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The overall slope angle (OSA) of pit walls plays a crucial role in the financial return of open pit mines. The paper showcases a novel design methodology where non-planar geotechnically optimal pit walls with an OSA steeper than what is used in current design practices are employed without compromising mine safety, i.e. the optimal profiles are featured by the same Factor of Safety (FoS) than their traditional design counterparts.
In the current design practice, pit wall profiles are often designed to be planar in cross-section and the profile in between ramps especially tend to be planar and defined by a constant inter-ramp angle. Sometimes rock layers exhibiting different strengths require the inclination of a pitwall to vary with depth, but the inclination across each layer is usually constant. In this study, a new proprietary slope design software, OptimalSlope, is employed to determine geotechnically optimal pitwall profiles of depth varying inclination for the design of each sector of the mine. OptimalSlope seeks the solution of a mathematical optimisation problem where the overall steepness of the pitwall, from crest to toe, is maximised for an assigned lithology, rock properties, and FoS. Bench geometries (bench height, face inclination, minimum berm width) are imposed in the optimisation as constraints that bind the maximum local inclination of the sought optimal profile, together with any other constraints such as geological discontinuities that may influence slope failure. The obtained optimal profiles are always steeper than their planar counterparts (i.e. the planar profiles exhibiting the same FoS) up to 8° depending on rock type and severity of constraints on local inclinations. The adoption of overall steeper profiles leads to a reduction in the amount of waste rock and, consequently, the stripping ratio.
This paper presents the results obtained from the design of three open pit mines, each characterised by different rock types and metal ores (copper and gold). The case study of the McLaughlin Mine, whose block model data are publicly available from the repository MineLib, is presented in detail whereas for the other two case studies already published elsewhere, a brief summary of the results is provided. To quantify the improvement obtained by adopting geotechnically optimal profiles, we performed two designs: one employing planar pit walls and another one adopting the optimal pitwall profiles determined by OptimalSlope. In determining the ultimate pit limit (UPL) and pushbacks, we sought to maximise the net present value (NPV) and achieve an annual production schedule as uniform as possible over the mine lifetime. The FoS adopted for both planar and optimal pitwall is the same, with verifications performed by limit equilibrium method (LEM) analyses (Morgenstein–Price method) run in Rocscience Slide2 and finite difference method analyses with strength reduction technique run in FLAC3D on the 2D UPL sections. Also, a 3D stability analysis of the entire UPL was performed in FLAC3D.
For each mine, we assess both financial gains (in terms of NPV) and environmental gains (measuring the reduction in carbon footprint and energy consumption). It emerges that the adoption of optimal profiles realises gains up to 52.7% NPV and substantial reductions of carbon footprint and energy consumption.
Keywords: OptimalSlope, open pit mine design, optimal pit walls, NPV optimisation, stripping ratio reduction, carbon footprint reduction
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