A method for block search and stability analysis

Abstract

The application discloses a kind of block search and stability analysis method, comprising the following steps: S 1, according to structural surface data and excavation surface data, determine the intersection trace of structural surface and excavation surface;S 2, determine all closed loops on excavation surface according to intersection trace;S 3, judge whether the first structural surface set in current closed loop can form finite block;If yes, enter step S 4;If no, the first structural surface set of current closed loop is combined with the second structural surface set to form new structural surface set, judge whether new structural surface set can form finite block;If yes, enter step S 4, if no, enter step S 5;S 4, finite block is added to block set;S 5, the next closed loop is set as current closed loop, return to step S 3;Until all closed loops are traversed;S 6, eliminate immovable block in block set, obtain block search result.Compared with prior art, the application can quickly and accurately complete block search.

Description

Technical Field

[0001] This invention relates to the field of water conservancy and hydropower technology, specifically to a block search and stability analysis method. Background Technology

[0002] With the development of the water conservancy and hydropower industry, the construction projects of underground powerhouses and slopes are increasing, and engineering safety is receiving more and more attention. Rock mass plays a crucial role in human engineering construction. Due to its complex heterogeneous, discontinuous, and anisotropic structural characteristics, compared to using numerical methods such as finite element and discrete element methods for block deformation and stability analysis, engineering designers and standards recommend using the limit equilibrium method for block stability analysis.

[0003] Compared with numerical methods such as the finite element method and the discrete element method, the limit equilibrium method does not consider the deformation of the block itself, but only the sliding of the block along the structural surface. Therefore, before using the limit equilibrium method to analyze the stability of the block, a block search should be conducted in conjunction with the topography of the slope or chamber and the structural surfaces contained in the rock mass to find the structural surfaces that can be combined to form the block.

[0004] The occurrence, length, spacing, internal friction angle, and cohesion of structural planes such as joints exhibit random development characteristics. Therefore, the shape, size, spatial distribution, and stability of the blocks formed by these structural planes are inevitably random as well. In current engineering projects, the geological parameters of structural planes such as joints are obtained by on-site geologists through geological surveys and are therefore deterministic parameters. Taking an underground chamber as an example, after completing the geological survey of the chamber, on-site geologists draw joint sketches based on the geometric and positional information of structural planes such as joints. Designers can then reconstruct all structural plane information within the chamber based on these joint sketches.

[0005] Currently, the main method used by engineering designers to search for blocks is to create a three-dimensional spatial model of the chamber and locate the blocks based on the structural planes cutting into the model. However, the number of joints and other structural planes contained in the joint sketch is enormous. Finding all the hidden blocks in the rock mass surrounding the chamber through modeling and other methods is a huge undertaking, not only time-consuming but also prone to missing blocks, resulting in low accuracy. Summary of the Invention

[0006] This invention provides a block search and stability analysis method to solve the technical problems of existing block search methods, which are not only computationally intensive and time-consuming, but also prone to missing blocks, resulting in low accuracy.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] On the one hand, a block search method is provided, including the following steps:

[0009] S1. Based on the structural surface data and the excavation surface data, determine the intersection trace of the structural surface and the excavation surface;

[0010] S2. Determine all closed loops on the excavation surface based on the intersecting traces;

[0011] S3. Determine whether the first set of structural surfaces in the current closed loop can form a finite block; if yes, proceed to step S4; if no, combine the first set of structural surfaces in the current closed loop with the second set of structural surfaces to form a new set of structural surfaces, and determine whether the new set of structural surfaces can form a finite block; if yes, proceed to step S4; if no, proceed to step S5.

[0012] The first set of structural surfaces is the set of structural surface equations contained in the current closed loop, and the second set of structural surface equations is the set of other structural surface equations.

[0013] S 4. Add the finite number of blocks to the block set;

[0014] S5. Set the next closed loop as the current closed loop and return to step S3; until all closed loops have been traversed;

[0015] S6. Remove immovable blocks from the block set to obtain the block search results.

[0016] In some embodiments, the method for determining the intersection trace of the structural surface and the excavation surface based on structural surface data and excavation surface data includes:

[0017] The structural surface equation is determined based on the structural surface data, and the excavation surface equation and the excavation surface boundary equation are determined based on the excavation surface data.

[0018] The intersection trace of the structural surface and the excavation surface is determined by solving the above equations simultaneously.

[0019] In some embodiments, a method for determining a closed loop existing on an excavation surface based on intersecting traces includes:

[0020] Determine the intersection point of the intersecting traces based on the intersecting traces;

[0021] Add the intersection points of the two traces of all common structural surfaces to the connected set to obtain an undirected connected set;

[0022] Determine closed loops on the excavation surface based on undirected connected sets.

[0023] In some embodiments, a nonlinear programming algorithm is used to determine whether a set of structural surfaces can form a finite block; the set of structural surfaces includes a first set of structural surfaces, a second set of structural surfaces, and a new set of structural surfaces formed by combining the first set of structural surfaces and the second set of structural surfaces.

[0024] It should be noted that nonlinear programming algorithms that can be used include the penalty function method and the barrier function method.

[0025] In some embodiments, the step of using a nonlinear programming algorithm to determine whether a set of structural surfaces can form a finite block includes: moving all structural surfaces in the set to the origin, such that the structural surfaces divide the space into a block side and an outer side; the equation of the i-th structural surface is A i x+B i y+C i z = 0, A i B i C i The parameters describing this plane are determined by geological elements; x, y, and z are coordinate values, and the coordinate system can be set according to the actual situation. The structural plane equation is flipped so that for all structural planes, A... i x+B i y+C i z>0 indicates the block side; the equation for the k-th excavation face is A. k x+B k y+C k z = 0, invert the excavation face equation so that for all excavation faces, A l+k x+B l+k y+C l+k z>0 indicates the block side;

[0026] If max(w) = 0, then the energy collection of the structural surfaces forms a finite block;

[0027] The nonlinear programming equation is:

[0028] Constraints:

[0029]

[0030] Objective function:

[0031] max: w = x 2 +y 2 +z 2 ;

[0032] Where l is the total number of structural surfaces contained in the structural surface set, and p is the total number of excavation faces contained in the structural surface set.

[0033] On the other hand, a method for analyzing the stability of a block is provided, comprising the following steps:

[0034] Determine whether the block is a hazardous block;

[0035] If so, based on the resultant external force, sliding mode, sliding direction, and sliding surface of the dangerous block, determine the minimum support force and the optimal support surface required to ensure its sliding stability; the optimal support surface is one of the structural surfaces of the dangerous block, and the minimum support force is an anti-slip force parallel to the optimal support surface and opposite to the sliding direction;

[0036] Wherein, the block is the block in the block search results obtained according to the above method.

[0037] In some embodiments, a method for determining whether a block is a hazardous block includes:

[0038] Determine the sliding pattern of the block;

[0039] Determine the stability safety factor of the block based on the slip pattern;

[0040] The stability safety factor is used to determine whether a block is a dangerous block.

[0041] This invention has at least the following technical effects or advantages: 1. Starting from the traces where the structural surface and the excavation surface intersect, this invention assumes that only when the traces can combine to form a closed loop can the corresponding structural surface potentially form a block. The subsequent block search process will be based on this closed loop, significantly reducing search time and enabling rapid and accurate block search. 2. This invention can automatically calculate the block load based on external environmental conditions, thereby identifying the most likely sliding mode, sliding direction, and sliding surface of the block, and finally calculating the safety factor under this sliding mode. 3. Based on the identified dangerous block sliding surface and sliding direction, this invention can analyze the minimum support force required to ensure the anti-sliding safety of the dangerous block, thus providing reference for engineering design and construction. This invention is applicable to tunnels, slopes, dam abutments, etc. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating a block search method in one embodiment of the present invention;

[0043] Figure 2 This is a flowchart illustrating a block stability analysis method according to an embodiment of the present invention;

[0044] Figure 3 This is a three-dimensional schematic diagram of an underground chamber in one embodiment of the present invention;

[0045] Figure 4 This is a cross-sectional schematic diagram of an underground chamber according to one embodiment of the present invention;

[0046] Figure 5 This is a development view of the outline traces of an underground chamber in one embodiment of the present invention;

[0047] Figure 6 This is an unfolded diagram of the closed loop of the outline of an underground chamber in one embodiment of the present invention;

[0048] Figure 7 This is a search result for underground chamber blocks and a three-dimensional display of hazardous blocks in one embodiment of the present invention. Detailed Implementation

[0049] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0050] Example 1

[0051] It should be noted that the structural surface data used in this invention are all derived from on-site geological survey statistics and are not part of the scope of this invention. This embodiment uses an underground chamber as an example and is limited to identifying blocks and calculating block stability based on known structural surface information and chamber shape. The flowchart is as follows. Figure 1 and Figure 2 As shown.

[0052] This embodiment uses an underground chamber as an example, and its three-dimensional diagram is as follows: Figure 3 As shown, the shape of the cross-section is as follows Figure 4 As shown.

[0053] like Figure 1 As shown, the block search method includes the following steps:

[0054] (1) Import the underground chamber design model or 3D scanning model and geological logging data to complete the 3D digital model reconstruction. The top surface of the chamber is arc-shaped, and multiple bounded planes are used to fit the top surface; it is assumed that the geological logging data contains a total of m structural planes, which generally include information such as the direction, dip, and dip angle of the structural planes, and the structural plane equations are calculated in combination with the coordinate system.

[0055] (2) Based on the structural surface equation, the chamber top surface equation, and the boundary conditions of the chamber top surface, three equations can be obtained. Solving these equations simultaneously allows for the calculation of the intersection points between the structural surface and the chamber boundary. Taking the top surface of a rectangular chamber as an example, the number of intersection points with the structural surface is generally two. The line connecting two intersection points is the intersection trace of the structural surface and the chamber top surface. Calculate all intersection traces between the structural surface and the chamber top surface, expand the chamber outline, and calculate the intersection points of the traces. Using trace p... i′ p j′ and p k′ p l′ For example, the method for calculating the intersection of traces is as follows:

[0056] ① Solve the equations of the traces simultaneously to calculate the coordinates of the intersection point. Assume the intersection point is p. m′ ;

[0057] ② Calculate vector p i′ p m′ p j′ p m′ p k′ p m′ p l′ p m′ ;

[0058] ③If p i′ p m′ ×p j′ p m′ <0, and p k′ p m′ ×p l′ p m′ If <0, then the intersection point p is considered to be... m′ If it exists, then the two traces will not intersect.

[0059] (3) Based on the coplanar relationship between the traces and the intersections, if two points share a structural plane, then the two points are considered to be connected; otherwise, they are not connected, forming a connected set of all trace intersections. This connected set is an undirected connected set.

[0060] (4) Based on the undirected connected set, the closed loops existing on the contour surface of the chamber are determined by using closed loop search algorithms (such as depth-first search, topological sorting algorithm, breadth-first search algorithm, disjoint-set data structure, etc.). Concave loops are not considered for the time being. It is assumed that there are n closed loops in total. All closed loops are denoted as loop(1,2,…j,j+1,…,n), where loop(j) is the j-th closed loop, and the elements contained are all the corner points that make up the loop.

[0061] (5) For a closed loop loop(j), sort the point set clockwise or counterclockwise.

[0062] (6) Collect the structural surface equations contained in the closed loop (j) and form the equation set face. j Other structural surface equations (i.e., structural surface equations not included in the closed loop(j)) constitute the equation set plane. j .

[0063] (7) Face the equation set j All plane equations are translated to the origin, and a nonlinear programming algorithm is used to construct a model based on the equation set face. j The block cone domain determination method is used to determine the equation set face. j Can a closed loop pointing to another element form a finite block?

[0064] The specific steps of the nonlinear programming algorithm are as follows:

[0065] ① Assume the closed loop contains l structural surfaces. Moving all structural surfaces to the origin, the structural surfaces divide the space into two half-spaces: the block side and the outer side. Taking the i-th structural surface as an example, its structural surface equation is A. i x+B i y+C i z = 0;

[0066] ② Reverse the equation of the structural surface so that for all structural surfaces, A i x+B i y+C i z>0 indicates the block side;

[0067] ③ Assuming there are p excavation faces, calculate the equation of each excavation face. The equation of the k-th excavation face is A. k x+B k y+C k When z = 0, flip the excavation face so that for all excavation faces, A l+k x+B l+k y+C l+k z>0 indicates the block side;

[0068] ④ The nonlinear programming equation is:

[0069] Constraints:

[0070]

[0071] Objective function:

[0072] max: w = x 2 +y 2 +z 2 ;

[0073] ⑤ The necessary and sufficient condition for a block to be a finite block is max(w) = 0.

[0074] (8) If the closed loop loop(j) can form a block, calculate the corner point of the block, add it to the block set block, and proceed to step (5) to proceed to the next closed loop loop; otherwise, continue to step (9).

[0075] (9) Face the equation set j With plane j The structural surfaces in the set are combined to form a new set of structural surfaces, face0. j Using the nonlinear programming algorithm in step (7), determine the structure surface set face0. j Can a finite block be formed?

[0076] (10) If face0 j If a finite number of blocks can be formed, calculate the corner points of the blocks, add them to the block set, and proceed to step (11); otherwise, proceed directly to step (11).

[0077] (11) Determine whether the loop has been completed for all closed loops in the loop. If it has been completed, proceed to step (12); otherwise, return to step (5) and perform the block search in the next closed loop.

[0078] (12) Perform a block mobility determination on all blocks in the block set, remove the immovable blocks, and thus complete the block search.

[0079] like Figure 2 As shown, the block stability analysis method includes the following steps:

[0080] (13) For each block in the block set, calculate the resultant external force on the block. The loads such as gravity, uplift pressure, and arch end thrust should be considered according to the actual environmental conditions of the block (the loads are external input data and are not considered in this patent).

[0081] (14) Analyze the block slip mode, slip direction and slip surface. There are three types of block slip: detachment motion, single-sided slip (slip surface a) and double-sided slip (slip surfaces a and b).

[0082] (15) Calculate the stability safety factor K of the block under this slip mode:

[0083]

[0084] In the formula, N a f is the normal force acting on the block in the same direction as the normal to the slip surface a. a Let C be the coefficient of friction of the slip surface a. a S is the cohesion of the slip surface a. a Let T be the area of ​​the slip surface a. a N is the sliding force along the slip surface a. b f is the normal force acting on the block in the same direction as the normal to the slip surface b. b Let C be the coefficient of friction of the slip surface b. b S represents the cohesion of the slip surface b. b Let T be the area of ​​the slip surface b. b The force represents the sliding force along the slip surface b, and all units are in the International System of Units (SI).

[0085] (16) If K < 1, then classify the block as a dangerous block, such as Figure 7 As shown, red represents dangerous blocks, and blue represents all blocks.

[0086] (17) For dangerous blocks, calculate the minimum support force required to ensure their sliding stability based on their resultant external force, sliding mode and sliding surface, and analyze the optimal support surface (the support surface should be one of the block's structural surfaces, and the support force is the anti-sliding force parallel to the structural surface and opposite to the sliding direction).

[0087] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0088] Similarly, it should be understood that, in order to streamline this disclosure and aid in understanding one or more of the various aspects of the invention, in the above description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof. However, this method of disclosure should not be interpreted as reflecting an intention that the claimed invention requires more features than expressly recited in each claim. Rather, as reflected in the claims, inventive aspects lie in fewer than all features of a single foregoing disclosed embodiment. Therefore, the claims following the detailed description are hereby expressly incorporated into that detailed description, wherein each claim itself is a separate embodiment of the invention.

[0089] Those skilled in the art will understand that the modules, units, or groups of devices in the examples disclosed herein can be arranged in the device as described in this embodiment, or alternatively, can be located in one or more devices different from the device in this example. The modules in the foregoing examples can be combined into a single module or further divided into multiple sub-modules.

[0090] Those skilled in the art will understand that modules in the device of the embodiments can be adaptively changed and placed in one or more devices different from that embodiment. Modules, units, or groups in the embodiments can be combined into a single module, unit, or group, and further, they can be divided into multiple sub-modules, sub-units, or sub-groups. Except where at least some of such features and / or processes or units are mutually exclusive, any combination can be used to combine all features disclosed in this specification (including the accompanying claims, abstract, and drawings) and all processes or units of any method or device so disclosed. Unless expressly stated otherwise, each feature disclosed in this specification (including the accompanying claims, abstract, and drawings) may be replaced by an alternative feature that serves the same, equivalent, or similar purpose.

[0091] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features included in other embodiments but not others, combinations of features from different embodiments are meant to be within the scope of the invention and form different embodiments.

[0092] Furthermore, some of the embodiments described herein are methods or combinations of method elements that can be implemented by a processor of a computer system or by other means of performing the functions. Therefore, a processor having the necessary instructions for implementing the methods or method elements forms means for implementing the methods or method elements. Furthermore, the elements described herein in the apparatus embodiments are examples of means for implementing the functions performed by elements for the purposes of carrying out the invention.

[0093] The various techniques described herein can be implemented in combination with hardware or software, or a combination thereof. Thus, the methods and apparatus of the present invention, or certain aspects or portions thereof, can take the form of program code (i.e., instructions) embedded in a tangible medium, such as a floppy disk, CD-ROM, hard disk, or any other machine-readable storage medium, wherein when the program is loaded into and executed by a machine such as a computer, the machine becomes an apparatus for practicing the present invention.

[0094] When the program code is executed on a programmable computer, the computing device generally includes a processor, a processor-readable storage medium (including volatile and non-volatile memory and / or storage elements), at least one input device, and at least one output device. The memory is configured to store program code; the processor is configured to execute the method of the present invention according to instructions in the program code stored in the memory.

[0095] By way of example, and not limitation, computer-readable media include computer storage media and communication media. Computer storage media stores information such as computer-readable instructions, data structures, program modules, or other data. Communication media generally embodies computer-readable instructions, data structures, program modules, or other data in the form of modulated data signals such as carrier waves or other transmission mechanisms, and includes any information delivery medium. Any combination of the above is also included within the scope of computer-readable media.

[0096] As used herein, unless otherwise specified, the use of ordinal numbers such as “first,” “second,” “third,” etc., to describe ordinary objects merely indicates different instances of similar objects and is not intended to imply that the objects being described must have a given order in time, space, ordering, or any other manner.

[0097] Although the invention has been described with reference to a limited number of embodiments, those skilled in the art will understand from the foregoing description that other embodiments are conceivable within the scope of the invention described herein. Furthermore, it should be noted that the language used in this specification has been chosen primarily for readability and instructional purposes, and not for the purpose of interpreting or limiting the subject matter of the invention. Therefore, many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the appended claims. The disclosure of the invention is illustrative and not restrictive, and the scope of the invention is defined by the appended claims.

[0098] Finally, it should be noted that this invention does not explain in detail the common knowledge recognized by those skilled in the art. The above description is only a specific embodiment of this invention and is not intended to limit this invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A block search method, characterized in that, The method includes the following steps: S1. Based on the structural surface data and the excavation surface data, determine the intersection trace of the structural surface and the excavation surface; S2. Determine all closed loops on the excavation surface based on the intersecting traces; S3. Determine whether the first set of structural surfaces in the current closed loop can form a finite block; If yes, proceed to step S4; if no, combine the first and second structural surface sets of the current closed loop to form a new structural surface set, and determine whether the new structural surface set can form a finite block; if yes, proceed to step S4; if no, proceed to step S5. The first set of structural surfaces is the set of structural surface equations contained in the current closed loop, and the second set of structural surface equations is the set of other structural surface equations. S4. Add the finite number of blocks to the block set; S5. Set the next closed loop as the current closed loop and return to step S3; until all closed loops have been traversed; S6. Remove immovable blocks from the block set to obtain the block search results; In step S3, a nonlinear programming algorithm is used to determine whether the set of structural surfaces can form a finite block; the set of structural surfaces includes a first set of structural surfaces, a second set of structural surfaces, and a new set of structural surfaces formed by combining the first set of structural surfaces and the second set of structural surfaces. The steps for determining whether a set of structure surfaces can form a finite block volume using a nonlinear programming algorithm include: Move all structural surfaces in the structural surface cluster to the origin, so that the structural surfaces divide the space into the block side and the outer side; The equations for the structural surfaces are: ; Reverse the equations for the structural surfaces to make it so that for all structural surfaces, Indicates the block side; The equation for the k-th excavation face is: Reverse the excavation face equation so that for all excavation faces, Indicates the block side; like Then the energy collection of the structural surfaces forms a finite block; The nonlinear programming equation is: Constraints: ； Objective function: ； in, This represents the total number of structural surfaces contained in this structural surface set. This represents the total number of excavation faces contained in this structural face set.

2. The block search method according to claim 1, characterized in that, Methods for determining the intersection traces of structural surfaces and excavation surfaces based on structural surface data and excavation surface data include: The structural surface equation is determined based on the structural surface data, and the excavation surface equation and the excavation surface boundary equation are determined based on the excavation surface data. The intersection trace of the structural surface and the excavation surface is determined by solving the above equations simultaneously.

3. The block search method according to claim 1 or 2, characterized in that, Methods for determining closed loops on the excavation surface based on intersecting traces include: Determine the intersection point of the intersecting traces based on the intersecting traces; Add the intersection points of the two traces of all common structural surfaces to the connected set to obtain an undirected connected set; Determine closed loops on the excavation surface based on undirected connected sets.

4. A method for analyzing the stability of a block, characterized in that, Includes the following steps: Determine whether the block is a hazardous block; If so, based on the resultant external force, sliding mode, sliding direction, and sliding surface of the dangerous block, determine the minimum support force and the optimal support surface required to ensure its sliding stability; the optimal support surface is one of the structural surfaces of the dangerous block, and the minimum support force is an anti-slip force parallel to the optimal support surface and opposite to the sliding direction; Wherein, the block is a block in the block search result obtained by the method according to any one of claims 1-3.

5. The block stability analysis method according to claim 4, characterized in that, Methods for determining whether a block is a hazardous block include: Determine the sliding pattern of the block; Determine the stability safety factor of the block based on the slip pattern; The stability safety factor is used to determine whether a block is a dangerous block.

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