Fundamentals of Chaos Theory and Fractal Geometry for Determination of Open Pit Mines’ Planning and Design Parameters regarding Sustainable Development

Since all mining projects are subjected to uncertainty, risk analysis of these projects is essential. It is also possible to know the exact amount of minable reserve, due to its location in the underground and the operating limitations, when the entire reserve is extracted. Therefore, the effective parameters in the technical and economic evaluation of mining projects are highly diverse and all of them are subject to wide variations with respect to the quantitative and qualitative dimensions of the data. This process is caused by causes beyond human control, and sometimes, no matter how much it costs, full information is not possible. Hence, in all mining projects, in calculating income and expenditure figures and therefore economic calculations, they have to take into account the margin of confidence and are required to calculate risk. It would make more logical to consider the probabilistic changes of effective parameters in the economic analysis of mining projects. And taking into account the least and most likely occurrence of each row. When one of the most important issues with uncertainty is the price of metal, then uncertainty in the ultimate pit limit determination is raised. Since metal price prediction is uncertain, chaos theory and fractal geometry can be used to predict metal price. In this study, chaos theory and fractal geometry have been used to estimate the metal price correctly, since the metal price changes follow fractal and chaotic behavior. Therefore, if a correct estimate of the metal price is obtained, the ultimate pit limit will be close to reality and based on that the optimal pit limit can be obtained, which according to the principles of sustainable development leads to the metal mining at a lower price and the ultimate pit limit is more sustainable and has better environmental protection.