A bench slope surface motion parameter acquisition method applied to open blasting

Abstract

The application belongs to the technical field of engineering blasting, and discloses a step slope surface motion parameter acquisition method applied to open-air blasting, which comprises the following steps: obtaining physical and mechanical property parameters of a blasting medium in a blasting area, i.e. lithology parameters; constructing a two-dimensional discrete element model to obtain initial motion velocity data of blocks; constructing a slope block motion velocity function relationship; obtaining the center of mass velocity of all blocks on the slope surface; obtaining the initial throwing angle of all blocks on the entire step slope surface under two-dimensional conditions; and obtaining the initial throwing velocity of all blocks on the entire step slope surface in each direction under three-dimensional conditions and the coordinates at different moments after throwing, i.e. the slope motion parameters. The application solves the problems of the prior art, such as simple form, single parameter, inability to consider influencing factors such as charge structure and free surface for complex engineering projects, large error, poor flexible application, low calculation efficiency and poor economic benefits.

Description

Technical Field

[0001] This invention belongs to the field of engineering blasting technology, specifically relating to a method for obtaining the motion parameters of a step slope in open-pit blasting. Background Technology

[0002] When explosives detonate, humans utilize their chemical energy to convert it into mechanical work, enabling them to perform tasks that are impossible or difficult for humans or machines to accomplish. Engineering blasting is a typical example of using explosives to perform work. However, while explosives detonate in rock, they also produce harmful effects such as blasting vibrations, air shock waves, noise, occasional flyrock, and toxic gases, which are currently difficult to avoid. In bench blasting, improper control of flyrock can lead to blasting errors such as casualties, equipment damage, and building damage. The causes of flyrock include variable geological conditions, flaws in blasting design, and inadequate construction management. Deficiencies in blasting design can be avoided by adjusting the design scheme. With increasing blasting difficulty and costs, the blast pile morphology is receiving increasing attention. It is not only an important parameter for measuring blasting effectiveness and reflects the rationality of blasting parameters and charge design, but also directly affects loading, transportation efficiency, and economic benefits. In bench blasting, obtaining the motion parameters of rock blocks on the slope can be used to predict the farthest throwing distance and angle, and the distribution of the blast pile can be calculated based on ballistic theory. This can avoid blasting fly rock accidents caused by blasting design defects, while improving loading efficiency and economic benefits.

[0003] The distance of flyrock from blasting is closely related to blasting parameters, plugging quality, and geological and topographical conditions, making it difficult to calculate in both theory and practice. In chamber blasting, the distance of individual flyrock fragments is often calculated using formulas, where the flyrock distance is a function of the safety factor, blasting action index, and minimum resistance line. The flyrock distance in deep-hole blasting is generally estimated using the same formula. The Weibull distribution model is currently widely used for analyzing the blast pile morphology, obtaining a two-dimensional blast pile morphology based on statistics. Three-dimensional simulations of blast flyrock and blast pile morphology can also be performed using large-scale commercial software through mechanical analysis to obtain relevant data.

[0004] In existing technologies, the calculation of blasting flyrock distance based on empirical formulas and Weibull models based on statistical principles is simple in form and has single parameters. It cannot take into account complex engineering projects with influencing factors such as charge structure and free surface. Moreover, obtaining reliable correlation coefficients requires a large number of field tests and measurements. The errors between measurement methods and statistical methods make this method have large errors and poor flexibility. Using large commercial software is inefficient, especially under three-dimensional conditions, the required computing resources increase exponentially. Summary of the Invention

[0005] To address the problems of existing technologies being simple in form, having single parameters, being unable to consider complex engineering projects involving factors such as charge structure and free surface, having large errors, poor flexibility of application, low computational efficiency, and poor economic benefits, the present invention aims to provide a method for obtaining step slope motion parameters for open-pit blasting.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for obtaining motion parameters of a bench slope applied to open-pit blasting includes the following steps:

[0008] Ore specimens are extracted from the area to be blasted, and physical and mechanical property tests are conducted on the ore specimens to obtain the physical and mechanical property parameters of the medium to be blasted in the area to be blasted, i.e., lithological parameters.

[0009] Based on the lithological parameters of the medium to be blasted and the explosive parameters of the explosive to be used, a two-dimensional discrete element model of the load volume of a single explosive charge set in the area to be blasted is constructed, and the initial velocity data of the blocks on the slope of the blasting step are obtained based on the two-dimensional discrete element model.

[0010] The characteristic resistance line and explosive energy of the two-dimensional discrete element model are obtained, and the characteristic resistance line and explosive energy are fitted with the initial motion velocity data of the block to construct the functional relationship of the motion velocity of the slope block;

[0011] Based on the two-dimensional discrete element model, the centroid velocities of all blocks on the slope surface of the entire step are obtained according to the velocity function relationship of the slope block motion in the two-dimensional case.

[0012] In the two-dimensional discrete element model, a single explosive charge is equivalent to several ball-shaped explosive charges. The centroid coordinates of the slope blocks in the two-dimensional discrete element model are obtained. Based on the relative position of each ball-shaped explosive charge and the centroid coordinates of each slope block, the initial throwing angle of all blocks on the slope of the entire step in the two-dimensional case is obtained.

[0013] Based on the initial throwing angles and corresponding centroid velocities of all blocks on the entire slope surface in the two-dimensional case, the initial throwing velocities and coordinates at different times after throwing of all blocks on the entire slope surface in the three-dimensional case are obtained in each direction. The initial throwing velocities and coordinates at different times after throwing in each direction constitute the slope motion parameters of the blocks.

[0014] Furthermore, ore samples include drill cores and rock blocks taken from pits / trench exploration.

[0015] Furthermore, the lithological parameters include the density, compressive strength, tensile strength, Young's modulus, and longitudinal wave velocity of the medium to be blasted.

[0016] Furthermore, the two-dimensional discrete element model is built based on open-source discrete element simulation tools, including Yade and ESYS-Particle.

[0017] Furthermore, the formula for the velocity function of the slope block motion is:

[0018] V = f(E, W) = 0.116Q 1.4 W -0.7

[0019] In the formula, V is the velocity of the slope block movement; f(*) is the fitting function; E is the explosive energy parameter; W is the characteristic resistance line parameter of the target point; and Q is the explosive energy calculation factor.

[0020] Furthermore, the formula for the characteristic resistance line of the target point is:

[0021]

[0022] In the formula, W is the characteristic resistance line parameter of the target point; w i Let be the distance from the centroid of the i-th equivalent ball explosive charge to the centroid coordinates of the slope block at the target point; i is the equivalent ball explosive charge indicator; I is the total number of equivalent ball explosive charges; n is the total number of slope blocks;

[0023] The formula for calculating the energy factor of explosives is:

[0024] Q = 0.25πD 2 ρ E

[0025] In the formula, Q is the explosive energy calculation factor; D is the borehole diameter; ρ E This refers to the density of the explosive.

[0026] Furthermore, the formula for the initial throwing angle of the block in the two-dimensional case is:

[0027]

[0028] In the formula, α is the initial throwing angle of the block in the two-dimensional case; α ij For characteristic resistance line W ij Direction angle; W ij The characteristic resistance line from the i-th equivalent ball charge to the j-th block on the slope is obtained based on the relative position of the centroid of each ball charge and the centroid of the slope block; n is the total number of slope blocks; i is the equivalent ball charge indicator; j is the block indicator.

[0029] Furthermore, in the two-dimensional case, an XOZ two-dimensional plane is set, the velocity of the center of mass of the block (x0, z0) is V0, and the initial throwing angle on the XOZ plane is α. In the three-dimensional case, a YOZ two-dimensional plane is set perpendicular to the XOZ two-dimensional plane, adding the Y direction. The initial throwing velocities of the block (x0, y0, z0) in each direction are:

[0030]

[0031] In the formula, V 0x V represents the initial throwing velocity component in the X direction; 0y V represents the initial throwing velocity component in the Y direction; 0z Let be the initial throwing velocity component in the Z direction; α be the initial throwing angle in the XOZ plane; and V0 be the center-of-mass velocity of the block (x0, y0, z0) in the two-dimensional case.

[0032] The initial throwing velocities of block (x0, y1, z0) at the same horizontal height as block (x0, y0, z0) in each direction are:

[0033]

[0034] In the formula, V 1x V represents the initial throwing velocity component in the X direction; 1y V represents the initial throwing velocity component in the Y direction; 1z α is the initial throwing velocity component in the Z direction; β is the initial throwing angle in the XOZ plane; V1 is the deviation angle in the XOY plane; and V1 is the centroid velocity of the block (x0, y1, z0) in three dimensions.

[0035] Furthermore, the formula for the deviation angle is:

[0036]

[0037] In the formula, β is the deviation angle on the XOY plane; y1 is the coordinate of the block (x0, y1, z0) in the Y direction; y0 is the coordinate of the block (x0, y0, z0) in the Y direction; W0 is the characteristic resistance line of the block (x0, y0, z0); W is the characteristic resistance line parameter of the target point.

[0038] The formula for the velocity of the center of mass of a block (x0, y1, z0) in three dimensions is:

[0039] V1 = (W0 / W) 3 V0

[0040] In the formula, V1 is the centroid velocity of the block (x0, y1, z0) in three dimensions; W0 is the characteristic resistance line of the block (x0, y0, z0); W is the characteristic resistance line parameter of the target point; and V0 is the centroid velocity of the block (x0, y0, z0) in two dimensions.

[0041] Furthermore, the formula for the coordinates of the block at different times after it is thrown is:

[0042]

[0043] In the formula, (x′, y′, z′) are the coordinates of the block at different times after it is thrown; (x original ,y original ,z original Let x be the initial coordinates of the block before it is thrown, where x is the initial coordinates of the block before it is thrown. original =0; V x V y V z denoted as the initial throwing velocities of the block in each direction; g is the gravitational acceleration; t is the time indicator.

[0044] The beneficial effects of this invention are as follows:

[0045] The present invention provides a method for obtaining slope motion parameters in open-pit blasting. This method employs two-dimensional numerical calculations to account for the influence of factors such as detonation method, charge structure, and free surface on the motion parameters. Compared to the three-dimensional mechanical calculation methods used in large commercial software, it offers better computational efficiency, saves computational resources, and is simple and easy to implement in a program. Furthermore, the efficient and high-precision prediction of slope motion parameters can better optimize blasting design, reduce blasting accidents caused by flyrock, and improve blasting efficiency and economic benefits.

[0046] Other beneficial effects of the present invention will be further explained in the specific embodiments. Attached Figure Description

[0047] Figure 1 This is a flowchart of the method for obtaining the motion parameters of the step slope in open-pit blasting, as described in Example 1. Detailed Implementation

[0048] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0049] Example 1:

[0050] like Figure 1 As shown in the figure, this embodiment provides a method for obtaining motion parameters of a bench slope applied to open-pit blasting, including the following steps:

[0051] Ore specimens were extracted from the area to be blasted, and physical and mechanical property tests were conducted on the ore specimens to obtain the physical and mechanical property parameters of the medium to be blasted in the area to be blasted, namely lithological parameters. The lithological parameters include the density, compressive strength, tensile strength, Young's modulus, and longitudinal wave velocity of the medium to be blasted. The sample density obtained by the specific gravity bottle method was 2400 kg / m3, the rock compressive strength obtained by the uniaxial compressive strength test was 21.1 MPa, the rock tensile strength measured by the Brazilian splitting method was 1.7 MPa, and the rock longitudinal wave velocity measured by the acoustic emission system was 1100 m / s. The blasting design parameters were: column charge diameter 0.31 m, charge length 10 m, minimum resistance line 4 m, hole spacing 3 m, and step height 10 m.

[0052] Based on the lithological parameters of the medium to be blasted and the explosive parameters of the ammonium nitrate explosive to be used, a two-dimensional discrete element model of the load volume of a single explosive charge set in the area to be blasted is constructed. The load volume is a calculation area of ​​3*4*10 cubic meters. The slope boundary condition is set as a free surface, and the contact surface between adjacent load volumes is set as a transmission boundary. The initial motion velocity data of the blocks on the slope of the blasting step are obtained based on the two-dimensional discrete element model.

[0053] The characteristic resistance line and explosive energy of the two-dimensional discrete element model are obtained, and the characteristic resistance line and explosive energy are fitted with the initial velocity data of the block. The explosive energy is measured by the charge mass per unit length, in kg / m, to construct a functional relationship between the slope block's velocity and the explosive energy. With a borehole diameter of 0.31m, the equivalent spherical charge radius is... The charge is 10m long, and the equivalent number of spherical charges is 26. Therefore, a single charge can be equivalent to the superposition of I = 26 spherical charges with a radius of 0.1898m.

[0054] Based on the two-dimensional discrete element model, the centroid velocities of all blocks on the slope surface of the entire step are obtained according to the velocity function relationship of the slope block motion in the two-dimensional case.

[0055] In the two-dimensional discrete element model, a single explosive charge is equivalent to several ball-shaped explosive charges. The centroid coordinates of the slope blocks in the two-dimensional discrete element model are obtained. Based on the relative position of each ball-shaped explosive charge and the centroid coordinates of each slope block, the initial throwing angle of all blocks on the slope of the entire step in the two-dimensional case is obtained.

[0056] Based on the initial throwing angle and the centroid velocity of all blocks on the slope of the entire step in two dimensions, the initial throwing velocity and coordinates of all blocks on the slope of the entire step in three dimensions in each direction are obtained. The initial throwing velocity and coordinates at different times after throwing in each direction constitute the slope motion parameters of the blocks.

[0057] In this embodiment, the energy source for the initial motion parameters of the rock blocks on the slope is the high-temperature and high-pressure gas generated by the explosion of explosives. Therefore, the rock blasting process is divided into two stages. The first stage is that the rock mass within the volume of the explosive charge is fractured into blocks under the action of the shock wave, stress wave and expansion pressure generated by the explosion. The second stage is that the fractured rock mass is accelerated by the explosive gas until the velocity reaches its maximum. The velocity at this time is the initial throwing parameter. From the physical process, we know that the slope motion parameters are only related to the explosive gas pressure and the resistance line, and are not related to the physical and mechanical properties of the rock (because the rock is formed by the pushing action of the explosive gas after the fracture process is completed). Based on this, the velocity function relationship of the slope block motion is established. Since the acceleration process of the rock blocks on the slope driven by the explosive gas is a dynamic process, an analytical solution cannot be obtained. The velocity of the rock block corresponding to the minimum resistance line under two-dimensional conditions is calculated using the discrete element method, and the value is extended to three-dimensional conditions according to the different characteristic resistance lines to obtain the slope motion parameters of the block.

[0058] As a preferred option, ore specimens include drill cores and rock blocks taken from pits / trench exploration. No artificial cracks are allowed in the specimen preparation process, and standard cylindrical specimens are made according to the specifications.

[0059] As a preferred approach, the two-dimensional discrete element model is built based on open-source discrete element simulation tools, including Yade and ESYS-Particle tools, as well as large-scale commercial software.

[0060] As a preferred option, the formula for the velocity function relationship of the slope block movement is:

[0061] V = f(E, W) = 0.116Q 1.4 W -0.7

[0062] In the formula, V is the velocity of the slope block movement; f(*) is the fitting function; E is the explosive energy parameter; W is the characteristic resistance line parameter of the target point; and Q is the explosive energy calculation factor.

[0063] Preferably, the characteristic resistance line of the target point is selected as the average distance from the centroid of all equivalent ball-shaped propellant charges to the target point, and the formula is:

[0064]

[0065] In the formula, W is the characteristic resistance line parameter of the target point; w iLet be the distance from the centroid of the i-th equivalent ball explosive charge to the centroid of the slope block at the target point; i is the equivalent ball explosive charge indicator; I is the total number of equivalent ball explosive charges; n is the total number of slope blocks; along the step height direction, the slope is evenly divided into 100 cubic blocks, and the size of a single cubic block is 0.1m. Therefore, the number of columns that can be formed along the hole spacing direction is (3 / 2-0.05) / 0.1=14.5, rounded to 14, 14 columns on one side, plus the middle column and the other side column, for a total of 29 columns of blocks, totaling n=2900 blocks;

[0066] The formula for calculating the energy factor of explosives is:

[0067] Q = 0.25πD 2 ρ E

[0068] In the formula, Q is the explosive energy calculation factor; D is the borehole diameter; ρ E This represents the density of the explosive.

[0069] Preferably, the formula for the initial throwing angle of the block in the two-dimensional case is:

[0070]

[0071] In the formula, α is the initial throwing angle of the block in the two-dimensional case; α ij For characteristic resistance line W ij Direction angle; W ij The characteristic resistance line from the i-th equivalent ball charge to the j-th block on the slope is obtained based on the relative position of the centroid of each ball charge and the centroid of the slope block; n is the total number of slope blocks; i is the equivalent ball charge indicator; j is the block indicator.

[0072] Preferably, in the two-dimensional case, an XOZ two-dimensional plane is provided, the velocity of the center of mass of the block (x0, z0) is V0, and the initial throwing angle on the XOZ plane is α. In the three-dimensional case, a YOZ two-dimensional plane is provided perpendicular to the XOZ two-dimensional plane, adding the Y direction. The initial throwing velocities of the block (x0, y0, z0) in each direction are:

[0073]

[0074] In the formula, V 0x V represents the initial throwing velocity component in the X direction; 0y V represents the initial throwing velocity component in the Y direction; 0z Let be the initial throwing velocity component in the Z direction; α be the initial throwing angle in the XOZ plane; and V0 be the center-of-mass velocity of the block (x0, y0, z0) in the two-dimensional case.

[0075] The initial throwing velocities of block (x0, y1, z0) at the same horizontal height as block (x0, y0, z0) in each direction are:

[0076]

[0077] In the formula, V 1x V represents the initial throwing velocity component in the X direction; 1y V represents the initial throwing velocity component in the Y direction; 1z α is the initial throwing velocity component in the Z direction; β is the initial throwing angle in the XOZ plane; V1 is the deviation angle in the XOY plane; and V1 is the centroid velocity of the block (x0, y1, z0) in three dimensions.

[0078] As a preferred option, the formula for the deviation angle is:

[0079]

[0080] In the formula, β is the deviation angle on the XOY plane; y1 is the coordinate of the block (x0, y1, z0) in the Y direction; y0 is the coordinate of the block (x0, y0, z0) in the Y direction; W0 is the characteristic resistance line of the block (x0, y0, z0); W is the characteristic resistance line parameter of the target point.

[0081] The formula for the velocity of the center of mass of a block (x0, y1, z0) in three dimensions is:

[0082] V1 = (W0 / W) 3 V0

[0083] In the formula, V1 is the centroid velocity of the block (x0, y1, z0) in three dimensions; W0 is the characteristic resistance line of the block (x0, y0, z0); W is the characteristic resistance line parameter of the target point; and V0 is the centroid velocity of the block (x0, y0, z0) in two dimensions.

[0084] As a preferred option, the formula for the coordinates of the block at different times after it is thrown is:

[0085]

[0086] In the formula, (x′, y′, z′) are the coordinates of the block at different times after it is thrown; (x original ,y original ,z original Let x be the initial coordinates of the block before it is thrown, where x is the initial coordinates of the block before it is thrown. original =0; V x V y V z denoted as the initial throwing velocities of the block in each direction; g is the gravitational acceleration; t is the time indicator.

[0087] The present invention provides a method for obtaining slope motion parameters in open-pit blasting. This method employs two-dimensional numerical calculations to account for the influence of factors such as detonation method, charge structure, and free surface on the motion parameters. Compared to the three-dimensional mechanical calculation methods used in large commercial software, it offers better computational efficiency, saves computational resources, and is simple and easy to implement in a program. Furthermore, the efficient and high-precision prediction of slope motion parameters can better optimize blasting design, reduce blasting accidents caused by flyrock, and improve blasting efficiency and economic benefits.

[0088] This invention is not limited to the optional embodiments described above, and anyone can derive other various forms of products based on the inspiration of this invention. The specific embodiments described above should not be construed as limiting the scope of protection of this invention; the scope of protection of this invention should be determined by the claims, and the specification can be used to interpret the claims.

Claims

1. A method for obtaining motion parameters of a bench slope in open-pit blasting, characterized in that: Includes the following steps: Ore specimens are extracted from the area to be blasted, and physical and mechanical property tests are conducted on the ore specimens to obtain the physical and mechanical property parameters of the medium to be blasted in the area to be blasted, i.e., lithological parameters. Based on the lithological parameters of the medium to be blasted and the explosive parameters of the explosive to be used, a two-dimensional discrete element model of the load volume of a single explosive charge set in the area to be blasted is constructed, and the initial velocity data of the blocks on the slope of the blasting step are obtained based on the two-dimensional discrete element model. The characteristic resistance line and explosive energy of the two-dimensional discrete element model are obtained, and the characteristic resistance line and explosive energy are fitted with the initial motion velocity data of the block to construct the functional relationship of the motion velocity of the slope block; Based on the two-dimensional discrete element model, the centroid velocities of all blocks on the slope surface of the entire step are obtained according to the velocity function relationship of the slope block motion in the two-dimensional case. In the two-dimensional discrete element model, a single explosive charge is equivalent to several ball-shaped explosive charges. The centroid coordinates of the slope blocks in the two-dimensional discrete element model are obtained. Based on the relative position of each ball-shaped explosive charge and the centroid coordinates of each slope block, the initial throwing angle of all blocks on the slope of the entire step in the two-dimensional case is obtained. Based on the initial throwing angle and the centroid velocity of all blocks on the slope of the entire step in two dimensions, the initial throwing velocity and coordinates of all blocks on the slope of the entire step in three dimensions in each direction are obtained. The initial throwing velocity and coordinates at different times after throwing in each direction constitute the slope motion parameters of the blocks.

2. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 1, characterized in that: The ore specimens include drill cores and rock blocks taken from pits / trench exploration.

3. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 2, characterized in that: The lithological parameters include the density, compressive strength, tensile strength, Young's modulus, and longitudinal wave velocity of the medium to be blasted.

4. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 3, characterized in that: The two-dimensional discrete element model is built based on open-source discrete element simulation tools, including Yade and ESyS-Particle.

5. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 4, characterized in that: The formula for the velocity function relationship of the slope block movement is as follows: V=f(E,W)=0.116Q 1.4 W -0.7 In the formula, V is the velocity of the slope block movement; f(*) is the fitting function; E is the explosive energy parameter; W is the characteristic resistance line parameter of the target point; and Q is the explosive energy calculation factor.

6. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 5, characterized in that: The formula for the characteristic resistance line of the target point is: In the formula, W is the characteristic resistance line parameter of the target point; w i Let be the distance from the centroid of the i-th equivalent ball explosive charge to the centroid coordinates of the slope block at the target point; i is the equivalent ball explosive charge indicator; I is the total number of equivalent ball explosive charges; n is the total number of slope blocks; The formula for the explosive energy calculation factor is as follows: Q=0.25πD 2 r E In the formula, Q is the explosive energy calculation factor; D is the borehole diameter; ρ E This represents the density of the explosive.

7. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 6, characterized in that: The formula for the initial throwing angle of the block in the two-dimensional case is: In the formula, α is the initial throwing angle of the block in the two-dimensional case; α ij For characteristic resistance line W ij Direction angle; W ij The characteristic resistance line from the i-th equivalent ball charge to the j-th block on the slope is obtained based on the relative position of the centroid of each ball charge and the centroid of the slope block; n is the total number of slope blocks; i is the equivalent ball charge indicator; j is the block indicator.

8. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 7, characterized in that: In the two-dimensional case, an XOZ plane is set, the velocity of the center of mass of the block (x0, z0) is V0, and the initial throwing angle on the XOZ plane is α. In the three-dimensional case, a YOZ plane is set perpendicular to the XOZ plane, and the Y direction is added. The initial throwing velocities of the block (x0, y0, z0) in each direction are: In the formula, V 0x V represents the initial throwing velocity component in the X direction; 0y V represents the initial throwing velocity component in the Y direction; 0z Let be the initial throwing velocity component in the Z direction; α be the initial throwing angle in the XOZ plane; and V0 be the center-of-mass velocity of the block (x0, y0, z0) in the two-dimensional case. The initial throwing velocities of block (x0, y1, z0) at the same horizontal height as block (x0, y0, z0) in each direction are: In the formula, V 1x V represents the initial throwing velocity component in the X direction; 1y V represents the initial throwing velocity component in the Y direction; 1z α is the initial throwing velocity component in the Z direction; β is the initial throwing angle in the XOZ plane; V1 is the deviation angle in the XOY plane; and V1 is the centroid velocity of the block (x0, y1, z0) in three dimensions.

9. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 8, characterized in that: The formula for the deviation angle is: In the formula, β is the deviation angle on the XOY plane; y1 is the coordinate of the block (x0, y1, z0) in the Y direction; y0 is the coordinate of the block (x0, y0, z0) in the Y direction; W0 is the characteristic resistance line of the block (x0, y0, z0); W is the characteristic resistance line parameter of the target point. The formula for the center-of-mass velocity of the block (x0, y1, z0) in the three-dimensional case is as follows: V1=(W0 / W) 3 V0 In the formula, V1 is the centroid velocity of the block (x0, y1, z0) in three dimensions; W0 is the characteristic resistance line of the block (x0, y0, z0); W is the characteristic resistance line parameter of the target point; and V0 is the centroid velocity of the block (x0, y0, z0) in two dimensions.

10. The method for obtaining step slope motion parameters applied to open-pit blasting according to claim 9, characterized in that: The formula for the coordinates of the block at different times after it is thrown is: In the formula, (x', y', z') are the coordinates of the block at different times after it is thrown; (x original y original , z original Let x be the initial coordinates of the block before it is thrown, where x is the initial coordinates of the block before it is thrown. original =0; V x V y V z denoted as the initial throwing velocities of the block in each direction; g is the gravitational acceleration; t is the time indicator.

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