OPEN-PIT AND UNDERGROUND MINING

E S T I M A T I O N O F T H E O U T P U T O F M I N I N G AND T R A N S P O R T I N G

E Q U I P M E N T W H E N P L A N N I N G AND O R G A N I Z I N G M I N I N G

O. B. Kortelev, A. S. Kuznetsov,

V. A. Sychev, and Yu. V. Ivanov

The effectiveness of the production and economic activity of any social-technical system, including a mining

enterprise, depends on a multitude of various factors, including decisions made at the stage of planning and organizing production.

The quality of these decisions in many respects is determined by the support system, which includes the methods and information base and the software for investigating and evaluating variants of development of the technological process.

When planning mining, the need constantly arises of estimating the expected output of the technological lines, stripping and mining equipment and units, or of the entire enterprise during a certain time interval (the base period of the planning interval) for various values of the parameters of the mining process.* The purposes of calculating these estimates can be quite different: investigation of the effect of various factors on production efficiency, analysis of variants of the development of the

system and its elements, methods of adaptation of mining to varying conditions and selection of decisions on the basis of the

parameters of the mining system, substantiation of the required resources, determination of the operating conditions of equipment, increase of the reliability of functioning of the enterprise, provision of stable deliveries, reduction of production costs, etc.

In the present work we will discuss a method of calculating estimates of the expected output of elements of the section (mining and transporting machines and units) during various base time periods (month, quarter, year) with a given position of the front of mining operations at initial times, resources, schemes of arranging the equipment, i.e., with fixed values of the main parameters of the transport and technological schemes of stripping, dumping, mining, and transporting coal. The need to refine the method of calculating the indicated estimates arises in connection with the random character of accidents, breakdowns, and time of repair of equipment, failures in the servicing system, substantial interrelatedness of

elements, dependence of the output or rate of advance of some faces on the rate of conducting mining operations at other horizons, uncertainty of some parameters in the future, and absence of recommendations on the given matter in existing

handbooks [1, 2]. In different situations, depending on the purposes of the investigations being conducted, the multitude of parameters

on the basis of which a decision is made, and the stage of planning, the same factors can be regarded as stochastic or deterministic and, accordingly, a decrease of the calculated output of equipment with respect to the some factor can be taken

into account only by means of a correction factor having a probabilistic nature or by means of restrictions imposed on the

output of equipment. In practice, the causes of unplanned downtimes of equipment are usually analyzed, the duration of these downtimes

are recorded, and their statistical analysis is carried out. The total duration of downtimes of reach of the factors being checked during a certain time period are random variables, on the basis of which the values of the availability factors of

equipment or units are calculated [3]. The availability factor k a is a mean statistical quantity and at the same time it depends on the duration of the base

period and those random factors with consideration of which it is calculated. Using various sets or combinations of random

*By technical line is meant the chain of elements through which passes the traffic from the stripping or mining face to the

unloading point.

Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk. Translated from Fiziko-Tekh- nicheskie Problemy Razrabotld Poleznykh Iskopaemykh, No. 4, pp. 70-73, July-August, 1992. Original article submitted March 10, 1992.

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factors (we denote this set by A), we can calculate the availability factors required during investigations as ka(A) = 1 -

ka(A), where ka(A ) is that most probable (average) part of the working time or calculated output of equipment during the

investigated period which is lost as a result of downtimes for a reason or a number of reasons A. The stripping and mining volumes expected (average) or most probable with consideration of certain factors are

determined by means of the availability factors. For a deeper investigation of the reliability of the volumes of coal mining and determining the "reliability-production" dependences, it is expedient to conduct numerical experiments on modeling the development of mining operations with the use of correction factors obtained by means of pseudorandom number generators.

To illustrate the aforesaid, we will give two formulations of the problem of estimating the output of mining and

transporting equipment and mathematical models which can be used when planning the development of mining operations on

the section. We will represent mining as a set of parallel-acting technological lines or mining-transporting units performing

works related to stripping, dumping, mining, and transporting coal. Let M B, M D be sets of stripping-dumping and mining units, M = M B U Md- We will examine the time period T for which are determined the calculated output 0i of each

complex i out of M and their availability factors k a without consideration of possible losses of work time (and, accordingly, possible decrease of output) with respect to conditions of no underworking of benches or other such conditions interrelating elements of the system with respect to distance, rate of advance, or output. It is required to determine the expected output of the units and volume of mining coal over the section during time period T with consideration of the indicated conditions.

It is assumed that the initial location of the front of the mining operations at time t o is given. We will write out the said conditions for the final moment of the time period T. Let Xi k and Xj k be the coordinates of the final position of the excavators figuring in the i-th and j-th complexes, ~ j ' , 2~ij" are respectively the minimum and maximum distances between two elements i and j, U is a certain subset of set M x M (a set of pairs of interrelated elements). Then we have

(1)

We note that coord ina t e s Xik are not known beforehand and depend also on the initial location of the excava to r s xiH ,

cross-sectional area of the faces S i, and expected output of the complexes Qi, m3 (mining output during period T). I-ia:ing expressed Xi k = Xi I-I + Qi/Si by these parameters and having substituted the data into (1), we obtain restrictions of the form

Qi<~a~Qj+b~j, (i, ])~U, (2)

where a~j = Si/S j, bij = (Xj H - Xi H -t- ~ij) .Si , ~ij = -Aij ' if the distance between elements i and j is bounded below by Aij' , and 2~ij = 2~ij" if the indicated distance is bounded above.

Thus the problem of estimating the output of mining-transporting units and of the entire section with consideration in an explicit form of the technological conditions pairwise relating elements of the system can be represented in the follow- ing way:

Q~ ~ max; ~ D Q (3)

under restrictions (2) and

(4)

If in the system there are common elements through which pass flows of coal from different faces (transfer points, stocking and blending yards, common transport lines), being the bottleneck or weak links in the technological scheme and having a substantial effect on output of the entire mining system of the section, then the assumption that the process of

stripping and mining coal can be represented by a collection of simultaneously operating technological lines is unacceptable. In that case, the possible decrease of output of the mining systems because of the reserves not being prepared for mining and because of the conditions of nonundercutting of the benches examined above (and those similar to them) is taken into account by the availability factors of the mining equipment. Conditions (2) are now regarded as a random factor of decrease of the calculated output of the mining systems.

We will depict the investigated technological scheme of mining and transporting coal in the form of a network G, on

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which are represented all paths of movement of the coal flows from the faces to the unloading points. We will denote by U

the set of edges and by V the set of vertices of network G. Certain equipment or units through which a certain coal flow Qu passes during time T corresponds to each edge u E U. Let (~u be the upper bound of the output of the equipment or through- put of edge u calculated without consideration of any random factors affecting the operation of the equipment. It is assumed that all these factors are taken into account when determining the availability factors of the equipment k u. We denote by Uj + ,

Uj- the sets of edges entering vertex j and leaving it; Vs, V t are the sets of sources (faces) and sinks of the network (unload- ing points); n = IV t is the power V or number of vertices in network G.

We introduce a common sink - the vertex t = n + 1 - and connect it with the vertices from B t by edges u with throughput (~u = ~ and availability factors k u = 1; V I = VW s is the set of internal vertices of the network obtained.

If a flow of coal Qu arrives at the entry of edge u during period T, then at the outlet of this edge we have flow kuQ u. With consideration of this, the investigated situation is formalized in the form of the known problem of maximum flow in a network with absorptions [4, 5]:

X.~ Qu -+ max, uEu + Q

.u

u~ U i' 7"~U 7

Thus, on the basis of the problems presented, we can find estimates of the output of mining-transporting units and of the entire section during a certain base time period with consideration of the reliability of the main mining and transporting equipment, transport lines, servicing system, capacity of the repair facilities, and other factors affecting processes of mining

useful resources. The use of the given models substantially increases the validity of estimates of the output of units and the quality of designs and plans of developing mining.

LITERATURE CITED

,

3. 4.

5.

Instructions on Calculating the Standard Operating Output of Excavators and Continuous Machine Sets [in Russian], Kiev (1980). Methods of Calculating the Standard Output of Excavators and Continuous Machine Sets [in Russian], Kiev (1991). Reliability of Engineering Systems (Handbook) [in Russian], Radio i Svyaz', Moscow (1985).

D. Phillips and A. Garcia-Dias, Network Analysis Methods [Russian translation], Mir, Moscow (1981). P. Jensen and S. Barnes, Flow Programming [Russian translation], Radio i Svyaz', Moscow (1984).

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