A method for quickly detecting fracture intersection based on improved SAP algorithm

Abstract

The application discloses a kind of based on improved SAP algorithm's fissure intersection fast detection method, comprising: using axisymmetric bounding box algorithm to convert all sample fissure into bounding box, simplify calculation process;Then using improved SAP algorithm to fissure bounding box preliminary collision determination, reduce the calculation amount of fine solution, obtain the fissure pair set that can occur intersection;Improved SAP algorithm includes ISAP algorithm for small sparse network and MSAP algorithm for large complex network;Finally, based on the space vector theory, the fissure pair in the fissure pair set is finely judged and solved intersection line.The application improves the short board of high cost in the process of three-dimensional fissure network intersection detection calculation, and is suitable for fissure network of different scales.

Description

Technical Field

[0001] This invention relates to a method for refining the solution of fracture network intersections in underground strata, specifically to a rapid fracture intersection detection method based on an improved SAP algorithm. Background Technology

[0002] Fractures are widely distributed in the Earth's surface, serving as the main channels for fluid transport and solute migration in low-permeability rock formations. Their spatial topology is particularly complex due to the coupling effects of weathering and geostress, directly impacting various underground engineering applications such as engineering construction, groundwater pollution treatment, and carbon dioxide geological storage. Compared to laboratory and field experiments, numerical simulation is clearly better suited to handle the enormous spatiotemporal scales in large-scale engineering research, such as the Discrete Fracture Network (DFN) model. Accurate analysis of fracture intersection relationships is fundamental to fracture numerical simulation and fracture network topology analysis.

[0003] In recent years, the bounding box algorithm and the sweep-and-pruning (SAP) algorithm have been widely used in crack intersection detection, but research has mostly been limited to small crack networks. The SAP algorithm, also known as the sweep-and-prune algorithm, typically determines whether objects have reached a proximity state where collision is likely by detecting the boundary overlap of their axisymmetric bounding boxes (AABBs) in one-dimensional space. In three-dimensional space, the SAP algorithm is usually simplified to a projection detection problem in three orthogonal directions, i.e., independently scanning and analyzing the intervals occupied by the objects along the x, y, and z coordinate axes, which suffers from high computational cost. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a low-computation-cost, fast fracture intersection detection method based on an improved SAP algorithm for fractured formations at multiple scales.

[0005] Technical solution: The present invention provides a rapid detection method for intersecting cracks based on an improved SAP algorithm, comprising:

[0006] (1) Collect basic data on fracture networks and construct a target discrete three-dimensional fracture network based on the basic data on fracture networks;

[0007] (2) The axisymmetric bounding box algorithm AABB is used to transform each slit in the network into the corresponding minimum bounding box;

[0008] (3) Based on the improved SAP algorithm, preliminary collision detection is performed on the bounding box to obtain the set of possible intersecting gap pairs; the improved SAP algorithm includes the ISAP algorithm for small sparse networks and the MSAP algorithm for large complex networks.

[0009] (4) Based on the spatial vector theory, the precise intersection line of the fracture pairs in the fracture pair set is solved to obtain the fine topological intersection information of the fracture network, including the fracture pairs and their corresponding fracture intersection line positions and lengths.

[0010] Furthermore, in step (1), the basic data of the fracture network includes fracture orientation distribution characteristics, fracture diameter distribution characteristics, and fracture density distribution characteristics.

[0011] Furthermore, in step (2), the axisymmetric bounding box is the smallest bounding rectangle whose edges are strictly aligned with the coordinate axes. The position of the bounding rectangle in space is defined by the minimum and maximum values ​​of the outer edge of the slit on each coordinate axis. The single slit must be polygonal in shape.

[0012] Furthermore, for the disk crack, 24 discrete points evenly distributed on the edge are used to discretize the continuous crack surface into an approximately circular 24-sided structure.

[0013] Further, in step (3), the ISAP algorithm includes: assuming the x-axis is the scanning axis, projecting all AABB bounding boxes onto the x-axis to form a one-dimensional interval segment; the projection of each AABB bounding box onto the x-axis is a linear interval containing two endpoints; when two AABB bounding boxes have potential intersections, their x-axis projection intervals will inevitably overlap.

[0014] Potential intersecting fracture pairs are obtained by performing a single scan along the x-axis to the starting endpoint of the interval. Subsequently, the overlapping of the projected intervals is verified in the y-axis and z-axis directions. Only when the projections in the three orthogonal directions overlap are they identified as potential intersecting fracture pairs.

[0015] Furthermore, the MSAP algorithm includes: dividing the large study area into several sub-domains, allocating the disk crack to the corresponding sub-regions based on the crack center coordinates, and then applying the ISAP algorithm to the interior of each sub-domain and the adjacent boundary regions.

[0016] Furthermore, the subdomains are divided as follows: the region is kept continuous along the longest side, and the other two axes are discretized into a grid based on 2.5 times the maximum diameter of a single slit; the region is set as the scanning axis along the longest side.

[0017] Furthermore, in step (4), the first step in solving the precise intersection line of the selected potential intersecting fracture pairs is to determine the spatial positional relationship between the two fracture planes; taking the normal vector and a point P1 on fracture P, for all endpoints on fracture G, we have:

[0018]

[0019] in, G represents the normal vector of the crack P; iRepresents the endpoints on the crack G, i = 1, 2, 3, ...; γ represents the vector. sum vector The included angle; S i It is a vector sum vector The sign of the result of the dot product operation;

[0020] When S i When the signs are the same, it proves that all endpoints of crack P are on the same side of the plane containing crack G, and the crack does not intersect the plane; conversely, when the signs of two adjacent endpoints of the crack are the same, it proves that all endpoints of crack P are on the same side of the plane containing crack G, and the crack does not intersect the plane. i At the same time, prove that the straight line formed by the two endpoints passes through the plane; and solve for the intersection point G of the plane containing the fracture and the other fracture according to the following equation. x1 G x2 ,P x1 ,P x2 :

[0021]

[0022] The relative positions of the fracture pairs are determined based on the four intersection points.

[0023] Furthermore, when the four intersection points lie on the same straight line, the fracture pairs may have three relative positions:

[0024] Case (I) is non-intersecting;

[0025] Case (II) intersects, and the line of intersection is

[0026] Case (III) Intersection, the line of intersection is

[0027] Furthermore, when crack pairs intersect, the length l of the intersection line is determined using Euclidean distance:

[0028]

[0029] Where (x1,y1,z1) and (x2,y2,z2) are the two endpoints of the intersection line.

[0030] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: The present invention improves the high computational cost in the intersection detection process of three-dimensional fracture networks by using the AABB algorithm and the improved SAP algorithm. It is applicable to fracture networks of different scales and can efficiently and reliably identify the topology of various three-dimensional fracture networks, providing strong support for the topology analysis of fracture networks. Attached Figure Description

[0031] Figure 1This is a flowchart of a rapid crack intersection detection method based on an improved SAP algorithm provided in an embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of the axisymmetric bounding box of the discretized disk crack in an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram of the ISAP algorithm in an embodiment of the present invention;

[0034] Figure 4 This is a schematic diagram of the fine solution for the intersection of cracks in an embodiment of the present invention;

[0035] Figure 5 (a) is a schematic diagram of the target discrete fracture network in an embodiment of the present invention. Figure 5 (b) is a schematic diagram of the region discretization of the MSAP algorithm in an embodiment of the present invention;

[0036] Figure 6 This is a schematic diagram illustrating the computational cost of intersection detection using the improved SAP algorithm under different crack densities in an embodiment of the present invention.

[0037] Figure 7 This is a schematic diagram illustrating the computational cost of intersection detection using the improved SAP algorithm under different region sizes in this embodiment of the invention.

[0038] Figure 8 This is a schematic diagram illustrating the intersection detection calculation cost of the MSAP algorithm under different discrete schemes in this embodiment of the invention. Detailed Implementation

[0039] The invention will now be further described with reference to the accompanying drawings.

[0040] like Figure 1 As shown, this embodiment of the invention provides a fast crack intersection detection method based on an improved SAP algorithm, comprising the following steps:

[0041] (1) Collect basic data on fracture networks and construct a target discrete three-dimensional fracture network based on the basic data on fracture networks;

[0042] The basic data of the fracture network includes the characteristics of fracture orientation distribution, fracture diameter distribution, and fracture density distribution.

[0043] (2) Use the axis-aligned bounding box (AABB) algorithm to transform each slit in the network into its corresponding minimum bounding rectangle;

[0044] An axisymmetric bounding box is the smallest bounding rectangle whose edges are strictly aligned with the coordinate axes of a single crack. The position of the bounding rectangle in space is defined by the minimum and maximum values ​​of the crack's outer edge on each coordinate axis. To ensure the method's adaptability to cracks of different shapes, the single crack must be polygonal. For example... Figure 2 As shown, for a disk crack, 24 discrete points evenly distributed on the edge are used to discretize the continuous crack surface into an approximately circular 24-sided structure.

[0045] (3) Based on the improved SAP algorithm, preliminary collision detection is performed on the bounding box to obtain the set of possible intersecting gap pairs; the improved SAP algorithm includes the ISAP algorithm for small sparse networks and the MSAP algorithm for large complex networks.

[0046] The ISAP algorithm is an improvement on the traditional SAP algorithm, significantly reducing computational complexity by optimizing the scanning process. For example... Figure 3 As shown, assuming the x-axis is the main scanning axis, all AABB bounding boxes are projected onto the x-axis to form a one-dimensional interval segment. The projection of each AABB bounding box onto the x-axis represents a linear interval containing its two endpoints. When two AABB bounding boxes potentially intersect, their x-axis projection intervals must overlap. The improved algorithm can obtain potential intersecting gap pairs by performing a single scan along the x-axis at the starting endpoints of the interval, and then verify the overlap of the projection intervals sequentially in the y-axis and z-axis directions. Only when the projections in all three orthogonal directions overlap are they determined to be potential intersecting gap pairs. Compared to the traditional SAP algorithm, which requires three independent scans for 3D applications, this method significantly reduces the computational cost of non-overlapping AABB pairs with a single scan.

[0047] The MSAP algorithm is a spatial divide-and-conquer optimization improvement proposed based on the ISAP algorithm to address the efficiency problem caused by large-scale fragmented networks. For example... Figure 5 As shown, the large research area is divided into several sub-regions. After the disk fracture is assigned to the corresponding sub-region based on the fracture center coordinates, the ISAP algorithm is applied to the internal and adjacent boundary regions of each sub-region. The sub-region division can be optimized according to the research objectives. In this embodiment, the longest side of the region is used to maintain continuity (set as the scanning axis), and the other two axes are discretized into a grid based on 2.5 times the maximum diameter of a single fracture piece.

[0048] (4) Based on the spatial vector theory, the precise intersection line of the fracture pairs in the fracture pair set is solved to obtain the fine topological intersection information of the fracture network, including the fracture pairs and their corresponding fracture intersection line positions and lengths.

[0049] The first step in accurately solving for the intersection line of the selected potential intersecting fracture pairs is to determine the spatial relationship between the two fracture planes. For example... Figure 4As shown, taking a normal vector on crack P and a point P1, for all endpoints on crack G, we have:

[0050]

[0051] in, G represents the normal vector of the crack P; i Represents the endpoints on the crack G, i = 1, 2, 3, ...; γ represents the vector. sum vector The included angle; S i It is a vector sum vector The sign of the result of the dot product operation.

[0052] When S i When the signs are the same, it proves that all endpoints of crack P are on the same side of the plane containing crack G, and the crack does not intersect the plane. Conversely, when the signs of adjacent endpoints of crack P and crack G are the same, it proves that all endpoints of crack P are on the same side of the plane containing crack G, and the crack does not intersect the plane. i At the same time, prove that the straight line formed by the two endpoints passes through the plane. Then, solve for the intersection point G of the plane containing the fracture and the other fracture using the following equation. x1 G x2 ,P x1 ,P x2 :

[0053]

[0054] When the four intersection points lie on the same straight line, the fracture pairs may have three relative positions:

[0055] Case (I) is non-intersecting;

[0056] Case (II) intersects, and the line of intersection is

[0057] Case (III) Intersection, the line of intersection is

[0058] When crack pairs intersect, the length l of the intersection line is determined using Euclidean distance:

[0059]

[0060] Where (x1,y1,z1) and (x2,y2,z2) are the two endpoints of the intersection line.

[0061] The fast fracture intersection detection method based on the improved SAP algorithm provided in this invention uses the axis-aligned bounding box (AABB) algorithm and the improved scan pruning (SAP) algorithm to detect intersecting fractures. It effectively overcomes the bottleneck problem of computational efficiency in the intersection detection of three-dimensional fracture networks, realizes the accurate analysis of the topological relationship of complex fracture systems, and provides reliable technical support for the topological structure analysis of rock fracture networks and engineering geological applications.

[0062] Here is a specific example.

[0063] This example presents a numerical experiment on topology detection of three-dimensional fracture networks based on an improved SAP algorithm. The experiment comprehensively considers both ideal fracture network conditions and actual site conditions, and mainly includes three parts: 1) effectiveness test of the improved SAP algorithm in intersection detection; 2) performance test of the improved SAP algorithm in intersection detection in different fracture networks; 3) comparative analysis of the improved SAP algorithm with existing research.

[0064] 1) Improve the effectiveness test of the SAP algorithm in intersection detection

[0065] This example uses a cubic fracture network model with a side length of 1m, where each fracture is constructed as a disk with a diameter of 0.1m. Their spatial orientation is determined by randomly generated dip angle and dip direction parameters. The MSAP method spatially divides the study area into 16 sub-regions by configuring 1, 4, and 4 grid cells along the x, y, and z axes, respectively. The test is based on the fracture density per unit volume (P). 30 Five control scenarios were set, corresponding to numerical models with 250, 500, 750, 1000, and 1250 fractures, respectively. Ten fracture network samples were generated for each scenario, meaning the test included a total of 50 fracture networks.

[0066] The reliability of the improved SAP algorithm was verified using the brute force (BF) test method. Test results showed that in all 50 test cases, the intersection detection results of the MSAP and ISAP algorithms were completely consistent with the BF method in terms of the number of intersection lines and spatial length, achieving a 100% agreement rate. This quantitatively verified the complete reliability of the improved SAP algorithm in three-dimensional crack intersection detection.

[0067] Table 1 shows the comparison of computational costs of BF, traditional SAP, ISAP, and MSAP under various scenarios. The improved SAP algorithm proposed in this invention has a significantly lower average computational cost than the traditional SAP and BF methods. When the fracture density is low (P... 30 When the fracture density is relatively small, the computational efficiency differences among the four methods are small; as the fracture density increases, the improved SAP algorithm exhibits an order-of-magnitude computational efficiency advantage over the BF and SAP methods. Comparing the two improved SAP algorithms, ISAP's efficiency advantage is more significant. For example, when P...30 When the value is 250, the computation time of ISAP is only 1 / 30 to 1 / 3 of that of the control method; however, as the number of fractures increases, the difference in computational efficiency between MSAP and ISAP gradually converges.

[0068] To evaluate the algorithm's stability, this example uses the coefficient of variation (COP) for robustness analysis. Except for the MSAP method exhibiting higher dispersion in low-density fracture networks, the improved SAP algorithm and the BF algorithm have similar COP levels, demonstrating that its computational stability is similar to that of the BF algorithm. Combining the computational efficiency and stability test results, the improved SAP algorithm proposed in this invention is proven to be reliable and efficient in three-dimensional fracture intersection detection.

[0069] Table 1. Computational costs of four intersection detection methods in different scenarios.

[0070]

[0071] 2) Performance testing of improved SAP algorithm for intersection detection in different fracture networks

[0072] Based on test 1), multiple sets of control variables (P) were used. 30 The performance of the improved SAP algorithm is comprehensively evaluated through tests (region size and discretization scheme), and three specific test schemes are proposed:

[0073] ① Number of cracks (P) 30 Sensitivity analysis: With a fixed region size (a cubic crack region with a side length of 1m) and a discrete scheme, network models containing 2000, 3000, 5000, 8000 and 10000 disk cracks were constructed to evaluate the impact of the number of cracks on the algorithm efficiency.

[0074] ②Regional-scale sensitivity analysis: Fixed fracture density (P) 30 =250) and discrete schemes were used to construct cubic crack regions with side lengths of 1m, 2m, 5m and 10m, corresponding to a total number of cracks of 1000, 8000, 125000 and 1000000 respectively, and the impact of spatial scale on algorithm efficiency was evaluated.

[0075] ③ Discrete scheme optimization analysis: Taking the 5m cubic crack region in scenario ② as an example, the x-axis is fixed as the main scanning axis and no mesh is performed. The y and z axes are set with 2, 4, 8, 12, 16 and 20 mesh units respectively, forming different sub-region partitioning schemes of 4 to 400 sub-regions. The optimization effect of sub-region density on computational efficiency is evaluated.

[0076] The remaining settings for the Slit Network and MSAP are the same as in Test 1).

[0077] The test results for scenario ① are as follows Figure 6As shown, when the number of fractures is small, ISAP has a small efficiency advantage over MSAP. When the number of fractures exceeds 3000, the computational advantage of MSAP gradually becomes apparent, and its efficiency advantage becomes more significant with the increase of the number of fractures. The test results for scenario ① are as follows. Figure 7 As shown, when the fracture density is the same, the computation time increases exponentially with the region scale, and the efficiency advantage of ISAP and MSAP is more obvious. When the region side length is 10, the average solution time of MSAP is 3952.10s, which is only one-third of the time taken by the ISAP method, proving that the discrete scheme has a significant computational advantage in large regions. Figure 8 The test results for different discrete schemes in scenario ③ are presented. Under the same fractured network, the computation time of the MSAP algorithm gradually stabilizes as the number of sub-regions increases. Compared with the ISAP algorithm, the MSAP algorithm improves computational efficiency by 27.60% and 42.85% when the number of sub-regions is equal to 2 and 4, respectively. However, when the number of sub-regions is greater than 4, the computational efficiency tends to stabilize and no longer shows significant improvement.

[0078] 3) Comparative analysis of the improved SAP algorithm and existing algorithms

[0079] Two existing algorithms were selected: the separating axis theorem and the BBSL algorithm. The separating axis theorem is a commonly used method for intersection detection, while the BBSL algorithm is a fast intersection detection algorithm for polygonal cracks, improved in recent years based on bounding boxes and scan lines. When the separating axis theorem was applied to a crack network containing 58 cracks, the intersection detection time was 170.5s, while the ISAP algorithm only took 0.004s for the same network, representing a four-order-of-magnitude improvement in efficiency. The BBSL algorithm was applied to a cubic crack region with a side length of 100m for fast intersection detection. The scenario settings and computation time are shown in Table 2. The results show that compared with BBSL, ISAP and MSAP have improved computational efficiency by 50%–61% and 49%–65%, respectively. Moreover, MSAP still shows a significant computational advantage when the number of cracks increases.

[0080] Table 2. Computational costs of three intersection detection methods under different scenarios.

[0081]

Claims

1. A rapid detection method for intersecting cracks based on an improved SAP algorithm, characterized in that, include: (1) Collect basic data on fracture networks and construct a target discrete three-dimensional fracture network based on the basic data on fracture networks; (2) The axisymmetric bounding box algorithm AABB is used to transform each slit in the network into the corresponding minimum bounding box; (3) Based on the improved SAP algorithm, preliminary collision detection is performed on the bounding box to obtain the set of possible intersecting gap pairs; the improved SAP algorithm includes the ISAP algorithm for small sparse networks and the MSAP algorithm for large complex networks. (4) Based on the spatial vector theory, the precise intersection line of the fracture pairs in the fracture pair set is solved to obtain the fine topological intersection information of the fracture network, including the fracture pairs and their corresponding fracture intersection line positions and lengths; In step (3), the ISAP algorithm includes: assuming the x-axis is the scanning axis, all AABB bounding boxes are projected onto the x-axis to form a one-dimensional interval segment; the projection of each AABB bounding box on the x-axis is a linear interval containing two endpoints; when two AABB bounding boxes have potential intersections, their x-axis projection intervals will inevitably overlap. Potential intersecting fracture pairs are obtained by performing a single scan along the x-axis at the starting endpoint of the interval. Subsequently, the overlapping of the projected intervals is verified sequentially in the y-axis and z-axis directions. Only when the projections in all three orthogonal directions overlap are they identified as potential intersecting fracture pairs. The MSAP algorithm includes: dividing a large study area into several sub-domains, allocating the disk cracks to the corresponding sub-domains based on the crack center coordinates, and then applying the ISAP algorithm to the internal and adjacent boundary regions of each sub-domain.

2. The rapid detection method for intersecting cracks according to claim 1, characterized in that, In step (1), the basic data of the fracture network includes the characteristics of fracture orientation distribution, fracture diameter distribution, and fracture density distribution.

3. The rapid detection method for intersecting cracks according to claim 1, characterized in that, In step (2), the axisymmetric bounding box is the smallest bounding rectangle whose edges are strictly aligned with the coordinate axes. The position of the bounding rectangle in space is defined by the minimum and maximum values ​​of the outer edge of the slit on each coordinate axis. The single slit must be polygonal in shape.

4. The rapid detection method for intersecting cracks according to claim 3, characterized in that, For the disk crack, 24 discrete points evenly distributed on the edge are used to discretize the continuous crack surface into an approximately circular 24-sided structure.

5. The rapid detection method for intersecting cracks according to claim 1, characterized in that, Subdomain division: The region is kept continuous along the longest side, and the other two axes are discretized into a grid based on 2.5 times the maximum diameter of a single slit; the region is set as the scanning axis along the longest side.

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