A method for determining the spatial location of data points inside the rock mass of a steep slope.

Abstract

This invention relates to a method for determining the spatial location of detection data points inside a steep slope rock mass, comprising the following steps: 1) setting up and recording the coordinates of the four corner points of the detection device; 2) calculating the coordinates of the center points of the four corner points of the detection device, the equations of the four planes they form, and their plane normal vectors; 3) calculating the unit normal vector of the detection plane formed by the four corner points of the small loop detection device using the normal vector addition method based on the normal vectors of the four planes; 4) for detection data points with known detection depths inside the steep slope rock mass, obtaining the spatial coordinates of the detection data points using the unit normal vector of the detection plane. Its advantages are: the detection device can be arbitrarily set up on flat ground or steep slopes, quickly locating its spatial position and detection normal, and identifying the differences in physical parameters inside the steep slope rock mass; the normal vector addition method is simple and fast; the detection data points are spatially digitized, representing the differences in physical parameters in the form of three-dimensional spatial coordinates.

Description

Technical Field

[0001] This invention belongs to the field of mine geophysical exploration technology, specifically relating to a method for determining the spatial location of exploration data points inside a rock mass on a steep slope. Background Technology

[0002] As open-pit mining activities continue, the depth of the pit increases, gradually forming steep slopes around the pit. The presence of these steep slopes alters the mechanical properties of the surrounding rock and soil, making them highly susceptible to secondary geological disasters such as collapses and landslides, seriously threatening the daily production safety of the mine. To prevent these secondary geological disasters, mines often employ slope surface deformation monitoring techniques. However, these techniques primarily monitor surface damage on steep slopes, failing to capture damage caused by internal fractures within the rock mass, thus affecting the safety assessment of the overall slope stability. In fact, the development of damage caused by internal fractures in steep slopes can be reflected by the induced differences in physical parameters, specifically through a transient electromagnetic method using a multi-turn overlapping small loop device with single-point, full-space moving detection. However, conventional transient electromagnetic multi-turn overlapping small loop devices are mostly used for all-space early warning detection in underground mines and for detecting physical property parameters within a certain depth range on flat ground in open-pit mines. These are detection spaces that people can safely enter and exit, and the detection points reflect the clear spatial distribution of physical property parameters. They can be achieved using conventional transient electromagnetic multi-turn overlapping small loop devices, and these devices have never had a positioning function. However, for the detection of physical parameters inside the rock mass of steep slopes in open-pit mines, where it is impossible to directly and safely place detection devices manually, auxiliary facilities are needed to indirectly place transient electromagnetic multi-turn overlapping small loop devices on the slope surface for fixed-point detection. Under current technological conditions, the above-mentioned placement method, due to the inability to directly intervene manually, presents the following two technical challenges that urgently need to be addressed: First, it is difficult to accurately measure the slope attitude of steep slopes, making it difficult to spatially locate the slope normal direction of the vertically inward rock mass detection point where the transient electromagnetic multi-turn overlapping small loop device is located. Second, this also makes it difficult to spatially locate the distribution of physical parameters characterizing the internal damage of the rock mass detected by the transient electromagnetic multi-turn overlapping small loop device. Ultimately, this affects the safety assessment of the stability of the entire slope rock mass. Summary of the Invention

[0003] In view of the above-mentioned technical problems existing under the current technology, the purpose of this invention is to provide a method for determining the spatial location of detection data points inside the rock mass of a steep slope, which can obtain the distribution of physical property parameters within a certain depth range inside the rock mass of a steep slope, thereby evaluating the damage inside the rock mass.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] The present invention provides a method for determining the spatial location of detection data points inside a high and steep slope rock mass, characterized by comprising the following steps:

[0006] Step 1: Four laser reflection positioning devices are set up on the surface of the steep slope rock mass to be investigated. Each laser reflection positioning device is a fixed device with a 360° reflecting prism. The coordinates of the four positioning devices are measured with a total station. The four laser reflection positioning devices are connected by receiving and transmitting wire frames to form a small loop detection device with multiple overlapping turns of transient electromagnetic method. The different coordinates of the four positioning devices are the coordinates of the four corner points of the detection device.

[0007] Step 2: Using the coordinates of the four corner points of the small loop detection device, calculate the coordinates of the center point, the equations of the four planes formed, and the normal vectors, thus obtaining the normal vectors of the four planes; the specific calculation process is as follows:

[0008] For the four corner points A, B, C, and D of a multi-transient electromagnetic method with multiple overlapping small loop detection devices, the method for calculating the center point coordinate O is as follows:

[0009]

[0010] In three-dimensional space, any three non-collinear known points can define a plane, and the corresponding equation of the plane can be solved. Let the coordinates of the three known points be A(x1, y1, z1), B(x2, y2, z2), and C(x3, y3, z3). The equation of the plane determined by these three non-collinear known points is as follows:

[0011] 1) Let the general form of the equation of the plane determined by the three known points be:

[0012] ax + by + cz + d = 0 (2)

[0013] Substituting the three known points into equation (2), we obtain the system of equations (3):

[0014]

[0015] Solving the system of equations (3) yields the plane equation determined by the three known points.

[0016] 2) Given three points A, B, and C, we can calculate vectors AB and AC, and have

[0017]

[0018]

[0019] Let the normal vector of the plane be...

[0020] n = (n x ,n y ,n z (5)

[0021] By the definition of a normal vector, we know that a normal vector is orthogonal to all vectors in a plane.

[0022]

[0023]

[0024] Right now

[0025] n x (x2-x1)+n y (y2-y1)+n z (z2-z1)=0

[0026] n x (x3-x1)+n y (y3-y1)+n z (z3-z1)=0 (7)

[0027] Solving the system of equations (7), we obtain a solution n = (n i ,n j ,n k If ), then the equation of the plane can be set as

[0028] n i x+n j y+n k z = d (8)

[0029] Substituting a known point, such as point A (x1, y1, z1), we have

[0030] n i x1+n j y1+n k z1=d (9)

[0031] Solving equation (9) for d yields the equation of the plane determined by the three non-collinear known points, and the normal vector of the plane is n = (n i ,n j ,n k ).

[0032] Step 3: Based on the normal vectors of the four planes obtained above, calculate the unit normal vector of the detection plane formed by the four corner points of the small loop detection device using the normal vector addition method; the specific calculation process is as follows:

[0033] Suppose the surface of the steep slope rock mass to be investigated is determined by four known non-coplanar vertices A, B, C, and D. Using the method described above, four different planes can be calculated from these four known points, yielding their equations and their normalized normal vectors n1, n2, n3, and n4. The formula for calculating the normalized normal vector n1 is:

[0034]

[0035] To synthesize the influence of the four planes, the normal directions of the four planes are averaged. This is done by adding the normal vectors together, resulting in:

[0036] n O =n1+n2+n3+n4 (11)

[0037] The normal vector n obtained by equation (11) O This is a normal vector on the surface of the steep slope rock mass to be investigated. After normalizing it, the unit normal vector n0 of the detection plane is:

[0038]

[0039] Step 4: For detection data points with known detection depths inside the rock mass of a steep slope, use the unit normal vector of the detection plane obtained in Step 3 to calculate the spatial coordinates of the detection data points; the specific calculation process is as follows:

[0040] Given the unit normal vector n0 of the detection plane obtained in step 3, and the depth of the detection data point is 10 meters, the spatial coordinates T of the detection data point are:

[0041] T = O + 10·n0 (13).

[0042] This invention addresses the technical challenge of detecting internal physical parameters of rock masses in steep slopes.

[0043] To investigate the variation characteristics of physical parameters within a certain depth range inside a steep slope rock mass, this invention designs a transient electromagnetic multi-turn overlapping small loop device with a measurement and positioning device. This device can be placed on the surface of a slope rock mass with any slope angle. The coordinates of the four corner points of the detection device can be collected by the measurement and positioning device, and multi-plane fitting is performed through the four-point positioning coordinates to accurately determine the normal direction of the detection surface of the steep slope rock mass. Then, through formula conversion, the difference in physical parameters of the slope surface normal direction from the detection rock mass surface to a certain detection depth range can be detected.

[0044] This invention addresses the technical challenge of spatially locating detection data points in the detection of internal physical parameters of rock masses on steep slopes. Specifically, for detecting internal physical parameters of rock masses on steep slopes, the direction of difference in physical parameters detected by a transient electromagnetic method multi-turn overlapping small loop detection device with a positioning device is within a spatial range from the detection surface to a certain depth, defined by the normal direction of the detection device's center point. In other words, locating the four spatial positions of the detection device can pinpoint the normal direction of the detection center. However, due to measurement errors, the four corner points of the multi-turn overlapping small loop device may not be coplanar, making it difficult to determine the actual normal direction. To determine the placement plane of the detection device and its true detection normal direction, this invention proposes an algorithm for calculating the fitting normal direction of multiple measurement points to the true detection surface. By calculating the true normal direction of the detection plane where the detection device is located, the spatial position and distribution changes of transient electromagnetic method detection data points within the steep slope rock mass along the normal direction of the detection plane from the detection surface to a certain depth range can be quickly calculated, thereby achieving accurate detection of changes in physical parameters within the rock mass along the normal direction. After conducting multi-point transient electromagnetic detection along the surface of the rock mass on a steep slope, the distribution of physical parameters within a certain depth range inside the rock mass can be obtained.

[0045] Compared with the prior art, the advantages of the present invention are as follows:

[0046] 1. A transient electromagnetic multi-turn overlapping small loop detection device with a laser reflection positioning device was developed. The advantage of this device is that it can be deployed arbitrarily, not limited to flat ground or steep slopes. Furthermore, deploying this device on a slope not only effectively detects differences in physical parameters within a certain depth of the slope and studies the integrity of the slope's interior, but also significantly reduces the safety risks for personnel directly entering the slope to deploy the detection device and obtain positioning points.

[0047] 2. The normal vector addition method proposed in this invention can quickly calculate the normal direction of the center point of the transient electromagnetic multi-turn overlapping small loop detection device, realizing rapid spatial positioning of the detection data point in the high and steep slope detection area, which is convenient for carrying out continuous mobile geophysical exploration in the depth space below the slope surface of high and steep slopes.

[0048] 3. This invention can spatially digitize the location of physical property parameter data points within a certain depth collected by the detection point, and record the difference information of physical property parameters within the detectable depth space of the transient electromagnetic method in the form of three-dimensional coordinates.

[0049] 4. This invention is not only applicable to the detection of steep slopes in open-pit mines, but also applicable to engineering geological surveys of dams, railways and other projects. Attached Figure Description

[0050] Figure 1It is a transient electromagnetic method multi-turn overlapping small loop device with laser reflection positioning device.

[0051] Figure 2 A simplified diagram of a transient electromagnetic multi-turn overlapping small loop detector with a laser reflection positioning device.

[0052] Figure 3 The detection space range of the transient electromagnetic method multi-turn overlapping small loop device with laser reflection positioning device.

[0053] Figure 4 This is a schematic diagram for calculating the equation of a plane and its normal vector in three-dimensional space.

[0054] Figure 5 This is a schematic diagram of the normal vector addition method. Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] Example

[0057] like Figure 1 , Figure 2 and Figure 3 As shown, the present invention provides a method for determining the spatial location of detection data points inside a high and steep slope rock mass, characterized by comprising the following steps:

[0058] Step 1: Set up four laser reflection positioning devices on the surface of the steep slope rock mass to be investigated. Use a total station to measure the coordinates of the four positioning devices. Connect the four laser reflection positioning devices with receiving and transmitting wire frames to form a small loop detection device with multiple overlapping turns of transient electromagnetic method. The different coordinates of the four positioning devices are the coordinates of the four corner points of the detection device.

[0059] Step 2: Using the coordinates of the four corner points of the small loop detection device, calculate the coordinates of the center point, the equations of the four planes formed, and the normal vectors, to obtain the normal vectors of the four planes:

[0060] For the four corner points A, B, C, and D of the multi-transient electromagnetic method's multi-turn overlapping small loop detection device, four known points are taken as the coordinates of the four corner points. Specifically, A = (5, 0, 0); B = (0, 8, 0); C = (0, 0, 5); D = (2, 2, 2).

[0061] Step 2.1: Determine the coordinates O of the center point O of the four corner points A, B, C, and D of the multi-turn overlapping small loop detection device recorded in Step 1. For the embodiment, we have:

[0062]

[0063] Step 2.2: The coordinates of the four known points can form four different planes: ABC, ABD, ACD, and BCD. The equations of these four planes are then solved using formulas. The specific process for solving the plane equations is as follows:

[0064] (1) In three-dimensional space, any three non-collinear known points can determine a plane, and the equation of the corresponding plane can be found. Assume the coordinates of the three known points are A(x1, y1, z1), B(x2, y2, z2), and C(x3, y3, z3). Then, let the general form of the equation of the plane determined by these three known points be:

[0065] ax + by + cz + d = 0 (2)

[0066] Substituting the three known points into equation (1), we obtain the system of equations (2):

[0067]

[0068] Solving the system of equations (3) yields the equations of the planes determined by the three known points. From equations (2) and (3), the equations of the four planes are respectively...

[0069] Plane ABC: -8x - 5y - 8z + 40 = 0

[0070] Plane ABD: -16x - 10y - 14z + 80 = 0

[0071] Plane ACD: -10x - 5y - 10z + 50 = 0

[0072] Plane BCD: -14x - 10y - 16z + 80 = 0 (4)

[0073] Step 2.3: Use the algorithm formula to obtain the plane normal vectors of the four faces ABC, ABD, ACD, and BCD. Assuming three non-collinear known points in three-dimensional space are A, B, and C, then vectors AB and AC can be calculated as follows:

[0074]

[0075]

[0076] Let the normal vector of plane ABC be...

[0077] n = (n x ,n y ,n z (6)

[0078] By the definition of a normal vector, we know that a normal vector is orthogonal to all vectors in a plane.

[0079]

[0080]

[0081] Right now

[0082] n x (x2-x1)+n y (y2-y1)+n z (z2-z1)=0

[0083] n x (x3-x1)+n y (y3-y1)+n z (z3-z1)=0 (8)

[0084] Solving the system of equations (8), we obtain a solution n = (n i ,n j ,n k If ), then the equation of the plane can be set as

[0085] n i x+n j y+n k z = d (9)

[0086] Substituting a random known point, here I substitute A(x1, y1, z1), we have

[0087] n i x1+n j y1+n k z1=d (10)

[0088] Solving for d in equation (10) yields the equation of the plane determined by the three non-collinear known points, and the normal vector of this plane is n = (n i ,n j ,n k ).

[0089] Using the above formulas, the normal vectors of the four planes in the example can be quickly calculated using programming software. The normal vectors of planes ABC, ABD, ACD, and BCD are respectively...

[0090]

[0091] Step 3: Based on the normal vectors of the four planes obtained above, calculate the unit normal vector of the detection plane formed by the four corner points of the small loop detection device using the normal vector addition method. The specific calculation process is as follows:

[0092] Suppose the surface of the steep slope rock mass to be investigated is determined by four known non-coplanar vertices A, B, C, and D. Using the method described above, four different planes can be calculated from these four known points, yielding their equations and their normalized normal vectors n1, n2, n3, and n4. The formula for calculating the normalized normal vector n1 is as follows:

[0093]

[0094] In a specific embodiment, the formula for calculating the normalized normal vector n3 is as follows:

[0095]

[0096] To synthesize the influence of the four planes, the normal directions of the four planes are averaged. This is done by adding the normal vectors together, resulting in:

[0097] n O =n1+n2+n3+n4 (14)

[0098] The normal vector n obtained by equation (14) O This is a normal vector on the surface of the steep slope rock mass to be investigated. After normalizing it, the unit normal vector n0 of the detection plane is:

[0099]

[0100] On a computer, programming software is used to plot the four planes in equation (4), and the unit normal vectors of each plane obtained using equation (13) are stretched and plotted by multiples. The results are as follows. Figure 4 As shown. A schematic diagram of the normal vector addition method is shown below. Figure 5 As shown.

[0101] Step 4: For detection data points with known detection depth inside the rock mass of a steep slope, use the unit normal vector of the detection plane obtained in Step 3 to obtain the spatial coordinates of the detection data points.

[0102] Given the unit normal vector n0 of the detection plane obtained in step 3, and the depth of the detection data point is 10 meters, the spatial coordinates T of the detection data point are (rounded to two decimal places):

[0103] T=O+10·n0=(-4.75,-1.44,-4.75) (16).

Claims

1. A method for determining the spatial position of a data point inside a high and steep slope rock mass, characterized in that, It comprises the following steps: Step 1, four laser reflection positioning devices are arranged on the surface of the high and steep slope rock mass to be detected, the positioning device is a 360° reflection prism, the coordinate data of the four positioning devices are measured by a total station, the four laser reflection positioning devices are connected by a receiving line frame and a transmitting line frame to form a multi-turn overlapping small loop detection device of transient electromagnetic method, and the different coordinates of the four positioning devices are the coordinates of the four corner points of the detection device; Step 2, the center point coordinates, the plane equation and the normal vector of the four planes formed by the four corner point coordinates of the small loop detection device are calculated, and the normal vectors of the four planes are obtained; Step 3, according to the normal vectors of the four planes obtained above, the unit normal vector of the detection plane formed by the four corner points of the small loop detection device is calculated by the normal vector addition method; Step 4, for the detection data points with known detection depth in the high and steep slope rock mass, the unit normal vector of the detection plane obtained in step 3 is used to calculate the spatial position coordinates of the detection data points.

2. The method of claim 1, wherein, In step 2, the specific calculation method of the center point coordinates, the plane equation and the normal vector of the four planes formed is as follows: For the four corner points A, B, C, D of the multi-turn overlapping small loop detection device of multi-transient electromagnetic method, the calculation method of the center point coordinates O is （1） In three-dimensional space, any three non-collinear known points can determine a plane, and the corresponding plane equation can be solved; suppose the coordinates of the three known points are A (x1, y1, z1), B (x2, y2, z2), C (x3, y3, z3), and the plane equation determined by the three non-collinear known points is as follows: 1) the general equation of the plane determined by the three known points is （2） Bring the above three known points into equation (2) to obtain equation (3): （3） Solve equation (3) to obtain the plane equation determined by the three known points, 2) for the three known points A, B, C, the vector AB and the vector AC can be calculated, and （4） Suppose the normal vector of the plane is （5） According to the definition of the normal vector, the normal vector is orthogonal to all vectors in the plane, that is, （6） That is, （7） Solving the equations of formula (7), we get one solution of the equations The equation of the plane can be set as （8） Substitute a known point, such as A (x1, y1, z1), into the equation, and （9） Solving d in equation (9) gives the plane equation determined by the three non-collinear known points, and the normal vector of the plane is .

3. The method of claim 2, wherein the method further comprises: determining the spatial position of the data point inside the high and steep slope rock mass based on the first and second sets of data points. In step 3, the specific calculation process of calculating the unit normal vector of the detection plane formed by the four corner points of the small loop detection device by the normal vector addition method is as follows: Suppose the surface of the high and steep slope rock mass to be detected is determined by four known non-coplanar vertices A, B, C, D, then four different planes are calculated by the method of calculating the plane equation and the normal vector, four different plane equations and their unitized normal vectors n1, n2, n3, n4 are obtained, and the formula for calculating the unitized normal vector n1 is （10） In order to integrate the influence of the four planes, the normal direction of the four planes is averaged, that is, the normal vectors are added by the normal vector addition method, that is, （11） The normal vector n obtained from formula (11) O That is, a normal vector of the surface of the high and steep slope rock mass to be detected and studied, and after unitization processing, the unit normal vector n0 of the detection plane is （12）。 4. The method of claim 1, wherein, In step 4, the specific calculation process of calculating the spatial position coordinates of the spatial detection data points of the high and steep slope surface depth is as follows: The unit normal vector n0 of the detection plane obtained in step 3 is known, and the depth of the detection data point is 10 meters, so the spatial position coordinates T of the detection data point are: （13）。

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