UNDERGROUND MINING METHOD SELECTION WITH THE APPLICATION OF TOPSIS METHOD

Multi-criteria decision-making methods are widely used to solve various problems in the industry, as well as to support the planning and designing industrial processes. Mining is a very complex and responsible activity, so when making a major decision, it is necessary to take into account several parameters and perform their detailed analysis. Due to the importance of proper decision making, multi-criteria optimization methods have a very wide application in mining. One of the most complex and important things in mining is the choice of mining method for underground exploitation, where the application of multi-criteria decision-making methods can help a lot in making the right decision. This paper will present the choice of the method of mining excavation by the TOPSIS method, according to which it was obtained that the Sublevel Caving is optimal for a given case.


INTRODUCTION
One of the biggest problems that every researcher or designer encounters when conducting research to open and operate a new mine or analyze an existing underground mine is mining method selection.When selecting a mining method for a particular underground mine, it is necessary to ensure safe and healthy working conditions.Also, one should always keep in mind the fact that the costs of excavation cover most of the total costs of mining, so the correct mining method selection will largely depend on whether the mine will operate with positive financial outcomes [1].
When making the final decision on which method of mining to use, several parameters should be taken into account, which can be quantitative or qualitative.Parameters influencing the choice of the method of mining excavation can be divided into three groups [2]: • mining and geological parameters, such as: geometry of deposit (depth below surface, general shape, plunge, ore thickness), rock mechanics characteristics (ore zone, footwall and hanging wall, i.e. rock substance strength, fracture shear strength, fracture spacing, structures, stability, stress), ore variability (grade distribution, ore uniformity, ore boundaries), quality of resource, etc.; • mining and technical parameters, such as: applied equipment, annual productivity, environmental impact, health and safety, mine recovery, ore dilution, machinery and mining rate, flexibility of methods; and • economic parameters, such as: ore value, ore body grades, mineable ore tons, operating cost and capital cost.

Figure 1. Underground mining method selection
When selecting a mining method rationally, the methods of mining are chosen according to mining and geological parameters that affect the choice of mining (geometry of deposit, rock mechanics characteristics, ore variability) [1].Rational choice gives a group of mining methods that are favourable for application in this case, in order to reduce the number of mining methods in the next phase.
There are several procedures for the selection, i.e., the selection of mining methods according to mining and geological parameters, such as: the procedure according to Boshkov and Wright, Laubscher, Morrison, Hartman, Nicholas, UBC and others.For the rational mining method selection, this paper uses the procedure according to UBC [4], according to which the best mining methods are ranked: Cut and fill stoping, Sublevel stoping, Shrinkage stoping and Sublevel caving.These methods of mining in the next phase will be alternatives in multi-criteria decision making.After the rational selection, the optimal choice and the underground mining method selection according to the economic and mining-technical parameters follows.
Many authors have conducted research on the underground mining method selection, using several methods of multi-criteria decision-making, such as: PROMETHEE, ELECTRE, AHP, VIKOR, WPM, EDAS, TOPSIS and others, together and separately. in 2020 [10] used the Fuzzy TOPSIS method for risk assessment at workplace in underground mine.Bouhedja et al. in 2020 [11] used the TOPSIS method for choosing the best supplier of quarry natural aggregate.In 2021 Mijalkovski et al. applied the PROMETHEE [12] and VIKOR methods [13] for mining method selection.Ali et al. in 2021 [14] used the TOPSIS method and modification of the UBC method for mining method selection.
The TOPSIS method will be used in this paper.

TOPSIS METHOD
One of the most commonly used multi-criteria decision-making methods are the TOPSIS method.The TOPSIS method was first developed by Hwang and Yoon [15], and later expanded by Chen [16].According to this method, the best alternative is the one closest to the positive ideal solution (PIS) and the farthest from the negative ideal solution (NIS).The Positive Ideal Solution (PIS) is a hypothetical alternative that maximizes the benefit criteria (BC) while minimizing the cost criteria (CC).The negative ideal solution (NIS) is the opposite of the positive ideal solution (PIS), i.e., it maximizes the cost criteria (CC), while minimizing the benefit criteria (BC).According to this method, the best alternative is the one with the shortest Euclidean distance from the PIS, and also the furthest from the NIS [17,18].According to this hypothesis, calculations involving eigenvectors, square roots, and sums are used to obtain relative proximity to the test criteria.Ranking the values for the relative proximity of the whole system is done by assigning the highest value for the relative proximity of the best attributes in the system.As already mentioned, the TOPSIS method takes into account the distance to both PIS and NIS at the same time.In the end, we get the ideal solution that is closest to the PIS, and furthest from the NIS.When the TOPSIS method is used, the calculations are performed according to the following steps [18,19].
Step 1: Once the decision matrix is assembled, a normalized decision matrix is formed using the following equation: where   is the performance value of alternative j against criterion i.
Step 2: The weighted, normalized decision matrix is obtained by multiplying the normalized decision matrix and the weights of the criteria, using the following equation: where   is the weight of the i-th criterion and ∑    =1 = 1.
Step 3: In this step, the negative and positive ideal solutions are determined.The ideal solution, A + (v + i, i=1,…,n), is made of all the best performance scores and the negative ideal solution, A -(v - i, i=1,…,n), is made of all the worst performance scores for the criteria in the weighted normalized decision matrix.They are calculated using equations 3 and 4.
In these equations, the criteria are divided into two parts: • the first part is an input or cost nature, denoted by the set I', and smaller performance scores for these criteria are preferred; Vol.68 (2022), No. 2 geoscience.czpp.125-133, ISSN 1802-5420 DOI 10.35180/gse-2022-0075 • the second part is an output or benefit nature, denoted by the set I'' and larger performance scores for these measures are preferred.
Step 4: The distance of each alternative from PIS and NIS is calculated using the n-dimensional Euclidean distance, using the following equations: Step 5: In this step, the relative proximity to the ideal solution is calculated.The relative closeness of the alternative aj with respect to A + is defined as: Step 6: Rank the preference order in the decreasing order of   + values.
In the TOPSIS method, the chosen alternative has the maximum value of   + with the intention to minimize the distance from the positive ideal solution and to maximize the distance from the negative ideal solution.

CASE STUDY
The paper considers an active underground mine of lead and zinc.In the mine, a new part will be opened at depth and it is necessary to choose the appropriate of excavation the new part [12,13].The geological parameters and physical-mechanical characteristics of the ore deposit are listed below (see Table 1).The following methods of mining excavation have been applied in the work of the mine so far: Sublevel caving, Sublevel stoping, Shrinkage stoping and Cut and fill stoping.There are orientation parameters for these mining methods, which have been confirmed in the available practice.These mining methods were also obtained as the best ranked mining methods according to rational choice, i.e., according to the UBC methodology [20].These mining methods will be alternatives for the optimal choice of the mining method (see Table 2).We will use the TOPSIS method for the optimal choice of the mining method.For optimal choice, we will use eight miningtechnical and economic parameters, which will be the criteria according to which we will compare alternatives (see Table 3).Each criterion has a different impact, i.e., weight on alternatives.In this paper, the weights of the criteria were adopted in consultation with a group of 15 experts in the field of underground mining, in order to minimize the subjectivity of optimization.Each expert gives their opinion on the weight of the criteria, and then the mean value is taken with which further calculations are performed with TOPSIS method (see Table 3).Table 3 shows the target targeted by the criteria (max or min) and the category of criteria classification (quantitative or qualitative).Some criteria are classified in the category of quantitative criteria (can be measured or calculated), and some criteria are classified as qualitative criteria (cannot be measured).The qualitative criteria are defined by descriptive estimates, so in order to be used for further calculations, they need to be transformed into numerical values.The transformation of descriptive estimates into numerical values can be performed in several ways, with the help of bipolar scale, qualitative scale, interval scale, linear transformation scale, etc.In this study, an interval scale was used to transform descriptive estimates into numerical values, i.e., qualitative into quantitative values.The value of mined ore is the net value of the useful component contained in 1 t of ore, after flotation and metallurgical processing, reduced by the costs of metallurgical processing.The values for criterion C1 were calculated for each alternative and then entered in table 4.

Geological parameters
The criterion C2 is qualitative, so qualitative marks are assigned to it for each alternative (see Table 4).
The value for the criterion C3 was taken from the literature [21], i.e., for each alternative (see Table 4).
The ore recovery coefficient is the ratio of the excavated ore from the deposit and the total amount of ore in the deposit.The value for criterion C4 was taken from the literature [21], i.e. for each alternative (see Table 4).
The coefficient of ore dilution is the ratio of unplanned ore and tailings mixed with ore and the total amount of run of mine ore.The value for criterion C5 was taken from the literature [21], i.e. for each alternative (see Table 4).
The criterion C6 is cost of one ton (1 t) of ore.The total cost of producing one ton of ore is called the "cost price".Thus, the term cost of ore production means the sum of all costs of production and flotation processing of ore (see Table 4).
The effect of mining represents the productivity of the worker in the excavation process.The value for criterion C7 was taken from the literature [21], i.e. for each alternative (see Table 4).
The criterion C8 is qualitative, so qualitative marks are assigned to it for each alternative (see When the analysis of the influence of criteria on each alternative is performed, then based on the theory and on the basis of our assessment, a multi-criteria model is defined (see Table 4).

Table 1 .
Rock mechanics characteristics

Table 2 .
Alternatives for underground mining method selection

Table 3 .
Criteria for underground mining method selection

Table 4 .
Input model for TOPSIS method

Table 5 .
The normalized decision matrix

Table 6 .
The final weighted normalised matrix

Table 7 .
The ideal positive and negative solutions for each criterion

Table 8 .
Alternative distances and their relative closeness criteria