BOULDER PREDICTION IN ROCK BLASTING USING ARTIFICIAL NEURAL NETWORK

Transcription

1 BOULDER PREDICTION IN ROCK BLASTING USING ARTIFICIAL NEURAL NETWORK P. Y. Dhekne, Manoj Pradhan, Ravi K. Jade and Romil Mishra Faculty, Department of Mining Engineering, National Institute of Technology, Raipur, India ABSTRACT This paper explains the development of an artificial neural network (ANN) model for estimating the number of boulders resulting from the blasts in Limestone quarries. A number of ANN models are available for prediction of postblast rock fragmentation distribution but none is available to predict boulder count. A data base of three hundred blasts was created for the development of the model. The records in the data base were generated from the blasts carried out in four Limestone quarries which have similar geotechnical set up. These quarries adopt different blast practice. The data base consists of blast design parameters, explosive type and the boulder count. 191records out of three hundred were used to train a two-hidden layer back-propagation neural network model to predict boulder count resulting from the blasts. The boulder count was considered to be a function of nine independent parameters. The ANN program code was developed inmatlabr2012a. The network was trained using Levenberg-Marquardt algorithm as it provides the highest stability and maximum learning speed. The network was extensively analyzed to assess its performance with different transfer functions and the number of hidden layers to estimate the optimum network architecture. 77 data sets were used to validate the results of the trained neural network model and the remaining 32 datasets were used for testing the developed model. Predictions of boulder count by the ANN model were compared with those using a statistical model developed in SPSS statistics It was observed that the prediction capability of the trained neural network model was found to be strong and it provides an easy option to the field engineers to optimize the blast design so that the boulder-count is the minimum. Diversity of the blast data in the similar geotechnical set up is one of the most important aspects of the developed model. The developed neural network model is suitable for practical use at the Limestone quarries having similar geotechnical set up. Keywords: artificial neural network, multiple regression, blasting, rock fragmentation, boulder count. INTRODUCTION Efficiency of the unit operations of quarrying viz. loading, transporting and crushing is the maximum with optimum rock fragmentation. Maximum efficiency minimizes the cost of production. Therefore optimum rock fragmentation is always one of the objectives in any production blasting. Rock fragmentation is said to be optimum if the rock needs no further treatment after the blast. A lot of research has already been conducted on the various aspects of the fragmentation with the sole objective of improving the same [1-2, 4-7, 17, 21-22, 24-31, 34-35, 38, 43,45-49, 51, 61-62, 65-71, 74-75, 78]. It is reported that more than 20 factors affect the blast results [19]. These factors can be grouped in four different categories: rock geotechnical parameters such as density, hardness, compressibility; explosive parameters such as density, velocity of detonation; technical parameters such as delay interval, primer strength and location and geometrical parameters such as burden, spacing, and stemming [3]. A number of empirical models are available to estimate post-blast rock fragmentation resulting from a blast [9-11, 39, 42, 64]. Concept of ANN has been applied to model various aspects of blast-induced ground vibrations [32, 37, 55, 76], air overpressure [72], fly rock [54,57,79], back break [15, 20, 36, 56, 73], powder factor [32-33, 44], estimation of blast geometry [13, 52, 59,77], estimation of an appropriate type of explosive [12], estimation of fragmentation [3, 15-16, 40-41, 50, 53, 58, 63, 80-81] etc. A critical analysis of the models indicates that the modeling using ANN is beneficial in rock blasting where a large number of affecting variables and their complicated mutual dependence sometimes create difficulties in the application of empirical modeling. Outputs of the developed ANN based fragmentation models have been expressed either as the fragment size or as the sieve analysis. Practicing mining engineers not only make use of this form of the output to evaluate the fragmentation but at the same time they are also interested in knowing the boulder count so that they can plan the secondary breakage operations. Extensive literature survey has indicated that no ANN model is available to predict the boulder count. Therefore an ANN model has been developed to predict the boulder count. The data sets required for the development of the model have been generated from the Limestone quarries. DESCRIPTION OF THE SITES The ANN model described in this paper has been developed from the blast records generated from Baikunth, Hirmi, Sonadih and Rawan Limestone quarries. The quarries are situated in Raipur district of Chhattisgarh province of India and are located within a radius of 20 km. The quarries have an overburden which is generally hard Laterite and Clay having a thickness from 4 m to 6 m. The deposits consist of horizontal, thick bedded Stromatolitic Limestone of Raipur Group. Patches of Dolomitic Limestone, Argillaceous Limestone and Shale are found associated with the deposits. The deposits are flat and their thickness ranges from 30 m to 35 m. The deposits are having three sets of joints. The joints are open and are 47

2 having an aperture of 2 mm to 5 mm. The joint surface is rough. The geotechnical properties of the deposits are summarized in Table-1. Name of the quarry Table-1. Geotechnical properties of limestone deposits (*Mean values). Uniaxial * compressive strength (M Pa) Density* (g/cc) Young s * Modulus (G Pa) Porosity* (%) Vertical * spacing between joints (m) Horizontal* spacing between joints (m) Baikunth Rawan Sonadih Hirmi A perusal of the properties indicates that the deposits of the four quarries have a similar geotechnical set-up and can be considered as competent. The quarries are under active production stage and the winning is done using conventional drilling and blasting method. The holes are drilled in two to three rows on staggered pattern. Row to row delay with cord relays is maintained at 50 ms whereas the delay with shock tube initiation is 42 ms. Blasts are carried out either with Ammonium Nitrate- Fuel Oil mixture (ANFO) or with Site-Mixed Emulsion (SME) Explosive. The other details of blast practice are given in Table-2. Name of the quarry Baikunth Dia (mm) Spacing (m) Burden (m) Table-2. Blast practice details. Depth (m) 8.0 Explosive type ANFO Primer Cartridge booster/cast booster SME Cast booster Rawan SME Cast booster Sonadih SME Cast booster Hirmi ANFO SME Cartridge booster/cast booster Initiation method Cord relays Shock tubes Shock tubes Shock tubes Cord relays Shock tubes Secondary breakage method Secondary blasting/ Rock breaker Rock breaker Rock breaker Rock breaker DATA COLLECTION It has been established by the research [8] that the order of influence of various parameters for the fragmentation in competent rocks is: a) Explosive energy per unit volume of rock mass, i.e. specific charge b) Explosive distribution within the rock mass c) Type of explosive d) Delay timing e) Joint system and its orientation with respect to blast direction. These findings have been the starting hypothesis for the selection of the input variables. Since the rock mass is competent; hence the specific charge has the most dominating role in deciding the quality of fragmentation. The specific charge is logically correlated with the number of holes/row, number of rows, average depth, average spacing, average burden and total quantity of explosive fired in one round. If all these parameters are considered separately for the development for the model; then one can assess the effect of variation in individual parameter on the boulder count, if required. This is why the individual parameters were considered instead of specific charge. On the similar considerations the type of the explosive replaces the VoD and the density of the explosive. The explosive distribution is represented by the diameter of the blast hole and the stemming height. The geotechnical parameters and the delay practice were similar in the referred mines hence they have not been considered as an input variable. This makes the model site specific. In order to use the model in different geotechnical environment and/or with different delay practice and with different criterion for oversize fragments; the model requires training, validation and testing with new blast records. 48

3 This is not a major problem as most of the mines maintain the records which are required for the operationalizing the model. Thus the input variables are number of holes per row, number of rows, average spacing, average burden, average depth, diameter, average stemming, type of the explosive and the total charge. The target variable is the boulder count. The maximum feed size of the crushers of the quarries is 1 m. Therefore the fragments having the size more than 1 m are considered as boulders. More than three hundred blast records were generated and assessed for their technical feasibility for multiple regressions modeling with SPSS. Subsequently, three hundred blast records were finalized for both statistical and ANN modeling. These three hundred records were divided in three groups. 191 records were used for training, 77 records for validation and 32 for testing of the ANN model. The records used for training and validation of ANN model were used for the development of statistical model whereas the 32 records used for testing of the ANN and statistical models were same. The Range of the data used for the development of the models is presented in Table-3. Table-3. Range of the data used for the development of models. Value Input variables Standard Minimum Maximum Mean Deviation Diameter, mm (D) Not Applicable Average burden, m (B) Average spacing, m (S) Average depth, m (H) Average stemming, m (T) Number of holes/row (N) Number of rows (n) 2 3 Not Applicable Type of the explosive ANFO and SME Quantity of explosive fired per round, kg (Q) Value Target variable Standard Minimum Maximum Mean Deviation Boulder count (N ) CONCEPT ANN mimics the function of human brain. Since its inception, ANN has become popular and applicable to various fields of science and technology to solve complicated simulation problems. The ANN is capable of calculating arithmetic and logical functions, generalizing and transforming independent variables to the dependent variables, parallel computations, nonlinearity processing, handling noisy data, function approximation and pattern recognition [3]. ANN is trained using a set of real inputs and their corresponding outputs. For a better approximation, sufficient number of datasets is required. Performance of the trained model is checked with part of the available data known as testing datasets. To find out the best possible network, various topologies are constructed and tested. The process of model trainingtesting has to be continued until the optimum model with minimum error and maximum accuracy is achieved. A neural network has a layered structure, and each layer contains processing units or neurons. Input variables are placed in the input layer, whereas target variables are put in the output layer. The neurons in the hidden layers are the intermediate computation components (black box) of the system. All of the layers are connected to each other by weighted connections. Each neuron is connected to the neurons in the subsequent layer. However, there is no connection between the neurons of the same layer. In the training process, the interconnections among the neurons are initially assigned specific weights. The network would be able to perform a function by adjusting the initial weights. In the process of ANN training, an initial arbitrary value (weight) is assigned to the connections and then to combine all of the weighted inputs and generate the neuron output the formula depicted in equation (1) is applied: O = x i w i + b (1) Where, x i is the input; w i is the connection weight and b is the bias. The neuron output is mapped to actual output by the function indicated in equation (2), y = f (O) = f ( x i w i + b) (2) 49

4 DEVELOPMENT OF ANN MODEL The ANN model described in this paper was developed using the syntax available in ANN tool box of MATLAB. A back-propagation neural network was selected due to its simplicity and uniform approximation of any continuous function. The number of neurons in the input layer was nine and the number of neurons in the output layer was one. The tool box provides a number of training functions and each is having its own advantages and disadvantages. The objective of the training function is to adjust the weights and the bias vectors so as to find the complicated relation between the input and output. The application of a training function depends on several factors, such as the complexity of the problem, the number of training samples, the structure of the network and error target. Levenberg Marquardt (LM) algorithm is used for training the network because it has good generalization ability and has the capability of providing good predictions. LM algorithm provides a numerical solution to the problem of minimizing a function over a space of parameters of the function. Not only the first derivative information but also the second derivative information of the target function is used in the LM algorithm. It can dynamically adjust the convergence direction of iteration according to the iteration result, so its convergence speed is very fast. Generally, Log-Sigmoid ((Logsig), Hyperbolic tangent Sigmoid (Tansig), Positive Linear (Poslin) and Linear (Purelin) transfer functions are used in back propagation neural network (BPNN) [73]. These four transfer functions are considered for optimization. The optimization is ascertained by regression coefficients (Table 4 and Figure-1). Table-4. Regression coefficients obtained with various transfer functions. S. No. Transfer function Regression coefficients Training Validation Testing Overall 1 Poslin Logsig Purelin Tansig Regression coefficients Training Validation Testing Overall the complexities of the function that is being approximated or the decision boundaries that are being implemented. Unfortunately, we don t normally know how complex the problem is until we try to train the network. The standard procedure is to begin with more neurons and then change it. The network was trained using different number of hidden layers and neurons. The regression coefficients were noted for each of the architectures. The architecture providing the maximum regression coefficient was selected for the prediction [23]. Asa result of optimization, a BPNN model (Figure-2) with one hidden layer with two neurons in it, Levenberg-Marquardt as training function and purelin function as transfer function is finalized. Figure-1. Regression coefficients obtained with various transfer functions Note- 1, 2, 3 and 4 indicate the serial numbers of the transfer functions indicated in Table-4. In the case of the multilayer network, which can be used for fitting or pattern recognition, the number of hidden layers is not determined by the problem, since any number of hidden layers is possible. The standard procedure is to begin with a network with one hidden layer. If the performance of the network is not satisfactory, then more number of layers can be used in the network. It would be unusual to use more than two hidden layers. The training becomes more difficult when multiple hidden layers are used which leads to slow convergence. The numbers of neurons in the hidden layers are determined by Figure-2. Developed artificial neural network. Testing of ANN model The model predicts the boulder count based on the input variables of 32 records comprising of ANFO blasts in 152 and 115 mm diameter holes. And, SME blasts in 152 and 100 mm diameter holes and the predictions are compared with target variables of these 32 records. The predictive ability of the neural network is evident from Figures 3 and 4. 50

5 Figure-3. Curves obtained in MATLAB during training, validation and testing of the data sets. Figure-4. Regression lines obtained in MATLAB during training, validation and testing of the data set. 51

6 Sensitivity analysis Sensitivity analysis is carried out to assess the influence on each of the parameter on the predictions of ANN. The results are expressed as the strength of relations between the input and variables. Cosine amplitude method (CAM) is used to identify the most sensitive factors affecting boulder count. In this method, all of the data pairs are expressed in common X-space. The data pairs used to construct a data array X defined in equation (3) is X = {X 1, X 2, X 3,...X n } (3) Each of the elements in the data array X is a vector of lengths of n, as shown in equation (4): X i = {X i1, X i2, X i3, X in } (4) Thus, each of the pairs is a point in n-dimensional space, where each point requires m coordinates for a full description. Each element of a relation, results in a pair wise comparison of two data pairs. The strength of the relation between the data pairs, and, is expressed by the membership function given in equation (5). n r = = x x n x n = x = The analysis is carried and the order of the influence of various input variables on the predictions is depicted in Table-5 and Figure-5 shows the strength of relations of input variables and the order of influence of each of the input variable on the boulder count. Table-5. Order of the influence of various input variables on the predictions and the order of influence. S. No. Input variable Strength of relation 1 No. of holes per row No. of rows Average spacing Average burden Average depth Diameter Average stemming Type of the explosive Total charge 0.81 (5) Strength of relations Input variables Figure-5. Strength of relations of input variables (1, 2, 3etc indicate the serial number of variables shown in Table-5). Since the investigated rock mass is competent hence the variables pertaining to the specific charge viz. number of holes per row, number of rows, average spacing, average burden, average depth and total charge and those related to explosive distribution viz. average stemming and total charge are expected to show a major influence on the boulder count. Table 5 indicates that each of the concerned variables except the number of rows has an influence of more than 70% on the boulder count. A low value of the strength of relation is owing to the fact that the number of rows is either two or three and as such there is no substantial variation in this variable. As per the starting hypothesis; type of the explosive comes last in the order of the influence amongst the variables considered in this research. This fact is further corroborated by the findings and the type of the explosive has an influence of 50 % on the predictions. The influence is less because there was not much variation in the type of the explosive and only ANFO and SME were available in this research. The benefits of the developed ANN model are: a) The model uses a limited number of input variables. The records of the required input and target variables are normally maintained in every mine. Requirement of a large number of records for training and validation of the model is therefore not a problem. b) The target variable i.e. boulder count helps to plan the secondary breakage operations properly. c) The delay practice and the geotechnical features can be incorporated in the model for prediction of boulder count. In such a case, the program can be easily modified to incorporate the changes. 52

7 d) The model can be used to assess the blast designs for minimizing the boulder count. The limitations of the developed ANN model are: a) The predictions of the model are site specific and in the present form; it can predict the boulder count accurately in respect of only those mines which have a similar rock mass and analogous delay practice. b) The model has been developed with target variable as boulder count which is; in this case; the fragments of size more than 1 m. Skewed predictions may be obtained, if the fragments of some other size are considered as boulders. c) MATLAB environment is necessary for the development of this ANN model and subsequent predictions. However, in the absence of the MATLAB; ANN program code can be developed for the prediction of the boulder count. DEVELOPMENT OF STATISTICAL MODEL The statistical model has been developed to validate the predictions by the developed ANN model since no model is available for validation that could predict the boulder count. The statistical model has been developed in SPSS environment using multiple regression analysis. Multiple regression analysis is widely used for prediction of various results in a complex phenomenon like rock blasting. The regression analysis establishes a statistical relationship between independent variables and a dependent variable in the form of a statistical model which is fitted to a set of experimental data. This method of modeling has been used for prediction of rock fragmentation [3, 15-16, 40-41, 50, 53, 58, 63, 73, 80-81]. The regression analysis can also be used for estimation in the variation of the dependent variable w.r.t. predictors. This can be ensured by using probability distributions t test and F test. A t test is used to know whether calculated effects are statistically significant or not. Referring the F tables, the degree of significance of the computed F value can be determined. F value is used to indicate whether the developed model is significant or not [14, 60]. Since the type of the explosive is a nominal variable; it was required to develop two separate models for ANFO and SME blasts. The relevant coefficients for the model are presented in Tables 5 and 6. The developed statistical models are as depicted in equations (6) and (7): For ANFO blasts: N =. Q +. NH S +. D B +. n. H +. T +. Q. (6) D For SME blasts: N =. Q +. NH S +. D B +. n. H +. T +. Q. (7) D It is seen from the regression equations that in case of ANFO and SME blasts; the independent variables of the multiple regression equation viz. total charge to the number of blast holes in a row and average depth of a blast hole are negatively correlated to the boulder count. This indicates that the boulder count depends upon the distribution of the explosive in a blast hole and a good distribution ensures fewer boulders. The boulder count is directly proportional to the average spacing to diameter ratio and average burden to diameter ratio which validates the basic blasting theory. The models further indicate that the average height of stemming column is directly proportional to boulder count which is a very well-known principle. The boulder count increases with total charge owing to the reason that boulder count increases with the volume of blasted in-situ rock mass and more rock is displaced with the increase in the total charge. The boulder count however reduces with the average depth. Table-6 indicates the results of the significance tests carried out using t test. It indicates that all the variables except the average depth are statistically significant in the prediction of boulder count in case of both ANFO and SME blasts. 53

8 Table-6. Results of significance test for ANFO and SME blasts. Variables ANFO Blasts SME Blasts t Sig t Sig (Constant) Total charge to the number of blast holes in a row and average depth of a blast hole Average spacing to diameter Average burden to diameter Number of rows Average depth of the blast holes Average height of stemming Total charge Testing of statistical model The testing of the models indicates that each of the predictors has its tolerance greater than 0.1 and the variance inflation factor for each of the independent variables is less than 10. Further, the Durbin-Watson statistic for the models on ANFO and SME blasts is and respectively indicating the independence of the predictors. The residuals have also been found to have normal distribution and the P-P plots indicate the normal distribution of the residuals. It is therefore found that the proposed model has all the desirable properties as required for a statistical model. The statistical model developed for ANFO blasts indicates that the R is and adjusted R 2 is It means that 95.7% of the variance in the boulder count can be explained by the independent variables considered in this regression whereas in case of SME blasts the R is whereas the adjusted R 2 is It means that 96.7% of the variance in the boulder count can be explained by the independent variables considered in this regression. The accuracy of the statistical model is corroborated by the F test. The test indicates that both the models in the present form are significant since p< It validates the assumption of linearity between the dependent and independent variables. The predictions by ANN model and the statistical model are presented in Table 7 and Figures 6, 7 and 8 represent the an overview of prediction capabilities of the two models against the actual boulder count, scatter obtained in actual boulder count and predicted boulder count by statistical model and scatter obtained in the predictions by ANN model and Statistical model respectively. 54

9 Table-7. Prediction results of boulder count by ANN and statistical model. S. No. Explosive used Actual boulder count Predicted boulder count by ANN Predicted boulder count by statistical model 1 ANFO ANFO ANFO ANFO ANFO ANFO ANFO ANFO ANFO SME SME SME SME SME SME SME SME SME ANFO ANFO ANFO ANFO ANFO ANFO ANFO ANFO SME SME SME SME SME SME

10 Boulder count Actual boulder count Predicted boulder count by ANN Predicted boulder count by statistical model Blast number Figure-6. An overview of prediction ability of the two models R² = Predicted boulder count by ANN Actual boulder count Figure-7. Scatter obtained between the actual boulder count and the predicted boulder count by ANN. 56

11 160 Predicted boulder count by statistical model R² = Predicted boulder count by ANN Figure-8. Scatter obtained between the predictions by ANN and statistical model. RESULTS Rock blasting is multi-faceted phenomenon, the results of which are affected are affected by the interaction of a number of uncontrollable parameters. It can therefore be safely said that an accuracy of more than 80 % in the predictions of boulder count is sufficient. It is observed that the correlation coefficient between the actual boulder count and predicted boulder count by ANN is more than 0.9; which can be considered as satisfactory. It was also found that in case of an ANN model; an accuracy of more than 80 % was achieved in 24 predictions out of 32. The accuracy was less than 80% but was around 75 % in four predictions out of 32 cases. It is difficult to state the exact cause of unexpected variation in the predicted boulder count in the remaining four cases as blasting is a complex phenomenon and the results can be affected because of unexpected changes in uncontrollable parameters. The boulder count may vary because of the unforeseen presence of subsurface cracks/fissures, due to unexpected localized changes in the elastic properties/joint properties, etc. The predictions by ANN and the statistical model are in close agreement. The coefficient of correlation between the actual boulder count and the predicted boulder count by the statistical model exceeds 0.9 and the value of the same between predictions by ANN and the statistical model is around 0.9. The test of significance indicated that in case of ANFO and SME blasts; all the variables except the average depth added statistically significantly to the prediction of boulder count with p< The statistical model has been developed to ascertain the accuracy of predictions by the ANN model which has nine input variables. The selection of these variables is based on the well-established research findings [8] and the presentation of full model is the best method to reflect the range of predictors investigated [18]. Therefore the average depth which is the statistically insignificant predictor has been retained in the proposed statistical models. The accuracy of the statistical model is corroborated by the F test. The test indicates that both the models in the present form are significant since p< CONCLUSIONS The artificial neural network seems to be a competence measure to predict rock fragmentation. In this study, a new ANN model was established to predict boulder count in rock blasting. The new model is a BPNN with two hidden layers with two neurons in each of the hidden layer. The model uses LM training algorithm and purelin transfer function. The model indicated an overall high correlation coefficient of The correlation coefficient between actual and predicted number of boulder count was more than The performance of the model was validated using a statistical model developed in SPSS which also showed a correlation coefficient around 0.9. A perusal of the results indicated that majority of the predictions by two models were in close agreement. It can therefore be concluded that the developed ANN model has satisfactory predictive abilities. The sensitivity analysis of the ANN model indicates that the spacing, burden and stemming have substantial influence on the boulder count. Further, the tests of significance indicate that the explosive distribution, height of stemming column and the ratios of spacing and burden to diameter are statistically significant in case of both ANFO and SME blast models. Due attention is therefore required to be paid to maintain the 57

12 accuracy in drilling and charging the blast holes so that the boulder count can be minimized in the referred quarries. ACKNOWLEDGEMENT The authors are thankful to the management of Rawan, Hirmi, Sonadih and Baikunth Limestone Quarries from where the blast records were generated. Without their unflinching support; the study could not be completed. REFERENCES [1] Aler J., Mouza J.D. and Arnould M Measurement of the fragmentation efficiency of rock mass blasting and its mining applications, Int J of Rock Mech and Min Sci and Geo Abstracts. 3: [2] Ash R The mechanics of the rock breakage (Part 1), Pit and Quarry. 56(2): [3] Bahrami A., Monjezi M., Goshtasbi K. and Ghazvinian A Prediction of rock fragmentation due to blasting using Artificial Neural Network, Engineering with Computers. 27: [4] Bhandari S Rock Fragmentation by Blasting Engineering In: Rock Blasting Operations, A. A. Balkema/Rotterdam/Brookfield. [5] Castro J.T., Liste A. V. and Gonzalez A.S Blasting index for exploitation of aggregates, 7 th Mine Planning and Equipment Selection Symposium, Calgary, Canada. pp [6] Chakraborty A. K., Jethwa J.L., and Paithankar A. G Effects of joint orientation and rock mass quality on tunnel blasting, Engineering Geology. 37: [7] Chakraborty A.K., Raina A. K., Ramlu M., Choudhury P.B., Haldar A., Sahu P. and Bandopadhyay C Parametric study to develop guidelines for blast fragmentation improvement in jointed and massive formations, Engineering Geology. 73: [8] Chiappetta R.F Choosing the right delay timing for the blasting application, optimization and maintainingfield control, 8th High-Tech Seminar on State-of-the Art, Blasting Technology, Instrumentation and Explosives Applications, Allentown PA, USA. pp [9] Chung S.H. and Katsabanis P.D Fragmentation prediction using improved engineering formulas, Int J for Blasting and Fragmentation. 4: [10] Cunningham C.V.B The Kuz-Ram Model for prediction of fragmentation from blasting, 1 st International Symposium on Rock Fragmentation by Blasting, Luleå University of Technology, Luleå, Sweden. pp [11] Cunningham C.V.B Fragmentation estimations and Kuz-Ram Model-Four years on, 2 nd International Symposium on Rock Fragmentation by Blasting, Keystone, Colorado. pp [12] Dhekne P.Y., Pradhan M. and Jade R Assessment of performance of explosives by estimating the number of oversize boulders using ANN Model, The Indian Mining and Engineering Journal. 53: [13] Dhekne P.Y., Pradhan M. and Jade R.K Assessment of the effect of blast hole diameter on the number of oversize boulders using ANN Model, Journal of the Institution of Engineers (India) Series D, DOI /s [14] Drape N.R. and Smith Jr H Applied Regression Analysis, 2nd ed, John Wiley and Sons Inc, New York, USA. [15] Ebrahimi E., Monjezi M., Khalesi M.R. and Armaghani D.J Prediction and optimization of backbreak and rock fragmentation using an Artificial Neural Network and Bee Colony Algorithm, Bulle Engineering geo and Environ, DOI 10,1007/s [16] Enayatollahi I., Aghajani B.A. and Asa A Comparison between Neural Network and multiple regression analysis to predict rock fragmentation in open pit mines, Technical Note, Rock Mechanics and Rock Engineering. 47: [17] Esen S., Onederra I., and Bilgin H.A Modelling the size of crushing zone around a blast hole, Int. J of Rock Mech and Min Sci. 40: [18] Forstmeier W. and Schielzeth H Cryptic multiple hypotheses testing in linear models: Overestimated effect sizes and the winner's curse, Behavioural Ecology and Sociobiology. 65:

13 [19] Gama D. D Use of comminution theory to predict fragmentation of jointed rock masses subjected to blasting, 1 st International Symposium on Rock Fragmentation by Blasting, Luleå University of Technology, Luleå, Sweden. pp [20] Gate W., Ortiz L. and Florez R Analysis of rock fall and blasting back break problems, American Rock Mechanics Conference, Vol 4, Anchorage, Alaska. pp [21] Ghosh A., Daemen J.J.K., and Vanzyl D Fractal based approach to determine the effect of discontinuities on blast fragmentation, 31 st U.S. Symposium on Rock Mechanics: Contributions and Challenges, Golden, Colorado. pp [22] Grundstrom C., Kanchibotla S., Jankovic A. and Thornton D.M Blast fragmentation for maximizing the SAG mill throughput at Porgera Goldmine, 27 th Annual Conference on Explosives and Blasting Technique, Orlando, Florida. pp [23] Hagan M.T., Demuth H.B., Beale M.H. and De Jesus O. Neural Network Design 2nd edition, [24] Hagan T.N The effect of rock properties on the design and results of tunnel blasts, J of Rock Mech and Tunnelling Tech. 1(1): [25] Hall J. and Brunton I Critical comparison of Kruttschnitt Mineral Research Center (JKMRC) blast fragmentation models, Fragblast: Int J for Blasting and Fragmentation. 6: [26] Hamdi E. and Mouza J.D A methodology for rock mass characterization and classification to improve blast results, Int J of Rock Mech and Min Sci. 42: [27] Hamdi E., Mouza J.D. and Fleurisson J.A Evaluation of the part of blasting energy used for rock mass fragmentation, Fragblast: The Int J of Blasting and fragmentation. 5: [28] Hjelmberg H Some ideas on how to improve calculations of the fragment size distribution in bench blasting, 1st International Symposium on Rock Fragmentation by Blasting, Luleå University of Technology, Luleå, Sweden. pp [29] Hustrulid W The Fragmentation System Concept, In: Blasting Principles for Open Pit Mining, A.A. Balkema, Rotterdam. [30] Jhanwar J.C., Jethwa J.L. and Reddy A.H Influence of air-deck blasting on fragmentation in jointed rocks in an open-pit Manganese mine, Engineering Geology. 57: [31] Jimeno C.L., Jimeno E.L. and Carcedo F.J.A Controllable Parameters of Blasting, In: Drilling and blasting of Rocks, Balkema A. A., Rotterdam. [32] Jong Y. and Lee C Application of Neural Networks to prediction of powder factor and peak particle velocity in tunnel blasting, 28 th Annual Conference on Explosives and Blasting Technique, Las Vegas, Nevada. 2: [33] Jong Y.H. and Lee C.I Influence of geological conditions on the powder factor for tunnel blasting, Int J of Rock Mech and Min Sci. 41: [34] Kanchibotla S.S., Valery W., and Morrell S Modeling fines in blast fragmentation and its impact on crushing and grinding, EXPLO 99 Conference, Kalgoorlie, Australia. pp [35] Karami A. and Afluni Z.S Sizing of rock fragmentation modeling due to bench blasting using adaptive neuro-fuzzy inference system (ANFIS), Int. J of Min Sci and Tech. 23: [36] Karami A. R., Mansouri H., Farsangi M.A.E. and Nezamabadi H Backbreak prediction due to bench blasting: An Artificial Neural Network approach, J of Mine, Metals and Fuels. 54: [37] Khandelwal M. and Singh T.N Prediction of blast induced ground vibrations and frequency in opencast mine: A Neural Network Approach, J of Sound Vibration. 289: [38] Kojovic T., Michaux S., and McKenzie C Impact of blast fragmentation on crushing and screening operations in quarrying, EXPLO 95 Conference, AusIMM, Brisbane, Australia. pp [39] Kou S. and Rustan A Computerised design and result prediction of bench blasting, 4 th International Symposium on Rock fragmentation by Blasting, Vienna, Austria. pp

14 [40] Kulatilake P.H.S.W., Hudaverdi T. and Qiong W New prediction models for mean particle size in rock blast fragmentation, Geotech and Geological Engineering, 30: [41] Kulatilake P.H.S.W., Qiong W., Hudaverdi T. and Kuzu C Mean particle size prediction in rock blast fragmentation using Neural Networks, Engineering Geology. 114: [42] Kuznetsov V. M Mean diameter of fragments formed by blasting rock, Soviet Mining Science. 9(2): [43] Latham J.P. and Lu P Development of an assessment system for the blastability of rock masses, Int J of Rock Mech and Min Sc. 36: [44] Leu S.S., Lin S.F., Chen C.K. and Wang S.W Analysis of powder factors for tunnel blasting using Neural Networks, Fragblast: Int J for Blasting and Fragmentation, 2: [45] Lilly P.A An empirical method of assessing rock mass blastability, Large Open Pit Conference, IMM, Australia. pp [46] Mckenzie S Cost of explosives-do you evaluate it properly? Mining Congress Journal. 52 (5): [47] Mishnaevsky Jr L.L. and Schmauder S Analysis of rock fragmentation with the use of the theory of fuzzy sets, ISRM International Symposium (Eurock '96), Torino, Italy [48] Mishra A. K., Kumar A., and Nizami A. A Digital blasting technology, Conference on Emerging Trends in Mining and Allied Industries, NIT Rourkela. pp [49] Mishra A.K Safety engineering in mine blasting operations, Course Material on Safe Mining Methods, Design and Technology, IIT, Kharagpur. [50] Moghadam M.J., Farsangi M.A.E., Mansouri H. and Nezamabadi H Muck -pile fragmentation prediction using Artificial Neural Networks, J of Mines, Metals and Fuels. 54: [51] Mojtabai N., Farmer I. W. and Savely J.P Optimisation of rock fragmentation in bench blasting, 31 st U.S. symposium on Rock Mechanics Contributions and Challenges, Golden, Colorado. pp [52] Monjezi M, Singh T.N., Khandelwal M., Sinha S., Singh V. and Hosseini I Prediction and analysis of blast parameters using Artificial Neural Network, Noise Vibration Worldwide. 37: [53] Monjezi M., Amiri H., Farrokhi A. and Goshtasbi K Prediction of rock fragmentation due to blasting in Sarcheshmeh Copper mine using Artificial Neural Networks, Geotech and Geological Engineering. 28: [54] Monjezi M., Dehghan H. and Samimi N.F Application of TOPSIS method in controlling fly rock in blasting operations, 7 th International Science Conference SGEM, Sofia, Bulgaria. pp [55] Monjezi M., Ghafurikalajah M. and Bahrami A Prediction of blast-induced ground vibration using Artificial Neural Networks, Tunnelling and Underground Space Technology. 26: [56] Monjezi M., Hashemi S.M., Hashemi R., Johari M.V. and Khandelwal M Artificial Neural Network as a tool for back break prediction, Geotech and Geo Engineering. 32: [57] Monjezi M., Mehrdanesh A., Malek A., and Khandelwal M Evaluation of effects of blast design parameters on flyrock using Artificial Neural Networks, Neural Computing and Applications. 23: [58] Monjezi M., Mohamadi H.A., Barati B. and Khandelwal M Application of soft computing in predicting rock fragmentation to reduce environmental blasting side effects, Arab Journal of Geoscience. 7: [59] Monjezi M., Yazdian A., and Hesami S.M Use of back propagation Neural Network to estimate burden in tunnel blasting, J of Mines, Metals and Fuels. 12: [60] Montgomery D.C., Peck E.A. and Vining G.G Introduction to Linear Regression Analysis, John Wiley & Sons Inc, New Jersey, USA. [61] Morin M.A. and Ficarazzo F Monte Carlo simulation as a tool to predict blasting fragmentation based on the Kuz Ram model, Computers and Geosciences. 32: [62] Nie S. L. and Rustan A Techniques and procedures in analysing fragmentation after 60

15 blasting by photographic method, 2 nd International Symposium on Rock Fragmentation by Blasting, Keystone, Colorado. pp [63] Oraee K. and Asi B Prediction of rock fragmentation in open pit mines using Neural Network Analysis, 15 th International Symposium on Mine Planning and Equipment Selection (MPES), Torino, Italy. pp [64] Ouchterlony F Influence of blasting on size distribution and properties of muckpile fragments: A state-of-the-art review, MinFo Project P , Swebrec, Luleå University of Technology, Sweden. pp [65] Ouchterlony F., Niklasson B. and Abrahamsson S Fragmentation monitoring of production blasts at Mrica, International Symposium on Rock Fragmentation by Blasting, Frag Blast 3, Brisbane, Australia. pp [66] Ozcelik Y Effect of discontinuities on fragment size distribution in open-pit blasting: A case study, Trans of the Institution of Mining and Metallurgy. 107: [67] Pal R. P Breakage assessment through cluster analysis of joint set orientations of exposed benches of opencast mines, Geotechnical and Geological Engineering. 13: [68] Rai P. and Baghel S.S Investigation of firing patterns on fragmentation in an Indian opencast limestone mine, Quarry Management Journal, UK. pp [69] Raina A. K., Ramulu M., Choudhary P.B., and Chakraborty A.K Fragmentation prediction in different rock masses characterized by drilling index, 7 th International Symposium on Rock fragmentation by Blasting, Met Industry Press, Beijing, China. pp [70] Rustan P.A Automatic image processing and analysis of rock fragmentation- Comparison of systems and new guidelines for testing the systems, Int J for Blasting and Fragmentation, Fragblast. 2: [71] Sanchidrian J.A., Segarra P. and Lopez L.M Energy components in rock blasting, Int J of Rock Mech and Min Sci. 44: [72] Sawmliana C., Pal R.P., Singh R. K. and Singh T.N Blast induced air overpressure and its prediction using Artificial Neural Network, Mining Technology, Trans, Inst, Min, Metall, A. 116: [73] Sayadi A., M Monjezi., Talebi N. and Khandelwal M A comparative study on the application of various Artificial Neural Networks to simultaneous prediction of rock fragmentation and back break, J of Rock Mech and Geotech Engineering. 5: [74] Schuhmann Jr R Energy input and size distribution in comminution, Am, Inst, Min, Metall, ANNME. 214: [75] Shao P., Xu Z. W., Zhang H.Q. and He Y. N Evolution of blast-induced rock damage and fragmentation prediction, Procedia Earth and Planetary Science, International Conference on Mining Science & Technology (ICMST2009), Xuzhou, China. 1: [76] Singh T. N A study of blast induced ground vibration at Dharapani Magnesite Mine, Pitthoragarh Himalaya, India, 3 rd International Symposium on Headwater Control, New Delhi, India. pp [77] Tawadrou A.S. and Katsabanis P.D Prediction of surface blast patterns in Limestone quarries using Artificial Neural Networks, Fragblast: Int J for Blasting and Fragmentation, 9: [78] Thote N. R. and Singh D.P Effect of airdecking on fragmentation: A few case studies of Indian mining, Explosive & Blasting Technique, Balkema. pp [79] Trivedi R., Singh T. N. and Raina A.K Prediction of blast induced fly rock in Indian Limestone mines using Neural Networks, J of Rock Mech and Geotech Engineering. 6: [80] Xiu S. Z., Dan H., Jian Z. and Shu Z Combined ANN prediction model for rock fragmentation distribution due to blasting, J of Information and Computational Science. 10: [81] Zhu H.B. and Wu L Application of Gray correlation analysis and Artificial Neural Network in rock mass blasting, J of Coal Science and Engineering. 11: