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Explosives are used as a source of energy to break the rock mass. Majority of explosive energy is lost in the form of ground vibrations, noise, air blasts, etc. Blastinduced ground vibration is influenced by many parameters such as rock mass, explosive characteristics, blast design etc. The prediction of blastinduced ground vibration using regression analysis sometimes becomes too conservative leading difficulties in operating the mine efficiently and safely. Scaled distance approach to vibration prediction is still a very reliable predicting approach, but there are other alternative approaches which produce close results with a high value of correlation coefficient. There are modern tools for analysis and prediction which in many types of research proved to performed with more accuracy. ANN (Artificial Neural Network) is one which in fact is proved by many researchers in their papers to be an excellent prediction method of vibrations. Another method used is an ensemble learning method for classification, regression, and other tasks, that operate by constructing a multitude of decision trees at training time and outputting the class i.e. Random forest method.
In this paper, it has been tried to predict the peak particle velocities for blasts at varying distances with different initiation system using Random forest, ANN, and scaled distance regression analysis approach. The correlation coefficients for each approach for different initiation system is obtained, higher values of correlation coefficients are obtained with increase in accuracy of initiation systems due to increase in actual charge per delay during blasting. Also, it has found that the prediction is more accurate while using ANN along with digital detonators
ANN, random forest, blast induced ground vibration, peak particle velocity, prediction
Despite the benefits of blasting as a reliable excavation technique, the main drawback of this approach lies in the induced ground vibration, which could occasionally affect structural safety during the excavation activities or it could initiate considerable rock damage and over break in underground construction. These adverse side effects of blasting may result in increased construction costs and in declining the structural stability [1]. Having in mind such an unfavorable outcome, it is of paramount importance to adequately predict the magnitude of blastinduced vibrations to avoid the possible occurrence of rock mass failure and support damage. The standard practice uses peak particle velocity (PPV) and spectrum of excitation frequency to estimate structural responses. In practice, PPV is usually estimated using various empirical relations, which are of significant interests for field engineers, since they enable them to predict the maximum ground vibration depending on the maximum charge per delay and distance from the blasting source [2]. In effect, these empirical equations represent various nonlinear relations between the values of PPV on one side, and scaled distance (distance from the explosion charge normalized by the amount of explosive used) [3], on the other side. Indeed, practical application has shown that this socalled ''conventional predictors'' give reasonable predicting values for engineering purposes. However, these empirical relations are typically developed for specific site conditions with particular local geological settings and field morphology and cannot predict PPV value with satisfying accuracy at other blasting locations, mainly due to heterogeneous and anisotropic rock mass properties. This further implies that the suggested ground motion relations could not give reliable estimation of PPV, mainly due to fact that these models are approximate, treating blastinduced ground vibrations dependence only on maximum charge per delay or distance to the blasting source, neglecting a number of other influential parameters, like total charge, stemming, hole depth, physical and mechanical properties of rock mass or explosive characteristics. Since the number of affecting parameters is large and the relations among them could be very complicated and often unknown, empirical methods may not always be suitable for accurate prediction of PPV [4]. Numerical methods are used now a day to predict the vibration produced by blasting by many researchers [5].
As far as numerical methods are concerned, different numerical methods like Artificial neural network [68], Support vector machine [911], Adaptive neurofuzzy interface system(ANFIS) [1213], Monte Carlo technique [14] and many more such methods have been used to predict and control blast induced ground vibration. All these methods use multiple input parameters to get the most suitable relation between input and output parameters. More advanced numerical approaches are related to the analysis of block systems [15]. In such models, systems of simultaneous equations are formulated and solved minimizing the energy of the system to bring the system into equilibrium. [16], Khandelwal et al. and Khandelwal and Singh [17] made use of such useful factors as the rock type, blasting pattern, and explosive type (in addition to factors like the maximum weight of the explosive per delay and the distance between the measuring point and the center of the explosion block) as the input parameters to the ANN to determine the PPV and compared their results with those of similar methods available at the time. [8], studied the effects of the number of blast holes rows on the PPV using the ANN. Bahadori et al. employed GA to improve the correlation coefficient for empirical relations used in the prediction of the PPV. Utilizing the GA Hybrid method, Soltani et al. [8] also predicted the allowable charge weight per delay in blasting operations in the construction of underground structures in Gotvand Olya Dam. Longjun Dong et al. [18] has used random forest algorithm and support vector machine for predicting blastinduced ground vibration.
Here in this paper out of different numerical methods, random forest algorithm, Artificial neural network (ANN) were taken in consideration with the Scaled distance regression analysis approach. All these three methods are applied to predict the blastinduced ground vibration in terms of peak particle velocities. The correlation coefficients for each approach for different initiation system is obtained, based on the values of the correlation coefficients for different initiating system it is found that the use of most precise digital/ electronic detonators in blasting with ANN as predicting tool is most suitable to enhance safety in blasting operations.
The most frequently used initiation systems were considered in this study. They were namely Detonating cord with cord relay, Nonelectric (NONEL) detonators, Electronic detonators Initiation system:
2.1 Detonating cord with cord relay
Detonating cord is a thin, flexible plastic tube usually filled with pentaerythritol tetranitrate (PETN). With the PETN exploding at a rate of approximately 6400 m/s, any common length of detonation cord appears to explode instantaneously. It is a highspeed fuse which explodes, rather than burns, and is suitable for detonating high explosives. The pyrotechnic detonators used with detonating cord shows a high cap scatter percentage and also high blastinduced ground vibrations.
2.2 Nonelectric (nonel) initiation system
A nonelectric detonator is a shock tube detonator designed to initiate explosions, generally for the the demolition of buildings and use in the blasting of rock in mines and quarries. Instead of electric wires, a hollow plastic tube delivers the firing impulse to the detonator, making it immune to most of the hazards associated with stray electric current. It consists of a small diameter, threelayer plastic tube coated on the innermost wall with a reactive, explosive compound, which, when ignited, propagates a low energy signal, similar to a dust explosion. The reaction travels at approximately 6,500 ft/s (2,000 m/s) along the length of the tubing with a minimal disturbance outside of the tube. The design of nonelectric detonators incorporates a patented technology, including the Cushion Disk (CD) and Delay Ignition Buffer (DIB) to provide reliability and accuracy in all blasting applications. Nonelectric detonators were invented by the Swedish company Nitro Nobel in the 1960s and 1970s, under the leadership of PerAnders Persson, and launched to the demolitions market in 1973. Nonel is a contraction of "Nonelectric detonators". The shock wave travels inside the shock tube initiates the pyrotechnic detonator. The pyrotechnic delay detonators with NONEL initiation system show a significant cap scatter.
2.3 Electronic initiation system
In mining, electronic detonators have a better precision for delays. Electronic detonators are designed to provide the precise control necessary to produce accurate and consistent blasting results in a variety of blasting applications in the mining, quarrying, and construction industries. Electronic detonators may be programmed in 1millisecond increments from 1 millisecond to 10,000 milliseconds using the dedicated programming device called the logger. Due to high precision in its timing the cap scatter is too low [19].
Random forest algorithm is a supervised classification algorithm. As the name suggests, this algorithm creates the forest with a number of trees. In general, the more trees in the forest, the more robust the forest looks like. In the same way in the random forest classifier, the higher the number of trees in the forest gives the high accuracy results. Decision tree concept is more to the rulebased system. Given the training dataset with targets and features, the decision tree algorithm will come up with some set of rules (Figure 1). The same set rules can be used to perform the prediction on the test dataset [20].
Advantages:
Figure 1. Pictorial representation of random forest algorithm
Artificial neural networks can be used to extract patterns and detect trends that are too complex to be noticed by humans or computer techniques. They can be used to provide projections of given new situations and answer "what if" questions. ANNs have some other advantages, which include:
There is a broad range of applications that can be found for artificial neural networks (Figure 2). The applications are expanding because artificial neural networks are good at solving problems, not just in
engineering, science, and mathematics, but in medicine, business, finance, and literature as well. Their application to a wide variety of problems in many fields makes them very attractive. Also, faster computers and faster algorithms have made it possible to use artificial neural networks to solve complex industrial problems that formerly required too much computation [21].
Figure 2. Representation of Artificial neural network (ANN) process
In this the multiple input parameters were taken for ANN and Random Forest analysis with a single output. While using ANN, 10 numbers of hidden neurons were selected.Where in random forest 100 number of iterations were performed. The input and output parameters taken for analysis are shown in Table 1 below.
Table 1. Input and output parameters taken for ANN and Random forest analysis
Input parameters are in ANN, and Random forest analysis are 
Output Parameter 


Scaled Distance regression analysis approach was given by USBM [22]. The scaled distance is a concept put forward by using the amount of explosive energy in shock and seismic waves, and the effects by distance. The scaled distance (SD) is derived by combining the distance between the source and measurement points, and the maximum charge per delay. This scaled distance is defined by the equation below:
$S D=D / \sqrt{W}_{d}$ (1)
where SD is the scaled distance (m/kg^{1/2}), D is the absolute distance between the shot and the station (m), and W_{d} is the maximum explosive charge per delay (kg).
The peak level of ground motion at any given point is inversely proportional to the square of the distance from the shot point [16]. The peak particle velocity (PPV) is given by the following equation:
$P P V=K \times(S D)^{n}$ (2)
where K and n are site/ geological constant factors. The site factors are determined from a logarithmic plot of peak particle velocity (PPV) versus scaled distance (SD). The straightline best representing the data has a negative slope n and an intercept K.
In this paper the blastinduced ground vibration data was collected with different initiation system (Electronic initiation, Nonel and Detonating cord with cord relay), actual peak particle velocity (PPV) and blast design parameters were recorded for each. After getting the actual values and blast design parameters, the data collected was processed individually for each initiation system using the random forest algorithm and Artificial Neural Network (ANN). The input data used are blast design parameters, the distance at which the vibration was recorded and maximum charge per delay to get the output of actual PPV values collected. The closest relation between input data and output data (Table 1) were generated with a minimum possible error with each approach (random forest and ANN), and values of PPV were predicted with its correlation coefficient for each initiating system. Also, the scale distance regression analysis is done with different initiations system, and correlation coefficient for the curve is calculated. After applying each approach (Random forest, ANN, and Scaled distance) for different initiation system, the values of correlation coefficient were analyzed to find the effect of accuracy of initiation systems on blastinduced ground vibrations.
6.1 Data collection
The study site (i.e. an opencast (OC) coal mine) is located in an part of Jharia Coalfield in Dhanbad district of Jharkhand (Figure 3). The OC Mine is being worked using shoveldumper combination for removal of (OB), extraction & transportation of coal. The rock strata in the mine area belong to Barakar Formation of Lower Gondwana group under cover of soil, alluvium and sandy soil.
The blastinduced ground vibration was measured by three numbers of MINIMATE PLUS (Instantel Inc. Canada) vibration monitors. These instruments are a microprocessorbased unit having triaxial transducers. The instrument measures Peak Particle Velocity (PPV) in three mutually perpendicular directions, i.e. longitudinal, transversal and vertical along with respective frequencies and amplitude.
Figure 3. Google Earth image of data collection site
The vibration data for each initiation system, i.e. Electronic initiation system, Nonelectric (NONEL) and detonating cord with cord relay were collected. Details of vibration data collected with each initiating system are shown in Table 2 below:
Table 2. Details of vibration data collected at an opencast coal mine
Details of Blast 
Initiation System 

NONEL 
Electronic Delay Detonator 
Detonating Cord 

No. of rounds 
10 
14 
10 
No. of observations 
36 
54 
38 
The depth of drill holes (m) 
4.4 – 5.9 m 
4.3 – 6.4 m 
3.9 – 6.1 m 
The diameter of hole (mm) 
160 
160 
160 
Burden (m) 
3 
3 
3 
Spacing (m) 
3.5 
3.5 
3.5 
Explosive charge/hole (kg) 
27.15 – 42.15 
30.15 – 60.15 
20.15 – 50.15 
Maximum charge/delay (kg) 
42.15 
60.15 
50.15 
Maximum charge/round (kg) 
1634.2 
1986.75 
1949.15 
As discussed above methodology the data collected is processed using Random forest algorithm, Artificial neural network (ANN) and Scaled distance regression analysis approach for each initiating system.
7.1 Detonating cord with cord relay
The vibration data collected were analyzed using the forest, ANN and scaled distance and predicted the of PPV and Correlation coefficient is calculated as shown in Table 3. Also, the analysis using scaled distance, ANN, the forest is shown in Figure 4, Figure 5 and Figure 6 respectively. Figure 4 is a plot between PPV and Scaled Distance as per scaled distance regression analysis which shows the power relation with correlations coefficient of 0.9429. Figure 5 is the representation of training, testing and validation of data using ANN with their correlation coefficients. Figure 6 is the report of random forest algorithms used for prediction of PPV with the collected data od PPV using Dcord.
Figure 4. Scaled distance regression analysis equation using the Detonating cord
Figure 5. Artificial neural network (ANN) analysis for Detonating cord initiation system
Figure 6. Random forest analysis for detonating cord initiation system
The predicted values of PPV using Scaled distance, ANN and random forest algorithm and actual values of PPV recorded for blasts using detonating cord with cord relay is plotted on a same curve in Figure 7.
Figure 7. Comparison curve b/w Actual PPV and RF, ANN, Scaled Distance predicted value for detonating cord
Table 3. The Predicted value of PPV using Random forest, ANN and Scaled distance for detonating cord
PPV Actual 
Predicted PPV 

Using Random Forest (R2 = 0.9534) 
Using ANN (0.9659) 
Using Scaled distance (R2 =0.9429) 

1.769 
3.03 
1.787914 
2.564921 
2.174 
2.851 
2.072367 
2.894409 
2.203 
2.888 
2.177766 
2.956755 
2.25 
2.653 
1.933229 
2.956755 
2.924 
3.582 
2.785779 
3.308113 
3.205 
4.488 
3.287279 
3.647218 
3.304 
3.929 
3.160113 
3.556777 
3.469 
4.104 
3.405996 
3.690769 
3.814 
3.583 
3.748549 
3.840978 
3.829 
4.663 
4.134037 
4.146625 
4.028 
4.516 
5.222822 
4.131416 
4.062 
4.07 
3.825649 
3.7928 
4.325 
3.932 
3.825649 
3.7928 
4.492 
4.688 
4.134037 
4.146625 
4.537 
4.24 
4.324689 
4.168523 
4.581 
4.062 
4.324689 
4.168523 
5.197 
6.561 
4.893068 
4.500235 
5.287 
5.241 
5.293765 
4.549625 
5.293 
5.29 
5.159811 
4.549625 
5.872 
4.745 
5.596651 
4.690787 
6.56 
5.043 
6.098105 
4.997879 
6.92 
8.787 
7.123752 
8.783503 
7.364 
9.142 
6.613665 
8.357367 
8.131 
7.994 
6.979745 
6.303098 
8.655 
9.729 
12.70883 
9.250129 
9.563 
7.255 
9.246324 
7.276709 
9.838 
8.649 
10.32998 
7.966846 
10.29 
9.352 
10.14682 
7.607803 
10.85 
13.224 
10.42117 
7.966846 
11.13 
11.9 
10.73303 
12.4393 
12.35 
11.162 
11.42628 
13.32202 
12.81 
20.314 
18.07711 
14.32341 
16.59 
13.752 
18.19589 
14.32341 
19.46 
15.931 
20.11885 
16.78696 
27.29 
26.063 
26.18906 
32.08309 
28.28 
21.503 
26.53367 
32.08309 
28.84 
25.109 
26.18906 
32.08309 
32.26 
21.355 
27.61853 
37.25097 
The vibration data collected using NONEL initiating system were analyzed using the forest, ANN and scaled distance and predicted of PPV and Correlation coefficient is calculated as shown in Table 4. Also, the analysis using scaled distance, ANN forest is shown in Figure 8, Figure 9 and Figure 10 respectively. Figure 8 is a plot between PPV and Scaled Distance as per scaled distance regression analysis which shows the power relation with correlations coefficient of 0.942. Figure 9 is the representation of training, testing and validation of data using ANN with their correlation coefficients. Figure 10 is the report of random forest algorithms used for prediction of PPV with the collected data od PPV using NONEL initiating system.
Table 4. Predicted value of PPV using Random forest, ANN and Scaled distance for Nonel initiating system
PPV Actual 
Predicted PPV 

Using Random Forest (R2 = 0.9568) 
Using ANN (R2=0.966) 
Using Scaled distance (R2 =0.942) 

2.275 
3.024 
2.439494 
2.711871 
2.376 
3.203 
2.862266 
2.781619 
2.492 
3.005 
2.817177 
2.485645 
2.53 
2.967 
2.483618 
2.781619 
2.658 
2.799 
2.907473 
2.538706 
2.768 
2.839 
2.452363 
2.781619 
2.843 
2.861 
2.552501 
2.854828 
2.965 
3.005 
2.686117 
2.931754 
2.973 
2.85 
2.997327 
2.593942 
3.016 
3.009 
2.899065 
3.097929 
3.061 
2.889 
3.086917 
2.651489 
3.238 
3.219 
3.011483 
3.187838 
3.336 
3.199 
3.11523 
3.282795 
3.522 
3.619 
3.27366 
3.438851 
3.637 
3.318 
3.238019 
3.383228 
3.65 
4.015 
3.591371 
3.783643 
4.006 
4.566 
4.014179 
4.528679 
4.127 
4.102 
4.054218 
4.132002 
4.176 
4.077 
4.220859 
4.287975 
4.229 
4.076 
4.404289 
4.455429 
4.301 
4.389 
4.428307 
4.711864 
4.355 
4.087 
4.831371 
4.830123 
4.529 
5.333 
5.25449 
5.123437 
5.039 
6.033 
5.622193 
5.355612 
5.718 
4.171 
6.22363 
5.268986 
5.842 
6.29 
5.662265 
5.190824 
5.996 
6.335 
6.142596 
5.458222 
6.142 
6.969 
6.726847 
6.780088 
6.361 
6.242 
6.142596 
5.458222 
7.113 
6.744 
6.380642 
5.884761 
7.589 
6.328 
6.896128 
6.187905 
7.925 
6.559 
8.19112 
7.302805 
7.972 
7.528 
8.663334 
7.762889 
9.341 
8.487 
9.184069 
10.63985 
9.808 
8.159 
9.184069 
10.63985 
Figure 8. Scaled distance regression analysis equation using Nonel initiating system
Figure 9. Artificial neural network (ANN) analysis for Nonel initiation system
Figure 10. Random forest analysis for NONEL initiation system
The predicted values of PPV using Scaled distance, ANN and random forest algorithm and actual values of PPV recorded for blasts using NONEL initiating system is plotted on a same curve in Figure 11.
Figure 11. Comparison curve b/w Actual PPV and RF, ANN, Scaled Distance predicted value for NONEL initiating system
The vibration data collected using electronic initiating system were analyzed using forest, ANN and scaled distance and predicted of PPV and Correlation coefficient is calculated as shown in Table 5. Also, the analysis using scaled distance, ANN forest is shown in figure 12, figure 13 and figure 14 respectively. Figure 12 is a plot between PPV and Scaled Distance as per scaled distance regression analysis which shows the power relation with correlations coefficient of 0.9418. Figure 13 is the representation of training, testing and validation of data using ANN with their correlation coefficients. Figure 14 is the report of random forest algorithms used for prediction of PPV with the collected data od PPV using electronic initiations system.
Figure 12. Scaled distance regression analysis equation using the Electronic initiating system
Figure 13. Artificial neural network (ANN) analysis for Electronic initiation system
Table 5. Predicted value of PPV using Random forest, ANN and Scaled distance for Electronic initiating system
PPV Actual 
Predicted PPV 

Using RF (R2 = 0.9793) 
Using ANN (R2= 0.980) 
Using Scaled distance (R2=0.9418) 

1.814 
2.719 
1.863577 
2.313641 
1.836 
2.588 
1.893469 
2.248813 
1.98 
2.682 
1.808023 
2.559409 
2.106 
2.24 
2.41516 
2.593936 
2.195 
2.589 
2.355597 
2.700735 
2.311 
2.909 
2.593305 
2.75085 
2.376 
2.343 
2.279329 
2.628355 
2.413 
2.897 
2.460693 
3.056178 
2.529 
2.913 
2.738952 
2.468794 
2.555 
3.064 
2.67389 
2.410246 
2.63 
2.611 
2.499497 
2.896252 
2.843 
2.521 
2.590475 
2.821858 
2.981 
2.49 
2.557442 
2.618138 
2.992 
2.779 
3.10345 
2.529966 
3.069 
2.81 
3.596864 
2.731044 
3.116 
3.364 
3.378178 
3.048418 
3.253 
3.418 
3.463081 
3.13838 
3.263 
3.126 
2.666989 
3.030064 
3.277 
3.328 
2.590428 
3.42885 
3.319 
3.495 
2.450034 
3.328229 
3.326 
3.453 
3.485032 
3.233261 
3.72 
3.109 
2.471426 
3.42885 
3.772 
3.352 
3.628103 
3.439424 
3.923 
5.192 
4.34306 
4.280846 
4.066 
4.847 
4.750226 
4.64867 
4.697 
4.423 
4.350185 
3.797097 
4.713 
4.675 
4.36847 
3.931638 
5.101 
4.971 
4.918485 
4.228228 
5.348 
5.212 
5.577978 
4.854733 
5.445 
4.829 
5.14294 
4.39214 
5.483 
4.954 
5.429902 
4.64867 
5.561 
5.208 
5.193582 
4.39214 
5.608 
5 
5.886405 
4.960411 
5.849 
6.318 
6.185736 
5.873697 
6.854 
4.466 
6.510324 
5.584686 
7.209 
6.166 
7.495926 
6.540609 
8.149 
8.788 
8.016308 
9.36057 
8.581 
8.464 
8.501341 
10.00748 
8.649 
8.739 
9.000617 
10.74006 
8.966 
10.944 
9.992867 
11.20451 
8.986 
8.811 
9.52164 
11.57576 
9.789 
10.099 
9.575193 
9.598574 
10.29 
9.273 
9.431857 
8.943855 
10.35 
9.549 
9.170657 
8.365697 
10.54 
11.476 
10.83264 
12.53698 
11.57 
10.66 
10.83264 
12.53698 
11.71 
11.985 
11.84679 
13.65298 
11.87 
12.95 
13.54578 
12.53195 
12.36 
11.56 
11.84679 
13.65298 
13.49 
12.423 
12.75992 
11.43506 
13.91 
13.047 
12.75871 
11.43506 
14.12 
11.778 
14.1605 
11.20451 
14.2 
11.85 
14.1847 
12.2019 
14.45 
12.603 
14.80748 
15.40605 
Figure 14. Random Forest (RF) analysis for Electronic initiation system
The predicted values of PPV using Scaled distance, ANN and random forest algorithm and actual values of PPV recorded for blasts using electronic initiating system is plotted on a same curve in Figure 15.
Figure 15. Comparison curve b/w Actual PPV and RF, ANN, Scaled Distance predicted value for Electronic initiating system
The analysis was made for different initiating system, i.e. Detonating cord, Nonel and Electronic initiation system using forest, ANN and Scaled distance regression analysis and the correlation coefficients obtained and presented below in Table 6 and Figure 16 below.
Table 6. Summary of correlation coefficient obtained using Scaled distance (SD), ANN and Random forest (RF) methods for different initiating system
Initiating System 
R2 value with RF 
R2 value with ANN 
R2 value with SD 
ED 
0.9793 
0.980 
0.9418 
NONEL 
0.9568 
0.966 
0.9429 
DF 
0.9534 
0.9659 
0.942 
Figure 16. Values of correlation coefficients obtained with different analysis for different initiation system
With the correlation coefficients obtained between predicted and actual PPV value with Random forest, ANN and scaled distance regression analysis while using different initiation systems, it can be seen that the highest value of correlation coefficient is observed with ANN analysis method. Whereas least value of correlation coefficient is obtained by Scaled distance regression analysis approach. A significant value of correlation coefficient which is higher than Scaled distance regression analysis approach is found using Random forest algorithm.
Further, it can be seen that the highest value of correlation coefficient has been obtained with the Electronic initiation system, and with Detonating cord. This implies that the relation generated by the Random forest method, ANN and Scaled distance method between the input parameters (blast design parameters, the distance at which vibration reading was recorded and maximum charge per delay) and an output parameter (vibration in PPV) is more accurate in case of an Electronic initiation system. This may be attributed to the fact that the measured charge per delay might have been different than the actual charge per delay experienced during blasting due to cap scattering or inaccuracies in firing time of detonators. The maximum charge per delay is more accurate or the actual charge per delay in case of Electronic initiation system. Electronic initiation system is accurate and each hole blasts at their designated time due to very less cap scattering (±0.05%). The value of charge per delay considered for NONEL and Detonating cord initiation system might have been different than the actual charge per delay as the higher cap scattering results overlapping of detonation of holes.
The study conducted in this paper has indicated the following useful inferences.
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