A method for identifying connected damaged regions in complex crack networks

Abstract

The invention discloses a method for identifying connected damaged areas of a complex network of fractures, and relates to the technical field of rock mass fracture identification. The method for identifying connected damaged areas assigns weight values ​​to fracture network nodes according to the length of the fracture, the Euclidean distance of the fracture, and the fracture width, and determines the fracture network adjacency matrix through the node weights; then, based on complex network theory and the adjacency matrix, the degree value and clustering coefficient of the fracture network are determined, and the fracture connected damaged area is identified based on the maximum connected area algorithm of graph theory; finally, the maximum connected area of ​​the fracture is determined according to the network node degree value, the clustering coefficient, and the weights of the nodes and edges.

Description

Technical Field

[0001] The invention relates to the technical field of rock mass crack identification, and in particular to a method for identifying connected damaged areas of a complex crack network. Background Art

[0002] In rock mass engineering construction, the stability of underground chambers and slopes is often involved, and the excavation surfaces of these engineering rock masses are often distributed with a large number of structural surfaces. In addition to the large-scale faults that are certain, the structural surfaces in the rock mass also contain thousands of joints and cracks. These tiny uncertain structural surfaces seriously affect the various mechanical properties of the rock mass.

[0003] At present, the research on rock mass fracture network is based on the principles of probability and statistics. The distribution law of fractures is obtained through statistical analysis, and the fracture network adapted to the statistical distribution is realized by random simulation. Then, the stability of the rock mass is determined by analyzing the obtained simulated fracture network. The related research mainly focuses on using fractal or statistical methods to explain the interaction of rock mass joint behavior, using continuous media and discrete fracture networks to establish fracture network models, and does not consider the study of fracture network topology from the perspective of fracture geometric parameters. In complex geological conditions, there are multiple large faults, discontinuities, and high porosity in rock mass. The requirements for fracture model reconstruction due to changes in fracture parameters have been ignored, and the coupling relationship between the fine-macro structure of the fracture network and the influence of connectivity on rock mass damage have been ignored. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a method for identifying connected damaged areas of a complex crack network.

[0005] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0006] A method for identifying connected damaged areas of a complex crack network comprises the following steps:

[0007] Step S1, fracture complex network modeling: fracture complex network modeling first analyzes the connection properties of each node according to the degree and degree distribution, and then calculates the clustering coefficient of the fracture node;

[0008] Step S2, calculate the node-edge weights, analyze the structural characteristics of the network according to the geometric characteristics of the cracks in the complex crack network; identify the crack connected damage area based on the maximum connected area algorithm of graph theory.

[0009] Preferably, in step S1, the node with the crack i The number of connected nodes is K, ∈K;

[0010] ;

[0011] in, represents the degree of the node, is the connection edge matrix.

[0012] Preferably, the clustering coefficient of the node is divided into a local clustering coefficient and a global clustering coefficient; i The percentage of the actual number of edges in the neighbor nodes of the node to the theoretical number of edges is called the local clustering coefficient. i Let the number of its neighbors be , the calculation formula is:

[0013] ;

[0014] in, It represents the local clustering coefficient. is the length of the crack;

[0015] The average of the local clustering coefficients of all nodes is taken as the global clustering coefficient. The global clustering coefficient represents the average clustering degree of the entire network. The calculation formula is:

[0016] ;

[0017] in, represents the global clustering coefficient, It represents the local clustering coefficient. n is the number of nodes.

[0018] Preferably, in step S2, the node weight is calculated based on the connected crack length, crack width and Euclidean distance, and is defined as:

[0019] ;

[0020] in, is the length of the crack, is the width of the crack, is the Euclidean distance of the crack, Represents weights; the weights of nodes in the fracture complex network are normalized to their maximum value.

[0021] Preferably, the connectivity damage identification based on graph theory specifically includes the following steps:

[0022] S2-2-1, traverse all nodes ( , , , ,… ), extract node coordinates and weights, and generate an adjacency matrix based on the connection relationship between nodes;

[0023] S2-2-2, find the most connected subset and calculate the degree of the node , local clustering coefficient and weights , the first one is not processed and has a degree greater than k , weight is greater than the threshold θ The node is used as the starting node of a connected damage subgraph;

[0024] S2-2-3, process all neighbors associated with this node, whose node weight is less than the threshold θ , the degree is less than k , the neighbor node is marked as processed; otherwise, the degree of association between the neighbor node and the first starting node is determined. If the number of common neighbors of the two nodes is greater than or equal to the threshold θ and k , determine that the two nodes are closely related, add the neighbor node to the subgraph, and use this neighbor node as a seed node, recursively process its neighbors, otherwise, do not determine this node anymore;

[0025] S2-2-4, find all nodes that are closely related to the first starting node and have a degree greater than k、 Weight greater than threshold θ The subgraph composed of nodes is taken as the first connected damage subgraph;

[0026] S2-2-5, find the next degree greater than k、 Weight greater than threshold θ The node is used as the starting node of the next dense subgraph, and all nodes with a degree close to this starting node greater than the threshold are found. θ The nodes of are taken as the second connected damaged subgraph;

[0027] S2-2-6, loop until all nodes in the image have been processed;

[0028] S2-2-7, output: connected damage subgraph set.

[0029] Compared with the prior art, the method for identifying connected damaged areas of a complex crack network provided by the present invention has the following advantages:

[0030] The method for identifying connected damaged areas of a complex network of fractures of the present invention first assigns weight values ​​to fracture network nodes according to the length, angle, and width of the fractures, determines the fracture network adjacency matrix through the node weights, and then determines the degree value and clustering coefficient of the fracture network based on complex theory and the adjacency matrix, finds the maximum connected subset of the fracture based on the maximum connected area algorithm of graph theory, and finally determines the maximum connected area of ​​the fracture based on the network node degree value, clustering coefficient, and maximum connected subset; the method can provide a theoretical basis for fracture seepage and fracture water inrush paths. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a crack distribution diagram in the experimental verification of the present invention.

[0032] Figure 2 It is the degree distribution graph of the nodes in the experimental verification of the present invention.

[0033] Figure 3 It is the node clustering coefficient diagram in the experimental verification of the present invention.

[0034] Figure 4 This is the experimental verification of the moderate value of the present invention Schematic diagram for greater than 4.

[0035] Figure 5 is the clustering coefficient in the experimental verification of the present invention Schematic diagram of greater than 0.4.

[0036] Figure 6 It is an experimental scanned picture in the experimental verification of the present invention.

[0037] Figure 7 It is the crack connection damage diagram when the weight is 1.5 in the experimental verification of the present invention.

[0038] Figure 8 is the weight in the experimental verification of the present invention The crack connection damage map is 0.1.

[0039] Fig. 9 is the weight in the experimental verification of the present invention The crack connection damage diagram of 2. DETAILED DESCRIPTION

[0040] The specific embodiments of the present invention are described in detail below. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0041] The method for identifying connected damaged areas of a complex fracture network of the present invention aims to solve the problem that the infiltration path and connected damaged areas of a fracture network are difficult to accurately determine during the seepage process, and studies the characteristics of fracture network nodes and connected edges. First, weight values ​​are assigned to fracture network nodes according to the length of the fracture, the Euclidean distance of the fracture, and the fracture width, and the fracture network adjacency matrix is ​​determined by the node weights. Then, based on complex network theory and the adjacency matrix, the degree value and clustering coefficient of the fracture network are determined, and the fracture connected damaged area is identified based on the maximum connected area algorithm of graph theory. Finally, the maximum connected area of ​​the fracture is determined according to the network node degree value, the clustering coefficient, and the weights of the nodes and edges.

[0042] The method for identifying connected damaged areas of a complex crack network of the present invention specifically comprises the following steps:

[0043] Step S1, fracture complex network modeling:

[0044] The fracture complex network modeling first analyzes the connection properties of each node according to the degree and its distribution, and then calculates the clustering coefficient of the fracture.

[0045] Specifically:

[0046] S1-1, Degree and degree distribution of complex networks:

[0047] How many other nodes a node is connected to is called the degree of the complex network. K is used to represent the number of nodes connected to a node, and the value of k is the degree of the node. The purpose of studying the degree and its distribution is to study the connection properties of each node in the complex network and the characteristics of the overall structure of the network. The fractured complex network includes the following contents:

[0048] (1) Degree:

[0049] The points where cracks intersect are nodes. The number of other nodes connected to a node is called the degree of the crack complex network. i The number of connected nodes is K, ∈K.

[0050] (1)

[0051] in, represents the degree of the node, is the connection edge matrix. If the importance of this node is high and there are many nodes connected to it, then its degree will be greater.

[0052] Based on this basic concept of degree, several other parameters related to degree are:

[0053] a) Maximum degree:

[0054] In a complex network, the maximum degree of all nodes is the maximum degree of the node :

[0055] (2)

[0056] b) Minimum degree:

[0057] In a cracked complex network, the minimum value of all node degrees is the minimum degree of the node :

[0058] (3)

[0059] In the damage identification process, the introduction of minimum degree can increase the reference range of the connected damage area of ​​the complex crack network, thereby improving the recognition rate.

[0060] c) Average degree:

[0061] In a complex network, the average of all node degrees is the average degree K of the node. μ :

[0062] (4)

[0063] in, N is the total number of nodes.

[0064] In complex networks, the recognition efficiency can be judged based on the calculation of the average degree.

[0065] (2) Distribution of degree:

[0066] The node degree distribution mainly refers to the distribution of the number of nodes with the same degree in the network, which is also called the degree distribution function. The constant distribution model corresponds to a network with equal or similar node degrees, but it is not suitable for most complex networks with fractures. The Poisson distribution model corresponds to a network in which nodes are evenly connected to other nodes. The degree distribution of a complex network composed of a small number of nodes with very large degrees and most nodes with small degrees shows power-law distribution characteristics, which is consistent with the distribution characteristics of complex networks with fractures. The topological structure and performance of the network are affected by the form of degree distribution. The power-law distribution network shows scale-free characteristics, that is, the node degrees are distributed in a power-law manner, and the "super nodes" with the most connections play a vital role in network establishment and stability. The distribution of complex network degrees has an important impact on the structure and function of the network. The node degree distribution form can reflect the connectivity structure of the network, thereby affecting the speed and efficiency of percolation transmission. Unbalanced degree distribution may produce some highly connected nodes, which are vulnerable to damage and threats, affecting the connectivity percolation damage characteristics of complex networks with fractures. Therefore, it is necessary to obtain the fracture extension, connectivity and damage characteristics of complex networks with fractures by analyzing the node degrees.

[0067] S1-2, clustering coefficient:

[0068] In the process of modeling fracture complex networks, an important influencing factor is the clustering coefficient of the fracture, which reflects the number of connecting edges between other nodes around a node in the complex network.

[0069] In a complex network graph, a node i The clustering coefficient is divided into two types: local clustering coefficient and global clustering coefficient.

[0070] node i The percentage of the actual number of edges in the neighbor nodes of to the theoretical number of edges is called the local clustering coefficient. i Let the number of its neighbors be , the calculation formula is:

[0071] (5)

[0072] in, It represents the local clustering coefficient. is the length of the crack.

[0073] The average of the local clustering coefficients of all nodes is called the global clustering coefficient. The global clustering coefficient is used to represent the average clustering degree of the entire network. The calculation formula is:

[0074] (6)

[0075] in, represents the global clustering coefficient, It represents the local clustering coefficient. n is the number of nodes.

[0076] Step S2, node-edge weight calculation:

[0077] In a complex network of fractures, the structural characteristics of the network are analyzed and understood based on the geometric characteristics of the fractures (such as fracture length, fracture width, and Euclidean distance between fractures).

[0078] S2-1, node weight calculation:

[0079] The node weight is calculated based on the length, width and Euclidean distance of the cracks it connects, and is defined as:

[0080] (7)

[0081] in: is the length of the crack, is the width of the crack, is the Euclidean distance of the crack, Represents weight.

[0082] In order to eliminate the impact of the singular number of samples on the data, the weights of the nodes in the complex network of fractures are normalized to the maximum value according to the maximum value of the fracture length measurement of 500, the maximum value of the width of 30, and the maximum value of the Euclidean geometric distance of 599:

[0083] (8)

[0084] The purpose of normalization is to eliminate the influence of outliers.

[0085] S2-2, Identification of connectivity damage based on graph theory:

[0086] The specific steps include:

[0087] S2-2-1, traverse all nodes ( , , , ,… ), extract node coordinates and weights, and generate an adjacency matrix based on the connection relationship between nodes.

[0088] S2-2-2, find the most connected damaged subset and calculate the node degree according to the formula , local clustering coefficient and weights , the first one is not processed and has a degree greater than k , weight is greater than the threshold θ The node of is used as the starting node of a connected damage subgraph.

[0089] S2-2-3, process all neighbors associated with this node, whose node weight is less than the threshold θ , the degree is less than k , the neighbor node is marked as processed; otherwise, the degree of association between the neighbor node and the first starting node is considered. If the number of common neighbors of the two nodes is greater than or equal to the threshold θ and k , then the two nodes are considered to be closely related, the neighbor node is added to the subgraph, and this neighbor node is used as the seed node, and its neighbors are processed recursively, otherwise this node is no longer considered.

[0090] S2-2-4, find all nodes that are closely related to the first starting node and have a degree greater than k、 Weight greater than threshold θ The subgraph composed of nodes is taken as the first connected damage subgraph.

[0091] S2-2-5, find the next degree greater than k、 Weight greater than threshold θ The node is used as the starting node of the next connected damage subgraph, and all nodes with a degree greater than the threshold θ that are closely related to this starting node are found as the second connected damage subgraph.

[0092] S2-2-6, loop until all nodes in the image have been processed.

[0093] S2-2-7, output: connected damage subgraph set.

[0094] Experimental verification:

[0095] The experimental samples are natural samples of rock mass, and the distribution of cracks is as follows: Figure 1 As shown in the figure, the blue line segment represents the distribution of cracks. Combining image processing technology with basic complex network theory, we explore the corresponding complex crack network connection topology characteristics, such as Figure 1 Shown are the fracture network structure and the characteristics of fracture nodes and edges.

[0096] like Figure 2 As shown in the figure, the degree value of the rock fracture network is obtained according to the small-world characteristics of the complex network. The distribution of node degree values ​​of the rock fracture network is shown in the figure. The maximum degree of the rock fracture network is is 11, the minimum The probability of nodes with a degree of 6 in all fracture networks is high, the average degree of the network is 6, and the number of nodes with a degree greater than 10 is small. The reason for the high probability of nodes with a degree of 6 is closely related to the expansion mechanism of seepage rock cracks. The reason why nodes with a degree greater than 10 are less distributed is mainly due to the localization of severely damaged areas inside non-uniform seepage rocks, and cracks only locally intersect in these severely damaged areas during the expansion process.

[0097] like Figure 3 As shown in the figure, for the rock fracture network, the larger the clustering coefficient C, the more concentrated areas where fractures extend and intersect, the greater the clustering of nodes, and the relatively good fracture connectivity in these areas. Correspondingly, these areas should also be places where the internal damage of the rock is more serious. Here, the clustering coefficient of each node is determined by calculation, and it is found that the maximum value of the clustering coefficient of the 300th to 600th nodes is 0.67, the minimum value is 0, the global clustering coefficient C is 0.13, and the clustering coefficient of 48% of the nodes is above 0.1. Therefore, the corresponding node concentrated damage area can be intuitively located by the node clustering coefficient.

[0098] like Figure 4 As shown in the figure, the smaller the degree value, the more blue nodes are connected to each other, and the areas with severe or mild crack damage can be divided according to the degree distribution and node characteristics. Figure 5 As shown in the figure, the blue nodes with clustering coefficient less than 0.4 are more than the red nodes, the connected area is larger, and the damage is milder. Figure 6 As shown in the figure, 1 is the maximum and 0 is the minimum. The greater the intensity of the wavelet coefficient, the more obvious the degree of crack damage. ) In contrast, the accuracy of damaged area recognition is low.

[0099] like Figure 7 As shown, the experimental scanned image based on wavelet analysis Figure 6 In contrast, the red nodes are subnetworks composed of nodes with better connectivity extracted by complex network theory. Figure 6 The connectivity trends of physical scanned images are similar. Figure 6 The thickened fracture connection area is Figure 7 The red nodes partially match.

[0100] The possible connected areas caused by cracks can be displayed according to the weight and degree of cracks. In the actual construction site, the specific threshold can be determined according to the flow velocity and permeability, and then the damaged area can be determined.

[0101] As the weight threshold increases, that is, the value of the crack parameters (such as crack length, angle, and Euclidean distance between cracks) increases, the damage degree of the damaged area can be divided, such as Figure 8 When the weight is 0.1, the damaged area is large, including areas with severe and mild damage. As the weight increases, the severely damaged nodes such as Fig. 9 shown.

[0102] From the above graphs, we can see that for complex networks with larger weights, the identification accuracy of node damage connected areas is higher.

[0103] from Figure 6 Comparison of the scanned images also shows that larger crack parameter values ​​(such as crack length, crack inclination, and crack) cause greater damage to the overall rock sample. For rock samples, nodes and edges with small weights reduce overall damage, which also verifies the damage law of real samples.

[0104] Therefore, the nodes and edges of the critical crack damage can be determined according to the setting of the weight threshold, and the damage within the value range can be repaired and improved. At the same time, according to the mechanical parameter characteristics of the sample, the damage range that the node may cause within the crack parameter range can be observed.

[0105] Experiments show that the method for identifying connected damaged areas of complex fracture networks of the present invention can provide a theoretical basis for fracture seepage and fracture water inrush paths. The specific conclusions are as follows:

[0106] 1) The more nodes with larger degree values ​​there are, the greater the probability of fracture network connectivity damage;

[0107] 2) The clustering coefficient reflects the largest connected subset of the fracture network;

[0108] 3) The fracture network with weights assigned according to fracture length and aperture can obtain the maximum connected subset of fractures.

[0109] The above implementation cases are only preferred embodiments of the present invention and are not intended to limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, they are not intended to limit the present invention. Therefore, any simple modification, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for identifying connected damaged areas of a complex crack network, characterized in that: The following steps are involved: Step S1, fracture complex network modeling, fracture complex network modeling first analyzes the connection properties of each node according to the degree and degree distribution, and then calculates the clustering coefficient of the fracture node; Step S2, calculating the node-edge weights, and analyzing the structural characteristics of the network according to the geometric characteristics of the cracks in the complex network of cracks; The maximum connected region algorithm based on graph theory identifies the crack connected damage area; The clustering coefficient of the node is divided into a local clustering coefficient and a global clustering coefficient; i The percentage of the actual number of edges in the neighbor nodes of the node to the theoretical number of edges is called the local clustering coefficient. i Let the number of its neighbors be , the calculation formula is: ; in, It represents the local clustering coefficient. is the length of the crack; The average of the local clustering coefficients of all nodes is taken as the global clustering coefficient. The global clustering coefficient represents the average clustering degree of the entire network. The calculation formula is: ; in, represents the global clustering coefficient, It represents the local clustering coefficient. n is the number of nodes; In step S2, the node weight is calculated based on the connected crack length, crack width and Euclidean distance, and is defined as: ; in, is the length of the crack, is the width of the crack, is the Euclidean distance of the crack, represents weight; The weights of the nodes in the fracture complex network are normalized to the maximum value; The connectivity damage identification based on graph theory specifically includes the following steps: S2-2-1, traverse all nodes ( , , , ,… ), extract node coordinates and weights, and generate an adjacency matrix based on the connection relationship between nodes; S2-2-2, find the most connected subset and calculate the degree of the node , local clustering coefficient and weights , the first one is not processed and has a degree greater than k , weight is greater than the threshold θ The node is used as the starting node of a connected damage subgraph; S2-2-3, process all neighbors associated with this node, whose node weight is less than the threshold θ , the degree is less than k , the neighbor node is marked as processed; otherwise, the degree of association between the neighbor node and the first starting node is determined. If the number of common neighbors of the two nodes is greater than or equal to the threshold θ and k , determine that the two nodes are closely related, add the neighbor node to the subgraph, and use this neighbor node as a seed node, recursively process its neighbors, otherwise, do not determine this node anymore; S2-2-4, find all nodes that are closely related to the first starting node and have a degree greater than k、 Weight greater than threshold θ The subgraph composed of nodes is taken as the first connected damage subgraph; S2-2-5, find the next degree greater than k、 Weight greater than threshold θ The node is used as the starting node of the next dense subgraph, and all nodes with a degree close to this starting node greater than the threshold are found. θ The nodes of are taken as the second connected damaged subgraph; S2-2-6, loop until all nodes in the image have been processed; S2-2-7, output: connected damage subgraph set.

2. The method for identifying connected damaged areas of a complex crack network according to claim 1, characterized in that: In step S1, the node with the crack i The number of connected nodes is K, ∈K; ； in, represents the degree of the node, is the connection edge matrix.

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