Abstract The inclusion of grade uncertainty for multivariate mineral deposits is of great importance for the correct management of subsequent decisions involved in mining planning. Mapping grade uncertainties allows maximization of profit and resource extraction. In this article, the co-simulation turning band algorithm is applied with the aim of predicting multivariate grade uncertainties. Moreover, a probabilistic analysis in long term mining sequencing is proposed in order to select the best given grade scheduling uncertainty derived from the simulations. A case study in a phosphate mine shows that the correlation of co-simulated variables honors the original data and there is an improvement in the project by an increase in Net Present Value (NPV) planning considering grade uncertainties. A comparison is performed with the results derived from the selected schedule and the results using the model based on kriged grades.

Abstract An existing cut slope on Highway RS-471/BR-153 is studied. The slope is composed of the Serra Geral Formation's material: a highly altered volcanic breccia and above it a slightly altered and very fractured rhyolite. A numerical analysis of the slope is carried out in two dimensions. Fracturing of the rhyolite necessitates the use of a constitutive model for materials with families of discontinuities (Ubiquitous-joint). To simplify the analysis of the problem and to examine some of the most sensitive variables, two more analyses are made, replacing the initial model by a Mohr's constitutive model, which considers the material as continuous. The results obtained from the Ubiquitous-joint model provide an acceptable representation of the field conditions, showing a failure mechanism type of rockfall from the face of the slope in the rhyolite, and the rupture surface of the breccia, without propagation of surface failure. In the analysis, when considering both materials as continuous, it is not possible to take account the fault conditions simultaneously, and this analysis also requires values of the mechanical parameters different from those recommended in literature.

Abstract Estimation of some mineral deposits involves chemical species or a granulometric mass balance that constitute a closed constant sum (e.g., 100%). Data that add up to a constant are known as compositional data (CODA). Classical geostatistical estimation methods (e.g., kriging) are not satisfactory when CODA are used, since bias is expected when estimated mean block values are back-transformed to the original space. CODA methods use nonlinear transformations, and when the transformed data are interpolated, they cannot be returned directly to the space of the original data. If these averages are back-transformed using the inverse function, bias is generated. To avoid this bias, this article proposes geostatistical simulation of the isometric logratio ratio (ilr) transformations back-transforming point simulated values (instead of block estimations), with the averaging being postponed to the end of the process. The results show that, in addition to maintaining the mass balance and the correlations among the variables, the means (E-types) of the simulations satisfactorily reproduce the statistical characteristics of the grades without any sort of bias. A complete case study of a major bauxite deposit illustrates the methodology.

Abstract Some mineral deposits show mineralization along layers. These layers may pass through several subsequent geological events such as folding and/or severe erosional processes. Grades within these deposits tend to be correlated along orientations where the mineralization was originally deposited or along the same geological period (stratigraphic level). Consequently, some locations close to each other in terms of geographical coordinates can show uncorrelated grades. Spatial continuity analysis can also be affected by error inflicted by combining samples from different stratigraphic levels. This article uses the coordinate transformation (unfolding) to align the grades measured along the same stratigraphic level. The modification in coordinates improved the spatial continuity modeling and the grade estimates at non-sampled locations. The results showed that the mean of the relative error between the estimated value and the real value of the samples using unfolding is -0.10%. However, when using the original coordinates, the mean of the relative error is -0.65%. Furthermore, the correlation between the real and estimated value using crossvalidation is greater using stratigraphic coordinates. A complete case study in a manganese deposit illustrates the methodology.

A modelagem geológica de depósitos estratiformes pode-se tornar muito complexa, muitas vezes fazendo uso de envelopes geológicos de pequena espessura e exigindo o uso de sub-blocos (com base em coordenadas cartesianas) para produzir um modelo de blocos coerente. No entanto, eventos geológicos após a formação do depósito (dobras, falhas, etc.) podem mudar a direção da continuidade espacial de certos atributos, com mistura de amostras pertencentes a épocas de formação geológicas diferentes (no caso de depósitos estratiformes) na mesma elevação. Esse estudo apresenta uma solução para depósitos com teores estratigráficos combinados com amostras de diferentes origens. A solução é uma estimativa bidimensional obtida pela acumulação da espessura de P2O5 em um depósito de fosfato (em comparação com a análise estatística tradicional em três dimensões).

The geological modeling of stratiform deposits can become very complex, often making use of geological envelopes of small thickness and requiring the use of subblocks (based on Cartesian coordinates) to produce a coherent block model. However, geological events after the formation of the deposit (folds, faults, etc.) can change the direction of spatial continuity of certain attributes, with the mixing of samples belonging to different formation eras (in the case of stratiform deposits) in the same elevation. This study presents a solution for deposits with stratigraphic grades combined with samples of different origins. The solution is a two-dimensional estimate obtained by accumulating the thicknesses of P2O5 in a phosphate deposit (as compared to traditional statistical analysis in three dimensions).