Method for quantitatively ranking importance of fractures in rock mass seepage process

Abstract

The invention relates to a method for quantitatively ranking importance of fractures in a rock mass seepage process. The method is suitable for the field of rock fracture network seepage. According to the technical scheme, the method for conducting quantitative ranking on the importance of fractures in the rock mass seepage process comprises the steps that a DFN model fracture network is converted into a complex network; and calculating characteristic parameters of the complex network, and determining the fracture importance index of each fracture in the fracture network based on the characteristic parameters. According to the method, the fracture network is converted into the complex network, so that the characteristic parameters capable of reflecting the importance of all the fractures are calculated based on the complex network, the fracture importance indexes of all the fractures in the fracture network are determined through the characteristic parameters, and then quantitative ranking of the fracture importance is achieved based on the fracture importance indexes. According to the method, the seepage contribution of each fracture to the fracture network can be accurately evaluated, and a new perspective is provided for quantifying the seepage contribution of each fracture to the fracture network.

Description

Technical Field

[0001] The invention relates to a method for quantitatively ranking the importance of cracks in the rock mass seepage process, and is applicable to the field of rock mass crack network seepage. Background Art

[0002] Many engineering activities, such as underground disaster prevention, environmental protection, and energy development, are closely related to rock seepage. The study of rock seepage is crucial for predicting and controlling fluid movement, and can help solve the two major engineering problems of enhancing seepage and preventing seepage. Natural rock mass consists of rock matrix (rock blocks) and fractures. Since fractures usually have higher permeability than the surrounding rock matrix, they become the main channels for fluid flow and solute migration, thus determining the seepage characteristics of the entire rock mass. In order to simulate the rock mass more accurately without considering the matrix permeability, the discrete fracture network (DFN) model is usually used. The DFN model can describe the specific location, occurrence, and size of each fracture, and is particularly suitable for rock masses with matrix permeability much lower than fracture permeability, and has great potential for accurately describing fluid flow.

[0003] However, natural rock mass is a three-dimensional structure with extremely complex fracture geometry and an intricate network between fractures. Traditional analysis methods often ignore the contribution of each fracture in the fracture network to the overall seepage, and usually only focus on the overall seepage characteristics of the fracture network. Although many scholars have conducted extensive research in this field and achieved remarkable results, these studies often ignore the interconnectedness between fractures. This neglect makes it difficult to quantitatively evaluate the contribution of each fracture to the overall seepage of the fracture network, which in turn limits the effective control and regulation of seepage in rock engineering. Summary of the invention

[0004] The technical problem to be solved by the present invention is: in view of the above existing problems, a method for quantitatively ranking the importance of cracks in the rock mass seepage process is provided.

[0005] The technical solution adopted by the present invention is: a method for quantitatively ranking the importance of cracks in the rock mass seepage process, comprising:

[0006] Convert the DFN model fracture network into a complex network;

[0007] The characteristic parameters of the complex network are calculated, and the fracture importance index of each fracture in the fracture network is determined based on the characteristic parameters.

[0008] The method of converting the DFN model crack network into a complex network includes:

[0009] Assuming that each fracture in the fracture network of the DFN model is disk-shaped, the plane equation corresponding to each disk-shaped fracture is calculated based on the size, normal vector coordinates and center point coordinates of the disk-shaped fracture.

[0010] Based on the plane equations of each disk-shaped crack, the intersection relationship of each crack in the DFN model is determined;

[0011] Based on the intersection relationship of each fracture in the DFN model, the fracture network in the DFN model is converted into data in the form of node-edge;

[0012] The node-edge data were imported into Gephi software to obtain a complex network corresponding to the fracture network.

[0013] The determining of the intersection relationship of each crack in the DFN model based on the plane equation of each disk-shaped crack includes:

[0014] Based on the plane equations of any two disc-shaped cracks, determine the equation of the straight line l formed by the intersection of the two planes;

[0015] Based on the distance from the center points of the two disk-shaped cracks to the straight line l, the intersection relationship of the two disk-shaped cracks is preliminarily determined;

[0016] Based on the plane equations of the two disk-shaped cracks and the straight line l, the intersection points of the two disk-shaped cracks and the straight line l are calculated.

[0017] Based on the intersection points of the two disk-shaped cracks and the straight line l, the intersection relationship of the two disk-shaped cracks is determined.

[0018] The characteristic parameters of the complex network include PageRank value and betweenness centrality.

[0019] The method of determining the fracture importance index of each fracture in the fracture network based on the characteristic parameters includes:

[0020] The case ranking method is used to add up the rankings of each crack based on the PageRank value and betweenness centrality, and finally determine the crack importance index of each crack.

[0021] A system for quantitatively ranking the importance of fractures in rock mass seepage, characterized by comprising:

[0022] Network conversion module, used to convert the DFN model crack network into a complex network;

[0023] The quantitative ranking module is used to calculate the characteristic parameters of the complex network and determine the fracture importance index of each fracture in the fracture network based on the characteristic parameters.

[0024] A method for determining equivalent permeability coefficient of a fracture network, characterized by comprising:

[0025] Determining the fracture ranking of each fracture in the fracture network based on the quantitative ranking method;

[0026] Based on the equivalent permeability of the fracture network composed of the top 50% fractures, the equivalent permeability of the initial fracture network was determined using an empirical formula.

[0027] The equivalent permeability coefficient of the fracture network composed of the top 50% fractures is determined by using an empirical formula to determine the equivalent permeability coefficient of the initial fracture network, including:

[0028] K=2*K 50％

[0029] Where K is the equivalent permeability of the initial fracture network, K 50％ is the equivalent permeability of the fracture network consisting of the top 50% fractures.

[0030] A storage medium stores a computer program executable by a processor, wherein the computer program implements the steps of the method when executed.

[0031] A data processing device comprises a memory and a processor, wherein the memory stores a computer program executable by the processor, and is characterized in that the steps of the method are implemented when the computer program is executed.

[0032] The beneficial effect of the present invention is as follows: the present invention converts the fracture network into a complex network, thereby calculating characteristic parameters that can reflect the importance of each fracture based on the complex network, and using the characteristic parameters to determine the fracture importance index of each fracture in the fracture network, and then realizing quantitative ranking of fracture importance based on the fracture importance index.

[0033] The present invention can accurately evaluate the contribution of each fracture to the seepage of the fracture network, and provides a new perspective for quantifying the contribution of each fracture to the seepage of the fracture network.

[0034] The invention is based on a fracture importance ranking method and utilizes the equivalent permeability of a fracture network composed of the top 50% fractures to determine the equivalent permeability of an initial fracture network, thereby overcoming the technical problems of long calculation time and difficult convergence in the calculation of equivalent permeability of a DFN model. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of the locations of two disc-shaped cracks in three-dimensional space.

[0036] Figure 2 Schematic diagram of converting a fractured network into a complex network.

[0037] Figure 3The equivalent permeability coefficients and their errors of 10 fracture networks in the DFN model along the X, Y, and Z directions (in the figure, the solid lines in the radar chart represent the equivalent permeability coefficients of the DFN after sequentially deleting fracture subsets 1-10, and the dashed lines represent the equivalent permeability coefficients of the initial DFN; the bar chart represents the errors between the equivalent permeability coefficients of the DFN after deleting fracture subsets 1-10 and the equivalent permeability coefficients of the initial DFN).

[0038] Figure 4 The equivalent permeability coefficients and errors of the DFN model calculated by numerical simulation and empirical formula (in the figure, K0 represents the equivalent permeability coefficient calculated by numerical simulation, K represents the equivalent permeability coefficient calculated by empirical formula, and ER is the error between the two). Specific implementation mode

[0039] Example 1: This example is a method for quantitatively ranking the importance of fractures in the seepage process of rock masses, specifically including the following steps:

[0040] S100. Convert the fracture network of the DFN model into a complex network.

[0041] S110. As shown in Figure 1 , assume that each fracture in the fracture network of the DFN model is disk-shaped, and based on the size, normal vector coordinates, and center point coordinates of the disk-shaped fracture, calculate the plane equation corresponding to each disk-shaped fracture:

[0042] A i (x - X i ) + B i (y - Y i ) + C i (z - Z i ) = 0 (1a)

[0043] A j (x - X j ) + B j (y - Y j ) + C j (z - Z j ) = 0 (1b)

[0044] In the formula, and are the normal vector coordinates of the i-th and j-th disks respectively; O i (X i , Y i , Z i ) and O j (X j , Y j , Z j ) are the center point coordinates of the i-th and j-th disks respectively.

[0045] S120. Based on the plane equations of the disk-shaped cracks, determine the intersection relationship of the cracks in the DFN model.

[0046] S121. Based on the plane equations of the two disc-shaped cracks, determine the equation of the straight line l formed by the intersection of the two planes. The equation of the straight line (l) formed by the intersection of the two planes is derived as follows:

[0047] (XX d ) / m=(YY d ) / n=(ZY d ) / p (2)

[0048] In the formula, is the direction vector of line l, and (m, n, p) = (B i C j -B j C i , C i A j -A i C j , A i B j -A j B i ), click l 0 (X d , Y d , Z d ) is any point on the line l.

[0049] S122. Determine the intersection relationship between the two disk-shaped cracks based on the distance from the center point of the disk-shaped crack to the straight line l.

[0050] When the distance from the center point of the disk to the straight line l is greater than the radius of the disk, the two disks do not intersect; if the distance from the center point of the two disks to the intersection line is less than their respective radii, the two disks intersect with the intersection line.

[0051] S123. Based on the plane equation of the disk-shaped crack and the straight line l, calculate the intersection point of the disk-shaped crack and the straight line l.

[0052] Then the intersection points of the two disks with the intersection line are calculated. If any intersection point of a disk is within the interval of the intersection point of the other disk, the two disks intersect; conversely, if none of the intersection points are within the interval, the two disks do not intersect.

[0053] The two intersection points P between the i-th disk and the line l 1i , P 2i The coordinates of the jth disk and the line l are determined by equations (1a) and (2); the two intersection points P between the jth disk and the line l 1j , P 2j The coordinates of are determined by equations (1b) and (2) as follows:

[0054]

[0055] S130. Based on the intersection relationship of each crack in the DFN model, the crack network in the DFN model is converted into a node-edge form compatible with the Gephi software.

[0056] S140, importing the node-edge data into Gephi software to obtain a complex network corresponding to the fracture network, thereby realizing the conversion of the fracture network to the complex network. The specific conversion process is as follows: Figure 2 shown.

[0057] S200, calculating characteristic parameters of the complex network, and determining the fracture importance index of each fracture in the fracture network based on the characteristic parameters, and then ranking the importance of each fracture according to the fracture importance index.

[0058] S210. Calculate the PageRank value and betweenness centrality of complex networks in Gephi software.

[0059] S220, ranking the cracks according to the characteristic parameters PageRank value and betweenness centrality. Using the case ranking method, the ranking of each crack according to the PageRank value and betweenness centrality is added up, and finally the crack importance index (FII) of each crack is determined:

[0060] FII i =R Pi +R Bi (4)

[0061] Where, FII i is the crack importance index of the i-th crack, R Pi is the ranking of the ith crack based on PageRank value, R Bi is the ranking of the i-th crack based on betweenness centrality.

[0062] S230. The importance ranking of each fracture in the fracture network in the rock mass seepage process is achieved through the fracture importance index.

[0063] Example 2: This example is a system for quantitatively ranking the importance of cracks in the rock seepage process, including: a network conversion module and a quantitative ranking module, etc., wherein the network conversion module is used to convert the crack network into a complex network; the quantitative ranking module is used to calculate the characteristic parameters of the complex network, and determine the crack importance index of each crack in the crack network based on the characteristic parameters.

[0064] Embodiment 3: This embodiment is a storage medium on which a computer program that can be executed by a processor is stored. When the computer program is executed, the steps of the quantitative ranking method in Embodiment 1 are implemented.

[0065] Embodiment 4: This embodiment is a data processing device having a memory and a processor. The memory stores a computer program that can be executed by the processor. When the computer program is executed, the steps of the quantitative ranking method in Embodiment 1 are implemented.

[0066] Embodiment 5: This embodiment is a method for determining the equivalent permeability coefficient of a fracture network, which specifically includes the following steps:

[0067] A. Based on the quantitative ranking method in Example 1, the importance ranking of each fracture in the fracture network in the rock mass seepage process is obtained.

[0068] B. Determine the equivalent permeability of the initial fracture network based on the equivalent permeability of the fracture network composed of the top 50% fractures.

[0069] The equivalent permeability coefficient of the fracture network composed of fractures in different proportions shows the following rule: as the proportion of fractures increases, the equivalent permeability coefficient gradually increases and presents an S-shaped curve, which conforms to the simplest S-shaped model - the Logistic model.

[0070] In the Logistic model, the lower asymptote of the curve is 0, the upper asymptote is the maximum value, and the inflection point is approximately 1 / 2 of the maximum value. Therefore, it can be deduced that the equivalent permeability of the fracture network composed of the top 50% fractures can be used to predict the equivalent permeability of the initial fracture network. The empirical formula is:

[0071] K=2*K 50％ (5)

[0072] Where K is the equivalent permeability of the initial fracture network, K 50％ is the equivalent permeability of the fracture network consisting of the top 50% fractures.

[0073] In order to verify the effectiveness of the method for determining the equivalent permeability coefficient of the fracture network in this embodiment, a hypothetical case was designed for verification, and the model parameters were set as follows: the three-dimensional fracture density was 3.1831 / m3, the disk radius was 0.05m, and the disk radius obeyed a power-law distribution with a standard deviation of 10% of the radius. To construct an anisotropic DFN model, the Fisher distribution parameter κ was set to 15. In order to reduce the significant changes in flow in different directions, the model consists of two groups of orthogonal fractures, one of which has an average normal vector inclination of 161° and an average dip of 41°; the other has an average normal vector inclination of 65° and an average dip of 7°. The model size is 20m×20m×20m. See Table 1 for specific parameters.

[0074] Table 1DFN model parameters

[0075] Crack group number 1 2 Length distribution Power Law Distribution Power Law Distribution Occurrence distribution Fisher Fisher Occurrence Fisher parameter κ 15 15 Average inclination (pole) / ° 161 65 Average inclination (pole) / ° 41 7 Mean radius / m 0.5 0.5 Radius standard deviation / m 0.05 0.05 <![CDATA[Three-dimensional density / (lines·m -3 )]]> 3.1831 / 2 3.1831 / 2

[0076] After converting the fracture network into a complex network, the fractures are ranked according to step S200, and the ranked fractures are divided into 10 subsets, as shown in Table 2. By deleting fracture subsets 1 to 10 in sequence, 10 new fracture networks are created, as shown in Table 3.

[0077] Table 2 Composition of fracture subsets

[0078] Fracture subset number Different proportions of cracks after ranking 1 0-10％ 2 10％-20％ 3 20％-30％ 4 30％-40％ 5 40％-50％ 6 50％-60％ 7 60％-70％ 8 70％-80％ 9 80％-90％ 10 90％-100％

[0079] Table 3 Fracture network composition

[0080] Fracture network number Deleted fracture subset #1 1 #2 2 #3 3 #4 4 #5 5 #6 6 #7 7 #8 8 #9 9 #10 10

[0081] Subsequently, the equivalent permeabilities of the new fracture network in Table 3 along the X, Y, and Z directions were calculated. Figure 3 The equivalent permeability coefficients and their errors of the 10 fracture networks are shown. As can be seen from the figure, as the fracture network number increases, the equivalent permeability coefficients along the X, Y and Z directions continue to increase and gradually approach the values ​​of the initial DFN model, while the errors gradually decrease. This trend shows that the influence of the fracture subsets deleted in sequence on the seepage process of the fracture network gradually weakens.

[0082] Then, the equivalent permeability coefficient of the DFN model was calculated using the empirical formula according to step B and compared with the results of numerical simulation, as shown in Figure 4 As shown in the figure, it can be seen that the equivalent permeability coefficient calculated by the empirical formula is close to the numerical simulation result. It can be seen that this method is effective and feasible.

[0083] Embodiment 6: This embodiment is a storage medium on which a computer program that can be executed by a processor is stored. When the computer program is executed, the steps of the method for determining the equivalent permeability coefficient of the fracture network in Embodiment 5 are implemented.

[0084] Embodiment 7: This embodiment is a data processing device having a memory and a processor. The memory stores a computer program that can be executed by the processor. When the computer program is executed, the steps of the method for determining the equivalent permeability coefficient of the fracture network in Embodiment 5 are implemented.

Claims

1. A method for quantitatively ranking the importance of fractures in rock mass seepage, characterized in that: include: Convert fractured networks into complex networks; The characteristic parameters of the complex network are calculated, and the fracture importance index of each fracture in the fracture network is determined based on the characteristic parameters.

2. The method for quantitatively ranking the importance of cracks in rock mass seepage according to claim 1, characterized in that: The converting of the fracture network into a complex network comprises: Assuming that each fracture in the fracture network is disk-shaped, and based on the size, normal vector coordinates and center point coordinates of the disk-shaped fracture, the plane equation corresponding to each disk-shaped fracture is calculated; Based on the plane equations of each disk-shaped fracture, the intersection relationship of each fracture in the fracture network is determined; Based on the intersection relationship of each fracture in the fracture network, the fracture network is converted into data in the form of node-edge; The node-edge data were imported into Gephi software to obtain a complex network corresponding to the fracture network.

3. The method for quantitatively ranking the importance of cracks in rock mass seepage according to claim 2, characterized in that: The determining of the intersection relationship of each fracture in the fracture network based on the plane equation of each disc-shaped fracture comprises: Based on the plane equations of any two disc-shaped cracks, determine the equation of the straight line l formed by the intersection of the two planes; Based on the distances from the center points of the two disk-shaped cracks to the straight line l, the intersection relationship of the two disk-shaped cracks is determined; Based on the plane equations of the two disk-shaped cracks and the straight line l, the intersection points of the disk-shaped cracks and the straight line l are calculated.

4. The method for quantitatively ranking the importance of cracks in rock mass seepage according to claim 1, characterized in that: Features: The characteristic parameters of the complex network include PageRank value and betweenness centrality.

5. The method for quantitatively ranking the importance of cracks in rock mass seepage according to claim 4, characterized in that: The method of determining the fracture importance index of each fracture in the fracture network based on the characteristic parameters includes: The case ranking method is used to add up the rankings of each crack based on the PageRank value and betweenness centrality, and finally determine the crack importance index of each crack.

6. A system for quantitatively ranking the importance of fractures in rock mass seepage, characterized in that: include: Network conversion module, used to convert fractured networks into complex networks; The quantitative ranking module is used to calculate the characteristic parameters of the complex network and determine the fracture importance index of each fracture in the fracture network based on the characteristic parameters.

7. A method for determining equivalent permeability of a fracture network, characterized in that: include: Determining the fracture ranking of each fracture in the fracture network based on the quantitative ranking method according to any one of claims 1 to 5; The equivalent permeability of the initial fracture network is determined based on the equivalent permeability of the fracture network composed of the top 50% fractures.

8. The method for determining equivalent permeability of a fracture network according to claim 7, characterized in that: The equivalent permeability coefficient of the fracture network based on the equivalent permeability coefficient of the fracture network composed of the top 50% fractures is determined, comprising: K=2*K 50％ Where K is the equivalent permeability of the initial fracture network, K 50％ is the equivalent permeability of the fracture network consisting of the top 50% fractures.

9. A storage medium having stored thereon a computer program executable by a processor, characterized in that: When the computer program is executed, the steps of the method according to any one of claims 1 to 5, 7 and 8 are implemented.

10. A data processing device comprising a memory and a processor, wherein the memory stores a computer program executable by the processor, wherein: When the computer program is executed, the steps of the method according to any one of claims 1 to 5, 7 and 8 are implemented.

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