The fastest solution method to calculate the balancing cutoff grade of lane

Articles in Press

Document Type : Research Paper

Author

Faculty of Mining Engineering, University of Sistan and Baluchestan, Iran.

10.22059/ijmge.2026.403566.595312

Abstract

The open pit method is one of the most common surface mining methods. In this method, two block models must be created based on grade and economics. Typically, the economic block model is created based on ore and waste blocks. The cutoff grade is the most significant factor for distinguishing blocks. Various researchers based on their goals have defined different models of cutoff grades. One of the common models is Lane's cutoff grade method. The nine equations of the cutoff grades have been defined in Lane's method. But only the three equations of them related to the balancing cutoff grade. The common method for solving the balancing cutoff grades of Lane is the linear interpolation method. But so far, no comprehensive mathematical formulation has been presented for calculating the balancing cutoff grades of Lane. Therefore, in this article, mathematics was used to increase the speed and accuracy of calculations of this cutoff grade. Accordingly, the eight new mathematical equations were defined in three different models. The validation of new mathematical equations was done by using the interpolation method and its results were confirmed in section 4. Finally, the calculation of Lane's balancing cutoff grade by new mathematical equations with greater speed and less error replaced the traditional method. Also, this is the first study to develop new mathematical equations of Lane’s balancing cutoff grades, and they are able to delete the interpolation method.

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References

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International Journal of Mining and Geo-Engineering

Articles in Press, Accepted Manuscript
Available Online from 10 May 2026

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