Rock block finiteness and movability determination method, device, medium and equipment

Abstract

A rock block finiteness and movability determination method, device, medium and equipment are disclosed, which belong to the technical field of rock mechanics numerical analysis. The method comprises the following steps: obtaining a discriminant matrix of a joint cone of a rock block to be determined; identifying the non-empty joint cone of the rock block to be determined according to the discriminant matrix of the joint cone; combining the non-empty joint cone with a near-empty surface to form a block cone of the rock block to be determined; obtaining a discriminant matrix of the block cone of the rock block to be determined through operation; and determining the finiteness and movability of the rock block to be determined according to whether the block cone of the rock block to be determined is an empty set. The device, medium and equipment can be used to realize the method. The method uses interval numbers to express the inclination and dip angle of a structural surface, and then uses interval vectors to express the normal vector of the structural surface, so that the interval vector form is used for operation in the vector operation method to form a discriminant matrix, and the finiteness and movability of the block are determined, and the result is more accurate.

Description

Technical Field

[0001] This invention relates to the field of numerical analysis technology in rock mechanics, and in particular to a method, apparatus, medium, and equipment for determining the finiteness and mobility of rock blocks. Background Technology

[0002] Rock masses contain structural planes of varying origins, sizes, and attitudes. The block problems formed by these structural planes often constitute a major issue in rock mass excavation stability evaluation and support treatment, playing a crucial role in the feasibility study and support design of rock mass engineering projects (including slopes and underground caverns). For a long time, block stability analysis has primarily focused on simple shapes such as tetrahedral wedges, while complex shapes have been handled with simplifications. The block theory established by Shi Genhua (1977) and Re. Goodman represents a significant breakthrough in rock mass block stability analysis methods. After more than 30 years of development, rock block stability analysis methods based on block theory have become an important approach in the stability analysis of fractured rock masses. Summary of the Invention

[0003] In view of this, the present invention provides a method, apparatus, medium and equipment for determining the finiteness and mobility of a rock block, which enables more accurate determination of the finiteness and mobility of the rock block to be determined, and thus is more suitable for practical use.

[0004] To achieve the first objective mentioned above, the technical solution for determining the finiteness and mobility of rock blocks provided by this invention is as follows:

[0005] The method for determining the finiteness and mobility of rock blocks provided by this invention includes the following steps:

[0006] Obtain the discrimination matrix of the joint cones of the rock block to be judged;

[0007] The non-hollow joint cones of the rock block to be determined are identified by the discrimination matrix of the joint cones.

[0008] The non-hollow joint cone of the rock block to be judged is combined with the free surface of the rock block to be judged to form the block cone of the rock block to be judged;

[0009] Based on the block cone of the rock block to be judged, the judgment matrix of the block cone of the rock block to be judged is obtained through calculation;

[0010] Based on whether the block cone of the rock block to be judged is an empty set, the finiteness and mobility of the rock block to be judged are determined. When the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be an immovable block.

[0011] The method for determining the finiteness and mobility of rock blocks provided by this invention can be further implemented using the following technical measures.

[0012] Preferably, obtaining the discrimination matrix of the joint cone of the rock block to be judged specifically includes the following steps:

[0013] Suppose that the joint cone JP of the rock block to be judged has n sets of structural planes, and let P be the dominant structural plane of each set. i The dip and dip angle are respectively A i and B i , A i and B i Interval number

[0014]

[0015]

[0016] in, α i =α i -Δα i , β i =β i -Δβ i , α i and β i These are the dominant structural surface groups P i The center vector's tendency and tilt angle, Δα i and Δβ i They are structural plane group P i The magnitude of the changes in dip and tilt angle;

[0017] Remember P i The upward normal vector is

[0018]

[0019] Let the intersection line between the structural planes be the edge vector.

[0020]

[0021] The total number of edge vectors of the intersecting edge line is

[0022] Calculate the direction parameter Forming the direction parameter matrix

[0023]

[0024] In the formula, the sign function in If is an interval number, then we have

[0025]

[0026] Form a matrix of JP symbol numbers for the joint cones of the rock block to be determined [D].

[0027]

[0028] Based on the symbol numbering matrix [D] of the joint cone JP of the rock block to be judged, establish the discrimination matrix [T] of the joint cone JP of the rock block to be judged.

[0029]

[0030] Preferably, in the step of forming the symbol numbering matrix [D] of the joint cone JP of the rock block to be determined, D(P i The assignment method is as follows: when the joint cone JP of the rock block to be determined is on the structural surface P i Above that is D(P) i ) = 1, when the joint cone of the rock block to be determined is on the structural plane P i Below that is D(P) i = -1.

[0031] Preferably, the discrimination matrix is ​​adjusted according to the discrimination matrix [T] of the joint cone JP of the rock block to be judged. row element discrimination The specific method for determining whether a row element is a real edge is as follows:

[0032]

[0033] As a preferred embodiment, the specific method for determining whether the joint cone JP of the rock block to be determined is as follows: if there is one edge in the discrimination matrix [T] that is a real edge of the joint cone JP, then JP is a non-empty set; if none of the edges are real edges of JP, then JP is an empty set.

[0034] Preferably, the non-hollow joint cone JP is combined with the free surface of the rock block to be judged to form a block cone BP; the judgment matrix of the block cone BP of the rock block to be judged is formed according to the calculation steps of the judgment matrix of the joint cone JP.

[0035] Preferably, the step of determining the finiteness and mobility of the rock block to be judged based on whether its block cone is an empty set includes the following steps: When the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be an immovable block.

[0036] By judging the discriminant matrix [T] of the rock block cone BP to be judged, if at least one edge of the discriminant matrix [T] of the rock block cone BP to be judged is a true edge of the rock block cone BP to be judged, then the rock block cone BP to be judged is a non-empty set; if none of the edges of the discriminant matrix [T] of the rock block cone BP to be judged are true edges of the rock block cone BP to be judged, then the rock block cone BP to be judged is an empty set.

[0037] Preferably, after the step of determining the finiteness and mobility of the rock block to be judged based on whether the block cone of the rock block to be judged is an empty set, wherein when the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block; and when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be a non-movable block, the step further includes a step of outputting the determination conclusion of the finiteness and mobility of the rock block to be judged, wherein when the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block, and the output result is 0; and when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be a non-movable block, and the output result is 1.

[0038] To achieve the second objective mentioned above, the technical solution of the rock block finiteness and mobility determination device provided by the present invention is as follows:

[0039] The device for determining the finiteness and mobility of rock blocks provided by this invention includes:

[0040] The discrimination matrix acquisition module is used to obtain the discrimination matrix of the joint cones of the rock block to be judged;

[0041] The discrimination matrix recognition module is used to identify the joint cones of the rock block to be judged based on the discrimination matrix of the joint cones, and to obtain the non-hollow joint cones of the rock block to be judged.

[0042] A block cone forming module is used to combine the non-hollow joint cone of the rock block to be judged with the free surface of the rock block to be judged to form the block cone of the rock block to be judged;

[0043] The calculation module is used to obtain the judgment matrix of the block cone of the rock block to be judged through calculation.

[0044] The determination module is used to determine the finiteness and mobility of the rock block to be determined based on whether the block cone of the rock block to be determined is an empty set. When the block cone of the rock block to be determined is an empty set, the rock block to be determined is determined to be a finite and movable block; when the block cone of the rock block to be determined is a non-empty set, the rock block to be determined is determined to be an immovable block.

[0045] The rock block finiteness and mobility determination device provided by the present invention can be further implemented by the following technical measures.

[0046] Preferably, the device for determining the finiteness and mobility of the rock block further includes:

[0047] The judgment result output module is used to output the judgment result of the judgment module. When the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite, movable block, and the output result is 0; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be an immovable block, and the output result is 1.

[0048] To achieve the third objective mentioned above, the technical solution of the computer-readable storage medium provided by the present invention is as follows:

[0049] The present invention provides a computer-readable storage medium storing a program for determining the finiteness and mobility of a rock block. When the program is executed by a processor, it implements the steps of the method for determining the finiteness and mobility of a rock block provided by the present invention.

[0050] To achieve the fourth objective mentioned above, the technical solution for the electronic device provided by this invention is as follows:

[0051] The electronic device provided by the present invention includes a memory and a processor. The memory stores a program for determining the finiteness and mobility of a rock block. When the program for determining the finiteness and mobility of a rock block is executed by the processor, it implements the steps of the method for determining the finiteness and mobility of a rock block provided by the present invention.

[0052] The method, apparatus, medium, and equipment for determining the finiteness and mobility of rock blocks provided by this invention use interval numbers to express the dip and tilt angle of structural surfaces, and then use interval vectors to express the normal vector of structural surfaces. Thus, the vector operation method uses interval vectors to perform calculations to form a determination matrix, thereby judging the finiteness and mobility of the rock block to be determined, and the judgment result is more accurate. Attached Figure Description

[0053] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0054] Figure 1 A flowchart illustrating the steps of the method for determining the finiteness and mobility of a rock block according to an embodiment of the present invention;

[0055] Figure 2 A schematic diagram showing the signal flow relationship between the various functional modules involved in the rock block finiteness and mobility determination device provided in the embodiments of the present invention;

[0056] Figure 3 This is a schematic diagram of a device for determining the finiteness and mobility of rock blocks in the hardware operating environment involved in an embodiment of the present invention;

[0057] Figure 4 A schematic diagram showing the change in the mobility of a rock mass caused by changes in the attitude of structural planes;

[0058] Figure 5 The diagram shows the results of the full-space stereographic projection analysis, where the attitude of the structural planes is taken as the median value.

[0059] Figure 6 The image shows the results of the full-space stereographic projection analysis, where the attitude of the structural planes is not represented by intermediate values. Detailed Implementation

[0060] To address the problems existing in the prior art, this invention provides a method, apparatus, medium, and equipment for determining the finiteness and mobility of a rock block, which enables a more accurate determination of the finiteness and mobility of the rock block to be determined, and thus is more suitable for practical use.

[0061] The core of block theory is to identify and analyze key blocks on free faces given the known combination of rock mass structural planes. To facilitate mathematical analysis, it introduces pyramids, discarding the volume concept of spatial blocks and preserving only their shape characteristics. Block theory first treats structural planes and excavated free faces as spatial planes, and blocks as geometric convex bodies composed of these spatial planes. Various applied loads are considered as spatial vectors. Geometric methods (topology and set theory) are applied to study the types of blocks that can form within the rock mass and their mobility under known spatial plane orientations. Then, through static equilibrium calculations, the sliding forces and safety factors of various movable blocks are determined, serving as the design basis for engineering reinforcement measures.

[0062] There are two analytical methods in block theory: vector manipulation and stereographic projection. Using full-space stereographic projection to determine the finiteness and mobility of blocks is a simple, fast, and intuitive method. However, a problem arises in practical engineering applications using full-space stereographic projection analysis: the analysis of the finiteness and mobility of blocks requires professional interpretation of the stereographic projection diagrams. When there are many structural surface groups, the combinations of structural surfaces are also numerous, making the drawing and interpretation work involved in the entire stereographic projection analysis very arduous and prone to errors. In this case, batch processing using vector manipulation is more concise, efficient, and less error-prone—the program automatically generates structural surface combinations, forms a judgment matrix for all generated structural surface combinations, judges the finiteness and mobility of the blocks, and outputs the results.

[0063] However, both vector analysis and full-space stereographic projection methods face a common problem—the intervalic nature of structural plane attitude data. Structural planes developed within rock masses are products of long-term geological tectonic movements, and therefore their spatial occurrence characteristics are related to the tectonic stress field, thus possessing relatively dominant characteristics. However, even structural planes within the same dominant group generally exhibit different attitudes; groups of parallel-developing structural planes are almost non-existent in reality. Therefore, the description of the dominant orientation of structural planes, like the geological recommendations for geophysical parameters, is usually described using a range of variation, such as N50°~80°E∠60°~80°. However, when performing block analysis, whether using full-space stereographic projection or vector analysis, deterministic attitude data must be input; the common practice is to take the intermediate value based on the range of structural plane attitude variation. But this approach may lead to misjudgment because the finiteness and mobility of the block itself may fundamentally change within the range of attitude variation.

[0064] The two-dimensional case is more intuitive, so we will use... Figure 4Let's take an example to briefly explain. Here, we assume AB is the excavation face, and its left side is the spatial cone SP. Consider the mobility of the block formed by the deterministic structural planes CD and EF, and the dominant structural plane (ON as its dominant center, OG and OM as boundary ranges). Here, ON is parallel to CD and perpendicular to AB, i.e., the excavation face. Clearly, when the dominant structural plane is located between ON and OG, the block is movable, meaning it can slide towards SP without being hindered by the surrounding rock; when the dominant structural plane is located between OM and ON, the block is immovable.

[0065] To further illustrate the technical means and effects adopted by the present invention to achieve the intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of the method, apparatus, computer-readable storage medium, and electronic device for determining the finiteness and mobility of rock blocks proposed according to the present invention. In the following description, different "embodiments" or "embodiments" do not necessarily refer to the same embodiment. Furthermore, features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0066] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships, such as A and / or B. Specifically, it can mean that A and B can be included at the same time, A can exist alone, or B can exist alone, and any of the above three situations can be met.

[0067] Methods for determining the finiteness and mobility of rock blocks

[0068] See appendix Figure 1 The method for determining the finiteness and mobility of rock blocks provided by this invention includes the following steps:

[0069] Step S1: Obtain the discrimination matrix of the joint cones of the rock block to be judged;

[0070] Step S2: Identify the non-hollow joint cones of the rock block to be determined based on the discrimination matrix of the joint cones;

[0071] Step S3: The non-hollow joint cone of the rock block to be judged is combined with the free face of the rock block to be judged to form the block cone of the rock block to be judged;

[0072] Step S4: Based on the block cone of the rock block to be judged, the judgment matrix of the block cone of the rock block to be judged is obtained through calculation;

[0073] Step S5: Determine the finiteness and mobility of the rock block to be judged based on whether the block cone of the rock block to be judged is an empty set. When the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be an immovable block.

[0074] The method for determining the finiteness and mobility of rock blocks provided by this invention uses interval numbers to express the dip and dip angle of structural surfaces, and then uses interval vectors to express the normal vector of structural surfaces. Thus, the vector operation method uses interval vectors to perform calculations to form a determination matrix, which is used to determine the finiteness and mobility of the rock block to be determined, resulting in a more accurate determination.

[0075] The specific steps for obtaining the discrimination matrix of the joint cones of the rock block to be judged include:

[0076] Suppose that the joint cone JP of the rock block to be judged has n sets of structural planes, and let P be the dominant structural plane of each set. i The dip and dip angle are respectively A i and B i , A i and B i Interval number

[0077]

[0078]

[0079] in, α i =α i -Δα i , β i =β i -Δβ i , α i and β i These are the dominant structural surface groups P i The center vector's tendency and tilt angle, Δα i and Δβ i They are structural plane group P i The magnitude of the changes in dip and tilt angle;

[0080] Remember P i The upward normal vector is

[0081]

[0082] Let the intersection line between the structural planes be the edge vector.

[0083]

[0084] The total number of edge vectors of the intersecting edge line is

[0085] Calculate the direction parameter Forming the direction parameter matrix

[0086]

[0087] In the formula, the sign function in If is an interval number, then we have

[0088]

[0089] Form a matrix of JP symbol numbers for the joint cones of the rock block to be determined [D].

[0090]

[0091] Based on the symbol numbering matrix [D] of the joint cone JP of the rock block to be judged, establish the discrimination matrix [T] of the joint cone JP of the rock block to be judged.

[0092]

[0093] In the step of forming the symbol numbering matrix [D] of the joint cone JP of the rock block to be determined, D(P i The assignment method is as follows: when the joint cone JP of the rock block to be determined is on the structural surface P i Above that is D(P) i ) = 1, when the joint cone of the rock block to be determined is on the structural plane P i Below that is D(P) i = -1.

[0094] Among them, based on the discrimination matrix [T] of the joint cone JP of the rock block to be judged, the corresponding discrimination matrix is... row element discrimination The specific method for determining whether a row element is a real edge is as follows:

[0095]

[0096] The specific method for determining whether a rock block joint cone JP is an empty set is as follows: if there is at least one edge in the discrimination matrix [T] that is a real edge of the joint cone JP, then JP is a non-empty set; if none of the edges are real edges of JP, then JP is an empty set.

[0097] Combine the non-hollow joint cone JP with the free surface of the rock block to be judged to form the block cone BP; and form the judgment matrix of the block cone BP of the rock block to be judged according to the calculation steps of the judgment matrix of the joint cone JP.

[0098] The process of determining whether the block cone of the rock to be judged is an empty set is as follows: The finiteness and mobility of the rock to be judged are determined based on whether its block cone is an empty set. Specifically, when the block cone is an empty set, the rock to be judged is considered a finite and movable block; when the block cone is a non-empty set, the rock to be judged is considered an immovable block. The method for determining whether the block cone of the rock to be judged is an empty or non-empty set includes the following steps:

[0099] By judging the discriminant matrix [T] of the block cone BP of the rock block to be judged, if at least one edge of the discriminant matrix [T] of the block cone BP of the rock block to be judged is a real edge of the block cone BP of the rock block to be judged, then the block cone BP of the rock block to be judged is a non-empty set; if none of the edges of the discriminant matrix [T] of the block cone BP of the rock block to be judged are real edges of the block cone BP of the rock block to be judged, then the block cone BP of the rock block to be judged is an empty set.

[0100] The process involves determining the finiteness and mobility of a rock block based on whether its block cone is an empty set. Specifically, if the block cone is empty, the rock block is determined to be finite and movable; if the block cone is non-empty, the rock block is determined to be immovable. Following this step, the process also includes outputting the finiteness and mobility determination results. Specifically, if the block cone is empty, the rock block is determined to be finite and movable, and the output result is 0; if the block cone is non-empty, the rock block is determined to be immovable, and the output result is 1.

[0101] Device for determining the finiteness and mobility of rock blocks

[0102] See appendix Figure 2 The device for determining the finiteness and mobility of rock blocks provided by the present invention includes:

[0103] The discrimination matrix acquisition module is used to obtain the discrimination matrix of the joint cones of the rock block to be judged;

[0104] The discrimination matrix recognition module is used to identify the joint cones of the rock block to be judged based on the discrimination matrix, and to obtain the non-hollow joint cones of the rock block to be judged.

[0105] The block cone forming module is used to combine the non-hollow joint cone of the rock block to be judged with the free surface of the rock block to be judged to form the block cone of the rock block to be judged;

[0106] The calculation module is used to obtain the judgment matrix of the block cone of the rock block to be judged through calculation.

[0107] The determination module is used to determine the finiteness and mobility of the rock block to be determined based on whether the block cone of the rock block to be determined is an empty set. Specifically, when the block cone of the rock block to be determined is an empty set, the rock block to be determined is determined to be a finite and movable block; when the block cone of the rock block to be determined is a non-empty set, the rock block to be determined is determined to be an immovable block.

[0108] The rock block finiteness and mobility determination device provided by the present invention uses interval numbers to express the dip and dip angle of the structural surface, and then uses interval vectors to express the normal vector of the structural surface. Thus, the vector operation method uses the form of interval vectors to form a determination matrix, and judges the finiteness and mobility of the rock block to be determined, so that the judgment result is more accurate.

[0109] The device for determining the finiteness and mobility of rock blocks also includes:

[0110] The judgment result output module is used to output the judgment result of the judgment module. When the block cone of the rock block to be judged is an empty set, the rock block to be judged is judged as a finite, movable block, and the output result is 0; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is judged as an immovable block, and the output result is 1.

[0111] Computer-readable storage media

[0112] The computer-readable storage medium provided by the present invention stores a program for determining the finiteness and mobility of a rock block. When the program for determining the finiteness and mobility of a rock block is executed by a processor, it implements the steps of the method for determining the finiteness and mobility of a rock block provided by the present invention.

[0113] The computer-readable storage medium provided by this invention uses interval numbers to express the dip and tilt angle of the structural surface, and then uses interval vectors to express the normal vector of the structural surface. Thus, the vector operation method uses interval vectors to perform operations to form a judgment matrix, which is used to judge the finiteness and mobility of the rock block to be judged, and the judgment result is more accurate.

[0114] electronic devices

[0115] The electronic device provided by the present invention includes a memory and a processor. The memory stores a program for determining the finiteness and mobility of a rock block. When the program for determining the finiteness and mobility of a rock block is executed by the processor, it implements the steps of the method for determining the finiteness and mobility of a rock block provided by the present invention.

[0116] The electronic device provided by this invention uses interval numbers to express the dip and tilt angle of the structural surface, and then uses interval vectors to express the normal vector of the structural surface. Thus, the vector operation method uses interval vectors to perform the operation to form a judgment matrix, which judges the finiteness and mobility of the rock block to be judged, and the judgment result is more accurate.

[0117] Reference Figure 3 , Figure 3 This is a schematic diagram of the device for determining the finiteness and mobility of rock blocks in the hardware operating environment involved in the embodiments of the present invention.

[0118] like Figure 3 As shown, the device for determining the finiteness and mobility of the rock block may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to establish communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface). The memory 1005 may be a high-speed random access memory (RAM) or a stable non-volatile memory (NVM), such as a disk drive. The memory 1005 may also optionally be a storage device independent of the aforementioned processor 1001.

[0119] Those skilled in the art will understand that Figure 3 The structure shown does not constitute a limitation on the device for determining the finiteness and mobility of rock blocks. It may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0120] like Figure 3 As shown, the memory 1005, which serves as a storage medium, may include an operating system, a data storage module, a network communication module, a user interface module, and a program for determining the finiteness and mobility of the rock block.

[0121] exist Figure 3 In the rock block finiteness and mobility determination device shown, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and memory 1005 in the rock block finiteness and mobility determination device of the present invention can be set in the rock block finiteness and mobility determination device. The rock block finiteness and mobility determination device calls the rock block finiteness and mobility determination program stored in the memory 1005 through the processor 1001 and executes the rock block finiteness and mobility determination method provided in the embodiment of the present invention.

[0122] Example

[0123] The data in Table 1 serves as an example. There are four sets of structural planes. The orientations of structural planes ① and ② are stable and have fixed values, while the orientations of structural planes ③ and ④ have a range of values. An analysis is performed on a 1000-type block (i.e., the block is located on the lower plate of structural plane ① and the upper plate of structural planes ②, ③ and ④) formed by the cutting of the above four sets of structural planes.

[0124] (1) Following the traditional approach, the median of the interval values ​​is used for the dominant structural plane group, i.e., the attitude of structural plane ③ is taken as 100°∠80°, and the attitude of structural plane ④ is taken as 310°∠80°. The results of the full-space stereographic projection analysis are shown in […]. Figure 5 As shown. From Figure 5 As can be seen, JP1000 is an empty set and has no domain on the stereographic projection. The discriminant matrix of JP can be obtained through vector analysis as follows:

[0125]

[0126] According to (6b), JP1000 has no real edges and is an empty set; this is consistent with the results of stereographic projection analysis.

[0127] (2) When the attitude of structural plane ③ is 75°∠80° and the attitude of structural plane ④ is 75°∠300°, the results of the stereographic projection analysis are as follows: Figure 6 As shown, it can be seen that JP1000 is a non-empty set and JP1000∈SP, that is, the corresponding BP is an empty set and JP1000 is a finite, movable block.

[0128] The decision matrix of JP1000 obtained using the vector operation algorithm is as follows:

[0129]

[0130] According to (6b), JP1000 has 3 real edges and is a non-empty set; after adding the free surface, i.e., the structural surface ⑤, further analysis yields the following decision matrix for BP1000:

[0131]

[0132] It is evident that BP1000 has no real edges and is an empty set. Therefore, satisfying JP≠Φ and BP=JP∩EP=Φ, BP1000 is a finite, movable block.

[0133] This means that when the attitudes of structural planes ③ and ④ change within their range of values, their finiteness and mobility will undergo fundamental changes. If the design is based solely on the analysis results of the intermediate attitude values, it will lead to misjudgments and omissions.

[0134] (3) The attitude of the structural plane is expressed using interval numbers (see Table 2). Analysis is performed using the method steps suggested in this invention, resulting in the following decision matrix for JP1000. It can be seen that JP1000 has 3 real edges and is a non-empty set. Further analysis yields the decision matrix for BP1000, showing that BP has no real edges and is an empty set. The calculation results reflect that the attitude of the structural plane changes within its range of variation due to variations in the finiteness and mobility of the block itself.

[0135]

[0136] Table 1. Structural Surface Information (Original Information)

[0137]

[0138]

[0139] Table 2 Structural surface information (structural surface attitude is expressed using interval numbers)

[0140]

[0141] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0142] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for determining the finiteness and mobility of a rock block, characterized in that, Includes the following steps: Obtain the discrimination matrix of the joint cones of the rock block to be judged; The non-hollow joint cones of the rock block to be determined are identified by the discrimination matrix of the joint cones. The non-hollow joint cone of the rock block to be judged is combined with the free surface of the rock block to be judged to form the block cone of the rock block to be judged; Based on the block cone of the rock block to be judged, the judgment matrix of the block cone of the rock block to be judged is obtained through calculation; Based on whether the block cone of the rock block to be judged is an empty set, the finiteness and mobility of the rock block to be judged are determined. When the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be an immovable block. The specific steps for obtaining the discrimination matrix of the joint cone of the rock block to be judged include the following: Suppose that the joint cone JP of the rock block to be judged has n sets of structural planes, and let P be the dominant structural plane of each set. i The dip and dip angle are respectively A i and B i , A i and B i Interval number in, α i =α i -Δα i , β i =β i -Δβ i , α i and β i These are the dominant structural surface groups P i The center vector's tendency and tilt angle, Δα i and Δβ i They are structural plane group P i The magnitude of the changes in dip and tilt angle; Remember P i The upward normal vector is Let the intersection line between the structural planes be denoted as the edge vector. The total number of edge vectors of the intersecting edge line is Calculate the direction parameter Forming the direction parameter matrix In the formula, the sign function in If is an interval number, then we have Form a matrix of JP symbol numbers for the joint cones of the rock block to be determined [D]. Based on the symbol numbering matrix [D] of the joint cone JP of the rock block to be judged, establish the discrimination matrix [T] of the joint cone JP of the rock block to be judged.

2. The method for determining the finiteness and mobility of rock blocks according to claim 1, characterized in that, In the step of forming the symbol numbering matrix [D] of the joint cone JP of the rock block to be determined, D(P i The assignment method is as follows: when the joint cone JP of the rock block to be determined is on the structural surface P i Above that is D(P) i ) = 1, when the joint cone of the rock block to be determined is on the structural plane P i Below that is D(P) i = -1.

3. The method for determining the finiteness and mobility of rock blocks according to claim 1, characterized in that, Based on the discrimination matrix [T] of the joint cone JP of the rock block to be judged, the corresponding [T] of the discrimination matrix is... row element discrimination The specific method for determining whether a row element is a real edge is as follows:

4. The method for determining the finiteness and mobility of rock blocks according to claim 3, characterized in that, The specific method for determining whether the joint cone JP of the rock block to be determined is as follows: if there is one edge in the discrimination matrix [T] that is a real edge of the joint cone JP, then JP is a non-empty set; if none of the edges are real edges of JP, then JP is an empty set.

5. The method for determining the finiteness and mobility of rock blocks according to claim 1, characterized in that, Combine the non-hollow joint cone JP with the free surface of the rock block to be judged to form the block cone BP; and form the judgment matrix of the block cone BP of the rock block to be judged according to the calculation steps of the judgment matrix of the joint cone JP.

6. The method for determining the finiteness and mobility of rock blocks according to claim 5, characterized in that, The step of determining the finiteness and mobility of the rock block to be judged based on whether its block cone BP is an empty set includes the following steps: When the block cone BP of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block; when the block cone BP of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be an immovable block. By judging the discriminant matrix [T] of the rock block cone BP to be judged, if at least one edge of the discriminant matrix [T] of the rock block cone BP to be judged is a true edge of the rock block cone BP to be judged, then the rock block cone BP to be judged is a non-empty set; if none of the edges of the discriminant matrix [T] of the rock block cone BP to be judged are true edges of the rock block cone BP to be judged, then the rock block cone BP to be judged is an empty set.

7. The method for determining the finiteness and mobility of rock blocks according to claim 1, characterized in that, The step of determining the finiteness and mobility of the rock block to be judged based on whether its block cone is an empty set, wherein when the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be a non-movable block, further includes a step of outputting the determination of the finiteness and mobility of the rock block to be judged, wherein when the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite and movable block, and the output result is 0; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be a non-movable block, and the output result is 1.

8. A device for determining the finiteness and mobility of a rock block, characterized in that, include: The discrimination matrix acquisition module is used to obtain the discrimination matrix of the joint cones of the rock block to be judged; The discrimination matrix recognition module is used to identify the joint cones of the rock block to be judged based on the discrimination matrix of the joint cones, and to obtain the non-hollow joint cones of the rock block to be judged. A block cone forming module is used to combine the non-hollow joint cone of the rock block to be judged with the free surface of the rock block to be judged to form the block cone of the rock block to be judged; The calculation module is used to obtain the judgment matrix of the block cone of the rock block to be judged through calculation. The determination module is used to determine the finiteness and mobility of the rock block to be determined based on whether the block cone of the rock block to be determined is an empty set. Specifically, when the block cone of the rock block to be determined is an empty set, the rock block to be determined is determined to be a finite and movable block; when the block cone of the rock block to be determined is a non-empty set, the rock block to be determined is determined to be an immovable block. The specific steps for obtaining the discrimination matrix of the joint cone of the rock block to be judged include the following steps: Suppose that the joint cone JP of the rock block to be judged has n sets of structural planes, and let P be the dominant structural plane of each set. i The dip and dip angle are respectively A i and B i , A i and B i Interval number in, α i =α i -Δα i , β i =β i -Δβ i , α i and β i These are the dominant structural surface groups P i The center vector's tendency and tilt angle, Δα i and Δβ i They are structural plane group P i The magnitude of the changes in dip and tilt angle; Remember P i The upward normal vector is Let the intersection line between the structural planes be denoted as the edge vector. The total number of edge vectors of the intersecting edge line is Calculate the direction parameter Forming the direction parameter matrix In the formula, the sign function in If is an interval number, then we have Form a matrix of JP symbol numbers for the joint cones of the rock block to be determined [D]. Based on the symbol numbering matrix [D] of the joint cone JP of the rock block to be judged, establish the discrimination matrix [T] of the joint cone JP of the rock block to be judged.

9. The device for determining the finiteness and mobility of a rock block according to claim 8, characterized in that, Also includes: The judgment result output module is used to output the judgment result of the judgment module. When the block cone of the rock block to be judged is an empty set, the rock block to be judged is determined to be a finite, movable block, and the output result is 0; when the block cone of the rock block to be judged is a non-empty set, the rock block to be judged is determined to be an immovable block, and the output result is 1.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program for determining the finiteness and mobility of a rock block, which, when executed by a processor, implements the steps of the method for determining the finiteness and mobility of a rock block as described in any one of claims 1-7.

11. An electronic device, characterized in that, The device includes a memory and a processor. The memory stores a program for determining the finiteness and mobility of a rock block. When executed by the processor, the program for determining the finiteness and mobility of a rock block implements the steps of the method for determining the finiteness and mobility of a rock block as described in any one of claims 1-7.

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