# Experiment and Analysis of Wedge Cutting Angle on Cutting Effect

Authors: Deqiang Yang; Xuguang Wang; Yinjun Wang; Huaming An; Zhen Lei
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

In the process of tunnel excavation, large charge wedge cutting blasting is widely used to improve the effect of cut blasting and speed up the excavation rate, which is tantamount to increasing the construction cost. In order to save economic cost and improve cutting blasting effect, wedge cutting models with five different cutting angles were experimented and studied by using concrete materials on the basis of similarity theory analysis. The relationships among cutting depth, blasting volume, blasting fragment, and cutting angle are studied and deduced by the dimensional analysis method. The polynomial fitting of cutting depth, blasting volume, blasting fragment, and cutting angle is carried out according to the experimental data, and the corresponding fitting formula is obtained. The optimum cutting depth, hole utilization rate, blasting volume, and blasting fragment were obtained when the wedge cutting angle was 67° under the same charge. The values were 1.665 × 10−1 m, 92.5%, 8.390 × 10−3 m3, and 49.07 mm, respectively. With the use of TC4850N type blasting vibration meter, the blasting vibrations on the wedge in four directions are tested and analyzed. The results show that when wedge cutting inclination is 65 degrees, the peak vibration velocity is the minimum and the vibration intensity of the wedge cutting inclined side is generally smaller than that of the vertical side. Considering the cutting depth, blasting volume, blasting fragment, blasting vibration hazard, drilling error, tunneling construction cost, and other factors, the 65°∼69° wedge cutting blasting in engineering practice can improve the blasting tunneling rate and increase economic benefits. The experimental results show that the blasting tunneling rate is increased and the economic benefit is increased with the minimum construction tunneling cost, which has certain engineering significance.


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## Body

## 1. Introduction

With the rapid progress of modernization, the construction of high-speed railways, freeways, and underground rock projects has grown rapidly. Currently, drilling and blasting methods are still the main methods of tunnel and underground rock space excavation. More than 95% of mountain tunnels are formed using drilling and blasting in China [1]. Cutting blasting is key to creating another free surface for subsequent blasting and influences the overall blasting procedure [2]. Wedge cuttings have the advantages of few boreholes, easy rock casting, and low drilling accuracy requirements; thus, these cuttings have been widely used in hard rock excavation. Langefors and Kihlstrom [3] studied cut blasting earlier and proposed some cutting patterns. Shapiro [4] compared wedge cuttings with other cuttings and believed that wedge cuttings ensured maximum efficiency in soft rock with relatively shallow blast holes, that is, shallower than 2.5 m. Cardu and Seccatore [5] offered statistics of industrial trends in which wedge cuttings appeared to be adopted in a wider variety of applications.Based on the above analysis, wedge cutting blasting technology is often used in tunnel excavation construction, and the key to improving excavation speed and blasting efficiency lies in the selection of wedge cutting angle. The best cutting angle determines the quality of the whole blasting construction, the tunneling effect, and even the progress of each tunneling cycle. References [6, 7] used fuzzy comprehensive evaluation theory to analyze and studied the cutting methods and parameters commonly used in tunnel excavation. Dai et al. [8] divided the formation process of groove cavity after triangular column straight hole cutting blasting into rock destruction stage and broken rock-throwing stage. Zhang et al. [9] studied the cutting blasting in the medium-deep hole blasting of rock-roadway and obtained the most suitable cutting method. Liu et al. [10] adopted a multirow one-way cutting method in the excavation construction of shaft and roadway, and the blasting effect was good. Pei et al. [11] determined a series of blasting parameters of double-wedge cutting mode through theoretical analysis. In the wedge cutting symmetrical blasting model experiments, Liang et al. [12] used RDX explosive to test cement mortar test blocks, and the blasting effects such as groove depth, volume, and hole utilization rate formed by blasting were comprehensively evaluated and analyzed. On the basis of on-site investigation and theoretical analysis, through wedge cutting blasting tests, Chu et al. [13] showed that the change of cutting hole inclination angle would seriously affect the utilization rate of blast hole, the depth of groove cavity, and the volume of groove cavity, especially when the inclination angle is asymmetric. Xiong et al. [14] applied the analytic hierarchy process to analyze various factors affecting wedge cutting blasting and concluded that the main factor affecting cutting blasting is the inclination angle of the blast hole. In the blasting model test research of different cutting methods, Yuan et al. [15] discovered that the wedge millisecond blasting can improve the utilization rate of blast holes and cutting volume. Pu et al. [16] used grey correlation theory to carry out grey correlation analysis on various factors affecting wedge cutting blasting and concluded that the biggest factor affecting cutting blasting is hole inclination angle. Hu et al. [17] adopted the joint modeling technology of AUTO CAD and ANSYS to conclude that the volume of vertical single-wedge cutting is larger than that of straight hole barrel cutting. Zhang et al. [18] concluded that the second-order and second-stage cutting is superior to the common wedge cutting technology. In references [19, 20], the cutting parameters are optimized and analyzed by numerical simulation. It is concluded that the blasting footage decreases obviously with the increase of cutting angle. Sun et al. [21] investigated the influence of the slant angle on cutting force and rock fracture pattern, and two new findings were made: (1) the rotational angle of the groove cut by a tilted pick was possibly different from the tilt angle and (2) all forces on a pick increased significantly with the increase of the slant angle. The findings of this study can help improve the rock cutting efficiency. Man et al. [22] found that the rock slag size of single-wedge and double-wedge cutting is uniform, which is beneficial to slag extraction. Moreover, the blasting vibration velocity and blasting energy have been analyzed. It is found that the energy distribution of single-wedge and double-wedge cutting is more uniform, mainly concentrated in the high-frequency part, while the energy of straight parallel hole cutting is more concentrated in the low-frequency part.Wedge cutting is the most common blasting excavation method because the number of drilling holes is small and the requirement for drilling accuracy is not high. It is easier to give full play to its advantages when cooperating with bench construction. However, its excavation efficiency needs to be studied when different cutting angles change. Due to that the results of field cutting tests are not easy to be statistically analyzed, this paper used concrete as similar materials to systematically and deeply study the wedge cutting depth, blasting volume, blasting fragment, and blasting vibrations with different cutting angles, to put forward the optimal wedge cutting angle, which is of great significance to guide engineering practice, improve tunnel excavation blasting efficiency, and save excavation cost.


## 2. Theoretical Analysis

### 2.1. Similarity of Model Experiments

Geometric similarity constant, material similarity constant, and blasting dynamic similarity constant are selected from the similarity law of tunnel excavation wedge cutting blasting model experiments and the similarity constant of model experiments.


#### 2.1.1. Geometric Similarity

Considering the experiment conditions, the model size should not be too large and the model boundary effect, the model experiment, determines that the geometric size ratio of the prototype to the model of wedge cutting is 15. Due to the reasons of charging and placing detonators, the diameter of the model blast hole should be 10 mm, while the diameter of the prototype blast hole is generally 45 mm, so the diameter ratio of the prototype blast hole to the model blast hole is 4.5. Although there are some differences with the requirements of geometric similarity, when the length-diameter ratio of the blast hole is large (L/db>10), it has little influence on the test results [23, 24].


#### 2.1.2. Material Similarity

In the process of carrying out model experiments, scholars at home and abroad generally use concrete materials to carry out rock blasting model experiments because it is difficult to find model materials that are completely consistent with the site rock mass conditions [25]. In this paper, concrete materials were also used to prepare wedge cutting models with various angles for blasting experiments.


#### 2.1.3. Similarity of Blasting Power

The diameter of the blast hole in the model is 10 mm, which is less than the critical diameter of emulsion explosive used in tunnel blasting on-site. Therefore, the simple substance high explosive Tai’an is used as the model explosive in the experiment and the No. 8 detonator is used for initiation.


### 2.2. Prediction Dimensional Analysis of Blasting Index

Cutting depthH, blasting volume V, and blasting fragment D are the main indexes to evaluate the blasting effect of wedge cutting at different angles, which are mainly affected by explosive quantity Q, explosive density ρc, concrete strength σm, vertical depth of blast holes h, hole spacing b1, and hole bottom spacing b2.The above three main indexes for evaluating the blasting effect of wedge cutting at different angles are written as follows:(1)H=fQ,ρc,σm,h,b1,b2,V=fQ,ρc,σm,h,b1,b2,D=fQ,ρc,σm,h,b1,b2.See Table1 for the dimensions of each physical quantity in the equation.Table 1
Blasting physical dimension.
Physical quantitySymbolsDimensionCutting depthHLBlasting volumeVL3Blasting fragmentDLExplosive quantityQMExplosive densityρcML−3Concrete strengthσmML−1T−2Hole vertical depthhLOrifice spacingb1LHole bottom spacingb2LTaking the vertical depth of the blast holeh, the explosive quantity Q, and the concrete strength σm as the basic physical quantities, according to the π theorem, the above relation can be expressed as follows:(2)πH=fπρc,πb1,πb2,πV=fπρc,πb1,πb2,πD=fπρc,πb1,πb2.For cutting depthH,(3)π=HHhαQβσmγ,where α, β, and γ are undetermined coefficients; because π is dimensionless quantities, the dimensions of the numerator and denominator should be equal, that is,(4)H=hαQβσmγ.Substituted dimensions are(5)L=LαMβML−1T−2γ.Thus, the solution isα=1, β=γ=0.So we can get(6)πH=Hh.The same process can be(7)πV=Vh3,πD=Dh,πρc=ρch−3Q,πb1=b1h,πb2=b2h.Then the cutting depthH, the blasting volume V, and the blasting fragment D can be expressed as(8)πH=Hh=fρch−3Q,b1h,b2h,(9)πV=Vh3=fρch−3Q,b1h,b2h,(10)πD=Dh=fρch−3Q,b1h,b2h.In the experiment, the explosive is Tai’an, the charge is fixed, the vertical depth of the blast hole and the distance between the orifices are also fixed, and the concrete model is of the same material and the same proportion. Therefore, the following parameters are constants in the experiment process, namely, the explosive quantityQ, explosive density ρc, concrete strength σm, vertical depth of the blast hole h, and the distance between the orifices b1. Equations (8)–(10) can be changed to(11)Hh=fb2h,Vh3=fb2h,Dh=fb2h.That is,(12)H=ϕb2h,(13)V=ϕb2h,(14)D=ϕb2h.In equations (12)–(14), the cutting depth H, blasting volume V, and blasting fragment D change with the hole bottom spacing b2.In Figure1, θ=arccotb1−b2/2h, the vertical depth of the blast hole and the distance between the orifices are fixed. Therefore, the change of hole bottom spacing b2 leads to the change of the wedge cutting hole angle θ.Figure 1
Layout of single-stage wedge cutting blast holes with different angles (unit: mm).Therefore, set(15)x=b2h∝θ,H=ϕb2h=ϕx,V=ϕb2h=ϕx,D=ϕb2h=ϕx.Since the function equation is an elementary function, it is analytical; that is, it can be derived indefinitely in the domain. According to Taylor’s theorem, if a functionϕ has a continuous derivative up to n order in a neighborhood of a point x0, then(16)ϕx=ϕx0+ϕ′x0x−x0+ϕ″x02!x−x02+⋯+ϕnx0n!x−x0n+Rnx,The above equation is Taylor’s equation of ϕ at the point x0, where Rnx is Lagrange remainder; that is,(17)Rnx=ϕn+1ξn+1!x−x0n+1,where ξ is between x and x0.Setx0=0, the Taylor equation at this time can be transformed into(18)ϕx=ϕ0+ϕ′0x+ϕ″02!x2+⋯+ϕn0n!xn+Rnx.In this case, the Lagrange remainder is(19)Rnx=ϕn+1ξn+1!xn+1,where ξ is between x and x0.Whenn=4,(20)ϕx=ϕ0+ϕ′0x+ϕ″02!x2+ϕ303!x3+ϕ404!x4+R4x,R4x=ϕ5ξ5!x5,where ξ is between x and x0.If the coefficients are replaced byA0B0,C0, A1B1,C1, A2B2,C2, A3B3,C3, A4B4,C4, respectively, then equations (12)–(14) can be reduced to(21)H=A0+A1θ+A2θ2+A3θ3+A4θ4+R4θ,(22)V=B0+B1θ+B2θ2+B3θ3+B4θ4+R4θ,(23)D=C0+C1θ+C2θ2+C3θ3+C4θ4+R4θ.In the equationsR4θ=ϕ5ξ/5!θ5, ξ is between x and x0.When fitting the equation, the Lagrange remainder can be discarded first, and then the error of the fitting equation can be calculated. If the error is within the allowable range, it means that the removal of Lagrange remainder has no effect on the equation.From equations (21)–(23), it can be seen that under the premise that only the explosion energy (regardless of the influence of gravity and other forces) and the medium properties do not change with the change of loading speed when the charge with the same charge quantity and the same charge density explodes in the same medium, the cutting depth H, the blasting volume V, and the blasting fragment D change with the angle θ of the wedge cutting hole.


## 2.1. Similarity of Model Experiments

Geometric similarity constant, material similarity constant, and blasting dynamic similarity constant are selected from the similarity law of tunnel excavation wedge cutting blasting model experiments and the similarity constant of model experiments.


### 2.1.1. Geometric Similarity

Considering the experiment conditions, the model size should not be too large and the model boundary effect, the model experiment, determines that the geometric size ratio of the prototype to the model of wedge cutting is 15. Due to the reasons of charging and placing detonators, the diameter of the model blast hole should be 10 mm, while the diameter of the prototype blast hole is generally 45 mm, so the diameter ratio of the prototype blast hole to the model blast hole is 4.5. Although there are some differences with the requirements of geometric similarity, when the length-diameter ratio of the blast hole is large (L/db>10), it has little influence on the test results [23, 24].


### 2.1.2. Material Similarity

In the process of carrying out model experiments, scholars at home and abroad generally use concrete materials to carry out rock blasting model experiments because it is difficult to find model materials that are completely consistent with the site rock mass conditions [25]. In this paper, concrete materials were also used to prepare wedge cutting models with various angles for blasting experiments.


### 2.1.3. Similarity of Blasting Power

The diameter of the blast hole in the model is 10 mm, which is less than the critical diameter of emulsion explosive used in tunnel blasting on-site. Therefore, the simple substance high explosive Tai’an is used as the model explosive in the experiment and the No. 8 detonator is used for initiation.


## 2.1.1. Geometric Similarity

Considering the experiment conditions, the model size should not be too large and the model boundary effect, the model experiment, determines that the geometric size ratio of the prototype to the model of wedge cutting is 15. Due to the reasons of charging and placing detonators, the diameter of the model blast hole should be 10 mm, while the diameter of the prototype blast hole is generally 45 mm, so the diameter ratio of the prototype blast hole to the model blast hole is 4.5. Although there are some differences with the requirements of geometric similarity, when the length-diameter ratio of the blast hole is large (L/db>10), it has little influence on the test results [23, 24].


## 2.1.2. Material Similarity

In the process of carrying out model experiments, scholars at home and abroad generally use concrete materials to carry out rock blasting model experiments because it is difficult to find model materials that are completely consistent with the site rock mass conditions [25]. In this paper, concrete materials were also used to prepare wedge cutting models with various angles for blasting experiments.


## 2.1.3. Similarity of Blasting Power

The diameter of the blast hole in the model is 10 mm, which is less than the critical diameter of emulsion explosive used in tunnel blasting on-site. Therefore, the simple substance high explosive Tai’an is used as the model explosive in the experiment and the No. 8 detonator is used for initiation.


## 2.2. Prediction Dimensional Analysis of Blasting Index

Cutting depthH, blasting volume V, and blasting fragment D are the main indexes to evaluate the blasting effect of wedge cutting at different angles, which are mainly affected by explosive quantity Q, explosive density ρc, concrete strength σm, vertical depth of blast holes h, hole spacing b1, and hole bottom spacing b2.The above three main indexes for evaluating the blasting effect of wedge cutting at different angles are written as follows:(1)H=fQ,ρc,σm,h,b1,b2,V=fQ,ρc,σm,h,b1,b2,D=fQ,ρc,σm,h,b1,b2.See Table1 for the dimensions of each physical quantity in the equation.Table 1
Blasting physical dimension.
Physical quantitySymbolsDimensionCutting depthHLBlasting volumeVL3Blasting fragmentDLExplosive quantityQMExplosive densityρcML−3Concrete strengthσmML−1T−2Hole vertical depthhLOrifice spacingb1LHole bottom spacingb2LTaking the vertical depth of the blast holeh, the explosive quantity Q, and the concrete strength σm as the basic physical quantities, according to the π theorem, the above relation can be expressed as follows:(2)πH=fπρc,πb1,πb2,πV=fπρc,πb1,πb2,πD=fπρc,πb1,πb2.For cutting depthH,(3)π=HHhαQβσmγ,where α, β, and γ are undetermined coefficients; because π is dimensionless quantities, the dimensions of the numerator and denominator should be equal, that is,(4)H=hαQβσmγ.Substituted dimensions are(5)L=LαMβML−1T−2γ.Thus, the solution isα=1, β=γ=0.So we can get(6)πH=Hh.The same process can be(7)πV=Vh3,πD=Dh,πρc=ρch−3Q,πb1=b1h,πb2=b2h.Then the cutting depthH, the blasting volume V, and the blasting fragment D can be expressed as(8)πH=Hh=fρch−3Q,b1h,b2h,(9)πV=Vh3=fρch−3Q,b1h,b2h,(10)πD=Dh=fρch−3Q,b1h,b2h.In the experiment, the explosive is Tai’an, the charge is fixed, the vertical depth of the blast hole and the distance between the orifices are also fixed, and the concrete model is of the same material and the same proportion. Therefore, the following parameters are constants in the experiment process, namely, the explosive quantityQ, explosive density ρc, concrete strength σm, vertical depth of the blast hole h, and the distance between the orifices b1. Equations (8)–(10) can be changed to(11)Hh=fb2h,Vh3=fb2h,Dh=fb2h.That is,(12)H=ϕb2h,(13)V=ϕb2h,(14)D=ϕb2h.In equations (12)–(14), the cutting depth H, blasting volume V, and blasting fragment D change with the hole bottom spacing b2.In Figure1, θ=arccotb1−b2/2h, the vertical depth of the blast hole and the distance between the orifices are fixed. Therefore, the change of hole bottom spacing b2 leads to the change of the wedge cutting hole angle θ.Figure 1
Layout of single-stage wedge cutting blast holes with different angles (unit: mm).Therefore, set(15)x=b2h∝θ,H=ϕb2h=ϕx,V=ϕb2h=ϕx,D=ϕb2h=ϕx.Since the function equation is an elementary function, it is analytical; that is, it can be derived indefinitely in the domain. According to Taylor’s theorem, if a functionϕ has a continuous derivative up to n order in a neighborhood of a point x0, then(16)ϕx=ϕx0+ϕ′x0x−x0+ϕ″x02!x−x02+⋯+ϕnx0n!x−x0n+Rnx,The above equation is Taylor’s equation of ϕ at the point x0, where Rnx is Lagrange remainder; that is,(17)Rnx=ϕn+1ξn+1!x−x0n+1,where ξ is between x and x0.Setx0=0, the Taylor equation at this time can be transformed into(18)ϕx=ϕ0+ϕ′0x+ϕ″02!x2+⋯+ϕn0n!xn+Rnx.In this case, the Lagrange remainder is(19)Rnx=ϕn+1ξn+1!xn+1,where ξ is between x and x0.Whenn=4,(20)ϕx=ϕ0+ϕ′0x+ϕ″02!x2+ϕ303!x3+ϕ404!x4+R4x,R4x=ϕ5ξ5!x5,where ξ is between x and x0.If the coefficients are replaced byA0B0,C0, A1B1,C1, A2B2,C2, A3B3,C3, A4B4,C4, respectively, then equations (12)–(14) can be reduced to(21)H=A0+A1θ+A2θ2+A3θ3+A4θ4+R4θ,(22)V=B0+B1θ+B2θ2+B3θ3+B4θ4+R4θ,(23)D=C0+C1θ+C2θ2+C3θ3+C4θ4+R4θ.In the equationsR4θ=ϕ5ξ/5!θ5, ξ is between x and x0.When fitting the equation, the Lagrange remainder can be discarded first, and then the error of the fitting equation can be calculated. If the error is within the allowable range, it means that the removal of Lagrange remainder has no effect on the equation.From equations (21)–(23), it can be seen that under the premise that only the explosion energy (regardless of the influence of gravity and other forces) and the medium properties do not change with the change of loading speed when the charge with the same charge quantity and the same charge density explodes in the same medium, the cutting depth H, the blasting volume V, and the blasting fragment D change with the angle θ of the wedge cutting hole.


## 3. Model Experiment Program and Fabrication

### 3.1. Model Program

On the basis of analyzing and summarizing the existing research results, in order to reduce the number of experiments, a typical program method is proposed to carry out blasting experiments on single-stage wedge cutting under different cutting angles, as shown in Figure1. In this model experiment, five wedge cutting angles with different cutting angles will be taken as the main factors to study and select wedge cutting with appropriate angles under the same explosive quantity.


### 3.2. Fabrication of Model Specimens

Based on the actual tunnel excavation cutting blasting as the prototype, the model experiment program is designed. The concrete model specimen is made, and the method of reserving the diameter of the blast hole in the concrete model specimen is designed. Five wedge cutting blast hole arrangements with different cutting angles (65°, 69°, 73°, 77°, and 81°) are designed.Considering the boundary effect of the model, the size of the model specimen in this experiment is 1200 mm × 1200 mm × 400 mm. Ten model specimens were made with a hole diameter of 10 mm and a vertical depth of 200 mm.The experiment model is made of concrete pouring, and the material and proportion of the model are as follows: the cement is 42.5 R ordinary Portland cement, the coarse aggregate is stones, the maximum particle size is not more than 2 cm, and the particle size of river sand is less than 1 mm. The mix proportion is cement: stone: river sand: water = 52 : 88 : 63 : 21 (weight ratio).Due to the large size of the model specimen, in order to prevent the mould from being extruded and expanded by concrete, the experimental mould adopts a hole positioning mould formed by welding steel bars and steel plates. In order to reduce bubbles in the model and ensure the strength of the model, concrete needs to be vibrated and tamped while pouring.In order to reserve blast holes while firing concrete specimens, a self-designed blast hole positioning mould is adopted. Wedge cutting angle control requires more accuracy. In order to ensure the accuracy of blast holes, an inclination angle controller is designed, as shown in Figure2. After insertion, gently rotate and pull out the steel bars in the concrete every 1 h∼3 h to prevent the steel bars from solidifying in the concrete until the model hardens to form the required hole gun.Figure 2
Cutting hole positioning diagram.After the clay concrete specimen is hardened, the steel bar is pulled out, and the plastic film is rolled into a cone to block the blast hole to prevent debris, water, and so forth from falling into the blast hole and affecting the quality of the blast hole. The model specimen shall be made, covered with felt cloth and regularly sprinkled with water to maintain the specimen for not less than 28 days to ensure that the coagulated specimen meets the predetermined strength requirements. Figure3 shows the clay concrete specimens.Figure 3
Forming of concrete specimens.According to the Standard for Test Methods of Mechanical Properties of Ordinary Concrete (GB50081-2002), when pouring the concrete model, take the concrete from the same batch of concrete to make three standard test blocks of 150 mm × 150 mm × 150 mm each for compressive strength test, splitting tensile strength test and longitudinal wave velocity test of ordinary concrete, and three standard test blocks of 150 mm × 150 mm × 300 mm each for axial compressive strength test, and static compressive modulus of elasticity test, and maintain for 28 days. After that, the static mechanical properties of the concrete model used in the blasting test will be tested. The standard model is shown in Figure4.Figure 4
Standard model of concrete test block. (a) Test blocks of 150  mm × 150  mm × 150 mm. (b) Test blocks of 150  mm × 150  mm × 300 mm.
(a)(b)The statistics of the test results of the mechanical properties of ordinary concrete measured in the laboratory are shown in Table2.Table 2
Test results of mechanical properties of ordinary concrete.
Density (kg/m3)2405.35Compressive strength (MPa)43.00Splitting tensile strength (MPa)2.34Axial compressive strength (MPa)36.11Static compressive modulus of elasticity (GPa)37.27Longitudinal wave velocity (m/s)4025


### 3.3. Model Experiment Blasting Parameters

The parameters of each model experiment program are shown in Table3.Table 3
Blasting model experiment program.
Cutting modeSpecimen no.Apertureϕ (mm)Row spacinga (mm)Hole distanceb1 (mm)Hole bottom distanceb2 (mm)Hole vertical depthh (mm)Hole lengthl (mm)Ultra-deep depthΔh (mm)65° wedge cuttingI-5, II-51050200132002212069° wedge cuttingI-6, II-61050200462002142073° wedge cuttingI-7, II-71050200782002092077° wedge cuttingI-8, II-810502001082002052081° wedge cuttingI-9, II-9105020013720020220


### 3.4. Model Blasting Experiment

Each group of cutting mode has 2 blasting model specimens, with a total of 5 groups of cutting modes and 10 blasting model specimens. Each charging hole shall be filled with 1 g Tai’an explosive, the detonator tube shall be connected for the initiation, the blast holes shall be blocked by quick-drying cement, the explosive slag shall be removed after the explosion, and the cutting depth, the volume of the blasting room, and the blasting fragment shall be measured. The effect of blasting model experiment is shown in Figure5. It can be seen that the I-5, II-6, I-7, I-8 model of postexplosion test is complete, and the cut part is thrown out to form a certain volume of the cavity, which does not affect the position of blasting vibration measuring point. The model of test I-9 is split into two parts along the direction of blast hole, and the cut part is only shaped through the crack and not thrown out.Figure 5
Experiment results of wedge cutting blasting with different angles. (a) 65° wedge cutting, (b) 69° wedge cutting, (c) 73° wedge cutting, (d) 77° wedge cutting, and (e) 81° wedge cutting.
(a)(b)(c)(d)(e)


## 3.1. Model Program

On the basis of analyzing and summarizing the existing research results, in order to reduce the number of experiments, a typical program method is proposed to carry out blasting experiments on single-stage wedge cutting under different cutting angles, as shown in Figure1. In this model experiment, five wedge cutting angles with different cutting angles will be taken as the main factors to study and select wedge cutting with appropriate angles under the same explosive quantity.


## 3.2. Fabrication of Model Specimens

Based on the actual tunnel excavation cutting blasting as the prototype, the model experiment program is designed. The concrete model specimen is made, and the method of reserving the diameter of the blast hole in the concrete model specimen is designed. Five wedge cutting blast hole arrangements with different cutting angles (65°, 69°, 73°, 77°, and 81°) are designed.Considering the boundary effect of the model, the size of the model specimen in this experiment is 1200 mm × 1200 mm × 400 mm. Ten model specimens were made with a hole diameter of 10 mm and a vertical depth of 200 mm.The experiment model is made of concrete pouring, and the material and proportion of the model are as follows: the cement is 42.5 R ordinary Portland cement, the coarse aggregate is stones, the maximum particle size is not more than 2 cm, and the particle size of river sand is less than 1 mm. The mix proportion is cement: stone: river sand: water = 52 : 88 : 63 : 21 (weight ratio).Due to the large size of the model specimen, in order to prevent the mould from being extruded and expanded by concrete, the experimental mould adopts a hole positioning mould formed by welding steel bars and steel plates. In order to reduce bubbles in the model and ensure the strength of the model, concrete needs to be vibrated and tamped while pouring.In order to reserve blast holes while firing concrete specimens, a self-designed blast hole positioning mould is adopted. Wedge cutting angle control requires more accuracy. In order to ensure the accuracy of blast holes, an inclination angle controller is designed, as shown in Figure2. After insertion, gently rotate and pull out the steel bars in the concrete every 1 h∼3 h to prevent the steel bars from solidifying in the concrete until the model hardens to form the required hole gun.Figure 2
Cutting hole positioning diagram.After the clay concrete specimen is hardened, the steel bar is pulled out, and the plastic film is rolled into a cone to block the blast hole to prevent debris, water, and so forth from falling into the blast hole and affecting the quality of the blast hole. The model specimen shall be made, covered with felt cloth and regularly sprinkled with water to maintain the specimen for not less than 28 days to ensure that the coagulated specimen meets the predetermined strength requirements. Figure3 shows the clay concrete specimens.Figure 3
Forming of concrete specimens.According to the Standard for Test Methods of Mechanical Properties of Ordinary Concrete (GB50081-2002), when pouring the concrete model, take the concrete from the same batch of concrete to make three standard test blocks of 150 mm × 150 mm × 150 mm each for compressive strength test, splitting tensile strength test and longitudinal wave velocity test of ordinary concrete, and three standard test blocks of 150 mm × 150 mm × 300 mm each for axial compressive strength test, and static compressive modulus of elasticity test, and maintain for 28 days. After that, the static mechanical properties of the concrete model used in the blasting test will be tested. The standard model is shown in Figure4.Figure 4
Standard model of concrete test block. (a) Test blocks of 150  mm × 150  mm × 150 mm. (b) Test blocks of 150  mm × 150  mm × 300 mm.
(a)(b)The statistics of the test results of the mechanical properties of ordinary concrete measured in the laboratory are shown in Table2.Table 2
Test results of mechanical properties of ordinary concrete.
Density (kg/m3)2405.35Compressive strength (MPa)43.00Splitting tensile strength (MPa)2.34Axial compressive strength (MPa)36.11Static compressive modulus of elasticity (GPa)37.27Longitudinal wave velocity (m/s)4025


## 3.3. Model Experiment Blasting Parameters

The parameters of each model experiment program are shown in Table3.Table 3
Blasting model experiment program.
Cutting modeSpecimen no.Apertureϕ (mm)Row spacinga (mm)Hole distanceb1 (mm)Hole bottom distanceb2 (mm)Hole vertical depthh (mm)Hole lengthl (mm)Ultra-deep depthΔh (mm)65° wedge cuttingI-5, II-51050200132002212069° wedge cuttingI-6, II-61050200462002142073° wedge cuttingI-7, II-71050200782002092077° wedge cuttingI-8, II-810502001082002052081° wedge cuttingI-9, II-9105020013720020220


## 3.4. Model Blasting Experiment

Each group of cutting mode has 2 blasting model specimens, with a total of 5 groups of cutting modes and 10 blasting model specimens. Each charging hole shall be filled with 1 g Tai’an explosive, the detonator tube shall be connected for the initiation, the blast holes shall be blocked by quick-drying cement, the explosive slag shall be removed after the explosion, and the cutting depth, the volume of the blasting room, and the blasting fragment shall be measured. The effect of blasting model experiment is shown in Figure5. It can be seen that the I-5, II-6, I-7, I-8 model of postexplosion test is complete, and the cut part is thrown out to form a certain volume of the cavity, which does not affect the position of blasting vibration measuring point. The model of test I-9 is split into two parts along the direction of blast hole, and the cut part is only shaped through the crack and not thrown out.Figure 5
Experiment results of wedge cutting blasting with different angles. (a) 65° wedge cutting, (b) 69° wedge cutting, (c) 73° wedge cutting, (d) 77° wedge cutting, and (e) 81° wedge cutting.
(a)(b)(c)(d)(e)


## 4. Analysis of Cutting Effect

Cutting depth, hole utilization rate, blasting volume, and blasting fragment are important indexes to evaluate blasting effect. After each experiment, the depth of blasting cutting, the utilization rate of blast holes, the blasting volume, and the blasting fragment are counted. The relevant indexes of each model after blasting are shown in Table4.Table 4
Statistical table of relevant indexes of blasting experiment.
Cutting modeSpecimen no.Hole vertical depth (10−1 m)Ultra-deep depth (10−1 m)Cutting depth (10−1 m)Utilization rate of blast holes (%)Blasting volume (10−3 m3)Blasting fragment (mm)Bulk rate (%)65° wedge cuttingI-52.0000.2001.53085.07.41049.7248.9069° wedge cuttingII-62.0000.2001.61189.58.21554.0249.2073° wedge cuttingI-72.0000.2001.42279.07.16557.5452.8677° wedge cuttingI-82.0000.2001.18866.05.92086.0666.2481° wedge cuttingI-92.0000.2000.0000.000.000∞100


### 4.1. Measurement of Model Cutting Depth

After each blasting experiment, remove the fragments falling around the groove cavity opening, delimit the boundary of the groove cavity opening, then take the center of the straight-eye connection line of the two auxiliary centers before blasting as the center, measure the cutting depths in 8 different directions at intervals of 45°, and then take the average value of these depths as the cutting depth of this experiment, as shown in Figure6.Figure 6
Cutting depth measurement.For the sake of intuition, the cutting depth data in Table4 can be obtained by fitting equation (21).(24)H=−4882.519028+272.701066θ−5.704857θ2+0.053004θ3−0.000185θ4.As can be seen from Table5, the maximum absolute error of blasting cutting depth is −0.013 × 10−1 m, and the maximum relative error is 1.09%, which indicates that the error is relatively small. Within the allowable range, the fitting value is very close to the measured value, and the curve fitting is good.Table 5
Error analysis table of cutting depth fitting formula.
Cutting angleH (measured value) (10−1 m)H∗ (fitting value) (10−1 m)H −H∗Relative error (%)65°1.5301.537−0.0070.4669°1.6111.619−0.0080.5073°1.4221.432−0.0100.7077°1.1881.201−0.0131.0981°0.0000.0000.0000.00From equation (24), the cutting depth of 67° wedge cutting model experiment can be calculated as the optimal value, with a cutting depth value of 1.665 × 10−1 m and a hole utilization rate of 92.5%, as shown in Figure 7.Figure 7
Fitting curves of wedge cutting models with different angles and cutting depth.


### 4.2. Measurement of Model Blasting Volume

After each experiment, dry fine sand is filled into the plastic film above the tank cavity so that the fine sand is flush with the horizontal plane of the model. The volume of the recovered fine sand measured by the dosage cylinder is the volume of the blasting room after blasting. The volume measurement of the blasting room is shown in Figure8.Figure 8
Blasting volume measurement.For the sake of intuition, the blasting volume data in Table4 can be obtained by fitting equation (22).(25)V=−26874.777744+1494.679753θ−31.139147θ2+0.288138θ3−0.000999θ4.As can be seen from Table6, the maximum absolute error of blasting volume is 0.035 × 10−3 m3, and the maximum relative error is 0.59%, which indicates that the error is relatively small. Within the allowable range, the fitting value is very close to the measured value, and the curve fitting is good.Table 6
Error analysis table of blasting volume fitting formula.
Cutting angleV (measured value) (10−3 m3)V∗ (fitting value) (10−3 m3)V −V∗Relative error (%)65°7.4107.3900.0200.2769°8.2158.1900.0250.3173°7.1657.1350.0300.4277°5.9205.8850.0350.5981°0.0000.0000.0000.00From equation (25), the blasting volume of 67° wedge cutting model experiment can be calculated as the optimal value, with a blasting volume value of 8.390 × 10−3 m3, as shown in Figure 9.Figure 9
Fitting curves of wedge cutting models with different angles and blasting volume.


### 4.3. Statistical Analysis of Model Cutting Blasting Fragmentation

#### 4.3.1. Histogram of Blasting Fragmentation Distribution

When the test is blasted, the blasting fragmentation of the plough cut model with different cutting angles is analyzed. Then use the ZBSX-92A shock-type dual-purpose vibrating pendulum screen machine produced by Zhejiang Shangyu Xinguang Instrument and Equipment Factory and the national new standard square hole stone screen machine to weigh and separate the different particle size and block size by electronic scale, which is shown in Figures10–12.Figure 10
Blasting fragments.Figure 11
ZBSX-92A shock-type dual-purpose pendulum screening machine.Figure 12
Fragments weighing.According to the distribution of blasting fragmentation, the particle size is divided into 7 grades. The block size distribution of the blasted plough cut with five different cutting angles will be shown in Table7.Table 7
Statistical table of blasting block degree of wedge-shaped notch model test.
Cutting modeSpecimen no.Fragment grade (mm)<9.59.5∼1919∼31.531.5∼5353∼7575∼90>9065° wedge cuttingI-5, II-5Mass (kg)0.5721.2532.7593.1264.5120.8612.522Cumulative mass (kg)0.5721.8254.5847.71012.22213.08315.605Mass percentage (%)3.6668.02917.68020.03228.9145.51716.162Cumulative mass percentage (%)3.66611.69529.37549.40778.32183.838100.00069° wedge cuttingI-6, II-6Mass (kg)0.2491.6592.5523.4424.2801.1252.891Cumulative mass (kg)0.2491.9084.4607.90212.18213.30716.198Mass percentage (%)1.53710.24215.75521.25026.4236.94517.848Cumulative mass percentage (%)1.53711.77927.53448.78475.20782.152100.00073° wedge cuttingI-7, II-7Mass (kg)0.4071.0561.9122.8614.6151.2363.119Cumulative mass (kg)0.4071.4633.3756.23610.85112.08715.206Mass percentage (%)2.6776.94412.57418.81530.3508.12820.512Cumulative mass percentage (%)2.6779.62122.19541.01071.36079.488100.00077° wedge cuttingI-8, II-8Mass (kg)0.2231.5921.3261.5131.8762.1315.816Cumulative mass (kg)0.2231.8153.1414.6546.5308.66114.477Mass percentage (%)1.54010.9979.15910.45112.95814.72040.175Cumulative mass percentage (%)1.54012.53721.69632.14745.10559.825100.00081° wedge cuttingI-9, II-9Mass (kg)0.0000.0000.0000.0000.0000.0000.000Cumulative mass (kg)0.0000.0000.0000.0000.0000.0000.000Mass percentage (%)0.0000.0000.0000.0000.0000.0000.000Cumulative mass percentage (%)0.0000.0000.0000.0000.0000.0000.000According to the statistical Table7 of the screening of blasting fragmentation, the histogram of blasting fragmentation distribution of plough cut model test with five different angle is obtained, as shown in Figure 13.Figure 13
Histogram of blasting fragments of wedge-shaped recessed model at different angles.Due to the large angle of 81° wedge cutting, the cutting was not successful. According to the analysis of Figure13, the other four plough cutting models with different angles all contain blasting blocks in models with ranges less than 9.5 mm. Among these, the mass percentage of the plough cutting model with an angle of 65° is the largest, while the mass percentage with an angle of 69° is the smallest. In the range of 9.5 mm–19 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 77° is the largest, while the mass percentage with an angle of 73° is the smallest. In the range of 19 mm–31.5 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 65° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of 31.5 mm–53 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 69° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of 53 mm–75 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 73° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of more than 75 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 77° is the largest, while the mass percentage with an angle of 65° is the smallest.


#### 4.3.2. The Relationship between the Cumulative Mass Percentage of Blasting Fragmentation and its Particle Size

According to the statistical Table7 of the screening of blasting fragmentation, the relation curve between the cumulative mass percentage of each block size and the particle size of blocks is obtained, as shown in Figures 14–17.Figure 14
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 65° wedge cutting.Figure 15
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 69° wedge cutting.Figure 16
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 73° wedge cutting.Figure 17
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 77° wedge cutting.From Figure14, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 65° is as follows:(26)yx=0.000002x4−0.000541x3+0.038735x2+0.104832x−0.133720.From equation (26), it can be calculated that the blasting fragmentation of plough cut with an angle of 65° is 49.72 mm. If the blasting fragmentation is larger than 55 mm, the block rate is(27)η=1−y55,calculated as η=1−y55=1−51.10%=48.90%.From Figure15, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 69° is as follows:(28)yx=0.000003x4−0.000702x3+0.047658x2−0.066457x−0.367026.From equation (28), it can be calculated that the blasting fragmentation of plough cut with an angle of 69° is 54.02 mm. The block rate is(29)η=1−y55=1−50.80%=49.20%.From Figure16, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 73° is as follows:(30)yx=0.000002x4−0.000404x3+0.031135x2+0.032831x+0.065647.From equation (30), it can be calculated that the blasting fragmentation of plough cut with an angle of 73° is 57.54 mm. The block rate is(31)η=1−y55=1−47.14%=52.86%.From Figure17, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 77° is as follows:(32)yx=0.000007x4−0.001158x3+0.056108x2−0.131097x−0.149017.From equation (32), it can be calculated that the blasting fragmentation of plough cut with an angle of 65° is 86.08 mm. The block rate is(33)η=1−y55=1−33.76%=66.24%.The average blasting fragmentation of 81° wedge cutting is ∞ and the bulk rate is 100% because the inclination of the hole of 81° wedge cutting model is large and the cutting is not successful in blasting.From the above calculation, the statistical table of the blasting fragmentation index of wedge cutting with different cutting angles can be obtained, as shown in Table4. According to the calculation, the trend of the plotted blasting fragment and block rate with the cutting angle is shown in Figures 18 and 19.Figure 18
Fitting curves of wedge cutting model and blasting fragments at different angles.Figure 19
The trend of wedge cutting model and the bulk rate at different angles.For the sake of intuition, the blasting fragment data in Table4 can be obtained by fitting equation (23).(34)D=1762.211188−50.924625θ+0.378438θ2,As can be seen from Table8, the maximum absolute error of blasting fragment is −3.87 mm, and the maximum relative error is 7.15%, which indicates that the error is relatively small. Within the allowable range, the fitting value is very close to the measured value, and the curve fitting is good.Table 8
Error analysis table of blasting fragment fitting formula.
Cutting angleD (measured value) (10−3 m3)D∗ (fitting value) (10−3 m3)D −D∗Relative error (%)65°49.7251.01−1.292.5969°54.0250.163.867.1573°57.5461.41−3.876.7377°86.0684.771.291.5081°∞∞0.000.00From equation (34), the blasting fragment of 67° wedge cutting model experiment can be calculated as the optimal value, with a blasting fragment value of 49.07 mm, as shown in Figure 18.Carrying out polynomial regression fitting on the relationship between the wedge cutting model at different angles and the block rate trend in Figure19, the relationship can be obtained as(35)yx=0.002212θ4−0.575658θ3+56.233179θ2−2443.763930θ+39914.165020.From equation (35), the block rate of 67° wedge cutting model experiment can be calculated as the optimal value, with a block rate value of 48.84%.In conclusion, when the explosive consumption of five wedge cutting model tests with different cutting angles is the same, the wedge cutting blasting effect with 67° cutting angle is the best in terms of cutting depth, blasting hole utilization ratio, blasting volume, blasting fragment, blasting block rate, and other main indexes after blasting.


## 4.1. Measurement of Model Cutting Depth

After each blasting experiment, remove the fragments falling around the groove cavity opening, delimit the boundary of the groove cavity opening, then take the center of the straight-eye connection line of the two auxiliary centers before blasting as the center, measure the cutting depths in 8 different directions at intervals of 45°, and then take the average value of these depths as the cutting depth of this experiment, as shown in Figure6.Figure 6
Cutting depth measurement.For the sake of intuition, the cutting depth data in Table4 can be obtained by fitting equation (21).(24)H=−4882.519028+272.701066θ−5.704857θ2+0.053004θ3−0.000185θ4.As can be seen from Table5, the maximum absolute error of blasting cutting depth is −0.013 × 10−1 m, and the maximum relative error is 1.09%, which indicates that the error is relatively small. Within the allowable range, the fitting value is very close to the measured value, and the curve fitting is good.Table 5
Error analysis table of cutting depth fitting formula.
Cutting angleH (measured value) (10−1 m)H∗ (fitting value) (10−1 m)H −H∗Relative error (%)65°1.5301.537−0.0070.4669°1.6111.619−0.0080.5073°1.4221.432−0.0100.7077°1.1881.201−0.0131.0981°0.0000.0000.0000.00From equation (24), the cutting depth of 67° wedge cutting model experiment can be calculated as the optimal value, with a cutting depth value of 1.665 × 10−1 m and a hole utilization rate of 92.5%, as shown in Figure 7.Figure 7
Fitting curves of wedge cutting models with different angles and cutting depth.


## 4.2. Measurement of Model Blasting Volume

After each experiment, dry fine sand is filled into the plastic film above the tank cavity so that the fine sand is flush with the horizontal plane of the model. The volume of the recovered fine sand measured by the dosage cylinder is the volume of the blasting room after blasting. The volume measurement of the blasting room is shown in Figure8.Figure 8
Blasting volume measurement.For the sake of intuition, the blasting volume data in Table4 can be obtained by fitting equation (22).(25)V=−26874.777744+1494.679753θ−31.139147θ2+0.288138θ3−0.000999θ4.As can be seen from Table6, the maximum absolute error of blasting volume is 0.035 × 10−3 m3, and the maximum relative error is 0.59%, which indicates that the error is relatively small. Within the allowable range, the fitting value is very close to the measured value, and the curve fitting is good.Table 6
Error analysis table of blasting volume fitting formula.
Cutting angleV (measured value) (10−3 m3)V∗ (fitting value) (10−3 m3)V −V∗Relative error (%)65°7.4107.3900.0200.2769°8.2158.1900.0250.3173°7.1657.1350.0300.4277°5.9205.8850.0350.5981°0.0000.0000.0000.00From equation (25), the blasting volume of 67° wedge cutting model experiment can be calculated as the optimal value, with a blasting volume value of 8.390 × 10−3 m3, as shown in Figure 9.Figure 9
Fitting curves of wedge cutting models with different angles and blasting volume.


## 4.3. Statistical Analysis of Model Cutting Blasting Fragmentation

### 4.3.1. Histogram of Blasting Fragmentation Distribution

When the test is blasted, the blasting fragmentation of the plough cut model with different cutting angles is analyzed. Then use the ZBSX-92A shock-type dual-purpose vibrating pendulum screen machine produced by Zhejiang Shangyu Xinguang Instrument and Equipment Factory and the national new standard square hole stone screen machine to weigh and separate the different particle size and block size by electronic scale, which is shown in Figures10–12.Figure 10
Blasting fragments.Figure 11
ZBSX-92A shock-type dual-purpose pendulum screening machine.Figure 12
Fragments weighing.According to the distribution of blasting fragmentation, the particle size is divided into 7 grades. The block size distribution of the blasted plough cut with five different cutting angles will be shown in Table7.Table 7
Statistical table of blasting block degree of wedge-shaped notch model test.
Cutting modeSpecimen no.Fragment grade (mm)<9.59.5∼1919∼31.531.5∼5353∼7575∼90>9065° wedge cuttingI-5, II-5Mass (kg)0.5721.2532.7593.1264.5120.8612.522Cumulative mass (kg)0.5721.8254.5847.71012.22213.08315.605Mass percentage (%)3.6668.02917.68020.03228.9145.51716.162Cumulative mass percentage (%)3.66611.69529.37549.40778.32183.838100.00069° wedge cuttingI-6, II-6Mass (kg)0.2491.6592.5523.4424.2801.1252.891Cumulative mass (kg)0.2491.9084.4607.90212.18213.30716.198Mass percentage (%)1.53710.24215.75521.25026.4236.94517.848Cumulative mass percentage (%)1.53711.77927.53448.78475.20782.152100.00073° wedge cuttingI-7, II-7Mass (kg)0.4071.0561.9122.8614.6151.2363.119Cumulative mass (kg)0.4071.4633.3756.23610.85112.08715.206Mass percentage (%)2.6776.94412.57418.81530.3508.12820.512Cumulative mass percentage (%)2.6779.62122.19541.01071.36079.488100.00077° wedge cuttingI-8, II-8Mass (kg)0.2231.5921.3261.5131.8762.1315.816Cumulative mass (kg)0.2231.8153.1414.6546.5308.66114.477Mass percentage (%)1.54010.9979.15910.45112.95814.72040.175Cumulative mass percentage (%)1.54012.53721.69632.14745.10559.825100.00081° wedge cuttingI-9, II-9Mass (kg)0.0000.0000.0000.0000.0000.0000.000Cumulative mass (kg)0.0000.0000.0000.0000.0000.0000.000Mass percentage (%)0.0000.0000.0000.0000.0000.0000.000Cumulative mass percentage (%)0.0000.0000.0000.0000.0000.0000.000According to the statistical Table7 of the screening of blasting fragmentation, the histogram of blasting fragmentation distribution of plough cut model test with five different angle is obtained, as shown in Figure 13.Figure 13
Histogram of blasting fragments of wedge-shaped recessed model at different angles.Due to the large angle of 81° wedge cutting, the cutting was not successful. According to the analysis of Figure13, the other four plough cutting models with different angles all contain blasting blocks in models with ranges less than 9.5 mm. Among these, the mass percentage of the plough cutting model with an angle of 65° is the largest, while the mass percentage with an angle of 69° is the smallest. In the range of 9.5 mm–19 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 77° is the largest, while the mass percentage with an angle of 73° is the smallest. In the range of 19 mm–31.5 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 65° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of 31.5 mm–53 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 69° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of 53 mm–75 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 73° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of more than 75 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 77° is the largest, while the mass percentage with an angle of 65° is the smallest.


### 4.3.2. The Relationship between the Cumulative Mass Percentage of Blasting Fragmentation and its Particle Size

According to the statistical Table7 of the screening of blasting fragmentation, the relation curve between the cumulative mass percentage of each block size and the particle size of blocks is obtained, as shown in Figures 14–17.Figure 14
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 65° wedge cutting.Figure 15
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 69° wedge cutting.Figure 16
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 73° wedge cutting.Figure 17
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 77° wedge cutting.From Figure14, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 65° is as follows:(26)yx=0.000002x4−0.000541x3+0.038735x2+0.104832x−0.133720.From equation (26), it can be calculated that the blasting fragmentation of plough cut with an angle of 65° is 49.72 mm. If the blasting fragmentation is larger than 55 mm, the block rate is(27)η=1−y55,calculated as η=1−y55=1−51.10%=48.90%.From Figure15, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 69° is as follows:(28)yx=0.000003x4−0.000702x3+0.047658x2−0.066457x−0.367026.From equation (28), it can be calculated that the blasting fragmentation of plough cut with an angle of 69° is 54.02 mm. The block rate is(29)η=1−y55=1−50.80%=49.20%.From Figure16, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 73° is as follows:(30)yx=0.000002x4−0.000404x3+0.031135x2+0.032831x+0.065647.From equation (30), it can be calculated that the blasting fragmentation of plough cut with an angle of 73° is 57.54 mm. The block rate is(31)η=1−y55=1−47.14%=52.86%.From Figure17, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 77° is as follows:(32)yx=0.000007x4−0.001158x3+0.056108x2−0.131097x−0.149017.From equation (32), it can be calculated that the blasting fragmentation of plough cut with an angle of 65° is 86.08 mm. The block rate is(33)η=1−y55=1−33.76%=66.24%.The average blasting fragmentation of 81° wedge cutting is ∞ and the bulk rate is 100% because the inclination of the hole of 81° wedge cutting model is large and the cutting is not successful in blasting.From the above calculation, the statistical table of the blasting fragmentation index of wedge cutting with different cutting angles can be obtained, as shown in Table4. According to the calculation, the trend of the plotted blasting fragment and block rate with the cutting angle is shown in Figures 18 and 19.Figure 18
Fitting curves of wedge cutting model and blasting fragments at different angles.Figure 19
The trend of wedge cutting model and the bulk rate at different angles.For the sake of intuition, the blasting fragment data in Table4 can be obtained by fitting equation (23).(34)D=1762.211188−50.924625θ+0.378438θ2,As can be seen from Table8, the maximum absolute error of blasting fragment is −3.87 mm, and the maximum relative error is 7.15%, which indicates that the error is relatively small. Within the allowable range, the fitting value is very close to the measured value, and the curve fitting is good.Table 8
Error analysis table of blasting fragment fitting formula.
Cutting angleD (measured value) (10−3 m3)D∗ (fitting value) (10−3 m3)D −D∗Relative error (%)65°49.7251.01−1.292.5969°54.0250.163.867.1573°57.5461.41−3.876.7377°86.0684.771.291.5081°∞∞0.000.00From equation (34), the blasting fragment of 67° wedge cutting model experiment can be calculated as the optimal value, with a blasting fragment value of 49.07 mm, as shown in Figure 18.Carrying out polynomial regression fitting on the relationship between the wedge cutting model at different angles and the block rate trend in Figure19, the relationship can be obtained as(35)yx=0.002212θ4−0.575658θ3+56.233179θ2−2443.763930θ+39914.165020.From equation (35), the block rate of 67° wedge cutting model experiment can be calculated as the optimal value, with a block rate value of 48.84%.In conclusion, when the explosive consumption of five wedge cutting model tests with different cutting angles is the same, the wedge cutting blasting effect with 67° cutting angle is the best in terms of cutting depth, blasting hole utilization ratio, blasting volume, blasting fragment, blasting block rate, and other main indexes after blasting.


## 4.3.1. Histogram of Blasting Fragmentation Distribution

When the test is blasted, the blasting fragmentation of the plough cut model with different cutting angles is analyzed. Then use the ZBSX-92A shock-type dual-purpose vibrating pendulum screen machine produced by Zhejiang Shangyu Xinguang Instrument and Equipment Factory and the national new standard square hole stone screen machine to weigh and separate the different particle size and block size by electronic scale, which is shown in Figures10–12.Figure 10
Blasting fragments.Figure 11
ZBSX-92A shock-type dual-purpose pendulum screening machine.Figure 12
Fragments weighing.According to the distribution of blasting fragmentation, the particle size is divided into 7 grades. The block size distribution of the blasted plough cut with five different cutting angles will be shown in Table7.Table 7
Statistical table of blasting block degree of wedge-shaped notch model test.
Cutting modeSpecimen no.Fragment grade (mm)<9.59.5∼1919∼31.531.5∼5353∼7575∼90>9065° wedge cuttingI-5, II-5Mass (kg)0.5721.2532.7593.1264.5120.8612.522Cumulative mass (kg)0.5721.8254.5847.71012.22213.08315.605Mass percentage (%)3.6668.02917.68020.03228.9145.51716.162Cumulative mass percentage (%)3.66611.69529.37549.40778.32183.838100.00069° wedge cuttingI-6, II-6Mass (kg)0.2491.6592.5523.4424.2801.1252.891Cumulative mass (kg)0.2491.9084.4607.90212.18213.30716.198Mass percentage (%)1.53710.24215.75521.25026.4236.94517.848Cumulative mass percentage (%)1.53711.77927.53448.78475.20782.152100.00073° wedge cuttingI-7, II-7Mass (kg)0.4071.0561.9122.8614.6151.2363.119Cumulative mass (kg)0.4071.4633.3756.23610.85112.08715.206Mass percentage (%)2.6776.94412.57418.81530.3508.12820.512Cumulative mass percentage (%)2.6779.62122.19541.01071.36079.488100.00077° wedge cuttingI-8, II-8Mass (kg)0.2231.5921.3261.5131.8762.1315.816Cumulative mass (kg)0.2231.8153.1414.6546.5308.66114.477Mass percentage (%)1.54010.9979.15910.45112.95814.72040.175Cumulative mass percentage (%)1.54012.53721.69632.14745.10559.825100.00081° wedge cuttingI-9, II-9Mass (kg)0.0000.0000.0000.0000.0000.0000.000Cumulative mass (kg)0.0000.0000.0000.0000.0000.0000.000Mass percentage (%)0.0000.0000.0000.0000.0000.0000.000Cumulative mass percentage (%)0.0000.0000.0000.0000.0000.0000.000According to the statistical Table7 of the screening of blasting fragmentation, the histogram of blasting fragmentation distribution of plough cut model test with five different angle is obtained, as shown in Figure 13.Figure 13
Histogram of blasting fragments of wedge-shaped recessed model at different angles.Due to the large angle of 81° wedge cutting, the cutting was not successful. According to the analysis of Figure13, the other four plough cutting models with different angles all contain blasting blocks in models with ranges less than 9.5 mm. Among these, the mass percentage of the plough cutting model with an angle of 65° is the largest, while the mass percentage with an angle of 69° is the smallest. In the range of 9.5 mm–19 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 77° is the largest, while the mass percentage with an angle of 73° is the smallest. In the range of 19 mm–31.5 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 65° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of 31.5 mm–53 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 69° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of 53 mm–75 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 73° is the largest, while the mass percentage with an angle of 77° is the smallest. In the range of more than 75 mm, four kinds of plough cutting models with different angles all contain blasting blocks. Among these, the mass percentage of the plough cutting model with an angle of 77° is the largest, while the mass percentage with an angle of 65° is the smallest.


## 4.3.2. The Relationship between the Cumulative Mass Percentage of Blasting Fragmentation and its Particle Size

According to the statistical Table7 of the screening of blasting fragmentation, the relation curve between the cumulative mass percentage of each block size and the particle size of blocks is obtained, as shown in Figures 14–17.Figure 14
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 65° wedge cutting.Figure 15
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 69° wedge cutting.Figure 16
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 73° wedge cutting.Figure 17
Relationship between cumulative mass percentage of blasting fragments and fragment size particle diameter of 77° wedge cutting.From Figure14, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 65° is as follows:(26)yx=0.000002x4−0.000541x3+0.038735x2+0.104832x−0.133720.From equation (26), it can be calculated that the blasting fragmentation of plough cut with an angle of 65° is 49.72 mm. If the blasting fragmentation is larger than 55 mm, the block rate is(27)η=1−y55,calculated as η=1−y55=1−51.10%=48.90%.From Figure15, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 69° is as follows:(28)yx=0.000003x4−0.000702x3+0.047658x2−0.066457x−0.367026.From equation (28), it can be calculated that the blasting fragmentation of plough cut with an angle of 69° is 54.02 mm. The block rate is(29)η=1−y55=1−50.80%=49.20%.From Figure16, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 73° is as follows:(30)yx=0.000002x4−0.000404x3+0.031135x2+0.032831x+0.065647.From equation (30), it can be calculated that the blasting fragmentation of plough cut with an angle of 73° is 57.54 mm. The block rate is(31)η=1−y55=1−47.14%=52.86%.From Figure17, it can be concluded that the relationship between the cumulative mass percentage of plough cut blasting with an angle of 77° is as follows:(32)yx=0.000007x4−0.001158x3+0.056108x2−0.131097x−0.149017.From equation (32), it can be calculated that the blasting fragmentation of plough cut with an angle of 65° is 86.08 mm. The block rate is(33)η=1−y55=1−33.76%=66.24%.The average blasting fragmentation of 81° wedge cutting is ∞ and the bulk rate is 100% because the inclination of the hole of 81° wedge cutting model is large and the cutting is not successful in blasting.From the above calculation, the statistical table of the blasting fragmentation index of wedge cutting with different cutting angles can be obtained, as shown in Table4. According to the calculation, the trend of the plotted blasting fragment and block rate with the cutting angle is shown in Figures 18 and 19.Figure 18
Fitting curves of wedge cutting model and blasting fragments at different angles.Figure 19
The trend of wedge cutting model and the bulk rate at different angles.For the sake of intuition, the blasting fragment data in Table4 can be obtained by fitting equation (23).(34)D=1762.211188−50.924625θ+0.378438θ2,As can be seen from Table8, the maximum absolute error of blasting fragment is −3.87 mm, and the maximum relative error is 7.15%, which indicates that the error is relatively small. Within the allowable range, the fitting value is very close to the measured value, and the curve fitting is good.Table 8
Error analysis table of blasting fragment fitting formula.
Cutting angleD (measured value) (10−3 m3)D∗ (fitting value) (10−3 m3)D −D∗Relative error (%)65°49.7251.01−1.292.5969°54.0250.163.867.1573°57.5461.41−3.876.7377°86.0684.771.291.5081°∞∞0.000.00From equation (34), the blasting fragment of 67° wedge cutting model experiment can be calculated as the optimal value, with a blasting fragment value of 49.07 mm, as shown in Figure 18.Carrying out polynomial regression fitting on the relationship between the wedge cutting model at different angles and the block rate trend in Figure19, the relationship can be obtained as(35)yx=0.002212θ4−0.575658θ3+56.233179θ2−2443.763930θ+39914.165020.From equation (35), the block rate of 67° wedge cutting model experiment can be calculated as the optimal value, with a block rate value of 48.84%.In conclusion, when the explosive consumption of five wedge cutting model tests with different cutting angles is the same, the wedge cutting blasting effect with 67° cutting angle is the best in terms of cutting depth, blasting hole utilization ratio, blasting volume, blasting fragment, blasting block rate, and other main indexes after blasting.


## 5. Blasting Vibration Test

### 5.1. Design of Blasting Vibration Test

TC4850N wireless network vibration meter produced by Chengdu Zhengzhou Measurement and Control Co.Ltd. was used to test the blasting vibration of each cutting model. The vibration meter is equipped with an integrated three-dimensional sensor, which is easy to install and simple to connect. It is particularly suitable for the unattended test site and long-term monitoring of complex environment. It can transmit data through 3G communication and Wi-Fi function and use special software for data processing and analysis. This description is as followed: four channels are available in parallel; the sampling rate is 100 sps–100 ksps, and multiple levels can be adjusted; the resolution of A/D level is 16 bits; the frequency response range is 0–10 kHz; single record, automatic repeat record, and continuous record are available; the recording time is adjustable from 1 to 5000 s; it can be triggered internally, externally, synchronously, and regularly; the measuring range is plus or minus10 V; the storage capacity is 256 MB.In order to compare the blasting vibration effect in different directions of the plough cutting, both sides of the slope of it are defined as an inclined side, and the other two ends are vertical side. Speed sensors are used in four directions of each group of test blastholes, andX-axis of all sensors is facing the explosion source, 500 mm away from the central line of blastholes. The layout of measuring points is shown in Figures 20 and 21.Figure 20
Schematic diagram of measuring points of wedge-shaped notch blasting vibration at different angles (unit: mm).Figure 21
Actual layout of blasting vibration sensors.


### 5.2. Blasting Vibration Test Results and Analysis

#### 5.2.1. Vibration Test Results

See Table9 for the test results of peak vibration speed and the main vibration frequency of blasting particle. The typical vibration waveform of the plough cut blasting is shown in Figure 22.Table 9
Test results of blasting peak vibration velocity.
Cutting modeLocationMeasuring point numberPeak vibration velocity (cm⋅s−1)Resultant velocity (cm⋅s−1)Average resultant velocity (cm⋅s−1)Main frequency (Hz)Radial directionTangential directionVertical directionRadial directionTangential directionVertical direction65° wedge cuttingInclined side1#10.067.7611.8218.5920.427.520.225.92#10.7110.3712.1322.255.812.339.1Vertical side3#18.157.9115.6827.0525.2117.219.232.34#13.226.1716.4723.3716.314.038.669° wedge cuttingInclined side1#13.137.9815.1121.8923.1111.418.566.92#11.6213.5718.8524.3237.816.990.1Vertical side3#17.9310.2921.2629.4130.238.220.878.24#22.7422.5220.3031.0455.633.366.773° wedge cuttingInclined side1#12.9316.7611.5524.9827.279.58.363.32#14.6818.1220.5829.5525.89.382.9Vertical side3#23.9125.4322.6032.4633.0618.626.2110.24#22.2010.0124.9333.6620.275.8125.077° wedge cuttingInclined side1#16.1519.3821.1233.1234.9253.863.716.62#15.5618.9320.7836.7290.558.5106.0Vertical side3#23.3024.8327.3944.1743.36125.076.930.34#25.1726.2321.5542.5513.7125.018.981° wedge cuttingInclined side1#19.9221.5526.1741.4442.3695.718.3106.52#21.3619.6627.7843.28110.5110.5110.5Vertical side3#27.6529.1135.4948.1948.76125.025.890.04#23.8124.7536.0449.33113.6125.0113.6Figure 22
Model waveform of wedge cutting blasting.


#### 5.2.2. The Maximum Peak Vibration Velocity

At present, the peak vibration velocity is widely used as the evaluation standard of the blasting vibration hazard effect. It can be seen from Table9 that the peak vibration velocity of horizontal radial and vertical blasting in each group of tests is larger, and the horizontal tangential direction is the smallest. The results show that the maximum peak vibration velocity is 81° wedge cutting > 77° wedge cutting > 73° wedge cutting > 69° wedge cutting > 65° wedge cutting. When the cutting angle is 81°, only through cracks are formed, and the cutting part is not thrown out. The energy generated by explosion is more converted into seismic wave, so the peak vibration velocity is the largest and the maximum peak velocity is 36.04 cm/s. When the cutting angle is 65°, the peak vibration velocity is the smallest and the maximum peak velocity is 18.15 cm/s.It can be seen from Figure23 that the maximum peak vibration speed in all directions increases with the increase of cutting angle, among which the change trend of tangential maximum vibration speed is the most obvious, and the change trend of radial and vertical maximum vibration speed is relatively stable.Figure 23
The curve of the maximum peak velocity with the change of cutting angle.It can be seen from Figure24 that with the increase of cutting angle, the overall value of the maximum peak vibration velocity on the vertical side is greater than that on the inclined side; the trend of the maximum peak vibration velocity on the vertical side is the most obvious, and the trend of the maximum peak vibration velocity on the radial and tangential sides is more stable; the trend of the maximum peak vibration velocity on the vertical side is the most obvious, and the change of the maximum peak vibration velocity on the radial and vertical sides is the most obvious The trend is relatively stable.Figure 24
The curve of the (a) inclined and (b) vertical side maximum peak velocity with the change of cutting angle.
(a)(b)


#### 5.2.3. Resultant Velocity

It can be seen from Table9 that the average closing speed on the inclined side is smaller than that on the vertical side. When the cutting angle is 65°, the minimum average closing speed of the inclined side is 20.42 cm/s.It can be seen from Figure25 that with the increase of cutting angle, the rising trend of average closing speed of the inclined side and vertical side is basically the same. When the cutting angle is 65°, the average closing velocity of the inclined side and the vertical side is the smallest.Figure 25
The curve of the inclined and vertical side average resultant velocity with the change of cutting angle.Therefore, considering the cutting depth, blasting volume, blasting fragment, blasting vibration hazard, and construction difficulty, wedge cutting blasting with an angle of 65°∼69° is recommended in engineering practice. And the blasting vibration intensity of the inclined side of wedge cutting is generally lower than that of the vertical side. In the excavation blasting of shallow buried tunnel, overlapping tunnel, and (super) small clear distance tunnel, it can effectively reduce the vibration hazard of excavation blasting by adjusting the layout direction of wedge cutting and making the inclined side face the key protection area.


## 5.1. Design of Blasting Vibration Test

TC4850N wireless network vibration meter produced by Chengdu Zhengzhou Measurement and Control Co.Ltd. was used to test the blasting vibration of each cutting model. The vibration meter is equipped with an integrated three-dimensional sensor, which is easy to install and simple to connect. It is particularly suitable for the unattended test site and long-term monitoring of complex environment. It can transmit data through 3G communication and Wi-Fi function and use special software for data processing and analysis. This description is as followed: four channels are available in parallel; the sampling rate is 100 sps–100 ksps, and multiple levels can be adjusted; the resolution of A/D level is 16 bits; the frequency response range is 0–10 kHz; single record, automatic repeat record, and continuous record are available; the recording time is adjustable from 1 to 5000 s; it can be triggered internally, externally, synchronously, and regularly; the measuring range is plus or minus10 V; the storage capacity is 256 MB.In order to compare the blasting vibration effect in different directions of the plough cutting, both sides of the slope of it are defined as an inclined side, and the other two ends are vertical side. Speed sensors are used in four directions of each group of test blastholes, andX-axis of all sensors is facing the explosion source, 500 mm away from the central line of blastholes. The layout of measuring points is shown in Figures 20 and 21.Figure 20
Schematic diagram of measuring points of wedge-shaped notch blasting vibration at different angles (unit: mm).Figure 21
Actual layout of blasting vibration sensors.


## 5.2. Blasting Vibration Test Results and Analysis

### 5.2.1. Vibration Test Results

See Table9 for the test results of peak vibration speed and the main vibration frequency of blasting particle. The typical vibration waveform of the plough cut blasting is shown in Figure 22.Table 9
Test results of blasting peak vibration velocity.
Cutting modeLocationMeasuring point numberPeak vibration velocity (cm⋅s−1)Resultant velocity (cm⋅s−1)Average resultant velocity (cm⋅s−1)Main frequency (Hz)Radial directionTangential directionVertical directionRadial directionTangential directionVertical direction65° wedge cuttingInclined side1#10.067.7611.8218.5920.427.520.225.92#10.7110.3712.1322.255.812.339.1Vertical side3#18.157.9115.6827.0525.2117.219.232.34#13.226.1716.4723.3716.314.038.669° wedge cuttingInclined side1#13.137.9815.1121.8923.1111.418.566.92#11.6213.5718.8524.3237.816.990.1Vertical side3#17.9310.2921.2629.4130.238.220.878.24#22.7422.5220.3031.0455.633.366.773° wedge cuttingInclined side1#12.9316.7611.5524.9827.279.58.363.32#14.6818.1220.5829.5525.89.382.9Vertical side3#23.9125.4322.6032.4633.0618.626.2110.24#22.2010.0124.9333.6620.275.8125.077° wedge cuttingInclined side1#16.1519.3821.1233.1234.9253.863.716.62#15.5618.9320.7836.7290.558.5106.0Vertical side3#23.3024.8327.3944.1743.36125.076.930.34#25.1726.2321.5542.5513.7125.018.981° wedge cuttingInclined side1#19.9221.5526.1741.4442.3695.718.3106.52#21.3619.6627.7843.28110.5110.5110.5Vertical side3#27.6529.1135.4948.1948.76125.025.890.04#23.8124.7536.0449.33113.6125.0113.6Figure 22
Model waveform of wedge cutting blasting.


### 5.2.2. The Maximum Peak Vibration Velocity

At present, the peak vibration velocity is widely used as the evaluation standard of the blasting vibration hazard effect. It can be seen from Table9 that the peak vibration velocity of horizontal radial and vertical blasting in each group of tests is larger, and the horizontal tangential direction is the smallest. The results show that the maximum peak vibration velocity is 81° wedge cutting > 77° wedge cutting > 73° wedge cutting > 69° wedge cutting > 65° wedge cutting. When the cutting angle is 81°, only through cracks are formed, and the cutting part is not thrown out. The energy generated by explosion is more converted into seismic wave, so the peak vibration velocity is the largest and the maximum peak velocity is 36.04 cm/s. When the cutting angle is 65°, the peak vibration velocity is the smallest and the maximum peak velocity is 18.15 cm/s.It can be seen from Figure23 that the maximum peak vibration speed in all directions increases with the increase of cutting angle, among which the change trend of tangential maximum vibration speed is the most obvious, and the change trend of radial and vertical maximum vibration speed is relatively stable.Figure 23
The curve of the maximum peak velocity with the change of cutting angle.It can be seen from Figure24 that with the increase of cutting angle, the overall value of the maximum peak vibration velocity on the vertical side is greater than that on the inclined side; the trend of the maximum peak vibration velocity on the vertical side is the most obvious, and the trend of the maximum peak vibration velocity on the radial and tangential sides is more stable; the trend of the maximum peak vibration velocity on the vertical side is the most obvious, and the change of the maximum peak vibration velocity on the radial and vertical sides is the most obvious The trend is relatively stable.Figure 24
The curve of the (a) inclined and (b) vertical side maximum peak velocity with the change of cutting angle.
(a)(b)


### 5.2.3. Resultant Velocity

It can be seen from Table9 that the average closing speed on the inclined side is smaller than that on the vertical side. When the cutting angle is 65°, the minimum average closing speed of the inclined side is 20.42 cm/s.It can be seen from Figure25 that with the increase of cutting angle, the rising trend of average closing speed of the inclined side and vertical side is basically the same. When the cutting angle is 65°, the average closing velocity of the inclined side and the vertical side is the smallest.Figure 25
The curve of the inclined and vertical side average resultant velocity with the change of cutting angle.Therefore, considering the cutting depth, blasting volume, blasting fragment, blasting vibration hazard, and construction difficulty, wedge cutting blasting with an angle of 65°∼69° is recommended in engineering practice. And the blasting vibration intensity of the inclined side of wedge cutting is generally lower than that of the vertical side. In the excavation blasting of shallow buried tunnel, overlapping tunnel, and (super) small clear distance tunnel, it can effectively reduce the vibration hazard of excavation blasting by adjusting the layout direction of wedge cutting and making the inclined side face the key protection area.


## 5.2.1. Vibration Test Results

See Table9 for the test results of peak vibration speed and the main vibration frequency of blasting particle. The typical vibration waveform of the plough cut blasting is shown in Figure 22.Table 9
Test results of blasting peak vibration velocity.
Cutting modeLocationMeasuring point numberPeak vibration velocity (cm⋅s−1)Resultant velocity (cm⋅s−1)Average resultant velocity (cm⋅s−1)Main frequency (Hz)Radial directionTangential directionVertical directionRadial directionTangential directionVertical direction65° wedge cuttingInclined side1#10.067.7611.8218.5920.427.520.225.92#10.7110.3712.1322.255.812.339.1Vertical side3#18.157.9115.6827.0525.2117.219.232.34#13.226.1716.4723.3716.314.038.669° wedge cuttingInclined side1#13.137.9815.1121.8923.1111.418.566.92#11.6213.5718.8524.3237.816.990.1Vertical side3#17.9310.2921.2629.4130.238.220.878.24#22.7422.5220.3031.0455.633.366.773° wedge cuttingInclined side1#12.9316.7611.5524.9827.279.58.363.32#14.6818.1220.5829.5525.89.382.9Vertical side3#23.9125.4322.6032.4633.0618.626.2110.24#22.2010.0124.9333.6620.275.8125.077° wedge cuttingInclined side1#16.1519.3821.1233.1234.9253.863.716.62#15.5618.9320.7836.7290.558.5106.0Vertical side3#23.3024.8327.3944.1743.36125.076.930.34#25.1726.2321.5542.5513.7125.018.981° wedge cuttingInclined side1#19.9221.5526.1741.4442.3695.718.3106.52#21.3619.6627.7843.28110.5110.5110.5Vertical side3#27.6529.1135.4948.1948.76125.025.890.04#23.8124.7536.0449.33113.6125.0113.6Figure 22
Model waveform of wedge cutting blasting.


## 5.2.2. The Maximum Peak Vibration Velocity

At present, the peak vibration velocity is widely used as the evaluation standard of the blasting vibration hazard effect. It can be seen from Table9 that the peak vibration velocity of horizontal radial and vertical blasting in each group of tests is larger, and the horizontal tangential direction is the smallest. The results show that the maximum peak vibration velocity is 81° wedge cutting > 77° wedge cutting > 73° wedge cutting > 69° wedge cutting > 65° wedge cutting. When the cutting angle is 81°, only through cracks are formed, and the cutting part is not thrown out. The energy generated by explosion is more converted into seismic wave, so the peak vibration velocity is the largest and the maximum peak velocity is 36.04 cm/s. When the cutting angle is 65°, the peak vibration velocity is the smallest and the maximum peak velocity is 18.15 cm/s.It can be seen from Figure23 that the maximum peak vibration speed in all directions increases with the increase of cutting angle, among which the change trend of tangential maximum vibration speed is the most obvious, and the change trend of radial and vertical maximum vibration speed is relatively stable.Figure 23
The curve of the maximum peak velocity with the change of cutting angle.It can be seen from Figure24 that with the increase of cutting angle, the overall value of the maximum peak vibration velocity on the vertical side is greater than that on the inclined side; the trend of the maximum peak vibration velocity on the vertical side is the most obvious, and the trend of the maximum peak vibration velocity on the radial and tangential sides is more stable; the trend of the maximum peak vibration velocity on the vertical side is the most obvious, and the change of the maximum peak vibration velocity on the radial and vertical sides is the most obvious The trend is relatively stable.Figure 24
The curve of the (a) inclined and (b) vertical side maximum peak velocity with the change of cutting angle.
(a)(b)


## 5.2.3. Resultant Velocity

It can be seen from Table9 that the average closing speed on the inclined side is smaller than that on the vertical side. When the cutting angle is 65°, the minimum average closing speed of the inclined side is 20.42 cm/s.It can be seen from Figure25 that with the increase of cutting angle, the rising trend of average closing speed of the inclined side and vertical side is basically the same. When the cutting angle is 65°, the average closing velocity of the inclined side and the vertical side is the smallest.Figure 25
The curve of the inclined and vertical side average resultant velocity with the change of cutting angle.Therefore, considering the cutting depth, blasting volume, blasting fragment, blasting vibration hazard, and construction difficulty, wedge cutting blasting with an angle of 65°∼69° is recommended in engineering practice. And the blasting vibration intensity of the inclined side of wedge cutting is generally lower than that of the vertical side. In the excavation blasting of shallow buried tunnel, overlapping tunnel, and (super) small clear distance tunnel, it can effectively reduce the vibration hazard of excavation blasting by adjusting the layout direction of wedge cutting and making the inclined side face the key protection area.


## 6. On-Site Tunneling Experiments with Different Cutting Angles

In order to verify the theoretical analysis conclusion, several single-stage wedge cutting blasting experiments with five different cutting angles were carried out in Jugezhuang Tunnel of JSJJSG-9 bid section of the Beijing-Hebei section of the newly-built Beijing-Shenyang Passenger Dedicated Line, as shown in Figures26 and 27. All cutting holes shall be enlarged 15 times according to the size in Figure 1 for manual drilling, and the cutting angle error shall be controlled within 1.5°. Under the condition that other blasting parameters remain unchanged, the effect of 65°, 69°, 73°, 77°, and 81° cutting angles on blasting excavation footage is discussed. The comparison of tunnel blasting footage when different cutting angles change is shown in Figure 28. The blasting footage takes the average value of multiple experiments.Figure 26
Layout of site blast holes.Figure 27
The picture of tunnel blasting effect.Figure 28
Comparison chart of tunneling footage when tunnel blasting cutting angle changes.As can be seen from Figure28, with the increase of cutting angle, the excavation footage of tunnel blasting becomes shorter and shorter, especially when the cutting angle is above 73°, and the blasting footage is slower than that of excavation below 73°, which shows that the cutting angle has a great influence on the excavation footage. Considering that there is an error of ±1.5° in the field drilling angle and the cutting angle is in the range of 65°∼69°, the footage of tunnel blasting excavation is the best, which is consistent with the theoretical analysis.


## 7. Conclusions

Based on the work presented, the following conclusions can be drawn regarding the experiment and the results thereof:(1)
Based on the similarity theory and the actual tunnel wedge cutting blasting, five kinds of tunnel section hole arrangement forms with different cutting angles were designed, concrete model specimens were made and blast holes were reserved, and wedge cutting blasting model experiments were carried out. Quantitative indexes such as cutting depth, blasting volume, blasting fragment, and blasting bulk rate of five kinds of wedge cutting ways with different angles were obtained.(2)
The relationship between cutting depth, blasting volume, blasting fragment, and cutting angle was studied and deduced by the dimensional analysis method, and the polynomial fitting of the relationship between cutting depth, blasting volume, blasting fragment, and cutting angle was carried out according to the experiment data, and the corresponding fitting equation was obtained.(3)
Through the quantitative analysis and research on the experiment indexes of wedge cutting blasting, it was concluded that the experiment indexes of wedge cutting blasting depth, blasting volume, blasting fragment, and blasting bulk rate are better than those of wedge cutting blasting at 67° cutting angle.(4)
The peak vibration velocity in radial and the vertical direction is larger than that in the tangential direction. The peak vibration velocity of wedge cutting with cutting angle of 65° is the smallest. And the vibration intensity of the inclined side of wedge-shaped cutting is generally lower than that of the vertical side.(5)
Considering the cutting depth, blasting volume, blasting fragment, blasting vibration hazard, drilling error, tunneling construction cost, and other factors, the 65°∼69° wedge cutting blasting in engineering practice can improve the blasting tunneling rate and increase economic benefits.



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*Source: 5126790-2020-05-28.xml*