Resumen La dilución operativa en la minería en rajo puede afectar la adherencia entre los planes diseñados y ejecutados, lo que afecta los resultados de la reconciliación. Este tipo de dilución puede ocurrir debido a suposiciones erróneas con respecto a los contactos, desempeño minero ineficiente e incertidumbres asociadas con las leyes planificadas. Utilizando los polígonos de planificación y los modelos de bloques, se propone una metodología para medir los rangos de dilución en cada región. La metodología considera la incertidumbre asociada con las leyes de mineral para verificar la probabilidad de ocurrencia de dilución en el plan de mina a corto plazo. Los resultados demostraron que el uso de incertidumbres permitió la identificación de las áreas con un mayor potencial de incurrir en una dilución operativa. Con esta información, los planes pueden ajustarse para minimizar la dilución, o el resultado puede usarse como un factor para corregir los datos planificados.

Abstract Operational dilution in open-pit mining can influence short-term mine planning and affect the adherence between designed and executed plans, impacting the reconciliation results. This type of dilution may occur due to several reasons, such as erroneous assumptions regarding contacts, inefficient mining performance and uncertainties associated with the planned grades. The use of uncertainties enables better predictability and achievement of planned targets. Using the mine planning polygons and grade models, a methodology is proposed to measure the dilution ranges in each region. The methodology considers the uncertainty associated with the ore grades to verify the probability of occurrence of dilution in the short-term mine plan. The results demonstrated that the use of uncertainties enabled identification of the areas with a higher potential of incurring operational dilution. Using this information, the plans can be adjusted to minimize dilution, or the result can be used as a factor to correct the planned data.

Abstract The traditionally and widely used Lerchs-Grossmann algorithm presents well-known limitations that newer propositions attempt to overcome. The direct block schedule (DBS) methodology, which has gained relevance with computational advances, obtains the final pit as a natural result of production sequencing, different from Lerchs-Grossmann-based algorithms. This process flow applies constraints in the final pit definition stage attempting to provide a more realistic result and to minimize risks. Slope instability is a common and inherent risk to open pit mining and may affect the project's net present value (NPV). A study of the impacts of slope angle variations on safety indexes and final pit NPV provides an auxiliary tool for the overall slope angle definition process. This article presents a case study in which the effects of variations of the overall slope angle on the safety factor (SF) and project NPV were analyzed. A total of 25 pits were generated by each studied final pit definition methodology, and each pit had the sections with the varied slope angles analyzed in the stability assessment, resulting in a total of 150 slopes analyzed. A comparison between the results obtained by the two different methodologies implemented in commercial software is presented. The results show no relationship between the NPV and the overall slope angle using the DBS methodology. An analysis of the results for each geotechnical sector obtained by the traditional methodology was conducted and may contribute to the trade-off analysis between the best slope angle to achieve a reasonable SF and the maximum NPV.

Abstract The production rate of a mining operation has an important effect on the operational cycle and gross profit, which are often evaluated based on engineering practices. Assessment of the economic performance of mine operations in mining engineering is of great importance because an incorrect production rate can result in significant financial losses. The production rate is composed of two bases: the cost estimation and the price scenario. Bureau of Mines studies performed on American mines indicated that processing costs can be estimated through the production rate. This article proposes to connect the model presented by the Bureau of Mines and queuing theory to describe the operational costs, which are used to develop a production optimization methodology. The proposed cost composition describes a production system to verify the law of diminishing returns and the economy of scale. Between these regions of the production curve, the optimum point was determined with mathematical precision.

Abstract The transport distance in a mining operation strongly influences a mine operation revenue and its operational cycle because it is a fundamental part of the total mining costs. Generally, the transport route is determined based on an engineer's practical knowledge, which does not consider any mechanism to optimize the possible routes to be taken. In an attempt to establish a methodology for calculating the path that results in minimum costs to transport the mined block to its destination, the Dijkstra methodology is applied to a tree graph analysis, where the mining blocks are analysed as nodes of the tree. The transport cost is reflected as the arc of the graphs, which can use the Euclidean distance or the transport time for the calculation of the minimum path. The result obtained from the Dijkstra algorithm provided a non-operational route; to overcome this problem, an adjustment was performed through non-parametric equations. In this manner, it was possible to determine the transport costs for each block of the model. The paths based on Euclidean distance and transport time showed a tendency to increase for deeper mining regions. Identifying areas of largest growth and correctly quantifying their values increase the efficiency of mining planning.

Abstract The design of room-and-pillar mines relies on the correct estimation of the safety indicator of the underground structures formed by the excavation of drifts. Thus, the study of the geomechanical behavior is of vital importance. The mathematical models play an important role in the identification of problematic areas and allows different configurations to be tested in a safe manner. This article presents the development and application of a flexible and automatic routine to quantify the safety of room-and-pillar mines in terms of the safety factor of pillar and room convergence. The commercial software package FLAC3D was used to implement a computation routine in FISH language that can automatically represent the main characteristics of the geomechanical conditions, lithology and geometric features of a room-and-pillar project in a fast and accurate manner. A case study was performed on a manganese ore mine in order to demonstrate the capabilities of the developed routine.

Abstract Geologic modeling is an important step in determining the benefits and final pit dimensions for mining operations. Geostatistical models and distance-based functions are the main methods used to estimate the grade behavior. However, these two methods, despite their similar mean values, differ in spatial variability. The objective of this article is to prove, by comparing the two methodologies, that models with different spatial variability using the Lerchs-Grossmann algorithm will output subtly different final pit dimensions and scheduling. Furthermore, with the direct block schedule (DBS), these differences can be considerable. The tests compared the methodologies using the following three models: inverse distance (ID), ordinary kriging (OK) and turning bands simulation (TBS). The results demonstrate that the Lerchs-Grossmann algorithm is only slightly sensitive to the spatial variability of the grade; however, DBS requires the model populations to be better defined because of its greater sensitivity to spatial variability.

Abstract Mineral projects are composed of geological, operational and market uncertainties, and reducing these uncertainties is one of the objectives of engineering. Most surveys assess the impact of geological and operational uncertainties on the mining planning. The objective of this work is to study the impact of market uncertainty on the mineral activity. The influence of iron ore price simulation on mining sequencing will be evaluated. The price of iron ore has random behavior that is best represented by the Geometric Brownian Movement system. This study analyzed the historical series of iron ore in order to determine the percentage volatility and drift. Traditionally, a constant and deterministic price is used for the ore mined in all periods of a mineral project. The direct block scheduling methodology was adopted because it is able to apply the appropriate financial discount factor to the simulated probabilistic price. The proposed methodology was able to quantify the market uncertainty.

Abstract Determination of the best possible ultimate pit for an open pit mine is a fundamental subject that has undergone a highly evolutionary process, reviewed in this study, since the correct choice carries substantial economic impact for the industry. The correct choice can be very beneficial for project analysis, whereas an incorrect choice has the potential to mask huge financial and economic future losses that could render a project unfeasible. The advent of computers in the 1960s allowed sophisticated analysis for the selection of the best ultimate pit determination, under specific modifying factors such as economic, social, environmental, and political, but only in deterministic situations, i.e., when the problem and variables for the ultimate pit determinations were considered deterministically and almost always based on average values. Techniques such as the Lerchs-Grossman algorithm and mixed-integer programming are among many standard tools now used by the mineral industry. Geological uncertainty and the associated risks as well as the need to consider the appropriate time to mine a block during a mine operation have a significant impact on the net present value of the resulting ultimate pits. Stochastic aspects embed a probabilistic component that varies in time and are now under intense investigation by researchers, who are creating algorithms that can be experimented with and tested in real mine situations. One can expect that once these algorithms demonstrate their efficiency and superior results, they will readily dominate the industry.

Abstract This study is focused on Direct Block Scheduling testing (Direct Multi-Period Scheduling methodology) which schedules mine production considering the correct discount factor of each mining block, resulting in the final pit. Each block is analyzed individually in order to define the best target period. This methodology presents an improvement of the classical methodology derived from Lerchs-Grossmann's initial proposition improved by Whittle. This paper presents the differences between these methodologies, specially focused on the algorithms' avidity. Avidity is classically defined by the voracious search algorithms, whereupon some of the most famous greedy algorithms are Branch and Bound, Brutal Force and Randomized. Strategies based on heuristics can accentuate the voracity of the optimizer system. The applied algorithm use simulated annealing combined with Tabu Search. The most avid algorithm can select the most profitable blocks in early periods, leading to higher present value in the first periods of mine operation. The application of discount factors to blocks on the Lerchs-Grossmann's final pit has an accentuated effect with time, and this effect may make blocks scheduled for the end of the mine life unfeasible, representing a trend to a decrease in reported reserves.

Abstract In open pit mining, dilution is not always a factor systematically analyzed and calculated. Often it is only an adjusted number, for example, calculated or even empirically determined for a certain operational condition perpetuating along time in the form of a constant applied to calculating reserves or mine planning in attendance of audit requirements. Dilution and loss are factors that should be always considered for tonnage and grade estimates. These factors are always associated and can be determined considering several particularities of the deposit and the operation itself. In this study, a methodology was determined to identify blocks adjacent to the blocks previously planned to be mined. Thus, it is possible to estimate the dilution caused by poor operating efficiency, taking into account the inability of the equipment to perfectly remove each block, respecting its limits. Mining dilution is defined as the incorporation of waste material to ore due to the operational incapacity to efficiently separate the materials during the mining process, considering the physical processes, and the operating and geometric configurations of the mining with the equipment available.