Analysis of Robust Pit Shells

"The science of “optimal economic pit design” has been highly refined in the last decades. Even with the proliferation of optimizing and heuristic algorithms exploiting ever faster computers, the most common input is a single block model and a single set of cost assumptions, each of which is an estimate and prone to errors. An analysis of price assumptions produces a suite of nested economic shells, each with its own quantities of ore, waste, grade, and profit, but due to irregularities in the mineralized body, the growth of these shells can be erratic. To control the impact of the errors of the model and cost assumptions when choosing the pit shell for design, graphs of pit shells characteristics, such as stripping ratio, cost per unit of product and profit/ton, can be analyzed to consider points with higher stability, or robust pits. Selection of robust shells for a pit limit and for push backs can help to understand the impact to profit and risk. The robust shells also guide the preferred solution sets for final pit and cutoff optimization. INTRODUCTION “An open pit mining operation can be viewed as a process by which the open surface of a mine is continuously deformed. The planning of a mining program involves the design of the final shape of this open surface.” Optimum Design of Open-Pit Mines, Lerchs, H. and Grossmann, I. Transactions C.I.M. Volume LXVIII 1965. Traditionally an analysis of economic pit shells and sensitivity was performed by varying the input metal price. This was done with both floating cone algorithms as well as early versions of the Lerchs-Grossmann (L-G) algorithm. This gave an indication of the pit sensitivity to price but since other variables also change, some with metal price (perhaps steel and equipment), and some independently (fuel and tires) the understanding of these different pits was restricted. In addition, a run of the program could take hours, making a detailed analysis of small changes unwieldy. The L-G algorithm was programmed by a variety of people and sold as part of commercial mining packages, however it was first and most successfully commercialized by Jeff Whittle in 1984. When Whittle’s 3-D™ was expanded to 4-D the parameterization of the economic inputs was considered and the ability to run a suite of “pit shells” became automatic. The competing NPV Scheduler™ program sold by DataMine™ offers similar pit shell analysis capabilities."