Probabilistic Pit Limit Design with Different Levels of Managerial Risk Tolerance, Considering the Uncertainty of Ore Grade and Final Product Price (Case Study: Afghanistan’s Ainak Copper Mine)

Document Type : Research Article

Authors

1 Dept. of Mining and Metallurgy Engineering, Yazd University, Yazd, Iran

2 Dept. of Mining Engineering, Faculty of Geology, Bamyan University, Bamyan, Afghanistan

Abstract

The ultimate pit limit actually shows pit location, size, shape, and depth at the end of its working life. Although most scientific research determines the final pit limit by assuming constant design parameters, the existence of design uncertainties leads to significant deviations between expected design results and actual implementation during mining. Two of the most important uncertainties in mining are the grade of the mineral and the price of the final product, which, considering the effect of these uncertainties in the design of the final pit limit, will lead to a more appropriate understanding of the probability of achieving various mining goals. In this research, the pit limit of the Ainak copper mine in Afghanistan has been investigated, assuming the simultaneous uncertainty of the product price and ore grade. by using the exploration data, the distribution of the grade of the ore mineral in different blocks has been determined, and then the historical copper price is investigated, and a lognormal distribution function has been assumed for it. Taking into consideration the price and grade distributions, 9 different pits were designed. In each of these pits, the copper price and mine blocks' ore grades have been assumed optimistically, logically, and pessimistically based on their probability distribution function. Then, by using the First-Order Reliability Method (FORM) and assuming a profit goal for mine pits, the success or failure probability of each designed pit in achieving management objectives was calculated. The results of this research show that although the logical pit has an expected profit of 28 billion dollars, for example, for achieving a profit of 10 billion dollars for a risk-averse manager, using the pessimistic price-logical grade pit (pit number 2) has the highest success probability (91.8 percent). In addition, for a risk-taking manager, reaching the profit goal of 40 billion dollars using the optimistic price-logical grade pit (pit no. 8) has the highest success probability (31.34 percent). The results show that, for different managerial risk tolerances, it is needed to design different final pit limits based on the highest probability of success in managerial goals, and a specific design is not sufficient for different managers.

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References

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History

  • Receive Date: 11 August 2024
  • Revise Date: 30 September 2024
  • Accept Date: 24 December 2024

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