which is used to construct the actual instability network of the block system. By iteratively identifying the unstable blocks and their adjacent rock blocks, gradually determine the order and level of instability;

[0043] An instability mode prediction and visualization module, which is used to predict the progressive instability mode of the block system based on the actual instability network, and display the instability process and the key instability path through a visualization tool.

[0044] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the method for analyzing the progressive instability mode of a rock block system based on complex networks.

[0045] The present invention also discloses a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the method for analyzing the progressive instability mode of a rock block system based on complex networks.

[0046] Compared with the prior art, the advantages of the present invention are as follows:

[0047] 1. Systematic analysis framework: The present invention provides a systematic analysis framework by detecting the adjacent relationship of the block system, analyzing the potential instability mode of a single block, constructing the potential instability network and the actual instability network, which can comprehensively evaluate the instability behavior of the rock block system, especially the progressive instability mode.

[0048] 2. High efficiency and reliability: Compared with traditional methods such as the discrete element method, the present invention avoids complex iterative calculations, significantly improves the analysis efficiency, and can more intuitively reflect the sequentiality and hierarchy of rock mass instability through a complex network model.

[0049] 3. Prediction of instability mode: By constructing a potential instability network and an actual instability network, the present invention can effectively predict the instability process of the rock block system, identify the unstable block clusters and their mutual relationships, providing a scientific basis for the evaluation of rock mass stability.

[0050] 4. Visualization and practicality: The present invention combines network visualization tools such as Gephi to intuitively display the instability network of the rock block system, helping engineering and technical personnel better understand the propagation mechanism of rock mass instability and enhancing the practicality and operability of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the AABB bounding box of the embodiment of the present invention;

[0052] Figure 2 It is a flowchart of the analysis of the potential instability mode of a single block in the embodiment of the present invention;

[0053] Figure 3 It is a network structure diagram of potential unstable blocks and instability modes of the rock block system generated by Gephi in the embodiment of the present invention;

[0054] Figure 4 It is a flowchart of the analysis of the actual unstable blocks and instability modes network in the embodiment of the present invention;

[0055] Figure 5 It is the actual instability network of the rock block system generated by Gephi in the embodiment of the present invention. (a) Block 0, unstable blocks and instability mode network. (b) Unstable blocks and instability mode network. (c) Unstable block network. DETAILED DESCRIPTION OF THE INVENTION

[0056] To make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the following further elaborates on the present invention with reference to the drawings and by way of examples.

[0057] The present invention provides a systematic framework for analyzing the progressive instability of a rock mass system and evaluating the stability of a rock block system. This process starts with the detection of adjacent rock blocks and then analyzes the potential failure modes of individual rock blocks. Next, the stability of the system is evaluated by constructing potential and actual failure networks and identifying unstable block clusters. The detection of adjacent blocks and the analysis of the instability mode of a single block are the basis for constructing the instability network of the block system. Therefore, it is necessary to first obtain the geometric parameters of a single block and the mechanical parameters of the structural planes.

[0058] The method for analyzing the progressive instability mode of a rock block system based on complex networks according to the present invention comprises the following steps:

[0059] (1) Parameter preparation

[0060] The input single-block geometric parameters include the vertex, edge, face, and volume data of each rock block, and the latter three geometric elements need to include direction attributes:

[0061] (a) Directed edge: Composed of two vertices, and the direction of the edge points from the starting point to the ending point.

[0062] (b) Directed face: Composed of directed edges, and the direction of the face is determined according to the right-hand rule.

[0063] (c) Directed volume: The spatial region enclosed by directed faces, and the direction points to the internal finite space or the external infinite space, depending on the direction of the directed faces

[0064] For the input mechanical parameters of the structural plane, the cohesion c of the structural plane is not considered in the present invention, and only the internal friction angle is considered

[0065] (2) Detection of block adjacency relationship

[0066] The detection of the block adjacency relationship in the present invention is divided into two steps: rough detection based on the bounding box and fine detection of the block.

[0067] Rough detection: The "bounding box" refers to a geometric structure that completely encloses or closes an object. If the bounding boxes of two discrete rock blocks do not intersect, it is obvious that the two rock blocks are separated from each other. Conversely, there is a possibility of intersection or adjacency between the two blocks. An axis-aligned bounding box (AABB, see Figure 1 ) is constructed for each rock block, and its construction process is as follows:

[0068] AABB = {(x, y, z)|x min ≤x≤x max , y min ≤y≤y≤y max , z min ≤z≤z max} (1)

[0069] Among them, x min and x max respectively represent the minimum and maximum values of the bounding box on the X axis; y min and y max respectively represent the minimum and maximum values on the Y axis; and z min and z max represent the minimum and maximum values on the Z axis. The determination methods of these parameters are as follows:

[0070]

[0071] Among them, i is the vertex number, and x i , y i and z i respectively represent the X, Y, and Z coordinates of the i-th vertex, and n represents the number of vertices of the rock block.

[0072] Detailed inspection: When the bounding boxes of two rock blocks intersect, it is necessary to further calculate to determine whether the two rock blocks are adjacent, that is, to perform a fine detection. In the rock block system, each directed face can only be used once. If the directed face P is defined as a→b→c→a (where a, b, and c are all vertices), then there must be a unique opposite face P’, denoted as a→c→b→a. If two rock blocks share a pair of such opposite faces, they are considered adjacent. Construct the matrix BR i for storing the adjacent rock block information of the i-th rock block, and its expression is as follows:

[0073]

[0074] Among them, B1, B2, …, B m , …, B N represent the numbers of the rock blocks adjacent to the i-th rock block B i ; P 11 , P 12 , P 21 , P 22 , …, P m1 , P m2 , P mn , …, P N1 , P N2 represent the numbers of the faces adjacent to the rock blocks B1, B2, …, B m , …, B N and the rock block B i . If the j-th face of the i-th rock block B i is adjacent to the n-th face of the m-th rock block B m , then the j-th row of the matrix BR i is [m, n], and the n-th row of the matrix BR m is [i, j]. In the matrix BR i , the faces without detected adjacent faces are recorded as free faces, denoted as [0, 0] in the matrix, while the faces with adjacent faces are recorded as non-free faces.

[0075] (3) Analysis of potential instability modes of single blocks

[0076] The instability modes of single blocks considered in the present invention include: falling instability, single-sided sliding instability, and double-sided sliding instability.

[0077] The overall flowchart is shown in Figure 2Let the resultant external driving force acting on the rock block be \(R\), and the corresponding unit vector be \(r\). Calculate the dot product \(D\) between \(r\) and the inward unit normal vector \(n\) of each non-free face. i between them. i (\(D\) i = \(r\cdot n\) i ). If \(D\) i < 0, then this face will prevent the rock block from falling and may serve as a potential slip surface for single-sided and double-sided slips. When no non-free face satisfies \(D\) i < 0, the rock block will become unstable in the falling mode.

[0078] Perform further calculations on the structural planes that satisfy \(D\) i < 0. If the cross product vector \(C\) of \(r\) and \(n\) i is non-zero, it indicates that the rock block has a tendency to slip along this structural plane. The potential single-sided slip direction \(s\) i can be expressed as: i where \(i\) is the serial number of the non-free face, \(n\)

[0079]

[0080] is the inward unit normal vector of the \(i\)-th face, and \(r\) is the unit vector of the resultant external driving force \(R\). Similar to the calculation of the falling instability mode, the non-free structural planes that satisfy \(D\) i < 0 ( \(D\) ’ j < 0 ( \(D\) ’ j = \(s\) i \(\cdot n\) j ) are regarded as the structural planes that prevent single-sided slips and prevent the rock block from sliding along the \(i\)-th structural plane. Its safety factor can be calculated by the following formula:

[0081]

[0082] Any two of the non-free structural planes can serve as potential slip surfaces for the double-sided slip instability mode. Therefore, there are possible double-sided slip failure modes, where \(n\) is the number of non-free structural planes. The slip direction \(s\) ij for double-sided slip is:

[0083]

[0084] where \(n\) i and \(n\) j are the inward unit normal vectors of the \(i\)-th and \(j\)-th structural planes respectively; \(r\) is the unit vector of the resultant external driving force \(R\); sign() satisfies the following conditions:

[0085]

[0086] It should be noted that when |n i ×n j | = 0, it means that the i-th and j-th structural planes are parallel, and the rock block will not slide along the intersection line of these two structural planes. At this time, this situation should be regarded as single-plane sliding for analysis. Those non-free discontinuous surfaces that satisfy D” k <0(D” k = s ij ·n k ) are classified as anti-double-plane sliding discontinuous surfaces, which prevent the rock block from sliding along the intersection line of the i-th and j-th structural planes. Its safety factor can be calculated by the following formula:

[0087]

[0088] Where:

[0089]

[0090]

[0091] (4) Construction of the potential instability network of the block system

[0092] Complex systems can be visualized as complex networks for analysis. Nodes in the network represent individual elements, and edges represent their interactions, and this structure helps to reveal how influences spread in the system. For the rock block system, each rock block may have multiple potential failure modes, and the blocking blocks are also different for each mode. Therefore, it is not feasible to directly construct a potential instability network that only contains rock blocks.

[0093] Gephi is a powerful open-source network visualization and analysis tool that provides intuitive layout and interactive exploration functions and can be used to process networks of various scales. Figure 3 Shows a network generated using Gephi, where red nodes represent potentially unstable blocks, yellow nodes represent their potential instability modes, and blue nodes correspond to blocks that are artificially assumed to be immovable. For example, the rock block labeled "291" has four directed edges pointing to the nodes "291_1", "291_2", "291_3", and "291_4", indicating that the rock block 291 has four potential instability modes. In addition, two outgoing edges from the rock block 291 connect to the nodes labeled "289_1" and "289_2", indicating that the rock block 291 prevents the rock block 289 from becoming unstable through the corresponding instability modes. This means that the instability of the rock block 291 may trigger the instability of the rock block 289 through its corresponding instability modes.

[0094] (5) Construction of the actual instability network of the block system

[0095] For a rock block system with determined geometric and mechanical properties, the instability state of the rock blocks and the corresponding instability modes should be determined. Theoretically, the actual instability network of the rock block system is a subset of the potential instability network. Therefore, the actual instability network can be constructed from the potential instability network. In the first batch of unstable blocks, most of the rock blocks are distributed on the exposed surfaces and fail in the most dangerous instability mode, that is, the instability mode with the lowest safety factor. Based on the i-th batch of unstable blocks and their block relationships, the affected rock blocks can be identified, and thus the unstable blocks of the (i + 1)-th batch can be determined.

[0096] For each affected rock block, extract the potential instability modes with safety factors lower than the threshold from the previous potential instability network and sort them in ascending order of safety factor. Then, check one by one whether the rock blocks that prevent its movement in each instability mode have become unstable. Repeat the iteration until no new affected rock blocks are identified, so as to determine the unstable blocks of the (i + 1)-th batch. The entire iterative process is as Figure 4 shown, and the instability process of the block system can be analyzed from the actual instability network of the block system. The actual instability network is shown in Figure 5 .

[0097] Figure 5 (a) Block 0 represents an air block, and the first layer of blocks connected to it are the first batch of unstable blocks. Different clusters of unstable blocks can be obtained in (b) and (c). The rock blocks in the same cluster of unstable blocks show a certain correlation, while the rock blocks that do not belong to the same cluster are independent of each other, that is, the behavior of the rock blocks in cluster A will not affect the behavior of the rock blocks in cluster B. The distribution characteristics of the rock block clusters can reflect the instability characteristics of the rock mass system, such as the instability of a large number of small-scale blocks or the instability of a small number of large-scale blocks.

[0098] In another embodiment of the present invention, a system for analyzing the progressive instability mode of a rock block system based on complex network is provided. This system can be used to implement the method for analyzing the progressive instability mode of a rock block system based on complex network. Specifically, it includes:

[0099] An adjacent relationship detection module, used to detect the adjacent relationship of the block system, and determine the adjacent relationship between rock blocks by rough inspection of the bounding box and fine inspection of the intersecting bounding boxes;

[0100] A potential instability mode analysis module, used to analyze the potential instability mode of a single block, calculate the dot product of the resultant external driving force and the unit normal vector of the non-free face, and judge the fall instability according to the dot product value; for the face that meets the fall instability condition, further calculate the single-face slip and double-face slip instability modes;

[0101] A potential instability network construction module, which is used to construct the potential instability network of the block system, represent the rock blocks and their potential instability modes as network nodes, and represent the influence relationship between the rock blocks through the instability modes as directed edges;

[0102] An actual instability network construction module, which is used to construct the actual instability network of the block system, and gradually determine the order and level of instability by iteratively identifying the unstable blocks and their adjacent rock blocks;

[0103] An instability mode prediction and visualization module, which is used to predict the progressive instability mode of the block system based on the actual instability network, and display the instability process and the key instability path through a visualization tool.

[0104] In another embodiment of the present invention, a terminal device is provided. The terminal device includes a processor and a memory. The memory is used to store a computer program. The computer program includes program instructions. The processor is used to execute the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions to implement the corresponding method process or corresponding function; the processor described in the embodiment of the present invention can be used for the method of analyzing the progressive instability mode of the rock block system based on complex networks.

[0105] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory). The computer-readable storage medium is a memory device in a terminal device, used to store programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, and this storage space stores the operating system of the terminal. And, in this storage space, there is also stored one or more instructions suitable for being loaded and executed by a processor. These instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory.

[0106] One or more instructions stored in the computer-readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the method for analyzing the progressive instability mode of the rock block system based on complex network in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor.

[0107] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0108] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the specified functions in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0109] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction means that implements the functions specified in one or more of the procedures Figure 1 one or more of the procedures and / or blocks Figure 1 specified in the blocks.

[0110] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one or more of the procedures Figure 1 one or more of the procedures and / or blocks Figure 1 specified in the blocks.

[0111] Those of ordinary skill in the art will appreciate that the embodiments described herein are provided to assist the reader in understanding the implementation of the present invention and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for analyzing the progressive instability mode of a rock block system based on a complex network, characterized in that: The following steps are involved: Detect the neighbor relationship of the block system, based on the rough inspection of the bounding box and the detailed inspection of the intersecting bounding boxes, to determine the neighbor relationship between the rock blocks; Analyze the potential instability mode of a single block, calculate the dot product of the combined external driving force and the unit normal vector of the non-free surface, and determine the falling instability mode based on the dot product value; For non-free-air surfaces that meet the conditions for preventing falling instability, calculate the single-side sliding and double-side sliding instability modes; Construct a potential instability network of the block system, represent the rock blocks and their potential instability modes as network nodes, and represent the influence relationship between rock blocks through instability modes as directed edges; The actual instability network of the block system is constructed, and the order and hierarchy of instability are gradually determined by iteratively identifying the unstable blocks and their adjacent rock blocks.

2. The method for analyzing the progressive instability mode of a rock block system based on a complex network according to claim 1, characterized in that: The calculation of the single-surface slip direction includes: calculating the cross product of the resultant external driving force and the unit normal vector of the structural surface, and calculating the potential slip direction based on the cross product vector.

3. The method for analyzing the progressive instability mode of a rock block system based on a complex network according to claim 1, characterized in that: The nodes of the potential instability network include: nodes representing rock blocks and nodes representing rock block instability modes.

4. The method for analyzing the progressive instability mode of a rock block system based on a complex network according to claim 1, characterized in that: The instability mode of each rock block is extracted from the potential instability network and sorted by safety factor, and whether the rock block is unstable due to the instability mode is checked step by step.

5. The method for analyzing the progressive instability mode of a rock block system based on a complex network according to claim 1, characterized in that: The analysis of the potential instability mode of the single block includes: calculating the dot product of the combined external driving force and the unit normal vector of the non-free surface, the formula is: D i =r·n i Among them, i is the number of the non-air-facing surface, D i represents the dot product of the driving force and the inward unit normal vector of the i-th non-air-facing surface, r is the unit vector of the combined external driving force, n i For the i The inward unit normal vector of the non-air-facing surface; When D i When <0, the surface will prevent the rock from falling and may serve as a potential slip surface for single-sided or double-sided slip.

6. The method for analyzing the progressive instability mode of a rock block system based on a complex network according to claim 1, characterized in that: The potential single-sided slip direction s is calculated i The formula is: Among them, i is the number of the non-airside surface, n i is the inward unit internal normal vector of the i-th structural surface, r is the unit vector of the resultant external driving force, × represents the cross product operation, and |·| represents the modulus of the vector.

7. The method for analyzing progressive instability modes of rock mass systems based on complex networks according to claim 1, characterized in that: The slip direction s of the potential two-sided slip is calculated ij The formula is: Among them, i and j are the numbers of the non-air-facing surface, n i and n j are the inward unit normal vectors of the i-th and j-th structural surfaces, r is the unit vector of the combined external driving force, sign() is the identifier, and satisfies: If x>0, sign(x)=1 If x=0,sign(x)=0 If x<0, sign(x)=-1.

8. The method for analyzing the progressive instability mode of a rock block system based on a complex network according to claim 1, characterized in that: Calculation of safety factor F for single-sided sliding s The formula is: Among them, i is the number of the non-airside surface, n i is the inward unit normal vector of the ith non-free surface, r is the unit vector of the combined external driving force, is the internal friction angle corresponding to the i-th surface.

9. The method for analyzing progressive instability modes of rock mass systems based on complex networks according to claim 1, characterized in that: Calculation of safety factor F for double-sided sliding s The formula is: Among them, i and j are the numbers of the non-air-facing surface, N i and N j are the anti-sliding force vectors corresponding to the i-th and j-th structural surfaces, and are the internal friction angles of the i-th and j-th structural surfaces respectively, and T is the sliding force vector.

10. A system for analyzing progressive instability modes of rock mass systems based on complex networks, characterized in that: The system can be used to implement the method for analyzing the progressive instability mode of a rock block system based on a complex network as described in any one of claims 1 to 9, specifically comprising: The adjacent relationship detection module is used to detect the adjacent relationship of the block system, and determine the adjacent relationship between rock blocks through rough inspection of bounding boxes and detailed inspection of intersecting bounding boxes; Potential instability mode analysis module is used to analyze the potential instability mode of a single block, calculate the dot product of the total external driving force and the unit normal vector of the non-free surface, and judge the falling instability based on the dot product value; for the non-free surface that meets the falling instability conditions, further calculate the single-side sliding and double-side sliding instability modes; Potential instability network construction module, used to construct the potential instability network of the block system, representing the rock blocks and their potential instability modes as network nodes, and representing the influence relationship between the rock blocks through the instability modes as directed edges; The actual instability network construction module is used to construct the actual instability network of the block system, and gradually determine the order and level of instability by iteratively identifying the unstable blocks and their adjacent rock blocks; The instability mode prediction and visualization module is used to predict the progressive instability mode of the block system based on the actual instability network, and display the instability process and key instability path through visualization tools.

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