# In Situ Stress Effects on Smooth Blasting: Model Test and Analysis

Authors: Renshu Yang; Shizheng Fang; Aiyun Yang; Huanzhen Xie; Liyun Yang
Journal: Shock and Vibration
 (2020)

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## Abstract

Most of the roadway excavation is completed by the drilling and blasting method. With the increase of buried depth, the existence of ground stress will generate a significant impact on the rock blasting, especially on the smooth blasting. In this study, self-made homogeneous similar materials and digital image correlation methods were used to determine influence of ground stress on the smooth blasting under uniform explosive charge parameters and various in situ stress conditions. The results show that the crack outline after blasting changes from zigzag to straight in shape, and multifractal calculation results of the rupture section between blastholes show that the fracture surface becomes flatter as ground stress increases, which is conducive to roadway formation. The strain and equivalent strain rate obviously decrease as the distance between the blasthole and measuring points increases. The same trend occurs as the confining pressure goes up. Meanwhile, a postexplosion acoustic wave test indicates that confining pressure inhibits damage of the retained rock, which is consistent with strain and equivalent strain rate results. Finally, we discussed the crack propagation mechanism of rock in smooth blasting.


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## Body

## 1. Introduction

Drilling-blasting techniques are often used in coal mining, tunnel excavation, and other projects [1–4]. The geological conditions are more complicated at greater depths which have grown more common in recent years. The influence of initial in situ stress on blasting becomes more significant as ground stress increases, for example. The blasting effect is strengthened or weakened by stress, and the deep blasting rock failure mechanism is very complex. Geological issues can cause serious safety problems in coal mining operations. Blasting engineers must ensure reasonable and effective crushing of the rock mass throughout the excavation process. It is also necessary to minimize damage to the rock masses outside the excavation profile as much as possible. Smooth blasting is conducted for this purpose [5].There are numerous research studies about blasting issues under an initial stress field [6–9]. Kutter and Fairhurst [10] explored the effects of explosion stress waves and explosive gas on crack propagation to find that blast-induced cracks extend toward the direction of the maximum principal stress in the static stress field. Rossmanith et al. [11] studied the dynamic evolution of three-dimensional cracks under a combination of blasting and uniaxial stress; they gathered valuable physical and mechanical information regarding crack propagation under blasting loading which can be utilized for numerical simulations. Liu et al. [12] conducted a photoelastic experiment to observe the propagation mechanism of the explosion stress wave under an initial stress condition. Liu and Xu [13] numerically simulated a rock blasting process to find that the influence of ground stress is related to the distance of the explosive charge. The stress wave dominates the region near the explosion charge over the ground stress. In the far-explosive area, the presence of ground stress significantly alters the stress wave propagation.There have been some valuable contributions to the smooth blasting. Lu et al. [14], for example, considered the effect of original stress field on the construction of an underground power station chamber. They suggested that when the in situ stress exceeds 10–12 MPa, that middle-cut blasting should be carried out first followed by presplit or smooth blasting. Dai [15] analyzed the effects of original ground stress on crack penetration between blastholes using the smooth blasting and presplit blasting, respectively. The results showed that original in situ stress is more conducive to smooth blasting than presplit blasting. Li et al. [16], through numerical results, studied the delay time effect in smooth blasting, and they explained how the delay time and the boreholes spacing affect the crack generation and propagation.When executing the drilling and blasting technique to excavate the rock mass, a middle-cut blasting detonation first provides a new free surface for subsequent smooth blasting. The formation of the new free surface releases the internal ground stress, altering the stress state of the rock mass. The part near the free surface, which is the main factor affecting roadway deformation, is under uniaxial vertical stress, as shown in Figure1. Extant studies have revealed little information regarding the surrounding rock damage in the near region of the roadway. Digital image correlation (DIC) technology can accurately reveal the strain and displacement full-field evolution of different materials, so a model test in conjunction with DIC technique was used in this study to observe smooth blasting under different ground stress conditions. The contour forming quality, strain evolution, and rock damage characteristics were analyzed to provide a workable reference for smooth blast engineering.Figure 1
Surrounding rock stress state under different conditions.


## 2. Sample Preparation and Test Procedure

### 2.1. Specimen Preparation and Confining Pressure Loading Device

Rock is a typical anisotropic brittle material. Its internal defects significantly affect stress wave propagation [17, 18]. To simulate the impact of confining pressure on blasting, the specimen selected for this test is an isotropic self-made gypsum wherein the influence of rock anisotropy can be ignored. The sample is comprised of gypsum, water, and retarder in a mass ratio of 1 : 0.4 : 0.005. The length, width, and height of the specimen are all 200 mm, as shown in Figure 2. The specimen has a density of 1.45 g/cm3, a Poisson’s ratio of 0.31, and a P-wave velocity of different specimens distributed between 1400 m/s and 1700 m/s. Differences in P-wave velocity across different measuring points in any one sample are within 30 m/s. The samples are uniform, homogeneous, and meet the relevant test requirements. The static test is conducted by a material test system (MTS) hydraulic servo control machine, and the static uniaxial compressive strength (UCS) is 3.7 MPa with a loading rate of 0.6 mm/min.Figure 2
Sample tested.The pressure loading system is an independently designed loading device [19]. The specimen is placed under pressure via a jack to simulate the ground stress environment in which the rock would normally be located. The loading direction is parallel to the direction of the blasthole layout. The loading pressure is measured by a pressure cell between the jack and a loading plate over the specimen. When the pressure reaches the design value, the jack is locked and the pressure is held at a steady value. The specimen pressure loading device is shown in Figure 3.Figure 3
Confining pressure loading device.


### 2.2. Explosive Charge and Blasting Parameter Design

The explosive used in this study is made of modified gunpowder (MGP). The outer covering of the charge is made of polyethylene. The height of the explosiveL0 is 30 mm, the length of the charge L1 is 40 mm, and the diameter of the charge D1 is 5 mm. The explosive charge parameters are shown in Table 1. A detonation probe is embedded in the charge, generating a high-pressure discharge to detonate the explosive.Table 1
Explosive charge parameters.
Type of explosive
Detonation velocityv, (m/s)
Charge weight (mg)
Explosive charge diameterD1 (mm)
Explosive charge heightL1 (mm)
Explosive heightL0 (mm)
Explosive densityρ (g/cm3)
MGP
400
250
5
40
30
0.523Three blastholes with same geometric dimensions are placed on one side of the specimen, each with diameterD2 and depth L2 of 7 mm and 60 mm, respectively. The distance between blastholes L3 is 40 mm, and the uncoupling coefficient is 1.4. The charge is placed at the bottom of the blasthole, and the detonation mode is indirect. Sand and glue are used for sealing. The layout of the blastholes and explosive charge are shown in Figure 4.Figure 4
Schematic diagram of blastholes and explosive charge. (a) Global view. (b) Top view of blasthole. (c) Parameters of explosive charge.
(a)
(b)
(c)


### 2.3. Test Principle and Equipment

DIC technique is a noncontact optical method for full-field strain measurement. The speckles on the sample surface move as the specimen deforms. The principle of DIC algorithm is to match the speckle image before and after object deformation to reveal the displacement and strain of the specimen [20–22]. It is operated as follows: the gray matrix of the digital speckle image is calculated before and after the specimen surface deformation to track the point spatial deformation, and then the surface displacement and strain information of the specimen can be obtained. The basic principle is shown in Figure 5.Figure 5
DIC basic principles.As shown in Figure5, the coordinate relationship of the subarea center P(x0, y0) before and after the deformation is calculated as follows:(1)x0′=x0+u,y0′=y0+v,where u and v are the vertical and horizontal displacement, respectively, and x0′,y0′ is the position of point P after deformation. Based on the theory of continuum mechanics, the displacement of a point can be expressed by the displacement and increment of its adjacent point. So, the displacement (uQ, vQ) of the Q(x, y), which was randomly selected in the reference subarea, can be expressed as follows:(2)uQ=u+∂u∂xΔx+∂u∂yΔy,vQ=v+∂v∂xΔx+∂v∂yΔy,where ∆x and ∆y are the horizontal and the vertical deformation increment, respectively. The area of interest (AOI) in this test is a partial area of the preserved rock mass, as shown in Figure 6. The surface of the specimen was cleaned to ensure it was sufficiently flat, and a spattering method was used to make speckles on the surface of the specimen, and then black speckles were printed onto it in randomly distributed sizes. The average grayscale gradient satisfies the recommended value [23, 24].Figure 6
Image of specimen with speckles.The high-speed DIC (HS-DIC) method test system [25] is mainly composed of a program-controlled multichannel pulse igniter, a signal source, a flash controller, a high-speed camera, a camera status indicator, and a computer. A schematic diagram of the setup is provided in Figure 7. A high-speed camera (Kirana) was selected because of its unique μCMOS sensor, 100 ns high-speed global electronic shutter, and image resolution fixed at 924 × 768 pixels. The image resolution does not decrease as the acquisition frequency increases. This effectively guarantees the feasibility of the camera’s full-field shooting and subsequent full-field deformation analysis of the specimen.Figure 7
Experimental system.This test mainly focused on the influence of ground stress on smooth blasting. Three sets of schemes were designed for the test and recorded asG1, G2, and G3. The blasting parameters were completely consistent and the vertical static load was set to 0, 1, or 2 MPa successively. After the test, the fracture morphology, strain evolution, and damage distribution characteristics of each specimen under different initial stress fields were analyzed and compared. The results are described in detail below.


## 2.1. Specimen Preparation and Confining Pressure Loading Device

Rock is a typical anisotropic brittle material. Its internal defects significantly affect stress wave propagation [17, 18]. To simulate the impact of confining pressure on blasting, the specimen selected for this test is an isotropic self-made gypsum wherein the influence of rock anisotropy can be ignored. The sample is comprised of gypsum, water, and retarder in a mass ratio of 1 : 0.4 : 0.005. The length, width, and height of the specimen are all 200 mm, as shown in Figure 2. The specimen has a density of 1.45 g/cm3, a Poisson’s ratio of 0.31, and a P-wave velocity of different specimens distributed between 1400 m/s and 1700 m/s. Differences in P-wave velocity across different measuring points in any one sample are within 30 m/s. The samples are uniform, homogeneous, and meet the relevant test requirements. The static test is conducted by a material test system (MTS) hydraulic servo control machine, and the static uniaxial compressive strength (UCS) is 3.7 MPa with a loading rate of 0.6 mm/min.Figure 2
Sample tested.The pressure loading system is an independently designed loading device [19]. The specimen is placed under pressure via a jack to simulate the ground stress environment in which the rock would normally be located. The loading direction is parallel to the direction of the blasthole layout. The loading pressure is measured by a pressure cell between the jack and a loading plate over the specimen. When the pressure reaches the design value, the jack is locked and the pressure is held at a steady value. The specimen pressure loading device is shown in Figure 3.Figure 3
Confining pressure loading device.


## 2.2. Explosive Charge and Blasting Parameter Design

The explosive used in this study is made of modified gunpowder (MGP). The outer covering of the charge is made of polyethylene. The height of the explosiveL0 is 30 mm, the length of the charge L1 is 40 mm, and the diameter of the charge D1 is 5 mm. The explosive charge parameters are shown in Table 1. A detonation probe is embedded in the charge, generating a high-pressure discharge to detonate the explosive.Table 1
Explosive charge parameters.
Type of explosive
Detonation velocityv, (m/s)
Charge weight (mg)
Explosive charge diameterD1 (mm)
Explosive charge heightL1 (mm)
Explosive heightL0 (mm)
Explosive densityρ (g/cm3)
MGP
400
250
5
40
30
0.523Three blastholes with same geometric dimensions are placed on one side of the specimen, each with diameterD2 and depth L2 of 7 mm and 60 mm, respectively. The distance between blastholes L3 is 40 mm, and the uncoupling coefficient is 1.4. The charge is placed at the bottom of the blasthole, and the detonation mode is indirect. Sand and glue are used for sealing. The layout of the blastholes and explosive charge are shown in Figure 4.Figure 4
Schematic diagram of blastholes and explosive charge. (a) Global view. (b) Top view of blasthole. (c) Parameters of explosive charge.
(a)
(b)
(c)


## 2.3. Test Principle and Equipment

DIC technique is a noncontact optical method for full-field strain measurement. The speckles on the sample surface move as the specimen deforms. The principle of DIC algorithm is to match the speckle image before and after object deformation to reveal the displacement and strain of the specimen [20–22]. It is operated as follows: the gray matrix of the digital speckle image is calculated before and after the specimen surface deformation to track the point spatial deformation, and then the surface displacement and strain information of the specimen can be obtained. The basic principle is shown in Figure 5.Figure 5
DIC basic principles.As shown in Figure5, the coordinate relationship of the subarea center P(x0, y0) before and after the deformation is calculated as follows:(1)x0′=x0+u,y0′=y0+v,where u and v are the vertical and horizontal displacement, respectively, and x0′,y0′ is the position of point P after deformation. Based on the theory of continuum mechanics, the displacement of a point can be expressed by the displacement and increment of its adjacent point. So, the displacement (uQ, vQ) of the Q(x, y), which was randomly selected in the reference subarea, can be expressed as follows:(2)uQ=u+∂u∂xΔx+∂u∂yΔy,vQ=v+∂v∂xΔx+∂v∂yΔy,where ∆x and ∆y are the horizontal and the vertical deformation increment, respectively. The area of interest (AOI) in this test is a partial area of the preserved rock mass, as shown in Figure 6. The surface of the specimen was cleaned to ensure it was sufficiently flat, and a spattering method was used to make speckles on the surface of the specimen, and then black speckles were printed onto it in randomly distributed sizes. The average grayscale gradient satisfies the recommended value [23, 24].Figure 6
Image of specimen with speckles.The high-speed DIC (HS-DIC) method test system [25] is mainly composed of a program-controlled multichannel pulse igniter, a signal source, a flash controller, a high-speed camera, a camera status indicator, and a computer. A schematic diagram of the setup is provided in Figure 7. A high-speed camera (Kirana) was selected because of its unique μCMOS sensor, 100 ns high-speed global electronic shutter, and image resolution fixed at 924 × 768 pixels. The image resolution does not decrease as the acquisition frequency increases. This effectively guarantees the feasibility of the camera’s full-field shooting and subsequent full-field deformation analysis of the specimen.Figure 7
Experimental system.This test mainly focused on the influence of ground stress on smooth blasting. Three sets of schemes were designed for the test and recorded asG1, G2, and G3. The blasting parameters were completely consistent and the vertical static load was set to 0, 1, or 2 MPa successively. After the test, the fracture morphology, strain evolution, and damage distribution characteristics of each specimen under different initial stress fields were analyzed and compared. The results are described in detail below.


## 3. Test Results and Analysis

### 3.1. Analysis of Specimen Fracture Profile Modes

Figure8 shows the specimen crack profile after testing and a schematic view extracted from the crack profile. As shown in Figures 8, when the confining pressure is 0 MPa, the shape of the edge of the crack is irregularly jagged; when the confining pressure is 1 MPa, the crack exhibits an irregular arc shape but the curvature is small. When the pressure rises to 2 MPa, the shape of the crack is regular. It appears that as the pressure of the surrounding rock increased, the crack gradually moved from an irregular zigzag shape to a regular straight line. The existence of confining pressure made the rupture more regular [10].Figure 8
Raw image and sketch of blasting crack outline. (a) 0 MPa, (b) 1 MPa, and (c) 2 MPa.To quantitatively analyze the variation characteristics of the fracture surface after smooth blasting, the fracture surface between the blastholes was extracted, as shown in Figure9. The multifractal spectrum theory [26] was used to analyze the roughness of the fracture surface between the blastholes. The multifractal spectrum can be expressed as follows:(3)fα=−lgNαlgbδ,where f (α) is the multifractal dimension, α is a scaling index singular value, N(α) is the number of corresponding boxes, δ is the spacing of the ruler to measure the fractal subset, and b(δ) is the size of the covering box. Figure 10 shows the multifractal curve of each fracture surface under different confining pressures.Figure 9
Cross section between blastholes after blasting.
(a)
(b)
(c)Figure 10
Multifractal curves of blast-induced fracture surface. (a) 0 MPa. (b) 1 MPa. (c) 2 MPa.
(a)
(b)
(c)The multifractal spectrum width Δα = αmax − αmin reflects the fluctuation amplitude of the surface roughness of the fracture surface as well as the degree of its unevenness. A larger Δα value indicates a rougher fracture surface between the blastholes after blasting. A smaller Δα indicates more similar crack surface undulations and a more uniform crack distribution on the surface.Table2 shows the multifractal spectrum calculation parameters. IAS is an asymmetry index, and its absolute value characterizes the degree of unevenness on the crack surface and the distribution tendency of microcracks to change from uneven to uniform. IAS = (L − R)/(L + R), where L and R are the horizontal distance from the left endpoint and the right endpoint to the maximum point in the multifractal spectrum curve, respectively. The corresponding dimensional difference Δf (Δf = f (αmin) − f (αmax)) reflects the variations in the maximum fluctuation amplitude and minimum fluctuation amplitude of the fracture surface. The multifractal parameter width Δα, the dimension difference Δf, and the maximum value fmax of the blasting fracture surface all decrease as confining pressure increases, which indicates that the microcrack distribution of the fracture was wider under nonconfining pressure and the blasting destructive effect was stronger. The absolute value of the multifractal spectrum IAS decreases as confining pressure increases, which reflects the tendency of the unevenness of the surrounding rock wall and the distribution of the cracks from uneven to regular after smooth blasting.Table 2
Multifractal parameters of blast-induced crack surface under different confining pressures.
Confining pressure (MPa)
∆α
∆f
f
max
I
AS
0
0.0261
0.0122
2.0017
−0.4176
1
0.0101
0.0029
2.0006
−0.3069
2
0.0032
0.0011
2.0002
−0.1875


### 3.2. Strain and Equivalent Strain Rate Attenuation of Retained Rock Mass

#### 3.2.1. Strain Field Evolution

Strain is a property representative of material deformation. The strain of a specimen surface reflects the blasting intensity. The strain evolution of specimen surfaces under the explosion loading was investigated using DIC techniques to observe the effects of the blasting on the retained part. In Figure6, the area in the yellow dotted box (808 × 343 pixels) is the calculated part. The left and right sides of the blasthole comprise the damaged rock mass (region A) and retained part (region B), respectively. The strain field of specimens (G1, G2, and G3) was calculated according to the method described in Section 2.3 and shown in Figure 11.Figure 11
Monitoring points.From Figure12, it can be seen that after detonation, the stress wave propagated inside the specimen until reaching the surface. The strain concentration emerged first around the blasthole. For ease of description, the blastholes are numbered 1, 2, and 3 from top to bottom, as shown in Figure 6. For specimens G1 and G3, the strain concentration zone first appeared at the periphery of the blastholes 1 and 2 and the concentration zone range was small. Over time, the strain concentration zone gradually coalesced between blasthole 1 and blasthole 2 and the strain field around the blasthole was chaotic. The crack continued to expand from blasthole 2 to blasthole 3, and the strain field around the blasthole gradually became stable. When the confining pressure was 1 MPa (G2), the strain concentration zone initially appeared around blasthole 2 and the crack expanded from blasthole 2 to blastholes 1 and 3 simultaneously.Figure 12
Strain field evolution of different specimens. (a) Strain field evolution ofG1. (b) Strain field evolution of G2. (c) Strain field evolution of G3.
(a)
(b)
(c)Two forms of crack propagation modes were discovered in this experiment. Firstly, a crack between the two blastholes preferentially penetrated and then extended to the third blasthole, likely due to insufficient precision of the detonation time difference. Secondly, the crack is simultaneously expanded from the middle blasthole to the other two blastholes at the same time.


#### 3.2.2. Peak Strain and Equivalent Strain Rate Attenuation of Retained Body

According to blasting theory, the blast-induced stress wave pressure is proportional to the specific distanceR (R = r/rhole, where r is the distance from the calculation point to the center of the blasthole and rhole is the blasthole radius) and decreases rapidly as distance increases. The unit Inspector was used to monitor and extract the strain signal on the surface of the specimen. An orthogonal coordinate was established for convenient analysis, and the center of blasthole 2 was chosen as the origin of the coordinate, the layout direction of the blasthole as the Y-axis, and the perpendicular direction as the X-axis, as shown in Figure 11. In this study, five monitoring points P1 (10 mm, 0 mm), P2 (15 mm, 0 mm), P3 (25 mm, 0 mm), P4 (75 mm, 0 mm), and P5 (125 mm, 0 mm) were chosen.The strains at five monitoring points were extracted, denoised, and smoothed to obtain their respective strain-time curves. The strain atP4 and P5 hardly changes during the whole loading process. Therefore, only the points P1, P2, and P3 are described here (Figure 13). Under the three different conditions, the explosive stress waves propagated to point P1 at 50, 100, and 100 μs, respectively, and rose to peak values at 400, 450, and 450 μs, respectively. Subsequently, due to the destruction of the rock mass around the blasthole, P1 point did not provide any further data. Points P2 and P3 are far from the blasthole, where the speckle was undamaged and more data could be obtained. The deformation greatly attenuated when the stress wave reached P2, and the peak strain attenuation amplitudes are 73.2%, 81.2%, and 78.7% compared to the value at P1, respectively. The peak strain at Point P3 in specimens G1, G2, and G3 continuously dropped down.Figure 13
Strain history curves at different points of specimens.
(a)
(b)
(c)The equivalent strain rate reflects the deformation rate of the material and is an important representation of the material’s dynamic response. The corresponding variability thus has crucial significance. The time at which the blast stress wave reaches the observation point is denoted here ast0 and the corresponding strain as ε0. The time at which the strain reaches the peak value of P1 is defined as t, the peak strain is denoted as ε, and the equivalent strain rate is deduced by ε˙=ε−ε0/t−t0. The peak strain and equivalent strain rates are listed in Table 3.Table 3
Peak strain and equivalent strain rate at each observation point.
Confining pressure (MPa)
Peak strainε
Equivalent strain rateε˙ (s−1)
P1
P2
P3
P1
P2
P3
0
4.59E − 02
1.23E − 02
8.31E − 03
191e − 6
105e − 6
67.14e − 6
1
3.82E − 02
7.20E − 03
3.00E − 03
126e − 6
55.1e − 6
17.6e − 6
2
3.19E − 02
6.80E − 03
2.30E − 03
120e − 6
51.7e − 6
13.1e − 6The curves of peak strain and the equivalent strain rate with respect to time of the observation point are demonstrated in Figure14. When the confining pressure was 0 MPa, the peak strain decreased from 4.59e − 2 at point P1 to 8.31e − 3 at point P3 and the attenuation amplitude was 81.9%. The confining pressure was 1 or 2 MPa from point P1 to point P3; the attenuation value of peak strain was 92.1% and 92.8%, respectively.Figure 14
Variation of (a) peak strain and (b) equivalent strain rate with time.
(a)
(b)For pointP1, when the confining pressure changed from a nonconfined state (0 MPa) to a confining pressure constraint (1 MPa), the equivalent strain rate decreased from 191e − 6 s−1 to 67.14e − 6 s−1. This reflects the effect of confining pressure on the material deformation. The equivalent strain rate of points P2 and P3 showed a similar tendency with respect to point P1. We also found that when the confining pressure was 1 or 2 MPa, the equivalent strain rates of P2 and P3 were nearly equal. This suggests that the material equivalent strain rate is not sensitive to the confining pressure within a certain range.The following conclusions can be drawn based on the above analysis. (1) The peak strain has an obvious attenuation with increasing distance. (2) When the observation point is close to the blasthole (10 mm), the peak value of the strain decreases as confining pressure increases. (3) When the observation point is far away from the blasthole (15 mm and 20 mm), the peak strain also decreases due to the effect of confining pressure. Under confining pressures of 1 MPa and 2 MPa, however, the peak strain is nearly unchanged. (4) Equivalent strain rate decreases as confining pressure increases, but the equivalent strain rate values are nearly consistent when the confining pressure is 1 MPa or 2 MPa.


### 3.3. Peak Strain Evolution between Blastholes

The strain-time curve between the blastholes indirectly reflects the inter-blasthole crack profile mode, so it is necessary to determine the strain evolution between the blastholes. Using the coordinate system established in Section3.2.2, the curves of strain at measurement points P6 (0 mm, 20 mm) and P7 (0 mm, −20 mm) were extracted as shown in Figure 15.Figure 15
P6 and P7 strain curves with respect to time.
(a)
(b)
(c)When confining pressure was 0 MPa, the peak value of theP6 point strain was 0.10721 and the peak value of P7 point strain was 0.032. Their average value is 0.070, and the difference is 0.075. When the confining pressure was 1 MPa, the peak strains at points P6 and P7 were 0.095 and 0.057, respectively; the average and difference between them are 0.076 and 0.037, respectively. When the confining pressure increased to 2 MPa, the peak strains at points P6 and P7 were 0.116 and 0.113, respectively. The average value of P6 and P7 is 0.115, and the difference is 0.003. Overall, as confining pressure increased, the average value of the peak strain between the blastholes of the specimen gradually increased and the difference gradually decreased.It can be concluded that confining pressure markedly influenced the strain evolution between blastholesP6 and P7. As the confining pressure increased, the strain difference between P6 and P7 decreased and the crack profile gradually changed from irregular zigzag to straight. The peak strain of the material between the blastholes also increased with confining pressure, indicating that the existence of confining pressure plays a guiding role in the release of blasting energy.


### 3.4. Damage Distribution of Surrounding Rock after Smooth Blasting

The damage degreeD is an important index characterizing the damage to the surrounding rock mass. According to continuous damage mechanics, the damage degree D can thus be described by the changes in rock density, elastic modulus, P-wave velocity and yield stress, and other factors [27]. The range of the D value is {0, 1}. When D = 0, the surrounding rock mass can be considered to be in an ideal nondamaged state. At D = 1, it can be assumed that the rock mass is completely broken. In this study, the initial damage of the specimen was ignored and only the damage of the specimen by blasting is considered. The damage calculation formula using the P-wave velocity method is shown as follows:(4)E=V2ρ1+μd1−2μd1−μd,D=1−EE0=1−VV02,where E0 is the elastic modulus of the gypsum before blasting, E is the specimen elastic modulus after blasting, V0 and V are the P-wave velocity of the gypsum before and after blasting, respectively, μd is Poisson’s ratio of the gypsum, and ρ is the density of the gypsum. The layout of the measuring points is shown in Figure 16, where the monitoring point distance from the blasthole is 25, 75, or 125 mm. The P-wave velocity data of the three monitoring points before and after blasting and the damage degree results calculated according to equation (4) are listed in Table 4.Figure 16
P-wave velocity acquisition position. (a) Global view. (b) Side view.
(a)
(b)Table 4
P-wave velocity and damage value of each specimen.
Type of specimen
Monitoring point
Average P-wave velocity before explosionV0 (m/s)
P-wave velocity after explosionV (m/s)
DamageD (%)
G1
1
1430
1391
5.2
2
1411
2.6
3
1421
1.2
G2
1
1471
1442
3.9
2
1452
2.5
3
1463
1.1
G3
1
1681
1657
2.9
2
1666
1.7
3
1670
1.2As shown in Figure17, the presence of confining pressure significantly affects the degree of damage. At the same monitoring point, a larger confining pressure resulted in less damage. When the confining pressure was equal, the damage value D gradually decreased as distance between the monitoring point and the blasthole increased. The slope of the curve becomes gentler as confining pressure increases; this again suggests that an increase in confining pressure can inhibit the damage to the surrounding rock under blast loading.Figure 17
Damage value of different specimen measurement points after blasting.


## 3.1. Analysis of Specimen Fracture Profile Modes

Figure8 shows the specimen crack profile after testing and a schematic view extracted from the crack profile. As shown in Figures 8, when the confining pressure is 0 MPa, the shape of the edge of the crack is irregularly jagged; when the confining pressure is 1 MPa, the crack exhibits an irregular arc shape but the curvature is small. When the pressure rises to 2 MPa, the shape of the crack is regular. It appears that as the pressure of the surrounding rock increased, the crack gradually moved from an irregular zigzag shape to a regular straight line. The existence of confining pressure made the rupture more regular [10].Figure 8
Raw image and sketch of blasting crack outline. (a) 0 MPa, (b) 1 MPa, and (c) 2 MPa.To quantitatively analyze the variation characteristics of the fracture surface after smooth blasting, the fracture surface between the blastholes was extracted, as shown in Figure9. The multifractal spectrum theory [26] was used to analyze the roughness of the fracture surface between the blastholes. The multifractal spectrum can be expressed as follows:(3)fα=−lgNαlgbδ,where f (α) is the multifractal dimension, α is a scaling index singular value, N(α) is the number of corresponding boxes, δ is the spacing of the ruler to measure the fractal subset, and b(δ) is the size of the covering box. Figure 10 shows the multifractal curve of each fracture surface under different confining pressures.Figure 9
Cross section between blastholes after blasting.
(a)
(b)
(c)Figure 10
Multifractal curves of blast-induced fracture surface. (a) 0 MPa. (b) 1 MPa. (c) 2 MPa.
(a)
(b)
(c)The multifractal spectrum width Δα = αmax − αmin reflects the fluctuation amplitude of the surface roughness of the fracture surface as well as the degree of its unevenness. A larger Δα value indicates a rougher fracture surface between the blastholes after blasting. A smaller Δα indicates more similar crack surface undulations and a more uniform crack distribution on the surface.Table2 shows the multifractal spectrum calculation parameters. IAS is an asymmetry index, and its absolute value characterizes the degree of unevenness on the crack surface and the distribution tendency of microcracks to change from uneven to uniform. IAS = (L − R)/(L + R), where L and R are the horizontal distance from the left endpoint and the right endpoint to the maximum point in the multifractal spectrum curve, respectively. The corresponding dimensional difference Δf (Δf = f (αmin) − f (αmax)) reflects the variations in the maximum fluctuation amplitude and minimum fluctuation amplitude of the fracture surface. The multifractal parameter width Δα, the dimension difference Δf, and the maximum value fmax of the blasting fracture surface all decrease as confining pressure increases, which indicates that the microcrack distribution of the fracture was wider under nonconfining pressure and the blasting destructive effect was stronger. The absolute value of the multifractal spectrum IAS decreases as confining pressure increases, which reflects the tendency of the unevenness of the surrounding rock wall and the distribution of the cracks from uneven to regular after smooth blasting.Table 2
Multifractal parameters of blast-induced crack surface under different confining pressures.
Confining pressure (MPa)
∆α
∆f
f
max
I
AS
0
0.0261
0.0122
2.0017
−0.4176
1
0.0101
0.0029
2.0006
−0.3069
2
0.0032
0.0011
2.0002
−0.1875


## 3.2. Strain and Equivalent Strain Rate Attenuation of Retained Rock Mass

### 3.2.1. Strain Field Evolution

Strain is a property representative of material deformation. The strain of a specimen surface reflects the blasting intensity. The strain evolution of specimen surfaces under the explosion loading was investigated using DIC techniques to observe the effects of the blasting on the retained part. In Figure6, the area in the yellow dotted box (808 × 343 pixels) is the calculated part. The left and right sides of the blasthole comprise the damaged rock mass (region A) and retained part (region B), respectively. The strain field of specimens (G1, G2, and G3) was calculated according to the method described in Section 2.3 and shown in Figure 11.Figure 11
Monitoring points.From Figure12, it can be seen that after detonation, the stress wave propagated inside the specimen until reaching the surface. The strain concentration emerged first around the blasthole. For ease of description, the blastholes are numbered 1, 2, and 3 from top to bottom, as shown in Figure 6. For specimens G1 and G3, the strain concentration zone first appeared at the periphery of the blastholes 1 and 2 and the concentration zone range was small. Over time, the strain concentration zone gradually coalesced between blasthole 1 and blasthole 2 and the strain field around the blasthole was chaotic. The crack continued to expand from blasthole 2 to blasthole 3, and the strain field around the blasthole gradually became stable. When the confining pressure was 1 MPa (G2), the strain concentration zone initially appeared around blasthole 2 and the crack expanded from blasthole 2 to blastholes 1 and 3 simultaneously.Figure 12
Strain field evolution of different specimens. (a) Strain field evolution ofG1. (b) Strain field evolution of G2. (c) Strain field evolution of G3.
(a)
(b)
(c)Two forms of crack propagation modes were discovered in this experiment. Firstly, a crack between the two blastholes preferentially penetrated and then extended to the third blasthole, likely due to insufficient precision of the detonation time difference. Secondly, the crack is simultaneously expanded from the middle blasthole to the other two blastholes at the same time.


### 3.2.2. Peak Strain and Equivalent Strain Rate Attenuation of Retained Body

According to blasting theory, the blast-induced stress wave pressure is proportional to the specific distanceR (R = r/rhole, where r is the distance from the calculation point to the center of the blasthole and rhole is the blasthole radius) and decreases rapidly as distance increases. The unit Inspector was used to monitor and extract the strain signal on the surface of the specimen. An orthogonal coordinate was established for convenient analysis, and the center of blasthole 2 was chosen as the origin of the coordinate, the layout direction of the blasthole as the Y-axis, and the perpendicular direction as the X-axis, as shown in Figure 11. In this study, five monitoring points P1 (10 mm, 0 mm), P2 (15 mm, 0 mm), P3 (25 mm, 0 mm), P4 (75 mm, 0 mm), and P5 (125 mm, 0 mm) were chosen.The strains at five monitoring points were extracted, denoised, and smoothed to obtain their respective strain-time curves. The strain atP4 and P5 hardly changes during the whole loading process. Therefore, only the points P1, P2, and P3 are described here (Figure 13). Under the three different conditions, the explosive stress waves propagated to point P1 at 50, 100, and 100 μs, respectively, and rose to peak values at 400, 450, and 450 μs, respectively. Subsequently, due to the destruction of the rock mass around the blasthole, P1 point did not provide any further data. Points P2 and P3 are far from the blasthole, where the speckle was undamaged and more data could be obtained. The deformation greatly attenuated when the stress wave reached P2, and the peak strain attenuation amplitudes are 73.2%, 81.2%, and 78.7% compared to the value at P1, respectively. The peak strain at Point P3 in specimens G1, G2, and G3 continuously dropped down.Figure 13
Strain history curves at different points of specimens.
(a)
(b)
(c)The equivalent strain rate reflects the deformation rate of the material and is an important representation of the material’s dynamic response. The corresponding variability thus has crucial significance. The time at which the blast stress wave reaches the observation point is denoted here ast0 and the corresponding strain as ε0. The time at which the strain reaches the peak value of P1 is defined as t, the peak strain is denoted as ε, and the equivalent strain rate is deduced by ε˙=ε−ε0/t−t0. The peak strain and equivalent strain rates are listed in Table 3.Table 3
Peak strain and equivalent strain rate at each observation point.
Confining pressure (MPa)
Peak strainε
Equivalent strain rateε˙ (s−1)
P1
P2
P3
P1
P2
P3
0
4.59E − 02
1.23E − 02
8.31E − 03
191e − 6
105e − 6
67.14e − 6
1
3.82E − 02
7.20E − 03
3.00E − 03
126e − 6
55.1e − 6
17.6e − 6
2
3.19E − 02
6.80E − 03
2.30E − 03
120e − 6
51.7e − 6
13.1e − 6The curves of peak strain and the equivalent strain rate with respect to time of the observation point are demonstrated in Figure14. When the confining pressure was 0 MPa, the peak strain decreased from 4.59e − 2 at point P1 to 8.31e − 3 at point P3 and the attenuation amplitude was 81.9%. The confining pressure was 1 or 2 MPa from point P1 to point P3; the attenuation value of peak strain was 92.1% and 92.8%, respectively.Figure 14
Variation of (a) peak strain and (b) equivalent strain rate with time.
(a)
(b)For pointP1, when the confining pressure changed from a nonconfined state (0 MPa) to a confining pressure constraint (1 MPa), the equivalent strain rate decreased from 191e − 6 s−1 to 67.14e − 6 s−1. This reflects the effect of confining pressure on the material deformation. The equivalent strain rate of points P2 and P3 showed a similar tendency with respect to point P1. We also found that when the confining pressure was 1 or 2 MPa, the equivalent strain rates of P2 and P3 were nearly equal. This suggests that the material equivalent strain rate is not sensitive to the confining pressure within a certain range.The following conclusions can be drawn based on the above analysis. (1) The peak strain has an obvious attenuation with increasing distance. (2) When the observation point is close to the blasthole (10 mm), the peak value of the strain decreases as confining pressure increases. (3) When the observation point is far away from the blasthole (15 mm and 20 mm), the peak strain also decreases due to the effect of confining pressure. Under confining pressures of 1 MPa and 2 MPa, however, the peak strain is nearly unchanged. (4) Equivalent strain rate decreases as confining pressure increases, but the equivalent strain rate values are nearly consistent when the confining pressure is 1 MPa or 2 MPa.


## 3.2.1. Strain Field Evolution

Strain is a property representative of material deformation. The strain of a specimen surface reflects the blasting intensity. The strain evolution of specimen surfaces under the explosion loading was investigated using DIC techniques to observe the effects of the blasting on the retained part. In Figure6, the area in the yellow dotted box (808 × 343 pixels) is the calculated part. The left and right sides of the blasthole comprise the damaged rock mass (region A) and retained part (region B), respectively. The strain field of specimens (G1, G2, and G3) was calculated according to the method described in Section 2.3 and shown in Figure 11.Figure 11
Monitoring points.From Figure12, it can be seen that after detonation, the stress wave propagated inside the specimen until reaching the surface. The strain concentration emerged first around the blasthole. For ease of description, the blastholes are numbered 1, 2, and 3 from top to bottom, as shown in Figure 6. For specimens G1 and G3, the strain concentration zone first appeared at the periphery of the blastholes 1 and 2 and the concentration zone range was small. Over time, the strain concentration zone gradually coalesced between blasthole 1 and blasthole 2 and the strain field around the blasthole was chaotic. The crack continued to expand from blasthole 2 to blasthole 3, and the strain field around the blasthole gradually became stable. When the confining pressure was 1 MPa (G2), the strain concentration zone initially appeared around blasthole 2 and the crack expanded from blasthole 2 to blastholes 1 and 3 simultaneously.Figure 12
Strain field evolution of different specimens. (a) Strain field evolution ofG1. (b) Strain field evolution of G2. (c) Strain field evolution of G3.
(a)
(b)
(c)Two forms of crack propagation modes were discovered in this experiment. Firstly, a crack between the two blastholes preferentially penetrated and then extended to the third blasthole, likely due to insufficient precision of the detonation time difference. Secondly, the crack is simultaneously expanded from the middle blasthole to the other two blastholes at the same time.


## 3.2.2. Peak Strain and Equivalent Strain Rate Attenuation of Retained Body

According to blasting theory, the blast-induced stress wave pressure is proportional to the specific distanceR (R = r/rhole, where r is the distance from the calculation point to the center of the blasthole and rhole is the blasthole radius) and decreases rapidly as distance increases. The unit Inspector was used to monitor and extract the strain signal on the surface of the specimen. An orthogonal coordinate was established for convenient analysis, and the center of blasthole 2 was chosen as the origin of the coordinate, the layout direction of the blasthole as the Y-axis, and the perpendicular direction as the X-axis, as shown in Figure 11. In this study, five monitoring points P1 (10 mm, 0 mm), P2 (15 mm, 0 mm), P3 (25 mm, 0 mm), P4 (75 mm, 0 mm), and P5 (125 mm, 0 mm) were chosen.The strains at five monitoring points were extracted, denoised, and smoothed to obtain their respective strain-time curves. The strain atP4 and P5 hardly changes during the whole loading process. Therefore, only the points P1, P2, and P3 are described here (Figure 13). Under the three different conditions, the explosive stress waves propagated to point P1 at 50, 100, and 100 μs, respectively, and rose to peak values at 400, 450, and 450 μs, respectively. Subsequently, due to the destruction of the rock mass around the blasthole, P1 point did not provide any further data. Points P2 and P3 are far from the blasthole, where the speckle was undamaged and more data could be obtained. The deformation greatly attenuated when the stress wave reached P2, and the peak strain attenuation amplitudes are 73.2%, 81.2%, and 78.7% compared to the value at P1, respectively. The peak strain at Point P3 in specimens G1, G2, and G3 continuously dropped down.Figure 13
Strain history curves at different points of specimens.
(a)
(b)
(c)The equivalent strain rate reflects the deformation rate of the material and is an important representation of the material’s dynamic response. The corresponding variability thus has crucial significance. The time at which the blast stress wave reaches the observation point is denoted here ast0 and the corresponding strain as ε0. The time at which the strain reaches the peak value of P1 is defined as t, the peak strain is denoted as ε, and the equivalent strain rate is deduced by ε˙=ε−ε0/t−t0. The peak strain and equivalent strain rates are listed in Table 3.Table 3
Peak strain and equivalent strain rate at each observation point.
Confining pressure (MPa)
Peak strainε
Equivalent strain rateε˙ (s−1)
P1
P2
P3
P1
P2
P3
0
4.59E − 02
1.23E − 02
8.31E − 03
191e − 6
105e − 6
67.14e − 6
1
3.82E − 02
7.20E − 03
3.00E − 03
126e − 6
55.1e − 6
17.6e − 6
2
3.19E − 02
6.80E − 03
2.30E − 03
120e − 6
51.7e − 6
13.1e − 6The curves of peak strain and the equivalent strain rate with respect to time of the observation point are demonstrated in Figure14. When the confining pressure was 0 MPa, the peak strain decreased from 4.59e − 2 at point P1 to 8.31e − 3 at point P3 and the attenuation amplitude was 81.9%. The confining pressure was 1 or 2 MPa from point P1 to point P3; the attenuation value of peak strain was 92.1% and 92.8%, respectively.Figure 14
Variation of (a) peak strain and (b) equivalent strain rate with time.
(a)
(b)For pointP1, when the confining pressure changed from a nonconfined state (0 MPa) to a confining pressure constraint (1 MPa), the equivalent strain rate decreased from 191e − 6 s−1 to 67.14e − 6 s−1. This reflects the effect of confining pressure on the material deformation. The equivalent strain rate of points P2 and P3 showed a similar tendency with respect to point P1. We also found that when the confining pressure was 1 or 2 MPa, the equivalent strain rates of P2 and P3 were nearly equal. This suggests that the material equivalent strain rate is not sensitive to the confining pressure within a certain range.The following conclusions can be drawn based on the above analysis. (1) The peak strain has an obvious attenuation with increasing distance. (2) When the observation point is close to the blasthole (10 mm), the peak value of the strain decreases as confining pressure increases. (3) When the observation point is far away from the blasthole (15 mm and 20 mm), the peak strain also decreases due to the effect of confining pressure. Under confining pressures of 1 MPa and 2 MPa, however, the peak strain is nearly unchanged. (4) Equivalent strain rate decreases as confining pressure increases, but the equivalent strain rate values are nearly consistent when the confining pressure is 1 MPa or 2 MPa.


## 3.3. Peak Strain Evolution between Blastholes

The strain-time curve between the blastholes indirectly reflects the inter-blasthole crack profile mode, so it is necessary to determine the strain evolution between the blastholes. Using the coordinate system established in Section3.2.2, the curves of strain at measurement points P6 (0 mm, 20 mm) and P7 (0 mm, −20 mm) were extracted as shown in Figure 15.Figure 15
P6 and P7 strain curves with respect to time.
(a)
(b)
(c)When confining pressure was 0 MPa, the peak value of theP6 point strain was 0.10721 and the peak value of P7 point strain was 0.032. Their average value is 0.070, and the difference is 0.075. When the confining pressure was 1 MPa, the peak strains at points P6 and P7 were 0.095 and 0.057, respectively; the average and difference between them are 0.076 and 0.037, respectively. When the confining pressure increased to 2 MPa, the peak strains at points P6 and P7 were 0.116 and 0.113, respectively. The average value of P6 and P7 is 0.115, and the difference is 0.003. Overall, as confining pressure increased, the average value of the peak strain between the blastholes of the specimen gradually increased and the difference gradually decreased.It can be concluded that confining pressure markedly influenced the strain evolution between blastholesP6 and P7. As the confining pressure increased, the strain difference between P6 and P7 decreased and the crack profile gradually changed from irregular zigzag to straight. The peak strain of the material between the blastholes also increased with confining pressure, indicating that the existence of confining pressure plays a guiding role in the release of blasting energy.


## 3.4. Damage Distribution of Surrounding Rock after Smooth Blasting

The damage degreeD is an important index characterizing the damage to the surrounding rock mass. According to continuous damage mechanics, the damage degree D can thus be described by the changes in rock density, elastic modulus, P-wave velocity and yield stress, and other factors [27]. The range of the D value is {0, 1}. When D = 0, the surrounding rock mass can be considered to be in an ideal nondamaged state. At D = 1, it can be assumed that the rock mass is completely broken. In this study, the initial damage of the specimen was ignored and only the damage of the specimen by blasting is considered. The damage calculation formula using the P-wave velocity method is shown as follows:(4)E=V2ρ1+μd1−2μd1−μd,D=1−EE0=1−VV02,where E0 is the elastic modulus of the gypsum before blasting, E is the specimen elastic modulus after blasting, V0 and V are the P-wave velocity of the gypsum before and after blasting, respectively, μd is Poisson’s ratio of the gypsum, and ρ is the density of the gypsum. The layout of the measuring points is shown in Figure 16, where the monitoring point distance from the blasthole is 25, 75, or 125 mm. The P-wave velocity data of the three monitoring points before and after blasting and the damage degree results calculated according to equation (4) are listed in Table 4.Figure 16
P-wave velocity acquisition position. (a) Global view. (b) Side view.
(a)
(b)Table 4
P-wave velocity and damage value of each specimen.
Type of specimen
Monitoring point
Average P-wave velocity before explosionV0 (m/s)
P-wave velocity after explosionV (m/s)
DamageD (%)
G1
1
1430
1391
5.2
2
1411
2.6
3
1421
1.2
G2
1
1471
1442
3.9
2
1452
2.5
3
1463
1.1
G3
1
1681
1657
2.9
2
1666
1.7
3
1670
1.2As shown in Figure17, the presence of confining pressure significantly affects the degree of damage. At the same monitoring point, a larger confining pressure resulted in less damage. When the confining pressure was equal, the damage value D gradually decreased as distance between the monitoring point and the blasthole increased. The slope of the curve becomes gentler as confining pressure increases; this again suggests that an increase in confining pressure can inhibit the damage to the surrounding rock under blast loading.Figure 17
Damage value of different specimen measurement points after blasting.


## 4. Discussion

According to the test results provided above, the presence of confining pressure is conducive to the formation of the roadway contour after smooth blasting and can inhibit damage to the surrounding rock. We will attempt here to explain this phenomenon as it relates to the explosion stress wave and in situ stress.


### 4.1. Explosive Stress Wave Effect

Figure18 shows the crack propagation mechanism after single hole blasting. An explosive stress wave is generated after the explosive detonates which acts on the blasthole wall to produce a crushing zone. The crushing zone not only consumes a large amount of energy but also deteriorates the propagation medium of the subsequent stress wave resulting in a sharp attenuation of the wave. A portion of the stress wave continues to propagate forward, but its working capacity is reduced. The extent of damage to the rock mass decreases, and only tiny cracks are generated. As the stress wave attenuates continuously, the rock only generates elastic vibration. The stress wave is called an “elastic vibration wave” at this time.Figure 18
Mechanism of crack propagation after single hole blasting.A large amount of high-temperature and high-pressure gas, “detonation gas,” is simultaneously generated after the explosive detonates. Unlike the explosive stress wave, the detonation gas propagates slowly at low intensity over a long duration. The detonation gas propagates around the blasthole, is wedged into the rock microcracks generated by the explosion stress wave, and produces an “air wedge” effect which causes the crack to further expand. The rock’s fracture toughness varies due to its anisotropy. Under the quasistatic action of the detonation gas, cracks preferentially expand along the weaker parts of the rock until forming several macroscopic main cracks. Unlike the transient stress wave, the detonation gas is actively regulated; the active adjustment process markedly affects crack propagation in the rock mass.There are multiple blasthole interactions which occur in a smooth blasting scenario. For simplicity, we discuss here only the interaction of an explosion stress wave and a crack between two blastholes (Figure19). After the explosion, the explosion stress wave behaves similarly to the single hole blasting scenario before reaching the crack generated by the adjacent blasthole. The P-wave of the explosion stress wave reaches the crack tip before the S-wave due to its greater velocity and has a certain inhibitory effect on the crack propagation. The subsequent S-wave interaction with the crack promotes the propagation of cracks along the blasthole line [28–30]. The existing crack in the direction of the blastholes further promotes other cracks to propagate in this direction while cracks in the other direction are slowed down and truncated due to transfer of the explosive gas. It is worth emphasizing that the propagation velocity of the stress wave is much greater than that of the crack and that the distance D between adjacent blastholes is short. Therefore, cracks are relatively underdeveloped in the blasthole wall before the stress wave acts on them; this is why the number of wing cracks around the a single blasthole after blasting is greater (and the cracks are longer) than after double hole blasting, as shown in Figure 20.Figure 19
Mechanism of crack propagation after blasting of adjacent blastholes.Figure 20
Crack distribution after (a) single hole and (b) double hole blasting.
(a)
(b)


### 4.2. Effect of In Situ Stress on Crack Propagation

The existence of ground stress influences the stress field around the blasthole and the stress state of the rock mass. According to literature [19], under unidirectional stress, the radial normal stress and shear stress values at the circular hole are both zero; the circumferential normal stress can be expressed as follows:(5)σφ=qv1+2cos2φ,σρ=τρφ=0,where qv is the initial vertical stress and σφ, σρ, and τρφ are the tangential stress, radial stress, and shear stress, respectively. When φ is 0° or 180°, the stress at the orifice is compressive. When φ is 90° or 270°, the orifice has the tensile stress at an absolute value equal to the compressive stress value, as shown in Figure 21(a). In the direction perpendicular to the vertical stress, the rock is in a state of compressive stress. In the direction parallel to the vertical stress, a tensile stress field lies near the orifice of the blasthole. Tensile stress results in favor of the initiation and propagation of cracks in the rock mass. The far region is the compressive stress field.Figure 21
Schematic diagram of superimposed stress field.The rock is under the action of the superimposed explosion stress field and the in situ stress field after the explosive is detonated (Figure21). As shown in Figure 22, in the direction perpendicular to the vertical stress, the compressive stress field restrains and decelerates crack propagation as local microcracks appear [31]. The crack propagation will be promoted in vertical direction and the length of cracks increases [16].Figure 22
Schematic diagram of cracks distribution after blasting under compressive stress.Meanwhile, in the retained rock mass, vibration damping increases rapidly under increasing confining pressure and stress propagation process consumes more energy than the specimen without confining pressure. The strain and strain rate decrease as well, reflecting a reduction in damage to the surrounding rock.The test method used in this study also has shortcomings, which may be remedied by further research. For example, gypsum with uniform, isotropic, and homogeneous characteristics was used as the test material; the anisotropy and nonuniformity of the rock mass were ignored, which should be considered in the future, and the effect of reflected stress wave on the rock damage is not considered [32]. Additionally, the explosive charge we used in the test is a uniform self-made charge and the charging parameters, detonation time, and detonation conditions were kept uniform. Other test conditions such as coupling coefficient, detonating time difference, and positive detonation were not considered. The impact of these factors on smooth blasting remains to be seen. In the future, we plan to explore this further.


## 4.1. Explosive Stress Wave Effect

Figure18 shows the crack propagation mechanism after single hole blasting. An explosive stress wave is generated after the explosive detonates which acts on the blasthole wall to produce a crushing zone. The crushing zone not only consumes a large amount of energy but also deteriorates the propagation medium of the subsequent stress wave resulting in a sharp attenuation of the wave. A portion of the stress wave continues to propagate forward, but its working capacity is reduced. The extent of damage to the rock mass decreases, and only tiny cracks are generated. As the stress wave attenuates continuously, the rock only generates elastic vibration. The stress wave is called an “elastic vibration wave” at this time.Figure 18
Mechanism of crack propagation after single hole blasting.A large amount of high-temperature and high-pressure gas, “detonation gas,” is simultaneously generated after the explosive detonates. Unlike the explosive stress wave, the detonation gas propagates slowly at low intensity over a long duration. The detonation gas propagates around the blasthole, is wedged into the rock microcracks generated by the explosion stress wave, and produces an “air wedge” effect which causes the crack to further expand. The rock’s fracture toughness varies due to its anisotropy. Under the quasistatic action of the detonation gas, cracks preferentially expand along the weaker parts of the rock until forming several macroscopic main cracks. Unlike the transient stress wave, the detonation gas is actively regulated; the active adjustment process markedly affects crack propagation in the rock mass.There are multiple blasthole interactions which occur in a smooth blasting scenario. For simplicity, we discuss here only the interaction of an explosion stress wave and a crack between two blastholes (Figure19). After the explosion, the explosion stress wave behaves similarly to the single hole blasting scenario before reaching the crack generated by the adjacent blasthole. The P-wave of the explosion stress wave reaches the crack tip before the S-wave due to its greater velocity and has a certain inhibitory effect on the crack propagation. The subsequent S-wave interaction with the crack promotes the propagation of cracks along the blasthole line [28–30]. The existing crack in the direction of the blastholes further promotes other cracks to propagate in this direction while cracks in the other direction are slowed down and truncated due to transfer of the explosive gas. It is worth emphasizing that the propagation velocity of the stress wave is much greater than that of the crack and that the distance D between adjacent blastholes is short. Therefore, cracks are relatively underdeveloped in the blasthole wall before the stress wave acts on them; this is why the number of wing cracks around the a single blasthole after blasting is greater (and the cracks are longer) than after double hole blasting, as shown in Figure 20.Figure 19
Mechanism of crack propagation after blasting of adjacent blastholes.Figure 20
Crack distribution after (a) single hole and (b) double hole blasting.
(a)
(b)


## 4.2. Effect of In Situ Stress on Crack Propagation

The existence of ground stress influences the stress field around the blasthole and the stress state of the rock mass. According to literature [19], under unidirectional stress, the radial normal stress and shear stress values at the circular hole are both zero; the circumferential normal stress can be expressed as follows:(5)σφ=qv1+2cos2φ,σρ=τρφ=0,where qv is the initial vertical stress and σφ, σρ, and τρφ are the tangential stress, radial stress, and shear stress, respectively. When φ is 0° or 180°, the stress at the orifice is compressive. When φ is 90° or 270°, the orifice has the tensile stress at an absolute value equal to the compressive stress value, as shown in Figure 21(a). In the direction perpendicular to the vertical stress, the rock is in a state of compressive stress. In the direction parallel to the vertical stress, a tensile stress field lies near the orifice of the blasthole. Tensile stress results in favor of the initiation and propagation of cracks in the rock mass. The far region is the compressive stress field.Figure 21
Schematic diagram of superimposed stress field.The rock is under the action of the superimposed explosion stress field and the in situ stress field after the explosive is detonated (Figure21). As shown in Figure 22, in the direction perpendicular to the vertical stress, the compressive stress field restrains and decelerates crack propagation as local microcracks appear [31]. The crack propagation will be promoted in vertical direction and the length of cracks increases [16].Figure 22
Schematic diagram of cracks distribution after blasting under compressive stress.Meanwhile, in the retained rock mass, vibration damping increases rapidly under increasing confining pressure and stress propagation process consumes more energy than the specimen without confining pressure. The strain and strain rate decrease as well, reflecting a reduction in damage to the surrounding rock.The test method used in this study also has shortcomings, which may be remedied by further research. For example, gypsum with uniform, isotropic, and homogeneous characteristics was used as the test material; the anisotropy and nonuniformity of the rock mass were ignored, which should be considered in the future, and the effect of reflected stress wave on the rock damage is not considered [32]. Additionally, the explosive charge we used in the test is a uniform self-made charge and the charging parameters, detonation time, and detonation conditions were kept uniform. Other test conditions such as coupling coefficient, detonating time difference, and positive detonation were not considered. The impact of these factors on smooth blasting remains to be seen. In the future, we plan to explore this further.


## 5. Conclusion

This paper mainly discussed the fracture mode, strain evolution, and damage degree of retained rock masses after smooth blasting under various ground stresses. The main conclusions can be summarized as follows:(1)
The crack profile after blasting shows that as the surrounding rock pressure increases, the crack profile between the blastholes gradually transitions from irregular zigzag to smooth and flat. The presence of confining pressure makes the crack outline more regular. The strain evolution between the holes suggests that crack formation effects are improved as the strain difference between the blastholes decreases.(2)
The strain evolution curves of the retained body indicated that peak strain decreases obviously with increased distance. The existence of confining pressure also appears to have a certain influence on strain attenuation. The peak strain value decreases as confining pressure increases, and the peak strain in the far field is not sensitive to confining pressure within the scope of this study. Equivalent strain rate evolution behaves similarly. The acoustic damage test revealed that the damage valueD gradually decreases as the distance between the monitoring point and the blasthole increases.(3)
Based on the strain evolution and damage distribution, confining pressure is largely responsible for the release direction of blasting energy. An increase in rock particle vibration damping also effectively prevents the growth in the strain and thus protects the surrounding rock from damage.Despite some shortcomings, the conclusions presented in this paper also can provide workable guidelines for related engineering applications.



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*Source: 2124694-2020-01-07.xml*