ORIGINAL ARTICLE

Evaluation of effect of blast design parameters on flyrockusing artificial neural networks

M. Monjezi • A. Mehrdanesh • A. Malek •

Manoj Khandelwal

Received: 22 September 2011 / Accepted: 16 March 2012 / Published online: 3 April 2012

� Springer-Verlag London Limited 2012

Abstract Flyrock, the propelled rock fragments beyond a

specific limit, can be considered as one of the most crucial

and hazardous events in the open pit blasting operations.

Involvement of various effective parameters has made the

problem so complicated, and the available empirical methods

are not proficient to predict the flyrock. To achieve more

accurate results, employment of new approaches, such as

artificial neural network (ANN) can be very helpful. In this

paper, an attempt has been made to apply the ANN method to

predict the flyrock in the blasting operations of Sungun copper

mine, Iran. Number of ANN models was tried using various

permutation and combinations, and it was observed that a

model trained with back-propagation algorithm having 9-5-2-1

architecture is the best optimum. Flyrock were also com-

puted from various available empirical models suggested by

Lundborg. Statistical modeling has also been done to com-

pare the prediction capability of ANN over other methods.

Comparison of the results showed absolute superiority of the

ANN modeling over the empirical aswell as statistical models.

Sensitivity analysis was also performed to identify the most

influential inputs on the output results. It was observed that

powder factor, hole diameter, stemming and charge per delay

are the most effective parameters on the flyrock.

Keywords Flyrock � Blasting � Sungun mine �Artificial neural network � Backpropagation

1 Introduction

Flyrock is defined as the blasting fragmented rocks propelled

beyond a designated area (IME [9]. A large number of human

injuries, fatalities, and property damages in and around the

surface mines are related to flyrock [3, 11]. Inappropriate

blast design is the main cause of the flyrock [10]. Many

studies have been conducted for understanding the phe-

nomenon and recognizing the influential parameters [19, 27].

As a matter of fact, effective parameters on the flyrock can be

grouped into controllable parameters (blast pattern specifi-

cations and explosive type) and uncontrollable parameters

(geo-mechanical characteristics) [26]. As concerned to the

controllable parameters, inadequate burden, high interval

delay timing, insufficient stemming length, deviation in

drilling, large diameter holes and high powder factor are the

main causes of the flyrock. From the uncontrollable param-

eters, presence of loose rocks and geological discontinuities

are considered to be the most important parameters in gen-

erating flyrock [4, 6, 20]. As it is seen, a number of param-

eters are effective in the flyrock incident. In the available

predictive empirical methods, only limited number of the

effective parameters is incorporated, hence the methods may

not be fully applicable to correctly predict flyrock.

In the recent years, artificial neural networks (ANNs), a

subdivision of the artificial intelligence, has widely been

implemented for solving complicated problems such as

prediction of the blasting operation results [2, 16, 17, 22–

24]. High performance of the modeling nonlinear multi-

variable problems has caused the method to be an appli-

cable tool in the field of rock engineering [5].

In this paper, an attempt has been made to establish a

new ANN model to predict blasting flyrock in a copper

mine and to evaluate the effect of blast design parameters

on the incident intensity. Also, the results obtained from

M. Monjezi � A. Mehrdanesh � A. Malek

Department of Mining Engineering, Tarbiat Modares University,

Tehran, Iran

M. Khandelwal (&)

Department of Mining Engineering, College of Technology

and Engineering, Maharana Pratap University of Agriculture

and Technology, Udaipur 313001, India

e-mail: mkhandelwal1@gmail.com

123

Neural Comput & Applic (2013) 23:349–356

DOI 10.1007/s00521-012-0917-2

the ANN modeling was compared with that of the previ-

ously developed empirical models.

2 Case study

Sungun copper mine situated in 38�3802000 north latitude and

46�4503500 east longitude is one the most important copper

deposits in Iran. Containing more than 388 million tons of

copper ore with the average grade of 0.63 %, Sungun mine

can play a vital role in the economics of the country. Domi-

nant geological phenomenon of the Sungun area is a hydro-

thermal intrusion. Mineralization of this porphyry type of

deposit is mostly hosted by altered quartz-monzonite rocks.

While copper is the major product of the mine, molybdenum

can be considered as the by-product.

In the blasting operation of the mine, ANFO is used as the

main explosive, and detonating cord is applied for initiation.

Also, blast holes are stemmed using drill cuttings. Flyrock is

one of the most frequently observed incidents in the blasting

operation. The location of Sungun copper mine in Iran is

shown in Fig. 1.

3 Artificial neural networks

ANN is a computational unit that has been emulated

according to natural neural network of human brains. It is

an information-processing system composed of a number

of fabricated layers that contain some simple elements or

neurons. The neurons of each layer are connected with the

neurons of next layer through connection links which have

a weight that multiplies into the transmitted signal [1, 22,

23]. The interior layer(s) in the network structure is called

hidden layer(s). The number of neurons in the hidden

layer(s) depends on complexity of the problem, whereas

the number of neurons in the first and last layers is equal to

the number of inputs and outputs, respectively. For pre-

diction purpose, the network has to be trained and reach to

an optimum condition with sufficient number of input–

output training pairs. In fact, during the network training,

weight of connection links is determined in a search loop

through sequential calculations. At the end of this step,

examination of the optimum network is performed using

data pairs that were not incorporated in training of the

network [12, 14–16, 21–23, 25]. Figure 2 is a flowchart of

an ANN process [1].

4 Network architecture and model evaluation

A database including 310 data sets was collected as per the

ISRM [8] standard from the Sungun mine blasting opera-

tion and used for neural network modeling. Burden, spac-

ing, charge per delay, hole diameter, hole depth, stemming,

specific drilling, powder factor, and RMR were considered

as the influential parameters (inputs) on flyrock incident

(output). It is well known fact that flyrock is dependent on

blast design, rock, and explosive parameters. So, relevant

and appropriate parameters were selected based on their

influence on flyrock [13]. The relevant parameters, their

respective symbols, and ranges are given in Table 1.

Tables 2 and 3 show the sample data sets for the training

and testing of ANN as well as statistical model.

To select the optimum network, root mean square of

error (RMSE; Eq. 1), mean absolute error (Ea; Eq. 2), and

mean relative error (Er; Eq. 3) value account for (VAF;

Eq. 4) were calculated for various models. The higher the

Fig. 1 Location map of Sungun copper mine

Compare

Target

Input

Assigning connection weights

Fig. 2 Artificial neural network process flowchart [1]

350 Neural Comput & Applic (2013) 23:349–356

123

VAF and obviously the lower the error, the better the

model performance [7] is.

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

N

X

N

i¼1

y� y0ð Þ2v

u

u

t ð1Þ

Ea ¼ y� y0j j ð2Þ

Er ¼y� y0j j

y0

� �

� 100 ð3Þ

VAF ¼ 1� varðy� y0ÞvarðyÞ

� �

� 100 ð4Þ

where, y and y0 are the measured and predicted values,

respectively.

Feed-forward back-propagation neural network was con-

sidered to be appropriate to establish a model for predicting

flyrock. The available data sets were divided into two parts:

training (90 %) and testing (10 %) data sets. Selection of the

testing data sets was managed in such a way that the selected

data sets are representative to all of the recognized patterns in

the database. To find out the best possible network topology, a

number of models were constructed and the model with

maximum accuracy was selected. The parameters including

number of hidden layer(s), number of neurons in each of the

hidden layers, and the applied transfer function are effective in

the model efficiency. As it can be seen from Table 4, a net-

work with architecture 9-5-2-1 with minimum error was found

to be optimum. Figure 3 is a graphical presentation of the

optimum model. To evaluate the model performance, deter-

mination coefficient between the ANN output and actual

flyrock was calculated. As it is seen from Fig. 4, high corre-

lation between predicted and measured values is a sign of the

model efficiency. Also indexes RMSE, Ea, Er, and VAF were

calculated 0.0354, 97.8 %, 0.012 m, and 1.84 %, respec-

tively, which confirm robustness of the applied method.

5 Statistical modeling

The SPSS software, which is widely adopted for standard

statistical analysis, was utilized to develop a relationship

between independent and dependent variables. Equation 5

is the output of SPSS software expressing the flyrock as a

function of relevant parameters as in the ANN.

Flyrock ¼ 121:467� 0:14 � A� 0:346 � Bþ 0:112 � C

þ 10:986 � Dþ 0:919 � E � 46:451 � F

� 34:56 � Gþ 38:604 � H þ 0:621 � I ð5Þ

As shown in Fig. 5, coefficient of determination

between measured and predicted flyrock is 0.883. It can

Table 1 Input parameters for ANN modeling

Type of data Parameter Symbol Range

Input Burden A (m) 2–5

Spacing B (m) 2.5–6.5

Charge per delay C (kg) 10–71.33

Hole diameter D (mm) 76–152

Hole depth E (m) 3–18

Output Stemming F (m) 1.6–4

Specific drilling G (m/m3) 0.09–0.23

Powder factor H (Kg/m3) 0.1–1.29

RMR I 37–47

Flyrock J (m) 10–100

Table 2 Sample training data sets

S.no. RMR Blasthole

diameter (inch)

Depth (m) Spacing (m) Burden (m) st (m) pf (kg/m3) SpD (m/m3) ANFO/delay Fly rock (m)

1 37.00 3.00 5.80 3.50 3.00 2.40 0.24 0.11 6.80 40.00

2 47.00 4.50 5.60 4.00 3.50 2.80 0.44 0.08 16.00 85.00

3 37.00 3.00 6.00 3.50 3.00 2.40 0.18 0.11 6.67 30.00

4 37.00 4.00 6.00 4.50 3.50 2.80 0.24 0.07 7.33 45.00

5 47.00 5.00 11.60 4.50 4.00 3.20 0.50 0.06 19.33 82.00

Table 3 Sample testing data sets

S.no. RMR Blasthole

diameter (inch)

Depth (m) Spacing (m) Burden (m) st (m) pf (kg/m3) SpD (m/m3) ANFO/delay Fly rock (m)

1 37.00 3.00 5.33 3.50 3.00 2.40 0.31 0.11 4.60 55.00

2 47.00 5.00 13.00 4.50 4.00 3.20 0.45 0.06 11.60 85.00

3 47.00 5.50 9.00 6.00 5.00 4.00 0.31 0.04 5.80 30.00

4 47.00 5.50 8.25 5.00 4.50 3.60 0.48 0.05 11.47 64.00

5 37.00 3.00 4.00 3.00 2.00 1.60 0.45 0.19 3.00 100.00

Neural Comput & Applic (2013) 23:349–356 351

123

be said that as compared to the ANN as well as

empirical equations, statistical analysis does not provide

an attractive correlation between the relevant input and

output parameters.

6 Empirical predictors

The most popular flyrock empirical predictors are pre-

sented in Table 5. In this model, d (inch) is the hole

Table 4 Results of a comparison between some of the models

Training algorithm Transfer function Model

architecture

RMSE VAF (%) Ea Er (%)

Scaled conjugate gradient (SCG) LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-2-1 0.0758 89.5654 0.0214 3.345

Scaled conjugate gradient (SCG) LOGSIG-LOGSIG-LOGSIG 9-5-1 0.0495 95.5777 0.0144 2.2518

Scaled conjugate gradient (SCG) LOGSIG-LOGSIG-LOGSIG 9-10-1 0.0606 93.4728 0.0189 2.9647

Scaled conjugate gradient (SCG) LOGSIG-LOGSIG-LOGSIG-TANSIG 9-5-2-1 0.0927 84.7655 0.0293 4.5835

Scaled conjugate gradient (SCG) LOGSIG-LOGSIG-LOGSIG-POSLIN 9-5-2-1 0.1108 79.7987 0.045 7.0524

Scaled conjugate gradient (SCG) LOGSIG-LOGSIG-LOGSIG-PURELIN 9-5-2-1 0.1108 79.7987 0.045 7.0524

Scaled conjugate gradient (SCG) LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0391 97.3914 0.0144 2.2611

BFGS Quasi-Newton (BFG) LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0758 89.5663 0.0214 3.3453

Resilient back propagation (RBP) LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0354 97.804 0.0118 1.8433

Conjugate gradient with Powell/

Beale restarts (CGB)

LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0828 87.9963 0.0276 4.3173

Fletcher-Powell conjugate gradient (CGF) LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0759 89.5622 0.0214 3.3485

Polak-Rebiere conjugate gradient (CGP) LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0759 89.5608 0.0214 3.3466

One-step secant (OSS) LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0758 89.566 0.0214 3.3458

Variable learning rate back

propagation (GDX)

LOGSIG-LOGSIG-LOGSIG-LOGSIG 9-5-2-1 0.0772 89.587 0.026 4.0761

Fig. 3 The optimum network

architecture

352 Neural Comput & Applic (2013) 23:349–356

123

diameter and q (kg/m3) is the powder factor that determine

flyrock (m). The correlation between the predicted and

actual values of flyrock was determined using these equa-

tions, and the results are shown in Figs. 6, 7. As can be

seen from the graphs, prediction capability of these models

is very poor as compared to the ANN and statistical

modeling. Figure 6 also shows that there is no correlation

between predicted and measured flyrock data sets, which

shows that Lundborg [18] equation is not capable to predict

the flyrock in appropriate manner.

7 Results and discussion

Figures 8 and 9 demonstrate the comparison between

measured and predicted flyrock values by different models.

Here, results of Lundborg [18] equations have been dis-

carded due to very high predicted values of flyrock com-

pared to measured values. Figures revealed that results of

ANN are more accurate as compared to statistical and

Lundborg model. Statistical model also shows better pre-

diction capability of flyrock rather than Lundborg et al.

[19] model.

8 Sensitivity analysis

To identify strength of the relations between input and

output parameters, sensitivity analysis was carried out. For

this purpose, cosine amplitude method (CAM) was selec-

ted. In this method, all the relevant data pairs are expressed

in a common X-space. The data array X can be defined as:

X ¼ fx1; x2; . . .; xmg ð6Þ

Each of the elements, xi, in the data array X is a vector of

lengths m, that is:

Xi ¼ fx1m; x2m; . . .; ximg ð7Þ

Thus, each of the data set is a point in m-dimensional

space, where each point requires m-coordinates for a full

Fig. 4 Relationship between actual and predicted flyrock by ANN

Fig. 5 Relationship between actual and predicted flyrock by statis-

tical modeling

Table 5 Empirical flyrock predictors

Predictor Equation

Lundborg [18] Flyrock = 260 9 d2/3

Lundborg et al. [19] Flyrock = 143 9 d 9 (q - 0.2)

Fig. 6 Relationship between actual and predicted flyrock by

Lundborg [18]

Fig. 7 Relationship between actual and predicted flyrock by

Lundborg et al. [19]

Neural Comput & Applic (2013) 23:349–356 353

123

description. Each point of this space has relation with the

final results in a pair wise comparison. The strength of the

relation between the data sets, xi and xj, is expressed by

Eq. 8.

rij ¼Pm

k¼1 xikxjkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Pmk¼1 X2

ik

Pmk¼1 X2

jk

q ð8Þ

As it is observed in the Fig. 10, powder factor, hole

diameter, stemming, and charge per delay are the most

effective parameters on the flyrock, whereas specific

drilling and hole depth are the least effective parameters

in this regard.

9 Conclusions

In this study, ANN method was effectively implemented to

predict the flyrock in the blasting operation of Sungun

copper mine using 9 input parameters. Robustness of the

method over empirical as well as statistical approaches was

examined. Among various types of the networks, it was

found that back-propagation learning algorithm provides

the most desirable environment for model construction. It

was also found that ANN has superiority in predicting

flyrock over Lundborg and statistical models. A model with

architecture 9-5-2-1 having maximum prediction capability

was found to be optimum. Also, sensitivity analysis

Fig. 8 A comparison between

measured and predicted flyrock

by different models

Fig. 9 Bar chart between

measured and predicted flyrock

by different models

354 Neural Comput & Applic (2013) 23:349–356

123

revealed that powder factor, hole diameter, stemming, and

charge per delay are the most effective parameters on the

flyrock, whereas specific drilling and hole depth are the

least effective parameters in this regard.

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