# Assessment of Blasting-Induced Ground Vibration in an Open-Pit Mine under Different Rock Properties

Authors: Zhi-qiang Yin; Zu-xiang Hu; Ze-di Wei; Guang-ming Zhao; Ma Hai-feng; Zhuo Zhang; Rui-min Feng
Journal: Advances in Civil Engineering
 (2018)

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## Abstract

In an open-pit mine slope, rock mass has multiple joint structures and blasting operations have an obvious influence on its stability. Therefore, accurately predicting the blasting vibration is necessary to ensure slope stability. In this study, the blasting vibration signals monitored at a blasting site with different rock masses were used to investigate the attenuation characteristics of blasting vibration through the peak particle velocity (PPV), frequency characteristics, and energy distribution of the blasting vibration signals analyzed with the time-frequency processing method. The results demonstrated that the main vibration frequency of the blasting vibration of dolomite was wider than that of shale, and these main vibration frequencies occurred at 25 kHz and 14 kHz for dolomite and shale, respectively, at a distance of 50 m from the blast area to the vibration monitoring point. With an increase in the distance from 50 m to 200 m, the main vibration frequencies decreased to less than 5 Hz. With increasing joint degree, the attenuation rate of the vibration velocity and energy attenuation of the blasting vibration increase, indicating that the structural parameters of the rock mass (such as the number of joints) have a significant impact on the attenuation law of blasting vibration. Furthermore, a modified equation that can be used for predicting PPV was developed by considering the effect of the number of joints in the rock mass on the blasting vibration. For the same ground vibration readings, the correlation factor increased from 0.8 to 0.85 for the Nicholls-USBM equation and the modified equation, respectively. The PPV of blasting under different rock masses of the Baideng open-pit phosphorite mine was used to verify the modified equation. The results show that a modified equation can be used for predicting the PPV of blasting engineering in the Baideng phosphorite mine and that the prediction accuracy is acceptable.


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## Body

## 1. Introduction

The primary operation in open-pit mines is rock blasting. In blasting, only 20%–30% of the energy produced by the explosives is converted into mechanical energy to fragment and displace the rock mass. The remainder of the explosive energy is wasted in the form of blast disturbances, such as rock vibrations, noise, and fly rock, among others. Rock masses are typically characterized by discontinuous and anisotropic inhomogeneous structures. These discontinuous structures, such as faults, joints, fissures, and fractured zones, are randomly distributed in the rock mass and have important implications for blasting engineering. In blasting operations, natural cracks in the rock mass structure are changed by additional stresses induced by the blasting, and the shear strength of the structural surface is significantly reduced, thereby decreasing the stability of the rock [1, 2]. Studies on blast vibration harm control are conducted based on analysis of blast vibrations. Peak particle velocity (PPV) is an evaluation criterion for the blasting vibration which has been used for many years; it is predicted by the distance and the charge weight scaling law [3, 4]. In recent years, many researchers have conducted studies on the mechanical properties and strength of structural planes [5, 6] and their influence on the slope stability of the surface structure of rock masses [7–11]. However, only a few studies have been carried out regarding the vibration wave propagation characteristics of structural planes. Studies on the vibration effects of blasting have described the transmission and reflection of the stress wave on the surface of the structure using theoretical analysis and have focused primarily on the amplitude attenuation effect of structures on the stress wave [12–14]. Therefore, research on the effect of rock mass media on the attenuation of blasting vibration and accurate analysis of the influence of rock structures on the propagation of vibration attenuation in blasting engineering is worth further investigation.Over the last several decades, additional sophisticated approaches, such as the finite element method and artificial neural networks, have been used to predict blast vibration [15–17]. Many researchers have successfully attempted to process and analyze unstable random blast vibration signals using signal time-frequency analysis [18–20]. Studies have also explored the influence of the distance from the blasting center on the frequency band energy distribution of blast vibration signals, and signal time-frequency analysis has become an effective method for investigating the energy distribution characteristics of a blast vibration signal under rock mass joints. Based on the results for the time-frequency characteristics of blasting signals, research on factors influencing blasting vibration, establishment of a regression formula describing blasting vibration, and analysis of signal time-frequency are effective and important methods for the study of blasting vibration hazards.In this study, ground vibration monitoring data were obtained from the Baideng open-pit phosphorite mine in China. The energy spectrum of the blast vibration signal obtained from the measurement data collected during blasting was then analyzed using a time-frequency analysis method. The influence of the rock mass structure on the attenuation of blast seismic waves was explored from the perspective of the blast vibration energy. Finally, these vibration monitoring data were used to develop a new relationship, in which the influence of discontinuous structures is included in the number of joints in rock masses. The PPV for different rock masses was used to verify this relationship.


## 2. Materials and Methods

### 2.1. General Project Site Information

This study was conducted at the Baideng open-pit phosphorite mine, which is a subsidiary of the Guangming Chemical Co., Ltd. This mine is located in Anning, Yunnan, China. The Baideng open-pit phosphorite mine lies at a latitude of 24°52′N and a longitude of 102°22′E. The dip of the strata is gently inclined and varies from 8° to 20°. The strata overlying the ore body are dolomite, shale, and quaternary eluvial alluvium. Deep-hole bench blasting at a height of 10 m is used in this mine, as illustrated in Figures1 and 2. In the mining area, blasting excavation has been used in dolomite and shale, and these rock strata have developed fault joints. Mechanical parameters of the intact rock masses such as the uniaxial compressive strength and tensile strength were tested according to the methods recommended by the International Society of Rock Mechanics (ISRM) [21–24]. The rock mass wave velocity and the number of joints were also measured [25]. The mechanical properties of the intact rock masses are summarized in Table 1.Figure 1
Geological profile of Baideng phosphorite.Figure 2
Bench of Baideng phosphorite.Table 1
Mechanical parameters of rock masses.
Rock type
UCS (MPa)
TS (MPa)
ρ (g/cm3)
E (GPa)
JF
V
r (m/s)
V
rm (m/s)
Dolomite
95.73
16.48
3.53
87.62
2.1
5247
2471
Shale
58.21
5.84
2.69
55.85
0.9
3813
2895
Note. UCS: uniaxial compression strength; TS: tensile strength; ρ: dry density; E: Young’s modulus; Vr: wave velocity of rock; Vrm: wave velocity of rock mass; JF: number of joints per 10 m.Ammonium nitrate-fuel oil (ANFO) and nonelectric detonators were used for the blasting excavation. The typical depth and diameter of the blast holes were 11 m and 130 mm, respectively, resulting in a blasting pattern with a burden of 4 m and spacing of 5 m. In-hole delay detonators operated at 400 ms. An initiation pattern was produced on the surface using NONEL with a delay of 25 ms. An example of the initiation network and pattern of drilling holes is shown in Figure3.Figure 3
Initiation network and drilling holes pattern.


### 2.2. PPV Monitoring and Prediction Methods

The vibration monitoring points and blasting area were located at the same elevation. The distances between the monitoring points and blasting area were 50, 100, 150, and 200 m, as shown in Figure4. A blasting vibration recorder (EXP 3850) and a sensor (CDJ-1) were used to monitor blasting vibrations. Each monitoring point was equipped with a vibration sensor. The sensor must be bonded to the surface of the intact rock with plaster, and the location of the monitoring points must be adjusted appropriately to ensure the accuracy of the measurements. Thus, the distance and azimuth were determined using GPS, as shown in Figure 5.Figure 4
Diagram for location of blasting vibration monitoring.Figure 5
Vibration sensor and GPS.Over the last half century, researchers have proposed several empirical equations to describe the attenuation characteristics of blast vibrations and predict the attenuation of the PPV [26–28]. The PPV equations that have been proposed by different researchers are summarized in Table 2. In most of these equations, the distance from the free face and the maximum charge weight per delay are considered the main parameters influencing PPV prediction. However, is well known that PPV is influenced by other factors, such as the rock strength, rock mass discontinuity conditions, and blast geometry, which have not been explicitly incorporated in these empirical equations. In this study, the Nicholls-United States Bureau of Mines (USBM) empirical equation is used as the prediction equation.Table 2
Empirical PPV predictor presented by different researches.
Name
Equation
Nicholls-USBM
PPV
=
k
Q
1
/
2
/
R
n
General Prediction by Davies
PPV
=
k
R
−
n
Q
a
Langefors and Kihlstrom
PPV
=
k
Q
1
/
2
/
R
1
/
3
n
Bureau of Indian Standard
PPV
=
k
Q
/
R
2
/
3
n
Ambressys–Hendron
PPV
=
k
Q
1
/
3
/
R
n
Ghosh–Daemen predictor
PPV
=
k
R
/
Q
1
/
2
−
n
e
−
α
R
Note. R: distance from the blast area to the vibration monitoring point; Q: maximum charge weight per delay; k, n, a, α: site constants.


### 2.3. Wavelet Packet Analysis Method

Wavelet packet analysis is a time-frequency processing method for a nonstationary random signal. This signal is decomposed into two parts, i.e., the low and high frequencies, using low- and high-pass filters, respectively. The two decomposed signals are then further divided into two parts corresponding to the low and high frequencies. Thus, the signal is continuously decomposed, thereby exhibiting a high-frequency resolution [29]. Analysis of the signal continued to the eighth decomposition level. The signal decomposition process is illustrated in Figure 6. The number of frequency bands in the blasting vibration signals at approximately 2n can be obtained, such that n is the decomposition level of the wavelet packet analysis. If the lowest frequency of the blast vibration signal, st, is 0 and the highest frequency is W, the width of the frequency band at the nth decomposition level will be W/2n.Figure 6
Diagram for signal decomposition process. A stands for low frequency, D stands for high frequency, and the numbers 1, 2, and 3 stands for decomposition levels.Based on the decomposition and reconstruction of the wavelet packet analysis method, the blast vibration signal,st, can be expressed as follows:(1)st=∑j2i−1si,j,where si,j is the reconstructed signal after wavelet packet decomposition, i is the decomposition level, and j is the order number of the frequency bands after decomposition, j=0,1,2,3,…,2i−1.The energy of each reconstructed signal,Ei,j, after wavelet packet decomposition is defined as(2)Ei,j=∫si,jt2dt=∑k=1mxj,k2,where xi,j is the amplitude of the discrete points of the reconstructed signal, m is the number of discrete sampling points, and k is the number of discrete points, k=1,2,3,…,m.The total energy of the analyzed signal,E0, is expressed as follows:(3)E0=∑j=02i−1Ei,j.The ratio of the energy in each frequency band to the total energy can be derived as follows:(4)Pj=Ei,jE0×100%.


## 2.1. General Project Site Information

This study was conducted at the Baideng open-pit phosphorite mine, which is a subsidiary of the Guangming Chemical Co., Ltd. This mine is located in Anning, Yunnan, China. The Baideng open-pit phosphorite mine lies at a latitude of 24°52′N and a longitude of 102°22′E. The dip of the strata is gently inclined and varies from 8° to 20°. The strata overlying the ore body are dolomite, shale, and quaternary eluvial alluvium. Deep-hole bench blasting at a height of 10 m is used in this mine, as illustrated in Figures1 and 2. In the mining area, blasting excavation has been used in dolomite and shale, and these rock strata have developed fault joints. Mechanical parameters of the intact rock masses such as the uniaxial compressive strength and tensile strength were tested according to the methods recommended by the International Society of Rock Mechanics (ISRM) [21–24]. The rock mass wave velocity and the number of joints were also measured [25]. The mechanical properties of the intact rock masses are summarized in Table 1.Figure 1
Geological profile of Baideng phosphorite.Figure 2
Bench of Baideng phosphorite.Table 1
Mechanical parameters of rock masses.
Rock type
UCS (MPa)
TS (MPa)
ρ (g/cm3)
E (GPa)
JF
V
r (m/s)
V
rm (m/s)
Dolomite
95.73
16.48
3.53
87.62
2.1
5247
2471
Shale
58.21
5.84
2.69
55.85
0.9
3813
2895
Note. UCS: uniaxial compression strength; TS: tensile strength; ρ: dry density; E: Young’s modulus; Vr: wave velocity of rock; Vrm: wave velocity of rock mass; JF: number of joints per 10 m.Ammonium nitrate-fuel oil (ANFO) and nonelectric detonators were used for the blasting excavation. The typical depth and diameter of the blast holes were 11 m and 130 mm, respectively, resulting in a blasting pattern with a burden of 4 m and spacing of 5 m. In-hole delay detonators operated at 400 ms. An initiation pattern was produced on the surface using NONEL with a delay of 25 ms. An example of the initiation network and pattern of drilling holes is shown in Figure3.Figure 3
Initiation network and drilling holes pattern.


## 2.2. PPV Monitoring and Prediction Methods

The vibration monitoring points and blasting area were located at the same elevation. The distances between the monitoring points and blasting area were 50, 100, 150, and 200 m, as shown in Figure4. A blasting vibration recorder (EXP 3850) and a sensor (CDJ-1) were used to monitor blasting vibrations. Each monitoring point was equipped with a vibration sensor. The sensor must be bonded to the surface of the intact rock with plaster, and the location of the monitoring points must be adjusted appropriately to ensure the accuracy of the measurements. Thus, the distance and azimuth were determined using GPS, as shown in Figure 5.Figure 4
Diagram for location of blasting vibration monitoring.Figure 5
Vibration sensor and GPS.Over the last half century, researchers have proposed several empirical equations to describe the attenuation characteristics of blast vibrations and predict the attenuation of the PPV [26–28]. The PPV equations that have been proposed by different researchers are summarized in Table 2. In most of these equations, the distance from the free face and the maximum charge weight per delay are considered the main parameters influencing PPV prediction. However, is well known that PPV is influenced by other factors, such as the rock strength, rock mass discontinuity conditions, and blast geometry, which have not been explicitly incorporated in these empirical equations. In this study, the Nicholls-United States Bureau of Mines (USBM) empirical equation is used as the prediction equation.Table 2
Empirical PPV predictor presented by different researches.
Name
Equation
Nicholls-USBM
PPV
=
k
Q
1
/
2
/
R
n
General Prediction by Davies
PPV
=
k
R
−
n
Q
a
Langefors and Kihlstrom
PPV
=
k
Q
1
/
2
/
R
1
/
3
n
Bureau of Indian Standard
PPV
=
k
Q
/
R
2
/
3
n
Ambressys–Hendron
PPV
=
k
Q
1
/
3
/
R
n
Ghosh–Daemen predictor
PPV
=
k
R
/
Q
1
/
2
−
n
e
−
α
R
Note. R: distance from the blast area to the vibration monitoring point; Q: maximum charge weight per delay; k, n, a, α: site constants.


## 2.3. Wavelet Packet Analysis Method

Wavelet packet analysis is a time-frequency processing method for a nonstationary random signal. This signal is decomposed into two parts, i.e., the low and high frequencies, using low- and high-pass filters, respectively. The two decomposed signals are then further divided into two parts corresponding to the low and high frequencies. Thus, the signal is continuously decomposed, thereby exhibiting a high-frequency resolution [29]. Analysis of the signal continued to the eighth decomposition level. The signal decomposition process is illustrated in Figure 6. The number of frequency bands in the blasting vibration signals at approximately 2n can be obtained, such that n is the decomposition level of the wavelet packet analysis. If the lowest frequency of the blast vibration signal, st, is 0 and the highest frequency is W, the width of the frequency band at the nth decomposition level will be W/2n.Figure 6
Diagram for signal decomposition process. A stands for low frequency, D stands for high frequency, and the numbers 1, 2, and 3 stands for decomposition levels.Based on the decomposition and reconstruction of the wavelet packet analysis method, the blast vibration signal,st, can be expressed as follows:(1)st=∑j2i−1si,j,where si,j is the reconstructed signal after wavelet packet decomposition, i is the decomposition level, and j is the order number of the frequency bands after decomposition, j=0,1,2,3,…,2i−1.The energy of each reconstructed signal,Ei,j, after wavelet packet decomposition is defined as(2)Ei,j=∫si,jt2dt=∑k=1mxj,k2,where xi,j is the amplitude of the discrete points of the reconstructed signal, m is the number of discrete sampling points, and k is the number of discrete points, k=1,2,3,…,m.The total energy of the analyzed signal,E0, is expressed as follows:(3)E0=∑j=02i−1Ei,j.The ratio of the energy in each frequency band to the total energy can be derived as follows:(4)Pj=Ei,jE0×100%.


## 3. Results and Discussion

Approximately 24 events from 6 blasts were recorded at the Baideng phosphorite open-pit mine, as summarized in Table3. The blasting areas were grouped into two locations: the dolomite bench and the shale bench. Figure 7 shows the velocity histories of the blasting vibration monitoring.Table 3
Summary of the blasting-induced vibration data at Baideng phosphorite.
No.
Dolomite
No.
Shale
JF
Q (kg)
R (m)
PPV (mm/s)
JF
Q (kg)
R (m)
PPV (mm/s)
D1
2.4
100
46
69.799
S1
0.8
75
57
39.461
97
14.713
112
15.026
151
3.771
168
7.815
202
0.963
215
2.231
D2
2.7
96
55
65.726
S2
1.2
87
73
27.564
105
6.285
133
13.566
147
2.168
185
6.258
198
0.884
223
1.083
D3
1.8
98
48
45.739
S3
1.0
80
55
23.216
111
12.218
97
9.843
172
5.375
152
4.761
237
1.832
201
2.926Figure 7
The velocity histories of blasting vibration monitoring. (a) D1. (b) S3.
(a)
(b)


### 3.1. Attenuation Law for the PPV of Blasting Vibration

The relationship between PPV and scaled distance revealed by the blasting vibration test data is shown in Figure8. The PPV of the dolomite and shale decreases steadily with increasing scaled distance. The PPV is larger in the dolomite than in the shale for a constant scaled distance. Lu et al. [30] reported that the total energy of a blast-induced seismic activity is directly proportional to the square of the PPV during the same blasting. Therefore, more explosive energy was converted to rock mass vibration in the dolomite bench than that in the shale bench. The field data were analyzed by regression using the least squares fitting method. The attenuation equations for dolomite (PPVd) and shale (PPVs) are presented as follows:(5)PPVd=3852QR2.57,PPVs=1367QR1.94.Figure 8
Scaled distance versus PPV of different positions at Baideng phosphorite.These relationships indicate that the PPV decays proportionally to1/R2.57 for the dolomite and 1/R1.94 for the shale with increasing distance for a constant explosive charge weight. The relationships also indicate that PPV decreases more rapidly in dolomite than shale.


### 3.2. Attenuation Law of Energy for Blasting Vibration

The sampling rate of the monitoring equipment during the blasting vibration monitoring is 0–4 kHz. Following the Nyquist sampling theory, the highest frequency of the signals being analyzed is 2 kHz. The Daubechies wavelet series exhibits smoothness, compact support, and symmetry compared to a conventional wavelet. This wavelet series has been widely used in the analysis of blasting vibration signals. In this study, the blasting vibration signal was decomposed into nine layers using wavelet packet analysis, and 29 frequency bands were generated in which each frequency band is 2000/29 = 3.90625 Hz.The blast vibration signals underwent decomposition and reconstruction using db5–db10 in the wavelet packet according to Equations (2) and (4), respectively. The errors in the reconstructed signals are listed in Table 4. The statistics in Table 4 indicate that the db8 wavelet packet has the smallest reconstruction error; thus, db8 is used to analyze the time-frequency energy of the signal in Figure 6. The energy distribution of the wavelet packet frequency band for the blasting vibration signals was obtained for the dolomite and shale. The results are listed in Table 5.Table 4
Reconstruction errors of wavelet packet analysis.
dbN
db5
db6
db7
db8
db9
db10
Error value (10−10)
9.896
7.708
4.141
2.537
14.81
15.29Table 5
The wavelet packet frequency band energy distribution for blasting vibration signals.
Frequency band (Hz)
D1
S3
46 (m)
97 (m)
151 (m)
202 (m)
55 (m)
97 (m)
152 (m)
201 (m)
0∼3.90625
2.82E−02
2.42E − 04
3.35E − 03
8.09E − 03
2.37E + 00
4.28E + 00
6.84E + 00
4.01E + 01
3.90625∼7.8125
3.07E − 02
2.03E − 02
1.52E − 02
3.87E − 03
7.39E + 00
1.40E + 01
3.05E + 01
9.76E + 00
7.8125∼11.71875
5.49E − 01
4.38E − 02
2.87E − 03
2.38E − 03
1.62E + 01
3.11E + 01
1.72E + 01
1.29E + 01
11.71875∼15.625
4.95E − 01
3.96E − 02
8.55E − 03
1.75E − 03
4.57E + 01
2.51E + 01
1.78E + 01
3.35E + 01
15.625∼19.53125
5.43E − 01
2.83E − 03
5.62E − 05
6.60E − 06
1.81E + 00
2.06E + 00
1.40E + 00
1.08E − 01
19.53125∼23.4375
1.84E − 01
6.83E − 03
1.06E − 04
1.67E − 05
3.05E + 00
2.90E + 00
3.21E + 00
9.02E − 02
23.4375∼27.34375
1.62E + 00
9.94E − 03
2.61E − 03
2.83E − 04
1.68E + 01
1.55E + 01
1.32E + 01
2.01E + 00
27.34375∼31.25
3.72E − 01
9.32E − 03
5.76E − 04
1.40E − 04
3.37E + 00
2.99E + 00
7.84E + 00
1.27E + 00
31.25∼35.15625
2.01E − 02
7.51E − 05
1.51E − 06
1.80E − 08
1.21E − 02
1.40E − 02
7.85E − 04
8.70E − 03
35.15625∼39.0625
1.28E − 02
1.38E − 04
2.43E − 06
6.44E − 08
2.99E − 02
1.05E − 02
2.57E − 03
1.13E − 02
39.0625∼42.96875
1.50E − 02
1.32E − 03
7.52E − 06
3.91E − 07
1.61E − 01
1.84E − 02
3.10E − 02
8.79E − 02
42.96875∼46.875
1.58E − 02
2.64E − 04
3.95E − 06
2.70E − 07
2.80E − 02
2.02E − 02
1.73E − 02
1.13E − 02
46.875∼50.78125
3.17E − 01
1.09E − 03
1.87E − 05
2.13E − 06
9.40E − 01
8.83E − 01
4.79E − 01
2.45E − 02
50.78125∼101.5625
2.12E − 01
3.70E − 03
3.83E − 05
1.06E − 05
1.86E − 02
1.44E − 03
2.98E − 04
2.97E − 06
101.5625∼203.125
5.74E − 02
1.48E − 04
2.67E − 06
1.64E − 07
1.79E − 03
6.70E − 05
4.79E − 06
1.77E − 06
203.125∼300.78125
3.87E − 03
9.82E − 07
8.22E − 07
6.79E − 08
1.90E − 04
7.50E − 06
6.89E − 07
1.77E − 07
300.78125∼500
1.03E − 02
6.78E − 07
1.65E − 06
1.93E − 07
9.14E − 06
6.71E − 07
3.06E − 08
1.87E − 07
500∼1000
3.86E − 03
4.74E − 06
3.07E − 06
1.62E − 06
9.67E − 08
1.61E − 07
1.08E − 09
1.22E − 07
1000∼2000
2.42E − 03
3.53E − 07
3.21E − 07
1.59E − 06
4.18E − 09
1.60E − 07
4.30E − 10
1.13E − 07The results presented in Table5 indicate that the energy of the blast vibration signal is widely distributed in the frequency band; however, most of the energy is concentrated at 0–50.78125 Hz. The energy ratios for the eight signals at 0–50.78125 Hz that comprise the total energy are 93.537%, 97.24%, 99.867%, 99.91%, 97.88%, 98.94%, 98.52%, and 99.88%. In Figure 9, the time-frequency spectrum distribution is considered in the range of 0–50 Hz to compare the influence of rock properties and propagation distance on the distribution of blasting vibration energy. The main vibration frequencies of the blasting vibration in dolomite and shale at a distance of 50 m from the blast area are 25 and 14 Hz, respectively. The main vibration frequency decreases gradually with increasing distance from the blast area to the vibration monitoring point. The main vibration frequencies of dolomite and shale are less than 5 Hz at a distance from the blast area of 200 m.Figure 9
Time-frequency energy spectrum distributions for blast vibration signals. (a) D1. (b) S3.
(a)
(b)The upper limit of the natural vibration frequency of a ground building is 10 Hz. The energy of the blasting vibration waves is in the range of 0–20 Hz and has an obvious effect on buildings. Therefore, the blasting vibration wave in this study is divided into primary (0–20 Hz) and secondary (20–50 Hz) influence frequency bands, and the energy attenuation law for the different frequency bands is analyzed. The energy of each frequency band is subject to a normalized analysis. The energy attenuation laws for the blasting vibration in different rock masses and frequency bands are shown in Figure10. In Figure 10, at distances of 50–200 m from the blast area to the vibration monitoring point, the attenuation rate for the dolomite and shale blasting is lower in the primary influence frequency band than in the secondary influence frequency band. The attenuation is lower in the shale blasting than in the dolomite blasting for the same frequency band. Figures 9 and 10 show that, in the near-blasting field (less than 50 m), the blasting vibration velocity and vibration energy of dolomite are higher than that of shale, and more vibration energy is distributed in the higher frequency range. In the far-blasting field (more than 50 m), the decay rate of the vibration velocity and energy attenuation of the blasting vibration of dolomite is higher than that of shale. The rock mechanics parameters in Table 1 indicate that the uniaxial compression strength, tensile strength, and elastic modulus of dolomite are higher than that of shale, but the dolomite also had more developed joints than the shale. These results demonstrate that, in the near-blasting field, the vibration attenuation of blasting is mainly affected by the mechanical properties of the rock; with increasing rock strength and elastic modulus, the blasting vibration velocity and vibration energy also increased, which is consistent with the testing results reported by Xu et al. [31]. However, in the far-blasting field, the vibration attenuation of blasting is mainly affected by the structural characteristics of the rock mass; with increasing number of joints in the rock mass, the attenuation rate of the vibration velocity and energy attenuation of blasting vibration increased. Therefore, under geological conditions leading to joint development, the function of the joint should be considered in blasting vibration predictions.Figure 10
The energy attenuation law of different frequency bands.


### 3.3. Development of a New Relationship

For simplicity, the distance from the blast area to the vibration monitoring point (R) and then to the square root of the maximum explosive charge per delay (Q) is called the scaled distance (SD), and their relationship can be expressed as follows:(6)SD=RQ−1/2.The PPV prediction with the Nicholls-USBM equation is written as follows:(7)PPV=kSD−n=kQRn,where k is the attenuation constant and n is the attenuation index.The results shown in Figure10 indicate that the attenuation law of the blasting vibration was affected by the number of joints in the rock mass. The influence of rock mass joints on the attenuation law of the blasting vibration should be considered comprehensively to predict the exact PPV of blasting, and thus the attenuation equation needs to be modified. According to the studies conducted by Simangunsong and Wahyudi [32], the influence of the number of coal seams should be considered in the prediction of blasting vibration. The proposed modified equation for PPV and SD can be expressed as follows:(8)PPV=kSDJF−n=k1+log1+JF×RRQ−n.If JR is 0, then the newSDJF will become the original SD (Equation (6)), in which no influence of the joint plane is considered in the prediction of PPV.A total of 24 ground vibration readings at the Baideng open-pit phosphorite mine are listed in Table2 and were used to examine the relationship between PPV, SD, and SDJF. The results are plotted in Figure 11. The modified equation PPVJF exhibits a better correlation factor (R2) than the original Nicholls-USBM relationship PPV; the correlation factors are 0.85 and 0.80, respectively. The newly modified equation, which considers the effect of joints, demonstrates superior accuracy and applicability for predicting blasting vibration at the Baideng open-pit phosphorite mine.Figure 11
Relationships between PPV and SD andSDJF.In an open-pit minefield, different rock properties are observed between the blasting area and the monitoring point, thereby corresponding to different joint degrees, as shown in Figure12. JF in the different rock masses are expressed by JF1, JF2, …, JFi, and the distances are expressed by R1,R2, …, Ri, respectively. Therefore, Equation (8) can be expressed as follows:(9)PPV=k1+log1+∑JFi⋅RiRQ−n.Figure 12
Schematic diagram of lithology changes between blasting area and monitoring point.A total of 15 vibration readings were obtained from the Baideng open-pit phosphorite mine, in which the blasting areas and monitoring points are located in the different rock masses, i.e., shale and dolomite, as summarized in Table6.Table 6
The blasting vibration data at bench of different rock properties.
No.
Q (kg)
R
s
∗ (m)
R
D (m)
JF
S
JF
D
PPV (mm/s)
PPV
1 (mm/s)
PPV
JF (mm/s)
Difference (%)
PPV
1
PPV
JF
1
1900
57
144
0.5
2.0
8.579
8.551
6.765
0
21
2
660
76
177
1.3
2.7
0.346
1.676
1.231
385
256
3
660
76
122
1.3
2.7
1.554
2.837
2.203
83
42
4
660
76
71
1.3
2.7
8.087
5.379
4.530
33
44
5
500
49
147
1.2
2.3
0.757
2.152
1.747
184
131
6
500
49
203
1.2
2.3
0.467
1.254
0.969
169
108
7
95
5
98
0.9
1.2
5.748
1.440
1.819
75
68
8
3515
102
15
0.5
1.5
61.029
52.937
62.651
13
3
9
3515
136
39
0.5
1.5
18.631
22.293
22.777
20
22
10
1770
150
713
1.0
2.6
0.158
0.346
0.201
120
27
11
830
87
3
0.3
2.4
33.838
19.737
34.558
42
2
12
126
216
114
0.8
1.4
0.149
0.160
0.166
7
12
13
81
134
206
0.5
1.3
0.105
0.093
0.101
11
4
14
81
134
66
0.5
1.3
1.538
0.292
0.381
81
75
15
81
60
10
0.5
1.3
7.521
2.782
5.061
63
33
R
S,D: distances of shale or dolomite; JFS,D: number of joints in shale or dolomite per 10 m; PPV1: predicted PPV by Nicholls-USBM; PPVJF: predicted PPV by modified relationship.The modified equation and Nicholls-USBM empirical equation were then used to predict the PPV of the remaining readings. The results are shown in Figure13, in which the monitored PPV is compared with the predicted results. In Figure 13, the PPV predicted by the modified equation is visually a better fit for the monitoring data than that predicted by the Nicholls-USBM equation. In particular, the prediction results are greater than the monitored data for predicting strong vibrations, which will benefit the analysis of slope stability during blasting. The results demonstrate that the modified equation can be used for predicting the PPV of blasting engineering in the Baideng open-pit phosphorite mine and that the accuracy of the predictions is acceptable.Figure 13
Comparison between predicted and monitored PPV.


## 3.1. Attenuation Law for the PPV of Blasting Vibration

The relationship between PPV and scaled distance revealed by the blasting vibration test data is shown in Figure8. The PPV of the dolomite and shale decreases steadily with increasing scaled distance. The PPV is larger in the dolomite than in the shale for a constant scaled distance. Lu et al. [30] reported that the total energy of a blast-induced seismic activity is directly proportional to the square of the PPV during the same blasting. Therefore, more explosive energy was converted to rock mass vibration in the dolomite bench than that in the shale bench. The field data were analyzed by regression using the least squares fitting method. The attenuation equations for dolomite (PPVd) and shale (PPVs) are presented as follows:(5)PPVd=3852QR2.57,PPVs=1367QR1.94.Figure 8
Scaled distance versus PPV of different positions at Baideng phosphorite.These relationships indicate that the PPV decays proportionally to1/R2.57 for the dolomite and 1/R1.94 for the shale with increasing distance for a constant explosive charge weight. The relationships also indicate that PPV decreases more rapidly in dolomite than shale.


## 3.2. Attenuation Law of Energy for Blasting Vibration

The sampling rate of the monitoring equipment during the blasting vibration monitoring is 0–4 kHz. Following the Nyquist sampling theory, the highest frequency of the signals being analyzed is 2 kHz. The Daubechies wavelet series exhibits smoothness, compact support, and symmetry compared to a conventional wavelet. This wavelet series has been widely used in the analysis of blasting vibration signals. In this study, the blasting vibration signal was decomposed into nine layers using wavelet packet analysis, and 29 frequency bands were generated in which each frequency band is 2000/29 = 3.90625 Hz.The blast vibration signals underwent decomposition and reconstruction using db5–db10 in the wavelet packet according to Equations (2) and (4), respectively. The errors in the reconstructed signals are listed in Table 4. The statistics in Table 4 indicate that the db8 wavelet packet has the smallest reconstruction error; thus, db8 is used to analyze the time-frequency energy of the signal in Figure 6. The energy distribution of the wavelet packet frequency band for the blasting vibration signals was obtained for the dolomite and shale. The results are listed in Table 5.Table 4
Reconstruction errors of wavelet packet analysis.
dbN
db5
db6
db7
db8
db9
db10
Error value (10−10)
9.896
7.708
4.141
2.537
14.81
15.29Table 5
The wavelet packet frequency band energy distribution for blasting vibration signals.
Frequency band (Hz)
D1
S3
46 (m)
97 (m)
151 (m)
202 (m)
55 (m)
97 (m)
152 (m)
201 (m)
0∼3.90625
2.82E−02
2.42E − 04
3.35E − 03
8.09E − 03
2.37E + 00
4.28E + 00
6.84E + 00
4.01E + 01
3.90625∼7.8125
3.07E − 02
2.03E − 02
1.52E − 02
3.87E − 03
7.39E + 00
1.40E + 01
3.05E + 01
9.76E + 00
7.8125∼11.71875
5.49E − 01
4.38E − 02
2.87E − 03
2.38E − 03
1.62E + 01
3.11E + 01
1.72E + 01
1.29E + 01
11.71875∼15.625
4.95E − 01
3.96E − 02
8.55E − 03
1.75E − 03
4.57E + 01
2.51E + 01
1.78E + 01
3.35E + 01
15.625∼19.53125
5.43E − 01
2.83E − 03
5.62E − 05
6.60E − 06
1.81E + 00
2.06E + 00
1.40E + 00
1.08E − 01
19.53125∼23.4375
1.84E − 01
6.83E − 03
1.06E − 04
1.67E − 05
3.05E + 00
2.90E + 00
3.21E + 00
9.02E − 02
23.4375∼27.34375
1.62E + 00
9.94E − 03
2.61E − 03
2.83E − 04
1.68E + 01
1.55E + 01
1.32E + 01
2.01E + 00
27.34375∼31.25
3.72E − 01
9.32E − 03
5.76E − 04
1.40E − 04
3.37E + 00
2.99E + 00
7.84E + 00
1.27E + 00
31.25∼35.15625
2.01E − 02
7.51E − 05
1.51E − 06
1.80E − 08
1.21E − 02
1.40E − 02
7.85E − 04
8.70E − 03
35.15625∼39.0625
1.28E − 02
1.38E − 04
2.43E − 06
6.44E − 08
2.99E − 02
1.05E − 02
2.57E − 03
1.13E − 02
39.0625∼42.96875
1.50E − 02
1.32E − 03
7.52E − 06
3.91E − 07
1.61E − 01
1.84E − 02
3.10E − 02
8.79E − 02
42.96875∼46.875
1.58E − 02
2.64E − 04
3.95E − 06
2.70E − 07
2.80E − 02
2.02E − 02
1.73E − 02
1.13E − 02
46.875∼50.78125
3.17E − 01
1.09E − 03
1.87E − 05
2.13E − 06
9.40E − 01
8.83E − 01
4.79E − 01
2.45E − 02
50.78125∼101.5625
2.12E − 01
3.70E − 03
3.83E − 05
1.06E − 05
1.86E − 02
1.44E − 03
2.98E − 04
2.97E − 06
101.5625∼203.125
5.74E − 02
1.48E − 04
2.67E − 06
1.64E − 07
1.79E − 03
6.70E − 05
4.79E − 06
1.77E − 06
203.125∼300.78125
3.87E − 03
9.82E − 07
8.22E − 07
6.79E − 08
1.90E − 04
7.50E − 06
6.89E − 07
1.77E − 07
300.78125∼500
1.03E − 02
6.78E − 07
1.65E − 06
1.93E − 07
9.14E − 06
6.71E − 07
3.06E − 08
1.87E − 07
500∼1000
3.86E − 03
4.74E − 06
3.07E − 06
1.62E − 06
9.67E − 08
1.61E − 07
1.08E − 09
1.22E − 07
1000∼2000
2.42E − 03
3.53E − 07
3.21E − 07
1.59E − 06
4.18E − 09
1.60E − 07
4.30E − 10
1.13E − 07The results presented in Table5 indicate that the energy of the blast vibration signal is widely distributed in the frequency band; however, most of the energy is concentrated at 0–50.78125 Hz. The energy ratios for the eight signals at 0–50.78125 Hz that comprise the total energy are 93.537%, 97.24%, 99.867%, 99.91%, 97.88%, 98.94%, 98.52%, and 99.88%. In Figure 9, the time-frequency spectrum distribution is considered in the range of 0–50 Hz to compare the influence of rock properties and propagation distance on the distribution of blasting vibration energy. The main vibration frequencies of the blasting vibration in dolomite and shale at a distance of 50 m from the blast area are 25 and 14 Hz, respectively. The main vibration frequency decreases gradually with increasing distance from the blast area to the vibration monitoring point. The main vibration frequencies of dolomite and shale are less than 5 Hz at a distance from the blast area of 200 m.Figure 9
Time-frequency energy spectrum distributions for blast vibration signals. (a) D1. (b) S3.
(a)
(b)The upper limit of the natural vibration frequency of a ground building is 10 Hz. The energy of the blasting vibration waves is in the range of 0–20 Hz and has an obvious effect on buildings. Therefore, the blasting vibration wave in this study is divided into primary (0–20 Hz) and secondary (20–50 Hz) influence frequency bands, and the energy attenuation law for the different frequency bands is analyzed. The energy of each frequency band is subject to a normalized analysis. The energy attenuation laws for the blasting vibration in different rock masses and frequency bands are shown in Figure10. In Figure 10, at distances of 50–200 m from the blast area to the vibration monitoring point, the attenuation rate for the dolomite and shale blasting is lower in the primary influence frequency band than in the secondary influence frequency band. The attenuation is lower in the shale blasting than in the dolomite blasting for the same frequency band. Figures 9 and 10 show that, in the near-blasting field (less than 50 m), the blasting vibration velocity and vibration energy of dolomite are higher than that of shale, and more vibration energy is distributed in the higher frequency range. In the far-blasting field (more than 50 m), the decay rate of the vibration velocity and energy attenuation of the blasting vibration of dolomite is higher than that of shale. The rock mechanics parameters in Table 1 indicate that the uniaxial compression strength, tensile strength, and elastic modulus of dolomite are higher than that of shale, but the dolomite also had more developed joints than the shale. These results demonstrate that, in the near-blasting field, the vibration attenuation of blasting is mainly affected by the mechanical properties of the rock; with increasing rock strength and elastic modulus, the blasting vibration velocity and vibration energy also increased, which is consistent with the testing results reported by Xu et al. [31]. However, in the far-blasting field, the vibration attenuation of blasting is mainly affected by the structural characteristics of the rock mass; with increasing number of joints in the rock mass, the attenuation rate of the vibration velocity and energy attenuation of blasting vibration increased. Therefore, under geological conditions leading to joint development, the function of the joint should be considered in blasting vibration predictions.Figure 10
The energy attenuation law of different frequency bands.


## 3.3. Development of a New Relationship

For simplicity, the distance from the blast area to the vibration monitoring point (R) and then to the square root of the maximum explosive charge per delay (Q) is called the scaled distance (SD), and their relationship can be expressed as follows:(6)SD=RQ−1/2.The PPV prediction with the Nicholls-USBM equation is written as follows:(7)PPV=kSD−n=kQRn,where k is the attenuation constant and n is the attenuation index.The results shown in Figure10 indicate that the attenuation law of the blasting vibration was affected by the number of joints in the rock mass. The influence of rock mass joints on the attenuation law of the blasting vibration should be considered comprehensively to predict the exact PPV of blasting, and thus the attenuation equation needs to be modified. According to the studies conducted by Simangunsong and Wahyudi [32], the influence of the number of coal seams should be considered in the prediction of blasting vibration. The proposed modified equation for PPV and SD can be expressed as follows:(8)PPV=kSDJF−n=k1+log1+JF×RRQ−n.If JR is 0, then the newSDJF will become the original SD (Equation (6)), in which no influence of the joint plane is considered in the prediction of PPV.A total of 24 ground vibration readings at the Baideng open-pit phosphorite mine are listed in Table2 and were used to examine the relationship between PPV, SD, and SDJF. The results are plotted in Figure 11. The modified equation PPVJF exhibits a better correlation factor (R2) than the original Nicholls-USBM relationship PPV; the correlation factors are 0.85 and 0.80, respectively. The newly modified equation, which considers the effect of joints, demonstrates superior accuracy and applicability for predicting blasting vibration at the Baideng open-pit phosphorite mine.Figure 11
Relationships between PPV and SD andSDJF.In an open-pit minefield, different rock properties are observed between the blasting area and the monitoring point, thereby corresponding to different joint degrees, as shown in Figure12. JF in the different rock masses are expressed by JF1, JF2, …, JFi, and the distances are expressed by R1,R2, …, Ri, respectively. Therefore, Equation (8) can be expressed as follows:(9)PPV=k1+log1+∑JFi⋅RiRQ−n.Figure 12
Schematic diagram of lithology changes between blasting area and monitoring point.A total of 15 vibration readings were obtained from the Baideng open-pit phosphorite mine, in which the blasting areas and monitoring points are located in the different rock masses, i.e., shale and dolomite, as summarized in Table6.Table 6
The blasting vibration data at bench of different rock properties.
No.
Q (kg)
R
s
∗ (m)
R
D (m)
JF
S
JF
D
PPV (mm/s)
PPV
1 (mm/s)
PPV
JF (mm/s)
Difference (%)
PPV
1
PPV
JF
1
1900
57
144
0.5
2.0
8.579
8.551
6.765
0
21
2
660
76
177
1.3
2.7
0.346
1.676
1.231
385
256
3
660
76
122
1.3
2.7
1.554
2.837
2.203
83
42
4
660
76
71
1.3
2.7
8.087
5.379
4.530
33
44
5
500
49
147
1.2
2.3
0.757
2.152
1.747
184
131
6
500
49
203
1.2
2.3
0.467
1.254
0.969
169
108
7
95
5
98
0.9
1.2
5.748
1.440
1.819
75
68
8
3515
102
15
0.5
1.5
61.029
52.937
62.651
13
3
9
3515
136
39
0.5
1.5
18.631
22.293
22.777
20
22
10
1770
150
713
1.0
2.6
0.158
0.346
0.201
120
27
11
830
87
3
0.3
2.4
33.838
19.737
34.558
42
2
12
126
216
114
0.8
1.4
0.149
0.160
0.166
7
12
13
81
134
206
0.5
1.3
0.105
0.093
0.101
11
4
14
81
134
66
0.5
1.3
1.538
0.292
0.381
81
75
15
81
60
10
0.5
1.3
7.521
2.782
5.061
63
33
R
S,D: distances of shale or dolomite; JFS,D: number of joints in shale or dolomite per 10 m; PPV1: predicted PPV by Nicholls-USBM; PPVJF: predicted PPV by modified relationship.The modified equation and Nicholls-USBM empirical equation were then used to predict the PPV of the remaining readings. The results are shown in Figure13, in which the monitored PPV is compared with the predicted results. In Figure 13, the PPV predicted by the modified equation is visually a better fit for the monitoring data than that predicted by the Nicholls-USBM equation. In particular, the prediction results are greater than the monitored data for predicting strong vibrations, which will benefit the analysis of slope stability during blasting. The results demonstrate that the modified equation can be used for predicting the PPV of blasting engineering in the Baideng open-pit phosphorite mine and that the accuracy of the predictions is acceptable.Figure 13
Comparison between predicted and monitored PPV.


## 4. Conclusions

In this study, blasting vibration signals were monitored for dolomite and shale blasting areas in the Baideng open-pit phosphorite mine. Moreover, the effect of attenuation laws on the blasting vibration signals in rock masses having different properties was analyzed using the wavelet packet time-frequency analysis method. Based on the results, the following conclusions can be made:(1)
The blasting vibration attenuation coefficient exhibits a clear relationship with the rock mass. The attenuation law coefficient,k, and n for the blasting vibration waves were (3852, 2.57) and (1367, 1.94) at the dolomite and shale blasting areas in the Baideng open-pit mine, respectively. The attenuation rates of the PPV and energy are higher in the dolomite than in the shale.(2)
The blasting vibration signal spectra based on the wavelet packet time-frequency analysis are mainly composed of low frequencies, whereas the spectra of the blasting vibration signals are mainly composed of low frequencies, with the main vibration frequency in the range of 0–50 Hz. The main vibration frequency decreases with increasing distance to the monitoring points.(3)
The degree of development that the rock mass joints have undergone influences the attenuation rate of the PPV, and the PPV attenuation rate is high when the number of joints in the rock mass is high. A new relationship was developed to improve the prediction of PPV in the different rock masses of the open-pit mine by accounting for the degree of development and number of joints in the rock mass.



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*Source: 4603687-2018-10-25.xml*