Journal of Mining Science, Vol. 45, No. 5, 2009
TRANSITION FROM OPEN-PIT TO UNDERGROUND AS A NEW OPTIMIZATION CHALLENGE IN MINING ENGINEERING
E. Bakhtavar, K. Shahriar*, and K. Oraee**
UDC 622.27.326
There are many deposits that have the potential to be mined by a combined method of open-pit and underground. In this manner, the most sensitive problem is the determination of the optimal transition depth from open-pit to underground or vice versa. To calculate this depth, a model based on block economic values of open-pit and underground methods together with the Net Present Value (NPV) attained through mining is first presented. During the model, NPV of open-pit is compared to the v alue of underground for the similar levels. A hypothetical example is used in order to analyze the model in detail. Based on the assumptions made such as: a discount rate of 15 %, each pair of contiguous level-cuts have to mine during one year, and one level as the height of crown pillar, the optimal transition depth was determined to be equal to 62.5 m. Then, level 6 was considered as the suitable crown pillar. Finally, maximum total NPV of the combined mining was calculated to be 25.54 units of currency. Transition depth, optimization challenge, open-pit, underground, discount rate, NPV INTRODUCTION
There are essentially two methods for mining: surface mining and underground mining. Open-pit being one of the surface mining methods is by and large regarded to be advantageous over underground methods, especially as regards recovery, production capacity, mechanizeability, grade control and cut off grade, ore loss and dilution, economics, and safety. Underground mining however can be considered as being more acceptable than surface mining from environmental and social perspectives. In addition, underground mining will often have a smaller footprint than an open-pit of comparable capacity. Many deposits can be mined entirely with the open-pit method; others must be worked underground from the very beginning. In addition, there are the near surface deposits with considerable vertical extent. Although they are initially exploited by open-pit method, there is often a point where decision has to be made whether to continue deepening the mine or changing to underground methods. The point at which economic considerations dictate the change of method from open-pit to underground methods is called “transition depth”. Accurate determination of the depth in mines where both methods are used is of utmost importance. Some of the biggest open-pit mines worldwide will reach their final pit limits in the next 10 to 15 years [1]. Furthermore, there are many mines planning to change from open-pit to underground mining due to increasing the extraction depths and environmental requirements [2]. In this way, it is likely that block and/or panel caving will enable the operations as an underground method to continue achieving a high production rate at low costs [3]. To date, and particularly in the past decade, limited research has been undertaken in order to determine the transition depth from open-pit to underground mining. The projects were conducted to solve the transition problem of some mines with combined Division of Mining Engineering, Urmia University of Technology, E-mail:
[email protected], Urmia, Iran. *Department of Mining & Metallurgy Engineering, Amirkabir University of Technology, E-mail:
[email protected], Tehran, Iran. **Department of Management, University of Stirling, E-mail:
[email protected], Stirling, UK. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 5, pp. 86-94, September-October, 2009. Original article submitted February 11, 2009. 1062-7391/09/4505-0485
©
2009 Springer Science Science+ + Business Media, Inc. 485
potential. In this regard, a few number of them led to what seemed to be an optimal basic method. Chuquicamata, for example is an open-pit mine located in Northern Chile. The present mine plan is for open-pit operations and is to cease operating in 2013 at a depth of 1100m and the remained deposit must be economically exploited by block caving [4, 5]. Grasberg copper-gold mine in Indonesia is known as a combined mine of open-pit and underground. Mining by open-pit method will finish by 2015 [6, 7]. Diavik diamond mine which uses open-pit method is expected to cease by 2012 and it will become totally underground thereafter [8]. Kanowna Belle gold mine in Australia is the other mine is another example where the transition to underground mining was done by early 1995 [9]. Current schedules in the Argyle diamond mine located in the eastern Kimberley region of Western Australia show the open-pit finishing production by the end of 2007, having reached its economic depth [10, 11]. Nearly all of the diamond production of the Ekati Diamond mines in the Northwest Territories of Canada has been from open-pit mining of multiple pipes. However, as some mines deepen, it is planned to be converted to underground such as the Koala North combined mine [12]. The Meng-Yin diamond mine consists of two ore deposits that one of them must be potentially mined being a combined mining. In order to exploit the deposit, Cut & Fill can be considered as the proper underground method [13]. At the Palabora mine, the transition to caving 400m below the bottom of the 800m deep open-pit resulted in a slope failure of the North wall that began in 2003, and is still mobile [14]. There are several other examples of completed open-pit mines, or those in the process of implementing a transition to underground mining; these are: Bingham Canyon in USA, Mansa Mina in Chile, Venetia in South Africa, Mount Keith and Telfer in Australia, and Kiruna mine in Sweden [15]. The first method for determining transition depth from open-pit to underground was the “Allowable Stripping Ratio”, which is a relation between the exploitation cost of 1 ton of ore in underground (and in open-pit) and the removal cost of waste in relation to 1 ton of ore extracting by open-pit [16, 17]. In 1982 an algorithm by Nilsson based upon cash flow and Net Present Value (NPV) was presented [18]. In 1992 however, in order to consider the transition depth as an important issue with respect to deposits with combinational extraction, the previous algorithm (1982) was again represented and reviewed [19]. Furthermore, in 1997 to state the transition depth problem, Nilsson underlined discount rate as the most sensitive parameter in the process [20]. In 1992 Camus introduced another algorithm for this target. This algorithm was presented on the basis of block models and considering net economic values of blocks for open-pit and underground exploitation. The approach consists basically in running the open-pit algorithm taking into account an alternative cost due to the underground exploitation [21]. In 1998, Whittle programming (4-x) which has been developed to assist in the interfacing of open-pit and underground mining methods was argued and studied. Due to the applied method in the programming, management can make decisions based on quantified operational scenarios of the open-pit to underground transition [22]. In 2001 and 2003, an approach with “Allowable Stripping Ratio” method was based and a mathematical form for the objective was introduced. Volumes of ore and waste within the open-pit limit were assumed as a function of constant (ultimate open-pit) depth [23, 24]. In order to determine the optimal transition depth from open-pit to underground mining a software on the basis of a heuristic algorithm was prepared by Visser and Ding in 2007 [25]. In the same year Bakhtavar and Shahriar introduced a simple heuristic method on the foundation of economical block models with open-pit and underground block values. The main process in the algorithm is a comparison between total values of open-pit and underground [26]. Attempting to solve the transition problem, a research by Bakhtavar and others was carried out recently. During the research a heuristic model established upon a two-dimensional block model with the values of open-pit and underground was presented [27]. The present study is conducted through improving and developing this version of research. research. In a different manner, a method with an economical block model base was introduced so that the transition problem might be solved. Some necessary 486
modifications were performed on the algorithm which was originally derived from Nilsson’s algorithm. The target of the method can be achieved by a comparison between the obtained values of various alternatives of combined mining [28]. Various researches through an analytical procedure were conducted in order to determine open-pit to underground transition depth of tabulate deposits. In this way, in relation to various states some formulae were concluded by using the allowable and overall stripping ratios. The contemplated states were variously combined from the deposits with outcrops or overburden and including maximum or minimum possible pit floor width [29]. Recently there have been many mines with a potential of combined mining that focused on the determination problem of optimal transition depth as a new challenge. It seems that accurate determination of the optimal transition depth will become an issue of utmost importance in the near future. Until now due to the researches and studies in this nature only some of the represented methods are able to solve the problem, but not carefully. In addition, because of the disadvantages of the few methods (algorithms) and their shortages in finding of transition depth optimally, it is essential for it to be a new effective model. To calculate this optimal depth, a more accurate heuristic model based on block economic values of open-pit and underground methods together with the NPV achieved by their mining is presented. The presented model is established upon the prior algorithm by Bakhtavar and others [27]. It is notable that the model can optimally solve the transition problem only on the basis of technical and economical considerations, without considering social effects, requirements of the working forces in relation to open-pit mining lifetime, equipments considerations after open-pit mining closure and so on. MODEL EXPLANATION
The methodology is established through a heuristic algorithm. It is founded on the basis of economical block models and consequently block economic values of open-pit and underground methods together. The authors seek to find an optimal transition depth including the maximum NPV achieved through open-pit and underground. If an ore deposit has exploitation potential initially by the open-pit method, and if it proves to greater depths the open-pit mine will economically transfer to a suitable underground mining method. On the other hand, it is essential to exploit the ore deposit in the initial levels by open-pit, where in the middle levels the transition problem should be considered. In some cases ore deposits are potentially mined by open-pit or underground separately. The present model also will distinguish these cases. The main idea in the model has been taken from the previous methodology which was introduced by Bakhtavar and others based on comparing block economical values gained by both open-pit and underground. The present model principally highlights the difference between the economical consideration and evaluation, and in its algorithm structure and framework. Unlike the prior methodology the economical evaluation in the present model is founded on the basis of a certain discount rate and NPVs achieved by both open-pit and underground methods. The following assumptions were made for this model: — In both open-pit and underground economical block models, dimensions of the blocks are 12.5×12.5 (as more conventional open-pit bench height and bench slope of 45 degree which is more common in open-pit optimization algorithms, also the dimensions are applicable being a multiple of underground working stopes dimensions); — A level can be mined at most once and through at most one method (open-pit or underground) with regard to sequencing constraints; — Definition of at most one uniform crown pillar with constant height being a multiple of level height considering the selected underground mining method and geotechnical investigations; — At most one underground stoping method known can be used; — All open-pit and underground levels are contiguous. 487
A general schematic of algorithm of the model is shown in Fig. 1. First, both open-pit and underground block models must be separately generated. Then, it is necessary to establish a long range mining plan for the deposit. Thus a new terminology, so-called “level-cut”, is introduced which assigns both open-pit and underground minable blocks in each level. The open-pit minable blocks in each level (open-pit level-cuts) and consequently optimal final pit limit can be determined using the optimization algorithms such as Lerchs & Grossmann [30] and Korobov [31]. Furthermore, it is essential to find underground level-cuts and as a result the optimum underground layout. Hence, the related optimization algorithms such as Floating Stope Optimizer [32] must be employed. With relation to open-pit level-cuts, besides the minable blocks in the dependent levels, some minable blocks in the upper levels may take place, similar to push backs. Nevertheless underground level-cuts are included in only underground minable blocks in the related levels. According to Fig. 1 the next step in the algorithm of the model is called “main process” which marks “A”. As it shown in Fig. 2, the main process dictates to make a comparison between NPVs achieved by open-pit and underground mining in each level. The beginning of this economical comparison is level 1 and it continues to level m which is identified as the optimal final level of open pit mining without considering any underground alternative. Figure 2 illustrates the structure and framework of the main process algorithm in detail. If Net Present Value obtaining from open-pit level-cut 1 were more than or equal to the similar value of underground level-cut 1, level 1 will be selected for mining by open-pit method and the evaluation process in the next step must be focused on level 2. Otherwise, it is essential to evaluate levels 1 and 2 together in this manner. In other words, if only open-pit total value achieving from level-cuts 1 and 2 together be more than or equal to the underground total value for these two level-cuts, both levels 1 and 2 will be chosen for open-pit; this will necessitate focusing on level 3. Otherwise, the evaluation in this manner must be considered in level 1, 2 and 3 together.
Fig. 1. A general sc hematic chart of the algorithm 488
Fig. 2. A schematic chart of the main process in the model
The evaluation from level 1 to level m is followed so that a certain level is assigned as an optimal transition depth (level). Now, among the remaining levels below the optimal transition level, one or more level / levels from m − y1 to m + y 2 can be assigned (where y1 ∈ {1, 2, ..., M } and
y2 ∈ {− M , ..., − 1, 0, 1, ..., M } ) even though they may be profitable by underground mining. Then the remaining levels below the crown pillar are emphasized and attended to extract but only utilize the underground stoping method (from level m + y 2 to n as final minable level). Once the optimal transition depth and crown pillar are allocated, the total NPV gained by combined mining van is calculated using relation (1): m − y1
NPVt =
n
∑ ( NPVopi ) + ∑ ( NPVui ) , y1 ∈ (0,1, 2, ..., M ) , y 2 ∈ (− M ...,−1, 0,1, ..., M ) , i =1
(1)
i = m + y 2
where NPVt is the total NPV the level-cuts (1 to n) extracted by both open-pit and underground mining; NPV NPVopi is tota totall NPV NPV achiev achieving ing from from the the levellevel-cut cutss (1 to to m − y1 ) using open-pit; NPVui is the total NPV getting from the level-cuts ( m + y2 to n) extracted only using underground. It is notable that NPV analysis is sensitive to the reliability of future cash inflows that an investment or project will yield. According to this kind of project (transition problem based on block economic values) if we assume that income comes or goes in annual bursts and that the discount rate will be constant in the future, then relation (2) is suitable to calculate NPV: T
NPV = ∑
I t
t t =1 (1 + r )
,
(2)
where I is income amounts for each year; r is constant discount rate value; t is number of years the investment lasts. 489
Fig. 3. Open-pit economical bock model
Fig. 4. Underground economical bock model
HYPOTHETICAL CASE EXAMPLE
In order to analyze the model in detail a hypothetical case example is used. This case embodies 154 blocks of 12.5x12.5m in 11 levels and 14 columns. The economical block models and the block economic values achieved by open-pit and underground are separately demonstrated in Figs. 3 and 4, respectively. Based on the economical block model of open-pit and using the Korsakov’s algorithm [31], open pit level-cuts and the optimal final limit are determined (Fig. 5). Figure 5 implies the condition that only the open-pit method is considered as a possible mining alternative for the deposit, level 7 will assign being optimal final depth (level). In next step, the optimum underground layout and consequently the underground level-cuts are determined through floating stope optimizer [32]. To optimally find the underground (stope) layout, minimum length and height of stope are selected as 2 contiguous blocks, with no limitation for their maximum amount (Fig. 6). Table 1 summarizes the profit gained by both open-pit and underground level-cuts without any discount rate included. Using the model, initial five levels should be profitably mined by open-pit method. Also, without any crown pillar considered, levels 6 to 11 can be more beneficial by underground. We shall assume that the height of the crown pillar is one level (12.5 m) on the basis of geotechnical considerations and the kind of mining method (during the hypothetical example).
Fig. 5. Open-pit level-cuts, optimal final pit limit and final working depth 490
Fig. 6. Underground block values, optimum underground layout and final working depth
Table 1 takes into consideration that 0.87, 0.76, 0.66, 0.57, 0.5, 0.43 are single present value factors for a discount rate of 15% and 1, 2, …, 6 years. It is assumed that each two contiguous levelcuts have to mine during one-year. Thus it is essential to assign the single present value of 0.87, 0.76, and so on, to the blocks take place in the level-cuts of 1 and 2, 2 and 3, etc., respectively. In this case and using the discount rate of 15%, the NPVs of the level-cuts achieved by both open-pit and underground are calculated and summarized in Table 2. Through the main process on the basis of NPV, the initial five levels are optimally assigned for mining by open-pit (Table 2 and Fig. 7). That is the optimal transition depth which is determined to be equal to 62.5 m. In the next step level 6 is allocated as the immediate level below the optimal final open pit level for crown pillar (Table 2 and Fig. 7). Remaining levels below the crown pillar, are considered for extracting by underground mining (Fig. 7). All components of transition problem and the results achieved by the new model for the hypothetical case are shown in Fig. 7. Finally, the maximum total NPV gained by both open-pit and underground method in combined mining is calculated to be 25.54 units of currency. TABLE 1. The Ec onomical Results without Any Discount Rate due to the Hypothetical Example Profit from Level-cuts 1 2 3 4 5 6 7 8 9 10 11
Open pit mining
Underground mining
0 +5 +4 +7 +6 +2 +2 — — — —
+2 +4 +3 +4 +2 +5 +3 +6 +2 +4 +3
Selected method Open-pit Open-pit Open-pit Open-pit Open-pit Underground Underground Underground Underground Underground Underground 491
TABLE 2. The Ec onomical Results Utilizing the Present Model due to the Hypothetical Example
Level-cut
1 2 3 4 5 6 7 8 9 10 11 Total profit
Year
Present value factor
1-й
0.87
2-й
0.76
3-й
0.66
4-й
0.57
5-й
0.5
6-й
0.43
—
—
NPV Open mining
Selected option NPV from Underground using the algorithm combined mining mining
0 + 4.35 + 2.93 + 4.88 + 3.96 – 0.73 +1.14 — — — —
+ 1.74 + 3.48 + 2.28 + 3.04 + 1.32 + 3.3 + 1.71 + 3.42
+ 16.53
+ 24.58
+1 +2 + 1.29
Open-pit Open-pit Open-pit Open-pit Open-pit Crown pillar Underground Underground Underground Underground Underground
0 + 4.35 + 2.93 + 4.88 + 3.96 Crown pillar + 1.71 + 3.42 +1 +2 + 1.29 25.54
Fig. 7. The components of optimal transition from open-pit to underground mining for the hypothetical case CONCLUSIONS
Due to the importance of optimizing transition from open-pit to underground mining as a new challenge in mining engineering, a model based on block economic values of open-pit and underground methods together with NPVs achieved by their mining is initially presented. In order to analyze the model in detail, a hypothetical example is used. During the example the assumptions were: discount rate to be equal to 15 %; extracting each pair of contiguous level-cuts during one-year; and one level as the height of crown pillar. After the model is used for the hypothetical ore deposit, the optimal transition depth from open-pit to underground mining is determined to be 62.5 m (level 5). Then level 6 is considered as the proper crown pillar. Finally, the maximum total NPV gained by combined mining is calculated to be equal to 25.54 units of currency. 492
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