APPLICATION OF TOPSIS METHOD IN CONTROLLING FLY ROCK IN BLASTING OPERATIONS

[3- 24]. TOPSIS method is a Technique for Order Preference by Similarity to Ideal Solution and proposed by Hwang and Yoon [11]. The ideal solution (also called positive ideal solution) is a solution that maximizes the benefit criteria/attributes and minimizes the cost criteria/attributes, whereas the negative ideal solution (also called anti-ideal solution) maximizes the cost criteria/attributes and minimizes the benefit criteria/attributes. The so-called benefit criteria/attributes are those for maximization, while the cost criteria/attributes are those for minimization. The best alternative is the one, which is closest to the ideal solution and farthest from the negative ideal solution [22]. Suppose a MCDM problem has m alternatives, mAA ,...,1 and n decision criteria/attributes, nCC ,...,1 . Each alternative is evaluated with respect to the m criteria/attributes. All the values/ratings assigned to the alternatives with respect to each criterion form a decision matrix denoted by mnijxX  )( . Let ),...,( 1 nwwW  be the relative weight vector about the criteria, satisfying 1 1   n i iw . Then the method can be summarized as follows: A- Calculate the decision matrix (D) as            mnm n XX XX D    1 111 (1) B- Calculate the normalized decision matrix or R matrix. The normalized value ijr is calculated as    m i ij ij ij x xr 1 2 ni ,...,1 , mj ,...,1 (2)            mnm n rr rr R    1

(3) 3 C- Calculate the criteria weighted matrix as            nw w w W    0 0 2

(4) D- Calculate the weighted normalized decision matrix. The weighted normalized value ijv is calculated as RWrwv ijiij  mj ,...,1 , ni ,...,1 (5) Where jw is the weight of the j th attribute or criterion, and 1 1   n i iw . E- Determine the positive ideal and negative ideal solution.    )min(),max(,..., JivIivvvA ijjijjn1   (6)    )max(),min(,..., JivIivvvA ijjijjn1   (7) Where I is associated with benefit criteria, and J is associated with cost criteria. F- Calculate the separation measures, using the n-dimensional Euclidean distance. The separation of each alternative from the ideal solution is given as      n i iijj VVS 1 2 mj ,...,1 (8) Similarly,the separation from the negative ideal solution is given as      n i iijj VVS 1 2 mj ,...,1 (9) G- Calculate the relative closeness to the ideal solution. The relative closeness of the alternative jA with respect to A is defined as     jj j j SS SC mj ,...,1 (10) Since 0 JS and 0 JS , then, clearly,  1,0JC . H- Rank the alternatives according to the relative closeness to the ideal solution. The bigger JC , is the better the alternative jA . The best alternative is the one with the greatest relative closeness to the ideal solution [22]. Case Study Tajareh limestone mine Tajareh limestone mine is situated in Lorestan province 12 km north-east of Khoramabad. From geological point of view the mine is in Zagros geo structural formation and the whole area is covered with cretaceous formations. The area is dominantly consists of limestone with rodesite and orbitoline. Crystals of calcite in the form of cripto-crystaline is observed which is fractured under tectonical factors and then the cracks have been filled with white calcite. Keeping in mind the type and application of limestone, exploitation is carried out by conventional method of drilling and blasting. The main explosive used is ANFO and 4 dynamite as primer. A complete cycle of extraction contains drilling, blasting, loading and hauling. The technical design parameters are given in Table 1. Table 1- Tajareh limestone mine design parameters amountParameteramountParameter

mWorking bench width150 mBench length

mSafety bench width8 mWorking bench high 72°Bench slope50°Pit slope Different drilling patterns applied in the mine The available drilling machines are suitable to make blast holes with various diameters, i.e. 42, 64, 76 and 100 mm. The maximum size of fragmented rocks proper for crusher should be 55 cm. To obtain an optimum drilling pattern and applying ASH and Longnforce formulae, 19 different drilling patterns were designed and applied in the mine (Table. 2) [2, 25, 26]. With the help of data practically gathered from the aforesaid patterns and using statistical method as well as TOPSIS, the optimum design parameters were selected among different alternatives. Table 2- Drilling patterns in Tajareh limestone mine Detonator typeStemmingHole depthDrilling patternFormulaeHole diameterNumber mmmm Delay 0.4-0.61.20-3.20rectangularAsh421 Zero-detonator0.4-0.61.20-3.20rectangularAsh422 Delay 0.5-0.71.20-3.20rectangularAsh423 Delay 0.5-0.71.60-3.20almondAsh424 Delay  0.4-0.61.20-2.80rectangularAsh425 Delay 1.206almondLong force646 Delay  0.63irregularLong force647 Delay  0.65irregularLong force648 Delay  0.63almondAsh649 Delay  1.206.5-8.5almondAsh6410 Delay 1.37almondAsh7611 Delay 1.57-10almondLong force7612 Cordex  0.83.60-4.50almondAsh7613 Delay 0.83-6almondAsh7614 Delay 0.63almondAsh7615 Delay  1.49almondAsh7616 Delay  15almondAsh7617 Zero-detonator1.206rectangularAsh10018 Delay 15rectangularAsh10019 Determination of design parameters using statistical method 5 With increasing diameter of blast hole the cost of drilling and blasting is reduced, penetration rate is diminished, degree of fragmentation is decreased and amount of fly rock is increased. It is mentioned that a suitable hole diameter should control fly rock and produce good fragmentation and on the other side should keep the costs of drilling and blasting at a minimum level. As it is observed from Fig 1, fly rock is 87 m and 157.5 m for blast hole diameters of 42 mm and 100 mm, respectively. Fig. 1- relationship between fly rock and blast hole diameter in Tajareh limestone mine Comparing practical results with that of obtained from available theoretical formulae and to fulfill the requirements of a good blasting operation, it seems that staggered V of ASH method with 3 rows, gives the best result in this mine. The other design parameters are given in table 3. Table 3- Design parameters of blasting operation in Tajareh limestone mine amountParameteramountParameter Burden1.7 mSub drilling0.5 m Spacing2.2 mHole dip72° Stemming1.2 mHole diameter64 mm Determination of design parameters using TOPSIS method To determine blasting pattern with TOPSIS method, in the first step various alternatives and affecting parameters should be distinguished (Table 4). Fly rock is a numeric figure but the other two parameters, fragmentation and costs are qualitative (non numeric). In the second step, normalized decision matrix is constructed as fallows: Matrix 1- normalized decision matrix

320.320.230.230.230.230.230.320.230.230.230.230.230.230.130.130.130.130.13

290.120.290.290.120.120.210.040.290.260.210.120.120.040.250.290.290.210.29 6

280.310.240.220.260.260.280.210.220.190.250.220.240.180.170.130.160.210.15 Table 4- Results of blasting operation in Tajareh limestone mine ParameterAlternative Fly rockFragmentationDrilling & Blasting costsMethodHole diameter Deterministic variableLinguistic VariableLinguistic Variable(mm) 80suitablehighAsh421 110mediumhighAsh422 85suitablehighAsh423 70suitablehighAsh424 90suitablehighAsh425 95unsuitablelowLong force646 130unsuitablemediumLong force647 120unsuitablemediumLong force648 135mediummediumAsh649 100suitablemediumAsh6410 120suitablemediumAsh7611 115unsuitablelowLong force7612 150mediummediumAsh7613 140unsuitablemol lowAsh7614 140unsuitablemol lowAsh7615 120suitablemol lowAsh7616 130suitablemol lowAsh7617 165unsuitablelowAsh10018 150suitablelowAsh10019 Due to differentiation among involved parameters, considering a specified weight for each parameter is inevitable (Table. 5). As the most important parameter is fly rock the corresponding weight is considered more comparing to other parameters. Using formula 11 and corresponding parameters, new weighting vector can be developed. Table 5- Parameters weight in blasting operation Fly rockDrilling & Blasting costsFragmentation

50.40.3Weight of each parameter

2040.2180.639Normal weight vector },...,2,1{; . . 1 nj w w w n j jj jj j      (11) W'= {0.249 –0.547 –0.204} 7 In the third step considering weighting vector new weighted normalized matrix is calculated. Matrix 2- weighted normalized matrix

080.080.050.050.050.050.050.080.050.050.050.050.050.050.030.030.030.030.03

160.070.160.160.070.070.110.020.160.160.110.070.070.020.140.160.160.110.16

050.060.050.040.050.050.050.450.040.030.050.040.050.030.030.020.030.040.03 In the final step, calculated ratings of each alternative are given in the table 6. Table 6- TOPSIS score for each alternative Score (%)MethodHole diameter (mm)NumberScore (%)MethodHole diameter (mm)Number

6Ash761175.5Ash421

2Long force761258.7Ash422

4Ash761375.5Ash423

6Ash761475.9Ash424

6Ash761569.7Ash425

6Ash761620.0Long force646

3Ash761735.2Long force647

5Ash1001835.9Long force648

6Ash1001962.6Ash649

8Ash6410 It is observed that alternative No. 10 is having the highest rating and alternative No. 6 is having the lowest rating. According to the TOPSIS method calculated design parameters are brought in the table 7. Table 7- Determined drilling pattern using TOPSIS method in Tajareh limestone mine amountParameteramountParameter Burden1.7 mSub drilling0.5 m Spacing2.2 mHole dip72° Stemming1.2 mHole diameter64 mm Conclusion Normally statistical methods are satisfactorily used to determine suitable blasting parameters and minimized fly rock. However simultaneous effect of concerned parameters is not possible with these methods. To overcome this problem, rather new methods such as TOPSIS can be utilized. TOPSIS method can effectively be used for minimizing fly rock in the blasting operations. The results obtained from statistical methods and TOPSIS are identical and both the methods are suggesting a hole diameter of 64 mm for blasting operation in Tajareh limestone mine. Applying this diameter, satisfying economical aspects, the problem of fly rock was reduced considerably. Reference

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