Technical Note

Prediction of blast-induced ground motion in a copper mine

Radojica Lapčević a, Srđan Kostić b,n, Radoje Pantović c, Nebojša Vasović d

a Department of Geotechnics, University of Belgrade Faculty of Mining and Geology, Đušina 7, 11000 Belgrade, Serbiab Department of Geology, University of Belgrade Faculty of Mining and Geology, Đušina 7, 11000 Belgrade, Serbiac Department of Mining Engineering, University of Belgrade Technical Faculty in Bor, Bor, Serbiad Department of Applied Mathematics, University of Belgrade Faculty of Mining and Geology, Đušina 7, 11000 Belgrade, Serbia

a r t i c l e i n f o

Article history:Received 18 September 2013Received in revised form31 December 2013Accepted 15 March 2014

1. Introduction

Drilling and blasting are commonly used rock excavationtechniques within the New Austrian Tunneling Method (NATM),as a method of producing underground space by using all availablemeans to develop the maximum self-supporting capacity of therock itself to provide the stability of the underground opening[1,2]. Even though Tunnel Boring Machines (TBMs) are now usedin many tunneling projects, most underground excavation in rockis still performed using blasting. In the absence of an initial freeface, the solid blasting method is employed for rock excavation.A greater proportion of annual tunnel advance is still achieved bydrilling and blasting [3]. The excavation of orebody “T” was alsoperformed using the NATM method with drilling and blasting,since this technique has an unmatched degree of flexibilityand can overcome the limitations of machine excavations. Unfor-tunately, blast-induced rock damage and overbreak in under-ground construction may result in increasing construction costsand declining stability of the chamber. Considering this, it is ofgreat importance to properly design the blasting operations, inorder to avoid the possible occurrence of rock mass and supportdamage and instability.

In practice, blast-induced ground motion is commonlyexpressed by a peak particle velocity (PPV), estimated using vari-ous empirical ground motion attenuation relations [4–6]. Theseequations are of great interest for engineers, since they enablethem to predict the maximum ground vibration depending on thescaled distance [7–12]. However, considering the fact that anumber of parameters affect the blast induced ground vibrations,empirical attenuation equations are sometimes not suitable for the

design of blasting patterns. In those cases, instead of theseconventional predictors, new techniques such as artificial neuralnetworks (ANN) are being used. Khandelwal and Singh [13]predicted the PPV by ANN, taking into consideration the distancefrom the blast face to monitoring point and explosive charge perdelay. A few years later, the same authors developed a three-layerfeed-forward back-propagation neural network for predicting thePPV and frequency and obtained a much higher coefficient ofdetermination in comparison to the conventional predictors [14].Monjezi et al. [15] also developed a feed-forward back-propaga-tion neural network model, with four input parameters, twohidden layers and one output parameter (PPV). In this case, theaccuracy of prediction by using ANN was much higher (R2¼0.95)in comparison to the conventional predictors or mutlivariateregression analysis (R2¼0.38–0.80).

In this paper, we develop a PPV prediction model for thespecific case study. Even though there are already many groundmotion predictors, which could give a reasonable prediction ofPPV, there is a justified need for updating the existing models byincluding PPV values of new recordings. This arises from the factthat conventional predictors represent only approximate models,which take into consideration a scaled distance as the mostimportant input unit, while the blast-induced ground motiondepends on a wide scale of different influential parameters, suchas total charge, stemming, hole depth, physico-mechanical proper-ties of rock mass and explosive characteristics [14]. The presentedanalysis is done for the recordings of ground vibrations induced byblasting at copper mine Bor in Serbia, during the excavation oforebody “Т”. The blasting was performed at fourteen differentlocations, with a total of 612 blast boreholes, and with maximum12–26 kg charge per delay. The ground vibrations were measuredat three monitoring points, placed at different distances from theexplosive charge.

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journal homepage: www.elsevier.com/locate/ijrmms

International Journal ofRock Mechanics & Mining Sciences

http://dx.doi.org/10.1016/j.ijrmms.2014.03.0021365-1609/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: þ381113219107.E-mail address: srdjan.kostic@rgf.bg.ac.rs (S. Kostić).

International Journal of Rock Mechanics & Mining Sciences 69 (2014) 19–25

2. Geological setting and rock excavation method

Bor mine deposit is one of the largest copper deposits inEurope, with production of almost 5.7 million mt of ore in thefirst six months of 2011 [16]. Several orebodies have been mined atthis site, but currently mining is concentrated in orebody “T”,a relatively small orebody with 200,000 mt of ore, but rich incopper (grading 5%-plus). Production from orebody “T” was10,000 mt/month in 2011 [16].

Orebody “T” is located in the central part of Bor copper mine,at relatively great depth, between 470 and 520 m below thesurface. It is 60 m long, 40 m wide and 45–50 m high [16]. Fromthe geological point of view, wider area is mainly built of theandesites, which are, in general, hydrothermally altered, due tochloritization and kaolinization. Some smaller parts of andesitesare silificated. Tectonically, orebody “T” is located between twolarge fault zones with east–west direction, as shown in Fig. 1.

During 2011, detailed geological and geotechnical analysisshowed that exploitation of this ore body with conventionalmining methods would be associated with higher risk, cost andpotential losses of very rich ore. Therefore, it was suggested thatfurther excavation should be done with complete ensuring ofstability, using the NATM method. In that way, an undergroundchamber of great dimensions was being formed. The ore excava-tion started from the upper zone, with the approach to theexcavated area through the spiral ramp and upper transportationramp. The excavated ore was transported through the verticalshaft to the transportation horizon. The excavation was performedin horizontal layers, about 5 m high, and was conducted from topto bottom in phases (Fig. 2).

Every excavation phase consisted of blasting and successiveinstallation of the support system, with grouted anchors of diffe-rent lengths (9 m, 15 m, 20 m and 25 m), connected with verticalribs and horizontal beams of reinforced concrete, inbetweenwhich a 25 cm thick shotcrete MBB35 is projected, with rein-forcing mesh R503 on both sides of the shotcrete. The excavatedunderground chamber is one of the deepest and biggest chambersin this part of Europe, approximately 50 m high, 40 m long, 50 mwide, and 470–520 m below the surface (Fig. 3).

3. Blasting and field measuring

Field work consisted of (a) blasting, performed at fourteendifferent locations inside the underground chamber and(b) recording of blast-induced ground motion, at three monitoringstations (Fig. 4). Every blasting series consisted of 20–82 horizon-tal boreholes, with two to fifteen boreholes per blasting interval,

Fig. 1. Geological cross-section of the orebody “T”: 1 – pelite and tuff; 2 – weaklysilificated andesite; 3 – silificated andesite; 4 – kaolinized andesite; 5 – chloritizedandesite; 6 – orebody “T”; 7 – orebody “F”; and 8 – old tailings. Red lines denotelarge fault zones. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

Fig. 2. (a) Middle phase of the excavation. The excavated area is approached through the spiral and upper transportation ramps. The excavated ore is transported through thevertical shaft. (b) Excavation phases of orebody “T”. Numbers denote phases of the excavation. Red line denotes the contour of orebody, while the black line denotes theexcavation contour. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

R. Lapčević et al. / International Journal of Rock Mechanics & Mining Sciences 69 (2014) 19–2520

drilled into the side wall of the underground chamber. Maximalamount of explosives per interval was 12–26 kg.

The ground vibrations were registered with 3 accelerometersof D110-T type, with dynamic range of 120 dB, and sensitivitythreshold of 10–1000 Hz. The accelerometer S1 was installed about12 m below the chamber (at �133 m depth), while accelerometersS2 and S3 were installed in the chamber (at �121.5 m and�121.2 m depth, correspondingly). All three accelerometers were

placed on metal platforms, tighten to rock and secured withspecial metal protection from the flying rock remnants (Fig. 5).This step was necessary, since the stability of the recording stationneeded to be secured, in order to obtain the valid data for theanalysis. We are aware of the fact that this acquisition systemwould affect the quality of the results, since the accelerometerswere not directly coupled to rock. However, we assume that theacquired data were recorded precisely enough for this analysis,considering the large registered values of peak particle velocities.

4. Data set

A total of forty-two blast vibration records were used fordevelopment of an ANN model, from which twenty-one data setswere used for training and the rest for the validation and testing ofthe neural network. Different blast parameters collected from thesite are PPV (mm/s), total charge (kg), maximum charge per delay(kg), charge per hole (kg), delay time (s) and distance between theshot point and monitoring station (m).

5. Prediction of peak particle velocity (PPV)

5.1. Prediction of PPV using conventional predictors

In order to justify the development of a new PPV prediction modelby using the ANN approach, first we turn to common empiricalattenuation equations, which represent prediction models for PPV asa function of scaled distance [17]. Various conventional predictorsproposed by different researchers are given in Table 1 [7–12]. Theseequations are developed on the basis of the assumption that the totalenergy of the ground motion generated by blasting varies directlywith the weight of detonated explosives per delay and the distancefrom the blasting shot point.

The site constants were determined from the multiple regres-sion analysis of the forty-two recordings (Table 2).

The relationship between measured and predicted PPV by con-ventional predictor equations is given in Fig. 6. As can be seen, in caseof using conventional predictors for estimating PPV, the coefficientof determination (R2) varies between 0.13 (Langefors–Kihlstrom) and0.31 (General predictor), which could be explained due to uncontrol-lable underground physical conditions and their effect on frag-mentation mechanism [18]. On the other hand, regarding the pastresearches on this subject, the values of R2 above 0.7 indicate that themeasurement data could be used for PPV prediction by deployingthe aforementioned equations [19,20], which is not the case inpresent study.

Fig. 3. Excavated underground chamber with installed support system.

Fig. 4. Distribution scheme of blasting series and measuring stations – bottom ofunderground chamber. Numbers 1–14 denote the distribution of blasting shots,while S1, S2 and S3 stand for the position of measuring stations. Chamber bottomhas irregular shape, indicated by different heights of particular points, denoted asnegative depth below the sea level. Station S1, located in the lower chamber, isshown in the same level with other points, due to simplicity, but with the clearlylower depth (�133 m).

Fig. 5. D110-T type accelerometers at the recording sites S1 (a), S2 (b) and S3 (c).

R. Lapčević et al. / International Journal of Rock Mechanics & Mining Sciences 69 (2014) 19–25 21

5.2. Prediction of PPV using artificial neural network approach (ANN)

Results of the analysis from the previous section indicate thatconventional methods did not give accurate prediction of PPV.

As a next step, we develop a neural network model, by usingthe same approach as in [21] with total charge, maximum chargeper delay, distance from monitoring station to blasting shot,charge per hole and delay times as input parameters, whereasPPV was considered as the single output parameter (Table 3).Stemming and hole depth were the same for all the boreholes(0.5 m and 3 m, correspondingly), so these parameters were notanalyzed.

In the present study, in order to create an adequate ANNmodel forprediction of PPV, a three-layer artificial neural network is used withthe back-propagation training rule optimized by Broyden–Fletcher–Goldfarb–Shannon (BFGS) algorithm and with sigmoid activationfunction. The mathematical summary of the back-propagation learn-ing algorithm is given in [22]. The back-propagation learning algo-rithm for multilayer networks performs a gradient descent in weightspace to search for a minimum of some cost function. A generaldrawback of gradient-based numerical optimization methods is theirslow convergence [23,24]. In learning problems, in particular, onetypically starts a long way from the solution, and spends most of thetime oscillating in weight space, because the gradient is sharp in somedirections, but shallow in others. Consequently, the learning para-meters tend to be selected in an ad-hoc manner, according to theparticular problem and the current performance of the network.We apply the BFGS algorithm, which is considered one of the bestof the quasi-Newton's techniques, that uses a local quadratic approx-imation of the error function, like Newton's method, but employs anapproximation of the inverse of the Hessian matrix to update theweights, thus getting the lowest computational cost. The BFGSalgorithm is error tolerant, yields good solutions and converges in asmall number of iterations [25]. The computational advantage of BFGS

Table 1Conventional predictors.a

Conventional predictor Equation

Duvall and Petkof (USBM) [7] v¼ K½R=ffiffiffiffiffiffiffiffiffiffiffiQmax

p��B

Langefors and Kihlstrom [8] v¼ K½ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðQmax=R

2=3Þq

�BGeneral predictor (Davies et al. [9]) v¼ KR�BðQmaxÞAAmbraseys and Hendron [10] v¼ K½R=

ffiffiffiffiffiffiffiffiffiffiffiQmax

3p

��B

CMRI (Pal Roy [12]) v¼ nþK½R=ffiffiffiffiffiffiffiffiffiffiffiQmax

p��1

a v is the peak particle velocity (PPV) in mm/s, Qmax is the maximum charge perdelay, in kg, R is the distance between the blasting source and vibration monitoringpoint, in meters, and K, B, A and n are site constants.

Table 2Calculated values of site constants.

Equation Site constants

K B A n

Duvall and Petkof (USBM) [7] 114.2 0.08 – –

Langefors and Kihlstrom [8] 97.46 �0.01 – –

General predictor (Davies et al. [9]) 210.46 0.14 �0.077 –

Ambraseys and Hendron [10] 124.8 0.1 – –

CMRI (Pal Roy [12]) 83.09 – – 90.95

Fig. 6. Measured PPV vs. predicted PPV by conventional predictors: (a) USBM, (b) Langefors–Kihlstrom, (c) General predictor, (d) Ambraseys–Hendron, and (e) CMRI. It isclear that each of the predictor gives rather low coefficient of determination, in the range R2¼0.13–0.31.

R. Lapčević et al. / International Journal of Rock Mechanics & Mining Sciences 69 (2014) 19–2522

especially holds for small to moderate sized problems [26], which isthe case in the present analysis.

After analyzing several cases of networks with various numbersof hidden nodes, the most precise model for PPV prediction wasobtained by a neural network with one hidden layer and twentyhidden nodes (Table 4).

In this case, we chose a feed-forward back-propagation neuralnetwork with logistic activation function and BFGS training algo-rithm, as it was already used in [14,15,27]. The total data setcomprising forty-two points has been divided as follows: 50% ofthe data for training (twenty-one recordings), 20% for validation(eight) and the remaining 30% for testing (thirteen).

We are aware of the fact that the analysis of this relatively smalldata set could lead to ambiguous results and interpretations.Common approach usually considers more than a 100 PPVrecordings, in order to obtain reliable results [14,15,28], enabling,in that way, a training of network with larger dataset, which is acrucial step towards the ANN model with high prediction accuracy.However, regarding the application of ANN approach for predic-tion of blasting vibration, the analysis of small data sets is not an

exception. Mohamadnejad et al. [29] examined even smallernumber of data (37) using support vector machine algorithmand regression neural network, obtaining rather high predictionaccuracy (R2¼0.92). Moreover, Monjezi et al. [21] developeda four-layer feed-forward back-propagation neural network, usingonly twenty data sets. In this case, high prediction accuracy wasalso obtained (R2¼0.927).

In order to utilize the most sensitive part of neuron and sinceoutput neuron being sigmoid can only give output between 0 and1, scaling of the output parameter was necessary, and wasperformed in the following way:

scaled value¼max value�unscaled valuemax value� min value

ð1Þ

In this way, numerical values of the analyzed parameter werenormalized in the range of [0,1]. The resulting neural networkmodel with scaled values for training, validation and testing set isshown in Fig. 7(a)–(c), while the same model with scaled, actuallymeasured values is given in Fig. 7(d). Rather high coefficient ofdetermination (R2¼0.916) demonstrates good performance of theproposed network.

6. Evaluation of models performance

If we compare the values of PPV predicted by different methods(conventional predictors and ANN), it is clear that prediction byANN is closer to the measured PPV, while conventional predictorsgive weaker prediction (Fig. 8). Performances of the developedpredictor models were evaluated using different standard statis-tical error criteria given in Table 5 [21]. Calculated statistical errorsare given in Table 6. It is clear that ANN has the lowest valuesof Mean Absolute Percentage Error (MAPE), Variance AbsoluteRelative Error (VARE) and MEDian Absolute Error (MEDAE), whileit has the highest value of Variance Account For (VAF), in com-parison to conventional predictors, which confirms the bestpredictive power of the suggested ANN model.

7. Sensitivity analysis

Sensitivity analysis represents a method that enables us todetermine the relative strength of effect (RSE) for each input uniton the final value of PPV [14,21]. In this case, it was carried out bythe hierarchical analysis [30], where the RSE parameter is deter-mined in the following way:

RSEki ¼ C∑jn

∑jn� 1

:::∑j1WjnkGðekÞWjn� 1 jnGðejn ÞWjn� 2 jn� 1

Gðejn� 1ÞWjn� 3 jn� 2

Gðejn� 2Þ:::Wij1Gðej1 Þ

ð2Þwhere C is normalized constant which controls the maximumabsolute values of RSEki, W is a connected weight, and G(ek)¼exp(�ek)/(1þexp(�ek))2 denotes the hidden units in the n, n�1,n�2,…,1 hidden layers [30].

Global sensitivity analysis, which was carried out for all theinput parameters, indicated that the distance from blasting shotpoint and delay time have the strongest impact on the PPV value(Fig. 9), which compares well with the previous research on thistopic [14,15,21].

8. Conclusions

We developed an artificial neural network model for PPVprediction, on the basis of the recorded ground vibrations inducedby blasting at fourteen different locations, during the excavation oforebody “T” in copper mine Bor in Serbia. The recording was

Table 3Input–output parameters for the ANN training and their range.

Type of data Parameter Range

Inputs Total charge (kg) 40–140Maximum charge per delay, Qmax (kg) 12–26Distance from blasting shot (m) 8–46.7a

Charge per hole (kg) 1.8–2Delay time (ms) 34–500

Output Peak particle velocity (mm/s) 28–1873

a Distance from the shot point to the monitoring stations was determined asthe minimal distance through rock along the edge of the chamber.

Table 4Proposed artificial neural network with various number of hidden nodes.

No. of hiddennodes

Data set Coefficient ofdetermination (R2)

Mean squarederror (MSE)

1 Training 0.645 0.012Validation 0.404 0.025Testing 0.624 0.047

3 Training 0.582 0.024Validation 0.712 0.017Testing 0.484 0.024

5 Training 0.684 0.010Validation 0.604 0.056Testing 0.658 0.022

7 Training 0.717 0.017Validation 0.392 0.042Testing 0.659 0.015

10 Training 0.724 0.015Validation 0.511 0.028Testing 0.648 0.019

12 Training 0.789 0.008Validation 0.539 0.035Testing 0.635 0.036

15 Training 0.769 0.007Validation 0.714 0.033Testing 0.694 0.021

20 Training 0.702 0.001Validation 0.501 0.077Testing 0.916 0.008

25 Training 0.692 0.023Validation 0.610 0.027Testing 0.672 0.054

30 Training 0.994 0.001Validation 0.599 0.013Testing 0.650 0.352

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performed at three different monitoring stations, with a totaldataset of forty-two measurements. Even though the analyzeddataset is relatively small from the perspective of ANN modeling, itrepresents valuable experimental datum that has never been

analyzed in such a manner for any excavated object in Serbia, asfar as the authors are aware.

The conducted analysis showed that, by using conventional equa-tions, a small coefficient of determination is obtained (R2¼0.13–0.31),indicating that these predictors may not be used for the purpose ofunderground blasting, probably due to large recorded values of PPVand complex surface geometry, which could significantly affect theseismic wave propagation. Moreover, structural-tectonic conditions,such as the large fault zones, or the existence of different joint systems,could determine the main propagation direction, which all makes theapplication of conventional predictors even more difficult.

On the other hand, by applying ANN, we developed a predic-tion model with satisfying accuracy (R2¼0.916). We applied theBFGS learning algorithm, which is error tolerant and converges ina small number of iterations. Another advantage of such anapproach is that the selection of hidden layers and number ofneurons in those layers demands no specific theorems, and it isusually obtained by trial and error. Further analysis showed thatANN has the lowest values of statistical error parameters MAPE,VARE, and MEDAE, while it has the highest value of VAF, incomparison to conventional predictors.

As for the influence of input parameters on PPV, globalsensitivity analysis showed that the distance from the blastingshot point and delay time have the strongest impact on the finalvalue of PPV in comparison to the other parameters (maximumcharge per delay, total charge and charge per hole).

Fig. 7. The comparison of the predicted and measured values of PPV for training (a), validation (b) and testing (c) set (scaled values); (d) the same comparison for theunscaled values (testing dataset).

Fig. 8. Comparison of recorded and predicted PPV by using different predictors.Abbreviations AH, GP and LK stand for Ambraseys–Hendron, General Predictor andLangefors–Kihlstrom, respectively. It is clear that ANN gives more accurate predic-tion in comparison to the conventional predicting techniques.

R. Lapčević et al. / International Journal of Rock Mechanics & Mining Sciences 69 (2014) 19–2524

However, even though the results of the analysis are satisfac-tory and encouraging (regarding the predictive power of ANN ina first place) there are still certain questions that remain open. Isthe developed model only valid for the investigated area (“T”orebody, particularly), or could it be used in a general case of blastinduced vibrations during the underground excavation? Also,could the developed model be improved by analyzing a largerdataset? Only in that way, by broadening the presented research,would the prediction power of the suggested model be fullyevaluated.

Acknowledgments

This research was supported by the Ministry of Education,Science and Technological Development of the Republic of Serbia(Grant nos. 36009, 176016 and 171017).

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Table 5Statistical error parameters used for models' evaluation. a

Statistical parameter Equation

Mean absolutepercentage error

MAPE¼ 1n � ∑n

i ¼ 1ti � xiti

��� ���h i� 100

Variance absoluterelative error

VARE¼ 1n � ∑n

i ¼ 1ti � xiti

��� ����mean ti � xiti

��� ���2� �� �

� 100

Median absolute error MEDAE¼medianðti�xiÞVariance account for VAF ¼ 1�var ti � xið Þ

varðti Þ

h i� 100

a ti represents measured value of PPV, while xi denotes predicted value of PPV.

Table 6Statistical errors of different models for predicting PPV.

Model MAPE VARE MEDAE VAF

Duvall and Petkof (USBM) [7] 64.29 57.07 314.22 68.42Langefors and Kihlstrom [8] 63.18 56.50 345.88 70.19General predictor (Davies et al. [9]) 72.00 63.52 353.57 68.05Ambraseys and Hendron [10] 64.46 57.19 326.00 68.57CMRI (Pal Roy [12]) 71.70 62.78 292.95 59.28ANN 16.38 16.07 110.885 91.17

Fig. 9. Relative strength of effect (RSE) of each input parameter on the recordedvalue of PPV, as a result of global sensitivity analysis.

R. Lapčević et al. / International Journal of Rock Mechanics & Mining Sciences 69 (2014) 19–25 25