Rock mass fracture blocking identification calculation method based on mathematical set theory

Abstract

The invention discloses a rock mass fracture blocking identification calculation method based on a mathematical set theory, and the method is based on the mathematical set theory, and comprises the following steps: collecting rock mass cracks to form a crack set, calculating the number of cracks which are intersected with, intersected with and communicated with a plurality of cracks in a rock mass, and forming an intersected crack set corresponding to each crack; forming a potential block crack set by the cracks which meet the condition that the cracks and other cracks form a closed area in the intersection crack set; taking each crack in the potential block crack set as an initial crack for circulation, searching whether the initial crack is contained in an intersection crack set, and if the intersection crack set contains the initial crack, forming a cracked block; and otherwise, circulating the intersection crack set, and carrying out recursive search on the intersection crack set corresponding to the cracks in the intersection crack set until all fractured blocks and cracks are searched. According to the method, the calculation efficiency is high, the block formed by fracture can be accurately identified, and convenience is provided for calculation of the rock mass fracturing or excavated rock mass cracking damage process.

Description

Technical Field

[0001] The present invention relates to the intersecting field of rock and soil underground engineering and computer systems, and in particular to a calculation method for identifying rock mass fracture blocks based on mathematical set theory. Background Art

[0002] During the construction of underground projects, rock mass structures are prone to damage and fracture. Multiple cracks propagate, forming cracked blocks that can trigger engineering disasters. These disasters are often associated with the formation of blocks within the rock mass structure. Furthermore, in-situ leaching of sandstone uranium and fracturing of shale oil and gas reservoirs inevitably involve complex cracking behaviors such as crack propagation, penetration, and convergence. This results in the formation of complex fractured blocks, making block identification and calculation a fundamental and fundamental challenge in rock mechanics.

[0003] The formation of fracture blocks is often the inevitable result of the expansion of multiple cracks. For the mechanical calculation and analysis process, static calculations are often impossible after the fracture forms blocks, resulting in a singular system matrix. On the other hand, the formation of blocks often affects the stability of underground engineering excavation and may affect the effect of fracturing and permeability enhancement. Therefore, block identification and calculation have developed rapidly in recent years and have made certain progress. For example, based on the concept of vectors, convex and concave bodies have been successfully unified in concept. Under this concept, the results have completed the automatic identification and calculation of three-dimensional block systems and solved the problem of concave body identification. There is also a concept based on sub-areas, which divides the rock mass into several sub-areas, uses structural surfaces to cut blocks and then merges sub-areas to realize curved surface block identification.

[0004] Currently, some research results have contributed to the development of block identification theory, but each has its own applicability and remains difficult to implement widely. For example, identification methods based on topological principles can only use simplified methods to determine the intersection of structural planes and boundaries; when using structural planes to identify rock mass cutting algorithms, the model volume is too large and cannot cut concave bodies; theories based on three-dimensional geological modeling technology are complex and require large amounts of data, making them mainly suitable for the initial modeling stage and difficult to use during the later crack propagation stage. Therefore, there is an urgent need to provide a theory and method for adaptive block identification in simulation analysis processes that is computationally efficient, requires minimal data and computational effort, and is suitable not only for early modeling but also for the later crack propagation calculation process. This method is of great significance for the accurate and rapid identification and calculation of rock mass fractures during crack propagation calculations. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a rock mass fracture block identification and calculation method based on mathematical set theory in response to the defects in the existing technology, so as to facilitate the identification and calculation of multi-crack rock mass fracture blocks.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] The present invention provides a method for calculating and identifying rock mass fracture blocks based on mathematical set theory. The method is based on mathematical set theory and includes:

[0008] The rock cracks are collected to form a crack set, and the number of cracks that intersect, merge and penetrate with each other in the rock mass is calculated to form an intersection crack set corresponding to each crack; the cracks in the intersection crack set that meet the conditions of forming a closed area with other cracks are combined into a potential block crack set; each crack in the potential block crack set is looped as a starting crack, and its intersection crack set is searched to see if it contains the starting crack. If the starting crack is contained in its intersection set, a cracked block is formed; otherwise, the intersection crack set is looped, and the intersection crack set corresponding to the crack in its intersection crack set is recursively searched until all fractured blocks and cracks are searched.

[0009] Furthermore, the method of the present invention specifically comprises the following steps:

[0010] Step 1: Collect rock cracks to form a crack set;

[0011] Step 2, the intersection, convergence and through-going cracks are grouped into an intersection crack set;

[0012] Step 3, calculate the number of elements in the intersection crack concentration;

[0013] Step 4: Cracks that meet the conditions for forming a closed area are grouped into a potential block crack set;

[0014] Step 5, calculating the number of concentrated cracks in the potential block cracks;

[0015] Step 6: cyclically identify cracked blocks;

[0016] Step 7, searching for a crack set consisting of blocks after formation;

[0017] Step 8: Separate the crack segments located at the block boundary of the cracks in the blocks formed by the search to obtain the information of the identified rock fracture blocks; return to step 1 to continue initializing and cyclically identifying cracks until no new blocks are identified, that is, the search for all cracks is completed.

[0018] Furthermore, the method of forming a crack set of the present invention includes:

[0019] The crack set consisting of all cracks in the rock mass is recorded as:

[0020] Cr={c i |i=1,2,3...,Nr}

[0021] Where C ris the crack set consisting of all cracks in the rock mass; c i is the rock crack numbered i; Nr is the maximum number of rock cracks.

[0022] Furthermore, the method of forming an intersection crack set of the present invention includes:

[0023]

[0024] Where s i The intersection crack set is the intersection, convergence and through-going cracks; c i 、c j are rock cracks numbered i and j respectively; Nr is the maximum number of rock cracks.

[0025] Furthermore, the method of forming a potential block crack set of the present invention includes:

[0026] c j with c i When there are 2 or more intersection points, i The intersection crack set is recorded twice, and the intersection crack set s i Number of elements n i for:

[0027] n i =card(s i )

[0028] Where n i The intersection crack set s i Number of elements; s i The intersection crack set is the intersection, convergence and through-crack of the cracks; card is the number of elements in the set; the block crack forms a closed area together with other cracks, satisfying:

[0029] n i =card(s i )≥2

[0030] The crack sets that meet the conditions are grouped into potential block crack sets, denoted as b:

[0031] b={c i |n i =card(s i )≥2,i=1,2,3,...,Nr}

[0032] Where b is the potential block crack set; c i is the rock crack numbered i; Nr is the maximum number of rock cracks.

[0033] Furthermore, the number of cracks in the potential block crack concentration of the present invention is recorded as m, and the formula is:

[0034] m=card(b)

[0035] Where m is the number of cracks that form the potential conditions of the block; b is the set of potential block cracks; and card is the calculation representation of the number of elements in the set.

[0036] Furthermore, the method of identifying cracked blocks in the method of the present invention specifically includes:

[0037] Step 61: Select any crack c from the potential block crack set b. i Loop, i=1,2,3,...,m respectively;

[0038] Step 62, in c i Select any crack c from the intersection crack set j , and loop j, j=1,2,3,...,n i ;

[0039] Step 63: If c j If the potential block crack set is b, the loop continues; otherwise, the process goes to step 62 and the value of j is updated to continue the loop.

[0040] Step 64: If c j Intersection crack set j Contains c i If there is a crack, the loop goes to step 7 to complete the current block identification. Otherwise, in c j Select any crack c from the intersection crack set k , loop over k, k=1,2,3,...,n k ;

[0041] Step 65: Return to step 63 to step 64 to continue the cyclic search;

[0042] Step 66: When returning to step 62, continue to execute steps 62 to 65 until the crack search in the m potential crack concentrations is completed or the block search in step 64 is completed.

[0043] Furthermore, the crack set Q of the block formed after the search of the present invention is:

[0044] Q={c i |i=1,2,3...,NQ}

[0045] Where Q is the crack set of the block after search formation; c i is the rock crack numbered i; NQ is the maximum number of rock cracks.

[0046] The present invention provides a rock mass fracture block identification and calculation system based on mathematical set theory, comprising:

[0047] a memory for storing executable computer programs;

[0048] The processor is configured to implement the rock fracture block identification calculation method based on mathematical set theory as described in any one of claims 1 to 7 when executing the executable computer program stored in the memory.

[0049] The beneficial effects produced by the present invention are:

[0050] 1. The present invention regards non-continuous surfaces in the rock mass, including excavation boundaries, structural surfaces, fissures, joints and cracks, as a generalized crack, and provides a method for accurately identifying and calculating blocks formed after multiple cracks converge and penetrate during the expansion process of rock cracks. The provided method takes into account multiple non-continuous structures such as cracks, excavation structures, joints and cracks, structural surfaces, etc., and is simple to operate, accurate in identification, and highly efficient. Identification and calculation can be carried out at any time during the numerical simulation process, facilitating subsequent calculations. Actual measurements and calculations have shown that the calculation method is accurate, has a small amount of data storage, is simple to operate, is suitable for reference in the numerical simulation process of fractures, and provides great convenience for the numerical simulation of multi-crack fractures.

[0051] 2. This invention provides an efficient method for identifying and calculating blocks formed by rock fractures. This method takes into account the complex intersections, convergences, and interconnections of multiple crack spaces, accurately identifying blocks formed by fractures and facilitating further calculations. Field measurements and calculations have demonstrated that this method is highly efficient and accurately identifies all blocks formed by fractures, facilitating the calculation of rock fracture and excavation cracking and failure processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0053] Figure 1 is a flow chart of calculation steps in an embodiment of the present invention;

[0054] Figure 2 is a schematic diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0056] Example 1

[0057] An embodiment of the present invention provides a method for calculating and identifying rock mass fractures based on mathematical set theory. The method, based on mathematical set theory, includes:

[0058] The rock cracks are collected to form a crack set, and the number of cracks that intersect, merge and penetrate with each other in the rock mass is calculated to form an intersection crack set corresponding to each crack; the cracks in the intersection crack set that meet the conditions of forming a closed area with other cracks are combined into a potential block crack set; each crack in the potential block crack set is looped as a starting crack, and its intersection crack set is searched to see if it contains the starting crack. If the starting crack is contained in its intersection set, a cracked block is formed; otherwise, the intersection crack set is looped, and the intersection crack set corresponding to the crack in its intersection crack set is recursively searched until all fractured blocks and cracks are searched.

[0059] Furthermore, the method principle of the present invention is:

[0060] By considering all discontinuous structures in the rock mass as generalized discontinuous structures, including excavation surfaces, joints and fissures, structural surfaces and cracks, etc., a potential block crack set is established by establishing a mathematical set of crack intersection relationship information. The search is performed using the potential block crack set as the search condition, with low computational complexity and simple algorithm, thereby obtaining cracked blocks in the rock mass. After searching a block, the next information update is performed according to the set method, the generalized cracks in the rock mass are reinitialized, and a new block search is carried out until the crack search in all potential block crack sets is completed and no new blocks are generated, that is, all cracked blocks in the rock mass are obtained.

[0061] Example 2

[0062] like Figure 1 and Figure 2 As shown, the embodiment of the present invention includes the following specific implementation steps based on the basic principles of embodiment 1:

[0063] 1) The crack set consisting of all cracks in the rock mass is recorded as:

[0064] Cr={c i |i=1,2,3...,Nr} (1)

[0065] In formula (1), C r is the crack set consisting of all cracks in the rock mass; c i is the rock crack numbered i; Nr is the maximum number of rock cracks;

[0066] 2) The intersection, convergence and through cracks of cracks are recorded as intersection crack set s i :

[0067]

[0068] In formula (2), s i The intersection crack set is the intersection, convergence and through-going cracks; c i、c j are rock cracks numbered i and j respectively; Nr is the maximum number of rock cracks;

[0069] 3)c j with c i When there are 2 or more intersection points, i The intersection crack set is recorded twice, and the intersection, intersection and through cracks in formula (2) are recorded as the intersection crack set s i Number of elements n i for:

[0070] n i =card(s i ) (3)

[0071] In formula (3), n i The intersection crack set s i Number of elements; s i The intersection crack set is the intersection, convergence and through-crack of the cracks; card is the number of elements in the set; the block crack forms a closed area together with other cracks, satisfying:

[0072] n i =card(s i )≥2 (4)

[0073] 4) The crack set that satisfies the conditions of formula (4) is recorded as the potential block crack set, denoted as b:

[0074] b={c i |n i =card(s i )≥2,i=1,2,3,...,Nr} (5)

[0075] In formula (5), b is the potential block crack set; c i is the rock crack numbered i; n i The intersection crack set s i The number of elements; card is the calculated representation of the number of elements in the set; Nr is the maximum number of rock cracks;

[0076] 5) The number of cracks that form the potential conditions of the block is recorded as m, and the formula is:

[0077] m=card(b) (6)

[0078] In formula (6), m is the number of cracks that form the potential conditions of the block; b is the set of potential block cracks; card is the calculation representation of the number of elements in the set;

[0079] 6) Perform block identification, and the identification steps are as follows:

[0080] ① For any crack c in the potential block crack set b, i Loop, i=1,2,3,...,m respectively;

[0081] ②In c i Select any crack c from the intersection crack set j , and loop j, j=1,2,3,...,n i ;

[0082] ③If c j If the potential block crack set is b, the cycle continues; otherwise, it goes to step ② and updates the value of j to continue the cycle.

[0083] ④If c j Intersection crack set j Contains c i If there is a crack, the loop goes to step 7) to complete the current block identification. Otherwise, in c j Select any crack c from the intersection crack set k , loop over k, k=1,2,3,...,n k ;

[0084] ⑤Continue the cycle search algorithm according to steps ③ and ④;

[0085] ⑥ According to ② to ⑤ and so on, until the search for m potential cracks is completed or the block search in link ④ is completed;

[0086] 7) The crack set Q of the block after search is:

[0087] Q={c i |i=1,2,3...,NQ} (7)

[0088] In formula (7), Q is the crack set of the block after search formation; c i is the rock crack numbered i; NQ is the maximum number of rock cracks;

[0089] 8) Separate the crack segments at the block boundary in formula (7) to form independent block information, and initialize the other cracks according to formulas (1) to (6), and then go to step 6) and continue the cycle until no new blocks are identified, that is, all crack searches are completed.

[0090] Example 3

[0091] like Figure 2 As shown in the figure, the discontinuous structure can be regarded as consisting of 8 generalized cracks. Figure 2As can be seen from the figure, crack c2 is a branch crack of crack c1, crack c3 and crack c1 intersect with crack c5, and crack c7 intersects with crack c4 and crack c6 respectively. Moreover, under the condition of multiple cracks forming, a block is formed.

[0092] Initialize according to formulas (1) to (6), and the crack set can be obtained as

[0093] Cr={c1,c2,c3,c4,c5,c6,c7,c8}, Nr=8 (15)

[0094] The branch crack set of each crack is denoted as

[0095] s1={c2,c3,c4} n1=card(s1)=3 (16)

[0096] s2={c1} n2=card(s2)=1 (17)

[0097] s3={c1,c5} n3=card(s3)=2 (18)

[0098] s4={c1,c7} n4=card(s4)=2 (19)

[0099] s5={c3,c6,c8} n5=card(s5)=3 (20)

[0100] s6={c5,c7} n6=card(s6)=2 (21)

[0101] s7={c4,c6} n7=card(s7)=2 (22)

[0102] s8={c5} n8=card(s8)=1 (23)

[0103] From equations (16) to (23), the potential block crack set can be obtained as

[0104] b={c1,c3,c4,c5,c6,c7} m=card(b)=6 (24)

[0105] According to the search steps ①~⑥,

[0106] Q={c1,c3,c5,c6,c7,c4} (25)

[0107] Depend on Figure 1 It can be seen that the formed block is composed of 6 cracks c1, c3, c5, c6, c7, and c4, and the search algorithm quickly obtains accurate search results.

[0108] By comparing the search and recognition algorithm of the traditional method, the present method is simple and clear, has sufficient theoretical basis, simple algorithm, small data storage volume and small calculation amount. It is found that the calculation method provided by the present invention is more efficient than the traditional method.

[0109] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0110] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A calculation method for identifying rock mass fracture blocks based on mathematical set theory, characterized in that: The method is based on mathematical set theory and includes: The rock cracks are collected to form a crack set, and the number of cracks that intersect, merge and penetrate with each other in the rock mass is calculated to form an intersection crack set corresponding to each crack; the cracks in the intersection crack set that meet the conditions of forming a closed area with other cracks are combined into a potential block crack set; each crack in the potential block crack set is looped as a starting crack, and its intersection crack set is searched to see if it contains the starting crack. If the starting crack is contained in its intersection set, a cracked block is formed; otherwise, the intersection crack set is looped, and the intersection crack set corresponding to the crack in its intersection crack set is recursively searched until all fractured blocks and cracks are searched.

2. The rock mass fracture block identification and calculation method based on mathematical set theory according to claim 1 is characterized in that: The method specifically comprises the following steps: Step 1: Collect rock cracks to form a crack set; Step 2, the intersection, convergence and through-going cracks are grouped into an intersection crack set; Step 3, calculate the number of elements in the intersection crack concentration; Step 4: Cracks that meet the conditions for forming a closed area are grouped into a potential block crack set; Step 5, calculating the number of concentrated cracks in the potential block cracks; Step 6: cyclically identify cracked blocks; Step 7, searching for a crack set consisting of blocks after formation; Step 8: Separate the crack segments located at the block boundary of the cracks in the blocks formed by the search to obtain the information of the identified rock fracture blocks; return to step 1 to continue initializing and cyclically identifying cracks until no new blocks are identified, that is, the search for all cracks is completed.

3. The rock mass fracture block identification and calculation method based on mathematical set theory according to claim 2 is characterized in that: Methods for forming crack sets include: The crack set consisting of all cracks in the rock mass is recorded as: Cr={c i |i=1,2,3...,Nr} Where C r is the crack set consisting of all cracks in the rock mass; c i is the rock crack numbered i; Nr is the maximum number of rock cracks.

4. The rock mass fracture block identification and calculation method based on mathematical set theory according to claim 3 is characterized in that: Methods for forming intersecting crack sets include: Where s i The intersection crack set is the intersection, convergence and through-going cracks; c i 、c j are rock cracks numbered i and j respectively; Nr is the maximum number of rock cracks.

5. The rock mass fracture block identification and calculation method based on mathematical set theory according to claim 4 is characterized in that: Methods for forming potential block crack sets include: c j with c i When there are 2 or more intersection points, i The intersection crack set is recorded twice, and the intersection crack set s i Number of elements n i for: n i =card(s i ) Where n i The intersection crack set s i Number of elements; s i The intersection crack set is the intersection, convergence and through-crack of the cracks; card is the number of elements in the set; the block crack forms a closed area together with other cracks, satisfying: n i =card(s i )≥2 The crack sets that meet the conditions are grouped into potential block crack sets, denoted as b: b={c i |n i =card(s i )≥2,i=1,2,3,...,Nr} Where b is the potential block crack set; c i is the rock crack numbered i; Nr is the maximum number of rock cracks.

6. The rock mass fracture block identification and calculation method based on mathematical set theory according to claim 5 is characterized in that: The number of cracks in the potential block crack concentration is recorded as m, and the formula is: m=card(b) Where m is the number of cracks that form the potential conditions of the block; b is the set of potential block cracks; and card is the calculation representation of the number of elements in the set.

7. The rock mass fracture block identification and calculation method based on mathematical set theory according to claim 6 is characterized in that: The method for identifying cracked blocks in the method specifically includes: Step 61: Select any crack c from the potential block crack set b. i Loop, i=1,2,3,...,m respectively; Step 62, in c i Select any crack c from the intersection crack set j , and loop j, j=1,2,3,...,n i ; Step 63: If c j If the potential block crack set is b, the loop continues; otherwise, the process goes to step 62 and the value of j is updated to continue the loop. Step 64: If c j Intersection crack set j Contains c i If there is a crack, the loop goes to step 7 to complete the current block identification. Otherwise, in c j Select any crack c from the intersection crack set k , loop over k, k=1,2,3,...,n k ; Step 65: Return to step 63 to step 64 to continue the cyclic search; Step 66: When returning to step 62, continue to execute steps 62 to 65 until the crack search in the m potential crack concentrations is completed or the block search in step 64 is completed.

8. The rock mass fracture block identification and calculation method based on mathematical set theory according to claim 2 is characterized in that: The crack set Q of the block after search formation is: Q={c i |i=1,2,3...,NQ} Where Q is the crack set of the block after search formation; c i is the rock crack numbered i; NQ is the maximum number of rock cracks.

9. A rock mass fracture block identification and calculation system based on mathematical set theory, characterized in that: include: a memory for storing executable computer programs; The processor is configured to implement the rock fracture block identification calculation method based on mathematical set theory as described in any one of claims 1 to 8 when executing the executable computer program stored in the memory.

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