A method and system for predicting the shape of a blast pile in open bench blasting

Abstract

The application discloses an open-air bench blasting and muck pile shape prediction method and system, and relates to the technical field of engineering blasting, which comprises the following steps: obtaining a two-dimensional profile curve and shape parameters of a test muck pile; randomly selecting a muck pile height at the farthest throwing distance and a slope of the two-dimensional profile curve to determine initial Weibull curve shape control parameters; comparing a curve drawn by using the shape parameters with the two-dimensional profile curve to determine the optimal muck pile height at the farthest throwing distance and the slope of the two-dimensional profile curve; calculating the throwing speed and the throwing angle of all spherical explosive packages to each broken block; calculating the predicted throwing distance of each broken block and comparing the predicted throwing distance to obtain the farthest predicted throwing distance; estimating a muck pile loose coefficient; obtaining the optimal curve shape control parameters; drawing an optimal Weibull distribution model curve; and correcting the curve by using a blasting crater visible depth to obtain an open-air bench blasting and muck pile shape prediction curve. The application can predict the profile shape of the muck pile.

Description

Technical Field

[0001] This invention relates to the field of engineering blasting technology, and in particular to a method and system for predicting the blast pile morphology of open-pit bench blasting. Background Technology

[0002] Open-pit bench blasting is a highly efficient method for excavating rock masses, producing smooth bench surfaces and allowing the blast piles to be thrown into designated areas, thus improving the efficiency of subsequent blast pile loading and transportation. Currently, open-pit bench blasting has become the most commonly used technique for rock mass excavation in open-pit engineering projects in my country's mining, hydropower, and transportation sectors.

[0003] With the development of green mining theory, open-pit bench blasting not only needs to improve the distribution of blasted blocks to meet engineering requirements, but also needs to control the throwing and accumulation pattern of the blast pile. After blasting excavation, a good blast pile pattern can not only reduce the proportion of rock fragmentation energy thrown, improve the energy utilization rate of explosives, but also reduce the auxiliary workload of loading and transport machinery, reduce the risk of loading and transport work, and thus save engineering costs. Therefore, the prediction of the blast pile pattern in open-pit bench blasting is of great significance for optimizing blasting design parameters and improving the economic benefits of enterprises.

[0004] Rock mass blasting and fragmentation is a highly complex thermo-mechanical-chemical coupled process. The physical and mechanical properties of the rock mass, blasting parameters, and explosive performance all influence the fragmentation, throwing, and deposition processes. Physical and mathematical models and calculation methods for predicting blast pile morphology are still relatively lacking. Currently, common methods for predicting blast pile morphology in engineering blasting include the volume balance method, ballistics method, Weibull stochastic statistical model method, and combinations of Weibull models and various artificial intelligence algorithms. Among these, the volume balance method and ballistics method are relatively mature theories for predicting the throwing and deposition patterns in chamber blasting. Soviet scientist Chernigovsky detailed ballistic prediction methods for blast pile morphology in chamber blasting with multiple charge packages and planar charge packages in his book "Directional Throwing Blasting." However, the charge structure in chamber blasting differs significantly from that in bench blasting. The fragmented blocks typically move radially from the center of the charge package, and the throwing velocity gradient also differs from that in bench blasting. Therefore, the prediction methods cannot be directly applied to open-pit bench blasting. To address this, Yu Yalen et al. first proposed a method in the 1990s to predict the blast pile morphology of bench blasting using the Weibull probabilistic statistical model. Based on this, Li Xianglong, Zhang Xiantang, and others proposed prediction methods for the blast pile morphology of high-bench blasting in open-pit coal mines and bench blasting in jointed and fractured rocks, respectively. Qi Liuyang et al. proposed a prediction method for the blast pile morphology of bench blasting that combines various artificial intelligence algorithms such as neural networks and support vector machines with the Weibull model. The blast pile morphology predicted by the above methods matches the measured blast pile contour line relatively well and can meet the needs of engineering practice to a certain extent, but the following shortcomings still exist:

[0005] (1) In open-pit bench blasting, the throwing of the blast pile is closely related to the initial velocity and throwing angle of the broken pieces. The throwing velocity and throwing angle mainly depend on the energy distribution of the explosive and the minimum resistance line of the bench surface during the breaking process. For example, the prediction method proposed by Zhang Xiantang et al. in the 50th issue of Coal Mine Blasting assumes that the throwing angle of the broken pieces is consistent with the bench inclination angle. The prediction method proposed by Li Xianglong et al. in the 33rd volume S1 issue of Explosion and Shock directly assumes the farthest throwing point and the throwing angle. That is, neither of them fully considers the physical and mechanical influencing factors of the blast pile throwing process.

[0006] (2) The curve shape of the Weibull distribution model is closely related to its shape control parameters α and β, but the values ​​of α and β are difficult to determine. According to theoretical derivation, α and β are greatly affected by the height H0 of the blast pile at the farthest throwing distance and the slope k0 of the blast pile profile curve at that location, but existing or publicly available prediction methods do not fully consider the influencing factors of the values ​​of α and β. For example, the method of predicting the blast pile shape of bench blasting using the Weibull model first proposed by Yu Yalun et al., and the method of simulating the blast pile shape using the Weibull model in step 4 of the blasting method for shallow buried goaf in open-pit mines disclosed in Chinese Invention (application number CN202110905758.X), did not disclose the method of determining the values ​​of α and β. The prediction method proposed by Li Xianglong et al. in Volume 33, Issue S1 of "Explosion and Shock" and Volume 36, Issue 9 of "Coal Science and Technology" randomly selects the values ​​of H0 and k0, without fully considering the influencing factors of the values ​​of α and β.

[0007] (3) The combination of various artificial intelligence algorithms with the Weibull model provides a new approach to predicting the morphology of a bursting reactor. For example, Chinese invention (application number CN201910313775.7) discloses a bursting reactor displacement prediction model based on a generalized regression neural network. When using this method to predict the morphology of a bursting reactor, a large number of field experiments are required to obtain a large amount of sample data. All kinds of algorithms need to undergo multiple training iterations to obtain the final prediction model. The whole process has a long experimental cycle, high cost, large data processing volume, and high requirements for the programming ability of engineers, resulting in poor usability. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for predicting the shape of blast piles in open-pit bench blasting. This method can predict the outline shape of the blast pile, and its calculation principle is clear, easy to use, and the prediction results are consistent with reality.

[0009] To achieve the above objectives, the present invention provides the following solution:

[0010] A method for predicting the blast pile shape in open-pit bench blasting, the method comprising:

[0011] Based on image processing technology, the two-dimensional contour curve and morphological parameters of the test blast pile are obtained from the field blasting test; the morphological parameters include: the farthest throwing distance, the blast pile rise height and the collapse height;

[0012] The initial Weibull curve shape control parameters are determined based on the height of the blast pile at the randomly selected farthest throwing distance and the slope of the two-dimensional profile curve at that location.

[0013] The Weibull distribution model curve is plotted based on the initial Weibull curve shape control parameters; the overlap between the Weibull distribution model curve and the two-dimensional contour curve is calculated. If the overlap is greater than or equal to the overlap threshold, the explosion height at the current farthest throwing distance and the slope of the two-dimensional contour curve at the farthest throwing distance are determined as the optimal explosion height at the farthest throwing distance and the optimal slope of the two-dimensional contour curve, and the next step is executed; if the overlap is less than the overlap threshold, the previous step is executed.

[0014] The columnar explosive charge and the rock mass on the bench surface in bench blasting are respectively equivalent to multiple ideal spherical explosive charges and multiple cubic fragmented blocks, and the throwing velocity and throwing angle of each spherical explosive charge for each fragmented block are calculated.

[0015] Based on the throwing velocity and the throwing angle, the predicted throwing distance of each fragment is calculated using the ballistic formula;

[0016] The farthest predicted throwing distance is obtained by comparing the predicted throwing distances of each broken piece;

[0017] Estimating the bulk density coefficient of a burst pile using empirical formulas;

[0018] The optimal curve shape control parameters are obtained by using the farthest predicted throwing distance, the pile loosening coefficient, the optimal pile height at the farthest throwing distance, and the slope of the optimal two-dimensional profile curve at the farthest throwing distance.

[0019] The optimal Weibull distribution model curve is plotted based on the optimal curve shape control parameters and the burst pile loosening coefficient.

[0020] By using the visible depth of the blasting funnel to correct the optimal Weibull distribution model curve at the last row of blast holes, the predicted curve of the blast pile morphology of open-pit bench blasting is obtained.

[0021] Optionally, the throwing velocity and throwing angle of all equivalent explosive charges for each fragment are calculated, specifically including:

[0022] Calculate the throwing velocity and throwing angle of each spherical explosive charge onto the fragmented material;

[0023] Calculate the sum of the throwing velocities and throwing angles of all spherical explosive charges for each fragment, based on the throwing velocity and throwing angle of each spherical explosive charge for each fragment.

[0024] Optionally, the formulas for calculating the throwing velocity and throwing angle of each spherical explosive charge on the fragmented material are as follows:

[0025]

[0026]

[0027] In the formula, V ij Let W be the initial velocity of the j-th cubic fragment when the i-th spherical explosive charge detonates. ij Let be the size of the resistance line between the i-th spherical medicine packet and the j-th fragment. Let be the throwing angle of the j-th fragment when the i-th spherical charge detonates, P be the explosive charge per meter in the borehole, H be the step height, and α0 be the step inclination angle; h i h is the distance from the i-th spherical explosive charge to the bottom of the hole. c For ultra-deep drilling; W0 is the size of the upper step resistance line; y j Let be the drop of the j-th broken piece; the drop is the vertical distance between the throwing point and the landing point of the broken piece.

[0028] Optionally, the formula for calculating the sum of the throwing velocities and the throwing angles of all spherical explosive charges for each fragment is as follows:

[0029]

[0030]

[0031] In the formula, V j0 Let θ be the sum of the throwing velocities of all spherical explosive charges for each fragment, θ be the sum of the throwing angles of all spherical explosive charges for each fragment, and m be the number of equivalent spherical explosive charges.

[0032] Optionally, the formula for calculating the predicted throwing distance is:

[0033]

[0034] In the formula, l j Let V be the predicted throwing distance of the j-th fragment, g be the acceleration due to gravity, and V be the acceleration due to gravity. j0 Let θ be the sum of the throwing velocities of all spherical explosive charges for each fragment, and y be the sum of the throwing angles of all spherical explosive charges for each fragment. j Let be the drop of the j-th broken block.

[0035] Optionally, the step of estimating the loosening coefficient of the explosive pile using empirical formulas specifically includes:

[0036] Calculate the borehole area per unit area based on borehole diameter, borehole spacing, and row spacing;

[0037] The loosening coefficient of the blast pile is calculated based on the explosive consumption, fluctuation coefficient, and borehole area per unit area.

[0038] Optionally, the formula for calculating the optimal curve shape control parameters is:

[0039]

[0040] In the formula, α and β are the optimal curve shape control parameters, A0 is the cross-sectional area of ​​the open-air step, and l m For the farthest predicted throwing distance, k0' is the slope of the two-dimensional profile curve at the optimal farthest throwing distance, H0' is the blast pile height at the optimal farthest throwing distance, and ξ is the blast pile loosening coefficient.

[0041] Optionally, the visible depth of the blasting funnel is calculated using the following formula:

[0042]

[0043] In the formula, n0 is the blasting effect index, W is the size of the resistance line of the last row of blast holes, and D2 is the visible depth of the blasting funnel.

[0044] Optionally, the blasting effect index is calculated using the following formula:

[0045]

[0046] In the formula, R1 is the radius of the bottom circle of the blasting funnel.

[0047] To achieve the above objectives, the present invention also provides the following solution:

[0048] An open-pit bench blasting blasting pattern prediction system, the prediction system comprising:

[0049] The image processing unit is used to obtain the two-dimensional contour curve and morphological parameters of the test blast pile based on the on-site blasting test; the morphological parameters include: the farthest throwing distance, the blast pile rise height and the collapse height;

[0050] The initial parameter determination unit is used to determine the initial Weibull curve shape control parameters based on the blast height at the randomly selected farthest throwing distance and the slope of the two-dimensional profile curve at that location.

[0051] The curve comparison unit is used to draw the Weibull distribution model curve based on the initial Weibull curve shape control parameters; and to calculate the overlap between the Weibull distribution model curve and the two-dimensional contour curve; the initial parameter determination unit is also used to re-determine the initial Weibull curve shape control parameters based on the blast height at the randomly selected farthest throwing distance and the slope of the two-dimensional contour curve at that location when the overlap is less than the overlap threshold.

[0052] The throwing speed and throwing angle calculation unit is used to calculate the throwing speed and throwing angle of all spherical explosive packets for each broken piece when the overlap is greater than or equal to the overlap threshold.

[0053] The predicted throwing distance calculation unit is used to calculate the predicted throwing distance of each fragment based on the throwing speed and the throwing angle using the ballistic formula;

[0054] The farthest predicted throwing distance determination unit is used to compare the predicted throwing distances of each broken piece to obtain the farthest predicted throwing distance;

[0055] The burst pile looseness coefficient estimation unit is used to estimate the burst pile looseness coefficient;

[0056] The optimal parameter determination unit is used to obtain the optimal curve shape control parameters by using the farthest predicted throwing distance, the pile loosening coefficient, the optimal pile height at the farthest throwing distance, and the slope of the two-dimensional profile curve at the farthest throwing distance.

[0057] The distribution model curve plotting unit is used to plot the optimal Weibull distribution model curve based on the optimal curve shape control parameters and the pile loosening coefficient.

[0058] The distribution model curve correction unit is used to correct the optimal Weibull distribution model curve at the last row of blast holes by utilizing the visible depth of the blasting funnel, so as to obtain the prediction curve of the blast pile morphology of the open-pit bench blasting.

[0059] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0060] This invention discloses a method and system for predicting the shape of a blast pile in open-pit bench blasting. The method obtains the two-dimensional contour curve and shape parameters of the test blast pile through on-site blasting tests; determines initial Weibull curve shape control parameters based on the blast pile height at a randomly selected furthest throwing distance and the slope of the two-dimensional contour curve at that location; plots a Weibull distribution model curve based on the initial Weibull curve shape control parameters; calculates the overlap between the Weibull distribution model curve and the two-dimensional contour curve; if the overlap is less than a threshold, the blast pile height at the furthest throwing distance is randomly selected again, and the slope of the two-dimensional contour curve at that location is recalculated, and the overlap is recalculated; if the overlap is greater than or equal to the threshold, the blast pile height at the current furthest throwing distance and the slope of the two-dimensional contour curve at the furthest throwing distance are determined, and the result is... The optimal blast pile height at the farthest throwing distance and the slope of the optimal two-dimensional profile curve are determined. The throwing velocity and throwing angle of each fragment for all spherical explosive charges are calculated. The predicted throwing distance for each fragment is calculated. The predicted throwing distances of each fragment are compared to obtain the farthest predicted throwing distance. The blast pile loosening coefficient is estimated. The optimal curve shape control parameters are obtained using the farthest predicted throwing distance, the blast pile loosening coefficient, the optimal blast pile height at the farthest throwing distance, and the slope of the optimal two-dimensional profile curve at the farthest throwing distance. Based on the optimal curve shape control parameters and the blast pile loosening coefficient, a Weibull distribution model curve is plotted. The Weibull distribution model curve at the last row of blast holes is corrected using the visible depth of the blasting funnel to obtain the predicted blast pile morphology curve for open-pit bench blasting.

[0061] Compared with existing technologies that directly assume the farthest throwing point and throwing angle, this invention fully considers the physical and mechanical influencing factors of the blast pile throwing process. Existing technologies require a large number of field tests to obtain a large amount of sample data, and various algorithms need to undergo multiple training iterations to obtain the final prediction model. This invention has a clear calculation principle, is easy to use, and the prediction results are consistent with reality. It can also predict the outline shape of the blast pile. Attached Figure Description

[0062] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0063] Figure 1 This is a flowchart illustrating the method for predicting the blasting pile shape in open-air bench blasting according to the present invention.

[0064] Figure 2(a) is a schematic diagram illustrating the influence of the ratio of the slope of the two-dimensional profile curve at the optimal farthest throwing distance to the blast pile height at the optimal farthest throwing distance on the curve shape control parameters.

[0065] Figure 2 (b) is a schematic diagram illustrating the influence of the blast pile height at the farthest throwing distance on the curve shape control parameters;

[0066] Figure 3 A schematic diagram showing the optimal curve and shape control parameters of the Weibull distribution model;

[0067] Figure 4 This is a schematic diagram comparing the horizontal throwing speed of the broken blocks of the present invention;

[0068] Figure 5 This is a schematic diagram comparing the vertical throwing speeds of the broken pieces of the present invention;

[0069] Figure 6 This is a schematic diagram comparing the throwing angles of the broken blocks of the present invention;

[0070] Figure 7 This is a schematic diagram comparing the farthest predicted throwing distance of the broken blocks in this invention;

[0071] Figure 8 A schematic diagram showing the predicted visible depth of the blasting crater;

[0072] Figure 9 This is a schematic diagram comparing the morphology prediction curve and the two-dimensional contour curve of the present invention.

[0073] Figure 10 This is a schematic diagram of the open-air bench blasting blasting pile morphology prediction system of the present invention;

[0074] Figure 11 A schematic diagram of the Weibull distribution model curve when H0 = 0.01; k0 = -0.1; l' = 30m;

[0075] Figure 12 A schematic diagram of the Weibull distribution model curve when H0 = 0.01, k0 = -0.001, and ξ0 = 1.2;

[0076] Figure 13 For different values ​​of H0 and k0, A schematic diagram showing the changes in the initial curve shape control parameters when ξ0 = 1.2 and l' = 30m;

[0077] Figure 14 For different values ​​of H0 and k0, A schematic diagram of the Weibull distribution model curve when ξ0=1.2 and l'=30m;

[0078] Figure 15 for The value range is -2.0 to -0.1, ξ0 = 1.2, and the diagram shows the change of the initial curve shape control parameters when the maximum throwing distance is different;

[0079] Figure 16 for A schematic diagram showing the changes in the initial curve shape control parameters when the value range is -0.20 to -0.01, ξ0 = 1.2, and l' = 30m;

[0080] Figure 17 for A schematic diagram of the Weibull distribution model curve when the value range is -2.0 to -0.1, ξ0 = 1.2, and l' = 30m;

[0081] Figure 18 for A schematic diagram of the Weibull distribution model curve when the value range is -2.0 to -0.1, ξ0 = 1.2, and l' = 35m;

[0082] Figure 19 for A schematic diagram of the Weibull distribution model curve when the value range is -0.1 to -0.01, ξ0 = 1.2, and l' = 30m;

[0083] Figure 20 for A schematic diagram of the Weibull distribution model curve when the value range is -0.2 to -0.1, ξ0 = 1.2, and l' = 30m;

[0084] Figure 21 for A schematic diagram of the Weibull distribution model curve with values ​​ranging from -0.15 to -0.13, ξ0 = 1.2, and l' = 30m.

[0085] Symbol explanation:

[0086] Image processing unit-1, initial parameter determination unit-2, throwing speed and throwing angle calculation unit-3, farthest predicted throwing distance determination unit-4, explosive pile looseness coefficient estimation unit-5, optimal parameter determination unit-6, distribution model curve drawing unit-7, distribution model curve correction unit-8, curve comparison unit-9, predicted throwing distance calculation unit-10. Detailed Implementation

[0087] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0088] The purpose of this invention is to provide a method and system for predicting the shape of blast piles in open-pit bench blasting. This method can predict the outline shape of the blast pile, and its calculation principle is clear, easy to use, and the prediction results are consistent with reality.

[0089] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0090] like Figure 1 As shown, the present invention provides a method for predicting the blast pile shape in open-pit bench blasting, the prediction method comprising:

[0091] S1: Based on image processing technology, the two-dimensional contour curve and morphological parameters of the test blast pile are obtained according to the on-site blasting test; the morphological parameters include: the farthest throwing distance, the blast pile bulge height and the collapse height.

[0092] S2: Determine the initial Weibull curve shape control parameters based on the pop-up height at the randomly selected farthest throwing distance and the slope of the two-dimensional profile curve at that location.

[0093] S3: Draw the Weibull distribution model curve based on the initial Weibull curve shape control parameters; calculate the overlap between the Weibull distribution model curve and the two-dimensional contour curve. If the overlap is greater than or equal to the overlap threshold, determine the current maximum throwing distance's blast height and the slope of the two-dimensional contour curve at the maximum throwing distance. If these are the optimal maximum throwing distance's blast height and the optimal slope of the two-dimensional contour curve, proceed to the next step S4; if the overlap is less than the overlap threshold, proceed to the previous step S3.

[0094] The ore and rock before and after the blasting satisfy the law of conservation of mass; the formula for the mass conservation equation is as follows:

[0095]

[0096] In the formula, ρ a ρ is the density of the ore and rock after blasting. b denoted as ρ, where ρ is the density of the ore and rock before blasting; h(x) is the height of the blast pile on the longitudinal section in the direction of blasting (x direction); A0 is the cross-sectional area of ​​the open-pit bench; and l' is the farthest blasting distance.

[0097] The mass conservation equation, after mathematical transformation, is as follows:

[0098]

[0099] In the formula, ξ0 is the initial loosening coefficient of the blast pile; H(X) is the probability density function; L m is the first mathematical transformation parameter.

[0100] The formula for H(X) is as follows:

[0101]

[0102] In the formula, α and β are shape control parameters; X is the second mathematical transformation parameter.

[0103] Let H0 be the height of the explosion at the furthest throwing distance, and let k0 be the slope of the two-dimensional profile curve at the furthest throwing distance. Then, the following formula applies:

[0104]

[0105] Substituting the probability density function, we get the following formula:

[0106]

[0107] The specific process of the trial calculation is as follows:

[0108] H0 and k0 were randomly selected, and tests were conducted based on the initial pile loosening coefficient and the farthest throwing distance. The Weibull distribution model curve and the two-dimensional profile curve were plotted and compared.

[0109] like Figure 11 As shown, with H0 = 0.01, k0 = -0.1, and the farthest throwing distance of 30m, the initial pile loosening coefficient takes different values ​​between 1.2 and 1.7, and the Weibull distribution model curve is plotted.

[0110] like Figure 12 As shown, with H0 = 0.01, k0 = -0.001, the initial pile loosening coefficient is 1.2, and the maximum throwing distance is taken in different values ​​between 29 and 34 m, the Weibull distribution model curve is plotted.

[0111] according to Figure 11 and Figure 12 It can be seen that when H0 and k0 are arbitrarily chosen, the control parameters of the initial curve shape vary over a large range (β differs by about 60 times when H0 = 0.01, k0 = -0.1 and H0 = 0.01, k0 = -0.001). Even if the farthest throwing distance and the initial pile loosening coefficient vary over a large range, the Weibull distribution model curve and the two-dimensional profile curve still have a large difference.

[0112] As shown in Table 1, the initial loosening coefficient of the blast pile is taken as 1.2, the maximum throwing distance is 30m, and the fixed... Let H0 and k0 take different values, the initial curve shape control parameters are as follows Figure 13 As shown, plot the Weibull distribution model curve (e.g.) Figure 14 (As shown).

[0113] Table 1 Initial Weibull Shape Parameter Calculation Table

[0114]

[0115] like Figure 13 As shown, l' = 30m, ξ0 = 1.2, when H0 < 0.000001, the initial curve shape control parameters basically do not change with the values ​​of H0 and k0. Figure 14 As shown, combined with the measured burst morphology curve, it can be seen that when l'=30m, ξ0=1.2, when When H0 < 0.000001, the Weibull distribution model curve and the two-dimensional contour curve are the same, so H0 should be less than 0.000001.

[0116] Fix H0 = 0.000001, let By taking different values, plot the Weibull distribution model curve and compare it with the two-dimensional contour curve to determine the appropriate value of k0.

[0117] like Figure 15 As shown, When taking different values, that is The initial blast pile loosening coefficient is fixed, and the initial curve shape control parameter varies with the maximum throwing distance. The range is -2.0 to -0.1. The changes are shown in Table 2. Figure 16 As shown, When taking different values, that is When the initial pile loosening coefficient and the maximum throwing distance are fixed, the initial curve shape control parameters are adjusted according to the range of -0.20 to -0.1. The changes. When When the initial curve shape control parameter α is taken to be between -0.20 and -0.1, it remains essentially unchanged. The value of varies.

[0118] Table 2 Initial Weibull shape parameter calculation table (H0=0.000001)

[0119]

[0120]

[0121] At the same time, such as Figure 17 The figure shows the Weibull distribution model curve when k0 / H0 takes values ​​from -2.0 to -0.1, ξ0 = 1.2, and l' = 30m. Figure 18 The figure shows the Weibull distribution model curve when k0 / H0 takes values ​​from -2.0 to -0.1, ξ0 = 1.2, and l' = 35m. Figure 19 The figure shows the Weibull distribution model curve when k0 / H0 takes values ​​from -0.10 to -0.01, ξ0 = 1.2, and l' = 30m. Figure 20 As shown, the Weibull distribution model curve is shown when k0 / H0 takes values ​​from -0.20 to -0.01, ξ0 = 1.2, and l' = 30m.

[0122] like Figure 15 As shown, the initial curve shape control parameters all increase to varying degrees with the increase of the furthest throwing distance, therefore, the furthest throwing distance is an important parameter for plotting the Weibull distribution model curve. Furthermore, the Weibull shape coefficient α0 increases with the increase of k0 / H0, while β0 decreases with the increase of k0 / H0. Figures 17-20 It can be seen that, regardless of how the farthest throwing distance changes, when 0.788 < α0 < 1.000, the Weibull distribution model curve and the two-dimensional contour curve basically match, and their degree of overlap is high.

[0123] like Figure 21 As shown, when comparing the Weibull distribution model curve with the two-dimensional contour curve, to achieve a higher degree of consistency, -0.15≤k0 / H0≤-0.13.

[0124] Based on the selected H0 and k0, α0 and β0 are determined according to the initial pile loosening coefficient and the farthest throwing distance; α0 and β0 are curve shape control parameters.

[0125] S4: The columnar explosive charge and the rock mass of the bench blasting are respectively equivalent to multiple ideal spherical explosive charges and multiple cubic fragmented blocks, and the throwing velocity and throwing angle of each spherical explosive charge for each fragmented block are calculated.

[0126] In open-pit bench blasting, the fractured rock mass is thrown along the free face with a certain initial velocity. The throwing velocity of the fragments significantly affects the maximum throwing distance and the accumulation morphology, making it a crucial parameter for predicting the blast pile morphology. However, from the initial bulging motion of the bench face rock mass to the end of the throwing process, the movement of the fragments involves a complex physical and mechanical process of acceleration-uniformity-secondary acceleration-deceleration, making the theoretical throwing velocity difficult to calculate. Theoretical analysis shows that under the action of a columnar explosive charge in an open-pit bench blast, the throwing velocity of the fragments is closely related to the free face constraint conditions, the angle between the explosive charge axis and the free face, and the explosive consumption per unit volume. Furthermore, according to the inventors' research, the shape of the fragments within the blast pile is mainly hexahedrons with relatively small differences in triaxial dimensions. In summary, the columnar explosive charge and the bench face rock mass in bench blasting can be equivalently represented as multiple ideal spherical explosive charges and multiple cubic fragments, respectively. The throwing velocities and throwing angles of all equivalent explosive charges for each fragment can be calculated, and the maximum predicted throwing distance of the bench face fragments can be predicted using ballistic formulas.

[0127] Specifically, step S4 includes:

[0128] S401: Calculate the throwing speed and throwing angle of each spherical explosive charge on the broken pieces.

[0129] The formulas for calculating the throwing velocity and throwing angle of each spherical explosive charge on the fragments are as follows:

[0130]

[0131]

[0132] In the formula, V ij Let W be the initial velocity of the j-th cubic fragment when the i-th spherical explosive charge detonates. ij Let be the size of the resistance line between the i-th spherical medicine packet and the j-th fragment. Let be the throwing angle of the j-th fragment when the i-th spherical charge detonates, P be the explosive charge per meter in the borehole, H be the step height, and α0 be the step inclination angle; h i h is the distance from the i-th spherical explosive charge to the bottom of the hole. c For ultra-deep drilling; W0 is the size of the upper step resistance line; y j Let be the drop of the j-th broken piece; the drop is the vertical distance between the throwing point and the landing point of the broken piece.

[0133] The formula for calculating the drop of the j-th broken block is:

[0134]

[0135] In the formula, j represents the j-th broken block; x0 is the size of a single broken piece; n is the number of broken pieces.

[0136] The formula for calculating the distance from the i-th spherical explosive charge to the bottom of the hole is:

[0137]

[0138] In the formula, i represents the i-th spherical medicine packet; d0 is the diameter of the spherical medicine packet; h s is the length of the blockage; m is the number of spherical medicine packets.

[0139] y j and h i Substitute into the following formula:

[0140]

[0141] Finally, the resistance line size of the i-th spherical medicine pack to the j-th fragment is obtained.

[0142] S402: Calculate the sum of the throwing velocities and throwing angles of all spherical explosive charges for each broken piece based on the throwing velocity and throwing angle of each spherical explosive charge for each broken piece.

[0143] The formulas for calculating the sum of the throwing velocity and the throwing angle for each fragment of the spherical explosive charge are as follows:

[0144]

[0145]

[0146] In the formula, V j0 Let θ be the sum of the throwing velocities of all spherical explosive charges for each fragment, θ be the sum of the throwing angles of all spherical explosive charges for each fragment, and m be the number of spherical explosive charges.

[0147] S5: Based on the throwing speed and the throwing angle, calculate the predicted throwing distance of each fragment using the ballistic formula.

[0148] The formula for calculating the predicted throwing distance is as follows:

[0149]

[0150] In the formula, l j Let be the predicted throwing distance of the j-th fragment, and g be the acceleration due to gravity.

[0151] Step S5 ignores factors such as air resistance and secondary collisions and breakage between rock blocks.

[0152] S6: Compare the predicted throwing distances of each broken piece to obtain the farthest predicted throwing distance, denoted as l.m .

[0153] S7: Estimate the loosening coefficient of the burst pile using empirical formulas.

[0154] Specifically, step S7 includes:

[0155] S701: Calculate the borehole area per unit area based on borehole diameter, borehole spacing, and row spacing.

[0156] The formula for calculating the borehole area per unit area of ​​blast hole is:

[0157]

[0158] In the formula, D is the borehole diameter; a is the borehole spacing; b is the row spacing; and s is the borehole area per unit area borehole.

[0159] S702: Calculate the loosening coefficient of the blast pile based on the explosive consumption, fluctuation coefficient and borehole area per unit area.

[0160] The formula for calculating the bulk density coefficient of a burst pile is as follows:

[0161]

[0162] In the formula, η is the fluctuation coefficient related to the blasting method, q is the explosive consumption per unit, and ξ is the loosening coefficient of the blast pile.

[0163] S8: The optimal curve shape control parameters are obtained by using the farthest predicted throwing distance, the pile loosening coefficient, the optimal pile height at the farthest throwing distance, and the slope of the optimal two-dimensional profile curve at the farthest throwing distance.

[0164] The formula for calculating the optimal curve shape control parameters is as follows:

[0165]

[0166] In the formula, α and β are the optimal curve shape control parameters, A0 is the cross-sectional area of ​​the open-air step, and l m For the farthest predicted throwing distance, k0' is the slope of the two-dimensional profile curve at the optimal farthest throwing distance, H0' is the blast pile height at the optimal farthest throwing distance, and ξ is the blast pile loosening coefficient.

[0167] S9: Based on the optimal curve shape control parameters and the burst pile loosening coefficient, draw the optimal Weibull distribution model curve.

[0168] S10: The optimal Weibull distribution model curve at the last row of blast holes is corrected by using the visible depth of the blasting funnel to obtain the prediction curve of the blast pile morphology of the open-pit bench blasting.

[0169] In open-pit bench blasting, due to the blasting funnel effect of the last row of blast holes, a funnel-shaped depression will appear in the blast pile. The shape of the blast pile at this point differs from the Weibull distribution model curve and needs to be corrected based on the blasting funnel.

[0170] The formula for calculating the visible depth of the blasting funnel is as follows:

[0171]

[0172] In the formula, n0 is the blasting effect index, W is the size of the resistance line of the last row of blast holes, and D2 is the visible depth of the blasting funnel.

[0173] The blasting effect index is calculated using the following formula:

[0174]

[0175] In the formula, R1 is the radius of the bottom circle of the blasting funnel.

[0176] Taking a specific embodiment as an example, in the limestone blasting mining process of a super-large sand and gravel mine project, four mining tests with different unit explosive consumption were designed. Based on the measured blast pile profile, a method for predicting the blast pile morphology of open-pit bench blasting was studied. The blasting design parameters are shown in Table 1 below.

[0177] Table 3. Limestone blasting mining test parameters for a super-large sand and gravel mine project.

[0178]

[0179] Each field blasting test was conducted according to the test parameters in Table 3. During the test, a high-speed camera was used to acquire image data of the blast pile being thrown perpendicular to the direction of the blast pile. Image processing techniques were used to obtain two-dimensional contour curves and morphological parameters through operations such as denoising, image segmentation and binarization.

[0180] The initial Weibull curve shape control parameters are determined based on the blast height at the randomly selected farthest throwing distance and the slope of the two-dimensional profile curve at that location.

[0181] The Weibull distribution model curve is plotted based on the initial Weibull curve shape control parameters; the overlap between the Weibull distribution model curve and the two-dimensional contour curve is calculated. If the overlap is greater than or equal to the overlap threshold, the explosion height at the current farthest throwing distance and the slope of the two-dimensional contour curve at the farthest throwing distance are determined as the optimal explosion height at the farthest throwing distance and the optimal slope of the two-dimensional contour curve, and the next step is executed; if the overlap is less than the overlap threshold, the previous step is executed.

[0182] like Figure 2 (a) and Figure 2 As shown in (b), the two-dimensional contour curve and Figure 2 , Figure 3 A comparison shows that during the limestone blasting mining process of a certain super-large sand and gravel mine project, when -0.15≤k0 / H0≤-0.13, the Weibull curve plotted based on the calculated curve shape control parameters α and β is closest to the measured blast pile shape. At this time, the value ranges of the shape control parameters α and β are 0.767~0.830 and 1.468~1.436, respectively.

[0183] Based on the varying length of the explosive charge in each borehole, the explosive charge was divided into 12 or 14 equivalent spherical charges. The rock face of the step was divided into 15 cubes with sides approximately 1m long. The equivalent spherical charges and the rock blocks on the step in front of the first row of boreholes were numbered from the bottom of the borehole to the borehole opening. Figure 4 and Figure 5 As shown, the final calculated throwing velocities of all spherical explosive charges on each fragment were obtained; as... Figure 6 As shown, the projection angles of all spherical explosive charges for each fragment were calculated; and the predicted projection distances of each fragment were calculated using ballistic formulas; as shown... Figure 7 As shown, the predicted throwing distances of each broken piece are compared to obtain the farthest predicted throwing distance of the four trials.

[0184] The loosening coefficient of the blast pile was estimated, and the optimal Weibull distribution model curve, which conforms to the actual engineering situation, was plotted based on the optimized shape control parameters α0 and β0 obtained from trial calculations. The estimated loosening coefficient of the blast pile in the limestone blasting mining test of a super-large sand and gravel mine project is shown in Table 4.

[0185] The optimal curve shape control parameters are obtained by using the farthest predicted throwing distance, the pile loosening coefficient, the optimal pile height at the farthest throwing distance, and the slope of the optimal two-dimensional profile curve at the farthest throwing distance.

[0186] Table 4. Estimation of the loosening coefficient of limestone blasting test pile in a super-large sand and gravel mine project.

[0187]

[0188] By correcting the visible depth of the blasting funnel with the optimal Weibull distribution model curve at the last row of blast holes, the final prediction curve for the open-pit bench blasting blast pile morphology is obtained. For example... Figure 8 As shown, this is a schematic diagram illustrating the predicted depth of the visible blasting hopper at the blasting boreholes after a limestone blasting test in a super-large sand and gravel mine project. Based on this, the Weibull distribution model curve is modified to obtain the predicted curve for the blast pile morphology of open-pit bench blasting; as shown... Figure 9As shown, the predicted blast pile morphology of each open-air bench blasting experiment is obtained and compared with the measured blast pile morphology.

[0189] like Figure 10 As shown, the present invention also provides an open-pit bench blasting blast pile shape prediction system, applied to the above-mentioned open-pit bench blasting blast pile shape prediction method. The prediction system includes: an image processing unit 1, an initial parameter determination unit 2, a throwing speed and throwing angle calculation unit 3, a maximum predicted throwing distance unit 4, a blast pile looseness coefficient estimation unit 5, an optimal parameter determination unit 6, a distribution model curve drawing unit 7, a distribution model curve correction unit 8, a curve comparison unit 9, and a predicted throwing distance calculation unit 10.

[0190] The image processing unit 1 is used to obtain the two-dimensional contour curve and morphological parameters of the test blast pile based on the on-site blasting test; the morphological parameters include: the farthest throwing distance, the blast pile bulge height and the collapse height.

[0191] The initial parameter determination unit 2 is used to determine the initial Weibull curve shape control parameters based on the blast height at the randomly selected farthest throwing distance and the slope of the two-dimensional profile curve at that location.

[0192] The curve comparison unit 9 is used to draw the Weibull distribution model curve based on the initial Weibull curve shape control parameters; and to calculate the overlap between the Weibull distribution model curve and the two-dimensional contour curve; the initial parameter determination unit is also used to re-determine the initial Weibull curve shape control parameters based on the blast height at the randomly selected farthest throwing distance and the slope of the two-dimensional contour curve at that location when the overlap is less than the overlap threshold.

[0193] The throwing speed and throwing angle calculation unit 3 is used to calculate the throwing speed and throwing angle of all spherical medicine packets for each broken piece when the overlap is greater than or equal to the overlap threshold.

[0194] The predicted throwing distance calculation unit 10 is used to calculate the predicted throwing distance of each fragment based on the throwing speed and the throwing angle using the ballistic formula.

[0195] The farthest predicted throwing distance determination unit 4 is used to compare the predicted throwing distances of each broken block to obtain the farthest predicted throwing distance.

[0196] The detonation loosening coefficient estimation unit 5 is used to estimate the detonation loosening coefficient.

[0197] The optimal parameter determination unit 6 is used to obtain the optimal curve shape control parameters by using the farthest predicted throwing distance, the pile loosening coefficient, the optimal pile height at the farthest throwing distance, and the slope of the two-dimensional profile curve at the farthest throwing distance.

[0198] The distribution model curve plotting unit 7 is used to plot the optimal Weibull distribution model curve based on the optimal curve shape control parameters and the burst pile loosening coefficient.

[0199] The distribution model curve correction unit 8 is used to correct the optimal Weibull distribution model curve at the last row of blast holes by utilizing the visible depth of the blasting funnel, so as to obtain the prediction curve of the blast pile morphology of the open-pit bench blasting.

[0200] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0201] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for predicting the blast pile shape in open-pit bench blasting, characterized in that, The prediction method includes: Based on image processing technology, the two-dimensional contour curve and morphological parameters of the test blast pile are obtained from the field blasting test; the morphological parameters include: the farthest throwing distance, the blast pile rise height and the collapse height; The initial Weibull curve shape control parameters are determined based on the height of the blast pile at the randomly selected farthest throwing distance and the slope of the two-dimensional profile curve at that location. The Weibull distribution model curve is plotted based on the initial Weibull curve shape control parameters; the overlap between the Weibull distribution model curve and the two-dimensional contour curve is calculated. If the overlap is greater than or equal to the overlap threshold, the explosion height at the current farthest throwing distance and the slope of the two-dimensional contour curve at the farthest throwing distance are determined as the optimal explosion height at the farthest throwing distance and the optimal slope of the two-dimensional contour curve, and the next step is executed; if the overlap is less than the overlap threshold, the previous step is executed. The columnar explosive charge and the rock mass of the bench blasting surface are respectively equivalent to multiple ideal spherical explosive charges and multiple cubic fragments, and the throwing velocities and throwing angles of all spherical explosive charges for each fragment are calculated. Specifically, the calculation of the throwing velocities and throwing angles of all equivalent explosive charges for each fragment includes: The throwing velocity and throwing angle of each spherical explosive charge on the fragments are calculated using the following formula: ； ； In the formula, For the first i When the spherical explosive charge explodes... j The initial velocity of the thrown fragment of the cube For the first i The spherical medicine packet and the first j Size of the resistance line between the broken pieces For the first i When the spherical explosive charge explodes... j The throwing angle of the broken pieces P This refers to the amount of explosive charged per meter inside the borehole. H The height of the step. The angle of inclination of the steps; For the first i The distance from the bottom of the hole to the spherical medicine packet; For ultra-deep drilling; The size of the resistance line on the upper step; For the first The drop of the broken block; the drop is the vertical distance between the throwing point and the landing point of the broken block; The sum of the throwing velocities and throwing angles of all spherical explosive charges on each fragment are calculated based on the throwing velocity and throwing angle of each spherical explosive charge on each fragment. The calculation formula is as follows: ； ； In the formula, For all spherical explosive charges, the sum and throwing velocities for each fragment. For all spherical explosive charges, the angle of throw is given for each fragment. m This refers to the number of equivalent spherical drug packets; Based on the throwing velocity and the throwing angle, the predicted throwing distance of each fragment is calculated using ballistic formulas; the formula for calculating the predicted throwing distance is: ； In the formula, For the first Predicted throwing distance for each fragment g It is the acceleration due to gravity. For all spherical explosive charges, the sum and throwing velocities for each fragment. For all spherical explosive charges, the angle of throw is given for each fragment. For the first The drop of the broken blocks; The farthest predicted throwing distance is obtained by comparing the predicted throwing distances of each broken piece; Estimating the bulk density coefficient of a burst pile using empirical formulas; The optimal curve shape control parameters are obtained by considering the farthest predicted throwing distance, the pile loosening coefficient, the optimal pile height at the farthest throwing distance, and the slope of the two-dimensional profile curve at the farthest throwing distance. The calculation formula for the optimal curve shape control parameters is as follows: ； In the formula, and The optimal curve shape control parameters. The cross-sectional area of ​​the open-air steps. To predict the furthest throwing distance, The slope of the two-dimensional profile curve at the optimal throwing distance. The optimal explosion height is determined by the maximum throwing distance. The bulk density coefficient of the explosive pile; The optimal Weibull distribution model curve is plotted based on the optimal curve shape control parameters and the burst pile loosening coefficient. By using the visible depth of the blasting funnel to correct the optimal Weibull distribution model curve at the last row of blast holes, the predicted curve of the blast pile morphology of open-pit bench blasting is obtained.

2. The method for predicting the blast pile morphology of open-pit bench blasting according to claim 1, characterized in that, The method of estimating the loosening coefficient of the blast pile using empirical formulas specifically includes: calculating the borehole area per unit area based on borehole diameter, borehole spacing, and row spacing; and calculating the loosening coefficient of the blast pile based on explosive consumption, fluctuation coefficient, and borehole area per unit area.

3. The method for predicting the blast pile morphology of open-pit bench blasting according to claim 1, characterized in that, The visible depth of the blasting funnel is calculated using the following formula: ； In the formula, The blasting effect index, W The size of the resistance line for the last row of gun holes; The visible depth of the blasting funnel.

4. The method for predicting the blast pile morphology of open-pit bench blasting according to claim 3, characterized in that, The blasting effect index is calculated using the following formula: ； In the formula, The radius of the bottom circle of the blasting funnel.

5. A prediction system for the blast pile shape of open-pit bench blasting, wherein the prediction system is applied to the prediction method for the blast pile shape of open-pit bench blasting according to any one of claims 1-4; characterized in that, The prediction system includes: The image processing unit is used to obtain the two-dimensional contour curve and morphological parameters of the test blast pile based on the on-site blasting test; the morphological parameters include: the farthest throwing distance, the blast pile rise height and the collapse height; The initial parameter determination unit is used to determine the initial Weibull curve shape control parameters based on the blast height at the randomly selected farthest throwing distance and the slope of the two-dimensional profile curve at that location. The curve comparison unit is used to draw the Weibull distribution model curve based on the initial Weibull curve shape control parameters; and to calculate the overlap between the Weibull distribution model curve and the two-dimensional contour curve; the initial parameter determination unit is also used to re-determine the initial Weibull curve shape control parameters based on the blast height at the randomly selected farthest throwing distance and the slope of the two-dimensional contour curve at that location when the overlap is less than the overlap threshold. The throwing speed and throwing angle calculation unit is used to calculate the throwing speed and throwing angle of all spherical explosive packets for each broken piece when the overlap is greater than or equal to the overlap threshold. The predicted throwing distance calculation unit is used to calculate the predicted throwing distance of each fragment based on the throwing speed and the throwing angle using the ballistic formula; The farthest predicted throwing distance determination unit is used to compare the predicted throwing distances of each broken piece to obtain the farthest predicted throwing distance; The burst pile looseness coefficient estimation unit is used to estimate the burst pile looseness coefficient; The optimal parameter determination unit is used to obtain the optimal curve shape control parameters by using the farthest predicted throwing distance, the pile loosening coefficient, the optimal pile height at the farthest throwing distance, and the slope of the two-dimensional profile curve at the farthest throwing distance. The distribution model curve plotting unit is used to plot the optimal Weibull distribution model curve based on the optimal curve shape control parameters and the pile loosening coefficient. The distribution model curve correction unit is used to correct the optimal Weibull distribution model curve at the last row of blast holes by utilizing the visible depth of the blasting funnel, so as to obtain the prediction curve of the blast pile morphology of the open-pit bench blasting.

Images