Building and structure stability evaluation method based on FLAC3D numerical simulation data
Through FLAC3D numerical simulation and 'octagonal star' analysis method, the deformation value of the building in 16 directions was calculated, which solved the accuracy and comprehensiveness of the surface deformation evaluation in the prior art, and achieved the fineness of the stability of the building , providing more reliable data support for mining enterprises and governments.
Patent Information
- Application Number
- CN202411079134.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-07
- Publication Date
- 2024-12-31
AI Technical Summary
The existing structural stability evaluation methods are difficult to accurately calculate surface deformation under complex geological conditions, especially for deformation values in non-NESW directions, which may lead to misjudgment and affect the safe operation of mining enterprises and government decisions.
FLAC3D numerical simulation data is used to generate a building point cloud, and the inclination, curvature and horizontal deformation values of the monitoring point in 16 directions are calculated through the ‘octagonal star’ analysis method, providing a more refined and comprehensive stability evaluation.
It realizes a refined evaluation of the stability of the building in different directions, provides more solid data support, avoids misjudgment, and ensures the accuracy and safety of decision-making.
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Figure CN119227175A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of building stability evaluation methods, and in particular relates to a building stability evaluation method based on FLAC3D numerical simulation data. Background Art
[0002] As mining depth and scale increase, the overlying rock strata in the goaf begin to move and deform, gradually extending toward the surface and causing surface movement, deformation and discontinuous damage, and even leading to surface collapse and crack damage. The stability of surface structures within the range of mine rock movement faces severe challenges.
[0003] The Code for Design of Nonferrous Metal Mining (GB50771-2012) specifies in detail the specific standards for the surface inclination, curvature and horizontal deformation values allowed for buildings and structures of different protection levels. However, in actual operation, there is no unified and accurate method or means to quickly and accurately calculate the deformation values of surface buildings and structures caused by underground mining activities. In recent years, many scholars have applied mathematical or numerical simulation methods to the study of the impact of underground mining on the stability of surface buildings and structures. For example, the probability integral method is used to perform theoretical calculations on surface settlement, and the surface settlement contours are obtained by combining the Matlab program to obtain the deformation values of the buildings and structures; numerical models are constructed using numerical simulation methods such as FLAC3D and 3DEC, and the surface inclination, curvature and horizontal deformation values on the sections are calculated by cutting sections at the buildings and structures.
[0004] The scope of application of the probability integral method for stability evaluation of structures is limited, and it is only applicable to rectangular mining areas or approximately rectangular mining areas. For metal mines with complex ore body conditions, it is difficult to estimate the key parameters of the probability integral method (such as surface subsidence coefficient, horizontal movement coefficient, main influence angle tangent, etc.), which affects the accuracy of stability evaluation.
[0005] The numerical simulation methods such as FLAC3D and 3DEC can better simulate the mining and filling process of metal mines. For the stability analysis of structures, two perpendicular sections are often intercepted, monitoring points are arranged on the surface of the section, and the XYZ displacement data are extracted. Based on this, the inclination, curvature and horizontal deformation of each monitoring point are calculated. This method has relatively limited accuracy, and the whole process is relatively cumbersome and time-consuming. In addition, since the movement deformation of the surface points is directional, the inclination, curvature and horizontal deformation values of each surface point in different directions are different. Therefore, only intercepting two sections can only reflect the deformation value of a certain monitoring point in the four directions of NESW, but cannot reflect the deformation value of the structure in other directions. If the maximum deformation of the structure happens to occur in the non-NESW direction, this method may lead to the omission of key information, which in turn leads to misjudgment, and the structure that is actually in an unstable state is mistakenly evaluated as stable. Such misjudgment may not only delay the necessary reinforcement or protection measures, but also have an adverse impact on the safe operation of mining enterprises and the decision-making of the government.
[0006] Therefore, it is urgent to develop a building stability evaluation method based on FLAC3D numerical simulation data to solve the above technical defects. Summary of the invention
[0007] In view of the problems existing in the background technology, the purpose of the present invention is to provide a method for evaluating the stability of buildings and structures based on FLAC3D numerical simulation data, which adopts FLAC3D numerical simulation and extracts surface deformation data, generates a point cloud of a building and structure according to the two-dimensional graphics of the building and structure, and performs three-dimensional displacement interpolation of the point cloud. On this basis, the "octagonal star" analysis method is adopted, which not only covers the traditional four basic directions of N, E, S, and W, but also considers 12 subdivided directions such as NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, and NW3, a total of 16 directions, and then comprehensively and accurately calculates the inclination, curvature and horizontal deformation values of the monitoring points in these directions, thereby realizing the refinement and comprehensiveness of the evaluation of the stability of buildings and structures, and providing more solid data support for decision-making.
[0008] To achieve the above-mentioned purpose, the present invention discloses a method for evaluating the stability of a structure based on FLAC3D numerical simulation data, constructs a three-dimensional solid model of an ore body, surrounding rock and ground surface, uses FLAC3D numerical simulation based on the three-dimensional solid model to extract ground surface deformation data, generates a point cloud of a structure according to a two-dimensional figure of the structure, and performs three-dimensional displacement interpolation of the point cloud to obtain the X, Y, and Z displacement values of all points in the point cloud; takes a point (x p ",y p"), taking this point as the center point, two concentrically arranged octagonal stars are used to set the surrounding points. The nodes of each octagonal star fall on the point cloud. The inclination, curvature and horizontal deformation values of the center point in multiple directions are calculated through the combination of the center point and the octagonal star nodes; the stability of the building is evaluated based on the inclination, curvature and horizontal deformation values of each node.
[0009] In a preferred embodiment of the present invention, any two adjacent corners of the octagonal star are arranged in mirror symmetry with each other, and any four adjacent corners of the octagonal star are arranged in mirror symmetry with each other, each side of the octagonal star includes 2 points, and any two adjacent sides are arranged at 45° or 90°.
[0010] In a preferred embodiment of the present invention, any two adjacent corners of the octagonal star are arranged in mirror symmetry with each other, and any four adjacent corners of the octagonal star are arranged in mirror symmetry with each other, each side of the octagonal star includes 3 points, and any two adjacent sides are arranged at 45° or 90°.
[0011] In a preferred embodiment of the present invention, the calculation method of the tilt deformation value is: when the ground surface sinks and there is a certain slope value along a certain direction, the value is the ratio of the sinking amount to the horizontal spacing: In the formula, α E-A is the tilt deformation value of point A toward direction E; W A , W B are the sinking values of points A and B respectively; l AB is the horizontal distance between point A and point B, point A is the center point, point B is the first point collinearly adjacent to the center point, and point C is the first point collinearly adjacent to point B.
[0012] In a preferred embodiment of the present invention, the curvature deformation value is calculated as follows: the curvature of the back section of the basin after the ground subsidence is calculated as the average value of the difference in inclination between two adjacent line segments divided by the horizontal length of the two line segments on the ground surface: In the formula, β E-A is the curvature deformation value of point A toward direction E; α E-B is the tilt deformation value of point A toward direction E; l BC is the horizontal distance between point B and point C, point A is the center point, point B is the first point collinearly adjacent to the center point, and point C is the first point collinearly adjacent to point B.
[0013] In a preferred embodiment of the present invention, the calculation method of the horizontal deformation value is: reflecting the horizontal movement difference per unit length between two adjacent observation points, and its value is the ratio of the horizontal movement difference between the two adjacent points to the horizontal distance between the two points: In the formula, ε E-A is the horizontal deformation value of point A toward direction E; U A , U BThey are the horizontal movement values of point A and point B respectively. Point A is the center point, point B is the first point collinearly adjacent to the center point, and point C is the first point collinearly adjacent to point B.
[0014] In a preferred embodiment of the present invention, the evaluation of the stability of structures based on the inclination, curvature and horizontal deformation values of each node includes: S1, according to the provisions of the protection level of surface buildings in the "Mining Design Manual", the structures are divided into protection levels I, II or III; S2, in accordance with the "Non-ferrous Metal Mining Design Code", the inclination, curvature and horizontal deformation values of each node are compared with the deformation limit of the corresponding protection level. If the deformation data of all directions of all nodes are within the limits specified in the code, it is determined that the surface structure is in a safe and stable state; conversely, if the deformation data of a certain direction of a certain node exceeds the requirements of the code, the surface structure is unstable.
[0015] In a preferred embodiment of the present invention, the inclination, curvature and horizontal deformation values of the center point in 16 directions are calculated by combining the center point and the octagonal star nodes, and the 16 directions include N, E, S, W, NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, and NW3.
[0016] The beneficial effects of the present invention are as follows: the present invention realizes the refined evaluation of the stability of buildings and structures in different directions, adopts FLAC3D numerical simulation and extracts the surface deformation data, generates the building point cloud according to the two-dimensional graphics of the building, and performs the three-dimensional displacement interpolation of the point cloud. On this basis, the "octagonal star" analysis method is introduced, which not only covers the traditional four basic directions of N, E, S, and W, but also considers 12 subdivided directions such as NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, and NW3, a total of 16 directions, and then comprehensively and accurately calculates the inclination, curvature and horizontal deformation values of the monitoring points in these directions, thereby realizing the refinement and comprehensiveness of the evaluation of the stability of buildings and structures, and providing more solid data support for decision-making. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] Figure 1 It is the FLAC3D numerical model diagram of the present invention;
[0018] Figure 2 It is a schematic diagram of grouping of model surfaces of the present invention;
[0019] Figure 3 It is a schematic diagram of the building structure and control nodes of the present invention;
[0020] Figure 4 It is a schematic diagram of the internal point cloud of the two-dimensional graphics of the expanded building structure of the present invention;
[0021] Figure 5 It is a schematic diagram of calculating the ground deformation values of nodes in different directions according to the present invention;
[0022] Figure 6 It is a schematic diagram of calculating the inclination, curvature and horizontal deformation of point A toward direction E of the present invention. DETAILED DESCRIPTION
[0023] The technical solution of the present invention (including the preferred technical solution) is further described in detail below by means of the accompanying drawings and by listing some optional embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0024] The present invention provides a building stability evaluation method based on FLAC3D numerical simulation data, and the specific steps are as follows:
[0025] Step 1: Numerical model construction and calculation
[0026] like Figure 1 As shown, the present invention uses 3DMine, Rhino and other software to construct a three-dimensional solid model of the ore body, surrounding rock and surface based on surface contour maps, exploration line profiles, stage plans and other drawings, and uses the Griddle2.0 plug-in to convert and export the solid model into a grid file in the .f3grid format that can be recognized by FLAC3D. In the FLAC3D software, numerical calculations are performed on the grid file through operations such as ore and rock parameter assignment, boundary condition constraints, ore body excavation, and goaf filling, and finally a calculation file in the .f3sav format that is calculated to balance is obtained.
[0027] Step 2: Extraction of three-dimensional displacement of the ground surface
[0028] like Figure 2 As shown, the present invention groups the model surface by the zone face skin command in FLAC3D, and the ground surface will be divided into the "Skin=Top" group. The spatial coordinates and X, Y, and Z displacement values of the nodes in the "Skin=Top" group are extracted separately by fish code, and exported as a .csv file. The file consists of 7 columns of data including node number, node X coordinate, node Y coordinate, node Z coordinate, node X displacement, node Y displacement, and node Z displacement.
[0029] Step 3: Generating building point cloud
[0030] like Figure 3As shown, the present invention abstracts the buildings into planar buildings (such as surface industrial sites, villages, etc.) and linear buildings (such as rivers, provincial roads, etc.) according to the shape characteristics of the buildings. The buildings are controlled by multiple control nodes (A, B, ...), and the control node coordinates are (x1, y1), (x2, y2), ..., (x n ,y n ).
[0031] Furthermore, the point cloud spacing in the X and Y directions is set to d. To facilitate the stability calculation at the edge of the building, the control nodes of the building are extended in the X and Y directions by 4d, and the extended two-dimensional figure of the building is obtained. The control node coordinates of the extended two-dimensional figure of the building are (x1′, y1′), (x2′, y2′), ..., (x n ′,y n ′). Perform interpolation point cloud operation on the expanded two-dimensional graphics of buildings and structures. The specific operation is as follows:
[0032] ① Determination of the bounding box of the graphic
[0033] The maximum and minimum values of the expanded building control figure in the X-axis and Y-axis directions are calculated through the following steps.
[0034] Minimum X coordinate: x min =min(x1′,x2′,...,x n ′)
[0035] Maximum X coordinate: x max =max(x1′,x2′,...,x n ′)
[0036] Minimum Y coordinate: y min =min(y1′,y2′,...,y n ′)
[0037] Maximum Y coordinate: y max =max(y1′,y2′,...,y n ′)
[0038] ②Point cloud coordinate calculation
[0039] The point cloud coordinates (x i ,y j ):
[0040] x i =x min +i*d, where i is an integer starting from 0, such that x i In [x min ,x max ] range.
[0041] y i =y min +j*d, where j is an integer starting from 0, such that y j In [y min ,y max ] range.
[0042] ③Filter points outside the graph
[0043] like Figure 4 As shown, the present invention uses the ray method to screen the generated grid points, that is, a ray is shot from the point in any direction, and the number of intersections between the ray and the polygon boundary is calculated. If the number of intersections is an odd number, the point is inside the polygon; if it is an even number, the point is outside the polygon. Ensure that the final point cloud is inside the closed figure, and derive the two-dimensional coordinates of all point clouds.
[0044] Step 4: Point cloud three-dimensional displacement interpolation
[0045] The coordinates of the nodes on the ground surface are known to be (X1, Y1), (X2, Y2), ..., (X m ,Y m ), the X, Y, and Z displacement values of each node on the ground surface are (DX1, DY1, DZ1), (DX2, DY2, DZ2), ..., (DX k ,DY k ,DZ k ).
[0046] The coordinates of each point in the known point cloud are (x1", y1"), (x2", y2"), ..., (x k ",y k "), and the inverse distance weighted interpolation method is used to calculate the X, Y, and Z displacements of each point cloud (DX1, DY1, DZ1"), (DX2, DY2, DZ2"), ..., (DX k ",DY k ",DZ k "), the calculation method is as follows:
[0047] Calculate each point in the point cloud (x p ",y p ") and the ground surface nodes (X1,Y1), (X2,Y2), ..., (X m ,Y m ), the calculation formula is as follows:
[0048]
[0049] All distances d p, sort from small to large, and select the three ground surface nodes with the smallest distance after sorting (X a ",Y a "),(X b ",Y b "),(X c ",Y c ").
[0050] A point in the point cloud (x p ",y p ") X, Y, Z displacement values (DX p ",DY p ",DZ p ") are the X, Y, and Z displacement values of the three ground surface nodes (DX i ",DY i ",DZ i ") and the weight function is defined as follows:
[0051]
[0052] According to the definition of weight function, a point in the point cloud (x p ",y p The X, Y, and Z displacement values of the
[0053]
[0054] The above operations are performed on all points in the point cloud to obtain the X, Y, and Z displacement values of all points in the point cloud.
[0055] Step 5: Calculation of point cloud tilt, curvature, and horizontal deformation values
[0056] Take a point (x p ",y p "), with this point as the center, two octagonal stars are used to set the surrounding points. The relative relationship of the two octagonal stars is shown in the figure below. The nodes of the octagonal stars all fall on the point cloud. Through the combination of the center point and different octagonal star nodes, the inclination, curvature and horizontal deformation values of the center point in different directions (N, E, S, W, NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, NW3) can be calculated.
[0057] like Figure 5 Shown and Figure 6 As shown, taking direction E as an example, the calculation formulas for the inclination, curvature and horizontal deformation value of point A toward direction E are as follows:
[0058] ① Tilt deformation value: The ground surface sinks and has a certain slope value along a certain direction. Its value is the sum of the sinking amount and the slope value.
[0059] Horizontal spacing ratio:
[0060]
[0061] In the formula, α E-A is the tilt deformation value of point A toward direction E; W A , W B are the sinking values of points A and B respectively; l AB is the horizontal distance between point A and point B.
[0062] ② Curvature deformation value: The curvature of the back section of the basin caused by the subsidence of the surface. Its value is the average value of the difference in inclination between two adjacent line segments divided by the horizontal length of the two line segments on the surface:
[0063]
[0064] In the formula, β E-A is the curvature deformation value of point A toward direction E; α E-B is the tilt deformation value of point A toward direction E; l BC is the horizontal distance between point B and point C.
[0065] ③Horizontal deformation value: reflects the horizontal movement difference per unit length between two adjacent observation points. Its value is the ratio of the horizontal movement difference between two adjacent points to the horizontal distance between the two points:
[0066]
[0067] In the formula, ε E-A is the horizontal deformation value of point A toward direction E; U A , U B are the horizontal movement values of points A and B respectively.
[0068] The present invention adopts the above method to calculate the inclination, curvature and horizontal deformation values of all nodes in the two-dimensional graph of the building in different directions (N, E, S, W, NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, NW3), and export the data to a .csv file, with a total of x p "、y p "、α N , α E , α S , α W , α NE1 , α NE2 , α NE3 , α SE1 , α SE2 , α SE3 , α SW1 , α SW2 , α SW3 , αNW1 , α NW2 , α NW3 , β N , β E , β S , β E , β NE1 , β NE2 , β NE3 , β SE1 , β SE2 , β SE3 , β SW1 , β SW2 , β SW3 , β NW1 , β NW2 , β NW3 , ε N , ε E , ε S , ε E , ε NE1 , ε NE2 , ε NE3 , ε SE1 , ε SE2 , ε SE3 , ε SW1 , ε SW2 , ε SW3 , ε NW1 , ε NW2 , ε NW3 There are 50 columns of data in total, of which the first two columns are the coordinates of the nodes in the two-dimensional figure of the building, the 3rd to 18th columns are the inclination deformation values of the nodes, the 19th to 34th columns are the curvature deformation values of the nodes, and the 35th to 50th columns are the horizontal deformation values of the nodes.
[0069] Step 6: Evaluation of building stability
[0070] According to the provisions on the protection level of surface buildings in the Mining Design Manual (Volume 2 of Mineral Deposit Exploitation), buildings and structures are divided into protection levels I, II or III.
[0071] In accordance with the "Design Code for Nonferrous Metal Mining" (GB50771-2012), the inclination, curvature and horizontal deformation values of each node are compared with the deformation limit of the corresponding protection level. If the deformation data of all directions of all nodes are within the limits specified in the code, it can be determined that the surface structures are in a safe and stable state; conversely, if the deformation data of a certain direction of a certain node exceeds the requirements of the code, it is considered that the surface structures are unstable and further corresponding measures need to be taken to ensure their safety.
[0072] The present invention generates a point cloud of a building according to a two-dimensional graphic of the building, and adopts an "octagonal star" analysis method to calculate the inclination, curvature and horizontal deformation values in 16 directions (N, E, S, W, NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, NW3) of the monitoring points, so as to realize a refined evaluation of the stability of the building in different directions, adopts FLAC3D numerical simulation and extracts surface deformation data, generates a point cloud of the building according to the two-dimensional graphic of the building, and performs three-way displacement interpolation of the point cloud. On this basis, the "octagonal star" analysis method was introduced, which not only covers the four traditional basic directions of N, E, S, and W, but also considers 12 additional sub-directions such as NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, and NW3, totaling 16 directions. The inclination, curvature, and horizontal deformation values of the monitoring points in these directions are calculated comprehensively and accurately, thereby realizing the refinement and comprehensiveness of the stability evaluation of buildings and structures and providing more solid data support for decision-making.
[0073] Those skilled in the art will readily appreciate that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, combinations, replacements, improvements, etc. made within the spirit and principles of the present invention are included within the protection scope of the present invention.
Claims
1. A building stability evaluation method based on FLAC3D numerical simulation data, characterized in that: Construct a three-dimensional solid model of the ore body, surrounding rock and surface. Use FLAC3D numerical simulation based on the three-dimensional solid model to extract surface deformation data. Generate a point cloud of the structure according to the two-dimensional graphics of the structure, and perform three-dimensional displacement interpolation of the point cloud to obtain the X, Y, and Z displacement values of all points in the point cloud. Take a point (x p ",y p "), taking this point as the center point, two concentrically arranged octagonal stars are used to set the surrounding points. The nodes of each octagonal star fall on the point cloud. The inclination, curvature and horizontal deformation values of the center point in multiple directions are calculated through the combination of the center point and the octagonal star nodes; the stability of the building is evaluated based on the inclination, curvature and horizontal deformation values of each node.
2. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 1 is characterized in that: Any two adjacent corners of the octagonal star are arranged in mirror symmetry with each other, and any four adjacent corners of the octagonal star are arranged in mirror symmetry with each other. Each side of the octagonal star includes 2 points, and any two adjacent sides are arranged at 45° or 90°.
3. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 1 is characterized in that: Any two adjacent corners of the octagonal star are arranged in mirror symmetry with each other, any four adjacent corners of the octagonal star are arranged in mirror symmetry with each other, each side of the octagonal star includes 3 points, and any two adjacent sides are arranged at 45° or 90°.
4. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 1 is characterized in that: The calculation method of the tilt deformation value is: the surface sinks and there is a certain slope value along a certain direction, and its value is the ratio of the sinking amount to the horizontal spacing: In the formula, α E-A is the tilt deformation value of point A toward direction E; W A , W B are the sinking values of points A and B respectively; l AB is the horizontal distance between point A and point B, point A is the center point, point B is the first point collinearly adjacent to the center point, and point C is the first point collinearly adjacent to point B.
5. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 1 is characterized in that: The calculation method of curvature deformation value is: the curvature of the back section of the basin caused by surface subsidence is the average value of the difference in inclination between two adjacent line segments divided by the horizontal length of the two line segments on the surface: In the formula, β E-A is the curvature deformation value of point A toward direction E; α E-B is the tilt deformation value of point A toward direction E; l BC is the horizontal distance between point B and point C, point A is the center point, point B is the first point collinearly adjacent to the center point, and point C is the first point collinearly adjacent to point B.
6. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 1 is characterized by: The calculation method of the horizontal deformation value is: reflecting the horizontal movement difference per unit length between two adjacent observation points, and its value is the ratio of the horizontal movement difference between the two adjacent points to the horizontal distance between the two points: In the formula, ε E-A is the horizontal deformation value of point A toward direction E; U A , U B They are the horizontal movement values of point A and point B respectively. Point A is the center point, point B is the first point collinearly adjacent to the center point, and point C is the first point collinearly adjacent to point B.
7. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 1 is characterized by: Evaluation of building stability based on the inclination, curvature and horizontal deformation values of each node includes: S1. According to the provisions of the Mining Design Manual on the protection level of surface buildings, the buildings and structures are classified into protection levels I, II or III; S2. In accordance with the "Design Specifications for Nonferrous Metal Mining", the inclination, curvature and horizontal deformation values of each node are compared with the deformation limit of the corresponding protection level. If the deformation data of all directions of all nodes are within the limits specified in the specifications, the surface structures are judged to be in a safe and stable state; conversely, if the deformation data of a certain direction of a certain node exceeds the requirements of the specifications, the surface structures are unstable.
8. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 1 is characterized by: The inclination, curvature and horizontal deformation values of the center point in 16 directions are calculated through the combination of the center point and the octagonal star node.
9. The building stability evaluation method based on FLAC3D numerical simulation data according to claim 8 is characterized by: The 16 directions include N, E, S, W, NE1, NE2, NE3, SE1, SE2, SE3, SW1, SW2, SW3, NW1, NW2, and NW3.
Citation Information
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