# Selection of an Appropriate Method to Extract the Dimensional Stones Using FDAHP & TOPSIS Techniques

Document Type: Regular Article

Authors

1 Mining and metallurgical department, Urmia university of Technology.

2 Department of Mining and Metallurgical Engineering, Urmia University of Technology, Urmia, Iran

3 Urmia University of Technology

4 Birjand university

Abstract

In this paper it was aimed to select a suitable method to extract the dimensional stone to increase dimensional stone quarries efficiency. The usual methods including diamond cutting-wire method, blasting method, plug and feather method, Katrock expanding material and Fract expanding material have compared using TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method by respecting to the following criteria: grass income, safety, desirability, reduction of environmental impacts, waste and reduction of extracting time. FDAHP (Fuzzy Delphi Analytic Hierarchy Process) approach was used in determining the degree of importance of the criteria by expert decision makers. Also, those criteria performed the same impacts were not considered. Consequently, the diamond wire saw method was suggested as the most appropriate method to extract the dimensional stones. It was concluded that the extraction of dimensional stone using diamond wire saw is the best method based on the mentioned criterion compared to other methods.

Highlights

Keywords

Main Subjects

# 1. Introduction

From the time humankind was thinking about a strong building, quarrying has been started. Hence it could be inferred that quarry has a history of many thousand years. Iran is a mineral-rich country with high potential in stone quarries, therefore mining has an important role in economic growth of the country. Studies show that Iran is the second country of the world for having stone quarries and the first for colorful and variant stones. Recently, some good industrial and laboratory tests in the field of the ability of dimensional stone cutting have been done in the country. Mikaeil et al. developed a statistical model to predict the production rate of diamond wire saws in carbonate rocks cutting [1]. Mikaiel et al. studied the vibration of circular diamond saw machine during rock sawing by using a fuzzy analytical hierarchy process [2]. Mikaeil et al. developed a new classification system for assessing of carbonate rock sawability [3]. Ataei et al. predicted the production rate of diamond wire saw using statistical analysis [4]. Mikaeil et al. studied the relationship between the production rate of dimensional stone with rock brittleness indexes [5]. Mikaeil et al. investigated the sawability of carbonate rock using fuzzy analytical hierarchy process and technique for order performance by similarity to ideal solution [6]. Mikaeil et al. estimated the power consumption of circular diamond saw in carbonate rock sawing process by using fuzzy Delphi analytical hierarchy process and technique for order performance by similarity to ideal solution [7]. Mikaeil et al. studied the relationship between specific ampere draw and rock brittleness indexes in rock sawing process [8]. Ataei et al. studied on ranking the sawability of carbonate rock by using fuzzy analytical hierarchy process approach [9]. Ghaysari et al. predicted the performance of diamond wire saw with respect to texture characteristic of carbonate rock [10]. Mikaeil et al. ranked the sawability of some Iranian famous dimensional stones using fuzzy Delphi and multi-criteria decision-making techniques [11]. Sadegheslam et al. predicted the production rate of diamond wire saw using multiple nonlinear regression analysis and neural network [12]. Mikaeil et al. investigated the relationship between system vibration of cutting machine and rock brittleness indexes during the dimensional stone sawing process [13]. Mikaeil et al. developed a ranking model for ranking the sawability of dimensional stone based on some important mechanical and physical properties [14]. Mikaeil et al. investigated the effect of freezing on strength and durability of dimensional stones using fuzzy clustering technique and statistical analysis [15]. Aryafar and Mikaeil estimated the ampere consumption of dimensional stone sawing machine using the artificial neural networks [16]. Mikaeil et al. predicted the performance of circular saw machine using imperialist competitive algorithm and fuzzy clustering technique [17]. Mikaeil et al. evaluated the performance of diamond wire saw by using harmony search algorithm [18]. Almasi et al. developed a new rock classification system based on the abrasiveness, hardness, and toughness of rocks and PA to predict the sawability of hard dimensional stone [19]. Almasi et al. investigated the prediction of the dimensional stone cutting rate based on rock properties and device pullback amperage in quarries using M5P model tree [20].Almasi et al. studied on the bead wear in diamond wire sawing based on some important mechanical and physical properties [21]. Akhyani et al. predicted the wear performance of circular diamond saw by combining fuzzy rock engineering system and genetic algorithm in hard rock cutting process [22]. Mikaeil et al. studied on the performance of diamond wire saw by using multivariate regression analysis [23].

There are few studies in the field of selection of dimensional stone extraction methods. There are various methods for extraction of dimension stones but the most common technique in vast majority of Irans quarries are plug and feather, diamond wire saw, blasting (low density) and expanding chemicals (FRACT and Katrock). All methods have advantages and disadvantages comparing with each other, so without a multi criteria method investigation, it could not be decided which of the methods is more effective. In order to choose the appropriate method, a set of factors including of gross profit, desirability, safety and … should be considered. In this article, after introducing each method and consideration of effective factors, the best extraction method due to the Technique for Order of Preference by Similarity to Ideal Solution Method (TOPSIS) is proposed.

# 2. Ordinary methods in quarrying

There are different methods in order to extract a dimensional stone cube. but the most common methods in vast majority of Irans quarries are plug and feather, diamond wire saw, blasting and expanding chemicals (FRACT and Katrock). Plug and feather is the oldest method of extraction. In this method some holes are dug on a line which is supposed to be cut. The diameter, depth and the amount of holes, depends on the stones type. The block is cut more easily if the distance between holes is decreased and the depth is increased. After boring holes, metal plugs and a metal feathers are put into the hole and then the feather is hit by a sledgehammer until the cube is cut due to the expansion of fractures. In blasting method, at first some horizontal and vertical holes are bored and then blasting process are used to cut the block. The main difference between explosive methods used in quarry and mining, is that in quarry, the cube must crack and loosen in the desired direction and not to destroy other blocks. One of the methods that is getting increasingly popular in Iran, is expanding powder. This material is used instead of blasting in quarries with a great increase of usage day after day. The mechanism of this method is more similar to plug and feather method rather than the explosive material method such as: gunpowder, dynamite and ANFO. In order to use the materials, parallel holes must be bored and then a mixture of this powder and water should be applied into the holes. After a while due to hydration and watering, the slurry will expand and this expansion will cause detaching of cube. In 1978 the first diamond wire saw machine was applied in Carrara Mine. Until now the method advanced rapidly both in equipment and wires. In this method, the diamond wire saw is looped around the cutting part and is cooled by water during the process. By applying the diamond wire saw through perpendicular holes, a loop is shaped. During the cutting process, the machine gets far from working face and by moving on rails while wire is in tension.

# 3. Effective factors in quarrying method selection

Factors including of gross profit, desirability, safety, time, environmental parameters and waste have effect on choosing quarry method. These factors could be divided into quantitative and qualitative groups. Some of these factors have negative effects on choosing a method and some have positive. For example, environmental effect is a negative and safety is a positive factor in choosing a method. Table 1 shows the quantitative and qualitative factors due to their negative and positive effects.

Table 1.

Effective factors in quarrying method selection due to their roles.

 Gross Profit Time Waste Safety Goodness Environmental parameters parameters Quantitative Quantitative Qualitative Qualitative Qualitative Qualitative Parameter specifications Positive negative negative Positive Positive Negative

Consider a block with a meter in its dimensions and 3 degree of freedom. To extract this block with each method such as: diamond wire saw, plug and feather, blasting and expanding chemicals FRACT and Katrock, extraction cost and income due to blocks price is shown in table below. The costs in table 2 are according to costs in some working mines in Iran [24, 25].

Table 2.

Gross Profit of different quarrying methods due to sell a cube meter of dimension rock.

 Expanding Materials Blasting Diamond cutting wire Plug and feather Cost (Toman per a cube meter) Katrock Fract 5000 35000 5000 3000 5000 Drilling cost 12000 21500 40000 - 10000 Used material cost - - - 30000 - Cutting Cost 800 500 800 400 800 Machines Cost 1800 1500 3600 - 1800 Excess Waste transportation cost 19600 27000 49400 33400 17600 Cost Total 360000 360000 240000 360000 340000 Sales Price 340400 333000 190600 333000 322400 Gross Profit

Again consider a block with a meter in its dimensions and 3 degree of freedom. In the methods include drilling parallel holes, as an average spacing, there is a hole in every 10 cm and hence in each non-free dimension of the block there is 10 holes that considering 10 m depth of each hole, about 30 m overall drillings is needed. Assume each meter takes 5 min, the total drilling time is 150 min. usually it takes 30 min to fill the holes with expanding chemicals and the operation time for Katrock is about 16 hours and for FRACT is 10 hours. Finally, the approximate time to produce a cube with one m3 volume for two methods is about 19 and 13 hours, respectively. In diamond wire saw method, boring 3 holes every 1 meter, takes 15 min and consuming time to apply wire is 30 min. According to average time of cutting of a cube with one m3 volume, total time to quarry a block is 4 hours. Of course, it should be mentioned that time consuming to produce the block in each method differs from mine to mine due to geo-mechanical properties of rock. In plug and feather and explosive methods, like the same as in parallel holes method, 30 holes in 3 non-free dimensions of the rock must be bored which due to the time needed for boring each hole, 150 min is needed totally for extraction. Also 3 hours needed for breaking the block, therefore 5.5 hours needed for extraction of a cube with one m3 volume. For filling the holes with explosives, each hole would take 5 min which in total comes to 2.5 hours for 30 holes. Therefore 5 hours needed to excavate a cube with one m3 volume using blasting method. Table 3 shows time consumption of each method.

Table 3.

Necessary time for quarrying using different methods.

 Expanding materials Blasting Diamond cutting wire Plug and feather Time(Hours) Katrock Fract 19 13 5 4 5.5

If the mineral resources are regarded as a national wealth, therefor wasting of them during extraction should be consider as quarry method disadvantages, then amount of wastes could be considered as an important factor in choosing a method. fissures created by explosive and plug and feather methods during extraction is considered as a one of the ways which lead to produce waste when cause the dimension stone to break during cutting process. Due to quarry mechanism, waste producing in diamond wire saw and expanding chemicals methods is less than other traditional methods. This is a qualitative factor according to quality of production. The results of waste producing in each method are given in table 4.

Table 4.

Qualitative comparison of produced waste form a cube meter quarrying for different methods.

 Expanding Materials Blasting Diamond Cutting Wire Plug and feather Waste Katrock Fract Middle Low High Seldom High

Lung diseases and eyesore are frequent healthy problem among workers which work with expanding powders. Although there is no evidence to prove the relationship between these healthy problems and expanding powders, but use of low quality and harmful ingredients in expanding powder produce which lead to low production price, could be a possible effective factor. Also, the possibility of producing harmful gas when using these nonstandard powders could not be neglected. Because of low quality of some of these materials, during usage especially in hot weather, they expand immediately after using and act like blasting. The blasting method has the least score in this case due to production of hazardous gases and uncontrolled rock fracturing. Safety of each method are shown in table 5.

Table 5.

Qualitative comparison of safety of different methods.

 Expanding materials Blasting Diamond Cutting Wire Plug and feather Safety Katrock Fract Low Middle Low High High

Diamond wire saws cubs has a major difference in quality compared with other methods produced cubs. This methods cube quality leads to reduction of transportation costs, increasing production efficiency, facility in movement and improvement of working face. Because blocks extracted by diamond wire saw dont need pre-cutting, therefore the final cost reduces in this method. In other words, the more quality of extracted blocks leads to more profit in markets. The quality of extracted blocks in blasting method, plug and feather and expanding chemicals, and diamond wire saw are weak, intermediate and high respectively. Table 6 shows the cubs quality of each method.

Table 6.

Qualitative comparison of different Quarrying Method Goodness.

 Expanding materials Blasting Diamond Cutting Wire Plug and feather Goodness Katrock Fract Low high Low Very high Low

Generally, mining activities will affect at least one of the environment components like water, soil and weather. According to environmental problems which each method produce, qualitative scores are given to each method that are shown in table 7.

Table 7.

Environmental Parameters Qualitative Comparison of different Quarrying Method

 Expanding materials Blasting Diamond Cutting Wire Plug and feather Safety Katrock Fract Low Middle Low High High

# 4. Selection a suitable extraction method using FDAHP & TOPSIS techniques

The TOPSIS method was first presented by Yoon and Hwang [27, 28]. Recently for multiple-criteria decisions, this method along with other methods such as AHP, FAHP, genetic algorithm and so on or alone have been used [26-37]. In this method, alternatives are categorized by their similarity to ideal solution. Therefore, when an alternative is more similar to the ideal solution, has a higher rank. To define this method, two concepts of “ideal solution” and “similarity to ideal solution” has been used. The ideal solution, is the solution that is the best in every aspect which generally doesn’t exist and we try to get near to it. In order to determine the similarity of a method to ideal and negative ideal solution, its distance from ideal and negative ideal solution is measured and alternatives are analyzed and categorized by relative distance from negative ideal solution to the sum of distance from ideal and negative ideal solutions. If in a multiple-criteria decisions problem, consisting of m alternatives and n criteria, in order to choose the best alternative using similarity to ideal solution method, steps are as following [26].

According to the number of cases and criteria and analyzing of all cases for different criteria, decision matrix is constructed as Equation 1.

 (1)

Where  is the operator of i alternative (i=1, 2, ..., m) to j criteria (j=1, 2 …, n).

According to existing methods for quarry of dimensional stones in Iran, five methods including plug and feather, diamond wire saw, expanding chemicals FRACT and Kat-rock and blasting as alternatives and factors including production cost, desirability, safety, time, ease of extraction, waste and environmental effects as problem criteria have been investigated. Qualitative and quantitative values for each factor and method (decision matrix) are shown in table 8.

Table 8.

Decision matrix.

 Gross Profit Goodness Safety Time Environmental effects waste Criteria 340400 Low Low 19 High Average Expanding Material (Katrock) 333000 High Average 13 Average Low Expanding Material (Fract) 190600 Low Low 5 High High Blasting 333000 Very High High 4 Low Very Low Diamond Cutting Wire 322400 Low High 5.5 Very Low High Plug and feather

Because considered criteria (production cost, desirability, safety, time, ease of extraction, waste and environmental effects) have quantitative and qualitative values, hence before making decision matrix, it is necessary to convert qualitative values in to quantitative (Table 8). To do so, table 9 can be used so that for qualitative values of very little to very much, equivalent quantitative values of 1 to 9 could be replaced. Table 10 shows the revised decision matrix (according to quantitative values).

Table 9.

Quantitating of qualitative parameters.

 Very Low Low Average high Very High Qualitative Parameters 1 3 5 7 9 Equivalent quantitative Value

Table 10.

Decision Matrix due to their quantitative value.

 Gross Profit Goodness Safety Time Environmental effects Waste Criteria 340400 3 3 19 7 5 Expanding Material (Katrock) 333000 7 5 13 5 3 Expanding Material (Fract) 190600 3 3 5 7 7 Blasting 333000 9 7 4 3 1 Diamond Cutting Wire 322400 3 7 5.5 1 7 Plug and feather

In the next step, various criteria with different dimensions is changed to dimensionless criteria and matrix R define as equation 2.

 (2)

There are different methods to dimensionless, but for similarity to ideal solution method, the equation 3 is used:

 (3)

To normalize the decision matrix, Equation 3 could be used. The normalized matrix is shown in table 11.

Table 11.

Normalized Decision Matrix

 Gross Profit Goodness Safety Time Environmental effects waste Criteria 0.492 0.239 0.253 0.775 0.607 0.434 Expanding Material (Katrock) 0.482 0.559 0.421 0.530 0.434 0.260 Expanding Material (Fract) 0.276 0.239 0.253 0.204 0.607 0.607 Blasting 0.482 0.718 0.589 0.163 0.260 0.087 Diamond Cutting Wire 0.466356 0.239 0.589506 0.224303 0.087 0.606977 Plug and feather

In this stage according to importance factor of different criteria in decision, we have a matrix as Equation 4.

 (4)

It is clear that W is a diametric matrix which elements on the diameter are non-zero and equal to related importance vector factor.

The most important part of decision making process in order to perform a comprehensive analyze and classification of a problem with a number of criteria, is to distinguish each criteria’s weight and their effect on that problem. Because executive decisions always made on some multi and relational criteria, each criterions effect lead to some difficulties in making decision. Therefore, defining the weight of each criteria is always the most important step. Two of the most recent methods for weighting effective criteria in a making decision problem, are simple weighting method and hierarchy analyze method. Existing methods are depended on personal experience and observation. Therefore, the possibility of making mistakes and choosing the wrong answer is high. To overcome this problem and use a vast opinion and experience of other researchers, new method like Delphi Fuzzy Hierarchy Analyze Method is introduced. This method's applicably and effectiveness rather than to the classic methods increase by using others. In this research using this method we tried to analyze and investigate the weight of criteria for choosing optimum dimension stone quarry method, according to the researcher's comments. In order to use others opinions for weighting criteria, a survey was conducted with university professors and investors around the country. Table 12 shows the survey. In this survey we ask professionals to score each factors effectiveness, based on their personal views (Table 13).

Table 12.

a Sample of sent Polls form to experts.

 Importance of parameters Very Important important Average Importance Less Importance Insignificant Quarrying method selection criteria Gross Profit * Time * Waste * Safety * Goodness * Environmental Parameters *

Table 13.

Numerical rate allocation of paired comparison [40].

 Numerical rates Relative comparison of criteria 9 Absolute importance 7 Very strong importance 5 Strong importance 3 Weak importance 1 Same importance 2, 4, 6, 8 Preferences of intervals

According to the survey, the corresponding comparison even matrix based on each professionals point of view is made. Table 14 shows some of these matrixes.

Table14.

Paired comparison matrix.

 Gross Profit Goodness Safety Time Environmental Parameters Waste Criteria 1 2 5 3 5 5 Gross Profit 1.2 1 3 2 3 3 Goodness 1.5 1.3 1 1.2 1 1 Safety 1.3 1.2 2 1 2 2 Time 1.5 1.3 1 1.2 1 1 Environmental Parameters 1.5 1.3 1 1.2 1 1 Waste

After doing the survey and forming comparison even matrix, the results were used to form fuzzy comparison even matrix. To form this matrix, fuzzy Delphi-analytical hierarchy process method (FDAHP), triangular membership function and therefore triangular fuzzy numbers have been used. Calculations are consisted of:

To calculate fuzzy numbers (ãij), opinions from survey have been used directly. In this research fuzzy numbers are calculated based on triangular membership function (Figure 1). Based on Figure 1, in fuzzy Delphi method, a fuzzy number is calculated by equations 9 to 12 [42].

 (9) (10) (11) (12)

Fig 1. Triangle Membership function in Fuzzy – Delphi Method [19].

In above relations γij and αij are upper and lower limit of referees’ ideas, respectively. Also, it is the relative importance of i parameter to j in opinion of k professional.

In this stage, using fuzzy numbers and Equation 13, fuzzy comparison even matrix is formed [42].

 (13)

Or in form of:

 (14)

The fuzzy comparison even matrix for this problem is shown in table 15. In this matrix, Ci is as each criterion which are compared with each other according to corresponding fuzzy numbers.

Table 15.

Paired Fuzzy Comparison Matrix.

 C1 C2 C3 C4 C5 C6 C1 (1, 1, 1) (1, 3.11, 5) (1, 2.27, 5) (2, 3.29, 5) (0.5, 1.08, 2) (2.4, 15, 9) C2 (0.2, 0.32, 1) (1, 1, 1) (0.33, 0.69, 2) (0.33, 1.13, 3) (0.2, 0.36, 0.5) (0.33, 1.69, 7) C3 (0.2, 0.44, 1) (0.5, 1.44, 3) (1, 1, 1) (1, 1.6, 3) (0.2, 0.49, 1) (0.5, 1.87, 7) C4 (0.2, 0.3, 0.5) (0.33, 0.89, 3) (0.33, 0.62, 1) (1, 1, 1) (0.2, 0.33, 1) (0.33, 1.28, 3) C5 (0.5, 0.93, 2) (2, 2.8, 5) (1, 2.01, 5) (1, 3.01, 5) (1, 1, 1) (1, 3.79, 9) C6 (0.11, 0.24, 0.5) (0.14, 0.59, 3) (0.14, 0.53, 2) (0.33, 0.78, 3) (0.11, 0.26, 1) (1, 1, 1)

Now each criterions fuzzy weight could be calculated, using equations 15 and 16 [42].

 (15) (16)

In equations 15 and 16,  and  are signs for fuzzy numbers multiplication and summation respectively. Finally, which is a row vector defines fuzzy weight of i parameter.

After finding each parameters fuzzy weight, all the numbers change to unfuzzy numbers, using Equation 17 [42].

 (17) (18)

So, each parameters weight is calculated by fuzzy Delphi-analytical hierarchy process and the relevant value of each is shown in table 16.

Table 16.

Final weights of Parameters obtained using AHP method.

 Parameters Final Weight C1 Gross Profit 0.3 C2 Time 0.11 C3 Waste 0.14 C4 Safety 0.09 C5 Goodness 0.28 C6 Environmental Parameters 0.08

The calculated eigenvector for total criteria after calculated by fuzzy Delphi-analytical hierarchy process is as followed:

 W= [0.3, 0.11, 0.14, 0.09, 0.28, 0.08]

The weighted decision matrix is equal to dimensionless decision matrix times to weighted criteria matrix (Equation 5).

 (5)

The weighted decision matrix is equal to dimensionless decision matrix multiplied by weighted criteria matrix:

 0.047 0.067 0.024 0.061 0.084 0.147 V= 0.033 0.156 0.04 0.037 0.057 0.147 0.047 0.067 0.024 0.086 0.022 0.083 0.02 0.201 0.056 0.012 0.018 0.134 0.007 0.067 0.056 0.086 0.024 0.14

A+ shows the ideal solution and A- the negative ideal solution, then:

 A+ = {v1+, v2+…, vi+…, vn+} A- = {v1-, v2-…, vi-…, vn-}

Where vi+ is the best value of i values and vi- is the worst value of i criteria from all alternatives respectively. Alternatives in A+ and A- are totally better and worse alternatives respectively. Ideal solution (  ) and negative ideal solution (  ) are equal to:

 (0.148, 0.018, 0.012, 0.056, 0.201, 0.007) (0.083, 0.084, 0.086, 0.024, 0.067, 0.047)

For each case, distance from ideal limit and negative ideal limit are calculated from Equations 6 and 7.

 (6) (7)

Where in these equations i index is the related criteria and the j is the related alternative.

Finally, the similarity index is calculated from Equation 8.

 (8)

The similarity index value varies from zero to 1 and whenever an alternative is closest to ideal, the similarity index value is near to 1. It is obvious that if  then, . Therefore, alternative ranking is based upon similarity index value. So, the alternative which has the highest similarity index value, has the first ranking and the one with lowest similarity index value has the last ranking [41].

For each method, distance from ideal and negative ideal solution and similarity index are calculated and shown in Table 17. As seen, ranking of priority methods is as: diamond wire saw, expanding chemicals FRACT, plug and feather, Katrock and blasting.

Table 17.

Separation from ideal and negative ideal solution and similarities index.

 Separation from negative Ideal Solution Separation from Ideal Solution Similarity Index Options 0.069 0.165 0.296 Expanding Material (Katrock) 0.124 0.072 0.633 Expanding Material (Fract) 0.062 0.174 0.262 Blasting 0.182 0.014 0.93 Diamond Cutting Wire 0.097 0.153 0.388 Plug and feather

# 6. Conclusion

The different methods have been developed and applied to extract the dimensional stones. As time goes by and improvement of technology, the primary methods that the human force played a significant role, might be abandoned. Thus, selection of the proper method among of all existing methods is a multi-criteria decision problem. Nevertheless, at first, the available criterions should be determined as well as considering their views; the appropriate method can be selected. Methods including of Plug and feather, diamond wire saw, blasting (low density) and expanding chemicals (FRACT and Katrock) are the most common methods in majority of Iran`s quarries. All methods have advantages and disadvantages comparing with each other, so without a precise investigation about effective factors and criteria, finding the ideal method is impossible. In this article the common dimension stone excavation methods including wedge and blades, diamond wire saw, explosives and expansive chemicals (FRACT and Katrock) in respect to different criteria such as production cost, desirability, safety, time, ease of extraction, waste and environmental effects have been compared. After that the most convenient method for extraction of dimension stones (closest method to ideal method) was chosen, using fuzzy- Delphi analytical hierarchy process method (FDAHP) and the technique for order of preference by similarity to ideal solution method (TOPSIS). The results showed that, the extraction of dimensional stones is suitable by using diamond wire saw method. According to the results, this method has a high safety, very high goodness, high gross profit, very low waste, low environmental effects and medium time for extraction.

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### History

• Receive Date: 24 September 2017
• Revise Date: 09 December 2017
• Accept Date: 13 December 2017