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Article

Investigation on Cutting Blasting Efficiency of Hard Rock Tunnels under Different Charge Diameters

by
Pengfei Gao
1,2,
Qi Zong
1,*,
Bing Cheng
1,3,*,
Haibo Wang
1,
Ying Xu
1 and
Binbin Zhang
3,4
1
School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China
2
Anhui Jiangnan Blasting Engineering Limited Company, Xuancheng 242300, China
3
School of Chemical Engineering, Anhui University of Science and Technology, Huainan 232001, China
4
Nuclear Industry Jingxiang Construction Group Limited Company, Huzhou 313000, China
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2022, 12(19), 9906; https://doi.org/10.3390/app12199906
Submission received: 6 September 2022 / Revised: 27 September 2022 / Accepted: 28 September 2022 / Published: 1 October 2022
(This article belongs to the Special Issue Advances in Rock Blasting and Mining)
Browse Figures
Versions Notes

Abstract

:
Considering the low efficiency of cutting blasting in hard rock mine tunnels, a novel solution of increasing the charge diameter of the cutting holes was put forward. To investigate the influence of the charge diameter on the cutting blasting results, three different working conditions of Φ 32 mm, Φ 42 mm, and Φ 50 mm blasting holes combined with Φ 27 mm, Φ 35 mm, and Φ 45 mm cartridges, respectively, were taken as the investigation objects. At first, the theoretical destruction ranges of single cutting holes under the three different charge diameters were computed. The computed results showed that the destruction range of the cutting holes could be expanded by increasing the charge diameter, which would be beneficial to the destruction of the rock far away from the cutting holes in the cutting cavity. Subsequently, numerical simulations of cutting blasting under the three different charge diameters were performed to display the dynamic propagation process of the blasting stress wave. Importantly, the stress field intensity in the cutting cavity was enhanced significantly with the charge diameter. The stronger stress field intensities generated by the larger diameter charges were more conducive to breaking the rock in the cutting cavity into small fragments that were easy to be discarded. Ultimately, a hard rock vertical slope was used instead of the driving face to carry out the cutting blasting experiments, and the hole utilizations of the cutting blasting were 70.4%, 82.0%, and 94.0%, respectively, under the three different charge diameters, from small to large. The experimental results forcefully substantiated that a higher cutting blasting efficiency could be achieved by increasing the charge diameter of cutting holes in hard rock mine tunnels.

1. Introduction

The blasting technique has always been extensively used in various rock excavation projects, especially in the driving of rock tunnels in coal energy mining engineering, because it has the obvious strengths of a higher work efficiency, a more flexible feasibility, and a lower economic input compared with the mechanical driving technique [1,2,3,4]. In the blasting driving process of rock tunnels, there are three steps from inside to outside, namely cutting blasting, stopping blasting, and contour blasting, as shown in Figure 1. Among them, cutting blasting is the first step of full section blasting and the critical link to control the rock breaking effect and the blasting cycle advance. A rational cutting blasting mode is conducive to inducing a large extra free surface and an adequate compensation volume for the subsequent blasting steps [5,6,7,8]. According to the angle relationship between the cutting holes and the heading face, the common cutting blasting modes can be distinguished into inclined hole and parallel hole cutting modes, and the most typical inclined hole cutting mode is wedge cutting blasting [9,10]. The outstanding weaknesses of straight hole cutting blasting are the many cutting holes, a low energy utilization, and a small cavity space, while wedge cutting blasting is obviously characterized by a small hole amount, a high energy utilization, and a large cavity space [11]. Consequently, wedge cutting blasting has been the most extensively adopted cutting mode in the blasting driving of rock tunnels in coal mines.
Differing from the conventional bench blasting, which has two free surfaces, cutting blasting is quite difficult because only the heading face can be used as a free surface [12,13,14,15]. Therefore, improving the cutting blasting efficiency through a rational cutting mode has always been a research focus in the field of rock tunnel blasting driving. In terms of wedge cutting blasting, many researchers and engineers have conducted an enormous amount of research, and have acquired some fascinating and useful research results. For instance, based on the field blasting data statistics, Shapiro [16] and Cardu et al. [17] have compared the blasting results of different cutting modes, and concluded that wedge cutting blasting was the most effective cutting mode for rock tunnel driving. Dai and Du [18] have presented an approach to computing the parameters of wedge cutting blasting after fully considering the major factors, such as the explosives and rock properties. Pu et al. [19] and Xiong et al. [20] have calculated the correlation degree and global priority of the diverse impacting factors of wedge cutting blasting by using gray system theory and an analytic hierarchy approach, respectively. Liang et al. [21] have studied the effect of hole angle symmetry on cutting blasting results, and believed that the symmetrical layout of the cutting holes could contribute to strengthening the stress superposition effect and maximizing the energy utilization. Yang et al. [22] have carried out cutting blasting model experiments by taking the hole angle as a single variable, and then they have determined a reasonable range of the hole angle after analyzing the fragmentation distribution and blasting vibration. Hu et al. [23] have constructed a wedge cutting blasting model by employing the finite element method, and acquired the cavity forming process by defining the rock element failure algorithm. Based on a user-defined rock damage model, Gao et al. [24] have simulated the rock damage distribution in the cutting cavity under different initiation points. In addition to the above studies on conventional wedge cutting modes, there have been many recent investigations involving various modified wedge cutting modes. For instance, Shan et al. [25], Lou et al. [26], and Cheng et al. [27] have elaborated on the effects of the auxiliary blasting of central parallel holes on wedge cutting blasting results, using many research methods. Furthermore, they have verified that the auxiliary blasting of central holes was beneficial to the formation of the cutting cavity conforming to the design cutting depth. Ding et al. [28] and Cheng et al. [29] have revealed the cavity forming principle of the double wedge cutting mode through a theoretical analysis and finite element simulation, respectively, and have achieved good application effects in rock tunnel blasting construction. Moreover, Zhang et al. [30] have added several central pre-splitting holes in the double wedge cutting mode, to reduce the difficulties of deep hole cutting blasting in hard rock tunnels. Nevertheless, although these modified wedge cutting modes are very effective in improving the cutting blasting effect, they could seize additional detonator segments, which would severely restrict their application and popularization in the large section rock tunnel with limited detonator segments. According to the above review of the related literature, there is presently no detailed study concerning the effect of charge diameter on cutting blasting in hard rock underground tunnels.
Generally, a uniform charge diameter is adopted for all types of holes in the blasting driving of rock tunnels in coal mines. The most commonly used is Φ 32 mm blasting holes with Φ 27 mm cartridges, and some have used Φ 42 mm blast holes with Φ 35 mm cartridges [31]. However, the blasting destruction range is limited in the hard rock tunnels with a hardness coefficient greater than 7. If the above small charge diameters are still adopted in the cutting holes, the rock in the cutting cavity is difficult to be effectively broken into rock fragments. At this time, the rock in the cutting cavity is still subjected to the strong clamping force from the surrounding rock and cannot be completely ejected out. Understandably, the poor cutting blasting effect is bound to lead to a small blasting cycle advance, thus resulting in the imbalance between coal energy mining and rock tunnel driving [32,33]. In recent years, with the fast development and progress of drilling machines, drilling speed has been greatly increased, which makes it possible to apply large diameter holes in the rock tunnels of coal mines. Therefore, in order to raise the cutting blasting efficiency in hard rock tunnels, it was proposed to adopt large diameter charges in the cutting holes. That is, by increasing the charge diameter of the cutting holes, the blasting destruction range of the cutting holes would be further expanded, and hence the hard rock in the cutting cavity would be effectively broken into small rock fragments that were easy to be discarded.
In order to investigate the influence of charge diameter on hard rock cutting blasting, three working conditions, namely, Φ 32 mm (Φ presents diameter) holes matching Φ 27 mm cartridges, Φ 42 mm holes matching Φ 35 mm cartridges, and Φ 50 mm holes matching Φ 45 mm cartridges, were taken as the study objects in the present study. Initially, the blasting destruction ranges of single holes under the three different charge diameters were calculated theoretically. Secondly, numerical simulations of the cutting blasting under the three different charge diameters were performed to visually display the dynamic propagation processes of the stress waves, and reveal the distribution characteristics of the blasting stress field in the cutting cavity. Finally, to compare the cutting blasting results under the three different charge diameters, a hard rock vertical slope was used as the heading face to carry out the cutting blasting experiments.

2. Destruction Range of Single Blasting Hole

When a cylindrical charge was detonated in the blasting hole, a shock wave with strong pressure was first aroused in the rock medium. The rock near the blasting hole was crushed into powdery rock particles under the shock wave, inducing the crushed zone. During the formation of the crushed zone, the stress amplitude of the shock wave decreased rapidly, and then the shock wave turned into a stress wave at the edge of the crushed zone. Due to stress attenuation, the stress wave could not lead to the crushed destruction of rock. However, the compressive stress exerted by the stress wave made the rock move outward along the radial direction of the blasting hole, and the rock outside the crushed zone would be subjected to the tangential tensile stress due to the Poisson effect. Then, because the tangential tensile stress was greater than the tensile capacity of the rock, radial fractures radiating around and penetrating the fracture zone would be generated [34]. After that, the stress wave attenuated to an earthquake wave at the edge of the fracture zone, which no longer induced the direct destruction of the rock and could only cause the elastic vibration of rock particles in the distant region. A diagram of the cylindrical charge blasting is presented in Figure 2.
Since the tensile strengths of brittle media such as rock are usually only about 5–10% of their own compressive strength, the range of the blasting fracture zone was bound to be much greater than that of the blasting crushed zone [35]. Therefore, it was believed that the range of the blasting fracture zone was the key basis of a practical blasting design, therefore only the ranges of the blasting fracture zone under the different charge diameters are compared here. Moreover, in practical rock blasting constructions, the radial decoupled charge structure was often employed to facilitate the loading of the cartridges. Thus, based on the tensile stress failure criterion, Wang et al. [36] have provided a formula for calculating the radius of the fracture zone after a radial decoupled cylindrical charge blasting, as shown below:
R = ( ρ e D e 2 K r − 6 N b 8 S t ) 1 α r b
where R represents the radius of the fracture zone; ρe represents the explosive density; De represents the detonation velocity; Kr represents the decouple coefficient, and Kr = db/dc; db and dc represent the diameters of the blasting hole and the cartridge, respectively; N represents the stress enhancement factor, taken as N = 8; b represents the lateral stress coefficient, and b = μ/(1 − μ); μ represents the Poisson ratio; α represents the attenuation exponent of the stress wave, taken as α = 2 − b; St represents the tensile strength; rb represents the radius of the blasting hole.
According to the detonation theory of a condensed explosive, the detonation velocity of the explosive would increase with the cartridge diameter in the range from a critical diameter and a limited diameter [37,38], as shown in Figure 3. Then, the detonation velocity tester was adopted to determine the detonation velocity of Φ 27 mm, Φ 35 mm, and Φ 42 mm cartridges, the testing results of which are presented in Table 1. In addition, the rock pieces taken from the later cutting blasting site were processed and polished into regular specimens to test the main physical and mechanical parameters of the rock, and the testing results are shown in Table 2. After that, the known charge parameters, explosive performance parameters, and rock mechanical parameters were submitted into Equation (1) to compute the radii of the fracture zone under the above three charges’ diameters, and the computed results are presented in Table 3.
From Table 3, according to the order of charge diameters from small to large, the radii of the fracture zones under the three charge diameters were equal to 288 mm, 396 mm, and 525 mm, respectively. It was observed that the radius of the fracture zones increased visibly with the charge diameter. Accordingly, when the charge diameter of the cutting holes was increased, the blasting fractures between the cutting holes could be connected easily and well with each other, which would enhance the destruction degree of the rock far away from the cutting holes in the cutting cavity. Thus, the hard rock in the cutting cavity could form the small rock fragments, which could be easily expelled out.

3. Numerical Simulation

3.1. Numerical Model Descriptions

As an important research method, numerical simulation currently has extensive applications in the research field of rock blasting engineering [39,40,41]. As shown in Figure 4a, the explicit dynamic program ANSYS/LS-DYNA was used to construct three cutting blasting numerical models with the same dimensions of 2500 mm × 2500 mm × 3000 mm (length × width × depth). The hole layout parameters of the three numerical models were consistent with each other. Six cutting holes with a vertical depth of 2500 mm were placed symmetrically on the left and right sides of the blasting model, and the included angle between the cutting holes and the driving face was 76.5°. The hole top spacing and hole bottom spacing between the left and right cutting holes were 1500 mm and 300 mm, respectively. In addition, the longitudinal spacings, vertical depths, and charge lengths of the cutting holes were 500 mm, 2500 mm, and 1320 mm, respectively. The main difference between these blasting models mainly lay in the charge diameters; the working conditions of the three groups of blasting models were Φ 32 mm holes matching Φ 27 mm cartridges, Φ 42 mm holes matching Φ 35 mm cartridges, and Φ 50 mm holes matching Φ 42 mm cartridges, respectively.
In this simulation, the Lagrange algorithm was used to simulate solid media including the rock and the tamping plug, and ALE (Arbitrary Lagrange-Euler) was employed to simulate fluid media, including the explosives and standard air [42,43]. The blasting dynamic load transfer between the two phase media could be realized by a fluid–solid coupling algorithm, which needed to employ the *CONSTRAINED_LAGRANGE_IN_SOLID keyword [44]. In addition to the heading face, the non-reflecting boundaries were applied to the other surfaces of the rock model to eliminate the harmful influences of the stress wave reflections on the simulation accuracy [45,46]. Moreover, the reverse detonation mode was adopted in all the cutting holes, that is the explosive detonation reaction started from the bottom of each cutting hole at 0 µs. The specific detonation points and detonation times were defined by the *INITIAL_DETONATION keyword.
In addition, a hexahedron was used for the mesh generation of the numerical model in this study. However, some recent studies [47,48] have suggested that a reasonable mesh size was extremely important to control the accuracy of the simulated results. In order to avoid the obvious distortion of the final results, the convergence tests were carried out to determine a reasonable mesh. During this process, the mesh size was continually reduced until the difference between the simulated results of two adjacent tests was reduced to 5% [49], and the evaluation index was the peak stress at the same position. Finally, the reasonable numbers of grids and nodes of the rock model were determined to be 1,441,920 and 1,512,152, respectively. The mesh division of the rock model is presented in Figure 4b.

3.2. Material Models and Parameters

In this simulation, a total of four materials were employed, namely, the explosives, the rock, standard air, and a tamping plug. However, the above four materials could be divided into two categories: fluid media and solid media, and the explosive and standard air used as fluid media usually needed to be described by using both a constitutive model and a state equation. Therefore, the *MAT_HIGH_EXPLOSIVE_BURN model and the JWL state equation were together used for the definition of the explosives. The JWL state equation possesses high accuracy in handling the relationship between the detonation pressure, relative volume, and internal energy of explosion products [50,51], as shown below:
P e = A ( 1 − ω R 1 V e ) e − R 1 V e + B ( 1 − ω R 2 V e ) e − R 2 V e + ω E 0 V e
where Pe represents the detonation pressure; A, B, R1, R2, and ω represent the constants; E0 represents the specific internal energy; and Ve represents the relative volume.
Similarly, the *MAT_NULL model and linear polynomial state equation were adopted to simulate the standard air. The linear polynomial state equation has superior advantages in simulating various ideal gases, such as standard air, and can be expressed as:
P 0 = C 0 + C 1 η + C 2 η 2 + C 3 η 3 + ( C 4 + C 5 η + C 6 η 2 ) E 1
where P0 represents the pressure, C0–C6 represent the material constants; η represents the viscosity coefficient; E1 represents the specific internal energy.
For the other two materials viewed as solid media, the dynamic description of the rock used the *MAT_PLASTIC_KINEMATIC model, which has integrated the special mechanical effects of hard brittle materials caused by the increase in the strain rate under strong dynamic loads [52,53]. The *MAT_DRUCKER_PRAGER model was adopted to simulate the soil used as a tamping plug, which is good at dealing with the mechanical deformation problems of various soft engineering materials. The main property parameters of the explosives and the rock have been given in Table 1 and Table 2, and the parameters of the JWL equation, standard air, and tamping plug were taken from [54,55,56] and are shown in Table 4, Table 5 and Table 6.

3.3. Simulated Results and Analysis

3.3.1. Dynamic Development of Stress Wave

The finite element solution files under the three different charge diameters were delivered into the nonlinear solver LS-DYNA, and the specific dynamic post-processor LS-PREPOST4.5 was employed to export the final simulated results. After the numerical simulation, in order to display the dynamic development of the blasting stress wave clearly, the rock numerical model was divided along the horizontal symmetry plane, and the placement angle of the rock numerical model was also adjusted to some extent. The dynamic developments of the blasting stress wave under the three different charge diameters are shown in Figure 5, Figure 6 and Figure 7.
As presented in Figure 5, Figure 6 and Figure 7, the explosive detonation reactions began at the bottom of each cutting hole, and a huge release of chemical energy induced a blasting stress wave in the rock. With the transmission of the explosive detonation reaction, the blasting stress wave propagated towards the driving face in a conical wave surface. In the middle area of the rock model, the stress waves generated from the cutting holes arranged on the left and right sides were superimposed on each other, which were conducive to the destruction of the rock in the cutting cavity. At 320 µs, the explosive detonation reaction in each cutting hole was terminated, and the blasting stress wave could still propagate towards the driving face in an arc wave surface. However, the intensity of the stress wave gradually decreased in the subsequent propagation process, resulting in a low degree of damage to the rock in the non-charge section. At 470 µs, the blasting stress wave reached the driving face and was reflected as a tensile wave, which propagated from the driving face to the cutting cavity. Since the tensile strength of rock is usually only about 5–10% of its compressive strength, the rock near the driving face would be prone to tensile destruction, which could make up for the insufficient destruction of the rock in the non-charge section. After that, the backward-propagating tension wave and the forward-propagating compression wave were superimposed on each other to induce a composite blasting stress field, which would be beneficial to the destruction of the rock in the cutting cavity.

3.3.2. Distribution Characteristics of the Stress Field

In order to further understand the distribution features of the stress field in the cutting cavity under the three different charge diameters, the measurement points were arranged at the cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m in the center of the rock numerical model. Then, the stress–time curves of these measurement points were exported, as illustrated in Figure 8.
According to Figure 8, under working condition 1, of Φ 32 mm blasting holes matching Φ 27 mm cartridges, the peak stresses at the measurement points with cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m were equal to 94.3 MPa, 61.6 MPa, 35.7 MPa, 29.9 MPa, and 25.3 MPa, respectively. For working condition 2, of Φ 42 mm blasting holes matching Φ 35 mm cartridges, the peak stresses at the measurement points with cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m were equal to 133.8 MPa, 94.6 MPa, 54.7 MPa, 44.5 MPa, and 39.1 MPa, respectively. At the above corresponding measurement points, the peak stresses of the measurement points under condition 2 were 1.42, 1.54, 1.53, 1.49, and 1.54 times those under condition 1, which indicated that the blasting stress field intensity in the cutting cavity under condition 2 increased by 42–54% on the basis of condition 1.
For working condition 3, of Φ 50 mm blasting holes matching Φ 42 mm cartridges, the peak stresses at the measurement points with cutting depths of 2.5 m, 2.0 m, 1.5 m, 1.0 m, and 0.5 m were equal to 186.4 MPa, 130.7 MPa, 78.6 MPa, 60.8 MPa, and 51.4 MPa, respectively. At the above corresponding measurement points, the peak stresses of the measurement points under condition 2 were 1.98, 2.12, 2.20, 2.03, and 2.03 times those under condition 1, and were 1.39, 1.38, 1.44, 1.37, and 1.32 times those under condition 2, respectively. The measurement results suggest that the stress field intensity in the cutting cavity under condition 3 was increased by 98–120% on the basis of condition 1, and increased by 32–44% on the basis of condition 2.
Based on the above quantitative analysis, it was observed that the blasting stress field intensity in the cutting cavity could be significantly enhanced by increasing the charge diameter of the cutting holes. Predictably, the increase in the blasting stress field intensity was bound to enhance the destruction of the rock in the cutting cavity, which was conducive to forming small rock fragments that were easy to be discarded. Therefore, a cutting cavity satisfying the design cutting depth could be obtained in the hard rock underground tunnels.

4. Cutting Blasting Experiments

4.1. Experimental Design and Implementation

In order to further explore the influence of charge diameters on the actual cutting blasting results, the hard rock cutting blasting experiments under the three different charge diameters were carried out. Because it was extremely difficult to implement and examine the cutting blasting separately without delaying the construction period of the rock tunnels of the coal mines, a hard rock vertical slope with high rock integrity was selected to replace the driving face of the underground mine tunnels.
The rock vertical slope used for the cutting blasting experiments was located in the Shenshan open-pit limestone mine, Chizhou, China. The main physical and mechanical parameters of the rock had been tested previously, and the testing results have been listed in Table 2. It was observed that the compressive strength of the rock was 92.4 MPa, that is, the hardness coefficient of rock greater than 9, which indicated that the rock belonged to the hard rock category. The rock vertical slope employed for one cutting blasting experiment is presented in Figure 9.
During the cutting blasting experiments, three kinds of drilling bits with diameters of 32 mm, 42 mm, and 50 mm were employed for the drilling constructions, and three kinds of water-gel explosive cartridges with diameters of 27 mm, 35 mm, and 42 mm were used as the blasting materials. It should be noted that the blasting hole arrangement and blasting parameters mentioned in the previous numerical simulation were taken from the cutting blasting experiments, thus the relevant information of the blasting scheme does not need to be repeated here.

4.2. Experimental Results and Analysis

Since it was very difficult to keep the rock conditions completely consistent in practical mine engineering, ten cutting blasting experiments were performed for each charge diameter to avoid the adverse effect of rock conditions on the experimental reliability. After the cutting blasting experiments, the final cutting depth of the cutting cavity was measured and the hole utilization was calculated. The measurement of the residual hole length used for the indirect calculation of cutting depth is shown in Figure 10. The statistics of the cutting blasting effects under the three different charge diameters are shown in Table 7.
As illustrated in Table 7, when the cutting holes adopted Φ 32 mm blasting holes and Φ 27 mm cartridges, the average final cutting depth and average hole utilization were 1.76 m and 70.4%, respectively. When the Φ 42 mm blasting holes and Φ 35 mm cartridges were employed in those cutting holes, the average final cutting depth and average hole utilization increased to 2.05 m and 82.0%, respectively. When the cutting holes used Φ 50 mm blasting holes and Φ 42 mm cartridges, the average final cutting depth and average hole utilization reached 2.35 m and 94.0%, respectively. The improvement of the final cutting depth and hole utilization powerfully confirmed that increasing the charge diameter could significantly improve the cutting blasting efficiency of hard rock tunnels.
The main reason for the above blasting results was that the increase in charge diameter could enhance the blasting stress field intensity and crack evolution capacity in the cutting cavity, and then the hard rock in the cutting cavity could be broken into small rock fragments that were easy to be discarded. The typical rock fragmentations under different the working conditions are shown in Figure 11. It is obvious that the rock fragmentation decreases significantly with the increase in the charge diameter. The sharp contrast of rock fragmentation under different charge diameters also strongly proves the validity of the results of the theoretical analysis and numerical simulation.

5. Conclusions

Through theoretical calculation, numerical simulation, and blasting experiments, the influence of the charge diameter on the cutting blasting efficiency of hard rock tunnels was discussed, and the main conclusions are as follows:
(1) The theoretical calculations indicated that the radii of the fracture zones under the three different charge diameters from small to large were equal to 288 mm, 396 mm, and 525 mm, respectively. An increase in the charge diameter could expand the destruction range of the cutting holes, and further enhance the destruction degree of the rock far away from the cutting holes in the cutting cavity.
(2) The developments of blasting stress waves were visually displayed by numerical simulation. The blasting stress field intensity in the cutting cavity under condition 2 increased by 42–54% on the basis of condition 1, and that under condition 3 increased by 32–44% on the basis of condition 2. The higher stress field intensity was more beneficial to encouraging the rock in the cutting cavity to form small rock fragments that were easy to be discarded.
(3) The experimental results showed that under the three different charge diameters from small to large, the average final cutting depths were 1.76 m, 2.05 m, and 2.35 m, respectively, and the average hole utilizations of the cutting blasting were 70.4%, 82.0% and 94.0%, respectively. The results powerfully validated that the increase in charge diameter had effectiveness in raising the cutting efficiency of hard rock mine tunnels.

Author Contributions

Conceptualization, P.G. and Q.Z.; methodology, P.G. and B.C.; software, B.C.; validation, P.G., Q.Z. and B.C.; formal analysis, P.G., Q.Z. and B.C.; investigation, P.G., Q.Z., B.C., H.W., Y.X. and B.Z.; data curation, P.G., Q.Z. and B.C.; writing—original draft preparation, P.G. and B.C.; writing—review and editing, P.G. and B.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China (nos. 51374012 and 52074009) and the Science Research Project of Zhejiang Province Construction (no. 2021K213).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Blasting driving process of rock tunnels. (a) Cutting blasting. (b) Stopping blasting. (c) Contour blasting.
Figure 1. Blasting driving process of rock tunnels. (a) Cutting blasting. (b) Stopping blasting. (c) Contour blasting.
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Figure 2. Diagram of cylindrical charge blasting.
Figure 2. Diagram of cylindrical charge blasting.
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Figure 3. Relationship between detonation velocity and cartridge diameter.
Figure 3. Relationship between detonation velocity and cartridge diameter.
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Figure 4. Numerical model and mesh division. (a) Numerical model of cutting blasting (unit: mm). (b) Mesh division of rock model.
Figure 4. Numerical model and mesh division. (a) Numerical model of cutting blasting (unit: mm). (b) Mesh division of rock model.
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Figure 5. Stress wave propagation under the condition of Φ 32 mm holes matching Φ 27 mm cartridges. (a) Time = 160 μs. (b)Time = 320 μs. (c) Time = 470 μs. (d) Time = 600 μs.
Figure 5. Stress wave propagation under the condition of Φ 32 mm holes matching Φ 27 mm cartridges. (a) Time = 160 μs. (b)Time = 320 μs. (c) Time = 470 μs. (d) Time = 600 μs.
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Figure 6. Stress wave propagation under the condition of Φ 42 mm holes matching Φ 35 mm cartridges. (a) Time = 160 μs. (b)Time = 320 μs. (c) Time = 470 μs. (d) Time = 600 μs.
Figure 6. Stress wave propagation under the condition of Φ 42 mm holes matching Φ 35 mm cartridges. (a) Time = 160 μs. (b)Time = 320 μs. (c) Time = 470 μs. (d) Time = 600 μs.
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Figure 7. Stress wave propagation under the condition of Φ 50 mm holes matching Φ 42 mm cartridges. (a) Time = 160 μs. (b)Time = 320 μs. (c) Time = 470 μs. (d) Time = 600 μs.
Figure 7. Stress wave propagation under the condition of Φ 50 mm holes matching Φ 42 mm cartridges. (a) Time = 160 μs. (b)Time = 320 μs. (c) Time = 470 μs. (d) Time = 600 μs.
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Figure 8. Stress–time curves of measurement points. (a) Φ 32 mm holes matching Φ 27 mm cartridges. (b) Φ 42 mm holes matching Φ 35 mm cartridges. (c) Φ 50 mm holes matching Φ 45 mm cartridges.
Figure 8. Stress–time curves of measurement points. (a) Φ 32 mm holes matching Φ 27 mm cartridges. (b) Φ 42 mm holes matching Φ 35 mm cartridges. (c) Φ 50 mm holes matching Φ 45 mm cartridges.
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Figure 9. Rock vertical slope used for a cutting blasting experiment.
Figure 9. Rock vertical slope used for a cutting blasting experiment.
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Figure 10. Measurement of residual hole length.
Figure 10. Measurement of residual hole length.
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Figure 11. Typical rock fragmentations. (a) Working condition 1. (b) Wording condition 2. (c) Working condition 3.
Figure 11. Typical rock fragmentations. (a) Working condition 1. (b) Wording condition 2. (c) Working condition 3.
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Table
Table 1. Detonation velocities under different cartridge diameters.
Table 1. Detonation velocities under different cartridge diameters.
dc (mm)Explosive Density (kg·m−3)De (m·s−1)
2711003175
3511003425
4211003665
Table
Table 2. Physical and mechanical parameters of rock.
Table 2. Physical and mechanical parameters of rock.
Density (kg·m−3)Poisson RatioSc (MPa)St (MPa)
25700.2392.48.8
Note: Sc represents the compressive strength.
Table
Table 3. Fracture radii under different charge diameters.
Table 3. Fracture radii under different charge diameters.
db (mm)dc (mm)KrR (mm)
32271.185288
42351.200396
50421.190525
Table
Table 4. Parameters of JWL state equation.
Table 4. Parameters of JWL state equation.
A (GPa)B (GPa)R1R2ωE0 (GPa)
2140.1824.150.950.154.20
Table
Table 5. Parameters of standard air.
Table 5. Parameters of standard air.
ρa (kg·m−3)C0–C3C4C5C6E1 (GPa)
1.250.000.400.400.002.5 × 10−4
Note: ρa represents the density.
Table
Table 6. Parameters of tamping plug.
Table 6. Parameters of tamping plug.
ρt (kg·m−3)G (GPa)Poisson RatioCohesion (GPa)φ (rad)
18500.020.281.8 × 10−40.56
Note: ρt represents the density. G represents the shear modulus. φ represents the friction angle.
Table
Table 7. Statistics of cutting blasting results.
Table 7. Statistics of cutting blasting results.
No.Working Condition 1Working Condition 2Working Condition 3
D (m)Q (%)D (m)Q (%)D (m)Q (%)
11.6967.62.0381.22.3594.0
21.7871.22.0883.22.3192.4
31.7570.02.1184.42.3895.2
41.7770.81.9778.82.3393.2
51.8172.42.0682.42.2991.6
61.7469.62.0983.62.3995.6
71.7268.82.0481.62.3493.6
81.8072.01.9979.62.4096.0
91.7670.42.0782.82.3794.8
101.7871.22.0682.42.3493.6
Average1.7670.42.0582.02.3594.0
Note: D represents the final cutting depth. Q represents the hole utilization.
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MDPI and ACS Style

Gao, P.; Zong, Q.; Cheng, B.; Wang, H.; Xu, Y.; Zhang, B. Investigation on Cutting Blasting Efficiency of Hard Rock Tunnels under Different Charge Diameters. Appl. Sci. 2022, 12, 9906. https://doi.org/10.3390/app12199906

AMA Style

Gao P, Zong Q, Cheng B, Wang H, Xu Y, Zhang B. Investigation on Cutting Blasting Efficiency of Hard Rock Tunnels under Different Charge Diameters. Applied Sciences. 2022; 12(19):9906. https://doi.org/10.3390/app12199906

Chicago/Turabian Style

Gao, Pengfei, Qi Zong, Bing Cheng, Haibo Wang, Ying Xu, and Binbin Zhang. 2022. "Investigation on Cutting Blasting Efficiency of Hard Rock Tunnels under Different Charge Diameters" Applied Sciences 12, no. 19: 9906. https://doi.org/10.3390/app12199906

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