# A Study on Cut Blasting with Large Diameter Charges in Hard Rock Roadways

Authors: Bing Cheng; Haibo Wang; Qi Zong; Ying Xu; MengXiang Wang; Qiangqiang Zheng; Chengjie Li
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

To overcome the problems of poor cutting effects in hard rock roadways, a cut blasting technique with large diameter charges was developed; that is, the cut holes employ 50 mm diameter blast holes and 45 mm diameter explosive sticks, while the other holes adopt 42 mm diameter blast holes and 35 mm diameter explosive sticks. First, the effect of charge diameter on damage range and cut cavity formation was analyzed. Next, simulation of wedge cut for different charge diameters was conducted to reveal the stress wave developments and compare the stress field intensities. Finally, field tests were conducted to verify the viability of this technique. The results indicate that large diameter charges can increase the damage range around cut holes to improve the fragmentation degree of the rock mass in the cut cavity and significantly enhance the cavity formation power to better expel the rock mass fragments. The stress wave evolution of wedge cut was visualized using numerical simulations, which confirmed that the use of large diameter charges in cut holes increases the stress field intensity in the cut cavity and hence increases the damage degree of the rock mass. In this study, the use of a large diameter charge for cut blasting increased the average footage by 0.30 m, and the average utilization rate of blast holes increased by 12.5%. Therefore, the cutting effects in hard rock roadways can be improved by using large diameter charges, which increase the blasting footage and the utilization rate of blast holes.


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## Body

## 1. Introduction

Drilling and blasting is a traditional, efficient, and economical construction method, which is widely used in mining excavation engineering [1–3]. During roadway excavation, cut blasting is the key to developing an additional free face for subsequent blasting, which affects the overall blasting effect and the average effective footage [4, 5]. Based on the spatial relationship between the cut hole and the working face, cut blasting is divided into two groups: parallel cuts and incline cuts [6]. Wedge cut is the most commonly used cutting method in incline cuts, because its significant advantage is that a large cavity volume can be achieved with few blast holes and low explosive consumption [7].For roadway excavation, cut blasting is challenging due to the lack of a free face. Therefore, finding ways to improve cut efficiency has been the focus of research in rock roadway excavation. Several researchers have studied wedge cut blasting and have obtained significant findings, some of which are reported here. Shapiro [8] compared the blasting effects of different cutting methods and proved that wedge cut is more effective than other cutting methods used for shallow hole blasting. Dai and Du [9] theoretically analyzed the mechanism of cavity formation and proposed a design method of blasting parameters for wedge cut. Cardu and Seccatore [10] presented the statistical data of industrial trends and found that wedge cut is adopted in a wide variety of applications. Zou et al. [11] analyzed the vibration suppression of stepped-wedge cut blasting by using millisecond blasting principle and conducted field tests to compare conventional-wedge cut blasting with stepped-wedge cut blasting, and they demonstrated the superiority of the latter. Pu et al. [12] determined the factors affecting wedge cut blasting based on cement mortar model tests and calculated the gray correlation degree of these factors using gray correlation theory. Zhang and Yang [13] developed a multistep cut blasting technique and performed cavity formation analyses and field blasting tests. Then they conclude that this technique has the advantages of low resistance to cavity formation and good cutting effects. Liang et al. [14] tested laboratory models and discussed the effect of cut hole angle symmetry on cut blasting and found that a symmetrical arrangement of cut hole angles can improve the utilization rate of blasting energy. Shan et al. [15] studied the effects of cut hole space, cut hole top space, and cut hole angle on cut blasting through orthogonal model tests and thus obtained the optimal layout parameters of cut holes. Yuan et al. [16] performed a model test for wedge millisecond cut blasting, using concrete as a similar material, and discussed the blasting results from the standpoints of cut cavity volume, utilization rate of blast holes, and rock fragmentation level. Man et al. [17] compared the blasting energy distribution of different cut blasting methods according to the field test results. They found that the energy distribution of wedge cut is more uniform and mainly concentrated at high frequencies, while the energy distribution of parallel cut is more concentrated at low frequencies. Using the explicit dynamic finite element software ANSYS/LS-DYNA, Yang et al. [18] simulated the duplex wedge cut with center blast holes, and the simulation results revealed the stress field distribution in the cut cavity and the process by which cavity forms at the bottom of the cut holes. Hu et al. [19] used AUTOCAD and ANSYS to establish a numerical model for wedge cut blasting and applied rock damage criterion in the explicit dynamic solver LS-DYNA to simulate cut cavity extension. They also further investigated the applicability of wedge cut blasting in roadway excavation from the perspectives of temporal and spatial evolution, with multidirectional cutaway views.At present, most coal mines use 42 mm diameter blast holes and 35 mm diameter explosive sticks for the blasting excavation of rock roadways [20]. When the hardness coefficient of the rock mass is greater than 7, it is difficult to obtain a good cut blasting effect, which results in a low utilization rate of blast holes in subsequent blasting. The rapid development of drilling equipment in recent years has led to the use of drilling jumbos, which have greatly increased drilling efficiency and reduced labor intensity, which, in turn, have resulted in an increased feasibility of using large diameter charges for cut blasting. As a result, a cut blasting technology with large diameter charges has been developed to overcome the difficulties associated with cut blasting in hard rock roadways, that is, the cut holes now adopt 50 mm diameter blast holes and 45 mm diameter explosive sticks, while the other holes still use 42 mm diameter blast holes and 35 mm diameter explosive sticks. In this paper, the effects of charge diameter on damage range and cut cavity formation are analyzed based on the relevant blasting theory. Using ANSYS/LS-DYNA, simulation of wedge cut blasting for different charge diameters was conducted to understand the stress wave formations and compare the stress field intensities. Finally, field comparison tests are performed in a hard rock roadway to verify the viability of cut blasting technique with large diameter charges.


## 2. Effect of Charge Diameter on Damage Range

Based on traditional blasting theory, the damage of the surrounding medium after charge blasting mainly depends on the dynamic action of shock waves (or stress waves) and the quasi-static pressure of the detonation gas [21]. As illustrated in Figure 1, three damage zones are formed around a blast hole after charge blasting: the crushing zone, the cracking zone, and the vibration zone [22, 23]. In the proximity of the blast hole, the rock mass within a small range is crushed by a strong compression from a shock wave to form the crushing zone. Beyond this zone, the shock wave rapidly attenuates to form a stress wave, which promotes the development of initial cracks. The simultaneous effect of the quasi-static pressure of detonation gas results in the propagation of these cracks. Thus, the cracking zone results from both the stress wave and the quasi-static pressure of the detonation gas. Finally, the stress wave attenuates to a seismic wave, which only causes an elastic vibration of the medium in the far area rather than a direct damage to the rock mass.Figure 1
Damage zones around a blast hole.For rock excavation engineering, the ranges of the crushing and cracking zones are the most important considerations in the selection of blasting parameters. Recent studies indicate that the process of cut blasting can be divided into two stages. In the first stage, the rock mass in the cut cavity is damaged by blasting loads and forms rock fragments. In the second stage, the rock fragments are thrown out from the cut cavity due to the quasi-static pressure of the detonation gas. To simplify the calculations of the ranges of the crushing and cracking zones around a cut hole, only the dynamic action of the shock wave (or stress wave) is considered, and the quasi-static pressure of detonation gas is ignored [24].When a cylindrical charged hole is initiated, it usually radiates P waves and shear-vertical (SV) waves. Depending on the magnitude of the detonation velocity, P-Mach or/and SV-Mach waves can be formed [25]. It is observed that the dynamic process of cylindrical charge blasting is complex. However, in the current research, a two-dimensional simplified model that only considers P waves is usually employed to calculate the damage range of cylindrical charge.


### 2.1. Blasting Load

The detonation pressure is an important performance index of explosives, which determines the damage level of the rock mass. Based on the Chapman-Jouguet (C-J) detonation theory, the semiempirical formula for detonation pressure is expressed as [26](1)P0=11+kρ0D02,where P0 is the C-J detonation pressure; k is the adiabatic exponent, taken as k = 3; ρ0 is the explosive density; and D0 is the detonation velocity.When a radial decoupled charge structure is deployed in a blast hole, the detonation products initially compress the air gap to form the shock wave, which then acts on the blast hole wall [27]. According to the acoustic approximation theory, the initial pressure exerted on the wall of the blast hole is given by(2)Pr=12P0K−2kn,where Pr is the initial pressure of the shock wave on the wall of the blast hole; K is the radial decoupled coefficient, and K=db/dc, with db and dc being the diameters of the blast hole and explosive stick, respectively; and n is the augmentation factor, where n = 10.The strong compression from the shock wave causes the formation of the crushing zone, which consumes a large amount of energy. This causes the shock wave to rapidly attenuate to a stress wave, which then spreads to the surrounding rock mass. Since the charge length is much greater than the charge diameter, this situation can be simplified to a plane strain problem, ignoring the special blasting effects at both ends of the blast hole, and the stress at a point in the rock mass can be expressed as [28](3)σr=Prr¯−α,σθ=−bσr,σz=μ1−bσr,where σr, σθ, and σz are the radial stress, tangential stress, and axial stress, respectively; r¯ is the relative distance, and r¯=r/rb; r is the distance between a point in the rock mass and the center of the blast hole; rb is the radius of the blast hole, where rb=0.5db; α is the attenuation exponent, where α1=2+b in the shock wave zone and α2=2−b in the stress wave zone, with b being the lateral pressure coefficient, and b=μ/1−μ; and µ is the dynamic Poisson ratio of the rock mass, where μ=0.8μ0, with μ0 being the static Poisson ratio.


### 2.2. Damage Criteria

The damage criteria are determined by the mechanical properties and real stress conditions of the rock mass. Under the blasting load, the rock mass around the blast hole is in a three-dimensional mixed stress state including compression, tension, and shear [29]. Thus, the equivalent stress of a point in the rock mass can be described as(4)σi=12σr−σθ2+σθ−σz2+σz−σr2.Substituting equation (3) into equation (4), we get(5)σi=12σr1+b2+2μ1−μ1−b2+1+b2.Assuming thatA=1+b2+2μ1−μ1−b2+1+b2, equation (5) can be simplified as(6)σi=12σrA.Based on the von Mises criterion and rock damage characteristics, the rock damage criteria can be expressed as(7)σi>σcd,crushing zone,σi>σtd,cracking zone,where σcd and σtd are, respectively, the dynamic compression strength and dynamic tensile strength of rock.In contrast to static loads, rock materials are sensitive to high strain rates that occur under blasting loads, which need to be considered in analyses involving the use of the mechanical properties of rock [30–32]. In general, the dynamic strength of rock increases with strain rate, but the sensitivity to strain rate varies for different rocks [33]. For common types of rocks, the dynamic strength varies linearly with the cube root of the strain rate [34] as follows:(8)σcd=σc⋅ε˙1/3,σtd=σt⋅ε˙1/3,where σc and σt are the static compression strength and static tensile strength of rock, respectively; and ε˙ is the strain rate, where ε˙1/3=5 in the shock wave zone and ε˙1/3=3 in the stress wave zone [24].


### 2.3. Blasting Damage Range

The radii of the crushing and cracking zones, after a radial decoupled cylindrical charge blasting in a blast hole, can be calculated based on the above blasting load and rock damage criteria as follows:(9)Rc=ρ0D2K−2knA82σcd1/α1rb,(10)Rt=ρ0D2K−2knA82σcd1/α1σcdσtd1/α2rb,where Rc and Rt are the radii of the crushing and cracking zones, respectively.According to explosive detonation theory, the detonation velocity increases, within a certain range, with an increase in explosive stick diameter. The detonation velocities of class 2 coal mine permissible water-gel explosives with different diameters were measured by a detonation velocity meter, and the results are presented in Table1. It is observed that the detonation velocity of a 45 mm diameter explosive stick is 8.4% higher than that of a 35 mm diameter explosive stick. Also, standardized pieces of rock roadway samples were tested for physical and mechanical properties, and the results are listed in Table 2.Table 1
Detonation velocities of explosives with different diameters.
dc (mm)ρ0 (kg·m−3)D (m·s−1)35110034254511003713Table 2
Physical and mechanical properties of rock mass.
Density (kg·m−3)μ0σc (MPa)σt (MPa)24500.2595.89.6The values of the parameters for the charges, detonation velocities, and the mechanical properties of rocks noted above were substituted into equations (9) and (10) to calculate the radii of the crushing and cracking zones for different charge diameters, and the results are shown in Table 3. It can be seen that the radii of the crushing and cracking zones increase with charge diameter, and the damage range generated by a 50 mm diameter blast hole with a 45 mm diameter explosive stick is 1.31 times that generated by a 42 mm diameter blast hole with a 35 mm diameter explosive stick. Thus, further penetration of blasting cracks can be realized by large diameter charges to improve the fragmentation degree of the rock mass in the cut cavity.Table 3
Damage ranges for different charge diameters.
db (mm)dc (mm)Rc (mm)Rt (mm)423569347504591453


## 2.1. Blasting Load

The detonation pressure is an important performance index of explosives, which determines the damage level of the rock mass. Based on the Chapman-Jouguet (C-J) detonation theory, the semiempirical formula for detonation pressure is expressed as [26](1)P0=11+kρ0D02,where P0 is the C-J detonation pressure; k is the adiabatic exponent, taken as k = 3; ρ0 is the explosive density; and D0 is the detonation velocity.When a radial decoupled charge structure is deployed in a blast hole, the detonation products initially compress the air gap to form the shock wave, which then acts on the blast hole wall [27]. According to the acoustic approximation theory, the initial pressure exerted on the wall of the blast hole is given by(2)Pr=12P0K−2kn,where Pr is the initial pressure of the shock wave on the wall of the blast hole; K is the radial decoupled coefficient, and K=db/dc, with db and dc being the diameters of the blast hole and explosive stick, respectively; and n is the augmentation factor, where n = 10.The strong compression from the shock wave causes the formation of the crushing zone, which consumes a large amount of energy. This causes the shock wave to rapidly attenuate to a stress wave, which then spreads to the surrounding rock mass. Since the charge length is much greater than the charge diameter, this situation can be simplified to a plane strain problem, ignoring the special blasting effects at both ends of the blast hole, and the stress at a point in the rock mass can be expressed as [28](3)σr=Prr¯−α,σθ=−bσr,σz=μ1−bσr,where σr, σθ, and σz are the radial stress, tangential stress, and axial stress, respectively; r¯ is the relative distance, and r¯=r/rb; r is the distance between a point in the rock mass and the center of the blast hole; rb is the radius of the blast hole, where rb=0.5db; α is the attenuation exponent, where α1=2+b in the shock wave zone and α2=2−b in the stress wave zone, with b being the lateral pressure coefficient, and b=μ/1−μ; and µ is the dynamic Poisson ratio of the rock mass, where μ=0.8μ0, with μ0 being the static Poisson ratio.


## 2.2. Damage Criteria

The damage criteria are determined by the mechanical properties and real stress conditions of the rock mass. Under the blasting load, the rock mass around the blast hole is in a three-dimensional mixed stress state including compression, tension, and shear [29]. Thus, the equivalent stress of a point in the rock mass can be described as(4)σi=12σr−σθ2+σθ−σz2+σz−σr2.Substituting equation (3) into equation (4), we get(5)σi=12σr1+b2+2μ1−μ1−b2+1+b2.Assuming thatA=1+b2+2μ1−μ1−b2+1+b2, equation (5) can be simplified as(6)σi=12σrA.Based on the von Mises criterion and rock damage characteristics, the rock damage criteria can be expressed as(7)σi>σcd,crushing zone,σi>σtd,cracking zone,where σcd and σtd are, respectively, the dynamic compression strength and dynamic tensile strength of rock.In contrast to static loads, rock materials are sensitive to high strain rates that occur under blasting loads, which need to be considered in analyses involving the use of the mechanical properties of rock [30–32]. In general, the dynamic strength of rock increases with strain rate, but the sensitivity to strain rate varies for different rocks [33]. For common types of rocks, the dynamic strength varies linearly with the cube root of the strain rate [34] as follows:(8)σcd=σc⋅ε˙1/3,σtd=σt⋅ε˙1/3,where σc and σt are the static compression strength and static tensile strength of rock, respectively; and ε˙ is the strain rate, where ε˙1/3=5 in the shock wave zone and ε˙1/3=3 in the stress wave zone [24].


## 2.3. Blasting Damage Range

The radii of the crushing and cracking zones, after a radial decoupled cylindrical charge blasting in a blast hole, can be calculated based on the above blasting load and rock damage criteria as follows:(9)Rc=ρ0D2K−2knA82σcd1/α1rb,(10)Rt=ρ0D2K−2knA82σcd1/α1σcdσtd1/α2rb,where Rc and Rt are the radii of the crushing and cracking zones, respectively.According to explosive detonation theory, the detonation velocity increases, within a certain range, with an increase in explosive stick diameter. The detonation velocities of class 2 coal mine permissible water-gel explosives with different diameters were measured by a detonation velocity meter, and the results are presented in Table1. It is observed that the detonation velocity of a 45 mm diameter explosive stick is 8.4% higher than that of a 35 mm diameter explosive stick. Also, standardized pieces of rock roadway samples were tested for physical and mechanical properties, and the results are listed in Table 2.Table 1
Detonation velocities of explosives with different diameters.
dc (mm)ρ0 (kg·m−3)D (m·s−1)35110034254511003713Table 2
Physical and mechanical properties of rock mass.
Density (kg·m−3)μ0σc (MPa)σt (MPa)24500.2595.89.6The values of the parameters for the charges, detonation velocities, and the mechanical properties of rocks noted above were substituted into equations (9) and (10) to calculate the radii of the crushing and cracking zones for different charge diameters, and the results are shown in Table 3. It can be seen that the radii of the crushing and cracking zones increase with charge diameter, and the damage range generated by a 50 mm diameter blast hole with a 45 mm diameter explosive stick is 1.31 times that generated by a 42 mm diameter blast hole with a 35 mm diameter explosive stick. Thus, further penetration of blasting cracks can be realized by large diameter charges to improve the fragmentation degree of the rock mass in the cut cavity.Table 3
Damage ranges for different charge diameters.
db (mm)dc (mm)Rc (mm)Rt (mm)423569347504591453


## 3. The Effect of Charge Diameter on Cut Cavity Formation

### 3.1. Wedge Cut Blasting Model

To study the influence of charge diameter on cut cavity formation, a wedge cut blasting model was established. As illustrated in Figure2, ACDF is the free face; AG, BH, CI, DJ, EK, and FL are the cut holes; x is the cut hole top space; y is the cut hole bottom space; a is the cut hole space; H/sinβ is the cut hole length; β is the cut hole angle; H is the vertical depth of the cut hole.Figure 2
Wedge cut blasting model.


### 3.2. Analysis of Resistance to Cavity Formation

In addition to ACDF as a free face, five other surfaces have resistance to cavity formation. The shear resistance of AFLG, CDJI, ACIG, and FDJL can be estimated by the Mohr-Coulomb criterion, and the tensile resistance of GIJL is related to the tensile strength of the rock mass and the bottom area of the cut cavity [35].The shear resistance of AFLG and CDJI is given by(11)QAFLG=QCDJI=c+σ1tanϕx+yH2,where c is the cohesion; φ is the internal friction angle; σ1 is the vertical normal stress.The shear resistance of ACIG and FDJL is calculated from(12)QACIG=QFDJL=c+σ2tanϕ2aHsinβ,where σ2 is the horizontal normal stress: σ2=σ1μ0/1−μ0.The tensile resistanceT of GIJL is expressed as(13)T=2ayσt.The cavity formation resistancef is represented as(14)f=QAFLG+QCDJI+QACIG+QFDJLsinβ+T.


### 3.3. Analysis of Cavity Formation Power

The cavity formation power is derived from the quasi-static pressure of the detonation gas. Based on adiabatic expansion theory, the force exerted directly on the rock mass, after charge blasting in cut holes with good stemming, is given by [36](15)F0=mP0K−2kLcdb,where m is the number of cut holes; F0 is the force from the detonating gas acting directly on the rock mass; Lc is the charge length.Since the force exerted directly on the rock mass is parallel to the radial direction of the cut hole and there is a certain angle between the cut hole and the free face, the component of the force towards the free face, which constitutes the cavity formation power, is described by(16)F=F0cosβ=mP0K−2kLcdbcosβ,where F is the cavity formation power.Based on the above analysis, rock fragments can be expelled from the cut cavity when the cavity formation power is greater than the cavity formation resistance, which is expressed as(17)F>f.When the number of cut holesm, charge length Lc, and cut hole angle β remain constant, it can be calculated that the cavity formation power generated by 50 mm diameter cut holes and 45 mm diameter explosive sticks is 2.22 times that generated by 42 mm diameter cut holes and 35 mm diameter explosive sticks. Therefore, for a constant cavity formation resistance, the cavity formation power of cut blasting with a large diameter charge is significantly greater than that of cut blasting with a small diameter charge, which is more conducive to expelling the rock mass fragments from the cut cavity.


## 3.1. Wedge Cut Blasting Model

To study the influence of charge diameter on cut cavity formation, a wedge cut blasting model was established. As illustrated in Figure2, ACDF is the free face; AG, BH, CI, DJ, EK, and FL are the cut holes; x is the cut hole top space; y is the cut hole bottom space; a is the cut hole space; H/sinβ is the cut hole length; β is the cut hole angle; H is the vertical depth of the cut hole.Figure 2
Wedge cut blasting model.


## 3.2. Analysis of Resistance to Cavity Formation

In addition to ACDF as a free face, five other surfaces have resistance to cavity formation. The shear resistance of AFLG, CDJI, ACIG, and FDJL can be estimated by the Mohr-Coulomb criterion, and the tensile resistance of GIJL is related to the tensile strength of the rock mass and the bottom area of the cut cavity [35].The shear resistance of AFLG and CDJI is given by(11)QAFLG=QCDJI=c+σ1tanϕx+yH2,where c is the cohesion; φ is the internal friction angle; σ1 is the vertical normal stress.The shear resistance of ACIG and FDJL is calculated from(12)QACIG=QFDJL=c+σ2tanϕ2aHsinβ,where σ2 is the horizontal normal stress: σ2=σ1μ0/1−μ0.The tensile resistanceT of GIJL is expressed as(13)T=2ayσt.The cavity formation resistancef is represented as(14)f=QAFLG+QCDJI+QACIG+QFDJLsinβ+T.


## 3.3. Analysis of Cavity Formation Power

The cavity formation power is derived from the quasi-static pressure of the detonation gas. Based on adiabatic expansion theory, the force exerted directly on the rock mass, after charge blasting in cut holes with good stemming, is given by [36](15)F0=mP0K−2kLcdb,where m is the number of cut holes; F0 is the force from the detonating gas acting directly on the rock mass; Lc is the charge length.Since the force exerted directly on the rock mass is parallel to the radial direction of the cut hole and there is a certain angle between the cut hole and the free face, the component of the force towards the free face, which constitutes the cavity formation power, is described by(16)F=F0cosβ=mP0K−2kLcdbcosβ,where F is the cavity formation power.Based on the above analysis, rock fragments can be expelled from the cut cavity when the cavity formation power is greater than the cavity formation resistance, which is expressed as(17)F>f.When the number of cut holesm, charge length Lc, and cut hole angle β remain constant, it can be calculated that the cavity formation power generated by 50 mm diameter cut holes and 45 mm diameter explosive sticks is 2.22 times that generated by 42 mm diameter cut holes and 35 mm diameter explosive sticks. Therefore, for a constant cavity formation resistance, the cavity formation power of cut blasting with a large diameter charge is significantly greater than that of cut blasting with a small diameter charge, which is more conducive to expelling the rock mass fragments from the cut cavity.


## 4. Numerical Simulation of Wedge Cut Blasting for Different Charge Diameters

### 4.1. Numerical Model

To investigate the formation of the stress wave and the intensity of the stress field, three-dimensional numerical models of wedge cut blasting for two charge diameters were established by a solid element of eight nodes in ANSYS/LS-DYNA [37]. As shown in Figure 3, for both numerical models, the size of the rock mass is 4000 mm × 3000 mm × 3000 mm with six cut holes symmetrically arranged on the left and right sides of the model; the cut hole angle is 77°, the cut hole top space is 1500 mm, the cut hole bottom space is 300 mm, the cut hole space is 500 mm, the cut hole depth is 2600 mm, and the charge length is 1320 mm. The difference between the two numerical models is that the model with the large diameter charge adopts 50 mm diameter cut holes and 45 mm diameter explosive sticks, while the model with the small diameter charge adopts 42 mm diameter cut holes and 35 mm diameter explosive sticks.Figure 3
Numerical model of wedge cut blasting (unit: mm). (a) Front view. (b) Left view. (c) Top view (or A-A section).
(a)(b)(c)In this simulation, the explosive and air were defined as ALE grids, and the Lagrange algorithm was performed for the rock mass and stemming. Using the keyword∗CONSTRAINED_LAGRANGE_IN_SOLID, the fluid-solid coupling algorithm was defined to realize the transfer of blasting energy from the detonation products to the rock mass and stemming [38, 39]. Nonreflecting boundaries were applied to the model surface in addition to the working face to reduce the influence of stress wave reflections on the simulation results [40, 41]. Also, the keyword ∗INITIAL_DETONATION was used in the calculation program to define the initiation points at the bottom of each cut hole [42].Blair [43, 44] noted that grid size has an important effect on calculation accuracy and time consumption. In this simulation, due to the limitation of computer capacity, small grids were used near the cut holes and at the bottom of the cut cavity to ensure precision, while large grids were adopted farther from the cut holes to reduce computational complexity and improve efficiency. Moreover, numerical convergence tests were performed to obtain a reasonable mesh. For this purpose, the number of grids was increased for successive tests until the difference between the results of two consecutive tests was less than 5% [45]. The meshing of the rock mass model used for numerical simulations is shown in Figure 4.Figure 4
Meshing of rock mass model.


### 4.2. Material Model

The key to conducting numerical simulations of engineering blasting is the determination of the blasting load. In this paper, the∗MAT_HIGH_EXPLOSIVE_BURN model embedded in the LS-DYNA was chosen as the explosive, and the JWL state equation was used to accurately describe the relationship between the expanding volume, pressure, and energy change of detonation products [46]. The JWL state equation is expressed as [47–49](18)peos=Aeos1−ωR1Ve−R1V+Beos1−ωR2Ve−R2V+ωE0V,where peos, E0, and V are the pressure, specific internal energy, and relative volume of the detonation products, respectively; and Aeos, Beos, R1, R2, and ω are material constants. Some of the main parameters of the JWL state equation are shown in Table 4.Table 4
Parameters used in the JWL state equation for the explosive.
Aeos (GPa)Beos (GPa)R1R2ωE0 (GPa)V02140.1824.150.950.154.191.0Air, being a fluid, is usually described by constitutive and state equations. In this simulation, the∗MAT_NULL model was used as the constitutive equation, and the following linear polynomial equation was selected as the state equation [50, 51]:(19)p0=C0+C1ξ+C2ξ2+C3ξ3+C4+C5ξ+C6ξ2E1,ξ=ρρa−1,where p0 is the pressure, and C0, C1,C2, C3, C4, C5, and C6 are material constants; ξ is the nonlinear coefficient of viscosity; E1 is the internal energy per unit volume; ρ is the density at test conditions; ρa is the nominal density. The parameters for air and the above linear polynomial state equations are listed in Table 5.Table 5
Parameters for air and state equation.
ρa (kg·m−3)C0C1C2C3C4C5C61.250.000.000.000.000.400.400.00The rock mass was modeled using the∗MAT_PLASTIC_KINEMATIC model, which considers the effect of strain under a blasting load [52]. Based on the Cowper and Symonds empirical formula, an amplification factor related to strain rate is introduced into the yield stress equation as follows [53, 54]:(20)σY=ησ0+β1Epεeff,η=1+ε˙C1/P,where σY is the current yield strength; η is the amplification factor of yield strength; σ0 is the initial yield strength; β1 is the hardening regulation parameter; Ep is the plastic hardening modulus; εeff is the effective plastic strain; ε˙ is the strain rate; C is the Cowper strain rate parameter; P is the Symonds strain rate parameter. The parameters for the rock mass material have been previously presented in Table 2.The stemming was modeled using the∗MAT_SOIL_AND_FORM model, which can effectively simulate the liquefaction characteristics of sand under dynamic load [55]. The parameters for the stemming material are listed in Table 6.Table 6
Parameters for the stemming material.
Density (kg·m−3)Bulk modulus (GPa)Shear modulus (GPa)Tensile cut-off (GPa)18001.320.0160.0


### 4.3. Analysis of Simulation Results

Numerical and material models have been used to simulate the stress wave evolution of cut blasting models with small and large diameter charges; then the numerical models were segmented along A-A section in LS-PREPOST. Figures5 and 6 show the evolution of effective stress field of the numerical models with the small and large charge diameters, respectively.Figure 5
Effective stress wave evolution of cut blasting model for a small charge diameter. (a)t = 045 μs; (b) t = 150 μs; (c) t = 320 μs; (d) t = 400 μs; (e) t = 490 μs; (f) t = 600 μs.
(a)(b)(c)(d)(e)(f)Figure 6
Effective stress wave evolution of cut blasting model for a large charge diameter. (a)t = 045 μs. (b) t = 150 μs. (c) t = 320 μs. (d) t = 400 μs. (e) t = 490 μs. (f) t = 600 μs.
(a)(b)(c)(d)(e)(f)As shown in Figures5 and 6, explosive detonation initiates at the bottom of the cut hole and propagates along the cut hole towards the free face, with the simultaneous propagation of the stress wave towards the free face with a conical wavefront. Due to the proximity of the bottoms of the cut holes, the resulting superposition of the stress waves appears in the middle of the cut cavity at t=45μs, which can enhance the damage of the rock mass in the cut cavity. With an increase in the distance between the cut holes, the superposition effect becomes weaker. Although the explosive detonation of each cut hole is completed at t=320μs, the stress wave continues to propagate towards the free face with a circular arc wavefront. When the stress wave reaches the free face at t = 490 μs, it is reflected as a tensile stress wave. The reflected tensile wave encounters the propagating compression wave, resulting in a complex stress superposition, which causes further damage to the rock mass in the cut cavity. The above analysis demonstrates that simulation results can reveal the stress wave evolution of wedge cut blasting.Comparing Figures5 and 6, the range of high stress around the cut hole in the numerical model with the large diameter charge is significantly larger than that in the numerical model with the small diameter charge. Likewise, the stress wave superposition effect in the middle of the cut cavity in the numerical model with the large diameter charge is more significant than that in the numerical model with the small diameter charge. To compare stress field intensities in the cut cavity for different charge diameters, a measuring line extending from the free face to the bottom was placed at the center of both numerical models, as shown in Figure 3. A measuring point was placed every 0.1 m along this measuring line, and the peak effective stress at these measuring points was output to plot the curve of peak effective stress with cut depth.As illustrated in Figure7, both numerical models have the same trend in the variation of the peak effective stress with cut depth along the central measuring line. Aside from a small fluctuation at a cut depth of 1.2 m, the peak effective stress increases with cut depth, for a cut depth in the range of 0∼2.5 m, and reaches a maximum value at a cut depth of 2.5 m. Thereafter, the peak effective stress decreases rapidly with an increase in cut depth. It also can be seen that the peak effective stress at all measuring points of the numerical model with the large diameter charge is higher than that of the numerical model with the small diameter charge. Furthermore, the difference in peak effective stress between the two numerical models remains approximately constant for a cut depth range of 0∼1.3 m and increases gradually for a cut depth range of 1.4∼2.5 m.Figure 7
Peak effective stress with cut depth along a central measuring line.As shown in Figure7, the maximum and average values of peak effective stress at the measuring points along the central measuring line of the numerical model with the small diameter charge are 216.8 MPa and 86.7 MPa, respectively. The corresponding maximum and average values of peak effective stress at the measuring points of the numerical model with the large diameter charge are 318.1 MPa and 122.7 MPa, respectively. Thus, the maximum and average values of peak effective stress at the measuring points along the central measuring line of the numerical model with the large diameter charge are 46.7% and 41.5% higher than that of the numerical model with the small diameter charge, respectively. This result demonstrates that the large diameter charge can increase the effective stress field intensity in the cut cavity and hence enhance the damage degree of the rock mass.


## 4.1. Numerical Model

To investigate the formation of the stress wave and the intensity of the stress field, three-dimensional numerical models of wedge cut blasting for two charge diameters were established by a solid element of eight nodes in ANSYS/LS-DYNA [37]. As shown in Figure 3, for both numerical models, the size of the rock mass is 4000 mm × 3000 mm × 3000 mm with six cut holes symmetrically arranged on the left and right sides of the model; the cut hole angle is 77°, the cut hole top space is 1500 mm, the cut hole bottom space is 300 mm, the cut hole space is 500 mm, the cut hole depth is 2600 mm, and the charge length is 1320 mm. The difference between the two numerical models is that the model with the large diameter charge adopts 50 mm diameter cut holes and 45 mm diameter explosive sticks, while the model with the small diameter charge adopts 42 mm diameter cut holes and 35 mm diameter explosive sticks.Figure 3
Numerical model of wedge cut blasting (unit: mm). (a) Front view. (b) Left view. (c) Top view (or A-A section).
(a)(b)(c)In this simulation, the explosive and air were defined as ALE grids, and the Lagrange algorithm was performed for the rock mass and stemming. Using the keyword∗CONSTRAINED_LAGRANGE_IN_SOLID, the fluid-solid coupling algorithm was defined to realize the transfer of blasting energy from the detonation products to the rock mass and stemming [38, 39]. Nonreflecting boundaries were applied to the model surface in addition to the working face to reduce the influence of stress wave reflections on the simulation results [40, 41]. Also, the keyword ∗INITIAL_DETONATION was used in the calculation program to define the initiation points at the bottom of each cut hole [42].Blair [43, 44] noted that grid size has an important effect on calculation accuracy and time consumption. In this simulation, due to the limitation of computer capacity, small grids were used near the cut holes and at the bottom of the cut cavity to ensure precision, while large grids were adopted farther from the cut holes to reduce computational complexity and improve efficiency. Moreover, numerical convergence tests were performed to obtain a reasonable mesh. For this purpose, the number of grids was increased for successive tests until the difference between the results of two consecutive tests was less than 5% [45]. The meshing of the rock mass model used for numerical simulations is shown in Figure 4.Figure 4
Meshing of rock mass model.


## 4.2. Material Model

The key to conducting numerical simulations of engineering blasting is the determination of the blasting load. In this paper, the∗MAT_HIGH_EXPLOSIVE_BURN model embedded in the LS-DYNA was chosen as the explosive, and the JWL state equation was used to accurately describe the relationship between the expanding volume, pressure, and energy change of detonation products [46]. The JWL state equation is expressed as [47–49](18)peos=Aeos1−ωR1Ve−R1V+Beos1−ωR2Ve−R2V+ωE0V,where peos, E0, and V are the pressure, specific internal energy, and relative volume of the detonation products, respectively; and Aeos, Beos, R1, R2, and ω are material constants. Some of the main parameters of the JWL state equation are shown in Table 4.Table 4
Parameters used in the JWL state equation for the explosive.
Aeos (GPa)Beos (GPa)R1R2ωE0 (GPa)V02140.1824.150.950.154.191.0Air, being a fluid, is usually described by constitutive and state equations. In this simulation, the∗MAT_NULL model was used as the constitutive equation, and the following linear polynomial equation was selected as the state equation [50, 51]:(19)p0=C0+C1ξ+C2ξ2+C3ξ3+C4+C5ξ+C6ξ2E1,ξ=ρρa−1,where p0 is the pressure, and C0, C1,C2, C3, C4, C5, and C6 are material constants; ξ is the nonlinear coefficient of viscosity; E1 is the internal energy per unit volume; ρ is the density at test conditions; ρa is the nominal density. The parameters for air and the above linear polynomial state equations are listed in Table 5.Table 5
Parameters for air and state equation.
ρa (kg·m−3)C0C1C2C3C4C5C61.250.000.000.000.000.400.400.00The rock mass was modeled using the∗MAT_PLASTIC_KINEMATIC model, which considers the effect of strain under a blasting load [52]. Based on the Cowper and Symonds empirical formula, an amplification factor related to strain rate is introduced into the yield stress equation as follows [53, 54]:(20)σY=ησ0+β1Epεeff,η=1+ε˙C1/P,where σY is the current yield strength; η is the amplification factor of yield strength; σ0 is the initial yield strength; β1 is the hardening regulation parameter; Ep is the plastic hardening modulus; εeff is the effective plastic strain; ε˙ is the strain rate; C is the Cowper strain rate parameter; P is the Symonds strain rate parameter. The parameters for the rock mass material have been previously presented in Table 2.The stemming was modeled using the∗MAT_SOIL_AND_FORM model, which can effectively simulate the liquefaction characteristics of sand under dynamic load [55]. The parameters for the stemming material are listed in Table 6.Table 6
Parameters for the stemming material.
Density (kg·m−3)Bulk modulus (GPa)Shear modulus (GPa)Tensile cut-off (GPa)18001.320.0160.0


## 4.3. Analysis of Simulation Results

Numerical and material models have been used to simulate the stress wave evolution of cut blasting models with small and large diameter charges; then the numerical models were segmented along A-A section in LS-PREPOST. Figures5 and 6 show the evolution of effective stress field of the numerical models with the small and large charge diameters, respectively.Figure 5
Effective stress wave evolution of cut blasting model for a small charge diameter. (a)t = 045 μs; (b) t = 150 μs; (c) t = 320 μs; (d) t = 400 μs; (e) t = 490 μs; (f) t = 600 μs.
(a)(b)(c)(d)(e)(f)Figure 6
Effective stress wave evolution of cut blasting model for a large charge diameter. (a)t = 045 μs. (b) t = 150 μs. (c) t = 320 μs. (d) t = 400 μs. (e) t = 490 μs. (f) t = 600 μs.
(a)(b)(c)(d)(e)(f)As shown in Figures5 and 6, explosive detonation initiates at the bottom of the cut hole and propagates along the cut hole towards the free face, with the simultaneous propagation of the stress wave towards the free face with a conical wavefront. Due to the proximity of the bottoms of the cut holes, the resulting superposition of the stress waves appears in the middle of the cut cavity at t=45μs, which can enhance the damage of the rock mass in the cut cavity. With an increase in the distance between the cut holes, the superposition effect becomes weaker. Although the explosive detonation of each cut hole is completed at t=320μs, the stress wave continues to propagate towards the free face with a circular arc wavefront. When the stress wave reaches the free face at t = 490 μs, it is reflected as a tensile stress wave. The reflected tensile wave encounters the propagating compression wave, resulting in a complex stress superposition, which causes further damage to the rock mass in the cut cavity. The above analysis demonstrates that simulation results can reveal the stress wave evolution of wedge cut blasting.Comparing Figures5 and 6, the range of high stress around the cut hole in the numerical model with the large diameter charge is significantly larger than that in the numerical model with the small diameter charge. Likewise, the stress wave superposition effect in the middle of the cut cavity in the numerical model with the large diameter charge is more significant than that in the numerical model with the small diameter charge. To compare stress field intensities in the cut cavity for different charge diameters, a measuring line extending from the free face to the bottom was placed at the center of both numerical models, as shown in Figure 3. A measuring point was placed every 0.1 m along this measuring line, and the peak effective stress at these measuring points was output to plot the curve of peak effective stress with cut depth.As illustrated in Figure7, both numerical models have the same trend in the variation of the peak effective stress with cut depth along the central measuring line. Aside from a small fluctuation at a cut depth of 1.2 m, the peak effective stress increases with cut depth, for a cut depth in the range of 0∼2.5 m, and reaches a maximum value at a cut depth of 2.5 m. Thereafter, the peak effective stress decreases rapidly with an increase in cut depth. It also can be seen that the peak effective stress at all measuring points of the numerical model with the large diameter charge is higher than that of the numerical model with the small diameter charge. Furthermore, the difference in peak effective stress between the two numerical models remains approximately constant for a cut depth range of 0∼1.3 m and increases gradually for a cut depth range of 1.4∼2.5 m.Figure 7
Peak effective stress with cut depth along a central measuring line.As shown in Figure7, the maximum and average values of peak effective stress at the measuring points along the central measuring line of the numerical model with the small diameter charge are 216.8 MPa and 86.7 MPa, respectively. The corresponding maximum and average values of peak effective stress at the measuring points of the numerical model with the large diameter charge are 318.1 MPa and 122.7 MPa, respectively. Thus, the maximum and average values of peak effective stress at the measuring points along the central measuring line of the numerical model with the large diameter charge are 46.7% and 41.5% higher than that of the numerical model with the small diameter charge, respectively. This result demonstrates that the large diameter charge can increase the effective stress field intensity in the cut cavity and hence enhance the damage degree of the rock mass.


## 5. Field Comparison Tests

### 5.1. Test Conditions and Blasting Parameters

To further verify the practicality of cut blasting technology using a large diameter charge, field comparison tests of two cut blasting methods were performed in a hard rock roadway, and the tests for each method were conducted 12 times. The field tests of cut blasting with a small diameter charge were conducted with a blast hole diameter of 42 mm for the cut holes and other holes and with 35 mm diameter explosive sticks. During the field tests of cut blasting with a large diameter charge, the cut holes were 50 mm diameter blast holes and 45 mm diameter explosive sticks were utilized, while the other holes were 42 mm diameter blast holes and 35 mm diameter explosive sticks were utilized.The field tests were conducted at the −650 m level rail roadway of the Panbei Coal Mine in Huainan, Anhui province, China. This rail roadway has a straight wall arch section with a width of 5.4 m, a height of 3.95 m, and a sectional area of 19.03 m2, where the height of the straight wall is 1.1 m. Based on geological survey data, the rock strata are mainly composed of hard fine sandstone with good integrity and few joint fissures, which cause difficulty in cut blasting. The physical and mechanical parameters of fine sandstone have been previously listed in Table 2.For the field tests, a dual-arm hydraulic drilling jumbo was used for drilling operations, and class 2 coal mine permissible water-gel explosive sticks with 1–5 segment millisecond delay electric detonators were used as blasting materials. The explosive sticks used were of two specifications:D45 mm × L400 mm × M700 g and D35 mm × L330 mm × M350 g. The blasting parameters for different cut methods are listed in Tables 7 and 8, and the layout of the blast holes is shown in Figure 8. Figure 9 shows some of the relevant construction operations of the field tests.Table 7
Blasting parameters for cut blasting with a small diameter charge.
Hole nameHole no.Number of holesHole diameter (mm)Charge diameter (mm)Charge quantityDetonator orderExplosive volume per holeTotal weight (kg)Cut hole1–6642354.08.401Auxiliary hole7–14842353.08.402Auxiliary hole15–251142353.011.553Auxiliary hole26–391442353.014.704Peripheral hole40–602142352.014.705Bottom hole61–68842353.08.405Total—68———66.15—Table 8
Blasting parameters for cut blasting with a large diameter charge.
Hole nameHole no.Number of holesHole diameter (mm)Charge diameter (mm)Charge quantityDetonator orderExplosive volume per holeTotal weight (kg)Cut hole1–6650453.313.861Auxiliary hole7–14842353.08.402Auxiliary hole15–251142353.011.553Auxiliary hole26–391442353.014.704Peripheral hole40–602142352.014.705Bottom hole61–68842353.08.405Total—68———71.61—Figure 8
Blast hole layout (unit: mm). (a) Front view. (b) Left view. (c) Top view.
(a)(b)(c)Figure 9
Construction operations of field tests. (a) Check of hole space. (b) Check of hole depth. (c) Charge of blast holes. (d) Measurement of footage.
(a)(b)(c)(d)


### 5.2. Results of Field Tests

Comparative data of the blasting effects are presented in Table9. For the 42 mm diameter blast holes with 35 mm diameter explosive sticks used for cut blasting, the average footage is 1.9 m, and the average utilization rate of the blast holes is 79.2%. For the 50 mm diameter blast holes with 45 mm diameter explosive sticks used for cut blasting, the average footage reaches 2.2 m, and the average utilization rate of the blast holes reaches 91.7%. Thus, in contrast to cut blasting with the small diameter charge, the average footage is increased by 0.30 m, and the average utilization rate of blast holes is increased by 12.5%, with the large diameter charge.Table 9
Comparative data of blasting effects.
No.Cut blasting with small diameter chargeCut blasting with large diameter chargeFootage (m)Utilization rate of blast hole (%)Footage (m)Utilization rate of blast hole (%)11.9581.32.2091.721.9079.22.2091.731.9079.22.1589.641.9079.22.2593.851.8577.12.1589.661.9079.22.2091.771.9581.32.2593.881.8577.12.2091.791.8577.12.1589.6101.9079.22.2593.8111.9581.32.2091.7121.9079.22.2091.7Average1.9079.22.2091.7The results of field comparison tests indicate that the use of a large diameter charge can improve the cut effect in hard rock roadway and hence increase the blasting footage and the utilization rate of blast holes.


## 5.1. Test Conditions and Blasting Parameters

To further verify the practicality of cut blasting technology using a large diameter charge, field comparison tests of two cut blasting methods were performed in a hard rock roadway, and the tests for each method were conducted 12 times. The field tests of cut blasting with a small diameter charge were conducted with a blast hole diameter of 42 mm for the cut holes and other holes and with 35 mm diameter explosive sticks. During the field tests of cut blasting with a large diameter charge, the cut holes were 50 mm diameter blast holes and 45 mm diameter explosive sticks were utilized, while the other holes were 42 mm diameter blast holes and 35 mm diameter explosive sticks were utilized.The field tests were conducted at the −650 m level rail roadway of the Panbei Coal Mine in Huainan, Anhui province, China. This rail roadway has a straight wall arch section with a width of 5.4 m, a height of 3.95 m, and a sectional area of 19.03 m2, where the height of the straight wall is 1.1 m. Based on geological survey data, the rock strata are mainly composed of hard fine sandstone with good integrity and few joint fissures, which cause difficulty in cut blasting. The physical and mechanical parameters of fine sandstone have been previously listed in Table 2.For the field tests, a dual-arm hydraulic drilling jumbo was used for drilling operations, and class 2 coal mine permissible water-gel explosive sticks with 1–5 segment millisecond delay electric detonators were used as blasting materials. The explosive sticks used were of two specifications:D45 mm × L400 mm × M700 g and D35 mm × L330 mm × M350 g. The blasting parameters for different cut methods are listed in Tables 7 and 8, and the layout of the blast holes is shown in Figure 8. Figure 9 shows some of the relevant construction operations of the field tests.Table 7
Blasting parameters for cut blasting with a small diameter charge.
Hole nameHole no.Number of holesHole diameter (mm)Charge diameter (mm)Charge quantityDetonator orderExplosive volume per holeTotal weight (kg)Cut hole1–6642354.08.401Auxiliary hole7–14842353.08.402Auxiliary hole15–251142353.011.553Auxiliary hole26–391442353.014.704Peripheral hole40–602142352.014.705Bottom hole61–68842353.08.405Total—68———66.15—Table 8
Blasting parameters for cut blasting with a large diameter charge.
Hole nameHole no.Number of holesHole diameter (mm)Charge diameter (mm)Charge quantityDetonator orderExplosive volume per holeTotal weight (kg)Cut hole1–6650453.313.861Auxiliary hole7–14842353.08.402Auxiliary hole15–251142353.011.553Auxiliary hole26–391442353.014.704Peripheral hole40–602142352.014.705Bottom hole61–68842353.08.405Total—68———71.61—Figure 8
Blast hole layout (unit: mm). (a) Front view. (b) Left view. (c) Top view.
(a)(b)(c)Figure 9
Construction operations of field tests. (a) Check of hole space. (b) Check of hole depth. (c) Charge of blast holes. (d) Measurement of footage.
(a)(b)(c)(d)


## 5.2. Results of Field Tests

Comparative data of the blasting effects are presented in Table9. For the 42 mm diameter blast holes with 35 mm diameter explosive sticks used for cut blasting, the average footage is 1.9 m, and the average utilization rate of the blast holes is 79.2%. For the 50 mm diameter blast holes with 45 mm diameter explosive sticks used for cut blasting, the average footage reaches 2.2 m, and the average utilization rate of the blast holes reaches 91.7%. Thus, in contrast to cut blasting with the small diameter charge, the average footage is increased by 0.30 m, and the average utilization rate of blast holes is increased by 12.5%, with the large diameter charge.Table 9
Comparative data of blasting effects.
No.Cut blasting with small diameter chargeCut blasting with large diameter chargeFootage (m)Utilization rate of blast hole (%)Footage (m)Utilization rate of blast hole (%)11.9581.32.2091.721.9079.22.2091.731.9079.22.1589.641.9079.22.2593.851.8577.12.1589.661.9079.22.2091.771.9581.32.2593.881.8577.12.2091.791.8577.12.1589.6101.9079.22.2593.8111.9581.32.2091.7121.9079.22.2091.7Average1.9079.22.2091.7The results of field comparison tests indicate that the use of a large diameter charge can improve the cut effect in hard rock roadway and hence increase the blasting footage and the utilization rate of blast holes.


## 6. Discussion

In rock blasting engineering, the effective energy used for rock breaking and rock excavation accounts for about 60∼70 percent of the total blasting energy, and the remaining energy results in blast hazards [56]. As mentioned in Section 2, with the blast hole as the center, there are the crushing zone, the cracking zone, and the vibration zone. The blasting vibration from roadway excavation might negatively impact the stability of surrounding rocks and supporting structures.Blasting vibration is usually expressed by the particle vibration velocity, which can be calculated from Sadov’s formula as follows:(21)V=K1W1/3Rmα3,where V is the particle vibration velocity; Rm is the distance from the blasting source; W is the single blasting charge quantity; K1 and α3 are the coefficient and attenuation exponent associated with geological conditions, respectively.According to equation (21), for identical geological conditions and distances from the source, the blasting vibration depends only on the single blasting charge quantity. The use of large diameter charges implies an increase in the single blasting charge quantity, which leads to an increase in particle vibration velocity. However, for the case presented in this study, after the use of a large diameter charge, the single blasting charge quantity of cut blasting increased from 8.40 kg to 13.86 kg, which is still less than the maximum single blasting charge quantity of 23.10 kg. It can be seen that the blasting vibration generated by cut blasting with large diameter charges is within a controllable range.


## 7. Conclusions

(1)
Based on theoretical analysis, the radii of the crushing and cracking zones caused by a 50 mm diameter blast hole and a 45 mm diameter explosive stick are 1.31 times that caused by a 42 mm diameter blast hole and a 35 mm diameter explosive stick. Further penetration of blasting cracks can be realized by a large diameter charge to enhance the fragmentation degree of the rock mass in the cut cavity. The cavity formation power generated by a 50 mm diameter blast hole and a 45 mm diameter explosive stick is 2.22 times that generated by a 42 mm diameter blast hole and a 35 mm diameter explosive stick. For constant cavity formation resistance, a large diameter charge is conducive to expelling the rock mass fragments from the cut cavity.(2)
Simulation results can depict the formation of stress wave in wedge cut blasting for different charge diameters. The maximum and average values of peak effective stress at measuring points along the central measuring line of the numerical model with a large diameter charge are 46.7% and 41.5% higher, respectively, than those obtained from the numerical model with a small diameter charge. The use of a large diameter charge in cut holes can increase the stress field intensity in the cut cavity and hence increase the extent of damage to the rock mass.(3)
A comparison of the blasting effects after field tests shows an average footage of 2.20 m and an average utilization rate of blast holes of 91.7% for 50 mm diameter blast holes and 45 mm diameter explosive sticks used in cut blasting, which represent an average increase in footage of 0.30 m and an average increase in the utilization rate of blast holes of 12.5% over cut blasting with 42 mm blast holes and 35 mm diameter explosive sticks. Thus, the cutting effects in hard rock roadways can be improved with the use of large diameter charges, which increase the blasting footage and the utilization rate of blast holes.



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*Source: 8873412-2020-09-10.xml*