# Optimization and Application of Spacing Parameter for Loosening Blasting with 24-m-High Bench in Barun Open-Pit Mine

Authors: Zuoming Yin; Desheng Wang; Xuguang Wang; Zhiheng Dang; Wantao Li
Journal: Shock and Vibration
 (2021)

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## Abstract

In view of the near slope blasting in Barun open-pit mine, which has merged sublevel mining, the operation safety conditions of middle-sized and large equipment in the second phase expansion are poor and need urgent improvement. To increase the efficiency of expansion and reduce costs, a 24-m-high bench and large spacing parameter for loosening blasting are proposed. The analysis of the physical mechanism of the stress wave attenuation in the rock indicates that the cylindrical charge is equivalent to several spherical charges. Considering the pressure attenuation, reflection, transmission, and superposition of the spherical charge after the equivalence, a double exponential function correction equation of the stress wave attenuation is obtained based on the Mises strength criterion. The stress of any point in the rock medium with various spacing parameter is obtained by calculation. ANSYS/LS-DYNA was used to simulate and study the stress distribution of a 24-m-high bench with various spacing parameter. Meanwhile, the accuracy of the correction equation was verified. The parameters of the high-bench blasting with good effect and low cost were determined to be 15 m  ×  5.5 m, and field tests were carried out. Results show that the large spacing parameter for 24-m-high bench loosening blasting in Barun open-pit mine is efficient and economical in medium-hard rock blasting. This study provides a reference for the practical exploration of the expansion of high benches in open-pit mines in China. The calculation error of the corrected double exponential function is near the numerical simulation result. It is suitable for all kinds of professional designers.


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## Body

## 1. Introduction

Most metal mines in China use 10 m to 12 m bench heights. With the advancement of open-pit mining technology, complete sets of large-scale equipment have improved the equipment level of mines [1–4] and the basic conditions to increase the bench height. At present, the upper bench of Barun open-pit mine is temporarily supported. The conventional bench-by-bench method of leaning on near slope blasting faces problems, such as steep slopes, narrow expansion sites, and difficulty in ensuring the safety of large equipment operations. Therefore, a technical solution that uses large spacing parameter for loosening blasting with a 24-m-high bench to expand the siding is proposed, and the need for high efficiency and low cost must be urgently addressed.According to Livingston’s blasting funnel theory, loosening blasting is a kind of blasting technology that breaks the medium without throwing [5]. By adjusting the spacing parameter, the blasting effect can be improved and the unit consumption of explosives can be reduced. Scholars have used numerical calculation methods to find that the spatial stress distribution is uniform when spacing parameters are between 1.7 and 3.7, which are conducive to rock fragmentation. The analysis of the changes in blasting conditions and the rock breaking mechanism caused by the change of spacing parameter indicates that it can be as high as 3 to 8. The reasonable spacing parameter for loosening blasting is from 1.5 to 2.0 [6–9]. Li et al. used a cement mortar model to study the influence of spacing parameter on the crack penetration time between bench blasting holes and concluded that a large spacing parameter delays the crack penetration time and improves the energy utilization rate of the explosive and the blasting effect [10]. Research on loosening blasting under homogeneous rock mass conditions with large spacing parameter and the influence of joints and fissures on blasting has produced many results [11–14]. However, the study of large spacing parameters for loosening blasting is limited in the case of steps and large resistance lines. The increase in the resistance line of the bench may produce large blocks, which subsequently affect the shovel loading. The increase in the charge of combined blasting will increase the mining cost and cause other unfavorable factors, such as the impact of blasting vibration, the increase of the large blocks rate, and the increase of the distance of flying stones. Therefore, the loosening blasting of a high bench with large spacing parameter must analyze the action mechanism of cylindrical charge and the dynamic response of rocks. The stress state of the rock medium at different resistance lines can reasonably control the size of blasting vibration and the rate of large blocks to achieve refined blasting. Raina et al. defined and determined the impulse pressure and time to make the application of fly-rock prediction equations highly scientific [15]. Singh et al. evaluated and analyzed the blasting delay time, the borehole depth, the charging structure, and other influencing factors through digital image analysis to reduce the bulk rate and improve the blasting effect [16]. Zhong et al. obtained a precise time delay by using a digital electronic detonator based on energy distribution theory of explosive charge in the rock mass and calculated the reasonable delay time interval between blasting holes; the effectiveness of the approach was proven by production practice [17]. Iwano et al. reproduced the vibration waveforms in delay blasting from a seed waveform recorded in single-shot blasting. The optimum delay interval determined accurately from the superposition method was nearly equal to the one simply estimated from the method with the autocorrelation coefficient or frequency analysis of the vibration waveform in single-shot blasting [18]. Azizabadi et al. simulated the surface vibration generated by blasting in the stability assessment of the rock slope of an open-pit mine through the vibration measurement data of a single blasting hole. The simulated production blast seismograms were then adopted as input to predict the time histories of particle velocity in the blast vibrations on the mine wall by using the universal distinct element code. The simulated time histories of particle velocity were consistent with the measured data [19]. Navarro Torres et al. collected data, which were processed with multiple regression techniques, to obtain the blasting vibration attenuation law and predict the levels of blasting-induced vibrations for the locality under study. They had knowledge of only the maximum explosive charge per delay and the distance to the blasting point. The Brazilian and international admissibility standards of blasting-induced vibration, the minimum distance between the mine and the community, and the constants obtained from the regression were used to establish the maximum explosive charge per delay for an acceptable ground vibration level that would not cause structural damage and human discomfort [20]. For the cylindrical charge, many scholars combined dynamic caustics, super dynamic strain testing, and numerical analysis methods to study the explosion stress and strain field of the cylindrical charge and the evolution law of the local stress field at the tip of the explosion crack [21–24]. Some scholars have also conducted intensive research on the different charge structures of columnar drug packs. Through different positions and proportions of air deck, the action time in the cylindrical charge hole is extended to improve the utilization rate of explosives and reduce the blasting vibration [25–29].At present, five technical problems must be solved for the expansion of the 24-m-high bench in Barun open-pit mine. First, the perforation depth of ordinary roller drills does not exceed 20 m and thus cannot meet the requirements of a 24-m-high bench and large diameter drilling. Second, limited by the slope of the bench, the height of the bench increases, and the resistance line of the front row is doubled. Effectively breaking and moving the rock at the bottom of the hole are greatly challenging. Third, if the high-bench deep hole adopts a continuous charge structure, then the unit consumption of explosives under the same hole layout condition is higher than that of ordinary bench blasting, and the cost will increase. Fourth, the increase of the height and charge of the bench will inevitably lead to an increase of blasting vibration in the middle and far areas. Fifth, the current dynamic response of the rock medium under the blasting load of the spherical or cylindrical charge will produce huge errors in the design of loosening blasting with a high bench and a large spacing parameter. In this study, the analysis of the physical mechanism of the stress wave attenuation in the rock indicates that the cylindrical charge is equivalent to several spherical charges. Considering the pressure attenuation, reflection, transmission, and superposition of the spherical charge after the equivalence, a double exponential function correction equation of the stress wave attenuation is obtained based on the Mises strength criterion. The stress of any point in the rock medium with various spacing parameter is obtained by calculation. ANSYS/LS-DYNA is used to simulate and study the stress distribution of a 24-m-high bench with various spacing parameters. Meanwhile, the accuracy of the correction equation is verified. The parameters of the high-bench blasting with good effect and low cost are determined. Finally, a field test is conducted to analyze the blasting effect.


## 2. Dynamic Response and Failure Criterion of Rock in Column Explosion Load

### 2.1. Stress Field Characteristics of Spherical Charge

When the charge blast hole is detonated, the explosive will explode to produce high-pressure gas, impacting the wall and propagating a strong pressure wave outward into the rock medium [30]. According to the degree of damage to the surrounding rocks, three zones are formed on the rocks: the cavity, broken, and elastic zones. The elastic zone is divided into the crack and vibration zones (as shown in Figure 1). Therefore, the blasting seismic wave is the propagation of the wave filtered through the broken and radial crack zones. The cavity wall propagates under the action of the continuous expansion and contraction of the explosive gas. This process involves the interaction between the high-pressure expansion of explosive detonation products and the rock mass, the constitutive characteristics of the rock mass state of the fracture zone and the fracture zone, the size of the failure zone, and the stress time history at the interface of the failure and elastic vibration zones. The study of this issue is the most basic and important in the study of blasting seismic wave effects.Figure 1
Blasting zones partitioned in the rock, indicating the (I) crush zone, (II) fracture zone, and (III) elastic vibration zone.The known characteristics of the stress field of the spherical charge indicate that the law of stress attenuation is proportional to the explosive quantity and inversely proportional to the distance [31]. The energy density (E) of the spherical charge decays according to the cubic relationship of the expansion path (R). Moreover, the explosive mass is only a representation of energy, so the energy density attenuation formula of the spherical charge can be abbreviated as(1)E=kfqR3=k4/3πrb3ρqR3,where q is the explosive heat, r is the radius of the spherical charge, ρ is the explosive density, R is the energy field radius of the spherical charge, and k is the correlation coefficient of energy attenuation.The local field characteristic theorem of waves points out that the reflection or transmission of the incident wavefront with arbitrary shapes at any point on the curved interface is the same as that of plane waves [32, 33]. Therefore, the transmission and reflection problems of arbitrary incident wavefront on the curved interface can be simplified as plane wave problems. The calculation method for the initial pressure of the wall of the borehole with a coupled charge is generally in accordance with the following equation:(2)P0=ρeDe2k+1,where ρe is the explosive density, De is the explosive velocity, ρeDe is the explosive wave impedance, and k is the adiabatic index, which is the slope of the pressure and volume curve when the entropy value is constant, and its value is related to explosive density and explosive heat. Jones proposed that(3)k=1+a+21+a−1×1.33ρe/G1+1.33ρe/G,where (1 + a) is the ratio of the specific heat of the detonation gas product in an ideal state and G is the part of the detonation heat of the detonation gas product. When the explosive density is very small, the adiabatic index can be k = 4/3. Chen et al. [34] believed that the adiabatic index is only related to the density of explosives and expressed their relationship as follows:(4)k=1.9+0.6ρe.For most explosives,k = 3 is generally approximated.Some scholars provided a double exponential function describing the stress wave attenuation with time excited by the spherical charge [35–37]:(5)Pt=P0e−At−e−Bt,ω=22cr0,A=nw2,B=mw2,where ω is the angular frequency, c is the propagational velocity of the longitudinal wave, and r0 is the radius of the cavity.(6)ψ=−r0p0/ρlω/2−A2+ω2e−At+r0p0/ρlω/2−B2+ω2e−Bt+r0p0/ρlω/2−A2+ω212−Aωsinωt+cosωte−ωt2−r0p0/ρlω/2−B2+ω212−Bωsinωt+cosωte−ωt2.From the second-order partial derivative of the displacement potential function, the particle strain potential function is as follows:(7)εl=∂2ψ∂l2=9p04ρc2lr0−2lr02−4n3lr0+4n29e−nωt23−2n+n2+e−ωt223−2n+n22lr02sinωt+α−433lr0sinωt+α−γ+43sinωt+α−2γ+2lr02−4m3lr0+4m29e−mωt23−2m+m2−e−ωt223−2m+m22lr02sinωt+β−433lr0sinωt+β−γ+43sinωt+β−2γ.The symbols are listed in Table1. Assuming that the rock medium obeys Hooke’s law, the radial stress at any point in the medium can be obtained.Table 1
List of symbols.
r0 = Radius of cavityc = propagational velocity of longitudinal wavee = base of the natural system of logarithmsm  = constant (when t = 0, m  = 0)n = constant (when t = 0, n = 0)p = variable pressurep0 = Constant pressuret = timel = radial distance from the center of the cavityA = constantB = constantα = phase angleβ = phase angleγ = phase angleεl = Radial strainψ = Displacement potential function


## 2.1. Stress Field Characteristics of Spherical Charge

When the charge blast hole is detonated, the explosive will explode to produce high-pressure gas, impacting the wall and propagating a strong pressure wave outward into the rock medium [30]. According to the degree of damage to the surrounding rocks, three zones are formed on the rocks: the cavity, broken, and elastic zones. The elastic zone is divided into the crack and vibration zones (as shown in Figure 1). Therefore, the blasting seismic wave is the propagation of the wave filtered through the broken and radial crack zones. The cavity wall propagates under the action of the continuous expansion and contraction of the explosive gas. This process involves the interaction between the high-pressure expansion of explosive detonation products and the rock mass, the constitutive characteristics of the rock mass state of the fracture zone and the fracture zone, the size of the failure zone, and the stress time history at the interface of the failure and elastic vibration zones. The study of this issue is the most basic and important in the study of blasting seismic wave effects.Figure 1
Blasting zones partitioned in the rock, indicating the (I) crush zone, (II) fracture zone, and (III) elastic vibration zone.The known characteristics of the stress field of the spherical charge indicate that the law of stress attenuation is proportional to the explosive quantity and inversely proportional to the distance [31]. The energy density (E) of the spherical charge decays according to the cubic relationship of the expansion path (R). Moreover, the explosive mass is only a representation of energy, so the energy density attenuation formula of the spherical charge can be abbreviated as(1)E=kfqR3=k4/3πrb3ρqR3,where q is the explosive heat, r is the radius of the spherical charge, ρ is the explosive density, R is the energy field radius of the spherical charge, and k is the correlation coefficient of energy attenuation.The local field characteristic theorem of waves points out that the reflection or transmission of the incident wavefront with arbitrary shapes at any point on the curved interface is the same as that of plane waves [32, 33]. Therefore, the transmission and reflection problems of arbitrary incident wavefront on the curved interface can be simplified as plane wave problems. The calculation method for the initial pressure of the wall of the borehole with a coupled charge is generally in accordance with the following equation:(2)P0=ρeDe2k+1,where ρe is the explosive density, De is the explosive velocity, ρeDe is the explosive wave impedance, and k is the adiabatic index, which is the slope of the pressure and volume curve when the entropy value is constant, and its value is related to explosive density and explosive heat. Jones proposed that(3)k=1+a+21+a−1×1.33ρe/G1+1.33ρe/G,where (1 + a) is the ratio of the specific heat of the detonation gas product in an ideal state and G is the part of the detonation heat of the detonation gas product. When the explosive density is very small, the adiabatic index can be k = 4/3. Chen et al. [34] believed that the adiabatic index is only related to the density of explosives and expressed their relationship as follows:(4)k=1.9+0.6ρe.For most explosives,k = 3 is generally approximated.Some scholars provided a double exponential function describing the stress wave attenuation with time excited by the spherical charge [35–37]:(5)Pt=P0e−At−e−Bt,ω=22cr0,A=nw2,B=mw2,where ω is the angular frequency, c is the propagational velocity of the longitudinal wave, and r0 is the radius of the cavity.(6)ψ=−r0p0/ρlω/2−A2+ω2e−At+r0p0/ρlω/2−B2+ω2e−Bt+r0p0/ρlω/2−A2+ω212−Aωsinωt+cosωte−ωt2−r0p0/ρlω/2−B2+ω212−Bωsinωt+cosωte−ωt2.From the second-order partial derivative of the displacement potential function, the particle strain potential function is as follows:(7)εl=∂2ψ∂l2=9p04ρc2lr0−2lr02−4n3lr0+4n29e−nωt23−2n+n2+e−ωt223−2n+n22lr02sinωt+α−433lr0sinωt+α−γ+43sinωt+α−2γ+2lr02−4m3lr0+4m29e−mωt23−2m+m2−e−ωt223−2m+m22lr02sinωt+β−433lr0sinωt+β−γ+43sinωt+β−2γ.The symbols are listed in Table1. Assuming that the rock medium obeys Hooke’s law, the radial stress at any point in the medium can be obtained.Table 1
List of symbols.
r0 = Radius of cavityc = propagational velocity of longitudinal wavee = base of the natural system of logarithmsm  = constant (when t = 0, m  = 0)n = constant (when t = 0, n = 0)p = variable pressurep0 = Constant pressuret = timel = radial distance from the center of the cavityA = constantB = constantα = phase angleβ = phase angleγ = phase angleεl = Radial strainψ = Displacement potential function


## 3. Blasting Load of Cylindrical Charge and Rock Dynamic Response

When the conditions are consistent, according to the quasi-static model of the spherical charge, Starfield approximates that the cylindrical charge is composed of multiple spherical charge stacks. The diameter of the spherical charge should be as near as possible or equal to the diameter of the cylindrical, as shown in Figure2.Figure 2
Cylindrical charge as near as possible or equal to the spherical charge.Each spherical charge has a stress effect on a certain point in the rock medium during the entire time of the positive pressure. Assuming that the stress wave of the spherical charge reaches the specified point when the stress peak occurs, the decay time difference can be obtained:(8)ft,ξ=t−t0−2r0ξ−1D,ξ=i,j,k,where i, j, and k are the spherical number in various cylindrical charge, ξ is the distance from the spherical charge to the detonation point, t is the starting time from the detonation point, t0 is the detonation delay time of the cylindrical charge, and D is the explosive velocity. According to the stress attenuation in the medium after spherical charge blasting, the radial stress at any point is calculated. The transmitted shock waves in the rock continue to propagate outward and finally become stress waves. For the force state of the element at any point in the rock as a plane strain problem, the tangential stress at any point in the rock can be obtained:(9)σr=FPt,ft,ξ=∑i=1iPft,i+∑j=1jPft,j+∑k=1kPft,k,(10)σθ=−bσr,(11)σz=μd1−bσr,where b is the coefficient of lateral, σr and σθ are the radial and tangential stresses in the rock, respectively, and σz is the normal surface stress formed by σr and σθ.


### 3.1. Stress State and Strength Failure Criterion of Rock Mass in Blasting Loading

The stress tensor at any point in the rock is usually described by six independent stress components or three principle stresses acting on mutually perpendicular planes. The magnitude and direction of the stress tensor component are different for different coordinate systems, but the stress tensor and stress deflection invariants at this point will not change with the coordinate system. Therefore, the invariants of stress and deviatoric stress tensor play an important role in strength theory. For plastic media, the deformation state in the deformation zone must be studied, that is, the initial yield and plastic states during the deformation process when a point is in the elastic state. Usually, the stress tensor is divided into two parts: one part is the spherical stress tensor or the hydrostatic stress tensor, and the other part is the deviatoric stress tensor. Therefore, when the stresses are equal in all directions, it is equivalent to hydrostatic pressure and does not produce plastic deformation. Therefore, separating the same stress in all directions from the stress tensor is convenient for studying plastic deformation:(12)σij=σmδij+sij,δij=1,i=j,0,i≠j,J1=sx+sy+sz=σx+σy+σz−3σm,J2=−sxsy+sysz+szsx+τxy2+τyz2+τzx2=16σx−σy2+σy−σz2+σz−σx2+6τxy2+τyz2+τzx2,J3=sxsysz+2τxyτyzτzx−szτyz2−syτzx2−szτxy2,where δij is the Kronecker symbol, σmδij is the stress sphere tensor, which represents the equal normal stress in three directions, sij is the stress deflection tensor, and J1, J2, and J3 represent the first, second, and third invariants of the stress deviator, respectively. When the x, y, and z axis directions coincide with the main axis,(13)J1=0,J2=16σ1−σ22+σ2−σ32+σ3−σ12,J3=s1s2s3.For any point in space, the size of the deviatoric stress tensor part vector NP can be represented byr, and R is the size of the deviatoric stress tensor length when yielding occurs (as shown in Figure 3). When r < R, point P is located inside the Mises yield cylinder and is in an elastic state; when r = R, point P is located on the Mises yield cylinder and is yielding; when r > R, point P is located outside the Mises yield cylinder and is in a plastic state phase:(14)σi=13σr−σθ2+σθ−σz2+σz−σr2=2J2.Figure 3
Mises yield criterion in the principle stress space.In the crushing area,σi≥σcd; in the fracture area, σi≥σtd; σcd is the dynamic compressive strength of the rock; σtd is the dynamic tensile strength of the rock.Equations (9)–(11) can be used to obtain the stress of a point in the medium in different directions (as shown in Figure 4). By substituting it into formula (14), the effective stress at any point can be obtained (as shown in Figure 5), and then, the effective stress attenuation with distance can be obtained (as shown in Figure 6).Figure 4
Principle stress of various direction attenuations with time.Figure 5
Effective stress attenuation from absolute zero time.Figure 6
Effective stress attenuation with distance.


## 3.1. Stress State and Strength Failure Criterion of Rock Mass in Blasting Loading

The stress tensor at any point in the rock is usually described by six independent stress components or three principle stresses acting on mutually perpendicular planes. The magnitude and direction of the stress tensor component are different for different coordinate systems, but the stress tensor and stress deflection invariants at this point will not change with the coordinate system. Therefore, the invariants of stress and deviatoric stress tensor play an important role in strength theory. For plastic media, the deformation state in the deformation zone must be studied, that is, the initial yield and plastic states during the deformation process when a point is in the elastic state. Usually, the stress tensor is divided into two parts: one part is the spherical stress tensor or the hydrostatic stress tensor, and the other part is the deviatoric stress tensor. Therefore, when the stresses are equal in all directions, it is equivalent to hydrostatic pressure and does not produce plastic deformation. Therefore, separating the same stress in all directions from the stress tensor is convenient for studying plastic deformation:(12)σij=σmδij+sij,δij=1,i=j,0,i≠j,J1=sx+sy+sz=σx+σy+σz−3σm,J2=−sxsy+sysz+szsx+τxy2+τyz2+τzx2=16σx−σy2+σy−σz2+σz−σx2+6τxy2+τyz2+τzx2,J3=sxsysz+2τxyτyzτzx−szτyz2−syτzx2−szτxy2,where δij is the Kronecker symbol, σmδij is the stress sphere tensor, which represents the equal normal stress in three directions, sij is the stress deflection tensor, and J1, J2, and J3 represent the first, second, and third invariants of the stress deviator, respectively. When the x, y, and z axis directions coincide with the main axis,(13)J1=0,J2=16σ1−σ22+σ2−σ32+σ3−σ12,J3=s1s2s3.For any point in space, the size of the deviatoric stress tensor part vector NP can be represented byr, and R is the size of the deviatoric stress tensor length when yielding occurs (as shown in Figure 3). When r < R, point P is located inside the Mises yield cylinder and is in an elastic state; when r = R, point P is located on the Mises yield cylinder and is yielding; when r > R, point P is located outside the Mises yield cylinder and is in a plastic state phase:(14)σi=13σr−σθ2+σθ−σz2+σz−σr2=2J2.Figure 3
Mises yield criterion in the principle stress space.In the crushing area,σi≥σcd; in the fracture area, σi≥σtd; σcd is the dynamic compressive strength of the rock; σtd is the dynamic tensile strength of the rock.Equations (9)–(11) can be used to obtain the stress of a point in the medium in different directions (as shown in Figure 4). By substituting it into formula (14), the effective stress at any point can be obtained (as shown in Figure 5), and then, the effective stress attenuation with distance can be obtained (as shown in Figure 6).Figure 4
Principle stress of various direction attenuations with time.Figure 5
Effective stress attenuation from absolute zero time.Figure 6
Effective stress attenuation with distance.


## 4. Numerical Simulation Research of Large Spacing Parameter for Loosening Blasting with 24-m-High Bench in Barun Open-Pit Mine

### 4.1. Engineering Overview

The 1120 horizontal loosening blasting project in Barun open-pit mine was selected as the test area. Three hole-blasting models with spacing parameter of 13 m  × 6 m and 15 m  × 5.5 m (concentration factor 2.73) were established. According to the Saint–Venant principle, the design parameters of the high-bench model are as follows: the total height is 40 m, the height of the bench is 24 m, the bottom square is 40 m  × 40 m, the top square is 19 m  × 40 m, the extra depth is 2 m, and the resistance line is 14.19 m. The model structure is shown in Figure7. The front and back of the bench model are defined as reflective boundaries, the slope and ground surfaces are defined as free boundaries, and the other surfaces in contact with air are defined as nonreflective boundaries. The detonation times of the first, second, and third holes are 0, 42, and 142 ms, respectively, and two detonation points in each hole detonate at the same time. The multimaterial ALE algorithm is used on the results of explosives and air, the Lagrange algorithm is used on the rocks and the stemming, and the fluid-solid coupling algorithm is used to reflect the stress transfer between explosives, air, and rocks.Figure 7
Schematic of blast holes location and charge structure.


### 4.2. Establishment of the Numerical Model

Many methods can accurately describe the pressure change process during charge detonation in numerical simulation. The basic principle is to describe the dynamic expansion of the entire detonation chamber by combining the detonation research results of explosives with the state equation of detonation gas. LS-DYNA program can directly simulate the detonation process of high-energy explosives. At any moment, the explosive pressure on the surrounding rock is as follows:(15)P=FPeosV,E,F=2t−t1DAemax3ve,t>t1,0,t≤t1,where P is the explosion pressure, F is the chemical energy release rate of the explosive, V is the explosive detonation velocity, t and t1 are the initiation times of the current time and inside the explosive, respectively, Aemax is the maximum cross-sectional area of the explosive unit, and νe is the unit volume of explosive.In this study, the high-performance explosive model (∗Mat_High_Explosive_Burn) and the JWL equation are adopted to simulate blasting. The parameters are shown in Table2.(16)Peos=A1−ωR1Ve−R1V+B1−ωR2Ve−R2V+ωE0V,where Peos is the pressure determined by the JWL equation of the state, V is the relative volume, E0 is the initial specific internal energy, and A, B, R1, R2, and ω are the five independent physical constants that describe the JWL equation.Table 2
Parameters of explosive and JWL equation.
Parametersρkg/m3Dm/sPCJGPaAGPaBGPaR1R2ωE0GPaV0Value125036005.4374.03.235.801.560.572.67281.0The parameters of the air model (∗Mat_Null) and the state equation (∗Eos_Linear_Polynomial) are shown in Table 3. The density of air is 1.225 kg/m3. The pressure is simulated by a linear polynomial equation of state (∗Eos_Linear_Polynomial). The equation is expressed as follows:(17)Ppoly=C0+C1μ+C2μ2+C3μ3+C4+C5μ+C6μ2E,μ=1V−1,where C0–C6 are constants, μ is the volume ratio, and E is the ratio of internal energy to initial volume.Table 3
Parameters of the air model and the state equation.
Parametersρ0E0voC0∼C3C4C5C6Value1.2252.5E51.000.40.40The plastic model (∗Mat_Plastic_Kinematic) is adopted for the rock and the blockage (parameters are shown in Table4). The Eulerian algorithm is used for the explosive, air, and blockage material models. The Lagrange algorithm is applied to the rock model. If the fluid-structure interaction algorithm is applied, no element distortion will occur. Given this advantage, the algorithm has been widely used in engineering numerical simulation with large deformation and high strain rate. Hence, the multimaterial fluid-structure interaction algorithm can be applied to deal with the interaction process of detonation products and the surrounding rock media. The maximum unit side length in the divided model mesh is 0.25 m, and the parts around blast holes are encrypted.Table 4
Parameters of the rock mass.
Parametersρkg/m3σtMPaσcMPaEGPaμDolomite30601466.7645.960.376


## 4.1. Engineering Overview

The 1120 horizontal loosening blasting project in Barun open-pit mine was selected as the test area. Three hole-blasting models with spacing parameter of 13 m  × 6 m and 15 m  × 5.5 m (concentration factor 2.73) were established. According to the Saint–Venant principle, the design parameters of the high-bench model are as follows: the total height is 40 m, the height of the bench is 24 m, the bottom square is 40 m  × 40 m, the top square is 19 m  × 40 m, the extra depth is 2 m, and the resistance line is 14.19 m. The model structure is shown in Figure7. The front and back of the bench model are defined as reflective boundaries, the slope and ground surfaces are defined as free boundaries, and the other surfaces in contact with air are defined as nonreflective boundaries. The detonation times of the first, second, and third holes are 0, 42, and 142 ms, respectively, and two detonation points in each hole detonate at the same time. The multimaterial ALE algorithm is used on the results of explosives and air, the Lagrange algorithm is used on the rocks and the stemming, and the fluid-solid coupling algorithm is used to reflect the stress transfer between explosives, air, and rocks.Figure 7
Schematic of blast holes location and charge structure.


## 4.2. Establishment of the Numerical Model

Many methods can accurately describe the pressure change process during charge detonation in numerical simulation. The basic principle is to describe the dynamic expansion of the entire detonation chamber by combining the detonation research results of explosives with the state equation of detonation gas. LS-DYNA program can directly simulate the detonation process of high-energy explosives. At any moment, the explosive pressure on the surrounding rock is as follows:(15)P=FPeosV,E,F=2t−t1DAemax3ve,t>t1,0,t≤t1,where P is the explosion pressure, F is the chemical energy release rate of the explosive, V is the explosive detonation velocity, t and t1 are the initiation times of the current time and inside the explosive, respectively, Aemax is the maximum cross-sectional area of the explosive unit, and νe is the unit volume of explosive.In this study, the high-performance explosive model (∗Mat_High_Explosive_Burn) and the JWL equation are adopted to simulate blasting. The parameters are shown in Table2.(16)Peos=A1−ωR1Ve−R1V+B1−ωR2Ve−R2V+ωE0V,where Peos is the pressure determined by the JWL equation of the state, V is the relative volume, E0 is the initial specific internal energy, and A, B, R1, R2, and ω are the five independent physical constants that describe the JWL equation.Table 2
Parameters of explosive and JWL equation.
Parametersρkg/m3Dm/sPCJGPaAGPaBGPaR1R2ωE0GPaV0Value125036005.4374.03.235.801.560.572.67281.0The parameters of the air model (∗Mat_Null) and the state equation (∗Eos_Linear_Polynomial) are shown in Table 3. The density of air is 1.225 kg/m3. The pressure is simulated by a linear polynomial equation of state (∗Eos_Linear_Polynomial). The equation is expressed as follows:(17)Ppoly=C0+C1μ+C2μ2+C3μ3+C4+C5μ+C6μ2E,μ=1V−1,where C0–C6 are constants, μ is the volume ratio, and E is the ratio of internal energy to initial volume.Table 3
Parameters of the air model and the state equation.
Parametersρ0E0voC0∼C3C4C5C6Value1.2252.5E51.000.40.40The plastic model (∗Mat_Plastic_Kinematic) is adopted for the rock and the blockage (parameters are shown in Table4). The Eulerian algorithm is used for the explosive, air, and blockage material models. The Lagrange algorithm is applied to the rock model. If the fluid-structure interaction algorithm is applied, no element distortion will occur. Given this advantage, the algorithm has been widely used in engineering numerical simulation with large deformation and high strain rate. Hence, the multimaterial fluid-structure interaction algorithm can be applied to deal with the interaction process of detonation products and the surrounding rock media. The maximum unit side length in the divided model mesh is 0.25 m, and the parts around blast holes are encrypted.Table 4
Parameters of the rock mass.
Parametersρkg/m3σtMPaσcMPaEGPaμDolomite30601466.7645.960.376


## 5. Comparison Analysis of Numerical Simulation Results and Theoretical Calculation

The boundary of the fissure circle formed after the cylindrical charge is detonated is determined by the dynamic tensile strength of the rock. According to previous research on the rock tensile strength of the main ore rocks in Barun open-pit mine, the dynamic tensile strength of the dolomite is taken asσ = 14.0 MPa. Therefore, if the effective stress peak value of each element in the model reaches or exceeds the dynamic tensile strength of this dolomite, then the rock represented by this element will be damaged. Otherwise, the rock will not be damaged to form a fractured ring. The center planes of the two holes on the bench slope are sequentially selected from the top to the bottom, and the effective stress-time diagram is drawn. Furthermore, the monitoring points are uniformly selected at the resistance line at the bottom of the bench slope, and the effective stress-time diagram is drawn.The middle point of the front row of holes and the position of the rear row of holes are selected as the cross-section, and the maximum effective stress is analyzed. The effective stress of the rock mass can reflect rock fragmentation. When hole 1 detonates for 1.99 ms, the effective stress in the middle of the section can reach 81.5 MPa, and the effective stress at the slope resistance line can reach up to 38.78 MPa. When the 43.39 ms hole 2 detonates at 1.39 ms, the stress wavefronts between the two holes are superimposed on each other, and the synergistic effect is obvious. When the 144 ms hole 3 detonates at 2 ms, the back row hole explosion stress wavefront reaches the front row hole center. The line position further plays the role of breaking the rock and pushing the rock forward.The comparison of the maximum effective stress at the top observation point of the two spacing parameter indicates that the stress values present a trend of decreasing first and then increasing. The maximum effective stress of the 13 m × 6 m section is larger than that of the 15 m × 5.5 m section, as shown in Figures8 and 9. The stress peak near the middle of the front holes indicates that the blasting action of the front row of holes sufficiently broke the rock between the two holes, creating a good free surface for the rear row of holes and achieving a good blasting effect.Figure 8
13 m × 6 m effective stress of the section between the front holes at different times. (a)t = 1.99 ms. (b) t = 43.49 ms. (c) t = 144.00 ms.
(a)(b)(c)Figure 9
15 m × 5.5 m effective stress of the section between the front holes at different times. (a)t = 1.99 ms. (b) t = 43.49 ms. (c) t = 144.00 ms.
(a)(b)(c)The maximum stress of the slope observation point of the two spacing parameters arrangement methods increases first and then decreases. As shown in Figures10 and 11, the maximum stress at the 13 m × 6 m spacing parameter observation point is far greater than the compressive strength of the rock, and the blasting energy is unevenly distributed along the bench slope, which can easily cause harmful effects, such as flying rocks. In comparison, the maximum stress at the observation point of the 15 m × 5.5 m spacing parameter is greater than the dynamic tensile strength of the rock, which can achieve the effect of rock breaking. Meanwhile, due to the existence of air gap, the rock breaking time is prolonged, and the energy distribution is more even. It not only will not cause the waste of blasting energy but also will not cause harmful effects, such as flying rocks and excessive vibration.Figure 10
13 m × 6 m effective stress of the section between the front holes at different times. (a)t = 1.99 ms. (b) t = 43.49 ms. (c) t = 144.00 ms.
(a)(b)(c)Figure 11
15 m × 5.5 m effective stress of the section between the front holes at different times. (a) t = 1.99 ms (b)t = 43.49 ms (c) t = 144.00 ms.
(a)(b)(c)As shown in Figures12 and 13, through numerical simulation, the maximum effective stress (22.6 MPa) at the bottom resistance line observation point of the 15 m × 5.5 m spacing parameter is much smaller than the maximum effective stress (29.58 MPa) at the 13 m × 6 m spacing parameter. Meanwhile, the existence of air gap equalizes the detonation gas pressure in the hole, and the stress at the 15 m × 5.5 m spacing parameter observation point is more uniform, which can achieve the rock breaking effect while avoiding the bedrock exit.Figure 12
13 m × 6 m effective stress of the section between the front holes at different times. (a)t = 1.99 ms. (b) t = 43.49 ms. (c) t = 144.00 ms.
(a)(b)(c)Figure 13
15 m × 5.5 m effective stress of the section between the front holes at different times. (a)t = 1.99 ms. (b) t = 43.49 ms. (c) t = 144.00 ms.
(a)(b)(c)Different combinations of spacing parameter will have different effects on the blasting effect. According to the maximum effective stress analysis of the simulated results of different section monitoring points and the comparison of the theoretical calculation values, as shown in Figures14–16, the three sections that meet the rock crushing requirements are selected for the field test. The evaluation of numerical simulation results of various spacing parameter indicates that the 15 m × 5.5 m combination comprehensive evaluation effect is the best.Figure 14
Effective stress of the section at the bottom resistance of bench.Figure 15
Effective stress of the section at the slope resistance of bench.Figure 16
Effective stress of the section at the top resistance of bench.


### 5.1. Field Test

The air deck charge structure and the large spacing parameter of the hole layout result in insufficient bench explosion energy and easily produce large blocks. During the blasting process, the resistance line at the bottom of the bench is extremely large, and the rock is difficult to break. Thus, high-bench blasting is more likely to produce the foundation than ordinary bench blasting. Through the improvement of Barun open-pit mine’s drilling rig, the drilling depth can reach 26 m to 27 m, which meets the requirements of 24-m-high bench drilling. At present, the large domestic air deck charge structure and the method of arranging holes with large spacing parameter have not been adopted in noncoal mines. Barun open-pit mine has carried out high-bench blasting tests and achieved significant results, but its use is still difficult to promote in mines. After improvement, the field test blasting area is designed to use vertical drilling for the 24-m-high bench blasting design. The drilling rig type is a YZ-55B roller drill with a drill bit diameter of 310 mm and a slope angle of 78°. The depth of the hole is 26 m, including the super deep is 2 m, the blockage is 7 m, the air deck is 7 m, and the remaining 12 m are used for charging. Considering the construction problems and the pressure bearing capacity of the air spacer and overcoming the bottom resistance line, the air spacer is arranged in the middle of the blast hole. Using a large spacing parameter, the spacing is 15 m, and the row spacing is 5.5 m. The hole-by-hole initiation method has a short interval of 25 ms. The main rock at the site is dolomite, and the other rock composition is relatively small. The simulation is performed under a single dolomite condition. This is the limitation of the simulation. Although some differences from the site exist, it can represent most of the site conditions and must be verified by experiments. The surface rock on-site is quaternary, with low hardness, small thickness, and uneven distribution, so the impact on blasting can be ignored.According to the existing shovel loading equipment in the mining area, the statistical analysis of the rock mass after blasting shows that the large lump rate in the experimental blasting area is only 0.01%, which meets the requirements of the shovel (as shown in Figure17). The TC-4850 blasting monitoring instrument was used to test the vibration of the field test explosion zone, which was compared with the conventional bench blasting vibration (Table 5). Analysis indicates that although the single-hole charge of high-bench blasting is greater than that of conventional blasting, the air deck weakens the peak pressure, so the blasting vibration increases slightly, and it meets safety requirements.Figure 17
Effective stress of the section between the front holes at different times.Table 5
Comparison of blasting vibration speed.
Blasting areaDirectionMaximum vibration speed (cm/s)1460 horizontal conventional blasting zoneX−5.551Y−3.707Z7.0321120 horizontal loosing blasting zoneX7.322Y−5.835Z8.763


## 5.1. Field Test

The air deck charge structure and the large spacing parameter of the hole layout result in insufficient bench explosion energy and easily produce large blocks. During the blasting process, the resistance line at the bottom of the bench is extremely large, and the rock is difficult to break. Thus, high-bench blasting is more likely to produce the foundation than ordinary bench blasting. Through the improvement of Barun open-pit mine’s drilling rig, the drilling depth can reach 26 m to 27 m, which meets the requirements of 24-m-high bench drilling. At present, the large domestic air deck charge structure and the method of arranging holes with large spacing parameter have not been adopted in noncoal mines. Barun open-pit mine has carried out high-bench blasting tests and achieved significant results, but its use is still difficult to promote in mines. After improvement, the field test blasting area is designed to use vertical drilling for the 24-m-high bench blasting design. The drilling rig type is a YZ-55B roller drill with a drill bit diameter of 310 mm and a slope angle of 78°. The depth of the hole is 26 m, including the super deep is 2 m, the blockage is 7 m, the air deck is 7 m, and the remaining 12 m are used for charging. Considering the construction problems and the pressure bearing capacity of the air spacer and overcoming the bottom resistance line, the air spacer is arranged in the middle of the blast hole. Using a large spacing parameter, the spacing is 15 m, and the row spacing is 5.5 m. The hole-by-hole initiation method has a short interval of 25 ms. The main rock at the site is dolomite, and the other rock composition is relatively small. The simulation is performed under a single dolomite condition. This is the limitation of the simulation. Although some differences from the site exist, it can represent most of the site conditions and must be verified by experiments. The surface rock on-site is quaternary, with low hardness, small thickness, and uneven distribution, so the impact on blasting can be ignored.According to the existing shovel loading equipment in the mining area, the statistical analysis of the rock mass after blasting shows that the large lump rate in the experimental blasting area is only 0.01%, which meets the requirements of the shovel (as shown in Figure17). The TC-4850 blasting monitoring instrument was used to test the vibration of the field test explosion zone, which was compared with the conventional bench blasting vibration (Table 5). Analysis indicates that although the single-hole charge of high-bench blasting is greater than that of conventional blasting, the air deck weakens the peak pressure, so the blasting vibration increases slightly, and it meets safety requirements.Figure 17
Effective stress of the section between the front holes at different times.Table 5
Comparison of blasting vibration speed.
Blasting areaDirectionMaximum vibration speed (cm/s)1460 horizontal conventional blasting zoneX−5.551Y−3.707Z7.0321120 horizontal loosing blasting zoneX7.322Y−5.835Z8.763


## 6. Conclusions

(1)
The theoretical calculations and the numerical simulation stress cloud diagrams were compared to analyze the rock stress state. Not only the distribution of holes with large spacing parameter has a good synergy effect between the holes but also the front row of holes can also provide a better facing surface for the rear row of holes to improve the blasting effect.(2)
The numerical simulation value has a larger stress value on the slope, and the coverage area on the top of the bench is larger than the theoretical calculation value, indicating that when the air deck is in the middle of the blast hole, the theoretical calculation value ignores the reflection of the stress after reaching the free surface. The stress value at the observation point has less dispersion. Combined with the explosive pile shape at the scene, the air deck charge effect in the middle of the blast hole is better. The application of air deck equalizes the detonation gas pressure in the hole and prolongs the rock breaking time, which not only reduce the number of explosives but also improve the crushing effect of the bottom rock.(3)
The theoretical calculation is basically consistent with the field test results. The application of loosening blasting technology with a large spacing parameter of 15 m × 5.5 m improves the quality of loosening blasting. This technology can reduce the bulk rate and the appearance of roots. It avoids harmful effects, such as flying rocks, reduces the blasting cost by approximately 20%, and achieves good results in the 1120 m horizontal blasting zone of Barun open-pit mine.(4)
The error between the theoretical and simulated values is small. Compared with the numerical calculation, the stress wave attenuation double exponential function correction equation based on the Mises strength criterion can be popularized in field production applications. The equation can be easily used by all kinds of technicians, which is beneficial to improving blasting efficiency and reducing the consumption of explosives.



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*Source: 6670276-2021-02-13.xml*