The paper proposes a problem-solving approach in the area of underground mining, related to the evaluation and selection of the optimal mining method, employing fuzzy multiple-criteria optimization. The application of fuzzy logic to decision-making in multiple-criteria optimization is particularly useful in cases where not enough information is available about a given system, and where expert knowledge and experience are an important aspect. With a straightforward objective, multiple-criteria decision-making is used to rank various mining methods relative to a set of criteria and to select the optimal solution. The considered mining methods represent possible alternatives. In addition, various criteria and subcriteria that influence the selection of the best available solution are defined and analyzed. The final decision concerning the selection of the optimal mining method is made based on mathematical optimization calculations. The paper demonstrates the proposed approach as applied in a case study.

Large capital intensive projects, such as those in the mineral resource industry, are often associated with diverse sources of both endogenous and exogenous risks and uncertainties. These risks can greatly influence the project profitability. Having the ability to plan for these uncertainties is increasingly recognized as critical to long-term mining project success. In the mining industry in particular, the relationships between input variables that are controllable, and those that are not, and the physical and economic outcomes are complex and often nonlinear. The value of managerial flexibility is assessed using data on prices, costs, discount rates, grades, ore extraction, and metal output. Monte Carlo simulation of the mean reversion process is used to forecast revenue data based on an initial metal price, by using annualized volatility. Monte Carlo simulation of the Geometric Brownian Motion is used to forecast operating costs. To quantify the uncertainty in the parameters within a project such as capital investment, ore grade, and mill recovery, we used triangular, uniform, and normal statistical distribution, respectively. To decrease uncertainty related to selection of the appropriate discount rate, we have applied the concept of fuzzy sets theory. The result is a Net Present Value (NPV) based on the cash flows generated by the simulation over the timeframe of the project. When using fuzzy numbers, the fuzzy NPV itself is the payoff distribution from the project. The model explains investment behavior satisfactorily, both from a statistical and from an economic point of view.

The explosion caused by detonation of explosive materials is followed by release of a large amount of energy. Whereby, a greater part of energy is used for rock destruction, and part of energy, in the form of seismic wave, is lost in the rock mass causing rock mass oscillation. Investigations of the character and behavior of the pattern of seismic wave indicate that the intensity and nature of the seismic wave are influenced by rock mass properties, and by blasting conditions. For evaluation and control of the seismic effect of blasting operations, the most commonly used equation is that of M.A. Sadovskii. Sadovskii's equation defines the alteration in the velocity of rock mass oscillation depending on the distance, the quantity of explosives, blasting conditions and geological characteristics of the rock mass, and it is determined based on trial blasting for a specific work environment. Thus, this paper offers analysis of the method for determination of parameters of the rock mass oscillation equation, which are conditioned by rock mass properties and blasting conditions. Practical part of this paper includes the experimental research carried out at Majdanpek open pit, located in the northern part of eastern Serbia and the investigations carried out during mass blasting at Nepričava open pit, located in central Serbia. In this paper, parameters n and K from Sadovskii's equation were determined in three ways-models in the given work environment. It was noted that, in practice, all three models can be successfully used to calculate the oscillation velocity of the rock masses.

Abstract:In order to evaluate and control the seismic effect of blasting, as well as its planning, it is required to determine the soil oscillation law, with the strike/mining facilities to be protected. One of the most commonly used equations is that of M.A. Sadovskii, defining the law of alteration in the oscillation velocity of the soil depending on distance, the explosive amount, and conditions of blasting and geologic characteristics of the soil; all of this being determined on the basis of test blasting for the specific work environment. In the Sadovskii equation two parameters, K and n appear and they are conditioned both by rock mass characteristics and blasting conditions. The practical part of this study includes experimental investigations performed in the Veliki Krivelj Open Pit in the Bor District located in Eastern Serbia and investigations carried out during mass mining in the Kovilovača Open Pit near Despotovac, Eastern Serbia. Thus this paper offers several modes for determination of parameters K and n in the Sadovskii equation. To determine the parameters in the Sadovskii formula, in addition to the usual least square method, two more new models were applied. In the models the parameters K and n were determined by applying the quotient of the relative growth of oscillation velocities and reduced distances for Model 2. The link between the parameters K and n is determined by applying the trapezoidal formula for finding the value of definite integral for Model 3. In doing so, it was noted that all three models can be used to calculate the oscillation velocity of the rock mass.

In this paper, a fuzzy programming model, incorporating fuzzy measures of costs and ore reserves, is developed to evaluate different design alternatives in the context of the selection of the underground mine development system. The bauxite deposit is usually mined using the sublevel mining method. This method extracts the ore via sublevels, which are developed in the ore body at regular vertical spacing. In such an environment, we consider the development system as a weighted network interconnecting all sublevels with surface breakout point using the minimum cost of development and haulages. Selection of the optimal development system is based on the application of Convex Index and composite rank. The uncertainties related to the future states of transportation costs are modeled with a special stochastic process, the Geometric Brownian Motion. The results indicate that this model can be applied for solving underground mine development problems.