A three-dimensional calculation method and storage medium for the overturning stability of unstable rocks

Abstract

This invention relates to the field of geological prediction and analysis methods, specifically to a three-dimensional calculation method and storage medium for the overturning stability of unstable rock formations. The method includes acquiring three-dimensional point cloud data of the unstable rock formation, acquiring information data on the fracture surfaces and their combinations, establishing a three-dimensional model of the unstable rock formation based on the point cloud data, fracture surfaces, and information data, and extracting parameters for overturning stability calculation. The method involves calculating the resultant force of water pressure in the rear-edge fractures and the coordinates of the point of application of the resultant force according to a first process; calculating the resultant force of tensile force in the non-penetrating fractures at the rear edge and the coordinates of the point of application of the resultant force according to a second process; calculating the lever arm of the resultant force of tensile force in the non-penetrating fractures at the rear edge and the lever arm of the resultant force of water pressure in the rear-edge fractures according to a third process and the coordinates of the overturning point; and calculating the overturning stability coefficient of the unstable rock formation based on the calculation results. This invention improves the accuracy and completeness of the calculated overturning stability coefficient by preserving the influence of the irregular shape of the unstable rock formation on its overturning stability.

Description

Technical Field

[0001] This invention relates to the field of geological prediction and analysis methods, specifically to a three-dimensional calculation method and storage medium for the overturning stability of unstable rocks. Background Technology

[0002] Dangerous rock masses or mountains that may collapse or landslide are mostly found in natural mountains or building slopes. To ensure proper safety protection measures at dangerous rock locations, stability analysis is necessary. Analytical calculation methods for rock mass stability are currently widely used in rock mass prevention research and specific engineering projects, serving as the most important means of rock mass stability analysis and evaluation.

[0003] In both domestic and international applications of rockfall prevention and control, the calculation of rockfall stability generally uses the rockfall profile as the calculation model, and this model is incorporated into numerous standards. However, the shapes of natural rockfalls are extremely irregular. The two-dimensional simplified calculation model using the rockfall profile cannot accurately reflect the stress situation in the three-dimensional space of the rockfall. This leads to a significant discrepancy between the stability calculations performed in rockfall prevention and control and the actual situation. Summary of the Invention

[0004] The present invention aims to provide a three-dimensional calculation method for the overturning stability of dangerous rocks, so as to solve the problem that the calculation results based on the existing two-dimensional simplified calculation model have a huge deviation from the actual situation.

[0005] The three-dimensional calculation method for the overturning stability of unstable rock masses in this scheme includes the following steps:

[0006] Step 1: Obtain three-dimensional point cloud data of the unstable rock and acquire information data on the fracture surfaces and their combination relationships of the unstable rock.

[0007] It also includes the following steps:

[0008] Step 2: Establish a 3D model of the dangerous rock based on the 3D point cloud data, fracture surface, and information data;

[0009] Step 3: Extract the parameters for overturning stability calculation from the three-dimensional model of the unstable rock mass. The parameters include the volume of the unstable rock mass, the coordinates of the centroid, the coordinates of the overturning point, the center of gravity lever arm, the horizontal seismic force, and the horizontal seismic force lever arm.

[0010] Step 4: Calculate the resultant force of water pressure in the trailing fracture and the coordinates of the point of application of the resultant force of water pressure in the trailing fracture according to the first process; calculate the resultant force of tensile force in the non-penetrating fracture at the trailing edge and the coordinates of the point of application of the resultant force of tensile force according to the second process.

[0011] Step 5: Calculate the lever arm of the resultant tensile force of the non-penetrating fracture at the rear edge relative to the resultant tensile force of the non-penetrating fracture at the rear edge of the overturning point based on the third process and the coordinates of the overturning point; and calculate the lever arm of the resultant water pressure of the fracture at the rear edge relative to the resultant water pressure of the fracture at the rear edge of the overturning point.

[0012] Step 6: Substitute the resultant force arm of the tensile force of the non-penetrating fracture at the rear edge, the resultant force arm of the tensile force of the non-penetrating fracture at the rear edge, the resultant force arm of the water pressure at the rear edge, the resultant force arm of the water pressure at the rear edge, the force arm of the horizontal seismic force, the horizontal seismic force, the force arm of the center of gravity, and the weight of the unstable rock into the preset stability formula to calculate the unstable rock overturning stability coefficient.

[0013] The beneficial effects of this plan are:

[0014] An irregular three-dimensional model of the unstable rock was established based on its actual geological conditions. Relevant parameters were obtained from the model to calculate the lever arms of the fracture surfaces in the actual rock formation. The overturning stability coefficient of the unstable rock was also calculated using these lever arms. The calculation process maintained the influence of the irregular shape of the unstable rock on its overturning stability, thus improving the accuracy and completeness of the calculated overturning stability coefficient.

[0015] Furthermore, in step 4, the first process includes the following sub-steps:

[0016] Sub-step 411: Obtain a simplified diagram of water pressure calculation from the three-dimensional model of the unstable rock mass.

[0017] Sub-step 412: Based on the principle of differentiation, take a differential strip dh of width L in the vertical direction of the simplified water pressure calculation diagram. The water pressure dV generated by this differential strip is expressed as:

[0018] dV=Lγ w hdh;

[0019] Where, γ w Let be the specific weight of water, and h be the distance from the center of the differential strip to the top of the water surface;

[0020] Sub-step 413 involves performing a surface domain integration on the trailing edge water pressure dV to obtain the resultant force of the trailing edge fracture water pressure, expressed as:

[0021] V=∫Lγ w hdh,

[0022] Considering the irregularity of the shape of the trailing fracture water pressure region, the integral expression of the resultant force of the trailing fracture water pressure is written in numerical integral form as follows:

[0023]

[0024] Sub-step 414: Based on the principle of equivalent torque balance, select any point in space, and represent its coordinates as M0(x0,y0,z0). Calculate the torque balance of the resultant force of the trailing fracture water pressure in the x, y, and z directions according to the first predefined formula, and calculate the coordinates M3(x3,y3,z3) of the point of application of the resultant force of the trailing fracture water pressure. The first predefined formula is expressed as:

[0025] ∑dV×l i =V×l′,

[0026] Among them, l i l is the distance from the centroid of the differential strip to point M0, and l′ is the distance from the point of application of the resultant force V of the trailing edge fissure water pressure to point M0.

[0027] The beneficial effects are: by using the differential strips in the first process and calculating the resultant force of the water pressure in the corresponding rear edge fractures and the coordinates of the resultant force, the actual irregular shape of the dangerous rock is considered on the three-dimensional model of the dangerous rock. The calculated water pressure-related parameters are more consistent with the actual shape of the dangerous rock, thus improving the accuracy and completeness of the calculation results.

[0028] Furthermore, in step 4, the second process includes the following sub-steps:

[0029] Sub-step 421: Obtain a simplified diagram of tensile force calculation for the non-penetrating fracture at the rear edge of the dangerous rock from the three-dimensional model of the dangerous rock.

[0030] Sub-step 422: Based on the principle of differentiation, take a differential strip dh of width L in the vertical direction of the simplified tensile force calculation diagram. The tensile force dF generated by this differential strip... σ Represented as:

[0031] dF σ =σLdh,

[0032] Where σ is the tensile bearing capacity of the non-penetrating crack at the trailing edge at the differential strip;

[0033] Sub-step 423 involves integrating over the tensile region of the non-penetrating crack at the trailing edge to obtain the resultant tensile force of the non-penetrating crack at the trailing edge, expressed as:

[0034] F σ =∫σLdh,

[0035] Considering the irregularity of the shape of the tensile region of the non-penetrating crack at the trailing edge, the integral expression of the resultant tensile force of the non-penetrating crack at the trailing edge is written in numerical integral form as follows:

[0036]

[0037] Where, σ i Obtained by linear interpolation;

[0038] Sub-step 424: Based on the principle of equivalent torque balance, select any point in space, and represent its coordinates as M0(x0,y0,z0). Using the second predefined formula, calculate the torque balance of the resultant tensile force of the non-penetrating crack at the rear edge in the x, y, and z directions. Calculate the coordinates M2(x2,y2,z2) of the point of application of the resultant tensile force of the non-penetrating crack at the rear edge. The second predefined formula is expressed as:

[0039] ∑dF σ ×S i =F σ ×S′,

[0040] Among them, S i S' is the distance from the centroid of the differential strip to point M0, and S' is the distance from the point of application of the resultant tensile force of the unconnected crack at the trailing edge to point M0.

[0041] The beneficial effects are: by setting the differential strips in the second process and calculating the resultant tensile force of the non-penetrating cracks at the rear edge of the differential strips, as well as the coordinates of the resultant force, the actual irregular state of the dangerous rock is considered on the three-dimensional model of the dangerous rock. The model calculation is more consistent with the actual morphology of the dangerous rock, thus improving the accuracy and completeness of the calculation results.

[0042] Furthermore, in step 4, the boundary coordinate sequence extracted from the three-dimensional model of the dangerous rock is used for interpolation to calculate the differential strip information, including the following sub-steps:

[0043] Sub-step 401: Extract the boundary coordinate sequence of the rear fracture surface from the 3D model of the unstable rock, and divide it into left and right sides, represented as: N0, N1, N2, N3, ..., N n ;Q0,Q1,Q2,Q3,...,Q n ;

[0044] Sub-step 402: Divide the two sets of point sequences into blocks according to the height dh, based on the z-direction coordinate z. i =z0-i×dh, interpolation to calculate the coordinates U of the two boundary points of the differential strip. Li and U ri ;

[0045] Sub-step 403, based on the coordinates of the two boundary points U of the differential strip. Li and U ri Calculate the length of the differential strip.

[0046] The beneficial effects are: by obtaining the boundary coordinate sequence of the trailing fracture surface from the three-dimensional model of the unstable rock, the coordinates of the boundary points of the differential strip are calculated, the length of the differential strip is calculated, and the size of the differential strip is considered on the established three-dimensional model, so that the differential strip can better reflect the actual fracture.

[0047] Furthermore, in step 5, the third process includes the following sub-steps:

[0048] Sub-step 501: The coordinates of the overturning point M1 determined from the three-dimensional model of the unstable rock are (x1, y1, z1), the direction of the straight line where the overturning point M1 is located is θ1, the dip of the rear edge fracture structure surface is θ2, and the dip angle is β.

[0049] Sub-step 502: Calculate the straight-line vector of the overturning point. The normal vector of the trailing edge structure surface is (sinθ1, cosθ1, 0). Given (sinθ2,cosθ2,tan(90°-β)), calculate the phasor. and Represented as:

[0050]

[0051] Sub-step 503, solve and The resultant tensile force lever L of the non-penetrating crack at the trailing edge is obtained. σ The resultant force arm L of the trailing edge fissure water pressure V They are represented as follows:

[0052]

[0053]

[0054] The beneficial effects are: by calculating parameters such as the coordinates and straight line direction of the overturning point, and based on this, calculating the lever arm of the resultant force of the tensile force and the resultant force of the water pressure, the mechanical relationship of the actual overturning point can be accurately analyzed in the three-dimensional model of the unstable rock, thus improving the accuracy of the analysis results.

[0055] Furthermore, in step 6, when the rock mass is controlled by the tensile strength of its trailing edge, and the center of gravity of the rock mass in the three-dimensional model of the rock mass is within the overturning point, the stability formula is expressed as:

[0056]

[0057] When the stability of a rockfall is controlled by its trailing edge tensile strength, and the center of gravity of the rockfall in the three-dimensional model is outside the overturning point, the stability formula is expressed as:

[0058]

[0059] Where: W is the weight of the unstable rock mass calculated based on its volume; a is the center of gravity lever arm, which is the horizontal distance from the center of gravity of the unstable rock mass to the overturning point; h0 is the horizontal seismic force lever arm, which is the vertical distance from the center of gravity of the unstable rock mass to the overturning point; Q is the horizontal seismic force; F σThe resultant tensile force of the unconnected crack at the trailing edge; L σ V is the resultant lever arm of the tensile force in the non-penetrating fracture at the trailing edge; L is the resultant force of the water pressure in the fracture at the trailing edge; V It is the lever arm of the resultant force of the water pressure in the trailing edge fissure.

[0060] The beneficial effect is that the overturning stability coefficient of irregularly shaped dangerous rocks can be calculated accurately and reliably using the stability formula.

[0061] Furthermore, in step 2, the three-dimensional model of the dangerous rock includes a three-dimensional surface model and a three-dimensional geological model of the dangerous rock, and the establishment process includes the following sub-steps:

[0062] Sub-step 201: Perform grid interpolation thinning on the 3D point cloud data;

[0063] Sub-step 202: Construct a triangular mesh surface on the surface of the dangerous rock using grid point cloud;

[0064] Sub-step 203: Extrude the triangular mesh surface to form a three-dimensional surface model of the unstable rock mass;

[0065] Sub-step 204: The obtained rock fracture occurrence and combination relationship are used to construct the fracture plane, and the rock mass is cut to form a three-dimensional geological model of the rock.

[0066] The beneficial effects are: establishing surface and geological models of the dangerous rock as three-dimensional models of the dangerous rock can make the model conform to the actual shape of the dangerous rock from different inventions, making the model more accurate.

[0067] Furthermore, in sub-step 201, a coordinate transformation method is used to transform the corresponding z-coordinate of each data point in the three-dimensional point cloud data in the original plane coordinate system x, y. The coordinate transformation method is as follows:

[0068] In the original coordinate system xyz, the angle between the main rockfall direction and the y-axis is set to α. The 3D point cloud data of the rockfall is transformed according to the transformation formula, so that the main rockfall direction is transformed into the z-axis. The resulting coordinates of the point cloud points on the surface of the rockfall are obtained in the new coordinate system (x′, y′, z′). The transformation formula is:

[0069]

[0070] Where Δx and Δy are coordinate translation transformation values. In the new coordinate system (x′,y′,z′), Kriging interpolation is used to thin the three-dimensional point cloud data by grid interpolation. The grid point cloud with a preset length spacing is thinned by Kriging interpolation. Then, the Delaunay model of the triangular mesh of the dangerous rock face is constructed using the grid point cloud.

[0071] The beneficial effects are: by using coordinate transformation, the uneven three-dimensional shape of the dangerous rock surface is avoided, which may cause the three-dimensional point cloud data of the dangerous rock surface obtained by oblique photography to have multiple corresponding z values ​​under a plane x,y coordinate. This allows for a more accurate depiction of the three-dimensional spatial shape of the dangerous rock surface and enables the analysis of the role of the actual cavities of the dangerous rock in overturning.

[0072] Furthermore, in sub-step 204, a solid is constructed by stretching the triangular mesh surface; then, according to the preset plane, the overall model of the dangerous rock is formed by cutting, and the obtained main control fracture structure surfaces of the dangerous rock are generalized into a plane;

[0073] Assuming the dipping direction of the structural plane is θ and the dip angle of the structural plane is... Then the unit normal vector of the structural plane is... The plane equation of the fracture surface of the unstable rock is:

[0074]

[0075] The three-dimensional surface model of the unstable rock was cut through the main control fracture plane to obtain several plate-shaped unstable rock individual models, thus constructing a three-dimensional geological model of the unstable rock.

[0076] The beneficial effect is that the construction of a three-dimensional geological model of the dangerous rock can accurately obtain the geological parameters of the dangerous rock.

[0077] A storage medium storing a computer program, which, when executed by a processor, implements the steps of the above method. Attached Figure Description

[0078] Figure 1 This is a flowchart illustrating an embodiment of the three-dimensional calculation method for the overturning stability of dangerous rocks according to the present invention.

[0079] Figure 2 This is a calculation diagram of a three-dimensional model of a dangerous rock obtained in an embodiment of the three-dimensional calculation method for the overturning stability of a dangerous rock in this invention;

[0080] Figure 3 This is a diagram illustrating the coordinate system transformation of the point cloud of a dangerous rock in an embodiment of the three-dimensional calculation method for the overturning stability of a dangerous rock in this invention;

[0081] Figure 4 for Figure 2 A simplified diagram for calculating water pressure in the region of action of water pressure in the middle and rear edge fractures;

[0082] Figure 5 for Figure 2 Simplified diagram for calculating the tensile strength of the rear edge rock mass in the tensile bearing zone of the mid-to-rear edge fractured rock mass;

[0083] Figure 6 This is a diagram illustrating the coordinate interpolation calculation of the plane strip coordinates of the trailing crack in an embodiment of the three-dimensional calculation method for the overturning stability of unstable rocks of the present invention.

[0084] Figure 7 These are calculation model diagrams of different morphologies of unstable rocks in the embodiments of the three-dimensional calculation method for the overturning stability of unstable rocks of the present invention;

[0085] Figure 8 This is an embodiment of the three-dimensional calculation method for the overturning stability of unstable rocks in the present invention. Figure 7 The diagram shows the relationship between the bottom width of the moderately dangerous rock mass (b) and the stability of the trapezoidal rock mass (b) with the variable bottom width as the rear edge.

[0086] Figure 9 This is an embodiment of the three-dimensional calculation method for the overturning stability of unstable rocks in the present invention. Figure 7 The diagram shows the relationship between the top width of the moderately dangerous rock mass (b) and the bottom width of the trapezoidal dangerous rock mass, with the trailing edge being a variable.

[0087] Figure 10 In the embodiments of the three-dimensional calculation method for the overturning stability of dangerous rocks of the present invention, Figure 7 The diagram shows the relationship between the width of the bottom surface of the trapezoidal dangerous rock mass (d) and its stability. Detailed Implementation

[0088] The following detailed description provides further details on specific implementation methods.

[0089] Example

[0090] Three-dimensional calculation method for the overturning stability of unstable rocks, such as Figure 1 As shown, it includes the following steps:

[0091] Step 1: Obtain 3D point cloud data of the unstable rock. The 3D point cloud data can be obtained through existing 3D oblique photography or lidar. Obtain information on the fracture surfaces and their combination relationships of the unstable rock. This information is obtained from the front-end exploration or surveying work.

[0092] Step 2: Based on the 3D point cloud data, fracture surface, and information data, establish a 3D model of the unstable rock mass. The 3D model of the unstable rock mass is as follows: Figure 2 As shown, the 3D model of the unstable rock includes a 3D surface model and a 3D geological model. The process of establishing the 3D model of the unstable rock includes the following sub-steps:

[0093] Sub-step 201 involves performing grid interpolation thinning on the 3D point cloud data, and using coordinate transformation to transform the corresponding z-coordinate of each data point in the original plane coordinate system x, y, as follows: Figure 3 As shown, the coordinate transformation method is as follows:

[0094] In the original coordinate system xyz, the angle between the main rockfall direction and the y-axis is set to α. The 3D point cloud data of the rockfall is transformed according to the transformation formula, so that the main rockfall direction is transformed into the z-axis. The resulting coordinates of the point cloud points on the surface of the rockfall are obtained in the new coordinate system (x′, y′, z′). The transformation formula is:

[0095]

[0096] Where Δx and Δy are coordinate translation transformation values. In the new coordinate system (x′,y′,z′), Kriging interpolation is used to thin the three-dimensional point cloud data by grid interpolation. The grid point cloud with a preset length spacing is thinned by Kriging interpolation. Then, the grid point cloud is used to construct the triangular mesh delaunay model of the dangerous rock free face.

[0097] Sub-step 202 involves constructing a triangular mesh surface on the surface of the unstable rock using grid point clouds, through existing software mounted on the processor.

[0098] Sub-step 203 involves stretching the triangular mesh surface to form a three-dimensional surface model of the unstable rock mass, using existing software mounted on the processor.

[0099] Sub-step 204: The obtained rock fracture orientation and combination relationship are used to construct a fracture plane, and the rock mass is cut to form a three-dimensional geological model of the rock. The solid is constructed according to the triangular network surface stretching. Then, according to the preset plane, the preset plane for the failure evolution of the Diaozui rock is the west gully plane and the east gully plane. The rock mass is cut to form an overall model of the rock. The obtained main rock fracture structure planes are generalized into a plane.

[0100] Assuming the dipping direction of the structural plane is θ and the dip angle of the structural plane is... The dip and dip angle here refer to geological concepts, and their interpretation will be followed; therefore, they will not be elaborated upon here. The unit normal vector of the structural plane is then... The plane equation of the fracture surface of the unstable rock is:

[0101]

[0102] The three-dimensional surface model of the unstable rock was cut through the main control fracture plane to obtain several plate-shaped unstable rock individual models, thus constructing a three-dimensional geological model of the unstable rock.

[0103] Step 3: Extract parameters from the 3D model of the unstable rock mass for overturning stability calculation. These parameters include the volume of the unstable rock mass, the coordinates of its centroid O, the coordinates of the overturning point, the center of gravity lever arm of the horizontal seismic force, and the horizontal seismic force lever arm h0. The centroid coordinates are represented as M. o (x o ,y o ,z oThe coordinates of the overturning point are M1(x1,y1,z1), and the centroid coordinates are used to calculate the central lever arm a. The calculation method is existing and will not be elaborated here.

[0104] Step 4: Calculate the resultant force of the trailing-edge fracture water pressure and the coordinates of the point of application of the resultant force of the trailing-edge fracture water pressure according to the first process. The first process includes the following sub-steps:

[0105] Sub-step 411: Obtain a simplified diagram of water pressure calculation from the 3D model of the unstable rock mass, such as... Figure 4 As shown, the simplified diagram for water pressure calculation is obtained through existing software, such as AutoCAD software, which extracts the diagram from the 3D model of the unstable rock. Figure 2 The region of action of water pressure in the trailing edge fracture, as marked in the figure, was extracted.

[0106] Sub-step 412: Based on the principle of differentiation, take a differential strip dh of width L in the vertical direction of the simplified water pressure calculation diagram. The water pressure dV generated by this differential strip is expressed as:

[0107] dV=Lγ w hdh;

[0108] Where, γ w Let be the specific weight of water, which is a constant value, i.e., the specific weight of water is the density of water multiplied by the acceleration due to gravity, and h is the distance from the center of the differential strip to the top of the water surface.

[0109] Sub-step 413 involves performing a surface domain integration on the trailing edge water pressure dV to obtain the resultant force of the trailing edge fracture water pressure, expressed as:

[0110] V=∫Lγ w hdh,

[0111] Considering the irregularity of the shape of the trailing fracture water pressure region, the integral expression of the resultant force of the trailing fracture water pressure is written in numerical integral form as follows:

[0112]

[0113] Sub-step 414: Based on the principle of equivalent torque balance, select any point in space, which is not necessarily on the three-dimensional model of the unstable rock, such as (0,0,0) in space, and let the coordinates of any point be represented as M0(x0,y0,z0). Then, calculate the torque balance of the resultant force of the water pressure in the rear fracture in the x, y, and z directions according to the first set formula, and calculate the coordinates M3(x3,y3,z3) of the point of application of the resultant force of the water pressure in the rear fracture. The first set formula is expressed as:

[0114] ∑dV×l i =V×l′,

[0115] Among them, l i l is the distance from the centroid of the differential strip to point M0, and l′ is the distance from the point of application of the resultant force V of the trailing edge fissure water pressure to point M0.

[0116] The second process calculates the resultant tensile force and the coordinates of the point of application of the resultant tensile force in the non-penetrating crack at the trailing edge. The second process includes the following sub-steps:

[0117] Sub-step 421: Obtain a simplified calculation diagram of the tensile strength of the non-penetrating fracture at the rear edge of the unstable rock from the 3D model of the unstable rock, as shown below. Figure 5 As shown, the simplified diagram for tensile force calculation is obtained through existing software, such as AutoCAD software, which extracts the 3D model of the unstable rock. Figure 2 The tensile bearing capacity zone of the rock mass with rear-edge fractures, as marked in the figure, was extracted.

[0118] Sub-step 422: Based on the principle of differentiation, take a differential strip dh of width L in the vertical direction of the simplified tensile force calculation diagram. The tensile force dF generated by this differential strip... σ Represented as:

[0119] dF σ =σLdh,

[0120] Where σ is the tensile bearing capacity of the non-penetrating crack at the trailing edge at the differential strip;

[0121] Sub-step 423 involves integrating over the tensile region of the non-penetrating crack at the trailing edge to obtain the resultant tensile force of the non-penetrating crack at the trailing edge, expressed as:

[0122] F σ =∫σLdh,

[0123] Considering the irregularity of the shape of the tensile region of the non-penetrating crack at the trailing edge, the integral expression of the resultant tensile force of the non-penetrating crack at the trailing edge is written in numerical integral form as follows:

[0124]

[0125] Where, σ i σ is obtained by linear interpolation. i In [0, -σ t The result is obtained by interpolation within the specified range.

[0126] Sub-step 424: Based on the principle of equivalent torque balance, select any point in space, which does not necessarily have to be on the three-dimensional model of the unstable rock, such as (0,0,0) in space, and let the coordinates of any point be represented as M0(x0,y0,z0). Then, according to the second set formula, calculate the torque balance of the resultant tensile force of the non-penetrating fracture at the rear edge in the x, y, and z directions, and calculate the coordinates M2(x2,y2,z2) of the point of application of the resultant tensile force of the non-penetrating fracture at the rear edge. The second set formula is expressed as:

[0127] ∑dF σ ×S i =F σ ×S′,

[0128] Among them, S i S' is the distance from the centroid of the differential strip to point M0, and S' is the distance from the point of application of the resultant tensile force of the unconnected crack at the trailing edge to point M0.

[0129] In step 4 above, the boundary coordinate sequence extracted from the 3D model of the dangerous rock is used for interpolation to calculate the differential strip information, such as... Figure 6 As shown, it includes the following sub-steps:

[0130] Sub-step 401: Extract the boundary coordinate sequence of the rear fracture surface from the 3D model of the unstable rock, and divide it into left and right sides, represented as: N0, N1, N2, N3, ..., N n ;Q0,Q1,Q2,Q3,...,Q n ;

[0131] Sub-step 402: Divide the two sets of point sequences into blocks according to the height dh, based on the z-direction coordinate z. i =z0-i×dh, interpolation to calculate the coordinates U of the two boundary points of the differential strip. Li and U ri ;

[0132] Sub-step 403, based on the coordinates of the two boundary points U of the differential strip. Li and U ri Calculating the length of the differential strip by using the coordinates of the two boundary points is an existing technique and will not be elaborated here.

[0133] Step 5: Calculate the lever arm of the resultant tensile force of the non-penetrating fracture at the rear edge with respect to the resultant tensile force of the non-penetrating fracture at the rear edge of the overturning point, based on the third process and the coordinates of the overturning point. Also calculate the lever arm of the resultant water pressure of the fracture at the rear edge with respect to the resultant water pressure of the fracture at the rear edge of the overturning point. The third process includes the following sub-steps:

[0134] Sub-step 501 determines the overturning point coordinates M1 (x1, y1, z1) from the three-dimensional model of the unstable rock, the strike of the straight line where the overturning point M1 is located is θ1, the dip of the rear edge fracture structure surface is θ2, and the dip angle is β. Strike, dip, and dip angle are all concepts of the three elements of rock strata occurrence in geology. For example, strike is the angle with the geological north, and dip angle is the angle between a straight line or plane and a horizontal line or plane, or the angle between a straight line and its projection on a plane, etc.

[0135] Sub-step 502: Calculate the straight-line vector of the overturning point. The normal vector of the trailing edge structure surface is (sinθ1, cosθ1, 0). Given (sinθ2,cosθ2,tan(90°-β)), calculate the phasor. and Represented as:

[0136]

[0137] Sub-step 503, solve and The resultant tensile force lever L of the non-penetrating crack at the trailing edge is obtained. σ The resultant force arm L of the trailing edge fissure water pressure V They are represented as follows:

[0138]

[0139]

[0140] Step 6: Substitute the resultant force arm of the tensile force of the non-penetrating fracture at the rear edge, the resultant force arm of the tensile force of the non-penetrating fracture at the rear edge, the resultant force arm of the water pressure in the fracture at the rear edge, the resultant force arm of the horizontal seismic force, the horizontal seismic force, the center of gravity arm, and the weight of the unstable rock into the preset stability formula to calculate the overturning stability coefficient of the unstable rock. When the unstable rock is controlled by the tensile strength at the rear edge, and the center of gravity of the unstable rock is within the overturning point in the three-dimensional model of the unstable rock, the stability formula is expressed as:

[0141]

[0142] When the stability of a rockfall is controlled by its trailing edge tensile strength, and the center of gravity of the rockfall in the three-dimensional model is outside the overturning point, the stability formula is expressed as:

[0143]

[0144] Where: W is the weight of the unstable rock mass calculated based on its volume, i.e., volume multiplied by density; a is the center of gravity lever arm, which is the horizontal distance from the center of gravity of the unstable rock mass to the overturning point, i.e., based on the coordinates of the centroid O (x... o ,y o,z o The calculation is performed, where h0 is the horizontal seismic force arm, which is the vertical distance from the center of gravity of the unstable rock to the overturning point; Q is the horizontal seismic force, which is the seismic force coefficient multiplied by the mass of the unstable rock. The seismic force coefficient is the ratio of the maximum ground acceleration to the gravitational acceleration during an earthquake, denoted by K, and is a quantitative indicator for determining seismic intensity. The seismic force coefficient is obtained by consulting the relevant specifications beforehand; F σ The resultant tensile force of the unconnected crack at the trailing edge; L σ V is the resultant lever arm of the tensile force in the non-penetrating fracture at the trailing edge; L is the resultant force of the water pressure in the fracture at the trailing edge; V It is the lever arm of the resultant force of the water pressure in the trailing edge fissure.

[0145] In another embodiment, a storage medium is included, which stores a computer program that, when executed by a processor, implements the steps of the above-described three-dimensional calculation method for the stability of rockfall overturning.

[0146] Construct dangerous rock masses of different shapes, such as Figure 7 As shown, they are: Figure 7 (a) in the text represents a dangerous rock mass with a rear-edge fracture surface that is an equilateral triangle. Figure 7 (b) in the text represents a dangerous rock mass with an isosceles trapezoidal fracture surface at its rear edge. Figure 7 (c) in the text indicates a dangerous rock mass with a rectangular rear-edge fracture surface. Figure 7 In the diagram, (d) indicates that the top and bottom surfaces are trapezoidal. The fracture surfaces behind the dangerous rock mass (a), (b), and (c) are the same as the free surface at the front edge. The dangerous rocks (a), (b), (c), and (d) have equal height, width, and thickness. Thickness BB1 = 10m, width BC = JH = 20m; the overturning point is located at the center of the bottom surface of the unstable rock, where DG = 5m.

[0147] Comparing the calculation results of the method in this embodiment with the calculation results of the existing two-dimensional simplified calculation model, the unstable rock masses (a), (b), (c), and (d) can all be simplified as follows: Figure 7 The two-dimensional profile calculation model shown in (e) is... Figure 7 In this context, (e) represents the two-dimensional profile calculation model.

[0148] Assume that B1C1 = 10m in both rock formations (b) and (d). The height of the tensile zone at the rear edge is 4m, and the water filling height is assumed to be 6m. The tensile strength σ of the rock mass... t The pressure is 250 kPa, and the specific gravity is 26.2 kN / m. 3 According to the calculation method of this embodiment, the overturning stability calculation results of the unstable rock masses (a), (b), (c), and (d) and their corresponding two-dimensional profile models are obtained, as shown in Table 1.

[0149] Table 1 Comparative Analysis of Overturning Stability of Rockfalls of Different Shapes

[0150]

[0151] As can be seen from Table 1, except for the overturning stability coefficient of the unstable rock mass (c) with a rectangular rear edge, which is consistent with the two-dimensional calculation results, the overturning stability calculation results of unstable rock masses (a), (b), and (d) differ greatly from the two-dimensional calculation results.

[0152] For the unstable rock mass (b), the morphology of the unstable rock mass was changed, that is, different widths of the bottom edge B1C1 were selected, and its overturning stability was analyzed. The results were compared with the two-dimensional calculation results, and the following results were obtained: Figure 8 The relationship shown. From Figure 8 As can be seen, the shape of the unstable rock mass has a significant impact on the overturning stability coefficient. Only when the bottom width of the unstable rock mass is 20m, i.e., the rear edge is nearly rectangular, are the two-dimensional and three-dimensional calculation results the same. For unstable rock mass (b), the top and bottom surfaces are swapped, adjusting it to be a rock mass with a larger top and a smaller bottom. The relationship between three-dimensional stability and two-dimensional calculation is calculated and analyzed for different top surface widths (when the top surface width is 0, it corresponds to the unstable rock mass (a) model), such as... Figure 9 As shown, the shape of the unstable rock mass has a significant impact on the overturning stability coefficient. Only when the top surface width is 20m, i.e., the trailing edge is nearly rectangular, are the two-dimensional and three-dimensional calculation results the same.

[0153] For the unstable rock mass (d), the three-dimensional stability of different free face widths was calculated and analyzed, and compared with the two-dimensional calculation, as shown below. Figure 10 The relationship diagram shown is from Figure 10 As can be seen, the shape of the unstable rock has a significant impact on the calculation results of the overturning stability coefficient. Only when the width of the free face is 20m, that is, when the top and bottom surfaces of the unstable rock are approximately rectangular, are the two-dimensional and three-dimensional calculation results the same.

[0154] In summary, the overturning stability coefficient calculated using a two-dimensional profile model only matches the three-dimensional calculation result when the rock mass is a standard cube. Simplifying a real rock mass into a two-dimensional calculation model and calculating based on unit width area has significant limitations. Only a very small number of rock masses conform to this simplification rule. Rock masses in nature have extremely irregular shapes, and the vast majority cannot actually be simplified into a two-dimensional calculation model. Calculating using only this simplified method would inevitably produce incalculable calculation errors; three-dimensional calculation is more reasonable. This embodiment establishes an irregular three-dimensional model of the rock mass based on its actual geological conditions and obtains relevant parameter indicators from the three-dimensional model to calculate the relevant lever arms of the fracture surfaces in the actual rock mass shape. The lever arms are also used to calculate the overturning stability coefficient. The calculation process maintains the influence of the irregular shape of the rock mass on its overturning stability, improving the accuracy and completeness of the calculated overturning stability coefficient.

[0155] The above descriptions are merely embodiments of the present invention, and common knowledge regarding specific structures and characteristics is not elaborated upon here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the structure of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A three-dimensional calculation method of rockfall overturning stability, comprising the following steps: Step 1, obtaining three-dimensional point cloud data of a rockfall, and obtaining information data of a fissure surface and a combination relationship of the rockfall; characterized in that it further comprises the following steps: Step 2, establishing a rockfall three-dimensional model of the rockfall according to the three-dimensional point cloud data, the fissure surface and the information data; Step 3, extracting a parameter index for overturning stability calculation from the rockfall three-dimensional model, wherein the parameter index comprises a rockfall body volume, a centroid coordinate, an overturning point coordinate, a gravity arm horizontal seismic force and a gravity arm of the horizontal seismic force; Step 4, calculating a rear edge fissure water pressure resultant force and a rear edge fissure water pressure resultant force action point coordinate according to a first process, and calculating a rear edge non-penetrating fissure tensile force resultant force and a rear edge non-penetrating fissure tensile force resultant force action point coordinate according to a second process; the first process comprising the following sub-steps: Sub-step 411, obtaining a water pressure calculation diagram of the rockfall body rear edge water pressure from the rockfall three-dimensional model; Sub-step 412, the water pressure is calculated from the differential principle to the vertical direction of the profile taking a width of L of the differential strip dh , the water pressure generated by the differential strip is expressed as: ， wherein, the specific weight of water, h is the differential strip center to water surface top distance; Sub-step 413, the water pressure of the trailing edge water pressure is area-integrated to obtain the resultant force of the trailing edge fracture water pressure, expressed as: ， Considering irregularity of a rear edge fissure water pressure area shape, an integral expression of the rear edge fissure water pressure resultant force is written in a numerical integral form, and is expressed as: ； Sub-step 414, according to the moment equivalent balance principle, select any point in space, and the coordinate is expressed as , according to the first setting formula, the moment balance of the resultant force of the rear edge fissure water pressure in x, y, z three directions is calculated, and the coordinate of the action point of the resultant force of the rear edge fissure water pressure is calculated , the first setting formula is expressed as: ， wherein, is the distance from the center of the differential strip to the point , is the distance from the point of action of the resultant of the back fissure water pressures to the point V , is the distance from the point of action of the resultant of the back fissure water pressures to the point Step 5, calculating a rear edge non-penetrating fissure tensile force resultant force arm of the rear edge non-penetrating fissure tensile force resultant force to the overturning point according to a third process and the overturning point coordinate, and calculating a rear edge fissure water pressure resultant force arm of the rear edge fissure water pressure resultant force to the overturning point; Step 6, substituting the rear edge non-penetrating fissure tensile force resultant force arm, the rear edge non-penetrating fissure tensile force resultant force, the rear edge fissure water pressure resultant force arm, the rear edge fissure water pressure resultant force, the gravity arm horizontal seismic force arm, the gravity arm horizontal seismic force, the gravity arm and the rockfall body gravity into a preset stability formula to calculate a rockfall overturning stability coefficient of the rockfall overturning.

2. The three-dimensional calculation method for unstable rockfall stability according to claim 1, characterized in that: in the step 4, the second process comprising the following sub-steps: Sub-step 421, obtaining a tensile force calculation diagram of the rockfall body rear edge non-penetrating fissure tensile force from the rockfall three-dimensional model; Sub-step 422, according to the differential principle, the vertical direction of the tension calculation diagram is taken as a width of L differential strip dh , the tensile resistance generated by the differential strip is represented as: ​ ， wherein, Tb is the tensile capacity of the trailing edge unpenetrated crack at the differential strip; Sub-step 423, integrating a rear edge non-penetrating fissure tensile area to obtain the rear edge non-penetrating fissure tensile force resultant force, and is expressed as: ， Considering irregularity of a rear edge non-penetrating fissure tensile area shape, an integral expression of the rear edge non-penetrating fissure tensile force resultant force is written in a numerical integral form, and is expressed as: ， wherein, Obtained by linear interpolation method; Sub-step 424, according to the moment equivalent balance principle, select any point in space, and the coordinate is expressed as According to the second setting formula, the moment balance of the x, y, z directions of the resultant tensile force of the rear edge non-penetrating crack is calculated to obtain the coordinate of the action point of the resultant tensile force of the rear edge non-penetrating crack The second setting formula is expressed as: ， wherein is the distance from the center of the differential strip to the point is the distance from the point is the distance from the point is the distance from the point 3. The three-dimensional calculation method for unstable rockfall stability according to claim 2, characterized in that: in the step 4, a boundary coordinate sequence extracted from the rockfall three-dimensional model is used for interpolation to calculate differential strip information, comprising the following sub-steps: Sub-step 401, from the dangerous rock three-dimensional model, the trailing edge crack surface boundary coordinate sequence is taken out, and is divided into left and right sides, and is expressed as: ; Sub-step 402, between the two sets of point sequences, by height dh Divide the strips, according to the z-direction coordinates , interpolate the coordinates of the coordinate points on both boundaries of the differential strip and ; Sub-step 403, calculate the length of the differential strip according to the coordinate points of the two boundaries of the differential strip and ​ 4. The three-dimensional calculation method for unstable rockfall stability according to claim 3, characterized in that: in the step 5, the third process comprising the following sub-steps: Sub-step 501, determining the coordinates of the overturning point from the three-dimensional model of the dangerous rock To , the straight line where the overturning point is located , the tendency of the back edge crack structure surface , the inclination ; Sub-step 502, calculate the overturning point straight line vector is , the trailing edge structural surface normal vector is , calculate the phasor and is expressed as: ； Sub-step 503, solving and obtained, the arm of the resultant force of the tensile resistance of the rear edge unpenetrated fissure and the arm of the resultant force of the water pressure of the rear edge fissure respectively ， 。 5. The three-dimensional calculation method for unstable rockfall stability according to claim 4, characterized in that: in the step 6, when the rockfall is controlled by a rear edge tensile strength, and a rockfall body gravity center is within the overturning point in the rockfall three-dimensional model, the stability formula is expressed as: ， when the rockfall is controlled by the rear edge tensile strength, and the rockfall body gravity center is outside the overturning point in the rockfall three-dimensional model, the stability formula is expressed as: ， wherein: W is the gravity of the dangerous rock mass calculated according to the volume of the dangerous rock mass; a is the gravity arm, the gravity arm being the horizontal distance from the gravity center of the dangerous rock to the overturning point, is the horizontal seismic force arm, the horizontal seismic force arm being the vertical distance from the gravity center of the dangerous rock to the overturning point; Q is the horizontal seismic force; is the resultant of the tensile resistance of the non-penetrative fissures in the trailing edge; is the resultant arm of the tensile resistance of the non-penetrative fissures in the trailing edge; V is the resultant of the water pressure of the fissures in the trailing edge; is the resultant arm of the water pressure of the fissures in the trailing edge.

6. The three-dimensional calculation method for unstable rockfall stability according to claim 5, characterized in that: in the step 2, the rockfall three-dimensional model comprises a rockfall three-dimensional surface model and a rockfall three-dimensional geological model, and the establishment process comprises the following sub-steps: Sub-step 201, performing grid interpolation thinning on the three-dimensional point cloud data; Sub-step 202, constructing a rockfall surface triangular net surface by using the grid point cloud; Sub-step 203, stretching the triangular net surface to form a rockfall body three-dimensional surface model; In the substep 204, the obtained dangerous rock fissure occurrence and combination relationship are used to construct a fissure plane, and the dangerous rock body entity is cut to form a dangerous rock three-dimensional geological model.

7. The three-dimensional calculation method for unstable rockfall stability according to claim 6, characterized in that: In the substep 201, a coordinate transformation method is used to transform the corresponding z coordinate of each data in the three-dimensional point cloud data in the original plane coordinate system x, y. In the original coordinate system xyz, the angle between the main collapse direction of the dangerous rock and the y-axis is set as The three-dimensional point cloud data of the dangerous rock is transformed according to the conversion formula, so that the main collapse direction of the transformed dangerous rock is changed into the z-axis, and a new coordinate system The conversion formula is: ， wherein, and are coordinate translation transformation values, in a new coordinate system The three-dimensional point cloud data is gridded and thinned by using the Kriging interpolation method, the gridded point cloud with a preset length interval is Kriging interpolated and thinned, and then the gridded point cloud is used to construct a dangerous rock free face triangular net Delaunay model.

8. The three-dimensional calculation method for unstable rockfall stability according to claim 6, characterized in that: In the substep 204, the entity is constructed according to the triangular net surface stretching, and then the overall model of the dangerous rock is cut according to the preset plane, and the obtained several dangerous rock master control fissure structural planes are generalized into a plane. Assuming that the structural surface is inclined to θ , the structural surface is inclined at φ , the plane unit normal vector of the structural surface is (cos θ , sin θ , tan φ ), and the plane equation of the rockfall fissure surface is ， The dangerous rock three-dimensional surface model is cut through the master control fissure plane to obtain several plate-shaped dangerous rock single body models, and a dangerous rock three-dimensional geological model is constructed.

9. A storage medium for storing a number of computer programs, characterized in that: The computer program is executed by the processor to realize the steps of the dangerous rock overturning stability three-dimensional calculation method in claim 8.

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