A blasting vibration prediction method based on an explosion source model

Abstract

The application discloses a blasting vibration prediction method based on an explosion source model, obtains vibration waveforms at different positions and distances from a blast center in spherical coordinates based on a spherical charge explosion source model, equivalent column charges are superimposed on multiple spherical charges, vibration waves generated by multiple equivalent spherical charges at space particles are superimposed according to a vibration wave superposition principle, so as to obtain vibration waveforms of space particles under column charge conditions, and considering the existence of a free surface, according to a wave reflection law, a reflected wave can be regarded as an incident wave generated by a virtual explosion source, and the incident wave of a real explosion source and the incident wave generated by a virtual explosion source corresponding to the real explosion source can be superimposed according to the vibration wave superposition principle, so that a complete vibration waveform of a target particle can be obtained, and waveform parameters such as a peak vibration velocity, a frequency and a frequency width can be obtained based on the waveform.

Description

Technical Field

[0001] This invention belongs to the field of blasting, specifically relating to a method for predicting blasting vibrations based on an explosion source model. 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 vibration, air shock waves, noise, occasional flyrock, and toxic gases, which are currently difficult to avoid. Among the harmful effects of blasting, blasting vibration has a wide range of impact and poses a significant threat. Blasting vibration can cause landslides on slopes around mines, roof collapses in tunnel engineering, cracks and collapses in surrounding buildings, and endanger the safety of nearby residential buildings and urban pipelines during urban demolition blasting. Improper prevention and control can lead to huge property losses and casualties, not only causing engineering blasting failure but also resulting in unpredictable legal liabilities. Therefore, effectively predicting blasting vibration and using the predicted data as a guide to optimize blasting design parameters is crucial to controlling blasting vibration within a safe range, reducing its negative impacts, and improving the economic efficiency of blasting projects.

[0003] In engineering practice, the Sadovsky formula is widely used to predict blasting vibrations. The Sadovsky formula can obtain the peak vibration velocity of different particles in the blast zone. Its basic form is exponential decay, and the correlation coefficient and decay exponent are related to blasting conditions, geological and topographical conditions, and are functions of the explosive charge and distance at the same time. The Sadovsky formula is derived from practical experience and is an empirical model. However, its simple form and single parameter make it unsuitable for complex engineering projects that consider factors such as charge structure and free surfaces. In practical engineering applications, obtaining reliable correlation coefficients and decay exponents requires multiple on-site blasting and vibration tests, using regression analysis, which also has significant errors and poor flexibility. With the development of artificial intelligence technology in recent years, vibration prediction using neural networks and machine learning methods has become increasingly common. However, artificial intelligence methods are based on statistical theory and do not involve the physical and mechanical processes of blasting. The models are essentially "black boxes" and are only applicable to mines with abundant blasting data. For newly opened mines or mines with limited blasting data, the prediction error is significant. Limited by computational resources, existing finite element method (FEM) software suffers from low computational efficiency, making its application in engineering practices involving numerous blasting operations extremely difficult. Therefore, a blasting vibration prediction method is needed that is computationally efficient, accurate, transparent to the physical and mechanical processes, and provides a refined representation of the particle vibration process. Summary of the Invention

[0004] In view of the above-mentioned shortcomings in the prior art, the present invention provides a method for predicting blasting vibration based on an explosion source model, which solves the problems existing in the prior art.

[0005] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a method for predicting blasting vibrations based on an explosion source model, comprising:

[0006] The lithological parameters and explosive parameters are obtained, wherein the lithological parameters and explosive parameters are pre-stored data or data input through human-computer interaction;

[0007] Based on the lithological parameters and explosive parameters, an explosion source model is constructed. The explosion source model is used to characterize the vibration velocity-time waveform at any target point at a distance from the explosion source.

[0008] Obtain the blasting design parameters, and construct a Cartesian coordinate system based on the blasting parameters to obtain the cylindrical charge, free surface, and corresponding geometric conditions of the cylindrical charge in the Cartesian coordinate system;

[0009] Based on the column charge and its corresponding geometric conditions, the column charge is equivalent to several spherical charges, and the geometric conditions corresponding to the spherical charges are obtained.

[0010] The target point is determined in the Cartesian coordinate system, and the vibration data generated by the spherical charge on the target point is determined based on the blasting design parameters, the geometric conditions corresponding to the spherical charge, and the blast source model.

[0011] The free surface is equivalent to a virtual explosion source, and the vibration data generated by the virtual explosion source on the target point is obtained based on the geometric conditions corresponding to the spherical charge and the explosion source model.

[0012] Vibration data of the target point is obtained based on the vibration data generated by the spherical charge on the target point and the vibration data generated by the virtual blast source on the target point.

[0013] Furthermore, the lithological parameters include the density of the medium, Poisson's ratio, and longitudinal wave velocity.

[0014] Furthermore, the explosive parameters include the detonation velocity and density of the explosive.

[0015] Furthermore, based on the aforementioned lithological parameters and explosive parameters, the explosion source model is constructed as follows:

[0016]

[0017]

[0018]

[0019]

[0020] Where U(r,t) represents the vibration data of a target point at time t at a straight-line distance r from the center of the explosion source, e represents the natural constant, η represents the first intermediate parameter, τ represents the second intermediate parameter, and ρ represents the second intermediate parameter. soil κ represents the density of the medium, c represents the longitudinal wave velocity, b0 represents the radius of the spherical blast cavity, r represents the straight-line distance from the blast source center to the target point, κ represents the third intermediate parameter, P represents the explosion pressure, σ represents the Poisson's ratio of the rock mass, γ represents the explosive gas constant, and t represents time.

[0021] The explosion pressure P is used to characterize the explosive detonation velocity VOD and the explosive density ρ. e The function is as follows:

[0022] P = ρ e VOD 2 / 8.

[0023] Furthermore, the blasting design parameters include the location of the detonation point, the detonation method, the spacing between blast holes, the row spacing, and the blast hole delay time.

[0024] Furthermore, based on the column charge and its corresponding geometric conditions, the column charge is equivalent to several spherical charges, and the geometric conditions corresponding to the spherical charges are obtained, including:

[0025] The relationship between the radius of a column charge and the radius of a spherical charge is as follows:

[0026]

[0027] Where r1 represents the radius of the spherical charge and r2 represents the radius of the cylindrical charge;

[0028] Based on the geometric conditions and radius relationships of the column charge, and using the principle of volume equivalence, the column charge is equivalent to several spherical charges, and the corresponding geometric conditions of the spherical charges are obtained.

[0029] Furthermore, the target point is determined in a Cartesian coordinate system, and the vibration data generated by the spherical charge on the target point is determined based on the blasting design parameters, the geometric conditions corresponding to the spherical charge, and the blast source model, including:

[0030] In a Cartesian coordinate system, the target point is determined, and the first straight-line distance r1 between the detonation point and the target point is determined based on the position of the detonation point; and the second straight-line distance r2 between each spherical charge and the target point is determined based on the geometric conditions corresponding to the spherical charge; the geometric conditions of the spherical charge are used to characterize the position of the spherical charge in the Cartesian coordinate system.

[0031] Based on the location of the detonation point and the detonation method, the spherical charge at the time of detonation is determined, and the target spherical charge is obtained;

[0032] Based on the target spherical charge and the borehole delay time, the spherical charge that vibrates first and the start time of vibration in each spherical charge are determined. The borehole delay time is used to characterize the start time difference between two adjacent spherical charges.

[0033] Based on the geometric conditions of the spherical charges, determine the distance between any two adjacent spherical charges, and based on the distance between any two spherical charges and the shelling velocity, determine the delay time between any two adjacent spherical charges.

[0034] The start-up time of each ball charge is determined based on the delay time between any two adjacent ball charges, the ball charge that vibrates first in each column charge, the start-up time of the ball charge that vibrates first in each column charge, and the delay time between any two adjacent ball charges.

[0035] Based on the first straight-line distance r1, the second straight-line distance r2, the oscillation time of the spherical charge, and the explosion source model, the vibration data generated by each spherical charge on the target point are determined.

[0036] Furthermore, the free surface is equated to a virtual explosion source, and based on the geometric conditions corresponding to the spherical charge and the explosion source model, the vibration data generated by the virtual explosion source on the target point is obtained, including:

[0037] Based on the free surface, virtual explosion sources are set up in an equivalent manner. The virtual explosion sources are symmetrical with respect to the real explosion sources about the free surface, and the start-up time of each virtual explosion source is the same as that of its corresponding real explosion source. The real explosion sources are used to characterize spherical explosive charges.

[0038] Based on the geometric conditions corresponding to the spherical charge of the virtual explosion source and the explosion source model, the vibration data generated by the virtual explosion source on the target point are obtained.

[0039] Furthermore, based on the vibration data generated at the target point by the spherical charge and the vibration data generated at the target point by the virtual explosion source, vibration data of the target point is obtained, including:

[0040] The vibration data generated by the ball charge at the target point is decomposed into vibration components along the X, Y, and Z axes.

[0041] The vibration data generated by the virtual explosion source on the target point is decomposed into vibration components along the X, Y, and Z axes.

[0042] Obtain the sum of vibration components along the X-axis, the sum of vibration components along the Y-axis, and the sum of vibration components along the Z-axis.

[0043] The vibration data of the target point is obtained based on the sum of the vibration components along the X-axis, Y-axis, and Z-axis.

[0044] Furthermore, based on the sum of vibration components along the X-axis, Y-axis, and Z-axis, the vibration data of the target point is obtained as follows:

[0045]

[0046] Among them, U X U represents the sum of the vibration components along the X-axis. Y U represents the sum of the vibration components along the Y-axis. Z This represents the sum of the vibration components along the Z-axis.

[0047] This invention provides a method for predicting blasting vibration based on an explosion source model. It obtains vibration waveforms at different locations at varying distances from the blast center in spherical coordinates based on a spherical charge explosion source model. A cylindrical charge is equivalent to the superposition of multiple spherical charges. According to the principle of vibration wave superposition, the vibration waves generated by these multiple equivalent spherical charges at spatial particles are superimposed to obtain the vibration waveform of the spatial particles under cylindrical charge conditions. Considering the existence of a free surface, the reflected wave can be considered as an incident wave generated by a virtual blast source (the symmetrical blast source corresponding to the real blast source when the free surface is the symmetrical plane) according to the wave reflection law. By combining the incident wave from the real blast source with the incident wave generated by the corresponding virtual blast source according to the principle of vibration wave superposition, the complete vibration waveform of the target particle can be obtained. Furthermore, waveform parameters such as peak vibration velocity, frequency, and bandwidth can be obtained based on this waveform. Attached Figure Description

[0048] Figure 1 The flowchart shows a method for predicting blasting vibrations based on an explosion source model, which is provided by the present invention.

[0049] Figure 2 This is a schematic diagram of vibration velocity synthesis provided by the present invention. Detailed Implementation

[0050] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0051] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0052] like Figure 1 As shown, a method for predicting blasting vibrations based on an explosion source model includes:

[0053] S1. Obtain lithological parameters and explosive parameters, wherein the lithological parameters and explosive parameters are pre-stored data or data input through human-computer interaction.

[0054] Optionally, staff will extract and sample the soil or ore from the area to be blasted, conduct physical and mechanical property tests in the laboratory, and store the samples in a database for direct retrieval. Test samples can be obtained from borehole cores or rock blocks taken from pits or trenches. Artificial cracks are not permitted during specimen preparation; standard cylindrical specimens should be prepared according to regulations. Rock density tests will use the hydrostatic bottle method or weighing method. Rock compressive strength will be measured using uniaxial compressive strength testing, with a pressure testing machine as the loading device. The Brazilian splitting method will be used to measure the tensile strength of the rock. A pressure machine and strain gauges will be used to determine the static Young's modulus, and an acoustic emission system will be used to determine the longitudinal wave velocity of the rock.

[0055] S2. Based on the lithological parameters and explosive parameters, construct an explosion source model. The explosion source model is used to characterize the vibration velocity-time waveform at any target point at a distance from the explosion source.

[0056] The explosion source model divides the explosion region into three regions: a cavity region, a plastic region, and an elastic region, each describing its own mechanical properties. The model assumes that the mechanical properties of each region are different and that they are in equilibrium at the interfaces. Equilibrium equations are established within each of the different regions and solved separately to obtain the vibration wave parameters at the elastic boundary.

[0057] S3. Obtain the blasting design parameters and construct a Cartesian coordinate system based on the blasting parameters to obtain the cylindrical charge, free surface, and corresponding geometric conditions of the cylindrical charge in the Cartesian coordinate system.

[0058] Blasting design parameters can include borehole spacing and row spacing, thus revealing the relative positions of each charge. Once the coordinates of one charge are determined, the coordinates of the other charges can be determined.

[0059] S4. Based on the column charge and its corresponding geometric conditions, the column charge is equivalent to several spherical charges, and the geometric conditions corresponding to the spherical charges are obtained.

[0060] In this embodiment, volume equivalence is chosen as the equivalent method, meaning the volume of a unit length of cylindrical charge is equivalent to the volume of a unit length of superimposed spherical charge. The equivalent sphere radius is r, and the cylinder radius is r1. This leads to the equation regarding volume, namely... The relationship between the equivalent sphere radius and the cylinder radius is obtained by solving the problem. It is worth noting that the center of the equivalent sphere should coincide with the axis of the cylinder.

[0061] S5. Determine the target point in the Cartesian coordinate system, and determine the vibration data generated by the spherical charge on the target point based on the blasting design parameters, the geometric conditions corresponding to the spherical charge, and the blast source model.

[0062] The setting of the initial blast time is crucial. The vibration process demonstrates the relationship between vibration velocity and time. When there is an initiation point, the actual moment when the equivalent spherical charge at that initiation point begins to vibrate is moment 0. The initial vibration time of the equivalent sphere within the same charge needs to be calculated by dividing its distance from the initial sphere by the detonation velocity of the charge. For smaller spheres not in the same charge as the initial sphere, the initial vibration time must include not only the calculated detonation propagation time but also the inter-bore delay time.

[0063] When the spherical and cylindrical equivalents are used, the cylindrical explosive charges are equivalent to the approximate superposition of spherical charges. Since the spherical explosive charges are in different spatial positions, the relative positions of different spherical explosive charges with a certain point in space are different. The vibration direction of the particle at the spatial position is also different for each explosive charge. Therefore, it is necessary to decompose the vibration of multiple spherical explosive charges. Taking the x and y directions in Cartesian coordinates as an example, they are superimposed separately and finally synthesized to obtain the sum and velocity.

[0064] S6. The free surface is equivalent to a virtual explosion source, and the vibration data generated by the virtual explosion source on the target point is obtained according to the geometric conditions corresponding to the spherical charge and the explosion source model.

[0065] S7. Obtain the vibration data of the target point based on the vibration data generated by the spherical charge on the target point and the vibration data generated by the virtual explosion source on the target point.

[0066] In one possible implementation, the lithological parameters include the density of the medium, Poisson's ratio, and longitudinal wave velocity.

[0067] In one possible implementation, the explosive parameters include the detonation velocity and density of the explosive.

[0068] In one possible implementation, based on the lithological parameters and explosive parameters, the explosion source model is constructed as follows:

[0069]

[0070]

[0071]

[0072]

[0073] Where U(r,t) represents the vibration data of a target point at time t at a straight-line distance r from the center of the explosion source, e represents the natural constant, η represents the first intermediate parameter, τ represents the second intermediate parameter, and ρ represents the second intermediate parameter. soildenoted by ρ, c represents the longitudinal wave velocity, b0 represents the radius of the spherical blast cavity, r represents the straight-line distance from the blast source center to the target point, κ represents the third intermediate parameter, P represents the explosion pressure, σ represents the Poisson's ratio of the rock mass, γ represents the explosive gas constant, and t represents time.

[0074] The explosion pressure P is used to characterize the explosive detonation velocity VOD and the explosive density ρ. e The function is as follows:

[0075] P = ρ e VOD 2 / 8.

[0076] In one possible implementation, the blasting design parameters include the location of the detonation point, the detonation method, the spacing between blast holes, the row spacing, and the blast hole delay time.

[0077] Optionally, the cylindrical charge is detonated at the bottom of the borehole using a detonator. The detonation sequence is determined by the borehole delay time. Currently, electronic detonators use their internal chips to set the detonation delay time. The inter-hole delay time in the blasting parameters means cascade detonation.

[0078] In one possible implementation, based on the column charge and its corresponding geometric conditions, the column charge is equivalent to several spherical charges, and the geometric conditions corresponding to the spherical charges are obtained, including:

[0079] The relationship between the radius of a column charge and the radius of a spherical charge is as follows:

[0080]

[0081] Where r1 represents the radius of the spherical charge and r2 represents the radius of the cylindrical charge.

[0082] Based on the geometric conditions and radius relationships of the column charge, and using the principle of volume equivalence, the column charge is equivalent to several spherical charges, and the corresponding geometric conditions of the spherical charges are obtained.

[0083] In one possible implementation, the target point is determined in a Cartesian coordinate system, and the vibration data generated by the spherical charge on the target point is determined based on the blasting design parameters, the geometric conditions corresponding to the spherical charge, and the blast source model, including:

[0084] In a Cartesian coordinate system, the target point is determined. Based on the location of the detonation point, the first straight-line distance r1 between the detonation point and the target point is determined. Then, based on the geometric conditions corresponding to the spherical charges, the second straight-line distance r2 between each spherical charge and the target point is determined. The geometric conditions of the spherical charges characterize their position in the Cartesian coordinate system.

[0085] Based on the location of the detonation point and the detonation method, the spherical charge at the time of detonation is determined, and the target spherical charge is obtained.

[0086] Based on the target spherical charge and the borehole delay time, the spherical charge that vibrates first and the start time of vibration in each spherical charge are determined. The borehole delay time is used to characterize the start time difference between two adjacent spherical charges.

[0087] Based on the geometric conditions of the spherical charges, determine the distance between any two adjacent spherical charges, and based on the distance between any two spherical charges and the shelling velocity, determine the delay time between any two adjacent spherical charges.

[0088] The oscillation time of each spherical charge is determined based on the delay time between any two adjacent spherical charges, the first vibrating spherical charge in each column charge, the oscillation time of the first vibrating spherical charge in each column charge, and the delay time between any two adjacent spherical charges.

[0089] The detonation time t1 of the detonation point can be determined based on the distance between the detonation point and the target point and the bombardment velocity. The time for the ball charge to reach the target point is the time t1 minus the detonation time t1. Thus, the oscillation data can be determined.

[0090] Based on the first straight-line distance r1, the second straight-line distance r2, the oscillation time of the spherical charge, and the explosion source model, the vibration data generated by each spherical charge on the target point are determined.

[0091] In one possible implementation, the free surface is equivalent to a virtual explosion source, and vibration data generated by the virtual explosion source on the target point is obtained based on the geometric conditions corresponding to the spherical charge and the explosion source model. This includes: setting up virtual explosion sources based on the free surface, wherein the virtual explosion sources are symmetrical to the real explosion sources about the free surface, and the vibration start time of each virtual explosion source is the same as that of its corresponding real explosion source, wherein the real explosion source is used to characterize the spherical charge.

[0092] Based on the geometric conditions corresponding to the spherical charge of the virtual explosion source and the explosion source model, the vibration data generated by the virtual explosion source on the target point are obtained.

[0093] In one possible implementation, vibration data of the target point is obtained based on vibration data generated by the spherical charge on the target point and vibration data generated by the virtual explosive source on the target point, including:

[0094] The vibration data generated by the ball charge at the target point is decomposed into vibration components along the X, Y, and Z axes.

[0095] The vibration data generated by the virtual explosion source on the target point is decomposed into vibration components along the X, Y, and Z axes.

[0096] Obtain the sum of vibration components along the X-axis, the sum of vibration components along the Y-axis, and the sum of vibration components along the Z-axis.

[0097] The vibration data of the target point is obtained based on the sum of the vibration components along the X-axis, Y-axis, and Z-axis.

[0098] In one possible implementation, the vibration data of the target point is obtained based on the sum of the vibration components along the X-axis, the sum of the vibration components along the Y-axis, and the sum of the vibration components along the Z-axis:

[0099]

[0100] Among them, U X U represents the sum of the vibration components along the X-axis. Y U represents the sum of the vibration components along the Y-axis. Z This represents the sum of the vibration components along the Z-axis.

[0101] like Figure 2 As shown, for ease of description, a planar composite velocity is used as an example. At a point A in space, when the seismic wave generated by the explosion of the first equivalent explosive charge reaches point A, its vibration velocity is U1(r1,t1), and the velocity component in the X direction is U. 1X (r1,t1), the velocity component in the y-direction is U 1Y (r1,t1), then:

[0102]

[0103]

[0104] Among them, L X L represents the distance from the equivalent drug packet to the target point in the X direction. Y This represents the distance in the Y direction from the equivalent drug pack to the target point.

[0105] For n equivalent spherical drug packets, then:

[0106] U X (r,t)=U 1X (r1,t1)+U 2X (r2,t2)+...+U nX (r n ,t n )

[0107] U Y (r,t)=U 1Y (r1,t1)+U 2Y (r2,t2)+...+U nY (r n ,t n )

[0108] The resultant velocity is:

[0109]

[0110] The sign of the resultant velocity depends on the vibration direction of the resultant velocity. Since the detonation velocity of the explosive is much greater than the propagation speed of the seismic wave in the rock, the vibration period of a certain point in space is much greater than that of the explosive detonation process. Therefore, the direction of the final resultant velocity is the same as the vibration direction of the seismic wave generated by each spherical explosive charge, and its sign is consistent with the sign of the resultant velocity in the X and Y directions.

[0111] This invention provides a method for predicting blasting vibration based on an explosion source model. It obtains vibration waveforms at different locations at varying distances from the blast center in spherical coordinates based on a spherical charge explosion source model. A cylindrical charge is equivalent to the superposition of multiple spherical charges. According to the principle of vibration wave superposition, the vibration waves generated by these multiple equivalent spherical charges at spatial particles are superimposed to obtain the vibration waveform of the spatial particles under cylindrical charge conditions. Considering the existence of a free surface, the reflected wave can be considered as an incident wave generated by a virtual blast source (the symmetrical blast source corresponding to the real blast source when the free surface is the symmetrical plane) according to the wave reflection law. By combining the incident wave from the real blast source with the incident wave generated by the corresponding virtual blast source according to the principle of vibration wave superposition, the complete vibration waveform of the target particle can be obtained. Furthermore, waveform parameters such as peak vibration velocity, frequency, and bandwidth can be obtained based on this waveform.

[0112] Based on the explosion source model, compared with the traditional cavity expansion model which ignores the nonlinear region generated after the explosion, the explosion source model focuses on the entire process of the generation and development of the nonlinear region after the explosion. The development of the near-field region of the explosion has a direct impact on the vibration of the far-field region of the explosion. A good near-field process can better obtain the vibration data of each mass point in the far-field region.

[0113] This invention can take into account the influence of factors such as initiation mode, charge structure and free surface on blasting vibration, and has higher prediction accuracy than traditional methods. Secondly, the physical process is transparent, avoiding the "black box" nature of artificial intelligence methods, and better reflects the physical process of the explosive's effect on the particles in the far-field of the blast. Finally, the calculation method proposed in this invention is simple and easy to use, convenient to program, and has better computational efficiency than the finite element method.

[0114] Example 2

[0115] This embodiment is based on the scheme described in Embodiment 1, as detailed below.

[0116] This embodiment aims to predict blasting vibration data for bench blasting in open-pit mines. The blasting design parameters are: charge radius of 0.045 meters, inter-hole delay time of 0.005 seconds, plugging length of 5 meters, and charge length of 10 meters; the detonation velocity of the explosive is 6900 meters per second, the charge density is 1650 kg / m³, and the explosive gas constant is 3.15. A blasting vibration prediction method based on an explosion source model is described in this embodiment, and the implementation steps are as follows:

[0117] Step 1: Extract and sample the ore from the area to be blasted, and conduct laboratory physical and mechanical property tests to obtain the physical and mechanical properties of the medium to be blasted, including parameters such as density, compressive strength, tensile strength, Young's modulus, and longitudinal wave velocity. The sample density obtained using the hydrometer bottle method is 2400 kg / m³. 3 The rock compressive strength obtained by uniaxial compressive strength test is 21.1 MPa, the tensile strength of the rock measured by Brazilian splitting method is 1.7 MPa, and the longitudinal wave velocity of the rock measured by acoustic emission system is 1100 m / s.

[0118] Step 2: Based on lithological and explosive parameters, construct an explosion source model to obtain the vibration velocity-time waveform function of a particle at any distance from the explosion source in spherical coordinates. In spherical coordinates (r, θ, φ) with the center of the spherical explosive charge as the origin, the spherically symmetric wave equation is:

[0119]

[0120] Where u is the vibration velocity, r is the distance, c1 is the wave velocity, and t is the time.

[0121] The initial condition is u(t=0)=0, and the boundary condition of the elastic zone is that the tensile stress equals the tensile strength of the rock, and according to the continuity principle, the stresses at both ends of the interface are equal. Solving the equilibrium equations yields the vibration parameters at a distance r from the explosion source:

[0122]

[0123] Step 3: Based on the blasting design parameters, establish a Cartesian coordinate system to obtain the cylindrical charge conditions, free surface, and geometric conditions. Equivalently convert the cylindrical charge to several spherical charges, and the condition of a free surface is equivalent to adding a virtual blast source; with a borehole radius of 0.045m, the equivalent spherical charge radius is... The charge is 10m long, and the equivalent number of spherical charges is 91. Therefore, a single charge can be equivalent to the stack of 91 spherical charges with a radius of 0.055m.

[0124] Step 4: Based on the location of the detonation point, the detonation method (row detonation or V-shaped detonation, etc.), and the inter-bore delay time, calculate the vibration data of the equivalent spherical charge acting on the target point hole by hole. The detonation time of the virtual detonation source equivalent to the free surface is consistent with its symmetrical real detonation source. In this embodiment, bottom detonation is used, so the initial vibration generated by the first equivalent spherical charge at the bottom is at time 0. The inter-bore delay time is 0.005 seconds. Calculate the initial vibration time of the equivalent spherical charge closest to the detonation point for the second charge. Here, the two times need to be added: one is the spatial delay time of 0.005 seconds, and the other is the detonation propagation time of 0.055 × 2 / 6900 = 0.0000015942 s. Therefore, the initial vibration time of this equivalent spherical charge is 0.0050015942 s.

[0125] Step 5: Decompose the multiple vibration velocity-time data obtained in Step 4 into vibration velocity components in three directions in a Cartesian coordinate system based on the relative positional relationship between the equivalent spherical charge and the target point. After decomposing all the vibrations generated by the equivalent spherical charge at the target point, add them together in the three directions to obtain the relationship between the vibration velocity components in the three directions and time at the target point in a Cartesian coordinate system under the condition of multiple cylindrical charges and multiple free surfaces. At a certain point A in space, when the seismic wave generated by the explosion of the first equivalent charge reaches point A, its vibration velocity is U1(r1,t1), and the velocity component in the X direction is U... 1X (r1,t1), the velocity component in the Y direction is U 1Y (r1,t1), the velocity component in the Z direction is U 1Z (r1,t1), then:

[0126]

[0127]

[0128]

[0129] For n spherical medicine packets, then:

[0130] U X (r,t)=U 1X (r1,t1)+U 2X (r2,t2)+...+U nX (r n ,t n )

[0131] U Y (r,t)=U 1Y (r1,t1)+U 2Y (r2,t2)+...+U nY (r n ,t n)

[0132] U Z (r,t)=U 1Z (r1,t1)+U 2Z (r2,t2)+...+U nZ (r n ,t n )

[0133] Step 6: Process the vibration velocity component versus time data obtained in Step 5 to obtain the relationship between the absolute value of vibration and velocity and time, as well as the vibration frequency, bandwidth and other fluctuation parameters.

[0134] The resultant velocity is

[0135] The sign of the resultant velocity depends on the vibration direction of the resultant velocity. Since the detonation velocity of the explosive is much greater than the propagation speed of the seismic wave in the rock, the vibration period of a certain point in space is much greater than that of the explosive detonation process. Therefore, the direction of the final resultant velocity is the same as the vibration direction of the seismic wave generated by each spherical explosive charge, and its sign is consistent with the sign of the resultant velocity in the x, y, and z directions.

Claims

1. A method for predicting blasting vibrations based on an explosion source model, characterized in that, include: The lithological parameters and explosive parameters are obtained, wherein the lithological parameters and explosive parameters are pre-stored data or data input through human-computer interaction; Based on the lithological parameters and explosive parameters, an explosion source model is constructed. The explosion source model is used to characterize the vibration velocity-time waveform at any target point at a distance from the explosion source. Obtain the blasting design parameters, and construct a Cartesian coordinate system based on the blasting parameters to obtain the cylindrical charge, free surface, and corresponding geometric conditions of the cylindrical charge in the Cartesian coordinate system; Based on the column charge and its corresponding geometric conditions, the column charge is equivalent to several spherical charges, and the geometric conditions corresponding to the spherical charges are obtained. The target point is determined in the Cartesian coordinate system, and the vibration data generated by the spherical charge on the target point is determined based on the blasting design parameters, the geometric conditions corresponding to the spherical charge, and the blast source model. The free surface is equivalent to a virtual explosion source, and the vibration data generated by the virtual explosion source on the target point is obtained based on the geometric conditions corresponding to the spherical charge and the explosion source model. Vibration data of the target point is obtained based on the vibration data generated by the spherical charge on the target point and the vibration data generated by the virtual explosion source on the target point; Based on the lithological parameters and explosive parameters, the explosion source model is constructed as follows: ； ； ； ； in, This represents the vibration data of a target point at time t, which is a straight-line distance r from the center of the explosion source. Represents the natural constant. Indicates the first intermediate parameter. This indicates the second intermediate parameter. Indicates the density of the medium. Indicates the longitudinal wave velocity. This represents the radius of the spherical blast cavity. This represents the straight-line distance from the center of the explosion source to the target location. This represents the third intermediate parameter. Indicates the explosion pressure. Indicates the Poisson's ratio of the rock mass. The constant of the explosive gas is represented by t, and time is represented by t. The explosion pressure P is used to characterize the explosive detonation velocity (VOD) and explosive density. The function is as follows: .

2. The method for predicting blasting vibration based on an explosion source model according to claim 1, characterized in that, The lithological parameters include the density of the medium, Poisson's ratio, and longitudinal wave velocity.

3. The method for predicting blasting vibration based on an explosion source model according to claim 2, characterized in that, The explosive parameters include the detonation velocity and density of the explosive.

4. The method for predicting blasting vibration based on an explosion source model according to claim 3, characterized in that, The blasting design parameters include the location of the detonation point, the detonation method, the spacing between blast holes, the row spacing, and the blast hole delay time.

5. The method for predicting blasting vibration based on an explosion source model according to claim 4, characterized in that, Based on the column charge and its corresponding geometric conditions, the column charge is equivalent to several spherical charges, and the geometric conditions corresponding to the spherical charges are obtained, including: The relationship between the radius of a column charge and the radius of a spherical charge is as follows: ； in, Indicates the radius of the spherical charge. Indicates the radius of the charge in the column; Based on the geometric conditions and radius relationships of the column charge, and using the principle of volume equivalence, the column charge is equivalent to several spherical charges, and the corresponding geometric conditions of the spherical charges are obtained.

6. The method for predicting blasting vibration based on an explosion source model according to claim 5, characterized in that, The target point is determined in a Cartesian coordinate system, and the vibration data generated by the spherical charge on the target point is determined based on the blasting design parameters, the geometric conditions corresponding to the spherical charge, and the blast source model, including: In a Cartesian coordinate system, the target point is determined, and the first straight-line distance r1 between the detonation point and the target point is determined based on the position of the detonation point; and the second straight-line distance r2 between each spherical charge and the target point is determined based on the geometric conditions corresponding to the spherical charge; the geometric conditions of the spherical charge are used to characterize the position of the spherical charge in the Cartesian coordinate system. Based on the location of the detonation point and the detonation method, the spherical charge at the time of detonation is determined, and the target spherical charge is obtained; Based on the target spherical charge and the borehole delay time, the spherical charge that vibrates first and the start time of vibration in each spherical charge are determined. The borehole delay time is used to characterize the difference in start time between two adjacent spherical charges. Based on the geometric conditions of the spherical charges, determine the distance between any two adjacent spherical charges, and based on the distance between any two spherical charges and the shelling velocity, determine the delay time between any two adjacent spherical charges. The start-up time of each ball charge is determined based on the delay time between any two adjacent ball charges, the ball charge that vibrates first in each column charge, the start-up time of the ball charge that vibrates first in each column charge, and the delay time between any two adjacent ball charges. Based on the first straight-line distance r1, the second straight-line distance r2, the oscillation time of the spherical charge, and the explosion source model, the vibration data generated by each spherical charge on the target point are determined.

7. The method for predicting blasting vibration based on an explosion source model according to claim 6, characterized in that, The free surface is equated to a virtual blast source, and based on the geometric conditions corresponding to the spherical charge and the blast source model, the vibration data generated by the virtual blast source on the target point is obtained, including: Based on the free surface, virtual explosion sources are set up in an equivalent manner. The virtual explosion sources are symmetrical with respect to the real explosion sources about the free surface, and the start-up time of each virtual explosion source is the same as that of its corresponding real explosion source. The real explosion sources are used to characterize spherical explosive charges. Based on the geometric conditions corresponding to the spherical charge of the virtual explosion source and the explosion source model, the vibration data generated by the virtual explosion source on the target point are obtained.

8. The method for predicting blasting vibration based on an explosion source model according to claim 7, characterized in that, Based on the vibration data generated at the target point by the spherical charge and the vibration data generated at the target point by the virtual blast source, the vibration data of the target point is obtained, including: The vibration data generated by the ball charge at the target point is decomposed into vibration components along the X, Y, and Z axes. The vibration data generated by the virtual explosion source on the target point is decomposed into vibration components along the X, Y, and Z axes. Obtain the sum of vibration components along the X-axis, the sum of vibration components along the Y-axis, and the sum of vibration components along the Z-axis. The vibration data of the target point is obtained based on the sum of the vibration components along the X-axis, Y-axis, and Z-axis.

9. The method for predicting blasting vibration based on an explosion source model according to claim 8, characterized in that, Based on the sum of vibration components along the X-axis, Y-axis, and Z-axis, the vibration data of the target point is obtained as follows: ； in, This represents the sum of the vibration components along the X-axis. This represents the sum of the vibration components along the Y-axis. This represents the sum of the vibration components along the Z-axis.

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