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Spatial Entropy for Quantifying Ore Loss and Dilution in Open-Pit Mines

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Abstract

Effective management of ore loss and dilution is essential for successful grade control and short-term mine planning due to their significant impact on the economic, environmental, and technical aspects of open-pit mining operations. Factors influencing ore loss and dilution fall into two categories: (i) controllable factors like mine equipment selectivity and blast design and (ii) uncontrollable factors such as spatial heterogeneity of ore and waste blocks on a bench. This paper focuses on the second category by applying spatial entropy concept to capture heterogeneity at the scale of selective mining units. In this paper, global spatial entropy is used to assess the impact of spatial heterogeneity between ore and waste blocks on the magnitude of ore loss and dilution, while the local spatial entropy can guide the allocation of blast movement monitoring balls pre-blast. High values of the global spatial entropy indicate increasing potential of ore loss and dilution, which reduce profit. Furthermore, the study investigates the relationship between spatial entropy, cut-off grades, blast movement, dig-limits optimization model running time, and profit through a number of case studies. The results show that changes in cut-off grade and blast movement can significantly affect spatial entropy post-blasting and increase ore loss, dilution, and profit reduction, revealing the need for controlled blasting at specific bench sections. Additionally, the results demonstrate an exponential increase in profit reduction due to ore loss and dilution with a rising global spatial entropy.

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Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (Fund number: NSERC RGPIN-2019–04763). The authors thank the NSERC for this support.

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  1. Department of Mining and Materials Engineering, McGill University, 3450 University Street, Montreal, QC, H3A 0E8, Canada

    Samer Hmoud & Mustafa Kumral

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  1. Samer Hmoud
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Correspondence to Mustafa Kumral.

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Article highlights

• Ore loss and dilution management are crucial for open-pit mining operations.

• Ore loss and dilution can be significantly influenced by the spatial heterogeneity of ore and waste blocks, cut-off grade, and blast movement.

• This paper utilizes the concept of spatial entropy to quantify the heterogeneity of ore and waste at the selective mining unit scale.

• Spatial entropy shows clear impact on ore loss, dilution, and mine profitability, and can improve blast designs in open-pit operations.

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Hmoud, S., Kumral, M. Spatial Entropy for Quantifying Ore Loss and Dilution in Open-Pit Mines. Mining, Metallurgy & Exploration 40, 2227–2242 (2023). https://doi.org/10.1007/s42461-023-00881-4

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