Toward predicting blast-induced flyrock: a hybrid dimensional analysis fuzzy inference system E. Bakhtavar, H. Nourizadeh & A. A. Sahebi
International Journal of Environmental Science and Technology ISSN 1735-1472 Int. J. Environ. Sci. Technol. DOI 10.1007/s13762-016-1192-z
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Author's personal copy Int. J. Environ. Sci. Technol. DOI 10.1007/s13762-016-1192-z
ORIGINAL PAPER
Toward predicting blast-induced flyrock: a hybrid dimensional analysis fuzzy inference system E. Bakhtavar1 • H. Nourizadeh2 • A. A. Sahebi3
Received: 17 December 2015 / Revised: 22 July 2016 / Accepted: 12 November 2016 Islamic Azad University (IAU) 2016
Abstract A hybrid dimensional analysis fuzzy inference system approach was introduced to predict blast-induced flyrock in surface mining, by integrating a dimensional analysis procedure and Mamdani’s fuzzy inference system. In the dimensional analysis, the blast-induced flyrock was considered as a function of the most effective parameters. Hence, a number of dimensionless products resulted and were used as input and output parameters of Mamdani’s fuzzy inference system. The capability of the hybrid approach was determined by comparing its results with the real measurement of flyrock in the case of a copper mine, based on a number of 320 in situ blasting datasets. Predictions by the system were close to the real measurements. Sensitivity analysis of the hybrid dimensional analysis fuzzy inference system showed that the most effective dimensionless products on flyrock distance were spacing, the multiplication of rock mass rating and hole length, and the subtraction of burden and hole length multiplication and stemming length.
Editorial responsibility: M. Abbaspour.
Electronic supplementary material The online version of this article (doi:10.1007/s13762-016-1192-z) contains supplementary material, which is available to authorized users. & E. Bakhtavar
[email protected] 1
Department of Mining and Materials Engineering, Urmia University of Technology, Urmia, Iran
2
Department of Mining Engineering, Sahand University of Technology, Tabriz, Iran
3
Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
Keywords Blasting operation Dimensionless products Undesirable environmental outcomes Uncertainty
Introduction During blasting operation in surface mining, a major part of energy produced by explosives results in undesirable environmental impacts, in the form of flyrock, ground vibration, air overpressure, and back break (Hajihassani et al. 2015). Phenomenon of blast-induced flyrock is an unwanted extreme throw of rock fragments which is produced by blasting, which may travel very long distances, causing serious risks to the mine working environment and the surrounding environment (Raina et al. 2014). Flyrock has been considered as a major source of accidents in bench blasting surface mines, as investigated in the literature (Faramarzi et al. 2014). Fatal accidents caused by blast-induced flyrock in surface mining were studied by Bajpayee et al. (2004). It was concluded that blast-induced flyrock is responsible for about 30% injuries and fatalities in comparison with other accidents resulting from blasting in the surface mining. Blast-induced flyrock zone lacks an isotropic nature in which there are at least two low-risk zones having the minimum probabilities of flyrock (Raina et al. 2013). Recently, the problem of blast-induced flyrock prediction has been the main subject of a lot of research. Attempts have been made to predict flyrock by developing some techniques. Here, the authors reviewed only the research that has been recently carried out to predict and assess blast-induced flyrock in surface mining, especially during 2010–2015. Older works, which were cited and reviewed in recent research such as Raina et al. (2014) and Hajihassani et al. (2015), are not of focus in this present research.
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Little and Blair (2010) presented a risk matrix-based method to assess the undesirable consequences and risks due to bench blasting. An artificial neural network was developed to predict simultaneously, fragmented rocks and induced flyrock by blasting in a surface iron ore mine (Monjezi et al. 2010). A risk-based criterion was developed to obtain a dynamic danger zone for blasting, based on the concept of safety factor and a threat ratio, which was defined as an allowable distance of flyrock to distance of the object of concern (Raina et al. 2011). A support vector machine was developed by Amini et al. (2011) to be applied in predicting flyrock in a surface copper mine. Considering the inaccuracies in the prediction models, a fuzzy model was developed to predict blast-induced flyrock in a surface mine (Rezaei et al. 2011). Approximate numerical solutions were used, together with a specific algorithm, for estimating the maximum distance of flyrock (Stojadinovic et al. 2011). An artificial neural network was developed to predict blast-induced flyrock range (Mohamad et al. 2012). A neuro-genetic model was developed to predict flyrock, together with backbreak (Monjezi et al. 2012). Monte Carlo simulation method was used, together with dimensional analysis, to predict flyrock distance in Sungun surface copper mine (Ghasemi et al. 2012). An approach which was based on specific risk studies was proposed by Blanchier (2013) in order to assess and estimate the blast-induced flyrock risk and its range. An approach was developed by incorporating particle swarm optimization algorithm with the artificial neural network in order to simulate blast-induced flyrock and peak particle velocity in surface mining (Armaghani et al. 2013). A research was carried out, based on rock engineering systems, in order to predict blast-induced flyrock, and level of risk associated with flyrock in Sungun surface mine was modeled and assessed (Faramarzi et al. 2014). Two separate models were developed by using the artificial neural network and fuzzy logic approaches in order to predict blast-induced flyrock distance (Ghasemi et al. 2014). The results, when compared, indicated that the fuzzy-based model had better performance than the developed artificial neural network model. An integrated approach based on an imperialist competitive algorithm and the artificial neural network was developed in order to predict blast-induced flyrock (Marto et al. 2014). Artificial neural network and adaptive neuro-fuzzy inference system were developed to predict blast-induced flyrock distance in four opencast limestone mines (Trivedi et al. 2015). This research was carried out in May 2015, at the Urmia University of Technology and Sungun copper mine located in the west of Iran, in order to develop a new approach by integrating dimensional analysis and fuzzy inference system to predict blast-induced flyrock in surface mining. The approach was named ‘‘hybrid dimensional analysis fuzzy
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inference system’’ (H-DAFIS). Although several models have been developed to predict blast-induced flyrock in the literature, none of them have contributed to any hybrid approach of dimensional analysis and fuzzy inference system.
Materials and methods Effective parameters In order to develop an integrated approach based on dimensional analysis together with fuzzy inference system, the most effective parameters which may cause the blastinduced flyrock in surface mining must first be determined. None of the reviewed research in the literature has specifically studied the most effective parameters, except the study by Faramarzi et al. (2014) and Raina et al. (2014) which considered these parameters better than others. For this purpose, and to find these parameters, most of the considerable research related to the blast-induced flyrock has been studied. Blast-induced flyrock can basically appear in three forms: face bursting, cratering, and rifling (Little 2007). In the case of intersecting the available charge within a blast hole to main geological weak structures in bench face, flyrock occurred in the form of face burst. Blast-induced gasses can easily burst out and propagate cracks in damaged rocks around stemming part of a blast hole caused by blasting in the upper bench. In this case, emitted gasses can cause flyrock in the form of cratering. In the case of insufficient stemming materials of a blast hole, blast-induced flyrock may occur in the form of rifling, by ejecting collar rock and stemming materials. Based on the three mentioned forms of flyrock, the main parameters which cause blast-induced flyrock are controllable blast design parameters (such as blast geometry), unfavorable geological conditions, and rock mass characteristics (Jimeno et al. 1995; Raina et al. 2014). After studying the related flyrock research, parameters that may influence blast-induced flyrock can be categorized as controllable and uncontrollable groups. The related research is summarized in Table 1, together with the most effective parameters considered in blast-induced flyrock under two groups: controllable and uncontrollable. Rezaei et al. (2011) concluded that among the considered parameters (as indicated in Table 1), powder factor and rock density, respectively, had the maximum and minimum influence on blast-induced flyrock. Ghasemi et al. (2012) concluded that powder factor, stemming and burden, respectively, were the most effective parameters among all that were considered. It was also concluded that the spacing and mean charge per blast hole had the
4
4
4
4
Faramarzi et al. (2014)
Armaghani et al. (2013)
6 4
9
4
Total 4
11
4
4
Trivedi et al. (2015)
Current research
4
4
Raina et al. (2014)
4
6
4
4
4 4
4
4
4
4
hl
Hole depth or length (m)
4
4
4
4
4
4
4
St
Stemming (m)
4
4
4
4
4
4
4
S
Spacing (m)
Ghasemi et al. (2014)
5
4
4
Monjezi et al. (2012)
Marto et al. (2014)
4
4
4
B
Burden (m)
4
4
Dh
Hole diameter (mm)
Controllable parameters
Ghasemi et al. (2012)
Rezaei et al. (2011)
Monjezi et al. (2011)
Kecojevic and Radomsky (2005)
Symbols
References
1
4
U
Subdrilling (m)
4
10
4
4
4
4
4
4
4
4
4
4
Specific charge or powder factor (kg/ton) Pf
Table 1 Effective parameters on blast-induced flyrock according to the literature
4
7
4
4
4
4
4
4
4
Qmax
Maximum charge per delay (kg)
3
4
4
4
SD
Specific drilling (m/m3)
5
4
4
4
4
4
Mean charge per hole (kg) qh
2
4
4
S/B
(Spacing/ Burden) ratio
1
4
FS
Stiffness factor
1
4
St/B
(Stemming/ Burden) ratio
1
4
B/Dh
(Burden/ Hole diameter) ratio
4
2
4
4
T
Time delay (ms)
4
2
4
4
N
Number of rows
2
4
4
Hole inclination and deviation () Ih
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1 1 4
1 2
Among the controllable ones, the parameters which were considered more in the reviewed research are taken into account as stemming (11 times), specific charge or powder factor (10 times), burden (9 times), spacing, stemming, hole length, maximum charge per delay, time delay, number of rows, and RMR. With the exception of the last parameter (RMR), which is in the category of the uncontrollable ones, the other eight parameters were categorized in the controllable ones. The first six parameters were selected because they were considered as the most effective parameters in the majority of the research as listed in Table 1. RMR was also selected as the most important uncontrollable parameter which comprised UCS, RQD, discontinuities spacing and filling materials, and groundwater conditions. Time delay and number of rows were selected by the authors because they indicated the volume of blasting and played a major role in controlling the blast-induced flyrock.
Dimensional analysis part of H-DAFIS
Current research
Total
Trivedi et al. (2015)
Raina et al. (2014)
3
4 Ghasemi et al. (2014)
4 Armaghani et al. (2013)
Monjezi et al. (2012)
Faramarzi et al. (2014)
Marto et al. (2014)
4 4 Ghasemi et al. (2012)
Rezaei et al. (2011)
Monjezi et al. (2011)
Kecojevic and Radomsky (2005)
Symbols
4
4
Uniaxial compressive strength (MPa) UCS Rock mass rating RMR
Uncontrollable parameters References
Table 1 continued
2
4 4
•
Rock density (gr/cm3) q
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minimum effect on flyrock. According to the obtained results by Monjezi et al. (2012), stemming and powder factor were the most effective parameters on blast-induced flyrock. Faramarzi et al. (2014) resulted that burden, spacing, stemming, maximum instantaneous charge, stemming per burden ratio, stiffness factor, time delay, and hole diameter had greater influence on blast-induced flyrock in comparison with powder factor, mean charge per hole, spacing per burden ratio, number of rows, hole deviation, burden per hole diameter ratio, and rock mass rating (RMR), which had negligible influence. After a sensitivity analysis, Marto et al. (2014) demonstrated that the maximum charge per delay and powder factor were the most effective parameters. Trivedi et al. (2015) concluded that specific charge and charge concentration had a positive correlation with blast-induced flyrock; however, burden, stemming, uniaxial compressive strength (UCS), and rock quality designation (RQD) had a negative correlation. In this research, among all parameters listed in Table 1 as given in the literature, the most critical ones were considered as follows:
1
4 4
Blastability index BI
Unfavorable geological conditions –
Schmidt hammer rebound number ns
4
Rock quality designation (%) RQD
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Dimensional analysis has been introduced as a technique of checking relations among physical quantities, based on their dimensions, in order to establish a set of dimensionless products on several dimensional variables (Khoshrou et al. 2010; Bakhtavar et al. 2010, 2015; Faramarzi et al. 2014). Dimensionless products are formed on the basis of mass and force systems which are two main basic physical dimensions in dimensional analysis. The mass system is based on three main units of mass (M), length (L), and time
Author's personal copy Int. J. Environ. Sci. Technol. Table 2 Dimensional matrix of variables with dimensions
Parameters
Quantity Fd
B
S
N
Qmax
T
RMR
hl
Pf
St
Dimensions
[L]
[L]
[L]
[1]
[FT-1]
[T]
[1]
[L]
[FL-3]
[L]
Variables
Z1
Z2
Z3
Z4
Z5
Z6
Z7
Z8
Z9
Z10
1
0
Main dimensions F
0
0
0
0
1
0
0
0
L
1
1
1
0
0
0
0
1
-3
1
T
0
0
0
0
-1
1
0
0
0
0
(T), whereas a force system is based on the units of force (F), length (L), and time (T). Only a limited number of researches have been performed based on the application of dimensional analysis in order to solve mining problems. Khoshrou et al. (2010) developed a relationship based on regression and dimensional analysis in order to determine the burden as the most important blasting design parameter. In the same year, a relationship was developed, which utilized statistical and dimensional analysis to determine a crown pillar thickness between open pit and underground mining (Bakhtavar et al. 2010). In the same way as two previous types of research, using regression and dimensional analysis, a model was developed based on the mass system to predict flyrock distance in the form of a nonlinear relationship among dimensionless products (Ghasemi et al. 2012). A research based on nonlinear regression and dimensional analysis was used to develop a model for predicting the mean particle size of fragmentation in bench blasting (Bakhtavar et al. 2015). The main purpose of this section, in addition to introducing dimensional analysis steps in details, is to determine a fundamental equation based on dimensional analysis. Equation (1) introduces the blast-induced flyrock distance as a function of effective parameters. All parameters in Eq. (1) are introduced in Table 1. Fd ¼ f ðB; S; N; Qmax ; T; RMR; hl ; Pf ; St Þ
ð1Þ
According to Buckingham’s p-theorem (Buckingham 1914), introduced as a dimensional analysis base to define a number of dimensionless groups based on one of physical unit systems (Bakhtavar et al. 2015), Eq. (2) describes the relationship between flyrock distance and the effective parameters given in Eq. (1). f ðFd ; B; S; N; Qmax ; T; RMR; hl ; Pf ; St Þ ¼ 0
ð2Þ
Based on the units of the effective parameters, in this study, force system base is considered for dimensional analysis of flyrock problem. Accordingly, all parameters as variables with their dimensions based on the adopted force system are given in Table 2. As a result, a dimensional matrix is created by setting variables as shown in Table 2.
In this step, a number of dimensionless products of variables are determined through the determinant of the right side of the dimensional matrix given in Table 2. The determinant is calculated to be zero as the following. Accordingly, the number of dimensionless products of variables can be calculated through Eq. (3). 0 1 0 1 3 1 ¼ 0 0 0 0 m¼nk
ð3Þ
where n, the number of dimensional variables; k, the number of independent base quantities. Based on the dimensional matrix (Table 2), n and k are 10 and 3, respectively. As a result, dimensionless products are given as seven by applying Eq. (3). Accordingly, three homogeneous linear equations can be derived from Table 2 as introduced in Eqs. (4)–(6). A matrix of responses is produced as given in Table 3 in order to solve Eqs. (4)–(6). Z5 þ Z9 ¼ 0
ð4Þ
Z1 þ Z2 þ Z3 þ Z8 3Z9 þ Z10 ¼ 0
ð5Þ
Z5 þ Z6 ¼ 0
ð6Þ
In this step, Eq. (2) is represented by Eq. (7), which includes seven effective dimensionless products instead of variables. Before considering dimensionless products as inputs and output in fuzzy part of H-DAFIS approach, these are taken into account based on each product multiplied by hole length as shown in Eq. (8). Finally, as a result of dimensional analysis as part of the H-DAFIS, flyrock distance is considered as a function of six combined parameters introduced in Eq. (9). They are used as input and output parameters to predict flyrock distance (FLY) by using the fuzzy part of the presented approach. Fd B S Qmax T Qmax T u ; ; ; N; ; ; RMR ¼ 0 ð7Þ hl Pf S2t h2l Pf St hl St hl Fd ¼ f
B hl Qmax T Qmax T ; ðSÞ; ðN hl Þ; ; ; ðRMR h Þ l Pf S2t hl Pf St St
ð8Þ
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Author's personal copy Int. J. Environ. Sci. Technol. Table 3 Matrix of the possible responses in the flyrock problem
Dimensionless products
Quantity Z1 Fd
Z2 B
Z3 S
Z4 N
Z5 Qmax
Z6 T
Z7 RMR
Z8 hl
P1
1
0
0
0
0
0
0
-1
0
0
0
1
0
0
0
0
0
0
0
-1
P3
0
0
1
0
0
0
0
-1
0
0
P4
0
0
0
1
0
0
0
0
0
0
P5
0
0
0
0
1
1
0
-1
-1
-2
P6
0
0
0
0
1
1
0
-2
-1
-1
P7
0
0
0
0
0
0
1
0
0
0
ð9Þ
Z derived as the overall output subjected to X and Y as crisp inputs, is shown in Fig. 1 (Jang and Siller 1997). As shown in the figure, A1 and B1 refer to the first and second fuzzy antecedents of the first rule, whereas A2 and B2 refer to the second rule. Accordingly, C1 and C2 refer to fuzzy consequent of the first rule and fuzzy consequent of the second rule, respectively (Ross 2004). For a set of disjunctive rules, the aggregated output for K rules is shown in Eq. (11) (Jang and Siller 1997).
Fuzzy part of the H-DAFIS Description of Mamdani’s fuzzy inference system Fuzzy set theory and fuzzy logic were introduced to represent linguistic vagueness, mathematically (Zadeh 1965). In this case, a membership function is used for the determination of inaccurate and uncertain data (Iphar and Goktan 2006). Fuzzy inference system (FIS) was introduced as a computing system based on the fuzzy set theory conceptions in the forms of if–then rules and fuzzy reasoning (Ross 2004). The most applicable FIS models are Mamdani, Takagi–Sugeno Kang, Tsukamoto, and Singleton. However, Mamdani’s fuzzy model is one of the most widespread algorithms in fuzzy applications among the aforementioned models. The Mamdani fuzzy inference algorithm as a rule-based system takes the form given in Eq. (10) (Iphar and Goktan 2006). An illustration of a two-rule Mamdani FIS, with
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Z10 St
P2
FLY ¼ f ðBHS; S; NH; QT; QTH; RHÞ
Fig. 1 The general structure of Mamdani fuzzy inference system (Jang and Siller, 1997)
Z9 Pf
If
X1 is Ai1 . . . and 8i ¼ 1; 2; . . .; k
Xr is Air
then
Y is Bi
lCk ðZÞ ¼ max½min½lAk ðinputðxÞÞ; lBk ðinputðyÞÞ k ¼ 1; 2; . . .; r
ð10Þ ð11Þ
where X1, Xr, input variables; Ai1, Air, Bi, linguistic terms (fuzzy sets); Y, output variable; K, number of rules; lCk, lAk, lBk, membership function of output Z for rule K, input X and Y, respectively. Defuzzification process is the final step of a fuzzy inference system. The most common defuzzification
Author's personal copy Int. J. Environ. Sci. Technol.
Fig. 2 Graphical indication of fuzzy reasoning mechanism Qmax T Qmax T l (BHS ¼ ðBh St Þ; S ¼ S; NH ¼ ðN hl Þ; QT ¼ ð Pf S2 Þ; QTH ¼ ðhl Pf St Þ;
RH ¼ ðRMR hl Þ; where FLY is flyrock distance and the other parameters are explained in Table 1)
methods are centroid of area (center of gravity), smallest maximum, and mean of maximum (Grima 2000). Centroid of area (COA) is the most applicable method which has been used to obtain the output crisp value through Eq. (12) (Grima 2000). R l ðzÞ Zdz ZCOA ¼ R A ð12Þ lA ðzÞ dz
antecedent, then consequent. The COA defuzzification method is performed to determine crisp output values. Figure 2 shows rule viewer and fuzzy reasoning mechanism in MATLAB environment. Triangular and trapezoidal membership functions of input and output parameters are considered in this model as illustrated in Fig. 3. In this case, some abbreviations are considered as ‘‘VVD’’ for ‘‘very very down’’, ‘‘VD’’ for ‘‘very down’’, ‘‘D’’ for ‘‘down’’, ‘‘M’’ for ‘‘medium’’, ‘‘U’’ for ‘‘up’’, ‘‘VU’’ for ‘‘very up’’, ‘‘VVU’’ for ‘‘very very up’’, etc. The range of FIS output is in the interval of [10,100]. A total of 290 rules for FIS were used by experts, and a decision made out of the combined input (premise part) and output (consequent part) membership functions based on the specialist experience and the applied database.
t
where Z*COA, the crisp value for ‘‘z’’ output; lA(z), the aggregated output membership function. Mamdani fuzzy inference system in the H-DAFIS A fuzzy model is constructed by using the knowledge of experts in the figure of linguistic decrees. In the model, COA defuzzification method is utilized in achieving the numerical value of output and also ‘‘min’’ and ‘‘max’’ as well as ‘‘and’’ and ‘‘or’’ are employed, respectively. As indicated in Eq. (9), the model includes FLY as output together with six inputs such as BHS, S, NH, QT, QTH, and RH. Fuzzy sets of membership functions are extracted from the relations between input and output due to a sufficient number of the available data for extracting sets. In this step, an attempt was made to construct the rule-based Mamdani fuzzy inference system in which the relationships among dissimilar variables are represented by means of fuzzy implications or fuzzy if–then rules of the form; if
Results and discussion In order to evaluate H-DAFIS model in practice for prediction of flyrock distance, Sungun copper mine has been studied as a surface mine located in the west of Iran. Sungun ore deposit is extracted through the method of bench-blast surface mining from levels 2362.5 to 600 m (Bakhtavar et al. 2015). For the purpose of the present study, in addition to blasting design parameters collected in the field, essential geomechanical parameters were also provided. It should be noted that the required database of input and output parameters was provided by investigating
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Author's personal copy Int. J. Environ. Sci. Technol. l b Fig. 3 Membership functions of inputs and output (BHS ¼ ðBh St Þ;
T Qmax T S ¼ S; NH ¼ ðN hl Þ; QT ¼ ðQPmax 2 Þ; QTH ¼ ðh P S Þ; RH ¼ ðRMR l f t f S t
hl Þ; where FLY is flyrock distance and the other parameters are explained in Table 1)
a number of 320 blasts in different levels of the mine. The minimum and maximum values of parameters with their symbols are given in Table 4. To assess the validity of H-DAFIS model, 30 datasets, which were not incorporated in model development, were used. A comparison between predicted flyrock by H-DAFIS model and measured flyrock is shown in Fig. 4. The real and predicted flyrock from H-DAFIS model for different blasting patterns is shown in Fig. 5. As clearly seen in these figures, the performance of H-DAFIS model in terms of the correlation coefficient (R2) of 0.9761 is close to the real value. As shown in Fig. 5, the predicted flyrock distances by H-DAFIS are mostly in accordance with the measured ones in the majority of the considered datasets. Totally, the average deviation of the predicted results from the measured results is 2.84%. This deviation Table 4 Description of the input and output parameters in the fuzzy model
is due to the inconsistency of some of the datasets. For example, dataset 1, 4, 9, 15, 21, 26, 28, 29, and 30 have deviations of 5.26, 3, 3.3, 6, 3.2, 4.8, 5.7, 21.2, and 16.7%, respectively. It should be noted that the predicted flyrock distances based on dataset 3, 6, 7, 10, 11, 12, 14, 16, 20, 22, 24, and 25 are completely in accordance with the measured results. The root-mean-square error (RSME) index for the results by H-DAFIS is 3.33. A sensitivity analysis is performed using Cosine Amplitude Method (Jong and Lee 2004) to determine the most effective products (inputs) on flyrock distance. To apply sensitivity analysis method, given data pairs, used to construct a data array X based on Eq. (13), are expressed in the form of common X-space. X ¼ fX1 ; X2 ; . . .; Xn g
ð13Þ
According to analysis method, as given in Eq. (14), each element (xi) in the data array X is a vector of lengths. xi ¼ fxi1 ; xi2 ; . . .; xim g1
ð14Þ
Therefore, each data pairs can be considered as a point in an m-dimensional space and m-coordinates. The strength
Type of data
Parameter
Symbol
Min
Max
Inputs
Bhl St
BHS
1.3
27
S
S
2
6.5
0.87
N hl
NH
6.6
228
38.82
Qmax T Pf S2t
QT
16.8
1200
249.57
Qmax T hl Pf St
QTH
9.6
597.9
95.07
RMR hl
RH
108
658
117.25
Fd
FLY
10
100
21.08
Output
Standard deviation 4.25
Fd Flyrock distance (m), B burden (m), St stemming (m), hl hole length (m), S spacing (m), N number of rows, Qmax maximum charge per delay (kg/ms), T time delay (ms), Pf powder factor (kg/m3), RMR Rock mass rating
Fig. 4 Comparison between the measured and predicted flyrock for the H-DAFIS model
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Author's personal copy Int. J. Environ. Sci. Technol. Fig. 5 Comparison between the predicted flyrock by H-DAFIS with measured
of the relations between inputs and output (rij) in the form of the membership value, which results in a pairwise comparison of two data pairs (xi and xj), can be calculated through Eq. (15). The results obtained from the sensitivity analysis are shown in Fig. 6, indicating RH, S, BHS as the most effective products in the prediction of flyrock distance. Therefore, they should be accurately estimated. QT has the least effect on predicting flyrock through HDAFIS model. !, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! m m m X X X rij ¼ xik xjk x2ik x2jk ð15Þ k¼1
k¼1
k¼1
In order to assess in detail the capability of the H-DAFIS approach, the predicted results by H-DAFIS are compared with the results of the models presented developed by Ghasemi et al. (2012, 2014). The main reason for selecting these two studies for comparison with the present research is the similarity of their case study, namely, Sugnun copper mine. Ghasemi et al. (2012) initially developed an equation using dimensional analysis and nonlinear regression based
Fig. 6 The results of sensitivity analysis in the flyrock estimation (; where all parameters are explained in Table 1)
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on seven parameters as listed in Table 1. The predicted results by the equation indicated that there is a correlation coefficient of 0.8338 and an RSME index of 6.09. Then, a model was developed based on Monte Carlo simulation to predict flyrock. The predicted flyrock based on Monte Carlo was 81.44 m, while the average measured flyrock was 72.43 m. As a result, the average deviation of the predicted flyrock by Monte Carlo from the measured result is 11.06%. It should be noted that the predicted results by the equation were closer to measured results than the Monte Carlo model. It indicates that the predictions of the Monte Carlo model include more RSME index than the equation. Ghasemi et al. (2014) developed two predictive models based on the artificial neural network and fuzzy logic to predict flyrock in Sungun copper mine. The performance of the models was assessed by comparing the predicted results with the measured ones based on a number of 45 datasets. It was concluded that the correlation coefficient for the fuzzy and artificial neural network models was 0.957 and 0.939, respectively. Furthermore, the RMSE indices were calculated as 4 and 4.73 for the fuzzy and artificial neural network models, respectively. Therefore, the results of the fuzzy model were closer to the measured results than the predicted ones by the artificial neural network. Among the models developed by Ghasemi et al. (2012, 2014), the fuzzy-based model developed by Ghasemi et al. (2014), which includes a correlation coefficient of 0.957 and an RSME index of 4, is more accurate. It is evident that the H-DAFIS predictions based on the correlation coefficient of 0.9761 and the RSME index of 3.33 are closer to the measured results than the fuzzy model (Ghasemi et al. 2014) which includes less correlation coefficient and higher RSME index. It should be noted that the other models reviewed in the literature, for example, the research by Faramarzi et al. (2014) includes less correlation coefficient and higher RSME than the
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H-DAFIS approach. Hence, the correctness of H-DAFIS approach is verified. It can be concluded that the H-DAFIS approach is more capable than the other models in the prediction of the blast-induced flyrock distance. The predictions with less error by H-DAFIS can be due to the integrated dimensional analysis and fuzzy inference system in which the most effective parameters were considered in the form of dimensionless products based on the dimensional analysis process. The main advantage of the present research is to study in details and consider the most effective parameters better than others in the literature. The contribution of the present study is to provide an approach to more accurately predict the blast-induced flyrock based on the dimensionless products of the most effective parameters and uncertainties in datasets using a fuzzy inference system.
Conclusion It is concluded that the proposed H-DAFIS model based on integrating dimensional analysis and fuzzy inference system was capable of predicting blast-induced flyrock with appropriate accuracy. In the fuzzy part of the model, Mamdani fuzzy inference technique was used. The most effective input parameters resulting from the dimensional analysis part of the model, which affected flyrock distance (output) were six multiple products, including burden, stemming, hole length, spacing, the number of rows, maximum charge per delay, time delay, powder factor, and RMR. To predict flyrock distance, H-DAFIS model based on fuzzy inference system including six inputs, one output, and 290 linguistic rules was developed. This model exhibited the most reliable predictions when compared with the real measurements. The correlation coefficient (R2) for the model was determined to be 97.61%. H-DAFIS model seemed to be a good tool to predict flyrock because fuzzy systems possessed sufficient flexibility for specific cases. Sensitivity analysis revealed that the most effective parameters on flyrock distance were RH, S, BHS and the least effective parameter was QT. Acknowledgements The authors would like to thank the Sungun copper mine management team for the aid during our research. Special thanks go to the others who gave us the valuable notes and comments.
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