A method for calculating the volume of dangerous rock masses based on three-dimensional images

Abstract

A method for calculating the volume of dangerous rock masses based on three-dimensional images provided by the present invention. The present invention analyzes the characteristics of dangerous rock masses cut by 3 or 4 groups of dominant structural planes through three-dimensional images, forms parallelepipeds, tetrahedrons, octahedrons, quadrangular frustums, and triangular prisms, and measures or calculates the vertex coordinates of the polyhedral dangerous rock masses, directly calculates the volume of the dangerous rock masses, or uses the segmentation method to solve the volumes of multiple simple polyhedrons, and then adds or subtracts them to obtain the volume of the dangerous rock masses. There is no need to carry out borehole or adit exploration at high and steep dangerous rocks, it is not affected by vegetation, the calculation efficiency is high, it improves the reliability, safety, accuracy, and economy of the prevention and control of dangerous rock and rockfall disasters, reduces the design changes in the prevention and control of dangerous rock and rockfall, saves construction funds, is more practical than the prior art, has a wide range of applicability, and has great significance for promotion and application prospects.

Description

Technical Field

[0001] The present invention belongs to the technical field of geological disaster investigation, and relates to a method for calculating the volume of dangerous rock masses based on three-dimensional images. Background Art

[0002] In China, the mountainous area accounts for a relatively large proportion, and the terrain and landform are steep. Dangerous rock masses often form on high and steep slopes. After the collapse of dangerous rock masses, it seriously threatens the safety of buildings such as railways, highways, houses and related personnel. Under the condition of the same rock density and height difference, the volume of a single falling rock of a dangerous rock mass determines the mass of the falling rock, and to a large extent determines the impact kinetic energy; an incorrect estimation of the volume of the falling rock of a dangerous rock mass often causes the failure of the prevention and control project or a substantial increase in unnecessary engineering treatment costs; therefore, in order to select an appropriate prevention and control method for dangerous rock fall disasters, determine the design strength of the retaining structure, and ensure the reliability, safety, accuracy and economy of the prevention and control of dangerous rock fall disasters, it is necessary to accurately calculate the volume of the collapsed boulders of the dangerous rock mass.

[0003] The existing methods for obtaining the volume of falling rocks of dangerous rock masses mainly include:

[0004] ① Determine the thickness and depth of the dangerous rock mass by means of on-site investigation of the slope surface, slope drilling and adit exploration. However, it is often difficult to place a drilling rig or carry out adit exploration on high and steep dangerous rocks, and the feasibility is poor; moreover, the construction operation costs of drilling and adit excavation are high and the time is long.

[0005] ② Obtain the volume of the dangerous rock mass by obtaining the surface shape of the dangerous rock mass through three-dimensional laser scanning technology. However, this method is only applicable to isolated dangerous rock masses without 360° occlusion. If there is vegetation occlusion around, only the slope surface characteristics of the dangerous rock mass can be obtained, and the calculation accuracy of the volume of the falling rock is very poor.

[0006] ③ Measure by using the volume measurement tool in Acute3D Viewer through the three-dimensional oblique photography model of the unmanned aerial vehicle. However, only the mean plane or horizontal plane within a certain range can be obtained to calculate the volume of the entire dangerous rock mass, and the measurement result accuracy is not high; in areas with developed vegetation, the volume of the vegetation will be measured into the volume of the entire dangerous rock mass, resulting in a serious exaggeration of the measurement result and an increase in the prevention and control cost. Summary of the Invention

[0007] The purpose of the present invention is to overcome the above deficiencies such as poor feasibility, high operation cost and low calculation accuracy of the existing methods for obtaining the volume of falling rocks of dangerous rock masses, and provide a method for calculating the volume of dangerous rock masses based on three-dimensional images.

[0008] In order to achieve the above invention purpose, the present invention provides the following technical solutions:

[0009] A method for calculating the volume of dangerous rock masses based on three-dimensional images, comprising the following steps:

[0010] a. Collect three-dimensional images of the dangerous rock mass to clarify the cutting characteristics of the dangerous rock mass by structural planes;

[0011] b. Obtain or calculate the coordinates of each vertex of the dangerous rock mass through measurement to obtain the polyhedron morphological structure characteristics of the dangerous rock mass;

[0012] c. Directly solve the volume of a simple polyhedron to obtain the volume of the dangerous rock mass; or use the segmentation method to solve the volumes of multiple simple polyhedrons, add or subtract the volumes of multiple simple polyhedrons, and finally obtain the volume of the dangerous rock mass.

[0013] Preferably, in step a, the dangerous rock mass is segmented by three or four groups of dominant structural planes with different attitudes.

[0014] Further preferably, when the dangerous rock mass is segmented by three groups of dominant structural planes with different attitudes and a parallelepiped is segmented due to the influence of joint fissure spacing, if the boundary of the parallelepiped in the image is clear, obtain the coordinates of any four adjacent vertices of the parallelepiped, then obtain the vectors from one vertex to the other three vertices, and further obtain the volume of the parallelepiped.

[0015] Further preferably, if the boundary of the parallelepiped in the image is not clear, obtain the coordinates of three points on each of any three faces of the parallelepiped, solve the plane equations of the corresponding faces, then obtain the plane equations of the other faces of the parallelepiped, then calculate the coordinates of any four adjacent vertices of the parallelepiped, and further obtain the volume of the parallelepiped.

[0016] Further preferably, when the dangerous rock mass is segmented by four groups of dominant structural planes with different attitudes and a triangular pyramid is segmented due to the influence of joint fissure spacing, if the boundary of the triangular pyramid in the image is clear, obtain the coordinates of the four vertices, then obtain the vectors from one vertex to the other three vertices, and further obtain the volume of the triangular pyramid.

[0017] Further preferably, if the boundary of the triangular pyramid in the image is not clear, obtain the coordinates of three points on each face of the triangular pyramid respectively, solve the plane equations of the corresponding faces, then calculate the coordinates of the four vertices, and further obtain the volume of the triangular pyramid.

[0018] Further preferably, when the dangerous rock mass is segmented by four groups of dominant structural planes with different attitudes and an octahedron is segmented due to the influence of joint fissure spacing, obtain the coordinates of the four exposed vertices of the octahedron, then obtain the vectors from one vertex to the other three adjacent vertices, and further obtain the volume of the octahedron.

[0019] Further preferably, when the dangerous rock mass is segmented by four sets of dominant structural planes with different attitudes and a frustum of a pyramid is segmented under the influence of the joint fissure spacing, if the boundary of the frustum of the pyramid in the image is clear, the coordinates of any six vertices of the frustum of the pyramid are obtained and the height of the frustum of the pyramid is calculated, and then the volume of the frustum of the pyramid is obtained.

[0020] Further preferably, if the boundary of the frustum of the pyramid in the image is not clear, the coordinates of three vertices in the same plane are obtained, and the plane equation of the plane where the three vertices are located and the plane equation of the corresponding parallel plane are solved. Then, combined with the coordinates of any three points on each of the remaining faces, the plane equations of the remaining four faces are obtained. Then, the coordinates of any three adjacent vertices among the remaining vertices and the height of the frustum of the pyramid are calculated, and then the volume of the frustum of the pyramid is obtained.

[0021] Further preferably, when the dangerous rock mass is segmented by four sets of dominant structural planes with different attitudes and a triangular prism is segmented under the influence of the joint fissure spacing, the coordinates of three points are obtained on each face of the triangular prism, the plane equation of the corresponding face is solved, and then the coordinates of each vertex and the coordinates of the intersection point of the extensions of the three side faces are calculated, and then the volume of the triangular prism is obtained.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention analyzes the characteristics of the dangerous rock mass cut by 3 or 4 sets of dominant structural planes through three-dimensional images, forms parallelepipeds, tetrahedrons, octahedrons, frustums of pyramids, and triangular prisms, and measures or calculates the vertex coordinates of the polyhedral dangerous rock mass, directly or uses the segmentation method to solve the volume of simple polyhedrons, and finally accurately obtains the volume of the dangerous rock mass. There is no need to carry out drilling or adit exploration at high-steep dangerous rocks, it is not affected by vegetation, the calculation efficiency is high, and it improves the reliability, safety, accuracy, and economy of the prevention and control of dangerous rock and falling rock disasters, reduces the design changes of the prevention and control of dangerous rock and falling rock, saves construction funds, is more practical than the prior art, has a wide range of applicability, and has great promotion significance and application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is a schematic structural diagram of the segmentation by three sets of dominant structural planes in Embodiment 1;

[0024] Figure 2 is a schematic structural diagram of the segmentation by four sets of dominant structural planes in Embodiment 1 Figure 1 ;

[0025] Figure 3 is a schematic structural diagram of the segmentation by four sets of dominant structural planes in Embodiment 1 Figure 2 ;

[0026] Figure 4 is a schematic structural diagram of the segmentation by four sets of dominant structural planes in Embodiment 1 Figure 3 ;

[0027] Figure 5 It is the structural schematic diagram of the structure divided by four groups of dominant structural planes in Embodiment 1 Figure 4 . Specific implementation manner

[0028] The present invention will be further described in detail below in conjunction with the embodiments and specific implementation manners. However, it should not be understood that the scope of the above-mentioned subject matter of the present invention is limited to the following embodiments. All technologies implemented based on the content of the present invention belong to the scope of the present invention.

[0029] Embodiment 1

[0030] A method for calculating the volume of a dangerous rock mass based on three-dimensional images, comprising the following steps:

[0031] A method for calculating the volume of a dangerous rock mass based on three-dimensional images, characterized in that it comprises the following steps:

[0032] a. Collect three-dimensional images of the dangerous rock mass to clarify the cutting characteristics of the dangerous rock mass by structural planes;

[0033] b. Obtain or calculate the coordinates of each vertex of the dangerous rock mass through measurement to obtain the polyhedral morphological structure characteristics of the dangerous rock mass;

[0034] c. Directly solve the volume of a simple polyhedron to obtain the volume of the dangerous rock mass; or use the segmentation method to solve the volumes of multiple simple polyhedrons, add or subtract the volumes of multiple simple polyhedrons, and finally obtain the volume of the dangerous rock mass.

[0035] In step a, the dangerous rock mass is segmented by three or four groups of dominant structural planes with different attitudes.

[0036] When the dangerous rock mass is segmented by three groups of dominant structural planes with different attitudes and a parallelepiped is segmented under the influence of the joint fissure spacing, if the boundary of the parallelepiped in the image is clear, obtain the coordinates of any four adjacent vertices of the parallelepiped, then obtain the vectors from one vertex to the other three vertices, and further obtain the volume of the parallelepiped.

[0037] As Figure 1 shown, directly obtain the intersection coordinates p(x1, y1, z1) of the structural planes S A , S B , S C in the three-dimensional real-scene model, obtain the intersection coordinates c(x2, y2, z2) of the structural planes S A , S B , S F , obtain the intersection coordinates b(x3, y3, z3) of the structural planes S A , S E , S C in the three-dimensional real-scene model, and obtain the intersection coordinates of the structural plane SD , S B , S C The intersection coordinates a(x4, y4, z4) of Therefore, the volume of the parallelepiped is:

[0038] That is, the volume of the dangerous rock mass is obtained.

[0039] If the boundary of the parallelepiped in the image is not clear, then the coordinates of three points are obtained on any three faces of the parallelepiped, and the plane equations of the corresponding faces are solved. Then, the plane equations of the remaining faces of the parallelepiped are obtained, and then the coordinates of any four adjacent vertices of the parallelepiped are calculated, and then the volume of the parallelepiped is obtained. For example, on S A , S B , S C , the coordinates of any 3 points are obtained, such as P A1 (x A1 , y A1 , z A1 ), P A2 (x A2 , y A2 , z A2 ), P A3 (x A3 , y A3 , z A3 ), and the plane equations of the structural planes S A , S B , S C are solved. For example, to find the plane of S A , let the plane equation passing through the three points P A1 , P A2 , P A3 be A A (x – x0) + B A (y – y0) + C A (z – z0) = 0. Simplify it to the general form: A A x + B A y + C A z + D A = 0. Substitute the values of the point P A1 (x A1 , y A1 , z A1 ) into the equation A A x + B A y + C A z + D A = 0. Then we can get: A A x A1 + B A yA1 +C A z A1 +D A = 0. Then D A = -(A A x A1 +B A y A1 +C A z A1 ). Then, based on P A1 (x A1 , y A1 , z A1 ), P A2 (x A2 , y A2 , z A2 ), P A3 (x A3 , y A3 , z A3 ) with the three - point coordinates, the values of A A , B A , C A can be obtained as follows:

[0040] A A = (y A2 - y A1 ) * (z A3 - z A1 ) - (z A2 - z A1 ) * (y A3 - y A1 );

[0041] B A = (x A3 - x A1 ) * (z A2 - z A1 ) - (x A2 - x A1 ) * (z A3 - z A1 );

[0042] C A = (x A2 - x A1 ) * (y A3 - y A1 ) - (x A3 - x A1 ) * (y A2 - y A1 );

[0043] Also, D A = -(A A * x A1 +BA *y A1 +C A *z A1 ), so the value of D can be obtained.

[0044] Substitute the obtained A A , B A , C A , D A values into the general equation, and the plane equation S A1 , P A2 , P A3 passing through P can be obtained. A : A A x + B A y + C A z + D A = 0.

[0045] Similarly, the plane equations of S B , S C can be obtained. Since the structural plane S A is parallel to the structural plane S D , the normal vector n D of the structural plane S D is the same as the normal vector n A of the structural plane S A . By obtaining a point P D on the plane S D1 (x D1 , y D1 , z D1 ), then D D = -(A A x D1 + B A y D1 + C A z D1 ). The plane equation S D is obtained. Similarly, the plane equations of S E , S F can be obtained. Then, using Cramer's rule, solve the non - homogeneous linear equations to obtain the intersection points of the three planes, that is, the coordinates of the four vertices: the intersection point coordinates p(x1, y1, z1) of the structural planes S A , S B , S C ; the intersection point coordinates c(x2, y2, z2) of the structural planes S A , S B , S F ; the intersection point coordinates b(x3, y3, z3) of the structural planes S A , S C , S E ; the intersection point coordinates of the structural planes S B , S C , SD The intersection coordinates a(x4, y4, z4), specifically, taking the structural plane S A 、S B 、S C The intersection coordinates p(x1, y1, z1) of, for example: P = S -1 D, Similarly, c(x2, y2, z2), b(x3, y3, z3), and a(x4, y4, z4) can be obtained,

[0046] Then The volume of the parallelepiped is:

[0047] That is, the volume of the dangerous rock mass is obtained.

[0048] When the dangerous rock mass is segmented by four sets of dominant structural planes with different attitudes and tetrahedrons are segmented under the influence of joint fissure spacing, if the boundaries of the tetrahedrons in the image are clear, the coordinates of the four vertices are obtained, then the vectors from one vertex to the other three vertices are obtained, and further the volume of the tetrahedron is obtained.

[0049] Such as Figure 2 As shown, directly obtain the structural plane intersection coordinates p(x1, y1, z1), c(x2, y2, z2), b(x3, y3, z3), and a(x4, y4, z4) in the 3D real scene model, then obtain:

[0050] Therefore, the volume of the tetrahedron is:

[0051] That is, the volume of the dangerous rock mass is obtained.

[0052] If the boundaries of the tetrahedrons in the image are not clear, the coordinates of three points are respectively obtained on each face of the tetrahedron, and the plane equations of the corresponding faces are solved, then the coordinates of the four vertices are calculated, and further the volume of the tetrahedron is obtained. The acquisition method refers to the foregoing.

[0053] When the dangerous rock mass is segmented by four sets of dominant structural planes with different attitudes and octahedrons are segmented under the influence of joint fissure spacing, the coordinates of the four exposed vertices of the octahedron are obtained, then the vectors from one vertex to the other three adjacent vertices are obtained, and further the volume of the octahedron is obtained.

[0054] Such as Figure 3 As shown, directly obtain p(x1, y1, z1), d(x2, y2, z2), c(x3, y3, z3), b(x4, y4, z4), and a(x5, y5, z5) in the 3D real scene model,

[0055] Then obtain:

[0056] Therefore, the volume of the octahedron is:

[0057] That is, the volume of the dangerous rock mass is obtained.

[0058] When the dangerous rock mass is segmented by four sets of dominant structural planes with different attitudes and a frustum of a pyramid is segmented under the influence of the joint fissure spacing, if the boundary of the frustum of the pyramid in the image is clear, the coordinates of any six vertices of the frustum of the pyramid are obtained and the height of the frustum of the pyramid is calculated, and then the volume of the frustum of the pyramid is obtained.

[0059] Such as Figure 4 shown, directly obtain the structural planes p(x1, y1, z1), c(x2, y2, z2), b(x3, y3, z3), a(x4, y4, z4), e(x5, y5, z5) and d(x6, y6, z6) in the three-dimensional real scene model, and then solve the corresponding plane equation. For example, given the points p(x1, y1, z1), c(x2, y2, z2), b(x3, y3, z3), then the plane equation of S pbgc can be solved. The specific process is as follows:

[0060] Substitute the numerical values of the point p(x1, y1, z1) into the equation A pbgc x + B pbgc y + C pbgc z + D pbgc = 0. Then we can get: A pbgc x1 + B pbgc y1 + C pbgc z1 + D pbgc = 0. Then D pbgc = -(A pbgc x1 + B pbgc y1 + C pbgc z1). The values of A pbgc , B pbgc , and C pbgc can be obtained respectively according to the three-point coordinates of pp(x1, y1, z1), c(x2, y2, z2), and b(x3, y3, z3). A pbgc , B pbgc , and C pbgc are any three points on the plane S pbgc respectively, as follows:

[0061] A pbgc = (y2 - y1)*(z3 - z1) - (z2 - z1)*(y3 - y1);

[0062] B pbgc=(x3 - x1)*(z2 - z1)-(x2 - x1)*(z3 - z1);

[0063] C pbgc =(x2 - x1)*(y3 - y1)-(x3 - x1)*(y2 - y1);

[0064] Furthermore, the plane equation S is obtained. pbgc :

[0065] A pbgc x + B pbgc y + C pbgc z + D pbgc = 0.

[0066] Similarly, the plane equation S passing through points a, d, and e can be obtained. adhe :

[0067] A adhe x + B adhe y + C adhe z + D adhe = 0.

[0068] On the plane S adhe any point f(x7, y7, z7) is obtained, then the height of the frustum of a pyramid is:

[0069]

[0070] Then the volume of the dangerous rock mass is:

[0071] That is, the volume of the dangerous rock mass is obtained.

[0072] Among them, the areas of the upper and lower surfaces are respectively:

[0073]

[0074]

[0075] If the boundary of the frustum of a pyramid in the image is not clear, then the coordinates of three vertices in the same plane are obtained, and the plane equation of the plane where the three vertices are located and the plane equation of the corresponding parallel plane are solved. Then, combined with the coordinates of any three points on each of the remaining faces, the plane equations of the remaining four faces are obtained. Then, the coordinates of any three adjacent vertices among the remaining vertices and the height of the frustum of a pyramid are calculated, and then the volume of the frustum of a pyramid is obtained.

[0076] That is, in the three-dimensional real scene model, a(x4, y4, z4), e(x5, y5, z5), and d(x6, y6, z6) are directly obtained, then the plane equation of S adhe can be solved, and the rest is the same as before.

[0077] When the dangerous rock mass is segmented by four groups of dominant structural planes with different attitudes and triangular prisms are segmented under the influence of the joint spacing, the coordinates of three points are obtained on each face of the triangular prism respectively, the plane equation of the corresponding face is solved, and then the coordinates of each vertex and the coordinates of the intersection points of the three side surfaces are calculated, and then the volume of the triangular prism is obtained.

[0078] As Figure 5 shown, on the structural plane S abc , S def , S abed , S adfc , S bcfe in the three-dimensional real scene model of the unmanned aerial vehicle, 3 point coordinates are obtained respectively, and the plane equations of the structural planes S abc , S def , S abed , S adfc , S bcfe are solved. Then, using Cramer's rule, the non-homogeneous linear equations are solved to obtain a(x1, y1, z1), b(x2, y2, z2), c(x3, y3, z3), d(x4, y4, z4), e(x5, y5, z5), f(x6, y6, z6) and the intersection coordinates p(x7, y7, z7) of the extended planes of the structural planes S abed , S acfd , S bcfe .

[0079] Then, it is obtained that:

[0080] Therefore, the volume of the triangular prism is:

[0081]

[0082] , that is, the volume of the dangerous rock mass is obtained.

[0083] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A method for calculating the volume of dangerous rock masses based on three-dimensional images, characterized in that, The method includes the following steps: a. Collect three-dimensional images of the dangerous rock mass, clarify the cutting characteristics of the dangerous rock mass by structural planes, and divide the dangerous rock mass using three or four sets of dominant structural planes with different attitudes; b. Obtain or calculate the coordinates of each vertex of the dangerous rock mass through measurement to obtain the polyhedron morphological structure characteristics of the dangerous rock mass; c. Directly solve the volume of a simple polyhedron to obtain the volume of the dangerous rock mass; or use the segmentation method to solve the volumes of multiple simple polyhedrons, add or subtract the volumes of multiple simple polyhedrons, and finally obtain the volume of the dangerous rock mass; When the dangerous rock mass is divided into parallelepipeds by three sets of dominant structural planes with different attitudes and affected by the joint spacing, if the boundary of the parallelepiped in the image is clear, obtain the coordinates of any four adjacent vertices of the parallelepiped, then obtain the vectors from one vertex to the other three vertices, and further obtain the volume of the parallelepiped. If the boundary of the parallelepiped in the image is not clear, obtain the coordinates of three points on each of any three faces of the parallelepiped, solve the plane equations of the corresponding faces, and then obtain the plane equations of the remaining faces of the parallelepiped. Then calculate the coordinates of any four adjacent vertices of the parallelepiped, and further obtain the volume of the parallelepiped; When the dangerous rock mass is divided into triangular pyramids by four sets of dominant structural planes with different attitudes and affected by the joint spacing, if the boundary of the triangular pyramid in the image is clear, obtain the coordinates of the four vertices, then obtain the vectors from one vertex to the other three vertices, and further obtain the volume of the triangular pyramid. If the boundary of the triangular pyramid in the image is not clear, obtain the coordinates of three points on each face of the triangular pyramid, solve the plane equations of the corresponding faces, then calculate the coordinates of the four vertices, and further obtain the volume of the triangular pyramid; When the dangerous rock mass is divided into octahedrons by four sets of dominant structural planes with different attitudes and affected by the joint spacing, obtain the coordinates of the four exposed vertices of the octahedron, then obtain the vectors from one vertex to the other three adjacent vertices, and further obtain the volume of the octahedron; When the dangerous rock mass is divided into frustums of a pyramid by four sets of dominant structural planes with different attitudes and affected by the joint spacing, if the boundary of the frustum of the pyramid in the image is clear, obtain the coordinates of any six vertices of the frustum of the pyramid and calculate the height of the frustum of the pyramid, and further obtain the volume of the frustum of the pyramid. If the boundary of the frustum of the pyramid in the image is not clear, obtain the coordinates of three vertices in the same plane, solve the plane equations of the plane where the three vertices are located and the corresponding parallel plane, then combine the coordinates of any three points on each of the remaining faces to obtain the plane equations of the remaining four faces. Then calculate the coordinates of any three adjacent vertices among the remaining vertices and the height of the frustum of the pyramid, and further obtain the volume of the frustum of the pyramid; When the dangerous rock mass is divided into triangular prisms by four sets of dominant structural planes with different attitudes and affected by the joint spacing, obtain the coordinates of three points on each face of the triangular prism, solve the plane equations of the corresponding faces, then calculate the coordinates of each vertex and the coordinates of the intersection points of the three side extensions, and further obtain the volume of the triangular prism.

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