1. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 Economico-Mathematical Analysis of Transition from Open-pit to Underground Mining Title of paper: Authors: 1- Kazem Oraee; Department of Management, University of Stirling, Stirling, UK 2- Ezzeddin Bakhtavar; Urmia University of Technology 3- Kourosh Shahriar; Amirkabir University of Technology 4- Peter Flett; University of Stirling

2. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 2 Introduction Methodology Two dimensional tabulate ore deposit and the transition depth Conclusions

3. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  If a deposit changes abundant in geometry along the dip, above all if the change occurs at the end of the deposit, the stripping ratio will be too large when the whole deposit is mined via open-pit mining.  This means that shallow ore deposits are mined by surface methods but a depth is reached in the case of most deposits after which underground methods are applied for the extraction of the remaining ore.  The determination of this depth and its analysis is the subject of this paper.  In order to determine transition depth from open-pit to underground mining on the basis of the allowable and economically feasible overall stripping ratios, an economico-mathematical equation is established. 3

4. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  Overall stripping ratio (Equation 1):  Allowable stripping ratio (Equation 2): 4

5. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 5 Methodology Two dimensional tabulate ore deposit and the transition depth Conclusions Introduction

6. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  Let’s assume that ore deposit be continues.  At the final pit depth, the overall stripping ratio becomes equal to the allowable stripping ratio:  Consequently:  The volumes of ore and waste within the pit limit can be considered being a function of transition depth (h t ) as the Equations 5 and 6, respectively. 6

7. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  By replacing Equations (5) and (6) into (4), Equation (7) can be deduced: 7 Replace into Then

8. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 EEquation (7) can be written as Equations (8) and (9), respectively: FFinally, to increase the accuracy of Equation (9) both ore recovery coefficient achieved through open-pit (R op ) and underground (R ug ) methods are considered. 8 Then

9. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 9 Introduction Methodology Two dimensional tabulate ore deposit and the transition depth Conclusions

10. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  It is remarkable that an effective formula can be concluded by employing Equation 10 and on the basis of:  Ore deposit shape,  Open-pit limits,  Final mining depth,  Suitable underground method and its recovery coefficient,  Open-pit mining cost per unit of ore volume or tonnage,  Underground mining cost per unit of ore volume or tonnage,  Stripping cost in relation to the unit of ore extracting using open-pit. 10 Two dimensional tabulate ore deposit and the transition depth

11. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  For clarity explanation of the considered parameters during the concluded economico-mathematical equation, a two dimensional section of a tabulate-shape ore deposit with transition problem is considered. For the target, an analytic geometry procedure is used.  In order to prove the suitable formulas for determining transition depth over from open-pit to underground, two states are considered. 11 Two dimensional tabulate ore deposit and the transition depth

12. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 tabulate ore deposit  State1: Let’s assume a tabulate ore deposit includes outcrop with an equal width of the deposit and pit floor (Fig. 1).  In this case, it is initially necessary to measure the volume of covered waste rocks and the related ore within the pit limits area. 12 Two dimensional tabulate ore deposit and the transition depth

13. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  Then, utilizing a geometric analytical procedure and the main Equation (10), Equation 11 can be proved. 13 Two dimensional tabulate ore deposit and the transition depth

14. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 as the same as exception  State2: This is as the same as the first state, with this exception that only minimum possible width of pit floor may be mineable (Fig. 2). 14 Two dimensional tabulate ore deposit and the transition depth

15. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  Due to the difference and based on the main Equation (10), to determine transition depth from open-pit to underground, Equation 12 is concluded: 15 Two dimensional tabulate ore deposit and the transition depth

16. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 16 Conclusions Introduction Methodology Two dimensional tabulate ore deposit and the transition depth

17. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  Here, based on allowable and overall stripping ratios and also using economico-mathematical analysis, an equation was initially proved.  Then, to introduce more clarity of the procedure and the effectiveness of the considered parameters in this regard, a two dimensional section of a tabulate-shape ore deposit with transition problem during two states were considered. 1. According to the tabulate deposits including outcrops and considering the maximum width of pit floor for exploitation, a simple formula was proved. 1. During the second state, to get the eventual deepening of the open-pit without extending it sideways, minimum possible width of pit floor was contemplated and consequently a formula is devised. 17

18. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010  The procedure explained in this paper can be also served as a useful tool for the mining design engineers when attempting to analyze varying depths or in different mining conditions. 18

19. 100 YEARS OF MINING RESEARCH: 100 YEARS OF MINING RESEARCH: Phoenix, Arizona; February 28 - March 03, 2010 19