Based on wavelet transform, the blasting vibration signals are analyzed here. For millisecond blasting, the blasting effect is mostly affected by the actual delay time. Local characteristics of the analyzed signals could be highlighted by the wavelet transform. The simultaneous initiation of large explosive quantity could be avoided by the use of multistage detonators, while the vibration resistance effect could be better. For the same level of detonator segment, the larger the arranged time interval, the less the possibility of initiation at the same time, which is not conducive to the vibration resistance. Therefore, it is suggested to use high-level detonators with detonating cord or high-precision digital electronic detonators to minimize the initiation error. Furthermore, by identifying the delay time using wavelet transform, the interval delay time of different detonator segments could be obtained. Moreover, the nominal delay time, actual delay time, and interval delay time are further compared and analyzed. It is suggested that the millisecond delay series of detonators should be selected in the whole section blasting, and the segment should be jumped as much as possible, so as to increase the secondary breakage time. Detonators with longer interval delay time should be avoided to the full.
Millisecond blasting is a kind of blasting technology, which is initiated in a certain sequence at millisecond intervals. This technology has been widely used in reducing seismic effect, rationally utilizing explosive energy, reducing explosive unit consumption, and improving blasting fragmentation [
Particularly, reliable electronic detonator has reached the level of practicality, and the delay control error of electronic detonator could be up to microsecond or even zero error. However, the cost of electronic detonator is always 10 times higher than that of ordinary detonator, which makes it still have a long time to be applied in engineering [
Therefore, it is very important to select an appropriate detonator and identify the accurate delay time. Furthermore, the appropriate detonator section and delay time should be selected based on the cross section of the tunnel, the layout of blasting boreholes and geological conditions, and so on [
Let
For any function
According to the inner product theorem, that is, Moyal theory [
Formula (
Here,
For the wavelet transform, the so-called scale
If a certain blasting could be considered as a system, the initiation of each detonator is the process of input energy to the system. In the meantime, a sudden change in the energy density of the system would be inevitably caused by each initiation [
Figure
Layout of blasting holes (mm).
Blasting parameters.
Hole name | Hole no. | Number of holes | Charge quantity | Detonator order | |
---|---|---|---|---|---|
Each hole | Total weight (kg) | ||||
Empty hole | 1 | 1 | 0 | 0.0 | |
Cutting hole | 2–7 | 6 | 5 | 9.0 | 1 |
Auxiliary hole | 8–10 | 3 | 5 | 4.5 | 3 |
Auxiliary hole | 11–12 | 2 | 5 | 3.0 | 5 |
Auxiliary hole | 13–18 | 6 | 4.5 | 8.1 | 7 |
Auxiliary hole | 19–21 | 3 | 4 | 3.6 | 8 |
Auxiliary hole | 22–27 | 6 | 3 | 5.4 | 9 |
Auxiliary hole | 28–32 | 5 | 3 | 4.5 | 10 |
Auxiliary hole | 33–38 | 6 | 2.5 | 4.5 | 11 |
Auxiliary hole | 39–46 | 8 | 2.5 | 6 | 13 |
Peripheral hole | 47–54 | 8 | 2 | 4.8 | 15 |
Peripheral hole | 55–72 | 18 | 1.5 | 8.1 | 19 |
Bottom hole | 74–79 | 6 | 3 | 5.4 | 15 |
Bottom hole | 73–80 | 2 | 3 | 1.8 | 19 |
Total | — | 80 | — | 68.7 |
Blasting vibration waveform can be analyzed intuitively by blasting vibration instrument system. Therefore, the vibration amplitude, main frequency, and duration could be obtained. The intuitive analysis method of blasting vibration signal is to directly analyze the measured waveform and determine the characteristic quantity of blasting vibration from the waveform diagram itself.
A typical blasting vibration signal is selected here to analyze the representative characteristics, as shown in Figure
Blasting vibration waveform.
From the definition of wavelet transform, the time-frequency window of wavelet transform has its uniqueness. It means that only the window position on the time axis of the phase plane is affected by the shifting factor
Millisecond blasting is often applied in engineering blasting, and the number of millisecond detonator sections depends on the specific blasting conditions and purposes. If a certain blasting is considered as a system, the initiation of each detonator is the process of input energy to the system, and the initiation of each detonator will inevitably cause a sudden change of energy in the system. Therefore, the monitored blasting vibration signal could be transformed using the wavelet transform method, and the time of signal mutation can be effectively identified by the modulus maxima of the wavelet transform. That is to say, the initiation time of each detonator in millisecond blasting can be precisely determined by the means mentioned above, and the actual millisecond delay time in blasting could be further confirmed.
For the signal processed by wavelet analysis, how to select an optimal wavelet base is much more important, because results could be various even for the same problem by different wavelet bases. Furthermore, the function with fast attenuation and good similarity between the waveform and the analyzed signal should be chosen as the wavelet basis function. Therefore, the selection of the wavelet basis is closely related to the properties and characteristics of the analyzed signal. Four common waveforms of wavelet basis functions are listed in the following, as shown in Figure
Several common series of wavelet functions.
When choosing a wavelet basis, besides the requirement of compact support, that is, the speed at which the function converges from a finite value to zero, and regularity, which has a great influence on the smoothing effect of signal reconstruction, the curve shape of the wavelet basis is also required to be similar to that of the analyzed signal.
The waveforms of the four main wavelet bases are similar to those of the analyzed signals. However, there is much more information contained in the sym7 and db8 waveforms and the waveforms of the analyzed signals could be matched better with them. That is, the information of the analyzed waveforms reflected by the two waveforms is more accurate.
Furthermore, the waveform of db8 is more consistent with the analyzed signal than that of sym7, and the fluctuation trend of db8 is more similar to that of the analyzed signal. Among these common series of wavelet functions, Daubechies wavelet series have good compactness, smoothness, and approximate symmetry and have been successfully applied to the analysis of nonstationary signal problems, such as blasting.
Therefore, db8 is chosen as the basis function of wavelet analysis for the blasting vibration signal. The original signal is modeled by continuous wavelet transform on scaling factor
Modulus value map by db8 continuous wavelet transform (
Through continuous wavelet transform using db8 wavelet method (scaling factor
The delay time interval of millisecond blasting can be defined as the time interval between the initiation time of two adjacent detonators. Here, for the identified convenience, the time position of the first local singularity point is determined as the initiation time of the lowest detonator segment (MS1). The actual initiation delay interval of each detonator obtained by this method is 43.87 ms, 82.98 ms, 74.5 ms, 30.9 ms, 101.7 ms, 90.2 ms, 73.5 ms, 210 ms, 256.1 ms, and 806.5 ms, respectively, as shown in Table
Initiation time and time interval of each detonator.
Detonator segment | Initiation time (s) | Detonator interval | Delay time interval (ms) |
---|---|---|---|
MS1 | 0.00075 | — | — |
MS3 | 0.04462 | MS1∼MS3 | 43.87 |
MS5 | 0.1276 | MS3∼MS5 | 82.98 |
MS7 | 0.2021 | MS5∼MS7 | 74.5 |
MS8 | 0.233 | MS7∼MS8 | 30.9 |
MS9 | 0.3347 | MS8∼MS9 | 101.7 |
MS10 | 0.4249 | MS9∼MS10 | 90.2 |
MS11 | 0.4984 | MS10∼MS11 | 73.5 |
MS13 | 0.7084 | MS11∼MS13 | 210 |
MS15 | 0.9645 | MS13∼MS15 | 256.1 |
MS19 | 1.771 | MS15∼MS19 | 806.5 |
Wavelet packet analysis can provide a more precise method for signal analysis. Wavelet packet analysis divides the time-frequency plane more carefully, and its resolution to the high-frequency part of the signal is higher than other wavelets. Moreover, it introduces the concept of optimal basis selection on the basis of wavelet analysis theory. According to the characteristics of the signal to be analyzed, dividing the frequency band into several levels, the best basis function is adaptively selected to match the signal, to improve the signal analysis ability.
Referring to the calibrated error intervals of different detonators provided by detonator manufacturers, the above analyzed time points correspond to the detonator segments 1, 3, 5, 7, 8, 9, 10, 11, 13, 15, and 19, respectively. The allowable errors of delay time of each detonator are ±10, ±15, ±20, ±25, ±30, ±35, ±40, ±50, ±60, and ±130, respectively. At the same time, the higher the detonator segment is, the worse the precision is.
Through longitudinal comparison, simultaneous initiation with a large amount of explosive can be avoided using different detonators with multisegments, which reduced the vibration effect better. However, as for a same one detonator segment, the larger the allowable error range of the detonator, the less possibility of simultaneous detonation would naturally occur. That is to say, with the increase of detonator segment, the detonators in the same segment but high section are liable to produce interference and fail to achieve a good vibration reduction effect.
The detonator segment, delay time, and actual time interval of detonators in this test are shown in Table
Detonator deferment stages, deferral times, and actual differential intervals.
Detonator segment | Initial time | Modulus maximum | Notional delay time (ms) | Error ratio of notional delay time | Arranged time interval (ms) | Monitored time interval (ms) | Whether early explosion or refusal |
---|---|---|---|---|---|---|---|
MS1 | 0.00075 | 0.2411 | <13 | — | 0∼13 | 0 | No |
MS3 | 0.04462 | 0.285 | 50 ± 10 | 0.2 | 0∼50 | 43.87 | No |
MS5 | 0.1276 | 0.2324 | 110 ± 15 | 0.1364 | 35∼85 | 82.98 | No |
MS7 | 0.2021 | 0.349 | 200 ± 20 | 0.1 | 55∼125 | 74.5 | No |
MS8 | 0.233 | 0.335 | 250 ± 25 | 0.1 | 5∼95 | 30.9 | No |
MS9 | 0.3347 | 0.3057 | 310 ± 30 | 0.0968 | 5∼115 | 101.7 | No |
MS10 | 0.4249 | 0.3836 | 380 ± 35 | 0.0921 | 5∼135 | 90.2 | No |
MS11 | 0.4984 | 0.4587 | 460 ± 40 | 0.0869 | 5∼155 | 73.5 | No |
MS13 | 0.7084 | 0.4793 | 650 ± 50 | 0.0769 | 100∼280 | 210 | No |
MS15 | 0.9645 | 0.4467 | 880 ± 60 | 0.0682 | 120∼340 | 256.1 | No |
MS19 | 1.771 | 0.3984 | 1700 ± 130 | 0.0765 | 630∼1010 | 806.5 | No |
The relationship between nominal delay time and error ratio of the nominal delay time of detonators is shown in Figure
Nominal delay time and its error ratio.
The relationship between the actual initiation time and the actual interval delay time of detonators is shown in Figure
Initiation time and monitored time interval of detonators.
Therefore, it is suggested to adopt a high-level detonator with detonating cord or a high-precision digital electronic detonator in peripheral holes to minimize the initiation error, in other words, to ensure the same detonator initiation at the same time, especially the high-level detonator segments.
Time intervals of kinds of detonator segments are shown in Figure
Interval delay time under kinds of detonator segments.
Furthermore, it can be seen from Table
The interval time between MS15 and MS19 detonators is 806.5 ms, and the interval time is too long, which leads to a long vibration duration. While the vibration energy accumulation is easy to be produced, it should be avoided to reduce the blasting negative effect.
Therefore, it is suggested that the millisecond delay series of detonators should be selected in the whole section blasting, and the segment should be jumped as much as possible, so as to increase the secondary breakage time. Detonators with longer interval delay time should be avoided to the full.
For millisecond blasting, the blasting effect is mostly affected by the actual delay time. The blasting vibration signals are analyzed using the wavelet transform method to identify the actual delay time, and the following conclusions are obtained here: Using the ability of wavelet transform to highlight the local characteristics of the analyzed signals, the initiation time of detonators can be effectively identified by wavelet transform, and then the actual delay time could be determined. Furthermore, the allowable error of different detonator segments is analyzed. It is considered that the simultaneous initiation of large explosive quantity can be avoided by the use of multistage detonators, and the vibration resistance effect could be better. However, for the same level of detonator segment, the larger the arranged time interval, the less the possibility of initiation at the same time, which is not conducive to the vibration resistance. Therefore, it is suggested to use high-level detonators with detonating cord or high-precision digital electronic detonators to minimize the initiation error, that is, to ensure that the same detonator segment initiates at the same time. By identifying the delay time, the interval delay time of different detonator segments is obtained. The nominal delay time, actual delay time, and interval delay time are further compared and analyzed. It is suggested that the millisecond delay series of detonators should be selected in the whole section blasting, and the segment should be jumped as much as possible, so as to increase the secondary breakage time. And detonators with longer interval delay time should be avoided fully.
The data used to support the findings of this study are available from the corresponding author upon reasonable request.
The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.
This work was supported by the National Natural Science Foundation of China (Grants nos. 51522903 and 51774184), Excellent project Fund in North China University of Technology (Grant no. 216051360020XN199/006), and Scientific Research Fund in North China University of Technology (Grant no. 110051360002).