SynopsisAn economic argument is presented for the incorporation of quantitative modelling of the uncertainty of grade, tonnage and geology into open-pit design and planning. Two new implementations of conditional simulation-the generalized sequential Gaussian simulation and direct block simulation-are outlined. An optimization study of a typical disseminated, lowgrade, epithermal, quartz breccia-type gold deposit is used to highlight the differences between the financial projections that may be obtained from a single orebody model and the range of outcomes produced when, for example, fifty deposit simulations are run. The effects on expectations of net present value, production cost per ounce, mill feed grade and ore tonnage are presented as examples and periods with a high risk of negative discounted cash flow are identified. Further integration of uncertainty into optimization algorithms will be needed to increase their efficacy.

High-order sequential simulation techniques for complex non-Gaussian spatially distributed variables have been developed over the last few years. The highorder simulation approach does not require any transformation of initial data and makes no assumptions about any probability distribution function, while it introduces complex spatial relations to the simulated realizations via high-order spatial statistics. This paper presents a new extension where a conditional probability density function (cpdf) is approximated using Legendre-like orthogonal splines. The coefficients of spline approximation are estimated using high-order spatial statistics inferred from the available sample data, additionally complemented by a training image. The advantages of using orthogonal splines with respect to the previously used Legendre polynomials include their ability to better approximate a multidimensional probability density function, reproduce the high-order spatial statistics, and provide a generalization of high-order simulations using Legendre polynomials. The performance of the new method is first tested with a completely known image and compared to both the high-order simulation approach using Legendre polynomials and the conventional sequential Gaussian simulation method. Then, an application in a gold deposit demonstrates the advantages of the proposed method in terms of the reproduction of histograms, variograms, and high-order spatial statistics, including connectivity measures. The C++ course code of the high-order simulation implementation presented

Grade control and ore/waste delineation in open pit mining operations was traditionally based on the comparison of estimated grades with an economic cutoff. In the 1990s, an alternative approach to ore selection was applied and established, taking into account financial indicators through the so-called economic classification functions in combination with grade uncertainty assessment. Grade uncertainty is assessed using multiple grade realisations from geostatistical or stochastic simulations. Ore/waste selection integrates and is supported by the evaluation of economic consequences of sending a block of mined material to a processing facility or to the waste dump, and the related asymmetric financial implications. The benefits and practical implications of this efficient alternative framework are best illustrated by comparing the performance of three economic functions when combined with three commonly used stochastic simulation methods under different conditions. The latter conditions include a sparse and a dense blasthole sampling patterns and three cutoff grades. A general observation is that the minimum loss classification function combined with the indicator sequential simulation presents the most consistently better performing combination. This observation is reinforced in an application at a gold mine where the above combination outperforms the already well reconciling conventional grade control approach of the mine. The extension of the framework of economic functions to account for geometallurgical properties follows. This extension shows the integration of ore and waste grindability, a key aspect of ore comminution. Finding shows the improvements that could be made over current best practice when grindability is considered, and suggests how other geometallurgical attributes may be further integrated into grade control, as long as economic classification functions and orebody uncertainty models are considered.

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