Method for obtaining geometric characteristic parameters of rock mass structural plane spacing

Abstract

The application discloses a method for obtaining geometric characteristic parameters of rock mass structure surface spacing, which comprises the following steps: selecting a rock mass region without vegetation obstruction as an analysis sample on a three-dimensional real scene model of a drone; determining n groups of the most developed dominant structure surfaces in the analysis sample, and counting the number of joint fissures of non-dominant structure surfaces in the sample; calculating and verifying all the dominant structure surfaces in the same group of dominant structure surfaces in the analysis sample in a preset order, and calculating the true spacing between two adjacent dominant structure surfaces; calculating the average spacing of each group of dominant structure surfaces according to the true spacing; taking the reciprocal of the average spacing of each group of dominant structure surfaces as the structure surface density; accumulating all the structure surface densities as the rock mass volume joint number, and correcting the rock mass volume joint number by using the area of the analysis sample and the number of joint fissures of the non-dominant structure surfaces; when n is 1 or 2, the rock mass is complete; when n is 3 or 4, the number of potential rockfalls of the analysis sample and the maximum and minimum block volumes are determined.

Description

Technical Field

[0001] This invention relates to the field of geological exploration technology, specifically to a method for obtaining geometric feature parameters of rock mass structure surface spacing using a high-precision three-dimensional real-scene model of a drone. Background Technology

[0002] Rock mass structural planes are planar geological interfaces with different orientations, scales, shapes, and properties developed within a rock mass. They are the basic units that constitute the rock mass structure and control its mechanical properties. Rock mass structural planes are relatively weak points in the rock mass's mechanical strength, leading to discontinuities, heterogeneity, and anisotropy in the rock mass's mechanical properties. Only by understanding the structural characteristics of the rock mass can we elucidate the stress distribution and differentiation within it under different loading conditions. The structural characteristics of a rock mass largely determine its medium characteristics and mechanical properties, controlling its deformation and failure modes and strength characteristics. They are important indicators for evaluating the quality of the rock mass structure. Structural plane analysis has very important applications in geological exploration, such as in the evaluation of slopes, landslides, collapses, rockfalls, and tunnel water inrushes. Correctly identifying and extracting structural planes is crucial for studying rock mass deformation, stability, and seepage. The spacing between structural surfaces refers to the average distance between two adjacent structural surfaces in the normal direction of the same set of structural surfaces. The geometric characteristic parameters of the spacing between structural surfaces mainly include the true spacing, average spacing, structural surface density, and number of joints in the rock mass volume. These parameters determine the size of the rock blocks to be cut in engineering, the location of the sliding surface, the rock mass quality classification, the volume of collapse and the number of blocks, and are important parameters of the geometric characteristics of structural surfaces.

[0003] Commonly used methods for measuring the spacing between structural surfaces of rock masses include: line measurement, photogrammetry, and three-dimensional laser scanning.

[0004] Traditional line surveying involves using long survey lines to manually measure rock joints and fissures at the outcrops of structural surfaces. The average spacing of these surfaces is calculated by dividing the length of the survey line by the number of structural surfaces it covers. This method suffers from significant workload, high operational risks, and inaccessibility in some areas. Photogrammetry typically uses a DSLR camera to capture multiple images of the rock mass. Multi-view image 3D reconstruction software is then used to construct a 3D point cloud model. Based on the obtained 3D point cloud data, and after roughly grouping and extracting structural surfaces, algorithms such as projection transformation and random point fitting are used to determine the spacing between the structural surfaces. However, photogrammetry has a limitation in terms of the area of ​​rock mass it can capture.

[0005] Three-dimensional laser scanning involves acquiring point cloud data of the rock mass to obtain a preliminary point cloud. This point cloud is then clustered using a mean-based clustering algorithm to obtain cluster planes. Two cluster planes belonging to the same structural plane are merged, and all cluster planes are sorted in ascending order. The nearest neighbor points of each point on the first cluster plane are searched for with points on other cluster planes. The distance between the two nearest neighbors is calculated, resulting in the distance between the two cluster planes corresponding to the two nearest neighbors, thus obtaining the spacing of the structural planes. However, current three-dimensional laser scanning methods are significantly affected by laser range and field of view. Generally, the farther the scanning distance, the fewer laser points are obtained, and the lower the accuracy. Furthermore, the scanning range is easily obstructed by mountains, resulting in data not being collected in some areas. Summary of the Invention

[0006] In view of the above-mentioned shortcomings in the prior art, the method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces provided by the present invention solves the problem that the existing three-dimensional laser scanning method is easily blocked by mountains and affected by the laser range, making it difficult to accurately obtain the geometric characteristic parameters of the spacing between rock mass structural surfaces.

[0007] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0008] A method for obtaining geometric characteristic parameters of the spacing between rock mass structural surfaces is provided, comprising the following steps:

[0009] S1. Select an unvegetated rock mass area as the analysis sample on the 3D real-world model and calculate the area of ​​the analysis sample.

[0010] S2. Determine the n most developed dominant structural surfaces in the analysis sample, and count the number of joints and fractures on the non-dominant structural surfaces in the analysis sample, 1≤n≤4;

[0011] S3. Calculate and verify all dominant structural planes in the same group of dominant structural planes in the analysis sample in a preset order, and calculate the true distance between two adjacent dominant structural planes.

[0012] S4. Calculate the average spacing of each group of dominant structural surfaces based on all true spacings of each group of dominant structural surfaces; use the reciprocal of the average spacing of each group of dominant structural surfaces as its structural surface density.

[0013] S5. Accumulate the density of all structural surfaces as the cumulative value, and correct the cumulative value by using the area of ​​the analysis sample and the number of joints and fractures of non-dominant structural surfaces to obtain the volumetric joint number of the rock mass.

[0014] S6. When n is 1 or 2, the rock mass is intact; when n is 3 or 4, determine the potential number of falling rocks and the maximum and minimum block volume of the analysis sample.

[0015] The beneficial effects of this invention are as follows: This solution utilizes measurement data from a UAV's 3D real-world model to accurately obtain seven parameters: true spacing of rock mass structural surfaces, average spacing, structural surface density, number of volumetric joints in the rock mass, number of potential rockfalls, and maximum and minimum block volumes. Smaller average spacing, higher structural surface density, and a larger number of volumetric joints indicate poorer rock stability. The number of potential rockfalls and the maximum and minimum block volumes can more accurately simulate and calculate the trajectory and maximum and minimum impact energy of falling rocks. This solution uses these seven parameters to quantitatively analyze the stability of slope rock masses and the risk of rockfall hazards.

[0016] This scheme adopts a digital mapping method, which is highly efficient, poses no personnel risk, has a large measurable range, is not obstructed by mountains, and does not require extensive drilling. It can be widely used in the stability analysis and evaluation of geological disaster slopes and the quality classification of engineering rock masses, and is particularly beneficial for the calculation and analysis of geometric characteristic parameters of structural surface spacing on steep slopes. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces.

[0018] Figure 2 This is a 3D realistic model of a steep slope of a hydropower station.

[0019] Figure 3 This is a reference diagram for calculating the spacing between structural surfaces and the range of its parameters.

[0020] Figure 4 A reference diagram obtained for calculating the area of ​​the region.

[0021] Figure 5 This is a reference diagram for numbering the structural surfaces within the defined area.

[0022] Figure 6 This is a schematic diagram of obtaining different points on the trace line of structure surface number 1.

[0023] Figure 7 This is a schematic diagram of obtaining different points on the trace line of structure surface number 2.

[0024] Figure 8 This is a schematic diagram of obtaining different points on the trace line of structure surface number 3.

[0025] Figure 9 This is a schematic diagram of the minimum volume (tetrahedron) of a potential rockfall. Detailed Implementation

[0026] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0027] refer to Figure 1 , Figure 1 A flowchart illustrating the method for obtaining the geometric characteristic parameters of the spacing between rock mass structural planes is shown; for example... Figure 1 As shown, the method S includes steps S1 and D6.

[0028] In step S1, a rock mass area without vegetation obstruction is selected as an analysis sample on the three-dimensional real scene model, and the area of ​​the analysis sample is calculated. The preferred method for obtaining the three-dimensional real scene model in this scheme is to use a drone to obtain high-definition real scene images of the area to be studied from multiple angles, and to construct a three-dimensional real scene model of the area to be studied based on the high-definition real scene images.

[0029] In step S2, the n most developed dominant structural surfaces in the analysis sample are determined, and the number of joints and fractures in the non-dominant structural surfaces in the analysis sample is counted, 1≤n≤4;

[0030] In one embodiment of the present invention, a method for determining the n most developed dominant structural surfaces in an analytical sample includes:

[0031] E1. Obtain a structural surface in the analysis sample, and select the spatial coordinates of three points in the structural surface that are not on a straight line: P1(x1,y1,z1), P2(x2,y2,z2), and P3(x3,y3,z3).

[0032] E2. Substituting the values ​​of P1(x1,y1,z1) into the equation A1x+B1y+C1z+D1=0, we get:

[0033] D1 = -(A1x1 + B1y1 + C1z1)

[0034] E3. The values ​​of the normal vector (A1, B1, C1) are calculated using P1(x1, y1, z1), P2(x2, y2, z2), and P3(x3, y3, z3) respectively:

[0035] A1=(y2-y1)*(z3-z1)-(z2-z1)*(y3-y1)

[0036] B1=(x3-x1)*(z2-z1)-(x2-x1)*(z3-z1)

[0037] C1=(x2-x1)*(y3-y1)-(x3-x1)*(y2-y1)

[0038] E4. Based on the calculated A1, B1, C1, and D1, the plane equation for the rock strata dip at the structural plane is: A1x + B1y + C1z + D1 = 0, and the normal vector is... Let the normal vector of the horizontal plane be...

[0039] E5. Calculate the angle between the rock stratum normal vector and the horizontal plane normal vector as the rock stratum dip angle:

[0040]

[0041] E6. The normal vector projected onto the XOY plane in the spatial rectangular coordinate system is: In a spatial rectangular coordinate system, the normal vector in the X direction is...

[0042] E7. When A1 > 0, the dip direction of this group of rock strata is:

[0043]

[0044] When A1 = 0, the dip of this group of rock strata is 180°;

[0045] When A1 < 0, the dip direction of this group of rock strata is:

[0046]

[0047] The attitude of the rock strata at that location is: β∠θ;

[0048] E8. Using the methods in steps E1 to E7, obtain the attitude of all structural planes in the analysis sample, conduct statistical analysis of joint fractures of the structural planes through joint rose diagram, and determine the n most developed dominant structural planes.

[0049] A1x+B1y+C1z+D1=0

[0050] A²x + B²y + C²z + D² = 0

[0051] ...

[0052] A n x+B n y+C n z+D n =0;

[0053] E9. Based on the joint rose diagram, statistically analyze the number G of joints and fissures on the non-dominant structural surfaces within the sample.

[0054] In step S3, all dominant structural planes in the same group of dominant structural planes in the analysis sample are calculated and verified in a preset order, and the true distance between two adjacent dominant structural planes is calculated.

[0055] In one embodiment of the present invention, step S3 further includes:

[0056] F1. Select the j-th structure plane closest to the bottom or left boundary of the analyzed sample in the n-th dominant structure plane, where n = 1, 2, 3 and 4, and the initial value of j is 1 for all of them;

[0057] F2. Determine whether at least one dominant structural surface in the nth group has been found. If yes, proceed to step F13; otherwise, proceed to step F3.

[0058] F3. Obtain the coordinates of point P on the j-th structural plane. nj1 (x nj1 ,y nj1 ,z nj1 Substitute into the plane equation A n x+B n y+C n z+D nj1 =0, we get:

[0059] D nj1 =-(A n x nj1 +B n y nj1 +C n z nj1 )

[0060] F4. Sequentially obtain different points P on the trace line of the j-th structural surface. nj2 (x nj2 ,y nj2 ,z nj2 ), P nj3 (x nj3 ,y nj3 ,z nj3 ...P njr (x njr ,y njr ,z njr ), and calculate the intercept D for each point. nj2 ...D njr r is the total number of points selected on the trace line of the j-th structural surface, r≥6;

[0061] F5. Determine all intercepts D nj2 ...D njr The maximum value D in njmax Minimum value D njmin ,average value Let D njmaxand D njmin The coordinates of the point on the corresponding structural surface are P njmax (x njmax ,y njmax ,z njmax ) and point P njmin (x njmin ,y njmin ,z njmin );

[0062] F6. Calculate P njmax (x njmax ,y njmax ,z njmax ) to D njmin Distance to the corresponding plane:

[0063]

[0064] F7, Calculate P nj1 (x nj1 ,y nj1 ,z nj1 ) and P njr (x njr ,y njr ,z njr ) in P njmin (x njmin ,y njmin ,z njmin The equation of the plane containing ) is A n x+B n y+C n z+D njmin =0 corresponding projection point Coordinates:

[0065]

[0066]

[0067]

[0068] Among them, t nj The transformation coefficient of the j-th structural surface in the n-th dominant structural surface group;

[0069] F8, Calculate projection points The distance L between nj，1r :

[0070]

[0071] F9, the maximum offset percentage R of the trace of the j-th structure surface in the n-th dominant structure surface group. nj for:

[0072]

[0073] F10, if R nj ≤10%, then The j-th structure surface is the dominant structure surface in the n-th group of dominant structure surfaces. Let its index be v, and let its average value be v. for v = 1, and its plane equation is: A n x+B n y+C n z+D nj =0, then proceed to step F12;

[0074] F11, If ​​R nj If the ratio is greater than 10%, then the j-th structural plane is not a dominant structure of the n-th dominant structural plane. This structural plane is counted as a joint and fracture of a non-dominant structural plane in the analysis sample, and G = G + 1 is set with an initial value of 0. Then proceed to step F12.

[0075] F12. Determine whether j of the dominant structural surface in the nth group is equal to its corresponding largest index structural surface. If yes, output all dominant structural surfaces in the nth group. Otherwise, let j = j + 1 and return to step F1.

[0076] F13. Obtain the coordinates P of different points on the trace line of the j-th structural surface. nj1 (x nj1 ,y nj1 ,z nj1 ...P njo (x njo ,y njo ,z njo ...P njk (x njk ,y njk ,z njk If P is on the j-th structural surface, then... njo (x njo ,y njo ,z njo The distance d from the first dominant structural surface in the nth dominant structural surface njo :

[0077]

[0078] Among them, (A) n B n C n ) is the normal vector of the first dominant structural surface in the nth dominant structural surface group; o is a variable, 1≤o≤k, k≥4;

[0079] F14, according to d njoThe calculation formulas are used to obtain the distance d from all points on the j-th structural plane to the first dominant structural plane in the n-th group. nj2 d nj3 ...d njk Calculate the maximum, minimum, and average values ​​of all spacings as follows: d njmax d njmin ,

[0080] F15, Point P nj1 (x nj1 ,y nj1 ,z nj1 ) and point P njk (x njk ,y njk ,z njk In plane equation A a x+B a y+C a The projection point corresponding to z+D1=0 The coordinates are:

[0081]

[0082]

[0083]

[0084] F16, Calculate the projection point The distance L between nj，1k :

[0085]

[0086] F17, the maximum offset percentage of the trace of the j-th structure plane in the n-th dominant structure plane group is:

[0087]

[0088] F18, If R nj If the value is ≤10%, then the j-th structural surface is the dominant structural surface of the n-th dominant structural surface, and its index is marked as v+1. Let the average value be... for v≥1;

[0089] F19. When v+1=2, what is the true distance between the (v+1)th dominant structural plane and the vth dominant structural plane? When v+1>2, the true distance between the (v+1)th dominant structural plane and the vth dominant structural plane. Then return to step F12;

[0090] F20, if R njIf the ratio is greater than 10%, then the j-th structural plane is not a dominant structural plane of the n-th group of dominant structural planes. This structural plane is counted as a joint and fracture of a non-dominant structural plane in the analysis sample, and G = G + 1 is set. Then, return to step F12.

[0091] In step S4, the average spacing of each group of dominant structural planes is calculated based on all true spacings of each group; the reciprocal of the average spacing of each group of dominant structural planes is used as its structural plane density.

[0092]

[0093] Where, ρ n S represents the surface density of the nth dominant structural plane; n The average spacing of the nth dominant structural planes;

[0094] In step S5, the densities of all structural surfaces are summed as the cumulative value, and the cumulative value is corrected by the area of ​​the analysis sample and the number of joints and fractures of non-dominant structural surfaces to obtain the volumetric joint number of the rock mass:

[0095]

[0096] Among them, S1, S2 and S n , representing the average spacing of the dominant structural surfaces in the first, second, and nth groups, respectively; s is the area of ​​the analyzed sample; and G is the number of joints and fractures on the non-dominant structural surfaces.

[0097] In step S6, when n is 1 or 2, the rock mass is intact; when n is 3 or 4, the potential number of falling rocks and the maximum and minimum block volumes of the analysis sample are determined.

[0098] In one embodiment of the present invention, when n is 3 or 4, the method for determining the potential number of falling rocks and the maximum and minimum block volumes of the analysis sample includes:

[0099] When n=3, and the rock mass is cut by 3 sets of dominant structural planes, the number of potential falling rocks is m=(i1-1)×(i2-1)×(i3-1), where i1, i2, and i3 are the total number of structural planes in the first, second, and third sets of dominant structural planes, respectively.

[0100] Obtain the maximum and minimum true spacing in the first, second, and third groups of dominant structural planes: l 1,max l 2,max l 3,max l 1,min l 2,min l 3,min And calculate the maximum and minimum volumes of potential falling rocks:

[0101]

[0102]

[0103] Among them, V max and V min Let A1, B1, C1 be the maximum and minimum volumes of potential falling rocks, respectively; (A1, B1, C1) be the normal vector of the first group of dominant structural surfaces; (A2, B2, C2) be the normal vector of the second group of dominant structural surfaces; and α be the angle between the normal vectors of the first and second groups of dominant structural surfaces.

[0104] When n=4, and the rock mass is cut by 4 sets of dominant structural planes, the potential number of falling rocks is:

[0105] m1 = (i1-1) × (i2-1) × (i3-1)

[0106] m2=(i1-1)×(i3-1)×(i4-1)

[0107] m3 = (i2-1) × (i3-1) × (i4-1)

[0108] Among them, m1, m2, and m3 represent the number of three potential rockfalls that may exist when the rock mass is cut by four sets of dominant structural planes.

[0109] The maximum value among m1, m2, and m3 is selected as the potential number of falling rocks when the rock mass is cut by four sets of dominant structural planes.

[0110] Obtain the maximum true spacing among the dominant structural planes in each group, and select the three largest as l. 1,max l 2,max l 3,max And calculate the maximum volume of potential falling rocks:

[0111]

[0112]

[0113] Obtain the plane equations corresponding to the structural planes with the smallest true spacing among the first to fourth groups of dominant structural planes:

[0114] A1x+B1y+C1z+D 1,min =0

[0115] A2x+B2y+C2z+D 2,min =0

[0116] A3x+B3y+C3z+D 3,min =0

[0117] A4x+B4y+C4z+D 4,min =0

[0118] Where (A3, B3, C3) are the normal vectors of the third group of dominant structural surfaces; (A4, B4, C4) are the normal vectors of the fourth group of dominant structural surfaces; D 1,min D 2,min D 3,min and D 4,min These are the intercepts in the plane equations of the first to fourth groups of dominant structural surfaces, respectively.

[0119] Using Cramer's rule, the non-homogeneous linear equations are solved. The intersection coordinates O1(x1,y1,z1) of the minimum true spacing structural planes in groups 1, 2, and 3; O2(x2,y2,z2) of the minimum true spacing structural planes in groups 1, 2, and 4; O3(x3,y3,z3) of the minimum spacing structural planes in groups 2, 3, and 4; and O4(x4,y4,z4) of the minimum spacing structural planes in groups 1, 3, and 4. A schematic diagram of the tetrahedron formed by the rock mass cut by the four dominant structural planes can be found in [reference]. Figure 9 .

[0120] Calculate the minimum volume V of potential falling rocks when the rock mass is cut by four sets of dominant structural planes. min :

[0121]

[0122] In this context, |·| represents the absolute value symbol.

[0123] In implementation, this scheme preferably uses the same method to calculate the intersection coordinates O1, O2, O3, and O4; Cramer's rule is used to solve the non-homogeneous linear equation system to calculate the intersection coordinates O1.

[0124] Let matrix K O1 = D, where K and D are both matrices;

[0125]

[0126] Where O = K-1D, since K and D are known, the coordinates O1(x1,y1,z1) can be calculated.

[0127] In this scheme, the method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces also includes:

[0128] Based on the minimum true spacing d of the nth dominant structural planes njmin The corresponding coordinate point P njmin (x njmin ,y njmin ,z njmin The plane equations of the weak structural surfaces of the nth dominant structural surface are obtained as follows:

[0129] A n x+Bn y+C n z+D n,min =0

[0130] Wherein, the intercept of the plane equation is D n,min =-(A n x njmin +B n y njmin +C n z njmin ).

[0131] The following section uses the slope of a hydropower station in Muli County, Liangshan Yi Autonomous Prefecture as an example to illustrate the method for obtaining the geometric characteristic parameters of the structural surface spacing in this scheme:

[0132] (1) Delineate the scope of analysis and calculation of the spacing between rock mass structural planes and their characteristic parameters.

[0133] A 3D realistic model of a steep slope at a hydropower station Figure 2 Select a bedrock location with exposed rock mass and clearly defined structural strata as the analysis sample for this scheme (e.g., Figure 3 and Figure 4 As shown in the figure, the area of ​​its calculation range is measured to be s = 179.46m². 2 .

[0134] (2) Solve the spatial plane equations of the main dominant structural planes and the number of joints and fissures.

[0135] By using a fixed coordinate system, the spatial coordinates of three points P1(x1,y1,z1), P2(x2,y2,z2), and P3(x3,y3,z3) that are not on a straight line are obtained from the dominant structural surface in the 3D oblique photogrammetry model. The attitude of the rock strata of 20 sets of joints and fractures in the sample area is then calculated.

[0136] Through statistical analysis of joints and fractures, the spatial plane equations of the attitude of rock strata with three dominant structural planes were obtained as follows:

[0137] 0.1247999x - 0.0516999y + 0.1145999z + 78756.3984845 = 0 (Equation 2-1)

[0138] -0.1361x-0.0278999y+0.0366z+177091.8605384=0 (Equation 2-2)

[0139] 0.2814x - 5.1112y - 2.0926z + 15788977.1861819 = 0 (Equation 2-3)

[0140] The rock strata attitudes corresponding to spatial plane equations 2-1, 2-2, and 2-3 are 113°∠50°, 257°∠75°, and 357°∠68°, respectively; where A1 = 0.1247999, B1 = -0.0516999, C1 = 0.1145999, A2 = -0.1361, B2 = -0.0278999, C2 = 0.0366, A3 = 0.2814, B3 = -5.1112, and C3 = 2.0926; the structural plane numbers in the first group of dominant structural planes can be referenced. Figure 5 .

[0141] (3) Calculation of true spacing between structural surfaces

[0142] First, let's take the 113°∠50° dominant structural plane as an example ( Figure 6 The calculation steps are as follows:

[0143] ① Under the same fixed coordinate system, obtain a point P on the first structural surface. 11 Substituting (661267.48, 3124577.11, 2247.54) into the plane equation 0.1247999x - 0.0516999y + 0.1145999z + D 11 =0, we get:

[0144] D 11 = -(0.1247999*661267.48 - 0.0516999*3124577.11 + 0.1145999*2247.54) = 78756.8869725533

[0145] And so on:

[0146] From left to right, obtain different points P on the structure surface trace. 12 (661267.82,3124577.39,2247.34), P 13 (661268.05,3124577.67,2247.21), P 14 (661268.88,3124578.39,2246.65), P 15 (661269.34,3124578.96,2246.34), P 16 (661269.66,3124579.34,2246.12), P 17 (661270.38,3124580.11,2245.55). Figure 5 )

[0147] D 12 =78756.8819365533;

[0148] D 13 =78756.8826065533;

[0149] D 14 =78756.8804225533;

[0150] D 15 =78756.8880095533;

[0151] D 16 =78756.8929315533;

[0152] D 17 =78756.9082065533.

[0153] The maximum, minimum, and average values ​​can then be obtained as: D 1max =D 17 =78756.9082065533; D 1min =D 14 =78756.8804225533;

[0154] Find the maximum intercept D of the plane equation. 1max Point P on the corresponding plane 17 (661270.38, 3124580.11, 2245.55) to the minimum intercept D of the plane equation 1min Distance to the corresponding plane:

[0155]

[0156] P 11 (661267.48,3124577.11,2247.54), P 17 (661270.38, 3124580.11, 2245.55) at point P 14 The coordinates P corresponding to the equation 0.1247999x-0.0516999y+0.1145999z+78756.8804225533=0 in the plane containing (661268.88,3124578.39,2246.65) are as follows: 11 '、P 17 'They are respectively:

[0157]

[0158] x 11 '=x 11 -A1t1=661267.506048809

[0159] y 11 '=y 11 -B1t1=3124577.09920895

[0160] z 11 '=z 11 -C1t1=2247.56391981996

[0161] x 17 '=x 11 -A1t1=661270.406048809

[0162] y 17 '=y 11 -B1t1=3124580.09920895

[0163] z 17 '=z 11 -C1t1=2245.57391981996

[0164] Then the projection point P 11 '、P 17 The distance between them is:

[0165]

[0166] The maximum offset percentage of the structural surface trace is:

[0167]

[0168] Since R1 ≤ 10%, the calculated average value If the requirements are met, then

[0169] That is, the plane equation of the first structural plane (113°∠50°) of the first group of dominant structural planes is obtained:

[0170] 0.1247999x-0.0516999y+0.1145999z+78756.8887265533=0

[0171] ② Obtain the second structural plane in the 3D reality model ( Figure 5 The coordinates of point P on the sequence number 2) 21 (661271.36,3124580.46,2246.03), P 22 (661271.05,3124580.07,2246.21), P 23 (661270.37,3124579.5,2246.75), P 24(661268.76, 3124578.03, 2247.87), these coordinates can be used as a reference. Figure 7 Then point P on the second structural surface 21 The true spacing from (661271.36,3124580.46,2246.03) to the first structural surface of the first dominant structural surface is:

[0172]

[0173] d is obtained from 3-4 respectively. 22 =0.8007m, d 23 =0.8373m, d 24 =0.8798m, then the maximum, minimum and average values ​​can be obtained as: d 2max =d 24 =0.8798m, d 2min =d b1 =0.7888m

[0174] P 21 (661271.36,3124580.46,2246.03), P 24 The coordinates P corresponding to the equation 0.1247999x-0.0516999y+0.1145999z+78756.8887265533=0 in the plane are (661268.76,3124578.03,2247.87). 21 '、P 24 'They are respectively:

[0175]

[0176] x 21 '=x 21 -A1t2=661270.804277506

[0177] y 21 '=y 21 -B1t2=3124580.69021517

[0178] z 21 '=z 21 -C1t2=2245.51969713318

[0179] x 24 '=x 24 -A1t2=661268.204277506

[0180] y 24 '=y 24-B1t2=3124578.26021517

[0181] z 24 '=z 24 -C1t2=2247.35969713318

[0182] Then the projection point P 21 '、P 27 The distance between them is:

[0183]

[0184] The maximum offset percentage of the structural surface trace is:

[0185]

[0186] Since R² ≤ 10%, the calculated average value... If the requirements are met, then the true distance between structural plane 2 and structural plane 1 is:

[0187] To verify whether this structural surface is the first group of dominant structural surfaces, structural surface number 3 of the first group of dominant structural surfaces was obtained from left to right in the 3D reality model. Figure 5 (3) Coordinates of different points P on the trace line 31 (661271.4,3124580.33,2246.37), P 32 (661271.15,3124580.09,2246.53), P 33 (661270.48,3124579.38,2247.02), P 34 (661269.59, 3124578.46, 2247.63), the diagram of these coordinate points can be found in the reference. Figure 8 Then point P on the second structural surface 31 The true spacing from (661271.4,3124580.33,2246.37) to the first structural surface of the first dominant structural surface is:

[0188]

[0189] d is obtained from 3-4 respectively. 32 =1.07231m, d 33 =1.12451m, d 34 =1.16062m, then the maximum, minimum and average values ​​can be obtained as: d 3max =d 34 =1.16062m, d 3min =d 32=1.07231m

[0190] P 31 (661271.4,3124580.33,2246.37), P 34 (661269.59,3124578.46,

[0191] The coordinates P corresponding to the equation A1x + B1y + C1z + D1 = 0 in the plane are 2247.63. 31 '、P 34 '

[0192] They are respectively:

[0193] x 31 '=x 31 -A1t3=661269.72273;

[0194] y 31 '=y 31 -B1t3=3124579.693705;

[0195] z 31 '=z 31 -C1t3=2246.32463;

[0196] x 34 '=x 31 -A1t3=661268.83274;

[0197] y 34 '=y 31 -B1t3=3124578.77370;

[0198] z 34 '=z 31 -C1t3=2246.93463;

[0199] Then the projection point P 31 '、P 34 The distance between them is:

[0200]

[0201] The maximum offset percentage of the structural surface trace is:

[0202]

[0203] Since R3 ≤ 10%, the calculated average value If the requirements are met, then the true distance between structural plane 3 and structural plane 2 is:

[0204] Following the steps above, the true spacing between structural planes 4 to 22 in the first group of dominant structural planes can be calculated sequentially, as follows:

[0205] l 1,3 =0.4220m, l 1,4 =0.1487m, l 1,5 =0.1895m, l 1,6 =0.8207m, l 1,7 =0.0903m, l 1,8 =1.503m, l 1,9 =0.8066m, l 1,10 =0.4903m, l 1,11 =0.2721m, l 1,12 =0.2273m, l 1,13 =0.2233m, l 1,14 =0.3017m, l 1,15 =0.2788m, l 1,16 =0.9385m, l 1,17 =0.8114m, l 1,18 =0.9409m, l 1,19 =1.3554m, l 1,20 =1.5194m, l 1,21 =1.4760m, l 1,22 =0.6853m.

[0206] (4) Calculate the horizontal distance, maximum distance, and minimum distance of the dominant structural surfaces, and determine the spatial plane equation of the weak structural surfaces.

[0207] a. Average spacing of dominant structural planes

[0208] The average spacing of the dominant structural planes in group 1 is:

[0209]

[0210] The average spacing of the dominant structural planes in the first group can then be obtained. Similarly, the average spacing of the dominant structural planes in the second and third groups can be obtained.

[0211] The maximum spacing of the dominant structural planes in group 1 is:

[0212] l 1,max =max(l 1,2 ,l 1,2 ,l 1,3 …l 1,21 ,l 1,22 ) = 1.5194m

[0213] The minimum spacing of the dominant structural planes and the plane equations of the weak structural planes in Group 1:

[0214] l 1,min =min(l 1,1 ,l 1,2 ,l 1,3 …l 1,21 ,l 1,22 )=0.0903m

[0215] The coordinate point through which the weak structural surface with the minimum spacing passes is: P 71 Given (661272.12, 3124580.28, 2248.04), the plane equation of the weak structural surface is:

[0216] D 71 =-(A1x 71 +B1y 71 +C1z 71 = -(0.1247999*661272.12-0.0516999*3124580.28)

[0217] +0.1145999*2248.04)=78756.4144895536

[0218] 0.1247999x-0.0516999y+0.1145999z+78756.4144895536=0, which is the plane equation corresponding to the weak structural surface.

[0219] (5) Surface density and number of volume joints in rock mass

[0220] The surface densities of the dominant structures in groups 1, 2, and 3 are respectively:

[0221] strips / m

[0222]

[0223] Through annotation analysis, there are also 8 other non-dominant structural joints G, with a calculated area of ​​s = 179.46 m². 2 .

[0224] The volumetric joint number of the rock mass is:

[0225]

[0226] (6) Number of potential falling rocks, maximum and minimum rock volume

[0227] Since the rock mass is cut by three sets of structural planes, the number of sets of structural planes within the delineated area is: i1 = 22, i2 = 11, i3 = 2. Therefore, the number of potential falling rocks is:

[0228] m = 22 × 11 × 2 = 484 blocks (Equation 6-1)

[0229] Based on the above formula, the maximum and minimum spacing of the three sets of structural planes have been obtained: l 1,max =1.5194m, l 2,max =2.5076m, l 3,max =1.8522m, l 1,min =0.0903m, l 2,min =0.2016m, l 3,min =1.8270m.

[0230] The maximum potential volume of falling rocks is:

[0231]

[0232]

[0233] The minimum volume of the potential falling rock is:

[0234]

[0235]

[0236] This method addresses the challenge of obtaining the geometric characteristic parameters of structural plane spacing in the rock mass of a steep slope at a hydropower station in Muli County, Liangshan Yi Autonomous Prefecture. Using UAV digital geological mapping, the following findings were made: ① Joint and fracture analysis revealed three groups of dominant structural planes in the analyzed sample; ② The average spacing of the dominant structural planes in groups 1, 2, and 3 were 0.6952 m, 0.8055 m, and 1.8396 m, respectively; ③ The structural plane densities of the dominant structural planes in groups 1, 2, and 3 were 1.438 joints / m, 1.2415 joints / m, and 0.5436 joints / m, respectively; ④ The volumetric joint count in the rock mass of the analyzed sample area was 3.82 joints / m. 3 ⑤ If a landslide occurs in the sample area, the potential number of falling rocks is 484, and the largest landslide block volume is 7.884 m³. 3 The minimum volume of the collapsed block is 0.0037 m³. 3 The mass of the potential rockfall block can be obtained by multiplying the volume of the collapsed block by the density of the rock mass.

[0237] In summary, compared to traditional line measurement methods, this scheme solves the problems of inaccessible sample areas and extremely high risks associated with manual measurement, thus saving measurement costs. Compared to photogrammetry using digital cameras, this method covers a larger and more comprehensive area, allowing evaluation of any high or steep slope within the power station. Compared to three-dimensional laser scanning, this method's analysis and calculations are unaffected by laser range and field of view, facilitating the analysis and acquisition of geometric characteristic parameters of rock mass structure surface spacing at any location. It achieves the acquisition of the potential number of falling rocks, the maximum and minimum block volumes, thereby accurately obtaining the mass of falling rock blocks and more accurately simulating and calculating the trajectory, maximum and minimum impact energy of dangerous rockfalls.

Claims

1. A method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces, characterized in that, Including the following steps: S1. Select an unvegetated rock mass area as the analysis sample on the 3D real-world model and calculate the area of ​​the analysis sample. S2. Identify the most developed individuals in the analyzed sample. n Group the dominant structural surfaces and statistically analyze the number of joints and fractures on the non-dominant structural surfaces in the sample, 1 ≤ n ≤4; S3. Calculate and verify all dominant structural planes in the same group of dominant structural planes in the analysis sample in a preset order, and calculate the true distance between two adjacent dominant structural planes. S4. Calculate the average spacing of each group of dominant structural surfaces based on all true spacings of each group of dominant structural surfaces; use the reciprocal of the average spacing of each group of dominant structural surfaces as its structural surface density. S5. Accumulate the density of all structural surfaces as the cumulative value, and correct the cumulative value by using the area of ​​the analysis sample and the number of joints and fractures of non-dominant structural surfaces to obtain the volumetric joint number of the rock mass. S6, when n When the value is 1 or 2, the rock mass is intact; when n When the value is 3 or 4, determine the potential number of falling rocks and the maximum and minimum block volume of the analyzed sample; Determine the most developed in the analysis sample n Methods for grouping dominant structural surfaces include: E1. Obtain a structural plane in the analysis sample, and select the spatial coordinates of three points on the structural plane that are not on a straight line. P 1 ( x 1, y 1, z 1) P 2 ( x 2, y 2, z 2) P 3 ( x 3, y 3, z 3); E2. Substituting the values ​​of P1(x1,y1,z1) into the equation A1x+B1y+C1z+D1=0, we get: D1 = -(A1x1 + B1y1 + C1z1) E3. Calculate the values ​​of the normal vector (A1, B1, C1) using P1(x1, y1, z1), P2(x2, y2, z2), and P3(x3, y3, z3) respectively: A1=(y2-y1)*(z3-z1)-(z2-z1)*(y3-y1) B1 =(x3-x1)*(z2-z1)-(x2-x1)*(z3-z1) C1 =(x2-x1)*(y3-y1)-(x3-x1)*(y2-y1) E4. Based on the calculated A1, B1, C1, and D1, the plane equation for the rock strata dip at the structural plane is: A1x + B1y + C1z + D1 = 0, and the normal vector is... (A1, B1, C1), let the normal vector of the horizontal plane be... (0,0,1); E5. Calculate the angle between the rock stratum normal vector and the horizontal plane normal vector as the rock stratum dip angle: θ=arccos( ) =arccos( ) E6. The normal vector projected onto the XOY plane in the spatial rectangular coordinate system is: (A) 1， B1), in a spatial rectangular coordinate system, the normal vector in the X direction is (0,1); E7. When A1 > 0, the dip direction of this group of rock strata is: β=arccos( ) * =arccos( ) * ; When A1=0, the dip of this group of rock strata is 180°; When A1 < 0, the dip direction of this group of rock strata is: β=360-arccos( ) * =360-arccos( ) * The attitude of the rock strata at that location is: β∠θ; E8. Using the methods in steps E1 to E7, obtain the attitude of all structural planes in the analysis sample, and use the joint rose diagram to carry out statistical analysis of joints and fractures of the structural planes to determine the n most developed dominant structural planes. A1x+B1y+C1z+D1=0 A²x + B²y + C²z + D² = 0 …… A n x+B n y+C n z+D n =0; E9. Based on the joint rose diagram, statistically analyze the number of joints and fractures on non-dominant structural planes within the sample. G .

2. The method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces according to claim 1, characterized in that, when n When the value is 3 or 4, methods for determining the potential number of falling rocks and the maximum and minimum block volumes of the analyzed sample include: when n =3, the number of potential rockfalls when the rock mass is cut by 3 sets of dominant structural planes. m = ( i 1-1)×( i 2-1) × ( i 3-1), of which i 1. i 2. i 3 represents the total number of structural surfaces in the first, second, and third groups of dominant structural surfaces, respectively; Obtain the maximum and minimum true spacing in the first, second, and third groups of dominant structural planes: l 1,max , l 2,max , l 3,max , l 1,min , l 2,min , l 3,min And calculate the maximum and minimum volumes of potential falling rocks: ， in, and These are the maximum and minimum volumes of the potential falling rock, respectively; A 1, B 1, C 1) is the normal vector of the first group of dominant structural surfaces; A 2, B 2, C 2) is the normal vector of the second group of dominant structural surfaces; The angle between the normal vectors of the first and second sets of dominant structural surfaces; when n =4. When the rock mass is cut by 4 sets of dominant structural planes, the potential number of falling rocks is: m 1=（ i 1-1）×（ i 2-1）×（ i 3-1） m 2=（ i 1-1）×（ i 3-1）×（ i 4-1） m 3=（ i 2-1）×（ i 3-1）×（ i 4-1） in, m 1. m 2、 m 3 represents the number of three potential rockfalls that may exist when the rock mass is cut by four sets of dominant structural planes; i 4 represents the total number of structural surfaces in the fourth group of dominant structural surfaces; Select m 1. m 2. m The maximum value in 3 is taken as the potential number of falling rocks when the rock mass is cut by the four sets of dominant structural planes; Obtain the maximum true spacing among the dominant structural planes in each group, and select the three largest as... l 1,max , l 2,max , l 3,max And calculate the maximum volume of potential falling rocks: Obtain the plane equations corresponding to the structural planes with the smallest true spacing among the first to fourth groups of dominant structural planes: A 1 x+B 1 y+C 1 z+D 1,min = 0 A 2 x+B 2 y+C 2 z+D 2,min = 0 A 3 x+B 3 y+C 3 z+D 3,min = 0 A 4 x+B 4 y+C 4 z+D 4,min = 0 in,( A 3, B 3, C 3) is the normal vector of the third group of dominant structural surfaces; A 4, B 4, C 4) is the normal vector of the fourth group of dominant structural surfaces; D 1,min D 2,min D 3,min and D 4,min These are the intercepts in the plane equations of the first to fourth groups of dominant structural surfaces, respectively. Using Cramer's rule, we solve the non-homogeneous linear equation system and calculate the coordinates of the intersection points of the minimum true spacing structural surfaces in the first, second, and third groups, respectively. O 1 ( x 1, y 1, z 1) Coordinates of the intersection points of the minimum true spacing structural surfaces in groups 1, 2, and 4. O 2 ( x 2, y 2, z 2) Coordinates of the intersection points of the minimum spacing structural surfaces in groups 2, 3, and 4. O 3 ( x 3, y 3, z 3) Coordinates of the intersection points of the minimum spacing structural surfaces in groups 1, 3, and 4. O 4 ( x 4, y 4, z 4); Calculate the minimum volume of potential falling rocks when the rock mass is cut by four sets of dominant structural planes. : ； in, It is the absolute value symbol.

3. The method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces according to claim 2, characterized in that, The intersection coordinates O1, O2, O3, and O4 are calculated using the same method; Cramer's rule is used to solve the non-homogeneous linear equation system to calculate the intersection coordinates O1. Let matrix K O1= D , K and D All are matrices; ， in, O = K -1 D Since it is known K and D Then the coordinates can be calculated. O 1 ( x 1, y 1, z 1).

4. The method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces according to claim 1, characterized in that, Number of rock mass joints The calculation formula is: in, S 1. S 2 and S n , respectively, represent the average spacing of the dominant structural surfaces in the first group, the second group, and the nth group; s is the area of ​​the analyzed sample; G This represents the number of joints and fissures on the non-dominant structural plane.

5. The method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces according to claim 1, characterized in that, Step S3 further includes: F1, Select the first n The first dominant structural plane closest to the bottom or left boundary of the analyzed sample j No. 6 structural plane, n= 1, 2, 3, and 4, j The initial values ​​are all 1; F2, Determine the first n If at least one dominant structural surface in the group has been found, proceed to step F13; otherwise, proceed to step F3. F3, Get the number j Coordinates of the structural surface No. P nj1 ( x nj1 , y nj1 , z nj1 Substitute into the plane equation A n x + B n y + C n z + D nj1 =0, therefore: D nj1 =-( A n x nj1 + B n y nj1 + C n z nj1 ) F4, sequentially obtain the... j Different points on the surface trace of structure number P nj2 ( x nj2 , y nj2 , z nj2 ), P nj3 ( x nj3 , y nj3 , z nj3 ... P njr ( x njr , y njr , z njr ), and calculate the intercept for each point. D nj2 ... D njr ; r For the first j The total number of points selected on the trace line of structure surface number 6. r ≥6; F5, Determine all intercepts D nj2 ... D njr The maximum value in D njmax Minimum value D njmin ,average value ;make D njmax and D njmin The coordinates of the point on the corresponding structural surface are P njmax ( x njmax , y njmax , z njmax ) and points P njmin ( x njmin , y njmin , z njmin ); F6. Calculate P njmax (x) njmax ,y njmax ,z njmax )arrive D njmin Distance to the corresponding plane: F7, Calculation P nj1 ( x nj1 , y nj1 , z nj1 )and P njr ( x njr , y njr , z njr )exist P njmin ( x njmin , y njmin , z njmin The equation of the plane containing ) A n x + B n y + C n z +D njmin = 0 corresponding projection point , Coordinates: = x nj1 - A 1 ， = y nj1 - B 1 ， = z nj1 - C 1 = x njr - A 1 ， = y njr - B 1 ， = z njr - C 1 in, For the first n The first group of dominant structural surfaces j The transformation coefficients of each structural surface; F8, Calculate projection points , Distance between : F9, No. n The first group of dominant structural surfaces j Maximum offset percentage of the trace on structure surface No. for: ； F10, if ≤10%, then D nj = , No. j The structural plane is the first n The dominant structural surfaces of the group are labeled with their sequence numbers. v Let its average value for , v =1, and its plane equation is: A n x + B n y + C n z + D nj =0, then proceed to step F12; F11, if >10%, then the first j The structural plane is not the first n The dominant structure of the dominant structure is statistically analyzed as the joints and fractures of the non-dominant structure within the sample, and G = G + 1 is set with an initial value of 0; then proceed to step F12. F12, Determine the first n Group Advantageous Structural Surface j Is it equal to its corresponding largest index structure surface? If so, output the first one. n All dominant structural surfaces of the group, otherwise, let j = j +1, and return to step F1; F13, Get the j Coordinates of different points on the surface trace of structure number P nj1 ( x nj1 , y nj1 , z nj1 ... P njo ( x njo , y njo , z njo ... P njk ( x njk , y njk , z njk ), then the first j A point on the structural surface of No. P njo ( x njo , y njo , z njo ) to the n The spacing of the first dominant structural plane in the group : in,( A n , B n , C n ) is the first n The normal vector of the first dominant structural surface in the group; o As variables, 1≤o≤ k , k ≥4; F14, according to The calculation formulas are used to obtain the first... j All points on the structural plane to the first n The spacing of the first dominant structural plane in the group d nj2 , d nj3 ... d njk Calculate the maximum, minimum, and average values ​​for all spacings as follows: d njmax , d njmin , ; F15, Point P nj1 ( x nj1 , y nj1 , z nj1 ) and points P njk ( x njk , y njk , z njk In plane equations A a x + B a y + C a z + D The projection point corresponding to 1=0 , The coordinates are: = x nj1 - A a ， = y nj1 - B a ， = z nj1 - C a = x njk - A a ， = y njk - B a ， = z njk - C a ； F16, Calculate the projection point , Distance between : ； F17, No. n The first group of dominant structural surfaces j The maximum offset percentage of the trace on structure surface number is: ； F18, if ≤10%, then the first j The structural plane is the first n The dominant structural surfaces of the group are identified and their sequence numbers are assigned. v +1, let the average value be... for , v≥ 1; F19, when v When +1=2, the first v +1 advantageous structural surface and the first v True spacing of each advantageous structural surface = ,when v When +1>2, the first v +1 advantageous structural surface and the first v True spacing of each advantageous structural surface = - Then return to step F12; F20, if >10%, then the first j The structural plane is not the first n The dominant structural plane is identified as the dominant structural plane, and this structural plane is statistically analyzed as the joints and fissures of the non-dominant structural planes within the sample. G is then set to G+1. The process then returns to step F12.

6. The method for obtaining the geometric characteristic parameters of the spacing between rock mass structural surfaces according to any one of claims 1-5, characterized in that, Also includes: According to the n Minimum true spacing of the dominant structural surfaces d njmin corresponding coordinates P njmin ( x njmin , y njmin , z njmin ), to obtain the first n The plane equations of the weak structural surfaces of the group of dominant structural surfaces are: A n x + B n y + C n z + D n,min = 0 Wherein, the intercept of the plane equation is D n,min =-( A n x njmin + B n y njmin + C n z njmin ).

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