Abstract
With common horseshoe cavern in underground engineering as the prototype, three singlehole blasting model experiments have been carried out. And coupled SPHFEM approach is adopted for analyzing the limit effect of preexcavated horseshoe cavern on blasting crater. During the experiment, the blasting vibration signals on the top surface of cemented sand model have been recorded. Then HilbertHuang transform has been applied to analyzing the timefrequency characteristics of recorded blasting vibration signals. Both experiment results and numerical cases indicate that the range of blasting crater is controlled effectively by preexcavating horseshoe cavern, and the limit effect of preexcavating on blasting crater has a close connection with its length. Moreover, the 50 mm preexcavated horseshoe cavern presents an amplification effect in blasting vibration effect both along the blasthole direction and perpendicular to the blasthole direction, and it also demonstrates a weaken effect in the main blasting vibration frequency of vertical blasting vibration signal. HHT analyses of vertical blasting vibration signals show that singlehole blasting vibration signals present a centralized distribution in time domain and an uneven distribution in frequency domain. The dominant energy of blasting vibration signal is distributed in several IMF components, where main blasting vibration frequency locates. When cutting the charge, the blasting vibration effect will be reduced, while the main blasting vibration frequency of blasting vibration signal will be increased.
1. Introduction
It is widely acknowledged that engineering blasting is a special method for engineering construction. However, the blasting vibration effect during blasting working is the most drawbacks of the technology and is of great concern to inhabitants in the vicinity of the work [1, 2]. Blasting vibration effect has become an important hazard problem in blasting engineering [3].
Blasting vibration signal analysis is one of the important foundations for studying the control technology of blasting vibration damage. According to the basic features of blasting vibration signal, Ling et al. [4] proposed a new wavelet basis construction method based on separated blasting vibration signal and verified its feasibility by comparing the practical effect with other known wavelets in signal processing. For delay time errors of electric detonators, Han and Ma [5] identified the real delay time in millisecond blasting by timeenergy analysis based on wavelet transform. After analyzing the relation between blasting parameters and blasting vibration signal, it was found that reasonable millisecond delay time could reduce the peak particle velocity of blasting vibration effectively. Zhao et al. [6] studied the timefrequency characteristics of blasting vibration signals in milliseconds by combination of RSPWVD and wavelet. The length of delay time affected the energy distribution of blasting vibration signals and duration of energy in frequency bands. Zhong et al. [7] carried out energy spectrum analysis for blasting vibration signal by wavelet packet analysis technology, and the signals were measured under different explosion parameters, such as the maximal section dose, the distance of blasting source to measuring point and the section number of millisecond detonator. To alleviate blasting vibration effect during vertical shaft excavation, Ma et al. [8] carried out millisecond blasting model experiment with twocircle vertical blastholes based on similarity theory. Zhang et al. [9] applied HilbertHuang transform (HHT) to analyze the blasting vibration signal. It showed that HHT method could draw timefrequency characteristics form blasting vibration signal and was more adaptive than other methods.
At present, geomechanical model experiment has become a significant way to carry out research work for large geotechnical engineering and underground engineering [10, 11]. With common horseshoe cavern in underground engineering as the prototype, three singlehole blasting model experiments have been carried out with cemented sand similar materials according to Froude’s similarity law. Then numerical simulations have been conducted by coupled SPHFEM approach. During the experiment, the blasting vibration effect on the top surface of cemented sand model have been monitored. Then HilbertHuang transform has been applied to analyzing the timefrequency characteristics of recorded blasting vibration signals.
2. Design of singlehole blasting model experiment
2.1. Preparation of cemented sand model
Common horseshoe cavern in underground engineering is selected as the prototype. According to Froude’s similarity law, the geometrical similarity ratio is 25 and the strength similarity ratio is 36. The height and width of practical horseshoe cavern in underground engineering are 3.88 m and 5.00 m respectively. Thus, the corresponding height and width of model horseshoe cavern are 155 mm and 200 mm respectively.
Cemented sand similar material has been used as a material simulating rock to fabricate experimental models with dimensions of 1000 mm×1000 mm×200 mm [12, 13]. Cemented sand similar material is made with sand as aggregate and P.C 32.5 composite Portland cement and gypsum as binder. The mass ratio of sand, Portland cement, gypsum, and water is 1:0.08:0.05:0.10. After curing 21 days, the singlehole blasting model experiments have been carried out. Before the experiment, the compressive strength of cemented sand similar material is tested, its value is 3.44 MPa.
2.2. Experimental scheme of singlehole blasting model
There is only one blasthole in the geometrical center of horseshoe cavern. The diameter and depth of blasthole are 10 mm and 110 mm respectively. During the experiment, only one electric detonator is charge in blasthole, and the rest length of blasthole is filled with mud. Two kinds of electric detonators are used. One is charged with 1.0 g RDX, and the other is charged with 0.3 g RDX. When electric detonator charged with 1.0 g RDX is used, two experiments have been carried out, with or without 50 mm preexcavated horseshoe cavern. When electric detonator charged with 0.3 g RDX is used, one experiment has been carried out with 50 mm preexcavated horseshoe cavern. Experimental scheme of singlehole blasting model is shown in Table 1.
Table 1Experimental scheme of singlehole blasting model
Number of singlehole blasting model  Explosive charge  Length of preexcavated horseshoe cavern 
S1  1.0 g RDX  0 mm 
S2  1.0 g RDX  50 mm 
S3  0.3 g RDX  50 mm 
2.3. Arrangement of blasting vibration measuring points
In the experiment, the blasting vibrations induced by singlehole blasting are propagated in cemented sand similar materials. Three NUBOX6016 intelligent blasting vibration monitors and matching TP3V4.5 threedimensional velocity sensors are applied to record the blasting vibration signals in singlehole blasting model experiments [14]. Three TP3V4.5 threedimensional velocity sensors are placed on the top surface of cemented sand model, which can be seen in Fig. 1. The distance of three TP3V4.5 threedimensional velocity sensors to blasthole are 200 mm, 300 mm, and 400 mm, which are marked as P1, P2, and P3 respectively. In order to record the blasting vibration signals reliably, vaseline is adopted as couplant to fix the TP3V4.5 threedimensional velocity sensors on the top surface of cemented sand model [15]. The highest sampling rate of NUBOX6016 intelligent blasting vibration monitor is 200 kHz, and the maximum achievable sampling rate under floating point mode is 50 kHz. The peak particle velocity range of detectable blasting vibration is from –30 cm/s to +30 m/s. During the experiment, the sample rate and sampling length of NUBOX6016 intelligent blasting vibration monitor are set as 10 kHz and 1.0 s respectively.
Fig. 1Arrangement of blasting vibration measuring points on top surface of model (Unit: mm)
3. Blasting crater of singlehole blasting model
3.1. Blasting carter of model experiments
Three cemented sand models after singlehole blasting experiment are shown in Fig. 2. None cracks have been found on the surface of cemented sand model.
The average crater radius of singlehole blasting model S1 is 136 mm, which is much bigger than the size of model horseshoe cavern. While the blasting craters of both singlehole blasting model S2 and S3 are all in the range of model horseshoe cavern, which indicates that the 50 mm preexcavated horseshoe cavern can control the range of blasting crater effectively.
3.2. Blasting crater of numerical cases
The numerical simulations of singlehole blasting are carried out by using LSDYNA, and the coupled smoothed particle hydrodynamicsfinite element method (SPHFEM) approach is adopted for assessing the blasting results from model experiments [1618]. In the study, SPH is used for explosion charges and near zone in large deformation, while FEM is used for far zone. For the contact interaction of FEs and SPH particles, Tie_nodes_to_surface is adopted for the coupling algorithm. During the calculation, SPH particles are joined with FEs as a single node. Owing to the symmetry about $yz$ plane, only a half of singlehole blasting model is set up, shown in Fig. 3.
Fig. 2Three cemented sand model after singlehole blasting experiment
a) Singlehole blasting model S1
b) Singlehole blasting model S2
c) Singlehole blasting model S3
Fig. 3Coupled SPHFEM model
In order to analyze the limit effect of preexcavated segment on blasting crater, four numerical cases have been performed, shown in Table 2.
Table 2Numerical cases of singlehole blasting model
Number of numerical case  Explosive charge  Length of preexcavated segment 
N1  1.0 g RDX  0 mm 
N2  1.0 g RDX  13.0 mm 
N3  1.0 g RDX  26.1 mm 
N4  1.0 g RDX  48.9 mm 
The material models used in singlehole blasting simulation include explosive (RDX) and cemented sand similar material.
For explosive (RDX), material model Highexplosiveburn and equation of state JonesWilkinsLee (JWL) are used. Parameters of RDX explosive are listed in Table 3.
For cemented sand similar material, material model JohnsonHolmquistConcrete (HJC) is used [19]. Parameters of cemented sand similar material are listed in Table 4.
Table 3Parameters of RDX explosive
$\rho $ / (g·cm^{}^{3})  ${V}_{D}$ / (m·s^{1})  ${P}_{CJ}$ / GPa  $A$ / GPa  $B$ / GPa  ${R}_{1}$  ${R}_{2}$  $\omega $  ${E}_{0}$ / GPa 
1.60  6950  6.125  524  7.678  4.2  1.1  0.34  8.5 
Table 4Parameters of cemented sand similar material
$\rho $ / (g·cm^{}^{3})  $G$ / GPa  ${f}_{c}$ / MPa  ${f}_{t}$ / MPa  $A$  $B$  $C$  $N$  ${S}_{max}$  ${\epsilon}_{min}$ 
1.80  0.931  3.44  0.39  0.79  1.60  0.007  0.61  4.0  0.00146 
${\stackrel{\xb4}{\epsilon}}_{0}$_{}/ s^{1}  ${p}_{c}$_{}/ MPa  ${\mu}_{c}$  ${D}_{1}$  ${D}_{2}$  ${p}_{lock}$ / GPa  ${\mu}_{lock}$  ${K}_{1}$ / GPa  ${K}_{2}$ / GPa  ${K}_{3}$ / GPa 
1.0×10^{}^{6}  1.15  0.000676  0.045  1.0  1  0.1  85  –171  208 
3.3. Effect of preexcavated segment on blasting crater
Taking numerical case N4 as example, the evolution of blasting crater for preexcavated model at different times ($t=$50 μs, 300 μs and 800 μs) are shown in Fig. 4.
Fig. 4Formation of blasting crater for preexcavated model
a)$t=$ 50 μs
b)$t=$ 300 μs
c)$t=$ 800 μs
It can be seen that the blasting crater expands outward equably when explosive detonating. And the initial shape of blasting crater turns to be a sphere. After the explosive stress wave reaches the upper free surface, the shape of blasting crater is changed into an inverted cone for reflected tensile wave. This agrees well with the general recognition about blasting crater [16].
The final shape of blasting crater for four numerical cases are shown seen in Fig. 5. Compared with Fig. 2, numerical results agree well with experiment results.
Seen from Fig. 5, with the length of preexcavated horseshoe cavern increasing, SPH particles in the range of blasting crater are less. Besides the SPH particles below the preexcavated horseshoe cavern, SPH particles near the vault and floor of preexcavated horseshoe cavern in both numerical case N2 and N3 still get a separation velocity. While in numerical case N4, SPH particles with separation velocity are all limited in a certain zone, just below the preexcavated horseshoe cavern. Considering the range and velocity value of SPH particles around preexcavated horseshoe cavern, numerical cases decreases in the following order, numerical case N1, numerical case N2, numerical case N3, and numerical case N4. Therefore, the limit effect of preexcavating on blasting crater has a close connection with its length. While the maximum velocity of SPH particles around explosive presents a weak correlation with length of preexcavated horseshoe cavern.
Combined experiment results and numerical cases, it can be seen that the range of blasting crater in certain explosive charge can be controlled in a limited zone by preexcavating, and its limit effect has a close connection with its length. The longer the preexcavated horseshoe cavern is, the more effective the limit effect of preexcavating on blasting crater is.
Fig. 5Relation between length of preexcavated segment and diameter of blasting crater
a) N1, $t=$ 1000 μs
b) N2, $t=$ 1000 μs
c) N3, $t=$ 1000 μs
d) N4, $t=$ 1000 μs
4. Timefrequency analyses of blasting vibration signals in singlehole blasting
4.1. Blasting vibration signals in singlehole blasting model experiment
During the experiment, blasting vibration signals in three directions have been recorded by TP3V4.5 threedimensional velocity sensors and intelligent blasting vibration monitors. The three directions are along the blasthole direction, perpendicular to the blasthole direction, and vertical direction, which are marked as $x$, $y$, and $z$ respectively in TP3V4.5 threedimensional velocity sensor. Recorded blasting vibration signals in three directions at measuring point P2 of singlehole blasting model S2 is shown in Fig. 6. The peak particle velocity of blasting vibration signals in singlehole blasting model experiments are shown in Table 5.
Seen from Fig. 6 and Table 5, the peak particle velocity of blasting vibration signal in the vertical direction is the biggest in three directions, while the peak particle velocity of blasting vibration signal perpendicular to the blasthole direction is the smallest in three directions. Therefore, the blasting vibration effect order from strong to weak in three direction is vertical direction, along the blasthole direction, and perpendicular to the basthole direction.
When electric detonator charged with 1.0 g RDX is used, the peak particle velocity of blasting vibration signals along the blasthole direction and perpendicular to the blasthole direction for singlehole blasting model S2 are slightly bigger than those for singlehole blasting model S1. Hence, the 50 mm preexcavated horseshoe cavern has an amplification effect in blasting vibration effect both along the blasthole direction and perpendicular to the blasthole direction. While when electric detonator charged with 0.3 g RDX is used, the peak particle velocity of blasting vibration signals in three directions for singlehole blasting model S3 are much smaller than those for singlehole blasting model S2.
Fig. 6Recorded blasting vibration signal at measuring point P2 of singlehole blasting model S2
a) Along the blasthole direction
b) Perpendicular to the blasthole direction
c) Vertical direction
Table 5Peak particle velocity of blasting vibration signals in singlehole blasting model experiments
Number of singlehole blasting model  Measuring point  Peak particle velocity /(cm·s^{1})  
Along the blasthole direction  Perpendicular to the blasthole direction  Vertical direction  
S1  P1  3.142  1.292  – 
P2  4.319  1.021  11.619  
P3  –  –  –  
S2  P1  6.064  1.836  7.100 
P2  5.406  1.550  11.224  
P3  4.091  1.502  5.810  
S3  P1  1.840  0.683  3.794 
P2  1.673  0.748  8.810  
P3  1.734  0.706  5.741 
4.2. Introduction of HilbertHuang transform
As blasting vibration signal is a shorttime nonstationary random signal, several kinds of analyzing methods have been put forward for blasting vibration signal processing, such as Fourier transform, shorttime Fourier transform, wavelet transform, and HilbertHuang transform [20]. HilbertHuang transform (HHT) takes advantage of the local information of a signal at a certain time to obtain its instantaneous information. Therefore, HHT method is a localized time and frequency analysis method, which is more adaptive than wavelet transform [21]. HilbertHuang transform consists of two main parts, empirical mode decomposition (EMD) and Hilbert transform [21].
Firstly, empirical mode decomposition has been carried out for blasting vibration signals. Then a set of intrinsic mode function (IMF) components in frequency order from high to low and a residue are obtained. With the help of fast Fourier transform, the frequency spectra of each IMF component are also achieved.
After empirical mode decomposition, Hilbert transform has been performed for each IMF component. Hence, the instantaneous frequency spectra of IMF components are got. The HHT timefrequency spectrum is achieved by combining all instantaneous frequency spectra.
Taking vertical blasting vibration signals at measuring point P2 as example, HilbertHuang transform has been carried out for three singlehole blasting models to get their timefrequency characteristics.
4.3. Empirical mode decomposition of blasting vibration signals in singlehole blasting
Empirical mode decomposition has been carried out for vertical blasting vibration signals at measuring point P2 of three singlehole blasting models. Then the IMF components of three singlehole blasting models have been obtained. Fig. 7 presents the 11 IMF components with corresponding frequency spectra and one residue of vertical blasting vibration signals at measuring point P2 of singlehole blasting model S1. The Energy percentage and frequency of IMF components of vertical blasting vibration signals at measuring point P2 of three singlehole blasting models are presented in Table 6.
Table 6Energy percentage and frequency of IMF components of vertical blasting vibration signals at measuring point P2 of three singlehole blasting models
IMF components  S1  S2  S3  
$E$ / %  $f$ / Hz  $E$ / %  $f$ / Hz  $E$ / %  $f$ / Hz  
IMF1  41.46  206  29.55  158  32.96  202 
IMF2  47.37  165  34.49  126  20.45  182 
IMF3  5.01  122  16.13  113  24.17  122 
IMF4  1.99  121  11.22  71  11.06  97 
IMF5  2.56  59  3.41  60  1.74  83 
IMF6  0.99  32  3.78  41  6.32  33 
IMF7  0.53  31  0.73  23  1.91  22 
IMF8  0.04  14  0.54  13  0.9  13 
IMF9  0.01  5  0.12  9  0.04  8 
IMF10  0.01  3  0.01  3  0.05  5 
IMF11  0.01  2  0.01  2  0.09  3 
IMF12  –  –  –  –  0.05  2 
Note: 1) IMF1 represents the first IMF component of blasting vibration signal; 2) $E$ is the energy percentage of IMF component to total blasting vibration signal, %; 3) $f$ is the average frequency of IMF component, Hz 
Seen from Fig. 7 and Table 6, the dominant energy of blasting vibration signals are mainly distributed in several IMF components, where main vibration frequency locates. For singlehole blasting model S1, the dominant energy of vertical blasting vibration signal at measuring point P2 is distributed in IMF1 and IMF2. For singlehole blasting model S2 and S3, the dominant energy of vertical blasting vibration signal at measuring point P2 is distributed in IMF1, IMF2, IMF3 and IMF4. However, the energy percentage and frequency band of IMF components are different for singlehole blasting model S2 and S3.
Fig. 7IMF components and frequency spectra of vertical blasting vibration signal at measuring point P2 of singlehole blasting model S2
4.4. Timefrequency spectra of blasting vibration signals in singlehole blasting
After empirical mode decomposition, Hilbert transform has been performed for each IMF component to get instantaneous frequency spectra. Then the HHT timefrequency spectra are obtained by combining all instantaneous frequency spectra. Fig. 8 is the HHT timefrequency spectra of vertical blasting vibration signals at measuring point P2 of three singlehole blasting models. The analyses of IMF component energy distribution and frequency indicates that the frequency domain of blasting vibration signal is within 1000 Hz, thus the frequency range in Fig. 8 is from 0 to 1000 Hz.
Seen from Fig. 8, the HHT timefrequency spectra describe the distribution of blasting vibration signal in both time and frequency domain clearly, which indicates a perfect capacity in localization analyses. Singlehole blasting vibration signals presents a centralized distribution in time domain and an uneven distribution in frequency domain.
Hilbert marginal energy spectra demonstrate the distribution of blasting vibration signal in frequency domain directly [22]. Fig. 9 presents the Hilbert marginal energy spectra of vertical blasting vibration signals at measuring point P2 of three singlehole blasting models. Multipeaks in the Hilbert marginal energy spectra correspond to the main frequencies of blasting vibration signal.
Fig. 8HHT timefrequency spectra of vertical blasting vibration signals at measuring point P2 of three singlehole blasting models
a) Singlehole blasting model S1
b) Singlehole blasting model S2
c) Singlehole blasting model S3
Combining the experiment results in Table 6 and Fig. 9, it can be found that singlehole blasting vibration signals are abundant and distributed unevenly in frequency domain. The dominant energy of blasting vibration signal is distributed in a range of frequency band where main blasting vibration frequency locates. For singlehole blasting model S1, the dominant energy of vertical blasting vibration signal is distributed in frequency band from 165 Hz to 224 Hz, and its main blasting vibration frequency is 209 Hz. For singlehole blasting model S2, the dominant energy of vertical blasting vibration signal is distributed in frequency band from 71 Hz to 158 Hz, and its main blasting vibration frequency is 104 Hz. For singlehole blasting model S3, the dominant energy of vertical blasting vibration signal is distributed in frequency band from 97 Hz to 202 Hz, and its main blasting vibration frequency is 152 Hz. Therefore, the 50 mm preexcavated horseshoe cavern reduces the main blasting vibration frequency of vertical blasting vibration signal. While cutting the charge magnifies the main blasting vibration frequency of vertical blasting vibration signal.
Fig. 9Hilbert marginal energy spectra of vertical blasting vibration signals at measuring point P2 of three singlehole blasting models
a) Singlehole blasting model S1
b) Singlehole blasting model S2
c) Singlehole blasting model S3
5. Conclusions
Both experiment results and numerical cases indicate that the range of blasting crater are controlled effectively by preexcavating horseshoe cavern, and the limit effect of preexcavating on blasting crater has a close connection with its length. The longer the preexcavated horseshoe cavern is, the more effective the limit effect of preexcavating on blasting crater is. Moreover, the 50 mm preexcavated horseshoe cavern presents an amplification effect in blasting vibration effect both along the blasthole direction and perpendicular to the blasthole direction, and it also demonstrates a weaken effect in the main blasting vibration frequency of vertical blasting vibration signal. HHT analyses of vertical blasting vibration signals show that singlehole blasting vibration signals presents a centralized distribution in time domain and an uneven distribution in in frequency domain. Singlehole blasting vibration signals are abundant and distributed unevenly in frequency domain. The dominant energy of blasting vibration signal is distributed in several IMF components, where main blasting vibration frequency locates. When cutting the charge, the blasting vibration effect will be reduced, while the main blasting vibration frequency of blasting vibration signal will be increased.
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About this article
This research was funded by National Natural Science Foundation of China (No. 51174004, No. 51374012). This research was also funded by Open Project Program Foundation of Engineering Research Center of Underground Construction, Ministry of Education (Anhui University of Science and Technology) (No. 2015KF02).
The authors declare no conflict of interest.