AN ANOTHER WAY FOR OPEN PIT MINE DESIGN OPTIMIZATION ...

106Towards the general equation (1), the next equationdetermines the value of open pit, where the block (b i,j,k) isthe lowest in the last slope that would be excavated.L−RL−RSi, j, k= ∑ Ei, j, k⋅( Ct −Cav)(8)Because towards the equation (3), average cost ofmining (C av) can be calculated dividing the total cost ofmining and total quantity of ore excavated, therefore theequation (8) can be transformed in the following shapeS E⎛C⎝∑∑L−RL−RL−Ri, j,ki, j, k= ∑ i, j,k⋅ t−⎜L−REi, j,kwhich after simplification turns into it’s final shape,intended for the computer useS = C ⋅ E − TTL−R L−R L−Ri, j, k t i, j, k i, j,k⎞⎟⎠∑ ∑ (9)where ∑E L-R is the sum of block ore quantities or coali,j,kequivalents if mining coal inside the pit outline, where theblock (b i,j,k) presents the lowest level of the last slope and∑T L-R is the sum of mining costs for blocks inside the piti,j,koutline, where the block (b i,j,k) presents the lowest level ofthe last slope.Addition of ore quantities, mining costs and netvalues of blocks are carried out along slopes, towards theuniversal formula for all three factorsEki,j,k+ bor Ti−2,j+2, kki,j,k+or Pki,j,k= bi,j,k+ bi−1,j+1, k... + bi−r+ 1, j+r−1,k+ bi−r, j+r,k+…..(10)where E k is the sum of ore quantities in the slope, wherei,j,kthe block (b i,j,k) presents the lowest level of the slope, T k i,j,kis the sum of mining costs in the slope, where the block(b i,j,k) presents the lowest level of the slope, P k is the sumi,j,kof net values of blocks in the slope, where the block (b i,j,k)presents the lowest level of the slope, b i,j,kis the belongingvalue (depending what is adding: cost, quantities or profit)in the lowest block of the slope (k n), b i-1,j+1,kis the secondblock of the slope (k n), which is positioned diagonallyabove the block (b i,j,k), b i-2,j+2,kis the third block of theslope (k n),which is positioned diagonally above the block(b i-1,j+1,k), b i-r+1,j+r-1,kis the next to the last block of the slope(k n) (the second block from the surface of the terrain),b i-r,j+r,kis the last-highest block of the slope (k n) (the firstblock from the surface of the terrain) and r is the totalnumber of blocks in the slope (k n) above the block (b i,j,k).Sum of the net values of blocks in one slope presentsprofit for that slope and this value is used for the promptacceptance or the rejection of that specific slope.Net value of any slope inside the pit outline iscalculated from the formulaRud.-geol.-naft. zb., Vol. 21, 2009.I. Galić, B. Janković, I. Mrakovčić: An another way for...k⋅∑ Ei,j ,k−∑kk = CT(11)i,j ,kti, j ,kwhere k i,j,kis the value of slope which begins on the block(b i,j,k).The expression for optimization of the open pit outlinein opposite direction is similar to (7), with reversedindexes.Order of the working phasesProcedure of optimum open pit design using FSMcomprises from more interdependence entirety whoseorder strictly has been determined, for example, it isnot possible to determine the value of blocks while thegeological model hasn’t been made and same model isn’tpartitioned on blocks.Procedure of FSM consists of the following phases:A. Building a geological databaseInside this database, among others, are results of onsiteinvestigations like core drilling, which are the mostimportant. These results provide data about:- heights (depths) of layers that proved to be positive (ore)and accompanying layers,- hanging wall and footwall of high-grade layer(s),- ore quality, etc.B. Construction of the deposit modelThe deposit model is, in fact, 3D interpretation ofgeometrical and geological data. This model has to betransformed into block model, so the main influentialfactors for the ore reserve estimation can be attached toindividual blocks. The summation of blocks provides areserve estimate quantity with analyses of certan cost andearnings data.C. Developing mining databaseThis database includes:1. Data about characteristics of mining equipment:- excavation equipment (the purchase price, hourcapacity, standards of consumption lubricationsand fuel, period of time for amortization),- transport equipment (the purchase price, hourcapacity, standards of consumption lubricationsand fuel, period of time for amortization),- auxiliary equipment (the purchase price, hourcapacity, standards of consumption lubricationsand fuel, period of time for amortization),- water pumps (the purchase price, hour capacity,standards of consumption materials and energy,period of time for amortization).