Optimization of Muck Removal During the Driving of Exploratory Mine Workings
Abstract Generated abstract
This paper addresses the optimization of muck removal during the driving of horizontal mineral exploration workings, a process described as accounting for a large share of the driving cycle and strongly influencing equipment choice, productivity, cost, and labor requirements. Using the conditions of adit driving at the Karamken deposit as a case context, the authors formulate mucking as a complex controllable system involving loading equipment, advance per cycle, mine cars, exchange methods, siding parameters, haulage distance, and locomotive type. They propose a graph theory based mathematical model in which selection of an optimal mucking technology is treated as a shortest path problem over feasible parameter combinations. The model defines objective functions for minimizing total driving time, total resource cost, and total labor expenditure, with solution intended by computer calculation.
Full Text
Optimization of Mucking During the Driving of Mineral Exploration Workings
V. G. Lukyanov, V. G. Krets, T. A. Petina
(Presented by the scientific seminar of the Department of Geodesy, Mining, and Construction)
Removal of the rock mass is one of the most costly and labor-intensive operations, taking up to 30–50% of the time of the driving cycle during the driving of horizontal mineral-exploration workings. The technological scheme for driving a working and its cross section are determined mainly by the equipment used for loading and hauling the rock. The technical-and-economic indicators of driving as a whole depend on which technical means, technological schemes, and their parameters for removal of the rock mass are adopted in the design and implemented in practice.
The choice of an optimal technology reduces to determining such parameter values as ensure the achievement either of maximum rates of driving, or of minimum cost of driving the working, or of minimum labor input for its driving.
Our aim is to select and refine certain parameters of an optimal technology for removing rock mass when driving adits at the operating mineral-exploration mine of the Karamken deposit, taking into account the equipment and machines available at the given enterprise.
The problem is solved by developing and subsequently implementing a mathematical model of the process of removing the rock mass—the system under study—from the standpoint of three criteria. Here we confine ourselves to an attempt at developing the model. The theoretical principles for constructing mathematical models of the technology of driving mine workings on the basis of graph theory are given in works (1, 2), where the technology of driving a mine working—the preparatory face—is assigned to the class of complex (large) systems.
The process of removing rock mass is part of this typical, labor-intensive, and systematically operating complex system in the mining industry, and even small changes in the technology lead to large savings of resources.
The object under study—removal of rock mass during the driving of a mine working—belongs to complex (large) systems according to the following features:
- The system is not amenable to experimentation or to large-scale physical modeling.
- People, machines, and the environment function within the system.
- The system is subject to many random influences.
- It is controllable.
Mucking includes loading proper, exchange operations, and haulage of the rock to the surface (dump); in each particular case different equipment is used. It contains a number of variable parameters, the main ones being the type of loading machines, the type and number of mine cars, the types of maneuvering and haulage electric locomotives, the types and parameters of reloading means, and the type of siding. The interaction of these variable factors determines the different cost and duration of driving a mine working.
The variable factors, in turn, depend on the possible state of the object in one or another period of time, as well as on a number of mining-geological and organizational conditions, which may include the cross section, length and curvature of the working, the number of faces being driven simultaneously, the lengths of sidings, the distance of the siding from the face, the method of exchanging mine cars (manual, by electric locomotive), the advance per cycle, and the rate of driving the workings.
Thus, it is obvious that the system under consideration is subject to the action of many random factors, and a rational solution for it is possible only with the aid of methods of mathematical modeling. The application of graph theory to the solution of various problems in optimizing mucking of rock mass during the driving of horizontal workings makes it possible to accomplish this at the proper level.
In general form, the problem of choosing the optimal variant of mucking technology may be represented as “finding the shortest path” on a graph.
The object considered by us is characterized as follows:
length of working 1200 m (2400; 3600);
cross section of the adit in the clear—5.8 m² (7.5 m²);
curvature of the working—straight;
rock-strength coefficient according to M. M. Protodyakonov
\(f = 16—18\);
the time for mucking the rock amounts to 40% of the cycle duration (accepted conditionally, on the basis of time-study data).
To express the state of the system under consideration, a graph is constructed that reflects the dependencies of the parameters sought. Figure 1 presents such a graph, where \(X_1, X_2 \ldots X_8\) are the sought parameters and their variants. At the same time, not all possible variables and their variants are included in the consideration, but only those expedient in this particular case. Since our main task is the fundamental verification of this meth-
Figure 1. Graph of the technological process of mucking rock mass.
data for solving problems under production conditions, the greatest possible simplifications have been made.
The system reflecting the state of operations for mucking the rock mass is characterized by the following variables:
rock-mass loading equipment \(X_1\)
\(X_{1,1}\)—PPN-1 loading machine;
\(X_{1,2}\)—PPN-1s loading machine.
Depth of advance per cycle \(X_2\)
\[ \begin{aligned} X_{2,1}&—1.1\ \text{m}\\ X_{2,2}&—1.3\ \text{m}\\ X_{2,3}&—1.5\ \text{m}\\ X_{2,4}&—1.7\ \text{m} \end{aligned} \]
Loading containers \(X_3\)
\(X_{3,1}\)—UVO-0.8 mine car
\(X_{3,2}\)—UVB-1.6 mine car
Method of exchanging mine cars \(X_4\)
\(X_{4,1}\)—stub-end passing siding;
\(X_{4,2}\)—stub-end passing siding and a reloader for 7 UVO-0.8 mine cars;
\(X_{4,3}\)—stub-end passing siding and a reloader for 11 UVO-0.8 mine cars.
Number of mine cars on the passing siding \(X_5\)
\[ \begin{aligned} X_{5,1}&—7\\ X_{5,2}&—11\\ X_{5,3}&—7\\ X_{5,4}&—11 \end{aligned} \]
Means of exchanging mine cars \(X_6\)
\(X_{6,1}\)—4.5 ARG electric locomotive;
\(X_{6,2}\)—manual haulage.
Distance to the passing siding \(X_7\)
\[ \begin{aligned} X_{7,1}&—40\ \text{m}\\ X_{7,2}&—60\ \text{m}\\ X_{7,3}&—80\ \text{m}\\ X_{7,4}&—100\ \text{m}\\ X_{7,5}&—150\ \text{m}\\ X_{7,6}&—200\ \text{m}\\ X_{7,7}&—250\ \text{m} \end{aligned} \]
Type of haulage electric locomotive \(X_8\)
\(X_{8,1}\)—4.5 ARG electric locomotive;
\(X_{8,2}\)—7KR.
In this case we shall have the following number of objective functions:
\[ 2\times4\times2\times3\times4\times7\times2\times2=4976, \]
which is quite realistic.
The objective function according to the first optimality criterion
\[ I \to \min \text{—the time for driving the entire working} \]
\[ I_1^i=\min \sum_{i=1}^{4} F_i,\ J\oplus M\delta=(G), \]
where \(F_1^i\)—time for loading (technical productivity of the machine), h.
\(F_2^i\)—time for exchanging mine cars, h.
\(F_3^i\)—time for constructing the passing siding, h.
\(F_4^i\)—time for haulage, h.
The objective function according to the second criterion \(I^2\to\min\)—the total expenditure of resources for driving the entire working over the whole driving period—will have the form
\[ I_2^i=\min \sum_{i=1}^{8} F_i,\quad l\in M\delta(G), \]
where \(F_1^i\) is the cost of loading in terms of wages, rubles;
\(F_2^i\) is the cost of constructing sidings in terms of wages, rubles;
\(F_3^i\) is the cost of exchanging mine cars in terms of wages, rubles;
\(F_4^i\) is the cost of haulage in terms of wages, rubles;
\(F_5^i\) is the cost of depreciation deductions, rubles;
\(F_6^i\) is the cost of expenditures on electric power, rubles;
\(F_7^i\) is the cost of expenditures on compressed air, rubles;
\(F_8^i\) is the cost of other unaccounted-for materials, rubles.
The objective function according to the optimality criterion \(I_3 \to \min\) (total labor expenditures for driving the entire working) for the whole period has the form:
\[ I_3^i=\min \sum_{i=1}^{4} F_i,\quad l\in M\delta(G), \]
where \(F_1^i\) is the labor intensity of loading, man-shifts;
\(F_2^i\) is the labor intensity of exchanging mine cars, man-shifts;
\(F_3^i\) is the labor intensity of constructing a siding, man-shifts;
\(F_4^i\) is the labor intensity of haulage, man-shifts.
The functionals are then deciphered, and their dependences on the parameters are given.
The model is solved with the aid of a computer.
LITERATURE
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E. I. Rogov. Theory and Methods of Mathematical Modeling of Production Processes in Mining. “Nauka,” Alma-Ata, 1973.
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E. I. Rogov, M. R. Shuruba. Selection of the Optimal Technology for Driving Horizontal Mine Workings. Alma-Ata, 1969.