Advanced Analysis of Collision-Induced Blast Fragmentation in V-Type Firing Pattern

Abstract

The firing pattern of blastholes influences the geometric aspects of a blast design in terms of change in blasting burden and spacing. This in turn changes the effective stiffness of a blasthole and confinement of the explosive and aids in better fragmentation. However, during the blasting, the fragments tend to collide and further fragment the rock. In comparison with other patterns, the V-type firing pattern increases the chances of collision between the fragments during flight. The process is scantly documented and accordingly field experiments were conducted using three firing patterns, viz., line, diagonal, and V-type, in a mine with minor variation in rock factor and minor to moderate changes in blast design variables. Sixteen blast design variables such as burden, spacing, charge per hole, in-hole charge density, etc. along with firing pattern were considered for the analysis and fragmentation modeled with the help of surface response analysis and artificial neural networks. The analysis revealed that there is a significant influence of firing patterns on fragmentation. The V-type pattern showed significant reduction in fragment sizes that can be ascribed to in-flight collision processes. A surface response model was developed using advanced ANOVA and resulted in an adjusted R² and RMSE of 0.89, 0.025, respectively. Further, modeling with ANN was attempted that showed better results than ANOVA with R² and RMSE of 0.96 and 0.040 in training, and 0.884 and 0.049 in validation tests. Since, diagonal and V-type patterns have similar design parameters, the reduction in fragment size in the former pattern can be ascribed to the collision of rock fragments during their flight in blasting.

1. Introduction

The objectives of blasting in mining are to ease the excavation operation by obtaining maximum yield through optimum fragment sizes while minimizing the adverse impacts of blasting such as blast-induced ground vibration, air overpressure, flyrock, and noise. To obtain the desired blast results, various blast design variables and factors, viz., burden, spacing, stemming length, type of explosive, powder factor, stiffness ratio, firing pattern, etc. are optimized as per the site-specific requirement. The end purpose of rock blasting in limestone mines, where investigations were carried out, is to produce the desired size feed for a crusher. Fragments produced by blasting should not only be small enough for economic loading of equipment, but should also pass easily through the crusher to realize equipment productivity [1]. To achieve the desired rock fragmentation by blasting, an effective way of determining the blast design variables should be selected [2]. There is ample evidence of the role of fragmentation on the overall mine–mill fragmentation system performance [3,4]. The efficiency of the system through fragmentation optimization is documented by several researchers [5,6,7,8,9,10] and can be achieved only when fragment sizes obtained from the blasting are measured. Therefore, fragmentation measurement of blasted muck piles is essential [11].

To reduce the production cost, the blast design should be revisited to match the cost of the mine–mill fragmentation system (MMFS) that includes unit operations such as drilling, blasting, loading, hauling, or conveying and crushing of primary or secondary nature [4]. In open pit mines, the cost of drilling and blasting operations covers approximately 15–20% of the total mining cost [12,13,14]. An increase in blasting cost reduces the cost of the downstream operations, viz., loading, hauling, crushing, and boulder breaking [3]. This requires the determination of an optimum fragment size range so that the cost of MMFS is optimized. If increasing the cost of blasting operations does not reduce the cost of successive operations, it will not impact the overall economics of the system.

Methods such as blast design evaluation or auditing lead to changes in main blast design variables such as burden, spacing, and stemming, hence, resulting in improved fragmentation and better system performance. One such method involves a change in firing sequence that can be considered as another critical blast design requirement for improving the rock fragmentation [15].

A proper design of the firing pattern, i.e., the delay required between hole to hole and row to row, plays a vital role not only in reducing fragmentation size but also helps to reduce ground vibration as well as back break. To maintain the continuous momentum for the inter-row displacement, a systematic release of the blasting energy is required which can be achieved with a proper burden. An improper delay in multi-row blast gives poor blast results, viz., poor rock fragmentation from the back rows, severe over/under break, large boulders from the collar region of the blasthole, and tight muck pile, etc. [16]. Different types of firing patterns, e.g., line, diagonal, and V-type are used in bench blasting. Each firing pattern has its own application and advantages [17,18]. The change in firing sequence from line firing to diagonal pattern changes the design geometries while blasting. This helps to reduce the blasted burden and increase the spacing and overall actual charge per unit mass of the blasthole. Thus, the effective stiffness and explosive confinement in the blasthole are modified significantly resulting in improved fragmentation particularly in the case of diagonal firing.

The V-type firing pattern has similar blasting design variables except those two limbs of a blast from the center fire towards each other. A distinction between the fragmentation in diagonal and V-type firing patterns should thus account for the fragmentation due to the collision of the fragments while in flight during blasting.

Although V-type and diagonal firing patterns provide a similar effective spacing to burden ratio, the V-type firing pattern is more suitable for achieving smaller fragmentation because it increases the opportunity for in-flight collision between broken rock fragments [15]. This particular characteristic of V-type firing is considered important to reduce fragment size and boulder occurrence within the blasted rock piles [17].

With this hypothesis studies have been conducted to document the reduction in blast fragmentation with V-type firing pattern. The primary focus of this paper is thus to evaluate the influence of in-flight collision between rock fragments on fragmentation and is probably the first of its kind study.

2. Influence of Firing Patterns on Fragmentation

As mentioned earlier, the firing patterns play a vital role in rock fragmentation size during blasting of the rock.

The firing pattern influences the rock fragmentation by following three ways, these are:

• By changing burden and spacing during blasting which is also known as effective burden (B_e) and effective spacing (S_e) or blasting burden and blasting spacing;
• Through possible in-flight collision between rock fragments during blasting and
• a combination of the above two mechanisms.

There are many variations in firing patterns, but the most known firing patterns are:

• Line firing pattern;
• Diagonal firing pattern;
• V-type firing pattern.

The objectives and effect of these patterns on rock fragmentation during blasting are summarized in

Table 1. Line firing pattern (a).

Firing Pattern	Line Firing Pattern (Holes in Same Row Fired Simultaneously)
Representative image
Main objectives	To achieve coarser fragmentation with lesser muck pile throw
Effect of firing pattern on fragmentation	Mb = Md where Mb is the ratio of Se to Be and Md is the ratio of S to B. With this type of firing pattern, effective burden (Be) is equal to the drill burden, which results in no advantage to the firing pattern on fragmentation. In addition, the movement of rock fragments is also in a single direction, with little possibility of inter collision of rock fragments during blasting. However, when rock fragments strike the ground, further fragmentation may take place which is governed by several variables, namely, discontinuities in the initial rock mass, their orientation at the time of impact, physicomechanical properties, incident angle, impact velocity, geometry and stiffness of the ground, and the presence of water [19].

,

Table 2. Line firing pattern (b).

Firing Pattern	Line Firing Pattern (Holes in Same Row Fired Individually, But Firing of Successive Row Starts after Completion of the Preceding Row)
Representative image
Main objectives	To achieve larger fragmentation with more muck pile throw.
Effect of firing pattern on fragmentation	Mb = Md Similar influence on rock fragmentation as provided by line firing pattern given in Table 1.

,

Table 3. Diagonal firing pattern (RHS).

Firing Pattern	Diagonal Firing Pattern (RHS)
Representative image
Main objectives	To achieve coarser and uniform fragmentation with medium muck pile throw.
Effect of firing pattern on fragmentation	Mb < Md Since effective burden (Be) increases than the drill burden (B) during firing, a coarser fragmentation is achieved. Since movement of rock fragments is only in a single direction, this pattern also has little possibility of in-flight collision of rock fragments during blasting.

,

Table 4. Diagonal firing pattern (LHS).

Firing Pattern	Diagonal Firing Pattern (LHS)
Representative image
Main objectives	To achieve medium and uniform fragmentation with medium muck pile throw.
Effect of firing pattern on fragmentation	Mb > Md Since effective burden (Be) decreases than the drill burden (B) during firing, a medium fragmentation is achieved. Since the movement of rock fragments is only in a single direction, this pattern also has little possibility of in-flight collision of rock fragments during blasting.

and

Table 5. V-type firing pattern.

Firing Pattern	V-Type Firing Pattern
Representative image
Main objectives	To achieve smaller and uniform fragmentation with optimum muck pile throw.
Effect of firing pattern on fragmentation	Mb < Md Since effective burden (Be) decreases than the drill burden (B) during firing, a smaller fragmentation is achieved. In addition, it provides in-flight collision of rock fragments during blasting leading to further fragmentation.

M_b = S_e/B_e, M_d = S/B, S = drill spacing, B = drill burden, S_e = effective spacing during blasting, B_e = effective burden during blasting.

.

3. Data Compilation and Analysis

The study was conducted in a limestone mine in India. The deposit belongs to a hilly terrain of the Precambrian age of the Delhi Super Group. The annual production of the mines was 6 MTPa. Compressive strength of limestone varied from 80 to 110 MPa. The mine uses a blasthole diameter of 115 mm. ANFO was used as the explosive having a density of 800 kg/m³ and the average VoD of the explosive measured through continuous in-hole method was 3700 m/s. The charging process of the blasthole is summarized in the following steps:

• Create an air deck at the bottom of the hole with a wooden spacer having a length of 0.75 cm placed first;
• Seal off the gap between the wooden spacer and the blasthole periphery, cut a primer cartridge, and put in the hole;
• Lower the primer cartridge, attached with DTH of 250 ms, into the hole as a base charge;
• Pour the prilled ANFO into the hole as a column charge;
• Stem the blasthole with the help of drill cutting;
• Connect blastholes of the first row with the help of TLD of 25 ms and the blasthole of the second and third row connected with the help of TLD of 42 ms as depicted in the figures given in Table 1, Table 2, Table 3, Table 4 and Table 5.

The blasts were initiated by a shock tube system with a delay sequencing of 17 ms, 25 ms, and 42 ms with a staggered drill hole pattern. The loading operations were performed by front end loader, shovel, and backhoe. The blast muck was transported by 55 MT rear dump trucks.

In order to achieve the objectives of this study, full scale blast trials were conducted in the mines by deploying line firing (L), diagonal firing (D), and V-type firing patterns (V). Other variables of the blast design varied over a narrow range and thus provided a means for comparing fragmentation in the above three firing patterns.

To assess the in-flight collision process between rock fragments during blasting in different firing pattern and its impacts, the following research methods were resorted to:

• Determination of rock type, its strength and variation. Three main types of the rock formations are present in the area which were assigned three values for rock factor (RF);
• Fragmentation analysis of blasted muck pile as explained in

  Table 6. Process of fragmentation assessment by the Fragalyst software.

  Step	Image	Description
  1		Images of muck pile captured with calibrator at different time intervals to cover the all sizes of fragments in the whole muck pile.
  2		Import the image in Fragalyst software.
  3		Calibrate the image by known dimensions of calibrator in software.
  4.1		Edge Deduction process (Boundary)
  4.2		Edge Deduction process (Super Impose)
  4.3		Edge Deduction process (Segmentation)
  5		Fragmentation analysis—the data of Blasted Block Size Distribution (BBSD) i.e., a “3DR.file”, is saved automatically in a folder in which images are kept.

• Data analysis was carried out using Surface response analysis and artificial neural networking methods as explained in the following sections.

Fragmentation Analysis of Blasted Muck Pile

A digital image analysis method using Fragalyst software was used for measurement of fragmentation in all the blasts monitored. The method requires muck pile images with a scale to calculate the size of fragments. The representative images of blasted muck pile, captured at different time intervals during the excavation operation to cover all the sizes of fragmentation in the whole muck pile, were thus taken. The process of fragmentation assessment by Fragalyst software is depicted in Table 6.

Ninety-two full-scale blasts were conducted while monitoring the blast design variables such as burden, spacing and stemming, bench height, specific charge, firing patterns, delay, and mean fragmentation, etc., with one free face availability. The statistics of the data generated are presented in

Table 7. General statistics of the variables measured.

Statistics	Burden (B) (m)	Spacing (S) (m)	Stemming Length (ls) (m)	Bench Height (Hb) (m)	Specific Charge (q) (kg/m3)	Mean Fragmentation Size (k50) (m2)
Mean	2.82	3.86	2.81	9.08	0.48	0.32
Standard Error	0.01	0.02	0.04	0.08	0.00	0.01
Median	2.83	3.91	2.50	9.36	0.48	0.30
Mode	2.80	4.00	2.50	9.85	0.50	0.30
Standard Deviation	0.09	0.18	0.40	0.80	0.04	0.10
Sample Variance	0.01	0.03	0.16	0.63	0.00	0.01
Kurtosis	1.03	0.76	−1.21	1.52	−0.68	1.34
Skewness	-0.44	−1.35	0.43	−1.26	0.16	1.18
Range	0.49	0.65	1.59	3.85	0.16	0.42
Minimum	2.53	3.41	2.00	6.14	0.41	0.20
Maximum	3.03	4.06	3.59	9.99	0.57	0.62
Sum	259.28	354.91	258.49	835.68	44.27	29.19
Count	92.00	92.00	92.00	92.00	92.00	92.00

. The difference in fragment sizes in the three types of firing patterns is evident from Figure 1d, wherein a reduction of around 26% in diagonal and around 45% in the case of the V-type firing pattern is registered in comparison with the fragmentation obtained in the line firing pattern.

Representative images of fragmentation obtained from different firing patterns are provided in Figure 1a–c and the distribution of fragmentation in all the three firing patterns representing the average fragment sizes of all the blasts monitored are plotted in Figure 1d.

The distribution of some important blast design variables along with their ranges is given in Figure 2a–f.

4. Model Development

4.1. Response Surface Analysis (RSA)

The impact of change in firing patterns on rock fragmentation during blasting can be evaluated properly if other variables of blasting are kept constant. However, it is important to note that in bench blasting there are variations in design pattern due to drilling, charging, and measuring errors. Moreover, there are conflicts in some factors and variables that make perfect modeling difficult. To develop an easy-to-use model for rock fragmentation prediction, response surface analysis (RSA) of the data was carried out while using the variables that most influence the fragmentation. The results of the RSA evaluation (

Table 8. Response surface design evaluation results.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	0.5322	7	0.076	106.42	<0.0001
A-A	0.1431	2	0.0715	100.14	<0.0001
B-RF	0.0146	1	0.0146	20.4	<0.0001
C-ρee	0.0161	1	0.0161	22.55	<0.0001
D-B × S	0.0146	1	0.0146	20.44	<0.0001
BC	0.0058	1	0.0058	8.12	0.0055
D2	0.0124	1	0.0124	17.38	<0.0001
Residual	0.0579	81	0.0007
Cor Total	0.59	88

) obtained through multivariate non-linear ANOVA method (

Table 9. ANOVA for the reduced RSA model.

Std. Dev.	0.0267	R2	0.90
Mean	0.3087	Adjusted R2	0.89
C.V. %	8.66	Predicted R2	0.88
		Adequate Precision	38.70

), were finally used in developing the model. A back propagation algorithm being robust in nature was deployed to evaluate the variables over p-value, R², Akaike information criterion (AiCC) and Bayesian information criterion (BiCC), to eliminate insignificant and redundant terms in a quadratic model suggested by the initial analysis.

The Model F-value of 106.42 implies that the model is significant. There is only a 0.01% chance that an F-value this large could occur due to noise and p-values less than 0.0500 indicating that the model terms are significant. In this case, A, B, C, D, BC, and D² (see Table 8 for terms) are significant model terms. Values of p > 0.1000 indicate the model terms are not significant. The modeling results are presented in Table 8.

The Predicted R² of 0.88 is in reasonable agreement with the Adjusted R² of 0.89, i.e., the difference is less than 0.2. Adequate precision, a measure of the signal to noise ratio, should be greater than four. In our case, the ratio of 38.70 indicates an adequate signal. This model can be used to navigate the design space. Several diagnostics were deployed (Figure 3) before accepting the final equation.

The plot of normal probability of externally studentized residuals follows a straight line (Figure 3a) indicating a proper transformation of the output, and that the residuals are within the expected ranges (Figure 3b) with no outliers. The Box-Cox plot for transformation (Figure 3c) confirms the transformation applied to the output, and all the data in the Cook’s distance (Figure 3d) are quite well within the limits. The diagnosis thus points to the well-behaved structure of the design and analysis. The predicted vs. observed plot of the mean fragmentation size (k₅₀) shows that the prediction is quite significant with an adjusted R² of 0.89 and predicted R² of 0.88. Accordingly, the final equation for prediction of mean fragmentation size (k₅₀) in terms of the independent variables is provided in Equation (1).

$$k_{50}=Int.+0.21RF+0.00204{\rho }_{ee}-0.256\left(B\times S\right)+0.0039\left(RF\times {\rho }_{ee}\right)+0.134{\left(B\times S\right)}^2$$

(1)

where Int. is the intercept and equals 0.471 for L, 0.389 for D, and 0.327 for the V-type firing patterns (for other symbols please see abbreviations at the end of this paper).

A comparison of mean fragmentation size predicted by the RSA model given in Equation (1) and measured value is shown in Figure 4 and confirms that the model can be used for mean fragmentation size (k₅₀) prediction.

To ascertain the surface response through the model and the interactions between the variables over space, several iterations were conducted while keeping two variables constant and varying one at a time. The results of such simulations are presented in Figure 5a–i.

Figure 5a–c show the relationship with RF and ρ_ee versus mean fragmentation size (k₅₀) with average (B × S). Similar trends are observed in all three firing patterns. However, there is significant reduction in fragment size despite the constant variables at average (B × S) in case of V-type of firing pattern.

Figure 5d–f shows the influence of RF and (B × S) on the mean fragmentation size (k₅₀) with an average value of ρ_ee and have similar trends of fragment size (k₅₀) irrespective of the type of firing pattern. The figure confirms that the relationship of burden and spacing is not linear with fragmentation and an optimum value is evident for achieving the best possible fragment size. However, a significant change in fragment size is observed in the case of the V-type firing pattern.

The influence of ρ_ee and (B × S) on the mean fragmentation size (k₅₀) with average value of RF is shown in Figure 5g–i. The trends in all the cases of firing patterns are similar, except the size of fragmentation that is varying over the three firing patterns tested. These figures also provide an optimum value of (B × S) at which we can achieve smaller fragmentation with the same value of ρ_ee. There is a marked change in fragment size in the case of diagonal and V-type firing patterns. Distinct trends in the change in fragmentation with variation in (B × S) and ρ_ee are, however, apparent from the figures.

4.2. Fragmentation Prediction Using Artificial Neural Network (ANN)

Artificial neural network (ANN) is a computational method consisting of several processing elements that receive inputs and deliver outputs based on their predefined activation functions. ANN consists of three layers, viz., input layer, the hidden layer, and the output layer. The input layer picks up the input signals and transfers them to the next layer and, finally, the output layer gives the prediction. The neural networks have to be trained with some training data to obtain a solution to a complex process output. The ANN and related methods have a capability to solve complicated problems, especially when the process and results are not fully understood [20]. The case is similar in blasting where the design variables present a complex relationship with rockmass, which in turn has several inconsistencies such as inhomogeneity and anisotropy.

Various algorithms have been suggested for training of the neural network, but the backpropagation algorithm is the most versatile and robust technique and provides the most efficient learning procedure for multy layer perceptron (MLP) networks. An experimental database including enough datasets is required to train the ANN model. Once the training process is completed, prediction can be made for a new input dataset.

Accordingly, to predict rock fragmentation by blasting, a back propagation ANN model was deployed for the data acquired and analyzed earlier by ANOVA. Several iterations were made to find the best possible network and hidden layers. The model that trained well and presented the best results is given in Figure 6. The plot of training progression thus obtained during the process is given in Figure 7.

In the above training process, the network is presented with a pair of patterns: an input pattern and the corresponding desired output pattern. The firing patterns can be treated as a string in the ANN training and therefore it is possible to estimate the mean fragment size from the trained network. The network can be queried for such results and hence compared.

Table 10. Input parameters used for developing the neural network and their ranges.

Input Parameters	Symbols	Ranges
Burden (m)	B	2.53–3.02
Spacing (m)	S	3.41–4.06
Stemming length (m)	ls	2.0–3.59
Bench Height (m)	Hb	6.13–9.98
Sub Drill (m)	lsub	0.0–0.2
Air Decking Length (m)	ldeck	0.0–1.7
Number of holes	Nh	11–27
Number of rows	Nr	2–5
Charge length (m)	lq	3.23–8
Charge/hole (kg)	Qhole	29.75–61.87
Charge/blast (kg)	Qblast	401.21–1246.95
Rock factor	RF	6–8
ρee (kg/m3)	ρee	0.38–0.60
Specific Charge, kg/m3)	q	0.41–0.57
firing pattern	FPat	L = 1, D = 2, V = 3
B × S	-	9.27–12.28

and

Table 11. Output parameter used for developing neural network and their ranges.

Output Parameters	Symbol	Range
Mean Fragmentation size (m)	k50	0.20–0.62

show the input parameters and output parameters with their symbols and range, respectively, considered for developing the neural network. For introducing fragmentation to the network, an image analysis method, i.e., “Fragalyst” software was employed to determine muck pile size distribution. The process of fragmentation assessment by Fragalyst software is illustrated in Table 6. The 50% passing size (k₅₀) was chosen to determine the fragmentation quality. Out of a total of 92 datasets, 73 datasets were used to train the ANN model and 19 separate datasets (not used in training) were utilized for the purpose of validation thus representing the standard 80:20 ratio.

The training results of the ANN model and the validation results are presented in Figure 8a,b respectively. The results of the analysis show R² and RMSE of 0.96 and 0.040 in the case of training and 0.884 and 0.049 in the case of validation tests. The results point to the fact that the ANN method can be well used for the prediction of fragmentation.

In addition to the above, the sum of the absolute weights of the connections from the input node to all the nodes in the first hidden layer defines the importance of the input variables. The relative importance can thus be worked out from such results. The results of such analysis are presented in Figure 9.

There are variables in the above list that can be grouped together or represent explosive distribution in a blasthole such as charge length, stemming length, decking length, and sub-drill length that has a significant contribution to fragmentation. This is probably the reason that some of the variables such as B and S assume less importance in ANN but have retained their importance in RSA when several such variables were combined in a single factor ρ_ee.

5. Conclusions

A hypothesis that there is further breakage by the collision effect during flight of fragments in the blasting process was evaluated in this study. An experimental scheme that presents similar trends in design variables was adopted and comparison was made with the help of fragmentation measured in three types of firing patterns in blasting. The effect of firing patterns on fragmentation were evaluated with the help of 92 blasts in which 12 blasts were taken with a line firing pattern, 36 blasts with diagonal, and 44 blasts with a V-Type firing pattern in a limestone mine. The results acquired showed that there is a significant reduction in fragmentation in the case of the V-Type and diagonal firing patterns, respectively, and counts for 45% and 26% reduction in fragmentation in comparison to that of the line firing pattern and diagonal firing pattern. Since design variables are similar in the case of diagonal and V-type firing patterns, the reduction in fragmentation in the case of the latter pattern can be assigned to the impact of collision.

A surface response model was developed for prediction of the mean fragmentation size (k₅₀) that provided excellent results while using a rock factor with effective energy density in a blasthole and (B × S) as modeling variables. The results of the analysis are provided in the form of models for the three types of firing patterns analyzed which showed significant R² and a strong agreement in adjusted and predicted R².

Further, the ANN method was deployed for assessing the predictability of the fragmentation using a back propagation algorithm and two hidden layers. The model trained well and validation tests yielded significant correlation between the predicted and observed values of mean fragment size of the blasts. Moreover, the importance of blast variables on rock fragmentation was evaluated with the help of ANN analysis in which the firing patterns and rock factor along with the charge distribution in the blasthole assumed higher significance.