A method for predicting fracture flow combining yield criterion and network topology

Abstract

The application discloses a kind of crack seepage prediction methods of combining yield criterion and network topology, belong to rock mass engineering construction field, including the following steps: topological analysis is carried out to crack network based on complex network theory, determine the degree centrality of crack network node and crack shear stress transmission coefficient;Based on Mohr-Coulomb yield criterion, establish shear stress equation, determine the criterion of crack network damage leakage according to yield criterion and seepage stress coupling relationship;Considering the degree distribution and clustering coefficient of crack network node, the damage evolution equation considering the importance of node and crack damage characteristics is established;Based on the established damage evolution equation, the percolation region of crack seepage damage evolution prediction is carried out.The application uses complex network index to identify the importance of crack network node, and carries out failure calculation on crack edge and node in combination with yield criterion and seepage-stress coupling relationship, which effectively improves the efficiency of crack network damage evolution and seepage prediction.

Description

Technical Field

[0001] This invention relates to the field of rock mass engineering construction, and in particular to a method for predicting fracture seepage by combining yield criterion and network topology. Background Technology

[0002] In rock mass engineering construction, the stability of underground chambers, slopes, and other structures is frequently involved, and the excavation faces of these rock masses often contain a large number of structural planes. The joints and fissures of these structural planes in the rock mass significantly affect various mechanical properties of the rock mass.

[0003] Current research on rock fracture networks is based on probability and statistics principles. After obtaining the distribution patterns of fractures through statistical analysis, stochastic simulation methods are used to create fracture networks that adapt to the statistical distribution. While these studies have improved the efficiency of network feature identification to some extent, they neglect the influence of seepage effects on the interactions between fracture network structures in terms of network evolution. Due to the multi-scale interactions between network structures, such as the formation of seepage clusters and other phenomena caused by seepage encroachment, the fluid flow and energy transfer between fracture channels during seepage are mechanical behaviors that directly affect the changes in the functional properties of the network structure. These are key influencing factors in the seepage changes of the entire fracture network, the prediction of abrupt seepage changes, and significant or subtle qualitative changes. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a simple and easy-to-implement method for predicting fracture seepage by combining yield criteria and network topology.

[0005] The technical solution of this invention to solve the above-mentioned technical problems is: a method for predicting fracture seepage by combining yield criterion and network topology, comprising the following steps:

[0006] S1: Based on complex network theory, topological analysis of the fracture network is performed to determine the degree centrality of the fracture network nodes and the fracture shear stress transmission coefficient.

[0007] S2: Establish the shear stress equation based on the Mohr-Coulomb yield criterion, and determine the criterion for crack network damage leakage based on the coupling relationship between the yield criterion and seepage stress.

[0008] S3: Considering the degree distribution and clustering coefficient of the fracture network nodes, establish a damage evolution equation that comprehensively considers the importance of nodes and the characteristics of fracture damage;

[0009] S4: Based on the established damage evolution equation, predict the permeable area by analyzing the damage evolution of fracture seepage.

[0010] S5: Determine the permeation threshold based on the stress conditions of the nodes and edges, and calculate the permeation area.

[0011] The above-mentioned fracture seepage prediction method combining yield criterion and network topology, in step S1, the process of performing topological analysis of the fracture network based on complex network theory is as follows:

[0012] Based on the small-world characteristics of fractured complex networks, a fractured network is defined as a weighted undirected graph, and the fracture node set is defined as... , ,in N Construct an adjacency matrix for the total number of nodes. , , for The Middle Line 1 Column elements:

[0013] .

[0014] The above-described fracture seepage prediction method combining yield criterion and network topology, in step S1, defines the degree centrality of a node as the number of direct connections between nodes, intuitively reflecting the node's influence within a local area. Degree centrality is used to measure a node's current ability to participate in stress transfer. Degree centrality of each node The calculation formula is as follows:

[0015]

[0016] In the formula: For the first Damage value of each node, For the first The damage value of a node is used to determine its degree centrality. When the damage value of a node is 1, its degree centrality is 0, which means it is a topological isolated node.

[0017] In the fracture seepage prediction method combining yield criterion and network topology described above, in step S1, the stiffness of the fracture network determines the stress transmission mode, which is influenced by both geometric shape and material properties. The calculation of the fracture shear stress transmission coefficient takes into account the fracture length, angle, and elastic modulus. The formula for calculating the fracture shear stress transmission coefficient is as follows:

[0018]

[0019] In the formula: For the first The node and the first Crack shear stress transfer coefficient between nodes For the elastic modulus of rock, For the first The node and the first Cross-sectional area of ​​the crack segment between nodes For the first The node and the first The length of the crack segment between nodes For the first The node and the first The angle between the crack segment between each node and the principal stress direction Poisson's ratio;

[0020] Penetration It is positively correlated with the effectiveness centrality and proportional to the square of the fracture aperture:

[0021]

[0022] Initial penetration rate, Topological influence factor, These are factors that affect damage.

[0023] The above-described fracture seepage prediction method, which combines yield criteria and network topology, in step S2, considers momentum conservation and incorporates the fracture network stress diffusion term, external loading term, and viscous dissipation term into the shear stress equation. Therefore, the shear stress equation for the node is:

[0024]

[0025] In the formula: the summation term applies to neighboring nodes. For time steps Time External load stress at each node, Let be the shear stress-strain ratio of the neighboring nodes. For viscous dissipation, Shear modulus For characteristic length, For node density, For viscosity parameters, For the first The node and the first Shear stress between nodes For time steps, For the first Shear stress at each node;

[0026] Introducing effective stress , The corrected shear stress equation is obtained by using the seepage stress coupling relationship:

[0027]

[0028] For the total stress, For Biot coefficient, The seepage pressure in the fracture. This represents the rate of change of fracture pressure.

[0029] In the above-mentioned method for predicting crack seepage by combining yield criterion and network topology, in step S2, a complex crack network is constructed, where nodes are crack intersections and edges are crack segments. The Mohr-Coulomb yield criterion is applied as the failure condition for nodes or edges. When the stress on a node or edge reaches the Mohr-Coulomb failure condition, the crack network is determined to be damaged and leaking, resulting in the edge of the crack network structure breaking and the node failing, thereby causing seepage in the entire crack network.

[0030] In the fracture seepage prediction method combining yield criterion and network topology described above, step S3 involves analyzing the dynamic behavior of the fracture network by combining the structural characteristics of the stress network, the degree distribution of nodes and edges, and the clustering coefficient. The damage value, clustering coefficient, and degree distribution are comprehensively evaluated to assess the seepage instability state of the fracture network. A comprehensive index for each node is calculated and assigned different weights. The importance of each node is calculated using the following formula:

[0031]

[0032] In the formula: For time steps Time The importance of each node For time steps Time Damage value of each node, For time steps Time Clustering coefficients of nodes, For time steps Time The degree value of each node. , , All are weights.

[0033] The above-described crack seepage prediction method combining yield criterion and network topology establishes the following damage evolution equation in step S3:

[0034]

[0035] In the formula: The damage rate constant is The importance rate constant, For the first Material cohesion at each node For the first Normal stress at each node, For the first The fracture fluid pressure at each node, For the first The friction angle of each node.

[0036] In the above-mentioned crack seepage prediction method combining yield criterion and network topology, the state of the crack in step S5 is divided into two types: stable and unstable. When the shear force on the damaged node and the crack reaches the Mohr-Coulomb strength, the corresponding crack expands and becomes unstable, leading to stress redistribution and triggering a sudden change in percolation in the connected region.

[0037] Define percolation threshold When the maximum connected cluster size satisfy:

[0038]

[0039] Then the fracture network enters a critical state of sudden change; From the adjacency matrix Damage index analysis and calculation; Subject to the current stress field Influence;

[0040]

[0041] In the formula, This is the initial percolation value. For normal stress is The percolation threshold at that time, For compressive strength, It is normal stress. This is the stress sensitivity coefficient.

[0042] The beneficial effects of this invention are as follows:

[0043] 1. This invention considers the degree distribution and clustering coefficient of fracture network nodes, establishes a fracture seepage damage evolution equation that comprehensively considers the importance of nodes, and obtains the shear force transmission coefficient by utilizing the degree centrality of complex networks and fracture scale characteristics. By incorporating the degree distribution and clustering coefficient of nodes in fractured rock mass into the seepage damage evolution, a damage evolution equation that can reflect the differences in node importance is established. This improves the ability of traditional seepage evolution models to characterize the multi-scale characteristics of fracture networks and their nonlinear evolution mechanisms, avoids predicting the seepage area by monitoring seepage flow during the experiment, and reduces experimental and time costs.

[0044] 2. This invention combines the yield criterion and the seepage stress coupling mechanism to determine the criteria for damage to nodes and edges of fracture networks. It also determines the permeability threshold based on the stress conditions of nodes and edges and calculates the permeability zone. The evolution of seepage damage to nodes and edges depends not only on seepage pressure but also on local stress state and material strength parameters. This improves upon the shortcomings of current methods that use a single indicator as a criterion. It considers seepage pressure and material yield strength as thresholds for calculating the permeability zone and derives the damage accumulation process of rock mass under the combined action of seepage and stress. This enhances the early identification capability of leakage and water inrush risks in fracture networks and helps to realize the early detection of potential leakage or water inrush hazards, formulate preventive measures, and conduct risk assessments. Attached Figure Description

[0045] Figure 1 This is the overall flowchart of the present invention.

[0046] Figure 2 This is a scanned image of a crack sample.

[0047] Figure 3 This is a schematic diagram of the damage evolution at time step 3.

[0048] Figure 4 This is a schematic diagram of the damage evolution at time step 11.

[0049] Figure 5 This is a schematic diagram of the damage evolution at time step 15.

[0050] Figure 6 This is a schematic diagram of the damage evolution at time step 18.

[0051] Figure 7 This is a schematic diagram of the percolation prediction region of the fracture network corresponding to time step 3.

[0052] Figure 8 This is a schematic diagram of the percolation prediction region of the fracture network corresponding to time step 11.

[0053] Figure 9 This is a schematic diagram of the percolation prediction region of the fracture network corresponding to time step 15.

[0054] Figure 10 This is a schematic diagram of the percolation prediction region of the fracture network corresponding to time step 18. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] like Figure 1 As shown, a fracture seepage prediction method combining yield criterion and network topology includes the following steps:

[0057] S1: Based on complex network theory, a topological analysis of the fracture network is performed to determine the degree centrality of the fracture network nodes and the fracture shear stress transmission coefficient.

[0058] The process of performing topology analysis on fracture networks based on complex network theory is as follows:

[0059] Based on the small-world characteristics of fractured complex networks, a fractured network is defined as a weighted undirected graph, and the fracture node set is defined as... , ,in N Construct an adjacency matrix for the total number of nodes. , , for The Middle Line 1 Column elements:

[0060] .

[0061] The degree centrality of a node is defined as the number of direct connections between nodes. It intuitively reflects the node's influence within a local area and measures its current ability to participate in stress transfer. Degree centrality of each node The calculation formula is as follows:

[0062]

[0063] In the formula: For the first Damage value of each node, For the first The damage value of a node is used to determine its degree centrality. When the damage value of a node is 1, its degree centrality is 0, which means it is a topological isolated node.

[0064] The stiffness of the fracture network determines the stress transmission mode, which is influenced by both geometry and material properties. The calculation of the fracture shear stress transmission coefficient takes into account the fracture length, angle, and elastic modulus. The formula for calculating the fracture shear stress transmission coefficient is as follows:

[0065]

[0066] In the formula: For the first The node and the first Crack shear stress transfer coefficient between nodes For the elastic modulus of rock, For the first The node and the first Cross-sectional area of ​​the crack segment between nodes For the first The node and the first The length of the crack segment between nodes For the first The node and the first The angle between the crack segment between each node and the principal stress direction Poisson's ratio;

[0067] Penetration It is positively correlated with the effectiveness centrality and proportional to the square of the fracture aperture:

[0068]

[0069] Initial penetration rate, Topological influence factor, These are factors that affect damage.

[0070] S2: Establish the shear stress equation based on the Mohr-Coulomb yield criterion, and determine the criterion for crack network damage leakage based on the coupling relationship between the yield criterion and seepage stress.

[0071] Considering momentum conservation, and incorporating the stress diffusion term, external loading term, and viscous dissipation term of the fracture network into the shear stress equation, the shear stress equation for the node becomes:

[0072]

[0073] In the formula: the summation term applies to neighboring nodes. For time steps Time External load stress at each node, Let be the shear stress-strain ratio of the neighboring nodes. For viscous dissipation, Shear modulus For characteristic length, For node density, For viscosity parameters, For the first The node and the first Shear stress between nodes For time steps, For the first Shear stress at each node;

[0074] Introducing effective stress , The corrected shear stress equation is obtained by using the seepage stress coupling relationship:

[0075]

[0076] For the total stress, For Biot coefficient, The seepage pressure in the fracture. This represents the rate of change of fracture pressure.

[0077] A complex fracture network is constructed, where nodes are fracture intersections and edges are fracture segments. The Mohr-Coulomb yield criterion is applied as the failure condition for nodes or edges. When the stress on a node or edge reaches the Mohr-Coulomb failure condition, the fracture network is deemed damaged, resulting in the edge of the fracture network structure breaking and the node failing, thereby causing seepage in the entire fracture network.

[0078] S3: Considering the degree distribution and clustering coefficient of the nodes in the fracture network, establish a damage evolution equation that comprehensively considers the importance of nodes and the characteristics of fracture damage.

[0079] By combining the structural characteristics of the stress network, the degree distribution of nodes and edges, and the clustering coefficient, the dynamic behavior of the fracture network is analyzed. The seepage instability state of the fracture network is comprehensively evaluated by damage value, clustering coefficient, and degree distribution. A comprehensive index for each node is calculated and assigned different weights. Nodes with high damage values ​​are highly important, but if a node is located in a region with a high clustering coefficient, it is prone to local failure, thus increasing its importance. Simultaneously, the degree distribution may affect the stability of the entire fracture network; the presence of nodes with high degrees poses a damage risk to the fracture network. The importance of each node is calculated using the following formula:

[0080]

[0081] In the formula: For time steps Time The importance of each node For time steps Time Damage value of each node, For time steps Time Clustering coefficients of nodes, For time steps Time The degree value of each node. , , All are weights.

[0082] The established damage evolution equation is as follows:

[0083]

[0084] In the formula: The damage rate constant is The importance rate constant, For the first Material cohesion at each node For the first Normal stress at each node, For the first The fracture fluid pressure at each node, For the first The friction angle of each node.

[0085] S4: Based on the established damage evolution equation, predict the permeable area by analyzing the damage evolution of fracture seepage.

[0086] S5: Determine the permeation threshold based on the stress conditions of the nodes and edges, and calculate the permeation area.

[0087] In step S5, the state of the crack is divided into two types: stable and unstable. When the shear force on the damaged node and the crack reaches the Mohr-Coulomb strength, the corresponding crack expands and the crack becomes unstable, resulting in stress redistribution, which in turn triggers the percolation change of the connected region.

[0088] Define percolation threshold When the maximum connected cluster size satisfy:

[0089]

[0090] Then the fracture network enters a critical state of sudden change; From the adjacency matrix Damage index analysis and calculation; Affected by the current stress field;

[0091]

[0092] In the formula, This is the initial percolation value. For normal stress is The percolation threshold at that time, For compressive strength, It is normal stress. This is the stress sensitivity coefficient.

[0093] Experimental verification:

[0094] The experimental sample was a natural sample of the rock mass, and the distribution of fractures was as follows: Figure 2 As shown, Figure 2 This is a wavelet analysis plot of a crack sample under stress. The color levels on the right represent the intensity of the wavelet coefficients; the more severe the damage, the larger the coefficients. The crack sample has 1132 nodes and 738 crack edges. , , The values ​​are 0.6, 0.2, and 0.2 respectively.

[0095] Figure 2 and Figure 3 — Figure 6 Compare the evolutionary processes. Figure 2 The severely damaged areas, namely the darker-colored cracks, are... Figure 3 — Figure 6 The cracks with higher damage values ​​during the evolution process, namely the red cracks, are consistent with the damage patterns of real-world samples.

[0096] Based on the characteristics of crack node length, angle, and elastic modulus, the crack shear stress transmission coefficient is calculated. Then, the network is updated according to the shear stress equation and the damage evolution equation. Points and edges where the stress reaches the failure threshold are deleted. The characteristic parameter values ​​of some nodes at different time steps are shown in Table 1.

[0097]

[0098] As shown in Table 1, the shear stress at node 25 gradually increases with the increase of time steps, indicating that the node is in a damaged state. At time step 18, the damage value is 1, and the clustering coefficient shows an increasing trend, thus indicating a risk of failure for this node. Node 41 has a lower damage value, a clustering coefficient of 0.2850 at time step 18, and an importance of 0.0960, indicating a relatively low risk. Node 334 in Table 1 has a damage value of 1 at time step 18, a clustering coefficient of 0.2109, and an importance of 0.8374. Therefore, the risk of this node being deleted is high, and the risk of abrupt seepage changes in this node region is also high.

[0099] As the damage progresses, the evolutionary process is as follows: Figures 3-6 ,from Figure 3 It can be seen that at time step 3, the damage distribution of the nodes is relatively dispersed, with the nodes at the two ends of the edges where the cracks are smaller showing lower damage values ​​(represented by blue). As stress is applied, by time step 11... Figure 4 The damage value at the edge of the crack with denser cracks gradually turns red, and the red edge... Figure 2 The damage cracks are quite similar; Figure 5 The damage evolution diagram at time step 15 shows that the crack edge was deleted when the stress reached the yield strength and exceeded the damage threshold. Figure 6 This is the damage evolution diagram at time step 18. Looking at the distribution of nodes and edges, as the time step increases, the stress on the edges and nodes reaches a threshold, the damage value gradually increases, and eventually all are deleted. Therefore, the evolution results diagram shows that combining damage value, clustering coefficient, and degree distribution indicators can effectively identify the damage evolution process. The dynamic evolution mechanism can assess seepage risk and improve the prediction of rock mass instability.

[0100] Considering the effects of parameters such as crack length and clustering coefficient on the real-time network topology and stress field calculation Nodes with damage values ​​> 0.95 are considered failed, and damaged nodes are filtered out and included in the permeation range: the adjacency matrix is ​​used to analyze the permeation connectivity components, and the largest connected cluster with damage values ​​exceeding the range is defined as the permeation range. Geometric boundary analysis is used to eliminate the misjudgment of discrete small clusters.

[0101] Figures 7-10 yes Figures 3-6 A schematic diagram of the percolation prediction region of the fracture network at the corresponding time step. From Figure 7 As you can see, in the initial stage of seepage, at time step 3, the area of ​​potential over-seepage risk occupies 25.7% of the fracture network; as the time step increases, the area of ​​potential over-seepage risk gradually expands to... Figure 8 At time step 11:00, the percolation range was 36.3%; expanding to Figure 9 At time step 15:00, the percolation range was 41.5%; expanding to Figure 10 At time step 18, the permeability range was 44.5%; the risk of abrupt changes in the fracture network increased, which may lead to the failure of all nodes and edges of the rock mass fracture network.

Claims

1. A method for predicting fracture seepage by combining yield criterion and network topology, characterized in that, Includes the following steps: S1: Based on complex network theory, topological analysis of the fracture network is performed to determine the degree centrality of the fracture network nodes and the fracture shear stress transmission coefficient. The process of performing topology analysis on fracture networks based on complex network theory is as follows: Based on the small-world characteristics of fractured complex networks, a fractured network is defined as a weighted undirected graph, and the fracture node set is defined as... , ,in N Construct an adjacency matrix for the total number of nodes. , , for The Middle Line number Column elements: ； The degree centrality of a node is defined as the number of direct connections between nodes. It intuitively reflects the node's influence within a local area and measures its current ability to participate in stress transfer. Degree centrality of each node The calculation formula is as follows: ； In the formula: For the first Damage value of each node, For the first The damage value of a node is used to determine its degree centrality. When the damage value of a node is 1, its degree centrality is 0, which means it is a topological isolated node. The stiffness of the fracture network determines the stress transmission mode, which is influenced by both geometry and material properties. The calculation of the fracture shear stress transmission coefficient takes into account the fracture length, angle, and elastic modulus. The formula for calculating the fracture shear stress transmission coefficient is as follows: ； In the formula: For the first The node and the first Crack shear stress transfer coefficient between nodes For the elastic modulus of rock, For the first The node and the first Cross-sectional area of ​​the crack segment between nodes For the first The node and the first The length of the crack segment between nodes For the first The node and the first The angle between the crack segment between each node and the principal stress direction Poisson's ratio; Penetration It is positively correlated with the effectiveness centrality and proportional to the square of the fracture aperture: ； Initial penetration rate, Topological influence factor, Damage influencing factors; S2: Based on the Mohr-Coulomb yield criterion and the coupling relationship between seepage stress, a shear stress equation is established, and the criterion for leakage due to crack network damage is determined according to the yield criterion. S3: Considering the degree distribution and clustering coefficient of the fracture network nodes, establish a damage evolution equation that comprehensively considers the importance of nodes and the characteristics of fracture damage; S4: Based on the established damage evolution equation, predict the permeable area by analyzing the damage evolution of fracture seepage. S5: Determine the permeation threshold based on the stress conditions of the nodes and edges, and calculate the permeation area.

2. The fracture seepage prediction method combining yield criterion and network topology according to claim 1, characterized in that, In step S2, considering momentum conservation, the stress diffusion term, external loading term, and viscous dissipation term of the fracture network are incorporated into the shear stress equation. Therefore, the shear stress equation for the node is: ； In the formula: the summation term applies to neighboring nodes. For time step Time External load stress at each node, Let be the shear stress-strain ratio of the neighboring nodes. For viscous dissipation, Shear modulus For characteristic length, For node density, For viscosity parameters, For the first The node and the first Shear stress between nodes For time steps, For the first Shear stress at each node; Introducing effective stress , The corrected shear stress equation is obtained by using the seepage stress coupling relationship: ； For the total stress, For Biot coefficient, The seepage pressure in the fracture. This represents the rate of change of fracture pressure.

3. The fracture seepage prediction method combining yield criterion and network topology according to claim 2, characterized in that, A complex fracture network is constructed, where nodes are fracture intersections and edges are fracture segments. The Mohr-Coulomb yield criterion is applied as the failure condition for nodes or edges. When the stress on a node or edge reaches the Mohr-Coulomb failure condition, the fracture network is judged to be damaged and leaking, resulting in the edge of the fracture network structure breaking and the node failing, thereby causing seepage in the entire fracture network.

4. The fracture seepage prediction method combining yield criterion and network topology according to claim 2, characterized in that, In step S3, the dynamic behavior of the fracture network is analyzed by combining the structural characteristics of the stress network, the degree distribution of nodes and edges, and the clustering coefficient. The seepage instability state of the fracture network is comprehensively evaluated by considering damage value, clustering coefficient, and degree distribution. A comprehensive index for each node is calculated and assigned different weights. The importance of each node is calculated using the following formula: ； In the formula: For time step Time The importance of each node For time step Time Damage value of each node, For time step Time Clustering coefficients of nodes, For time step Time The degree value of each node. , , All are weights.

5. The fracture seepage prediction method combining yield criterion and network topology according to claim 4, characterized in that, In step S3, the damage evolution equation is established as follows: ； In the formula: The damage rate constant is The importance rate constant, For the first Material cohesion at each node For the first Normal stress at each node, For the first The fracture fluid pressure at each node, For the first The friction angle of each node.

6. The fracture seepage prediction method combining yield criterion and network topology according to claim 5, characterized in that, In step S5, the state of the crack is divided into two types: stable and unstable. When the shear force on the damaged node and the crack reaches the Mohr-Coulomb strength, the corresponding crack expands and the crack becomes unstable, resulting in stress redistribution, which in turn triggers the percolation change of the connected region. Define percolation threshold When the maximum connected cluster size satisfy: ； Then the fracture network enters a critical state of sudden change; From the adjacency matrix Damage index analysis and calculation; Subject to the current stress field Influence; ； In the formula, This is the initial percolation value. For normal stress is The percolation threshold at that time, For compressive strength, It is normal stress. This is the stress sensitivity coefficient.

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