SELECTION OF THE MOST PROPER DRILLING AND BLASTING PATTERN BY USING MADM METHODS (A CASE STUDY: SANGAN IRON ORE MINE, IRAN)

Drilling is the first stage of open pit mining that has a considerable effect on the other stages of mining, including blasting, loading, hauling and crushing. An unsuitable drilling pattern may lead to undesirable results such as poor fragmentation, back break and fly rock that not only results in technical and safety issues but also increases the operating cost of the mine. Multi-Attribute Decision-Making (MADM) methods can be useful approaches to select the appropriate drilling pattern among various alternatives, performed previously. This paper aims to select the most proper drilling and blasting pattern for Sangan Iron Mine, Iran. To achieve this, in the first step, rock fragmentation, back break, fly rock, specific charge and specific drilling were considered as the decision criteria and their degree of importance was calculated using the AHP method under a fuzzy environment. Then, TOPSIS and PROMETHEE methods were used to select the most proper alternative. The results of this study show that the drilling pattern with a spacing of 5 m, burden 4 m, hole depth 10 m, and hole diameter 15 cm is the most suitable one. The stemming length and powder factor of the suggested pattern are 2.3 m and 2.6 gr/cm3, respectively.


Introduction
Drilling and blasting play a vital role in mining projects. The quality of the blasting operation and subsequently, the adequate rock fragmentation are effective parameters that have a considerable effect on the mine productivity (Shi et al. 2012). Reduction of the mineral size to suitable fragmentation is necessary for either hauling or crushing processes. Poor fragmentation increases the operating cost of a mine and also the amount of dust in the mine atmosphere. The main aim of drilling and blasting pattern (DBP) selection is to reduce the costs of rock crushing and then improve the operational effectiveness. Nowadays, many researchers have been trying to propose the most suitable DBP. In some studies, back break was considered as a destructive phenomenon (Gate et al. 2005 Regarding the past stud-ies, effective factors in selecting the most appropriate DBP can be categorized into technical (fragmentation and back break), economical (specific charge and drilling) and safety parameters (such as fly rock, ground and air vibrations). Drilling patterns suggested by the experimental methods are not accurate enough and cannot consider all the effective criteria, mentioned earlier, simultaneously. These parameters are varied from one site to another and their degree of importance is also not the same in all cases. In such conditions, using multi-criteria decision-making (MCDM) methods to select the most proper pattern among all the options seems essential.

Monjezi et al. (2012b) used the Technique for Order of
Preference by Similarity to Ideal Solution, the TOPSIS method for the selection of the most appropriate DBP in the limestone Tajareh mine in Iran. In this study, drilling and blasting cost, fragmentation and fly rock were considered as decision criteria and the most proper DBP was selected among 19 patterns, performed previously. In other studies, the most suitable DBP was proposed for the Sungun Copper Mine in Azerbaijan Sharghi Province, Iran using MADM methods among 27 performed patterns (Yari et al. 2013(Yari et al. , 2014a(Yari et al. , 2014b(Yari et al. , 2017. In these studies, specific drilling, powder factor, fly rock, back break and fragmentation were considered as attributes. Regarding the results of these studies, the TOPSIS method showed that the drilling pattern with a diameter of 12.7 cm, burden of 3 m, spacing of 4 m and hole Rudarsko-geološko-naftni zbornik i autori (The Mining-Geology-Petroleum Engineering Bulletin and the authors) ©, 2020, pp. 97-108, DOI: 10.17794/rgn.2020.3.10 length of 11.8 m was the most proper one (Yari et al. 2013). Based on the Taxonomy method, the selected pattern with a hole diameter of 15.24 cm, burden of 3 m, spacing of 4 m and stemming rate of 3.2 m was selected as the most suitable drilling pattern (Yari et al. 2014a that was consistent with the ELECTRE method results (Yari et al. 2013). At the same time, the application of the liner assignment method showed that the pattern with a burden of 3.5 m, spacing of 4.5 m, stemming of 3.8 m and hole length of 12.1 m was selected as the most suitable pattern (Yari et al. , 2017. These results indicate that, a single MADM method is not efficient to enable a complete and correct analysis and therefore to obtain a more reliable result, two or more methods should be used by utilizing the strengths of each one. A review of past studies, mentioned above, shows that the conventional MCDM methods were used to select the most appropriate DBP is some cases. However, in most cases, it is difficult for experts and decision-makers to compute verbal and linguistic variables. In such circumstances, the uncertainties should be interpreted in a fuzzy environment. This paper aims to select the most appropriate DBP for the Sangan Iron Ore Mine in Razavi Khorasan Province, Iran among different proposed drilling patterns, performed previously. To achieve this, fragmentation, fly rock, specific drilling, back break, and specific charge have been selected as the decision criteria. To avoid ambiguities and uncertainties in obtaining the importance weight of each criterion, calculations should be done under a fuzzy environment instead of crisp values. Therefore, the degree of importance of each criterion is determined using the Analytical Hierarchy Process (AHP) method under a fuzzy environment. To select the most proper DBP, the technique for the order of preference by similarity to an ideal solution (TOPSIS) and the preference ranking organization method for enrichment evaluation (PROMETHEE) methods are used. TOPSIS is an understandable and straightforward method that is applicable to handle both qualitative and quantitative data sets. PROMETHEE is one of the new and simple MCDM methods that can derive the partial and full ranking of alternatives. This method includes both qualitative and quantitative criteria and supports grouplevel decision-making to identify the positive and negative aspects of the alternatives. PROMETHEE is a clear and stable MADM and there is no need for preferences to be expressed as linear relationships. Characterized by different types of preference functions, being a userfriendly method, and the successful application in reallife planning problems are the main advantages of this method. Nowadays, PROMETHEE has been applied in many applications in the field of mining engineering . Although, the TOPSIS and PRO-METHEE methods have been used in various fields of mining engineering, the application of these methods to select the most suitable DBP has not yet been reported. This paper aims to integrate the fuzzy-AHP-TOPSIS and also the fuzzy-AHP-PROMETHEE methods for the selection of the most proper drilling pattern for the Sangan Iron Ore mine in Razavi Khorasan Province, Iran. This paper is divided into four sections. In section 2, the Fuzzy AHP, TOPSIS and PROMETHEE methods are represented. In section 3, the case study and the geometrical specifics of all the performed DBP are presented. Finally, in section 4, first the weight of each criterion is obtained by using the fuzzy AHP method and then the TOPSIS and PROMETHEE methods are applied to find the most proper DBP.

Theoretical foundation; MCDM methods
Multi-criteria decision-making (MCDM) is one of the branches of operation research used to prioritize and select the best available alternative considering various criteria which are sometimes opposite indices. Multiobjective decision-making (MODM) and multi-attribute decision-making (MADM) are two kinds of MCDM (Pohekar and Ramachandran 2004). MODM methods are generally used to design and optimize problems while the MADM methods are applied to select the most proper alternative among different options. Nowadays, different methods have been presented for MADM problems. This section is devoted to representing the steps of the fuzzy AHP, TOPSIS, and PROMETHEE, as the most applied MADM methods in selection problems.

AHP under fuzzy environment
AHP is one of the most powerful and simplest methods used to define a criteria's degree of importance in MADM problems. Nowadays, many successful applications of AHP have been reported in vague decision-making problems such as the selection of opencast mining equipment (Samanta et al. 2002), underground mining method selection (Gupta and Kumar 2012), the selection of a primary crusher (Rahimdel and Ataei 2014), the selection of a transportation system (Despodov et al. 2011), plant species selection for mine reclamation (Alavi 2014) and groundwater potential zones in coal mining (Kumar and Krishna, 2018). In the first step of AHP, the hierarchy structure of the problem is constructed and then pairwise comparison matrixes are created. Finally, the relative weights are calculated. In conventional AHP, the pairwise comparison is made using crisp scale values. A nine-point scale is a frequently used scale (ranging from 1 for equally important to 9 for extremely preferred). Although the application of crisp values is simple and straightforward, it does not consider uncertainties and vagueness in expert judgments. To overcome this scarcity, fuzzy numbers ( ) are used in order to capture ambiguous. In this study, a triangular fuzzy number (TFN) is used. A character "~" represents a fuzzy set and the TFN is expressed with = (a,b,c). The parameters a, b and c indicate the smallest possible, most promising and largest possible values, respectively (Alavi 2014; Kumar and Krishna 2018).
The steps of AHP under a fuzzy environment are given as below (Rahimdel and Bagherpour 2018):

Constructing the Fuzzy Judgment Matrix
In the first step of the fuzzy AHP, a fuzzy decision matrix with TFNs ( is constructed as Equation 1: This matrix contains fuzzy numbers . The fuzzy linguistic variables include just equal to extremely preferred and the fuzzy numbers corresponding to them are given in Table 1.

Calculating the fuzzy synthetic extent value
After forming the fuzzy decision-making matrix, the synthetic extent value (S i ), a triangle fuzzy number, is calculated for the i th criterion as shown in Equations 2 and 3: (2) (3) Where: Symbol g -the row number Symbols i and j -the alternatives and criteria

TOPSIS method
TOPSIS is another MADM method offered by Hwang and Yoon (1981). In this technique, alternatives are ranked based on the distance from an ideal solution and negative ideal solution. On the other hand, the alternative with the shortest distance from the positive ideal solution (the best one) and the biggest distance from the negative ideal solution (the worst case) is ranked in a higher order. This method is understandable and straightforward, and it is used to handle both qualitative and quantitative data sets. The TOPSIS method has been applied to different mining-related decision problems (Wu et The normalized decision matrix (R) is created as Equation 8: Where: r ij -the normalized value, calculated as Equation 9: The weighted normalized decision matrix, with v ij as weighted normalized values, is calculated as Equation 10: Where: W j -the weight of j criterion that are calculated from the fuzzy AHP method.

Determine the positive-ideal and negative-ideal solution
Positive ideal solution ( ) and negative ideal solution ( ) for benefit (I) and cost (J) criteria are respectively calculated from the following Equation 11. (11)

Calculating the separation measures and ranking the preference order
To calculate the separation measures, the n-dimensional Euclidean distance is used. In this way, the separation of each alternative from the positive-ideal solution ( ) and negative-ideal solution ( ) are calculated as Equation 12: , (12) For ranking the alternatives, relative closeness ( ) to the ideal solution is used as Equation 13: The order of all alternatives is determined by considering the descending order of such that the higher , the better is the alternative.

PROMETHEE (Preference Ranking Organization
Method for Enrichment Evaluation) is a new MADM method proposed by Brans (1982) and then developed by Brans and Vincke (1985). PROMETHEE shows the opposition between all alternatives and considers both qualitative and quantitative attributes with high flexibility and accurate calculations. It also has simpler and more straightforward equations in comparison to other MADM methods. PROMETHEE has been applied in different fields of mining engineering such as the selection of an ore transport system for an underground mine parison to others. In fact, this function represents an increasing function of deviation. On the other hand, smaller deviations mean weaker preference degrees and larger ones indicate a stronger preference. Six preference functions with specific shapes have been presented in PRO-METHEE. The shape of each function is dependent on two thresholds, named P and Q. Threshold Q represents the largest deviation, considered negligible while, P (cannot be smaller than Q) indicates the smallest deviation, considered as decisive (Brans 1982;Brans and Vincke 1985). In PROMETHEE, two parameters, named positive flow (φ + ) and negative flow (φ -), are calculated for each alternative regarding the given importance degree for each criterion. The character φ + expresses how much each alternative is higher than all other ones. This means the higher the φ + , the better the alternative. On the other hand, φindicates the superiority of an alternative over the other ones (Behzadian et al. 2010). The steps of the PROMETHEE method are represented below.

Implementing the preference function and calculating overall preference
After constructing a decision matrix, the preference function in the creation j, (P j (a,b)), is applied to decide how much the value a is preferred to b for this criterion. Then, the overall preference index ( ), which takes all the criteria into account, is calculated as Equation 14: Where: W j -the weight of criteria j.

Calculating positive and negative flows for each alternative
The positive flow (φ + ) and negative flow (φ -) for each alternative are respectively, calculated as Equation 15: It is noted that the PROMETHEE I provides a partial ranking of the alternatives while, PROMETHEE II used the net flow ( ) for the ranking of alternatives such that, the alternatives are ranked based on their net flow (Anand and Kodali 2008).

Final rank of alternatives
When there is a difference between the achieved scores for alternatives in applying different MCDM methods, a robust aggregation method needs to be considered. Since, there is no guarantee to obtain the optimum results in averaging the obtained ranks, other methods such as Borda and Copeland rules are applied (Pomerol and Barba-Romero 2012). In the Borda method, a pairwise comparison matrix between the alternatives is constructed regarding their scores obtained from the MCDM methods. This matrix is a zero-one matrix. If the alternative in that row is more rational than the alternative in that column, then the alternative obtains one. Otherwise, it obtains zero. Then, the row sum for each row is calculated for alternative ranking. In the Copeland method, that is a modified version of the Borda, the number of times that an alternative is preferred over the others is subtracted (row-sum) from the number of times that an alternative is subordinated. A column-

Case study; Sangan Iron Ore Mine
The Sangan iron ore mine is located 16 km north of Sangan city and 300 km southeast of Mashhad in Razavi Khorasan Province, Iran. The location of this mine is shown in Figure 2. The total geological reserve of this mine was evaluated to be about 1.2 billion tons of iron ore with an average grade of 50 percent Fe 3 O 4 . The annual production of the mine is 4.5 million tons of which 2.6 million tons of iron pellets are produced per year. Drilling equipment is used for blasting holes with different diameters from 76 to 200 mm. In the blasting operation of the mine, vertical blast holes with a diameter of 10, 15, and 20 cm are drilled in length ranging from 8.5 to 10.5 m. Pattern geometry is staggered and ANFO is the main explosive. The dynamite cartridges are used as a primer and a detonating cord is utilized as the initiation system. The consumed charge per period is 159-964 kg and the burden to spacing ratio is about 0.65 to 0.87. More details on these patterns are given in Table 2.
In the first step of the research, the decision-making criteria are defined. In this study, to evaluate DPB, five criteria including specific charge (SC), specific drilling (SD), rock fragmentation (RF), Flyrock (FR) and back break (BB) were considered regarding the past studies and experts' opinions. Specific charge (SC) is the amount of explosives needed to break one ton of rock. This parameter represents the distribution of explosives in the rock mass and has a considerable impact on the blasting results. Specific drilling (SD) is the hole length drilled per one cubic volume of the rock. With an increase in SD, mining costs increase, therefore this parameter has a negative effect on the drilling operation. Rock fragmentation (RF) has a direct effect on the drilling and blasting costs and also on future mining operations such as material transportation and crushing process. RF depends on both rock mass properties (that are uncontrollable) and drilling and blasting design parameters, which can be controlled. An efficient blasting operation can be reached by investigating the relationship between blast design parameters and rock fragmentation. Fly rock (FR) refers to rock pieces that fly beyond the blast site which may cause injuries to people and also damage to equipment, machinery or even structures. This parameter is one of the major issues in blasting operations which must be efficiently controlled. Back break (BB) is defined as the broken rocks beyond the specified limits of the rear row of the drilled holes. This phenomenon is another nega-tive issue resulting from a poor blasting operation. BB causes instability of the mine walls, falling down of machinery and improper fragmentation (Gokhale 2010;

Morin and Ficarazzo 2006; Cho and Kaneko 2004).
A description of the drilling pattern of the mine, performed previously, is considered as problem attributes.

Results and discussion
This section is devoted to the selection of the most proper drilling and blasting pattern for the Sangan Iron Ore mine. In the first step, the degree of importance (or weight) of criteria is calculated by using AHP in a fuzzy environment. Then, a decision matrix that includes values of the criteria for the 17 drilling pattern (see Table 2) is created and the TOPSIS and PROMETHEE methods are applied to find the most proper DBP pattern.

Calculation of the weight vector
In the first step of the fuzzy AHP, a decision-making group used linguistic scales (see Table 1) to obtain the TFN comparison matrix. To achieve this, data collected from 14 expert's opinions was applied. Then, the fuzzy comparison matrix for all criteria is created as given in Table 3.
The synthetic extent values (S i ) were calculated for each criterion and then, the possibility degrees of each pairwise criteria were calculated as follows:    According to the possibility degree values, the normalized weight of the criteria was calculated and shown in Figure 3. The results indicate that rock fragmentation and fly rock have the highest and lowest importance, respectively.

Selection of the most proper DBP using the TOPSIS method
This subsection tried to select the most proper DBP for the studied mine by using the TOPSIS method. To achieve this, the practical results of the formerly performed pattern were considered as the decision matrix as given in Table 4. It is noted that all criteria except RF and BB are expressed in the form of numerical values which means they are not measured systematically. Therefore, in the first step, the qualitative criteria (RF and BB) were converted to numerical values while considering values 1, 2 and 3 as acceptable, fairly acceptable and unacceptable levels, respectively. Then, a normalized decision matrix was created using Equation (12). The weighted normalized decision matrix was formed using Equation (13) and Table 4 and given in Table 5. The positive ideal solution () and negative-ideal solution () were computed using Table 5 and Equation (14) and given in Table 6. The distance between each alternative and and was calculated and then the closeness coefficient of the alternatives was calculated to rank a drilling pattern. The results are given in Table 6. Regarding the results, alternatives P16 and P4 are the best and worst patterns, respectively.

Selection of the most proper DBP
using the PROMETHEE method In this subsection, the most suitable drilling pattern is selected using the PROMETHEE method. In this meth-od, to select the most proper alternative, the comparison matrix for all alternatives is created. Regarding the high volume of calculations and the limitation of page numbers, the details of the calculations have been omitted. The overall preference index (π(a,b)) is calculated by using Equation (14) and Table 5 and given in Table 8. The positive, negative and net flows are calculated regarding Table 8 and Equation (15). The results are presented in Table 9. Regarding Table 9, pattern No. 16 is selected as the most proper drilling pattern, which is consistent with the TOPSIS results.
The final rank of the pattern in the application of the Copeland aggregation method is given in Table 10. Regarding the results, pattern No. 16 is selected as the most suitable alternative. It is worth noting that the specific charge and specific drilling of this pattern is 38.77 and 16.70 percent lower than the average ones, respectively. The rock fragmentation of the pattern no. 16 equals the average rock fragmentation of all studied patterns and the back break is acceptable.

Conclusion
Drilling and blasting is the most common method applied in open pit mining which is a very important part of a mining operation. Improper drilling and blasting operations may lead to adverse technical and safety consequences such as fly rock, back break and therefore, increases in the operating costs of mines. In this paper, the most ideal drilling and blasting pattern was proposed for the Sangan Iron Mine, Iran. Specific charge, fly rock, rock fragmentation, back break and specific drilling were considered as decision criteria and the most suitable drilling pattern was selected among 17 patterns, all previously performed. The AHP method under a fuzzy environment was used to define the weight of criteria and the TOPSIS and PROMETHEE methods were applied to select the most ideal drilling and blasting pattern. Regarding the results of this study, rock fragmentation, specific charge and specific drilling have the highest degree of importance, respectively. A drilling and blasting pattern with a spacing of 5 m, a burden of 4 m, a hole depth of 10 m, and a hole diameter of 15 cm is proposed as the most proper alternative. Considering the effect of the suggested pattern on direct and indirect costs of the mining operation, studying the effect of the proposed pattern on ground vibration and air blast and applying other multi-attribute decision-making methods to find the most suitable alternative could be recommended for future studies.