Abstract
A 3D model of optimal contours phased development of oval-shaped open pit mines is proposed in the article. It is assumed that with enough accuracy the volumetric contour of the open pit mine is interpolated by an elongated elliptic hyperboloid. The calculation formulas for mineral resources are derived and optimal volumes of overburden are determined depending on the mining phase. In this case, the total number of mining phases is set in advance. The stripping ratio is used as a quality criterion of the optimization task. The problem of optimal control is solved using the Bellman function in dynamic programming. All the necessary calculation formulas are obtained in the final form by solving the optimization problem. Their simplicity and substantiation of each conclusion ensure that the results of this study can be successfully applied in practical calculations of the design and planning of mining operations in open pit mining.
Highlights
One of the constraints of implementing innovative technologies in open pit mining is the lack of a methodology for their implementation in design practice
We considered the case of round-shaped mineral occurrences when creating a 3D model for the phased development of the open pit contours [1 – 3]
It is necessary to ensure an even distribution of ore reserves being extracted with the minimization of the phased stripping ratio on the perimeter of the open pit edges during each mining phase
Summary
One of the constraints of implementing innovative technologies in open pit mining is the lack of a methodology for their implementation in design practice. The open pit mine turned out to have a form of a truncated cone, which is characteristic mainly in mining of kimberlite deposits. It was possible to solve this problem on digital models of open pit mines using phased contours of an open pit mine along the horizontal sections of a one-dimensional spline of the second order, and a two-dimensional spline in depicting the lateral surfaces of the ore body in 3D modelling. Practice shows that most of the open pit mines are oval
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