An open-pit mine blasting block size prediction method based on an explosion seismic source model

Abstract

This invention belongs to the field of engineering blasting technology and discloses a method for predicting the block size of open-pit mine blasting based on an explosion source model. The method includes the following steps: constructing a spherical charge explosion source model and obtaining the wave equation under spherical symmetry conditions; obtaining the time-position function of particle displacement in the medium; establishing the equivalent relationship between spherical charges based on spherical charges and cylindrical charges based on explosive charges; obtaining the strain at each point on the step from each equivalent spherical charge; obtaining the stress at each point in each direction; obtaining the average energy density value of the total stress wave at each point; dividing the energy density into several energy density levels according to the numerical value; obtaining the block size corresponding to each energy density level; obtaining the undersize accumulation rate; and constructing a block size distribution curve based on all undersize accumulation rates, i.e., the block size prediction result. This invention solves the problems of low computational efficiency and accuracy, poor flexibility of application, and inability to reflect the physical process of explosive damage to rock in existing technologies.

Description

Technical Field

[0001] This invention belongs to the field of engineering blasting technology, specifically relating to a method for predicting the block size of blasting in open-pit mines based on an explosion source model. Background Technology

[0002] Rock blasting is a fundamental construction process in water conservancy and hydropower projects, mining, and transportation. During rock blasting excavation, a large amount of blasted rock fragments are formed. The size of the blasted rock fragments is a microscopic component of the blast pile morphology, and its size is a crucial indicator for evaluating blasting effectiveness. It affects subsequent loading, transportation, secondary crushing, subsequent mineral processing, and economic benefits, and even the safety of mine workers. Therefore, rapid and accurate identification of blasted rock fragment size, and using it as a result-oriented approach to optimize blasting design parameters, has a positive impact on all aspects of open-pit mining blasting.

[0003] The most widely used blasting block size prediction models in engineering practice are the Kuz-Ram block size prediction model and the Swebrec model. These traditional models are derived from mining practice experience and are empirical models. However, they are simple in form and have single parameters, making them unable to consider complex engineering projects with influencing factors such as charge structure and free surfaces. In practical engineering applications, they have significant errors and poor flexibility. With the development of artificial intelligence technology in recent years, various block size prediction methods based on neural networks, support vector machines, and other models have emerged. Artificial intelligence methods are based on statistical theory and do not involve the physical and mechanical processes of blasting. The models are in a "black box" and are only applicable to mines with abundant blasting data. The prediction error is large for newly opened mines or mines with less blasting data. Limited by computing resources, existing finite element and discrete element software have low computational efficiency, and the size of the mesh or particles directly affects the blasting block size prediction results. Summary of the Invention

[0004] To address the problems of low computational efficiency and accuracy, poor flexibility of application, and inability to reflect the physical processes of explosive damage to rocks in existing technologies, the present invention aims to provide a method for predicting the block size of blasting in open-pit mines based on an explosion source model.

[0005] The technical solution adopted in this invention is as follows:

[0006] A method for predicting the blasting block size in open-pit mines based on an explosion source model includes the following steps:

[0007] Based on the spherical coordinate system with the center of the basic spherical explosive charge as the origin, a spherical explosive charge explosion source model is constructed, and based on the spherical explosive charge explosion source model, the wave equation under spherical symmetry conditions is obtained;

[0008] Based on the boundary conditions and initial conditions of each zone in the spherical charge explosion source model, the wave equation is solved to obtain the time position function of the particle displacement in the medium.

[0009] Establish an equivalence relationship between ball-shaped propellant charges based on ball-shaped propellant packs and column-shaped propellant charges based on propellant columns, and equate the propellant column in the column-shaped propellant charge case to several ball-shaped propellant packs in the ball-shaped propellant charge case;

[0010] Based on the time-position function of particle displacement, and according to the blasting design parameters, the sphere-cylinder equivalent relationship, and the wave reflection law, the strain of each point on the step from each equivalent spherical explosive charge is obtained.

[0011] The step is divided into several blocks, and the centroid of each block is used as the coordinate point of the block. Based on the corresponding strain, the stress in each direction at each point is obtained.

[0012] Based on the stress in each direction at each point, the average energy density value of the total stress wave at each point in the grid formed by all points of the step is obtained.

[0013] Based on the average energy density value of the total stress wave at each point, the energy density is divided into several levels according to the numerical value, and the number of spatial points in each interval is counted.

[0014] Based on the energy density level, the corresponding number of spatial points, and the energy required to generate a unit of new surface, the block size corresponding to the energy density level is obtained;

[0015] Based on each block size and its volume, the corresponding undersize cumulative rate is obtained, and based on all undersize cumulative rates, a block size distribution curve is constructed, which is the block size prediction result.

[0016] Furthermore, the wave equation under spherical symmetry conditions is formulated as follows:

[0017]

[0018] In the formula, u is displacement; c is longitudinal wave velocity; r is radial distance from the origin; and t is time.

[0019] Furthermore, the formula for the time-position function of the particle displacement is:

[0020]

[0021] In the formula, U(r',t) is the displacement function of a particle at a distance r from the explosion source at time t; ρ soil ρ is density; c is sound velocity; b0 is the radius of the spherical blast cavity; r' is the straight-line distance from the center of the blast source to the target point; P is blast pressure; κ and η are intermediate parameters; t is the time indication.

[0022] Furthermore, the boundary conditions for each zone are as follows: the compressive stress at the interface between the fractured zone and the fissure zone is equal to the compressive strength of the rock, and the stress at both ends of the interface is set to be equal according to the principle of continuity; the tensile stress at the interface between the fissure zone and the elastic zone is equal to the tensile strength of the rock, and the stress at both ends of the interface is set to be equal according to the principle of continuity.

[0023] The initial condition is: the particle displacement U(r',0) at time t=0 is 0.

[0024] Furthermore, the equivalent relationship between spherical and cylindrical charges is a volume equivalence relationship, meaning that the volume of a unit length of cylindrical charge is equivalent to the volume of a unit length of spherical charge superimposed on top of each other. The equivalent formula is:

[0025]

[0026] In the formula, r1 is the original cylinder radius; r2 is the equivalent sphere radius.

[0027] Furthermore, the stresses at each point in each direction, including the normal stresses and corresponding shear stresses in the three directions of the spherical coordinate system (r, θ, φ), are the sum of the stress components of the direct wave, the reflected longitudinal wave, and the reflected transverse wave.

[0028] The formula for the stress components from the direct wave is:

[0029]

[0030] In the formula, σ r,dp λ is the normal stress component in the r direction from the direct wave; r' is the straight-line distance from the center of the explosion source to the target point; λ is Lamé's first constant; μ is Lamé's second constant; t dp It is the time it takes for the direct wave to reach the target point; u0(t) dp ) for t dp The displacement of particles at the time-bound cavity boundary; u p (r') represents the particle displacement corresponding to the distance r'; v0(t) dp ) for t dp The vibrational velocity of the particles at the boundary of the burst cavity over time; C L u is the propagation velocity of elastic longitudinal waves in rock mass. r (r',t dp ) represents the distance in the direction r at r', τ dp Displacement of a particle corresponding to time;

[0031]

[0032] In the formula, σ θ,dp σ φ,dp These are the normal stress components in the θ and φ directions, respectively, originating from the direct wave;

[0033] τ rθ,dp =τ θφ,dp =τ rφ,dp =0

[0034] In the formula, τ rθ,dp τ θφ,dp τ rφ,dp These are the shear stress components in the r, θ, and φ directions, respectively, originating from the direct wave;

[0035] The formula for the stress components from the reflected longitudinal wave is:

[0036]

[0037] In the formula, σ r,rp λ represents the normal stress component in the r direction from the reflected longitudinal wave; r' is the straight-line distance from the center of the explosion source to the target point; λ is Lamé's first constant; μ is Lamé's second constant; i is the indicator quantity of the virtual explosion source related characteristic parameters about free-plane symmetry; t rp u0(t) represents the time it takes for the reflected longitudinal wave to travel to the target point. rp ) for t rp The displacement of particles at the time-bound cavity boundary; u pi (r' i ) is r' i The displacement of the particle corresponding to the distance; For t rp The vibrational velocity of the particles at the boundary of the burst cavity over time; v rp (r' i ,t rp ) represents the direction of r in r' i Distance, τ rp Displacement of the particle corresponding to time; C L This represents the propagation velocity of elastic longitudinal waves in the rock mass medium.

[0038]

[0039] In the formula, σ θ,rp σ φ,rp These are the normal stress components in the θ and φ directions, respectively, from the reflected longitudinal wave;

[0040]

[0041] In the formula, τ rφ,rp τ rθ,rp τ θφ,rp These are the shear stress components in the r, θ, and φ directions, respectively, originating from the reflected longitudinal wave;

[0042] The formula for the stress components from the reflected transverse wave is:

[0043]

[0044] In the formula, σ r,rs λ represents the normal stress component in the r direction from the reflected shear wave; r' is the straight-line distance from the center of the explosion source to the target point; λ is Lamé's first constant; i is the indicator quantity of the virtual explosion source related characteristic parameters about free-plane symmetry; t rs u0(t) represents the time it takes for the reflected transverse wave to travel to the target point. rs ) for t rs The displacement of particles at the time-bound cavity boundary; u sp (r' i The displacement of the particle caused by the reflected transverse wave at a distance r' is the vibrational displacement of the particle.

[0045]

[0046] In the formula, σ θ,rs θ represents the normal stress component in the θ direction from the reflected transverse wave; μ is Lamé's second constant.

[0047]

[0048] In the formula, σ φ,rs This represents the normal stress component in the φ direction from the reflected transverse wave;

[0049]

[0050] τ θψ,rs =τ rθ,rs =0

[0051] In the formula, τ rψ,rs φ rθ,rs τ θψ,rs These are the shear stress components from the reflected transverse wave in the r, θ, and φ directions, respectively; C L This represents the propagation velocity of elastic longitudinal waves in the rock mass medium. For t rs The vibration velocity of the particles at the explosion cavity of a free-face symmetrical explosion source at any given moment.

[0052] Furthermore, the formula for the average energy density value is:

[0053]

[0054] In the formula, U p The average energy density value; K is a parameter given by the user; t p U is the period of the elastic wave; j is the indicator quantity; m is the equivalent number of spherical charges; n is the number of free surfaces; U 0,j (δ) represents the specific strain energy of the stress wave reaching the j-th point of the step at time δ. The specific strain energy is obtained based on the stress at that point.

[0055] Furthermore, based on the energy density level, the corresponding number of spatial points, and the energy required to generate a unit of new surface, the block size corresponding to the energy density level is obtained, including the following steps:

[0056] The volume corresponding to an energy density level is obtained by the ratio of the number of spatial points corresponding to the energy density level to the total number of spatial points.

[0057] The corresponding block size is obtained based on the energy density level, the corresponding volume, the average block size, and the energy required to produce a unit of new surface.

[0058] Furthermore, the formula for block size is:

[0059]

[0060] In the formula, d i V represents the block size corresponding to the i-th energy density level; i (e i (e) represents the energy density level. i The corresponding volume; c s c is the area index; v S is the volume index; i The corresponding distribution density for generating a new surface; q is the energy required to generate a unit of new surface; e i is the energy density level; i is the indicator quantity.

[0061] Furthermore, the formula for the cumulative rate of screening is:

[0062]

[0063] In the formula, F i (d j ≤d i V represents the cumulative percentage of cells not screened out; j (e j (e) represents the energy density level. j The corresponding volume; d j d i All are block size; i and j are both indicator values; J is the total number of energy density levels.

[0064] The beneficial effects of this invention are as follows:

[0065] The open-pit mine blasting block size prediction method based on the explosion source model provided by this invention can take into account the influence of factors such as explosive properties, charge structure and free surface on blasting block size. It has higher prediction accuracy than traditional methods. Its prediction process is transparent, avoiding the "black box" nature of artificial intelligence methods. It better reflects the physical process of explosive damage to rocks. Moreover, the prediction method is simple to use and easy to program. It has better computational efficiency compared with discrete element and finite element calculation methods.

[0066] Other beneficial effects of the present invention will be further explained in the specific embodiments. Attached Figure Description

[0067] Figure 1 This is a flowchart of the open-pit mine blasting block size prediction method based on the explosion source model in Example 1.

[0068] Figure 2 This is a block size distribution curve of Example 1. Detailed Implementation

[0069] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0070] Example 1:

[0071] like Figure 1 As shown in the figure, this embodiment provides a method for predicting the blasting block size in open-pit mines based on an explosion source model, including the following steps:

[0072] Based on the spherical coordinate system (r,θ,φ) with the center of the basic spherical explosive charge as the origin, a spherical explosive charge explosion source model is constructed, and based on the spherical explosive charge explosion source model, the wave equation under spherical symmetry conditions is obtained;

[0073] The formula for the wave equation under spherical symmetry is:

[0074]

[0075] In the formula, u is displacement; c is longitudinal wave velocity; r is radial distance from the origin; and t is time.

[0076] Based on the boundary conditions and initial conditions of each zone in the spherical charge explosion source model, the wave equation is solved to obtain the time position function of the particle displacement in the medium.

[0077] The formula for the time-position function of particle displacement is:

[0078]

[0079] In the formula, U(r',t) is the displacement function of a particle at a distance r from the explosion source at time t; ρ soil ρ is density; c is sound velocity; b0 is the radius of the spherical blast cavity; r' is the straight-line distance from the center of the blast source to the target point; P is blast pressure; κ and η are intermediate parameters; t is the time indication.

[0080] Establish an equivalence relationship between ball-shaped propellant charges based on ball-shaped propellant packs and column-shaped propellant charges based on propellant columns, and equate the propellant column in the column-shaped propellant charge case to several ball-shaped propellant packs in the ball-shaped propellant charge case;

[0081] The boundary conditions for each zone are as follows: the compressive stress at the interface between the fractured zone and the fissure zone is equal to the compressive strength of the rock, and the stress at both ends of the interface is set to be equal according to the principle of continuity; the tensile stress at the interface between the fissure zone and the elastic zone is equal to the tensile strength of the rock, and the stress at both ends of the interface is set to be equal according to the principle of continuity.

[0082] The initial condition is: the particle displacement U(r',0) at t=0 is 0;

[0083] The equivalent relationship between spherical and cylindrical charges is a volume equivalence relationship, meaning that the volume of a unit length of cylindrical charge is equivalent to the volume of a unit length of spherical charge superimposed on top of each other. The equivalent formula is:

[0084]

[0085] In the formula, r1 is the original cylinder radius; r2 is the equivalent sphere radius; the borehole diameter is 300 mm. The total length of the propellant column is 10m, and the number of equivalent spherical charges is 27. Therefore, a single column charge can be equivalent to the stack of 27 spherical charges with a radius of 183.7mm.

[0086] Based on the time-position function of particle displacement, and according to the blasting design parameters, the spherical-cylinder equivalence relationship, and the wave reflection law, the strain at each point on the step from each equivalent spherical charge is obtained. The blasting design parameters are: borehole diameter 300mm, step height 12m, over-depth 2m, charge length 10m, base resistance line 8m, borehole spacing 8m, step slope angle 90 degrees; using ammonium nitrate fuel oil (ANFO) explosive, detonation velocity 3500m / s, density 1g / cm³. 3 Rock parameters: P-wave velocity 5500 m / s, density 3 g / cm³ 3 The surface energy per unit area is 15000 J / m². 2 ;

[0087] 1m 3 The step is divided into several blocks based on the volume cube as the basic size. The centroid of each block is used as the coordinate point of the block, and the stress in each direction at each point is obtained according to the corresponding strain.

[0088] The stresses experienced at each point in each direction include the normal stresses and corresponding shear stresses in the three directions of the spherical coordinate system (r, θ, φ). The total stress wave is the sum of the stress components of the direct wave, the reflected longitudinal wave, and the reflected transverse wave. In this embodiment, the plugging length and the resistance line length in the charge parameters are 2m and 8m, respectively. The reflected wave sources are set at positions 2m from the top free surface and 8m from the slope. Under the conditions of this embodiment, the effects of one incident longitudinal wave, two reflected longitudinal waves, and two reflected transverse waves are obtained, respectively.

[0089] The formula for the stress components from the direct wave is:

[0090]

[0091] In the formula, σ r,dp λ is the normal stress component in the r direction from the direct wave; r' is the straight-line distance from the center of the explosion source to the target point; λ is Lamé's first constant; μ is Lamé's second constant; t dp It is the time it takes for the direct wave to reach the target point; u0(t) dp ) for t dp The displacement of particles at the time-bound cavity boundary; u p (r') represents the particle displacement corresponding to the distance r'; v0(t) dp ) for t dp The vibrational velocity of the particles at the boundary of the burst cavity over time; C L u is the propagation velocity of elastic longitudinal waves in rock mass. r (r',t dp ) represents the distance in the direction r at r', τ dp Displacement of a particle corresponding to time;

[0092]

[0093] In the formula, σ θ,dp σ φ,dp These are the normal stress components in the θ and φ directions, respectively, originating from the direct wave;

[0094] τ rθ,dp =τ θφ,dp =τ rφ,dp =0

[0095] In the formula, τ rθ,dp τ θφ,dp τ rφ,dp These are the shear stress components in the r, θ, and φ directions, respectively, originating from the direct wave;

[0096] The formula for the stress components from the reflected longitudinal wave is:

[0097]

[0098] In the formula, σ r,rp λ represents the normal stress component in the r direction from the reflected longitudinal wave; r' is the straight-line distance from the center of the explosion source to the target point; λ is Lamé's first constant; μ is Lamé's second constant; i is the indicator quantity of the virtual explosion source related characteristic parameters about free-plane symmetry; t rp The time it takes for the reflected longitudinal wave to travel to the target point; u0(t) rp ) for t rp The displacement of particles at the time-bound cavity boundary; u pi (r' i ) is r' iThe displacement of the particle corresponding to the distance; For t rp The vibrational velocity of the particles at the boundary of the burst cavity over time; v rp (r' i ,t rp ) represents the direction of r in r' i Distance, τ rp Displacement of the particle corresponding to time; C L This represents the propagation velocity of elastic longitudinal waves in the rock mass medium.

[0099]

[0100] In the formula, σ θ,rp σ φ,rp These are the normal stress components in the θ and φ directions, respectively, from the reflected longitudinal wave;

[0101]

[0102] In the formula, τ rφ,rp τ rθ,rp τ θφ,rp These are the shear stress components in the r, θ, and φ directions, respectively, originating from the reflected longitudinal wave;

[0103] The formula for the stress components from the reflected transverse wave is:

[0104]

[0105] In the formula, σ r,rs λ represents the normal stress component in the r direction from the reflected shear wave; r' is the straight-line distance from the center of the explosion source to the target point; λ is Lamé's first constant; i is the indicator quantity of the virtual explosion source related characteristic parameters about free-plane symmetry; t rs u0(t) represents the time it takes for the reflected transverse wave to travel to the target point. rs ) for t rs The displacement of particles at the time-bound cavity boundary; u sp (r' i The displacement of the particle caused by the reflected transverse wave at a distance r' is the vibrational displacement of the particle.

[0106]

[0107] In the formula, σ θ,rs θ represents the normal stress component in the θ direction from the reflected transverse wave; μ is Lamé's second constant.

[0108]

[0109] In the formula, σ φ,rs This represents the normal stress component in the φ direction from the reflected transverse wave;

[0110]

[0111] τ θψ,rs =τ rθ,rs =0

[0112] In the formula, τ rψ,rs τ rθ,rs τ θψ,rs These are the shear stress components from the reflected transverse wave in the r, θ, and φ directions, respectively; C L This represents the propagation velocity of elastic longitudinal waves in the rock mass medium. For t rs The vibration velocity of the particles at the explosion cavity at a free-face symmetrical explosion source at any given moment;

[0113] Taking the average value of one wavelength, and based on the stress in each direction at each point, the average energy density value of the sum of stress waves at each point in the grid formed by all points of the step is obtained; the load volume of a single propellant grain is 768 m³. 3 According to 1m 3 The basic volume generates a total of 768 grid points;

[0114] The formula for the average energy density value is:

[0115]

[0116] In the formula, U p The average energy density value; K is a human-given parameter used to compensate for the blasting effect of high-temperature gases on the rock mass, generally taken as 2; t p U is the period of the elastic wave; j is the indicator quantity; m is the equivalent number of spherical charges, m = 27; n is the number of free surfaces, n = 2; U 0,j (δ) represents the specific strain energy of the stress wave reaching the j-th point of the step at time δ. The specific strain energy is obtained based on the stress at that point.

[0117] The formula for specific strain energy is:

[0118]

[0119] In the formula, U0 is the specific strain energy of the stress wave reaching each point on the step; σ r σ θ σ φ Let τ be the normal stress components in the directions r, θ, and φ, respectively; rθ τ θφ τ φr denoted as r, θ, and φ, respectively; v is the Poisson's ratio of the rock mass to be blasted, and E is the elastic modulus of the rock mass to be blasted;

[0120] Based on the average energy density value of the total stress wave at each point, the energy density is divided into several levels according to the numerical value, and the number of spatial points in each interval is counted.

[0121] e1>e2>e3>…>e i >e i+1 >…>e J

[0122] Based on the energy density level, the corresponding number of spatial points, and the energy required to generate a unit of new surface, the block size corresponding to the energy density level is obtained, including the following steps:

[0123] The volume corresponding to an energy density level is obtained by the ratio of the number of spatial points corresponding to the energy density level to the total number of spatial points.

[0124] The corresponding block size is obtained based on the energy density level, the corresponding volume, the average block size of the rock block, and the energy required to generate a unit of new surface area; all the stress wave energy in the stepped rock mass is converted into surface energy for rock destruction to form a new surface area;

[0125] The formula for block size is:

[0126]

[0127] In the formula, d i V represents the block size corresponding to the i-th energy density level; i (e i (e) represents the energy density level. i The corresponding volume; c s c is the area index; v S is the volume index; i The corresponding distribution density for generating a new surface; q is the energy required to generate one unit of new surface, q = 15000 J / m 2 ;e i For energy density level; i is the indicator quantity;

[0128] Based on each block size and its volume, the corresponding undersize cumulative rate is obtained, and based on all undersize cumulative rates, a block size distribution curve is constructed, such as... Figure 2 As shown, this is the block size prediction result; the horizontal axis of the block size distribution curve is the block size, and the vertical axis is the total volume occupied by rock blocks smaller than that size, which is the undersize accumulation rate. The finer the energy density division, the smoother the curve and the higher the accuracy.

[0129] The formula for the cumulative rate of screening is:

[0130]

[0131] In the formula, F i (d j ≤di V represents the cumulative percentage of samples that pass through the screening process; j (e j (e) represents the energy density level. j The corresponding volume; d j d i All are block size; i and j are both indicator values; J is the total number of energy density levels.

[0132] The open-pit mine blasting block size prediction method based on the explosion source model provided by this invention can take into account the influence of factors such as explosive properties, charge structure and free surface on blasting block size. It has higher prediction accuracy than traditional methods. Its prediction process is transparent, avoiding the "black box" nature of artificial intelligence methods. It better reflects the physical process of explosive damage to rocks. Moreover, the prediction method is simple to use and easy to program. It has better computational efficiency compared with discrete element and finite element calculation methods.

[0133] 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 predicting the blasting block size in open-pit mines based on an explosion source model, characterized in that: Includes the following steps: Based on the spherical coordinate system with the center of the basic spherical explosive charge as the origin, a spherical explosive charge explosion source model is constructed, and based on the spherical explosive charge explosion source model, the wave equation under spherical symmetry conditions is obtained; The formula for the wave equation under the spherical symmetry condition is as follows: ； In the formula, For displacement; For longitudinal wave velocity; This is the radial distance from the origin; For time indication; Based on the boundary conditions and initial conditions of each zone in the spherical charge explosion source model, the wave equation is solved to obtain the time position function of the particle displacement in the medium. The formula for the time-position function of the particle displacement is: ； In the formula, for Distance from the epicenter at all times Displacement function of a particle at a given location; Density; Speed ​​of sound; The radius of the spherical explosion cavity; This is the straight-line distance from the center of the explosion's epicenter to the target location; For burst pressure; , These are all intermediate parameters; For time indication; Establish an equivalence relationship between ball-shaped propellant charges based on ball-shaped propellant packs and column-shaped propellant charges based on propellant columns, and equate the propellant column in the column-shaped propellant charge case to several ball-shaped propellant packs in the ball-shaped propellant charge case; Based on the time-position function of particle displacement, and according to the blasting design parameters, the sphere-cylinder equivalent relationship, and the wave reflection law, the strain of each point on the step from each equivalent spherical explosive charge is obtained. The step is divided into several blocks, and the centroid of each block is used as the coordinate point of the block. Based on the corresponding strain, the stress in each direction at each point is obtained. Based on the stress in each direction at each point, the average energy density value of the total stress wave at each point in the grid formed by all points of the step is obtained. Based on the average energy density value of the total stress wave at each point, the energy density is divided into several levels according to the numerical value, and the number of spatial points in each interval is counted. Based on the energy density level, the corresponding number of spatial points, and the energy required to generate a unit of new surface, the block size corresponding to the energy density level is obtained; Based on each block size and its volume, the corresponding undersize cumulative rate is obtained, and based on all undersize cumulative rates, a block size distribution curve is constructed, which is the block size prediction result.

2. The method for predicting the blasting block size in open-pit mines based on an explosion source model according to claim 1, characterized in that: The boundary conditions for each zone are as follows: the compressive stress at the interface between the fractured zone and the fissure zone is equal to the compressive strength of the rock, and the stress at both ends of the interface is set to be equal according to the principle of continuity; the tensile stress at the interface between the fissure zone and the elastic zone is equal to the tensile strength of the rock, and the stress at both ends of the interface is set to be equal according to the principle of continuity. The initial conditions are as follows: displacement of the particle at time t =0.

3. The method for predicting the blasting block size in open-pit mines based on an explosion source model according to claim 2, characterized in that: The equivalent relationship between spherical and cylindrical propellant charges is a volume equivalence relationship, meaning that the volume of a unit length of cylindrical propellant is equivalent to the volume of a unit length of spherical propellant superimposed on top of each other. The equivalent formula is: ； In the formula, The original column radius; The radius is the equivalent sphere radius.

4. The method for predicting the blasting block size in open-pit mines based on an explosion source model according to claim 3, characterized in that: The stresses experienced by each point in each direction, including those in spherical coordinates. The normal stress and corresponding shear stress in three directions, the total stress wave is the sum of the stress components of the direct wave, the reflected longitudinal wave and the reflected transverse wave; The formula for the stress components from the direct wave is: ； In the formula, For the direct wave in Normal stress components in the direction; This is the straight-line distance from the center of the explosion's epicenter to the target location; It is Lamé's first constant; It is Lamé's second constant; It is the time it takes for the direct wave to reach the target point; for Displacement of particles at the boundary of the burst cavity over time; for The displacement of the particle corresponding to the distance; for The vibration velocity of the particles at the boundary of the burst cavity over time; This represents the propagation velocity of elastic longitudinal waves in the rock mass medium. For the r direction in distance, Displacement of a particle corresponding to time; ； In the formula, , They are respectively from direct waves , Normal stress components in the direction; ； In the formula, , , They are respectively from direct waves , , Shear stress components in the direction; The formula for the stress components from the reflected longitudinal wave is: ； In the formula, For the reflected longitudinal wave in Normal stress components in the direction; This is the straight-line distance from the center of the explosion's epicenter to the target location; It is Lamé's first constant; Let be Lamé's second constant; i is an indicator of the virtual explosion source related to free-face symmetry; This is the time it takes for the reflected longitudinal wave to travel to the target point; for Displacement of particles at the boundary of the burst cavity over time; for The displacement of the particle corresponding to the distance; for The vibration velocity of the particles at the boundary of the burst cavity over time; For the r direction in distance, Displacement of a particle corresponding to time; This represents the propagation velocity of elastic longitudinal waves in the rock mass medium. ； In the formula, These are respectively from the reflected longitudinal wave. , Normal stress components in the direction; ； In the formula, , , These are respectively from the reflected longitudinal wave. , , Shear stress components in the direction; The formula for the stress components from the reflected transverse wave is: ； In the formula, For the reflected transverse wave in Normal stress components in the direction; This is the straight-line distance from the center of the explosion's epicenter to the target location; Let be Lamé's first constant; i is an indicator of the virtual explosion source related to free-face symmetry; This is the time it takes for the reflected transverse wave to travel to the target point; for Displacement of particles at the boundary of the burst cavity over time; ; ； In the formula, For the reflected transverse wave in Normal stress components in the direction; It is Lamé's second constant; ； In the formula, For the reflected transverse wave in Normal stress components in the direction; ； ； In the formula, , , These are respectively from the reflected transverse wave. , , Shear stress components in the direction; This represents the propagation velocity of elastic longitudinal waves in the rock mass medium. for The vibration velocity of the particles at the explosion cavity of a free-face symmetrical explosion source at any given moment.

5. The method for predicting the blasting block size in open-pit mines based on an explosion source model according to claim 4, characterized in that: The formula for the average energy density value is: ； In the formula, This represents the average energy density value. Parameters are given by humans; The period of the elastic wave; is the indicator quantity; m is the number of equivalent ball-shaped charges; n is the number of free surfaces; for The specific strain energy of the stress wave reaching point j of the step at time j is obtained from the stress at that point.

6. The method for predicting the blasting block size in open-pit mines based on an explosion source model according to claim 5, characterized in that: Based on the energy density level, the corresponding number of spatial points, and the energy required to generate a unit of new surface, the block size corresponding to the energy density level is obtained, including the following steps: The volume corresponding to an energy density level is obtained by the ratio of the number of spatial points corresponding to the energy density level to the total number of spatial points. The corresponding block size is obtained based on the energy density level, the corresponding volume, the average block size, and the energy required to produce a unit of new surface.

7. The method for predicting the blasting block size in open-pit mines based on an explosion source model according to claim 6, characterized in that: The formula for the block size is: ； In the formula, Let be the block size corresponding to the i-th energy density level; Energy density level The corresponding volume; Area coefficient; This is the volume factor; To generate the corresponding distribution density of the new surface; The energy required to create a unit of new surface area; Energy density level; For indication.

8. The method for predicting the blasting block size in open-pit mines based on an explosion source model according to claim 7, characterized in that: The formula for the cumulative rate of under-screening is: ； In the formula, Cumulative rate of screening; Energy density level The corresponding volume; , All are block-sized; Both j and j are indicative quantities; This represents the total number of energy density levels.

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