Theoretical and Numerical Research on V-Cut Parameters and Auxiliary Cuthole Criterion in Tunnelling

Lou, Xiaoming; Wang, Bao; Wu, En; Sun, Mingwu; Zhou, Ping; Wang, Zhenchang

doi:https://doi.org/10.1155/2020/8568153

Advances in Materials Science and Engineering

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Abstract Introduction Numerical Simulation Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2020 | Article ID 8568153 | https://doi.org/10.1155/2020/8568153

Theoretical and Numerical Research on V-Cut Parameters and Auxiliary Cuthole Criterion in Tunnelling

Xiaoming Lou,^1,2Bao Wang,^1,2En Wu,^1,2Mingwu Sun,^1,2Ping Zhou,^1,2and Zhenchang Wang^1,2

Academic Editor: Hossein Moayedi

Received09 Dec 2019

Revised17 Jan 2020

Accepted18 Jan 2020

Published18 Feb 2020

Abstract

This paper aims at providing a sound theoretical solution to auxiliary central hole and the cutting parameters. For this purpose, the forming mechanism of V-cut cavity for cutting blasting was performed based on the hypothetical rock breaking mechanism of V-cut blasting. A theoretical solution for increasing the critical depth of the auxiliary center cuthole and the criteria for increasing the cuthole diameter of various types of cutholes when the rock attributes, explosive properties, and cuthole dip angle are constant are proposed. (1) If charging length l_e < 0.75H/sin θ, no auxiliary cuthole is needed. (2) If 0.75H/sin θ < l_e < 0.75H/sin θ + (2∼4) × 0.1, a central vertical auxiliary hole is needed. (3) If 0.75H/sin θ + (2∼4) × 0.1 < l_e < 0.75(H/sin θ + H_i/sin θ_i), a shallow inclined hole is needed. (4) If l_e > 0.75(H/sin θ + H_i/sin θ_i), both the central vertical cuthole and the shallow inclined cuthole are needed. Meanwhile, the theoretical solution was verified by numerical modelling with ANSYS/LS-DYNA. Moreover, the field implementation of the V-cut and the auxiliary hole effectively improved the blasting effect in both efficiency and economy.

1. Introduction

During the tunnel excavation of V-cut blasting, the minimum burden of V-cutholes and the rock clamping force are bound to increase with the depth of V-cuthole. However, the rock residues left at the V-cuthole bottom after blasting may result in bulging and even cutting failure. To prevent the bulging phenomenon, the central auxiliary hole has been widely employed to improve the cyclic advancement and reduce the rock clamping force at the hole bottom. For the past decades, much attention has been paid to the blasting mechanism, cutting method, and cutting parameters. But there are still no mature theoretical results to guide field practice. V-cutting is the key to the entire blasting technology. In order to obtain a satisfactory blasting effect, it is obviously very important to theoretically study and determine reasonable V-cut blasting parameters. Scholars at home and abroad have carried out corresponding research in the related fields.

In terms of the cuthole blasting mechanism, Ma and An [1] investigated the fracture and fragmentation mechanism of rock blasting with modified LS-DYNA considering the Johnson-Holmquist damage model. Using LS-DYNA software, Wang and Konietzky [2] explored the crack propagation and rock fragmentation in rock masses with free surface but no boundaries. Cho and Kaneko [3] numerically simulated the fragmentation and dynamic fracture of rock under explosion, obtained the dynamic fracture process of rock under different wave pressures, and verified the dynamic failure mechanism of cutholes. Similarly, Zhu et al. [4] modelled the columnar rock with a center hole by the nonlinear dynamic analysis program AUTODYN (Century Dynamics) and examined the fracture and fragmentation mechanism of rock under dynamic blasting loads. Focusing on a rock blasting test, Stepanov [5] discussed the maximum blasting fracture range of two rows of parallel holes. By the dynamic finite-element method, Guo et al. [6] studied the effect of instantaneous unloading on rock fragmentation process under blasting. These studies have provided some basic understanding of rock fragmentation mechanism in cut blasting and useful instructions on how to determine the row distance of cutholes.

In terms of the cutting method, Shapiro [7] performed a detailed analysis on different soft rock cutting arrangements (e.g., V-cut, parallel cut, parallel cut compensated with big cuthole, and composite cut), revealing that V-cut outperforms the other arrangements in blasting efficiency when the hole is less than 2.5 m deep. Soroush et al. [8] analyzed the effect and sensitivity of the hole diameter and tunnel face area on blasting results in different blast models, pointing out that V-cut needed more cutholes than parallel cut in similar conditions. Shan et al. [9] invented the quasiparallel cutting with a center hole, which combines the merits of parallel cut and angled cut, and achieved desirable blasting and economic effects with the cutting arrangement. Shaprio [7] investigated the feasibility of replacing many shallow cutholes with a few deep ones in tunnelling. Over the years, some innovative methods have been developed for cutting blasting. For example, Chen et al. [10] found the shell radial shaped charge effective in cutting blasting, for it can elevate blasting efficiency, boost cyclic advancement, and lower the drifting costs. Combining middle-space charging and toe-space charging, Zhang et al. [11] noticed that the cutting effect of vertical large-diameter cutholes is enhanced by central large-diameter cuthole, stage-by-stage cutting blasting, and deck toe-space charging. The novel cutting blasting method boasts high usage of cutholes, big cavity, low chunk rate, even lumpiness, and efficient use of energy. Recently, Kim and Song [12] replaced cutting blasting with abrasive water jet cutting and assessed the control of the ground vibration during tunnelling. According to experimental and numerical results, this new cutting method is more effective than conventional drilling and blasting.

Concerning the effect of the central hole, Xie et al. [13] simulated the parallel cutting with central hole and attributed the fracture formation among adjacent cutholes to the superposition of stress wave and the tension wave reflected by the wall of the central hole. Based on the stress concentration effect of the central hole, Yang et al. [14] studied the parallel cuthole cutting blasting with central holes, revealing that the central hole can reduce blasting vibration, enhance cuthole usage, and ensure blasting smoothness. Liu et al. [15] performed field tests on the stress concentration effect of central hole and proved that the hole enhances rock fragmentation via the reflection of tensile waves and thereby boosts the cyclic advancement. Probing into the blasting effect of 12-hole compound V-cut, Yang et al. [16] proved that the central hole can significantly improve the throwing effect of broken rocks and cuthole usage. Similarly, Qu et al. [17] simulated the cavity formation and propagation of stress wave of parallel cuthole blasting with ANSYS/LS-DYNA. It is concluded that the detonation of charged holes caused the interaction between stress wave and the wall of uncharged holes and that the initial rock cracking and displacement to adjacent uncharged holes are the key to cavity formation in the early phase. Through repeated numerical modelling, Gong et al. [18] optimized the cutting parameters for the excavation of Lvshuidong Mine. The main findings of their research include the following: the peak effective stress at the cuthole bottom was 40% higher in the presence than the absence of a central hole, revealing the importance of the central hole in the formation of cavity bottom; the in situ tests show that the per cycle advancement increased by 31%∼65% due to the addition of central cutholes under the conventional blast loads.

In terms of cutting parameters, Shapiro et al. [19] investigated the compensated hole volume of different straight hole cutting methods, laying a good basis for determining the diameter and depth of the supplemental hole. Based on cutting blasting tests, Bezmatemykh et al. [20] put forward the theoretical solutions of minimum burden and the other cutting parameters. Owe and O [21] employed grey relative analysis to analyze the effects of the parameters like hole depth, dip angles, and hole spacing on the V-cut blasting charged at the bottom. Andrievskii [22] optimized the parameters for drill-and-blast operation chart in mining with direct slot stage cutting. In addition, Qiao et al. [23, 24] research on optimization algorithms, wave transformation, and hybrid model prediction of improved deep learning, Lou et al. [25, 26] research on impact pressure on blasthole wall with radial air-decked charge, and so on obviously have better parameter value for blasting parameter optimization.

Despite the extensive research on cutting in tunnelling, there is a severe lack of theoretical or empirical analysis on when to add a central hole. For the need of a systematic understanding of central holes, the implementation of central holes may face numerous challenges during the variation in rock attributes, explosive properties, and/or cuthole depths. This calls for a sound theoretical solution to auxiliary central hole and the cutting parameters.

In light of the above, this paper is based on V-cut blasting rock breaking mechanism hypothesis [27], the relationship between the cutholes parameters is studied, the theoretical formula of each cutholes parameter is deduced, and the addition of an auxiliary center is proposed. Calculation method of critical depth of holes and the theoretical analysis results were verified by numerical simulations. The results show that when the depth of the blasthole or the length of the charge satisfies certain conditions, the addition of a central auxiliary slot can significantly improve the effective dynamic effect of the bottom of the blasting cavity, which is beneficial to the ideal cut blasting depth and cavity shape.

2. Hypothesis on V-Cut Blasting Mechanism

The V-cut, consisting of two or more rows of symmetrical oblique holes, helps to form a wedge cavity after blasting. For simplicity, this study mainly focuses on a single V-cut made up of three pairs of inclined holes. The cuthole arrangement in V-cut is presented in Figure 1, where H is the vertical depth of cuthole, d_l is cuthole spacing, a is hole bottom spacing, b is orifice spacing, E_iC_i and F_iD_i are charged sections with a length of l_e, and A_iE_i and B_iF_i are uncharged sections with a length of l_s.

The 3D model of the horizontal single V-cut blasting cavity is displayed in Figure 2. Since the rock masses around the cutholes are tightly compressed by explosive wave after the blasting of the three pairs of inclined cutholes [28], a broken zone will form under the interaction of adjacent holes and two inclined planes (i.e., E₁C₁C₃E₃ and F₁D₁D₃F₃) across the same column holes. Considering the inclination between the cuthole and working face, the cuthole detonation will release a force acting on the outside normal direction of the working face. The force will drive the rock away from the cavity area, leaving a shearing effect on surrounding rocks. In this case, the surfaces of A₁B₁D₁C₁, A₃B₃D₃C₃, A₁E₁E₃A₃, and B₁F₁F₃B₃ will suffer from shear-slip failure. The rocks at the hole bottom will be crushed and cut through due to their small spacing between cuthole bottoms, forming a cut-through face C₁D₁D₃C₃. In this way, the rock masses in the cavity will be completely separated from surrounding rocks, and a cavity will eventually appear under the throwing effect of the quasistatic pressure of the explosive gas.

3. Cavity Formation Mechanism

According to the hypothesis on the V-cut blasting mechanism, a trapezoid cavity will appear only through the separation of surfaces in the cavity (i.e., A₁B₁D₁C₁, A₃B₃D₃C₃, A₁E₁E₃A₃, B₁F₁F₃B₃, E₁C₁C₃E₃, F₁D₁D₃F₃, and C₁D₁D₃C₃) from surrounding rock masses. However, the separation mechanism differs from one face to another, depending on the specific location relative to cutholes. In general, surfaces E₁C₁C₃E₃, F₁D₁D₃F₃, and C₁D₁D₃C₃ are the result of explosive stress wave, while surfaces A₁B₁D₁C₁, A₃B₃D₃C₃, A₁E₁E₃A₃, and B₁F₁F₃B₃ are attributed to the shear failure induced by the explosive force along the normal direction of the working face. Here, it is assumed that every cuthole wall withstands equal initial impact pressure from explosion, and the uncharged sections are filled up with explosive gas, which is distributed uniformly along the internal cuthole wall.

3.1. Cavity Shear Strength

According to the location of each cavity surface, the shear strength of the upper cavity A₁B₁D₁C₁ equals that of the lower cavity A₃B₃D₃C₃, and the shear strengths of two inclined planes in uncharged sections (A₁E₁E₃A₃ and A₁E₁E₃A₃) are the same. Let the rock shear strength be τ_s. Then, the shear strength of the upper and lower sides of the cavity and the two inclined planes in uncharged sections can be expressed as

For a given dip angle between the cuthole and the free surface, (1) can be rewritten as follows according to the geometric relation:whereas the rock fragments in the cavity are thrown out along the normal direction of the free surface, the total shear strength of the minimum burden can be obtained by the relative location of the cavity surface and the free surface:

3.2. Explosive Force in the Normal Direction of the Free Surface

To ensure the effectiveness of cutting blasting, the explosive force must be strong enough to cause a shear failure on the upper and lower sides of the cavity and on the two inclined planes in uncharged sections. As shown in Figure 3, after the detonation in cuthole A₂C₂, the horizontal and radial resultant force F of the explosive gas on the hole wall can be expressed aswhere P (P = ρ₀D²/8) is the average detonation pressure in the hole; ρ₀ is the density of explosive; D is the detonation velocity of explosive; r_a is the hole radius; and φ is the angle between any point and the horizontal radius of the cross section passing through the point.

Due to the symmetrical arrangement of cutholes, the resultant force on the horizontal radius of hole wall B₂D₂ equals that of cuthole A₂C₂. According to Figure 3, the force obtained by (5) is perpendicular to the axis of the cuthole. Since the rocks in the cavity are eventually thrown out along the outer normal direction of the free surface, the effective acting force of the explosive gas is the component along this direction:

For the three pairs of cutholes, the effective forces of the explosive gas on the four corners of the cutholes account for only a half of that of cutholes in the central row:

Based on (6) and (7), the resultant force of the three pairs of cutholes in the normal direction of the free surface can be obtained as

3.3. Cavity Separation Conditions

According to the first strength criterion, the cavity will not appear until the rocks in the cavity reaches an ultimate equilibrium under the quasistatic action of the explosive gas; that is,

When the shear stresses on the upper and lower end surfaces of the cavity and the two inclined surfaces between the uncharged sections of the blasthole satisfy formula (9), shear-slip surfaces A₁B₁D₁C₁, A₃B₃D₃C₃, A₁E₁E₃A₃, and B₁B₃F₃F₁ can be formed.

4. Determination of Cutting Parameters

The important parameters of cutting blasting include cuthole bottom spacing, row spacing, and charge coefficient. Meanwhile, the critical cuthole depth was introduced as the criterion for the addition of auxiliary central hole. Based on the above theoretical analysis, the parameters of each cuthole are derived as follows.

4.1. Distance between Cutholes and Rows

To determine the row spacing in the cutting, there should be a blasting-induced crack extending across different rows, which separates the rocks in the cavity from surrounding rocks. For the hole bottom spacing, the rock at the cavity bottom must be fully broken, so as to separate from surrounding rocks under the shock wave.

The cuthole spacing is usually calculated by the radius ratio between the crushed zone and the fracture zone caused by the explosion. In general, the hole bottom spacing is twice that of the crushed zone radius, and the row spacing is twice that of the fracture zone radius. Therefore, the hole bottom spacing a and the row spacing d₁ can be expressed aswhere r₁ is the radius of crushed zone; r₂ is the radius of fracture zone.

In cutting blasting, the rock withstands both tension and compression from all directions. The crushed zone is caused by the compressive stress and the fracture zone is caused by the tensile stress. Thus, the radius of the crushed zone r₁ and the radius of the fracture zone r₂ can be expressed aswhere

Formulas (11a) and (11b), respectively, indicate the radius of the crushing area under the conditions of coupled charge and uncoupled charge. Among them, is the uniaxial dynamic compressive strength of the rock, , is for the strain rate under load, Hakailehto suggested [29], and desirably .

The crack zone radius is obtained aswhere is the stress wave attenuation coefficient, .

If the dynamic effects of fracture circle and rock strength are ignored, it can be calculated according to formula (14) [30]:where is the explosive load acting on the wall of the blasthole.

4.2. Distance between Cuthole Bottoms

As with the row distance, too large and too small distance at the bottom of the holes are not conducive to rock fragmentation and throwing. From [31], it can be known that too small distance between hole bottoms may cause explosives to be squeezed and explosion rejection will occur. If the distance between hole bottoms is too large, the intensity of the shock wave will rapidly decay during the propagation process, rocks within the range of the hole bottom cannot be destroyed completely, and it is easy to cause a bulged phenomenon.

When determining distance of the bottom cutholes, it is required that the rock at the bottom of the cut blasting cavity is fully damaged, and the rock at the bottom of the blasthole in the cut blasting cavity can be separated from the cavity wall under the action of a shock wave. For the boundary of the shock waves excited at the bottom of adjacent cutholes, it can be regarded as being on the center line of the cutholes after the two groups of adjacent drug packs are blasted together. Studies have shown that the stress wave will be superimposed between the cutholes and the stress on the connecting line will be strengthened. In order to meet the blasting requirements, the crushed area at the bottom of adjacent cutholes should intersect, and formula (15) can be used to calculate the bottom hole distance :

4.3. Distance between Cuthole Heads and Inclined Angle

According to the analysis of the formation mechanism of the cut blasting cavity, it can be known that there is a relationship between the distance between cuthole heads and the inclined angle as in formula (16), which affects each other:

4.4. Charging Coefficient

The cavity force shows that (9) is the precondition for separating cavity rocks from surrounding rocks. If the charge length le is replaced by the explosive charge coefficient k and then k can be derived as

Substitute (4) and (16) into (9). Then, the charging coefficient k can be expressed as

The charging coefficient k in (17) is applicable to coupled charging, which is difficult to realize in practice. Instead of coupled charging, the uncoupled charging is commonly adopted for blasting. In tunnel blasting, the cuthole is usually 40 mm in diameter and the cartridge is 32 mm in diameter. Meanwhile, the charging coefficient k should be greater than 0.75 to ensure the effective stemming and utilization of explosive energy [28]. Hence, (17) can be transformed to

4.5. Critical Cuthole Depth and Auxiliary Cuthole Criterion

For better drifting footage, the blasting operation usually adopts a high charge coefficient. However, the resulting reduction in stemming length may result in insufficient stemming and the loss of explosive energy. To solve the problem, extra central holes should be added perpendicularly to the free surface, together with some shallow inclined holes in the middle part of the cutting area. The number of additional holes hinges on the charging dosage. Additionally, the depth of the auxiliary central hole is equal to H, and only 2∼4 sections are charged at the hole bottom. The depth of an additional inclined hole can be expressed as [32]where ΔH (ΔH = 0.2 m) is the length of subdrilling.

The critical cuthole depth is defined as the depth when auxiliary cutholes are added to cutting blasting. Since the critical condition for (18) is k = k_c = 0.75 [30], there iswhere k_c is the critical charging coefficient.

Then, the charge quantity for the first cuthole is

Without changing the rock attributes, explosive properties, and cuthole dip angle, cutholes should be added when the hole depth exceeds the critical value H_c. Meanwhile, the type of the auxiliary cuthole depends on the charging length:(1)If charging length l_e < 0.75H/sin θ, no auxiliary cuthole is needed.(2)If 0.75H/sin θ < l_e < 0.75H/sin θ + (2∼4) × 0.1, a central vertical auxiliary hole is needed.(3)If 0.75H/sin θ + (2∼4) × 0.1 < l_e < 0.75(H/sin θ + H_i/sin θ_i), a shallow inclined hole is needed.(4)If l_e > 0.75(H/sin θ + H_i/sin θ_i), both the central vertical hole and the shallow inclined hole are needed.

5. Theoretical Calculation

Four types of rocks (i.e., shale, sandstone, limestone, and granite) were selected for the theoretical calculation. The physical-mechanical parameters of rocks are presented in Table 1. The 2# rock emulsion explosive (density: ρ₀ = 1,300 kg/m³; detonation velocity D = 4,000 m/s; length: 300 mm; diameter: 32 mm; weight: 0.3 kg) was adopted for the calculation. The critical hole depth of each type of rock at different hole depths and dip angles were obtained according to the theoretical solution (Section 3). Then, the relationships between the critical hole depths and the slope angles of four rocks were determined based on the calculated results in Table 2. As shown in Figure 4, the critical hole depth decreased gradually with the increase of dip angle for all cases.

According to Table 2, the critical cuthole depth-inclined angle relationship curve that can be used for four types of rocks is shown in Figure 4. From Figure 4 and Table 2, it can be seen that as the dynamic compressive strength, tensile strength, and shear strength increase, the critical cuthole depth gradually decreases; as the inclination angle of the cuthole increases, the clamping force decreases; and as the base resistance increases, the critical cuthole depth of the hole gradually decreases. This is consistent with the current theoretical research results and field practice. In addition, taking sandstone as an example, when the inclination angle of the cuthole is 45 degrees, the critical depth of the blasting hole is 3.68 meters, which is also the same as the center hole when the depth of the cuthole is 3.5∼4 meters when the sandstone tunnel is blasted in practice.

6. Numerical Simulation

6.1. Model Building

In light of the hole arrangement in Figure 5, two numerical models (I and II) of the same dimensions (length: 500 cm; width: 300 cm; height: 280 cm) were established by ANSYS/LS-DYNA. Six single V-shaped cutholes were arranged in the two models (A₁C₁, A₂C₂, A₃C₃, B₁D₁, B₂D₂, and B₃D₃). The parameters are details as follows: the vertical depth of the cuthole H_m1 = 3 m, the hole diameter 2r_a1 = 40 mm, the dip angle of the hole θ_m1 = 60°, the row spacing of the cuthole = 80 cm, and the hole bottom spacing = 30 cm.

Model I was designed without any central hole, while model II was added with two central holes vertical to the free surfaces (P₁Q₁; P₂Q₂) in the middle of the cutting area. The charging lengths for cutholes in models I and II were 2.7 m and 2.6 m, respectively. The calculation formulas are, respectively, 0.75H_m1/sin θ_m1 = 2.6 m and 0.75H_m1/sin θ_m1 + 2 × 0.1 = 2.8 m. In the meantime, the central holes in model II were also charged 0.3 m in length and 32 mm in diameter, with the orifices blocked with stemming. According to the tunnelling environment, the plane of cutholes was set as a free surface, and the other five planes were set as nonreflecting boundaries.

6.2. Selections of Material and State Equation

To improve the accuracy of the numerical simulation, the MAT-PLASTIC-KINEMATIC, MAT-HIGH- EXPLOSIVEBURN, MAT-NULL, and MAT-SOIL-AND-FOAM models were adopted to describe the rock mass, the explosive, the air, and stemming materials, respectively. In addition, the state equations of the explosive and the air were modelled by EOS-JWL and EOS-LINEAR-POLYNOMAIAL, respectively. The parameters of each material model and its state equation are listed in Tables 3∼6. During the calculation, the ALE algorithm was applied for the explosive, the air, and stemming materials, while the Lagrangian algorithm was adopted for the rock mass.

6.3. Simulation Results

To compare the cutting effect of models I and II, especially the morphology of the cavity formed at the bottom of the cutting area, a 0.5 m section near the hole bottom in the central axis of the cutting area (GH) was selected for monitoring the effective dynamic stress. The monitoring points were arranged along the cuthole wall at an interval of 0.05 m.

Figure 6 illustrates the effective stress contours at different stages after detonation. It can be seen from Figure 6 that, in the initial stage of the explosion of the V-cut blasting hole, the explosion stress wave is cylindrical and propagates outward with the blasthole as the center. The maximum effective stress at the bottom of the blasthole can reach 300 MPa or more, which is much greater than the compressive strength of the rock. Then the rock is crushed. Subsequently, the stress wave continued to propagate outward and superimposed, and the effective stress began to decrease. A saddle-shaped stress isosurface was formed between the V-cut blasting holes, which significantly reduced the compression failure of the rock, indicating that when the rock hardness is greater, the V-cut blasting hole exploded. After that, the rock at the bottom of the trough cavity cannot be fully destroyed; at the same time, due to the large clamping force of the rock at the bottom of the hole, part of the rock mass in the area can be retained. After the central hole is detonated, the stress at the center of the cavity is rapidly increased, and the isoline density is also increased. The blasting of the two central holes plays the role of breaking the rock body that has not fully broken after the V-cut blasting hole detonated. It helps to throw the secondary broken rock body out of the trough cavity and provides more space for broken rock compensation for subsequent blasthole blasting. In addition, after the blasting of the central hole, the stress field at the bottom of the slot cavity is uniformly distributed, with a larger range of action and uniform energy distribution. An approximately rectangular stress concentration area is formed at the bottom of the V-cut blasting cavity. According to the results of numerical simulation calculations, it can be known that the method of undercutting with a central hole is conducive to reducing the occurrence of the bulged phenomenon, thereby forming a larger V-cut blasting cavity volume.

Figure 7 presents the distributions of effective stress within the monitored sections in the two models. As shown in Figure 7, model II has a much higher maximum effective stress of blasting than model I. The dynamic compressive strength of sandstone (the dotted line in Figure 7) was 78.4 MPa, while all effective stresses in model I were below the dotted line. This means that the effective stress at the bottom of the cutting area is smaller than the compressive strength of sandstone. In other words, the rock in this area is barely broken after blasting, and the rock residues tend to exhibit a bulging phenomenon.

According to Figure 7, the maximum and average effective stresses in model I were 66 MPa and 59.3 MPa, respectively, and those in model II were 133 MPa and 118.1 MPa, respectively. Hence, the addition of auxiliary central holes increased the maximum and average effective stresses by 101.6% and 99.2%, respectively. In addition, the auxiliary central holes also strengthened the cutting blasting stress field at the cavity bottom. Thanks to the clamping effect of the rock at the hole bottom, the rocks in this area are very unlikely to be broken and thrown out and tend to remain at the hole bottom. Furthermore, when hole depth and charging length meet certain requirements, an auxiliary central hole can improve the effective dynamic stress at the bottom of the cutting area and further enhance the crushing and throwing of the rock, making it possible to reach an ideal cutting depth and cavity shape.

In contrast, all effective stresses in model II were far above the dotted line, indicating that the effective stress at the bottom of the cut area far exceeds the compressive strength of rock. Thus, the rock masses in this area must be fragmented, thrown out, and separated from the surrounding rocks under the shock wave. This gives birth to a regular cavity. Hence, it is feasible to increase the cutting depth and improve the cuthole use with auxiliary central holes.

7. Engineering Applications

The study object is Banjie Tunnel in Southwest China’s Yunnan Province. The physical-mechanical parameters of the surrounding rocks are given in Table 7. The cuthole diameter 2r_a was 40 mm, the cartridge diameter 2r_b was 32 mm, and the 2# rock emulsion explosive was adopted for the blasting. The surrounding rock masses (grade III) were excavated by double horizontal V-cut with the vertical hole depth being 4 m. The cuthole arrangement is shown in Figure 8.

Using the double horizontal V-cut, the tunnel advanced about 3.33 m per cycle, only 83% of cutholes were utilized, and the specific charge was 0.976 kg/m³. As shown in Figure 9, the blasting failed to meet the construction criteria in that the rock fragments were unevenly distributed large boulders. The construction criteria specify that the monthly advancement in grade III rock should be 110 m, that is, 3.7 m per day. Due to the poor blasting effect and limited cyclic advancement, it is virtually impossible to make further advancement following the original design.

(a)

(b)

Considering the construction schedule, the driving cycle should be 4 m in grade III surrounding rocks. The vertical hole depth should increase to 4.5 m so as to utilize 90% of cutholes. Hence, the cuthole depth was designed as 4.7 m, 0.1∼0.2 m deeper than the normal hole. According to the size of the tunnel section, V-cut blasting holes were adopted. The cutting blasting parameters were calculated with the dip angle of 60° and corresponding hole length L of 5.4 m.

For Banjie Tunnel, the hole bottom spacing a = 158 mm, the row spacing of the cuthole d₁ = 0.819 m, the charging coefficient k = 1.232, and the charging length l_e = 6.87 m. In this case, the charging length l_e > 0.75(H/sin θ + H_i/sin θ_i), an evidence for the need of both auxiliary central holes and shallow inclined holes. The vertical depth of each auxiliary inclined hole was 2.4 m and the dip angle was 45°.

Similarly, the vertical depth of the cut blasting hole was designed as 2.9 m for grade IV surrounding rocks, and the hole length L was 3.8 m at the dip angle of 50°. Following the above theoretical solution, the hole bottom spacing a was calculated as 175 mm, the row spacing d₁ was 0.888 m, and the charging coefficient k was 0.64. Since the charging coefficient k was smaller than the critical charge coefficient (0.75), no auxiliary cuthole is needed.

At the construction site, the actual hole bottom spacing a was 0.2 m, and row spacing d₁ was 0.8 m for grade III rocks; the hole bottom spacing and row spacing were 0.2 m and 0.88 m, respectively, for grade IV rocks. The cuthole arrangements in grade III and grade IV surrounding rocks are presented in Figure 10, and the cutting blasting parameters for grade III rocks are given in Table 8.

(a)

(b)

The specified cutting method was consistently used in the excavation of Banjie Tunnel. The technical statistics of cutting blasting in grade III rocks are listed in Table 9 and the field blasting effect is shown in Figure 11. The results of quasiparallel cutting indicate that the blasting effect was moderately improved with the addition of auxiliary central holes or shallow cutholes. The advancement per cycle increased by 27%, and the cuthole utilization ratio climbed up from 83% to over 90%.

8. Conclusion

Based on the V-cut blasting mechanism hypothesis, this paper analyzes the formation process of the cut blasting cavity, deduces the theoretical formula of each cut blasting parameter, proposes a calculation method for increasing the critical depth of the central hole, and calculates the value based on the charge length coefficient. Differences in the various types of auxiliary cutholes were proposed. Combining numerical simulation and field industrial test verification, it is concluded that when the rock attributes, explosive properties, and the cuthole dip angle are constant, the hole increasing criteria for various types of cutholes are as follows:(1)When the charge length satisfies l_e < 0.75H/sin θ, there is no need to increase the slot.(2)When the charge length satisfies 0.75H/sinθ < l_e <0.75H/sin θ + (2∼4) × 0.1, the center vertical hole needs to be added.(3)When the charge length satisfies 0.75H/sin θ + (2∼4) × 0.1 < l_e < 0.75(H/sin θ + H_i/sin θ_i), a shallow hole with a shallow depth needs to be added.(4)When the length of the charge satisfies l_e < 0.75(H/sin θ + H_i/sin θ_i), it is necessary to add a central hole and a shallow inclined hole.

Data Availability

All data and models generated or used during the study appear in the submitted article.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grants nos. 51679093 and 51374112).

References

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