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By D. F. Malan, L. Scheepers

Seismic risk in the deep gold mines of South Africa has been studied for many decades. A clear understanding of the effect of geotechnical conditions on the seismic hazard nevertheless remains elusive. Certain reef types seem to be associated with a higher risk of rockbursts. The stability and deformation behaviour of excavations on the different reef horizons are affected by the rock types and the varying strength properties. The seismic response to mining is therefore also expected to differ according to the geotechnical conditions. As a case study of this behaviour, the seismicity at Mponeng mine was investigated. On the VCR (Ventersdorp Contact Reef) horizon, two areas can be delineated. On the eastern side of the mine, the footwall is shale, and on the western side it is a strong brittle quartzite. More large-magnitude events occur in the area with the shale footwall than the area with the quartzite footwall. Moment tensor analyses indicated that the majority of the large-magnitude events are not related to geological structures, but are face-related, implying that shear failure of intact rock is occurring ahead of the mining front. Preliminary modelling indicated that the closure volume for the shale footwall may be higher than that for the quartzite footwall, providing a possible explanation for the observed difference in seismic response.

Mar 2, 2022

By T. N. Matveev, V. V. Getman, A. Yu. Karkeshkina, L. B. Lantsova, N. K. Gromova

Sulfide-type tin deposits in Russia are characterised by the complex mineral composition of ores and dump products of their processing. Tin-sulfide ores contain industrial quantities of copper, lead, zinc, tungsten, silver, rare and trace elements (indium, scandium, etc.). In addition, the ores are characterised by uneven dissemination of sulfide minerals (chalcopyrite, galena, arsenopyrite, etc.) and tin minerals (cassiterite, stannine, etc.). X-ray phase and spectral analysis, scanning electronic microscopy (SEAM), laser SIM and AFM microscopy helped to identify the selective fixing of sodium dibutyl dithiocarbamate (DBDTC) on chalcopyrite and galena, as well as the tall oil fatty acids (TOFA) and IM-50 on cassiterite. For the first time, collectors and flocculants of slurry fractions of silver and tin, thermomorphic polymers TMPF were used to isolate more than 80% silver from the tin tailings of the Solnechny mine into a copper-silver rough concentrate. It has been established that preliminary ultrasonic treatment and desliming according to the 0.02 mm class removes up to 20% of sludge material, which impairs the process of gravity separation. The combined flotation-gravity scheme using new reagent compositions helped to obtain tin concentrate with a tin content of 5.42%, which meets the requirements for further metallurgical processing (at least 5%). This work was supported by the RSF according to the research project No. 17-17-01292. Keywords: Flotation, flotation reagents, tin-sulfide ores, casiterite, adsorption, flocculation

Jan 1, 2020

By S. O. Choi, H. -S. Shin, W. -K. Song

Nuclear waste should be disposed with the best warranty for the national health and welfare. Among the several repository systems, the deep underground disposal is considered to be a most suitable system in Korean peninsula. However it demands basically the comprehensive stability analysis such as the behaviour of discontinuities in rock mass, the behaviour of ground water, and the reaction of rock stress according to the heat from the nuclear waste. For these purposes, the underground nuclear waste disposal repository was simulated in two- and three- dimensions. It shows that emphasis will be given to the thermal conductivity of discontinuities and the thermal convection of ground water as well as the thermal stress generated by the nuclear waste for design and construction of repository system, and they should be obtained from the field measurements. Déchets nucléaires devront tre déposés avec la meilleure garantie pour la santé et le bien public. Parmi les plusieurs systèmes de dépôt, la disposition en souterrin profond est considérée au système le plus approprié en Corée. Pourtant ce système demande essentiellement l’analyse éten-due de stabilité comme le comportement des discontinues en masse rocheuse, le comportement de l’eau souterrin et la réaction des contraintes de roche selon la chaleur depuis les déchets nucléaires. Pour ce but, le dépôt des déchets nucléaires en sous-sol a étè simulé en deux et trois dimensions. Il montre que l’accent sera donné à la conductivité thermale des discontinues et la convection thermale de l’eau souterrin aussi bien que la contrainte thermale générée par les déchets nucléaires pour le plan et la construction du systèmes de dépôt, et ils devront tre obtenus depuis les mesures sur place. Die Kernwüste muß mit der besten Gewähr für die nationale Gesundheit und die Wohlfahrt angeordnenet werden. Unter einigem Fundgrubesystem, das tief unterirdisch Wegwerfen werde in Betracht das passendest System in der koreanisch Halbinsel gezogen. Jedoch, es verlangt grundzätzlich die umfassend Stabilitätsberechnung so wie das Behnehmen mangelnder Konti-nuität in der Felsmasse, das Behnehmen des Grundwasser, und die Reaktion der Felsenbelastung nach der Hitze von der Kernwüste. Für diesen Zwecke, die unterirdische Wegferfenfundgrube der Kernwüste wurde in der zwei und drei Dimensionen gesimuliert. Es beweist daß die Betonung wird zur thermisch Leitfähigkeit mangelnder Kontinuität und thermisch Konvektion des Grund-wasser sowie die thermisch Belastung ergezeugt durch die Kernwüste für den Entwurf und die Konstruktion des Fundgrubesystem gegeben werden, und sie müssen von den Feldmaße ergelangt werden .

Jan 1, 2003

By A. G. Journel, CH. Huijbregts

"Centre de Morphologie MathématiqueSpecial problems arise in the evaluation of lateritic-type orebodies (Ni-Co, bauxite) or, more generally, orebodies affected by surface weathering. In this type of orebody, the vertical grade distribution shows, from the hangingwall downwards, a systematic increase followed sometimes by a certain decrease, or vice-versa. These trends appear together with irregular variations from one drill bole to the other.The problem is to characterize a vertical structure that is representative not only of the drill hole but of an entire panel or zone of influence, in order to define mineable thicknesses for given cut-off grades. The vertical grade distribution observed on the drillhole is replaced by a new curve, called 'derive' (drift), which is computed by 'universal kriging'.Once the vertical study is completed, new 'service-variables' are defined in the horizontal plane, such as mineable thickness and the corresponding average grade, economical functions (combination of the grades of several minerals). The local and global estimation of these variables can then be performed by a simple bi-dimensional kriging plan. The global estimation is summed up by several tonnage-cut-off grade curves.The practical valuation according to the above scheme of a New Caledonian lateritic nickel orebody is presented."

Jan 1, 2014

By H. -U. Lim, C. -H. Kim

The sixth underground pumped powerhouse cavern is under construction now in Korea. For the stability analysis of the five underground powerhouses, finite element method was used. For this analysis, in-situ rock stresses were measured by overcoring method and horizontal to vertical stress ratio was calculated 1.07-1.32 at four sites. Rock mass strength and elasticity were assumed from intact rock properties. The ratio of elasticity of rock mass was 0.16-0.55 of intact rock core elasticity. In general, elasto-plasticity with Mohr-Coulomb failure criterion was applied and the input cohesion and internal friction angle were approximately 0.12-0.22, 0.6-0.87 of intact rock strength parameters, respectively. Der sechste Untergrund-gepumpt-Powerhouse-Cavern ist jetzt im Bau in Korea. Für die vergan-gene Stabilitätsanalyse des fünf unterirdischen Powerhouses in Gebrauch wurde ein begrenztess Elementsmethode benutzt. Für die Analyse wurden In-Situ Felsenspannungen von overcoring Methode gemessen und Horizontale zu senkrechtem Spannungsverhältnis waren als 1.07-1.32 an vier Stellen kalkuliert. Felsenmassenkraft und Elastizität wurden von unversehrtem Felsenei-gentümern angenommen. Das Verhältnis der Elastizität von Felsenmasse war 0.16-0.55 von un-versehrter Felsenkernelastizität. Im allgemeinen wurde Elasto-Plasticity mit Ausfallskriterium des Mohr-Coulombs verwendet. Die Eingabebindekraft und die innere Reibungswinkel waren unge-fähr 0.12-0.22, 0.6-0.87 von unversehrtem Felsenkraftsparametern, jeweilig. En Coree, la sixieme centrale souterraine de la pompe d'accumulation dans la caverne est en construction. La methode d'element fini a ete utilisee pour analyser la stabilite de cinq dernieres centrales en service. Dans cette analyse, la reaction de la roche sur place etait mesuree par la methode d'overcoring et celle du rapport horizontal-vertical etait calculee de 1.07-1.32 en quatre places. L'intensite et l'elasticite de la masse de roche ont ete estimees de la roche intacte. Quant a l'elastic-ite, sa masse de roche etait 0.16-0.55 fois que celle de la roche intacte. En general, elasto-plasticite avec le critere de defaut Mohr-Coulomb etait utilisee et sa cohesion d'energie et son angle de friction interieure etaient supposees respectivement 0.12-0.22, 0.6-0.87 fois que la parametre de l'intensite de roche intacte.

Jan 1, 2003

By A. G. Royle

The reasons for constructing a model of an orebody for which both the parent population and the sampling distribution are known are discussed and details of the model are given. A brief summary of Matheron's theory of regionalized variables is included, with particular reference to his kriging estimators and their variances. Using the model, a comparison is then made between these kriging estimators and other commonly-used estimators. These are compared to find the one with the minimum variance, and an analysis is included to investigate whether any of the estimators is biased. Also included is a comparison between theoretical and experimental variances for some of the estimators.

Jan 1, 2014

By E. Lutz, M. Momayez, K. W. Brown Requist

As real-time air quality monitoring becomes more prevalent in US underground mines, it is important to provide the highest data reliability with the fewest possible sensors. Real-time sensors remain costly, and these costs are not exclusively financial; the time required to install, calibrate, and maintain real-time sensors poses a large barrier to widespread implementation. Current atmospheric monitoring systems typically rely on displaying point-specific values. This requires operators to infer real-time airborne contamination distributions. Monitoring and control software utilizing mine ventilation network (MVN) solvers has been implemented in limited cases because of their ability to simulate ventilation systems quickly, but these solvers use a one-dimensional representation of the mine, limiting spatial resolution of estimated distributions. Computational fluid dynamics (CFD) has likewise been considered as a means to improve spatial resolution, but processing times prevent its use as a basis for monitoring and control. For the real-time monitoring of airborne contamination distributions, we propose a spatial interpolation method that can estimate the distribution of airborne contaminants in near-real time. This method provides a middle ground between fast processing times and increased spatial resolution. With the use of a pathfinding algorithm and optimization through absolute percentage error minimization, this method outperforms spatial interpolation with a Euclidean distance. By providing contamination distribution information to operators, this method and its derivatives stand to outperform current atmospheric monitoring systems.

Apr 16, 2024

"SAMPLING: THE IMPACT ON COSTS AND DECISION MAKING1. INTRODUCTIONFor years those in the minerals industry have been taking samples to assist them in making decisions; whether they be about investing billions of rand in a new mining operation, or simply whether a truck load of mineralised material should go to the mill or the waste dump, - we need a sample to help us make our decisions. This paper emphasises the importance and significance of sampling as a process, some of the associated technical problems and some of the advantages, especially in the light of traditional approaches that has usually left mine sampling to the least educated and lowest paid individuals on the mine. Perhaps the most important aspect that requires attention is the variability, usually measured in terms of precision, that tends to infect the sampling procedures. Francis Pitard 12 has stated: ""There is no such thing as reliable feasibility studies, unbiased ore grade control, accurate environmental assessments or effective process control, if you cannot identify and minimize the seven (ten) major sources of sampling variability. "" It is these ten sources of sampling variability and the way they arise that are briefly investigated. Variability is measured in terms of variances and rather than being self-compensating, there is good evidence to indicate that they are in fact additive at every step in the sampling and analytical process."

Jan 1, 2014

By W. Newcomen, D. Brox

The assessment of the stability performance of open pit highwalls has traditionally been based on consideration of surface movement rates. Although generally accepted in industry, this approach presents challenges for establishing appropriate threshold values to allow for safe mining operations and does not address the issue of total strain. Surface movement monitoring data from a limited number of open pit mining operations in North and South America has been evaluated in terms of highwall strain, rock mass quality and inferred mechanism of instability. Threshold strain levels for key stages of highwall stability proposed from previous work has been reviewed and are endorsed based on evaluation of additional data. An empirical highwall strain criteria for the assessment of highwall stability performance is postulated based on relatively consistent trends in highwall strain data. L’évaluation du niveau de stabilité des hauts murs de carrières a traditionnellement été basée sur les taux de mouvements de surfaces. Bien que cette approche soit généralement acceptée à travers l’industrie, elle présente des défis pour la définition de seuils appropriés concernant la sécurité des opérations minières et n’adresse pas la notion de déformations totales. Des données de mouvements de surface provenant d’un nombre limité d’opérations minières à ciel ouvert d’Amérique du Nord et du Sud ont été évaluées en terme de déformation des hauts murs, de qualité de la masse rocheuse et des mécanismes inférés d’instabilité. Des seuils de déformation pour différentes phases clefs de stabilité de hauts murs ont été revus et sont endossés, basé sur l'évaluation de donnés additionnelles. Un critère de déformation empirique pour l’évaluation de la stabilité des hauts murs est postulé, basé sur des tendances relativement consistantes de données de déformations de hauts murs. Die Beurteilung der Stabilität von hohen Felsböschungen basiert traditionellerweise von Oberflächenbewegungen. Obwohl dieses Verfahren im Allgemeinen akzeptiert wird, stellt es jedoch gewisse Probleme für die Festlegung von Grenzwerten für die Sicherheit dar. Die totalen Dehnungen werden bei dieser Betrachtungsweise vernachlässigt. Eine beschränkte Anzahl von Oberflächenbewegungs Daten von Bergbauwerke in Nord- und Südamerika sind in Bezug auf die Dehnungen von hohen Felsböschungen, Felsqualität und davon abgeleiteten Bruchmechanismen untersucht worden. Grenzwerte für die Belastung von hohen Felsböschungen während den massgebenden Bauetappen aus bisherigen Projekten sind begutachtet und durch zusätzliche Untersuchungen bestätigt worden. Gestützt auf relativ konsitenten Trends, ist hier ein empirisches Verfahren der Dehnungen in hohen Felsböschungen zur Beurteilung der Stabilität vorgestellt.

Jan 1, 2003

By S. Liaghat, J. Rosenkranz, P. Semsari Parapari, S. Chehreh Chelgani, A. Tohry

It is commonly accepted that the energy consumption for comminution within mineral processing is responsible for around 3% of the global electrical energy usage. However, it was clearly noted that inside mills, less than 1% of this energy efficiency is actually consumed for particle size reduction. Therefore, monitoring of grinding parameters and modelling of product particle size distribution (e.g. characterised by the 80% passing size P80) play an essential role in operating costs of a mineral processing plant. Several empirical models have been introduced for the prediction of the P80. Since in the industrial scale usually a few numbers of grinding variables are monitored, these models cannot identically be used in plants. In addition, these empirical models do not always indicate the magnitude of correlations between milling variables. This study proposes to introduce the Hilbert-Schmidt independence criterion (HSIC) as an intelligent model for exploring linear and nonlinear relationships between grinding variables and P80 for an industrial scale data assessment. HSIC can rank variables based on their importance and help to select the most effective one for the generation of predictive models. HSIC modelling through various monitored grinding variables (ball charge, feed input rate, F80, power draw and work index) of an industrial plant indicated that F80 as a feed property has the highest effect on P80 of the ball mill products. Modelling results highlighted that the P80 can be accurately predicted, based on effective variables by using a HSIC model. These outcomes showed that HSIC as a powerful modelling tool can assess the relationships between monitored grinding parameters, select the most effective grinding parameters and satisfactorily predict the P80. Keywords: Product particle size, variable importance measurement, Hilbert-Schmidt independence criterion, mill charge

Jan 1, 2020

By A. P. I. Popoola, D. O. Okanigbe

Copper smelter dust (CSD) is a byproduct of copper smelting and is composed of considerable amounts of copper values and also contaminants (like silica and mullite). Silica in CSD forms Siloxane, a low density material, which is difficult to separate from the aqueous phase during solvent extraction. The need therefore arises to reduce/remove the aluminosilicates for better grade and recovery of copper in subsequent processes. This paper reports the use of two types of centrifugal gravity concentrators, namely Knelson (KGC) and Falcon (FGC), for upgrade of copper in CSD. The aim was achieved by an initial characterisation (Particle Size Distribution (PSD) and mineralogical analysis), together with Density Separation (DS) experimentation, premised on a hypothetical density difference between copper oxide and silicon/aluminum oxide. Wet screening results showed that 88.52 % of CSD particles were in -53 μm fraction. Further PSD study using laser diffraction showed the -53 μm fraction to be composed mainly of 26 μm, 22 μm and 18.5 μm fractions. Mineralogical analysis showed copper to occur mainly as oxides (24.34 wt%), but also as sulphides (7.95 wt%), and a substantial amount of aluminosilicates (42.97 wt%) were identified. Density of CSD was determined as 2.83 g/cm3. Copper content (18.02 wt%) in CSD was upgraded to 35.94 wt% in concentrate using KGC. In conclusion, the results showed good convergence between hypothesis and experiment. Additionally, it was also concluded that KGC performed better than FGC for copper upgrade in CSD. However, roasting CSD prior density separation was recommended for enhanced copper upgrade. Keywords: Copper smelter dust, density separation, solvent extraction, mineralogy

Jan 1, 2020

By W. J. Whiten

"Models of cone crushers and vibrating screens are described. These models have been constructed from actual plant data using a systematic model-building technique. Included in this technique is regression analysis using multi-dimensional spline functions.The models have been used to simulate complete crushing plants and hence to design and evaluate a control system for crushing plants."

Jan 1, 2014

By I. J. Geldenhuys

South Africa’s mining and metals industries have an illustrious history dating back to the Late Iron Age. We live in a complex and data-intensive world that has already fundamentally changed how we work and live. The outbreak of the global COVID-19 pandemic in 2020 resulted in immeasurable suffering worldwide, but the crisis also accelerated many technological developments and altered the way we think about, and experience, technology and work. Problem-solving requires new and rapidly changing skills to manage the data tsunami. Whether at the rock face or on the processing plant, the fundamentals have not changed, although how we interact with minerals and their properties has changed dramatically. Sustainable processing and design are non-negotiable if we genuinely want to achieve the aim of the cradle-to-cradle principle. As we venture forth, what can scientists, engineers, technologists, and mathematicians learn from history? History is data presented in a context; sometimes, the context is also important. We exist in an age of data, with most of the world’s data created in only the past two years. History can enhance our understanding of the present and enhance our future outcomes. Lessons from history can help provide insights into making ethical and sustainable choices related to technology or engineering in the mining and metallurgical industry. Shifting the perspective of mining and metallurgy professionals from a narrow focus on complex technical solutions towards a broader context for problem-solving and designs that includes the entire ecosystem is crucial. In other words, using or reflecting on historical process development is, at its core, systems thinking.

Sep 1, 2021

By M. Asghari, R. Amiri, A. Haratian, M. Noue Parast, S. Haji

Today the roller screen has a wide range of applications in the steel-making industry. It is used for screening of green pellets before using the kiln. Since the appropriate size of a green pellet is -16+9 mm, there are different gaps between rollers that make green pellets classified in three categories: -9 mm (undersize), -16+9 mm (onsize) and +16mm (oversize). The efficiency of a roller screen is specified according to the weight percent of undersize in onsize as a fine material, and weight percent of onsize in oversize (loss). This efficiency is influenced by different operational parameters such as roller diameter, roller speed, and roller gap, material type of rollers and inclination of roller screen. This study investigates the effect of different material types of rollers in efficiency of Ardakan roller screens, located in the Yazd province of Iran. The rollers of the existing roller screens in this pelletising plant are made of polyurethane which according to this investigation, has a maximum lifetime of about six months. Operating the polyurethane rollers beyond its lifetime generates serious problems such as high wear of rollers, and consequently, material buildup on the roller surface which then significantly decreases the roller screen efficiency. So, after examining different roller materials, stainless steel 304 with higher surface roughness to help pellets move properly on the roller screen surface was selected as a solution to this problem. The new roller screen was constructed by Fakoor Meghnatis Spadana (FMS) and replaced the previous one. In this way, the maximum capacity of the roller screen was increased about 17% and the roller screen efficiency was increased about 15%. Keywords: Roller screen, green pellets, efficiency, onsize, operational parameters

Jan 1, 2020

By H. Schunnesson, H. Fredriksson, D. Johansson, E. Söderström, S. Manzoor, A. Gustafson, M. Danielsson

Fragmentation analysis is an essential part of the optimization process in any mining operation. The costs of loading, hauling, and crushing the rock are strongly influenced by the size distribution of the blasted rock. Several direct and indirect methods are used to analyse or predict fragmentation, but none is entirely applicable to fragmentation assessment in sublevel caving mines, mainly because of the limitations imposed by the underground environment and the lack of all the required data to adequately describe the rock mass. Over the past few years, measurement while drilling (MWD) data has emerged as a potential tool to provide more information about the in-situ rock mass. This research investigated if MWD can be used to predict rock fragmentation in sublevel caving. The MWD data obtained from a sublevel caving mine in northern Sweden were used to find the relationship between rock fragmentation and the nature of the rock mass. The loading operation of the mine was filmed for more than 12 months to capture images of loaded load-haul-dump (LHD) buckets. The blasted material in those buckets was classified into four categories based on the median particle size (X50). The results showed a stronger correlation for fine and medium fragmented material with rock type (MWD data) than coarser material. The paper presents a model for prediction of fragmentation, which concludes that it is possible to use MWD data for fragmentation prediction.

Mar 2, 2022

By A. Kotze, D. Messina, E. Nagels, Y. Cryns, S. Arnout

The FlashPhos process aims to recover white phosphorus (P4) from sewage sludge by drying, flash combustion/gasification, and carbothermic refining steps. This study evaluates the material behaviour of sewage sludge ash melting and reduction in a refining furnace for the novel FlashPhos process. Thermodynamic modelling in FactSage 8.2 is combined with experiments from a tube furnace to determine the possible phosphorus recovery and minor element behaviour. For the two studied sludges, a yield of 40% and 75% white phosphorus is achieved after 1 hour at 1600°C, corresponding with a 60% and 25% loss to the metal phase. This is slightly above the calculated equilibrium yield of 28%–73%, which depends mainly on the Fe/P ratio of the sludge. Temperature is found to have a significant influence on the final phosphorus yield when leading to incomplete melting of the ash. A clean slag is produced in the process free of heavy metals making it suitable to be used as a cement-like binder material. The main heavy metals that co-evaporate with the phosphorus are Zn, Pb, As, Sb, and Sn. Additional processing steps will be required to remove these to produce a pure P4 product. The metal alloy consists of mostly Fe and P with smaller amounts of other components such as Mo, Cr, Cu, Mn, Sn, Sb, and V. The final slag consists of CaO, SiO2, MgO, and Al2O3 with virtually complete removal of P and heavy metals.

Oct 2, 2025

By J. A. Maritz, D. F. Malan

Pillar strength is affected by pillar shape, but this has largely been ignored in past research studies. Bord-and-pillar layouts are typically designed using empirical strength equations developed for square pillars. Owing to the poor quality of pillar cutting, many hard-rock pillars have an irregular shape and it is not clear how this affects pillar strength. Furthermore, the strength of rectangular pillars in comparison with square pillars is also difficult to quantify. The ‘perimeter rule’ is widely adopted for rectangular pillars, but its applicability for pillars with irregular shapes has never been tested. We used numerical modelling in this study to investigate the effect of pillar shape on strength. An analytical limit equilibrium model of a square and a strip pillar also provided useful insights. For slender pillars, the strength of a long rib pillar is essentially similar to that of a square pillar. In contrast, for rib pillars with a large width to height ratio, there is a substantial increase in strength. The study found that the perimeter rule should not be used for irregularly shaped pillars. Displacement discontinuity modelling, using a limit equilibrium approach, is proposed as an alternative to determine the strength of these pillars.

May 3, 2023

By M. Hopf

Numerous developments and improvements have been made to tap-hole designs. On the other hand, there are very specific designs in operation that have endured for many years without any modification. Nobody likes design changes because of risk - the risk of atypical wear, potential hazards, and costly repairs entailing enormous production losses. So the philosophy ‘never touch a running system’ is maintained, because among other things there is no efficient working monitoring technology for tap-holes. In the past few years a couple of new technical solutions have been investigated and developed. Not all theoretical solutions are possible in practice. However, metallurgists are inventive, and the last word regarding efficient working tap-hole monitoring technologies has not yet been spoken.

Jan 1, 2014

By R. E. Robinson

I shall present a concept for the development of the resources of this country and its neighbours that repre¬sents a fantastic challenge to our scientists and entre¬preneurs. This concept offers prospects of development that must make our previous achievements seem equivalent only to the first act in a drama enacted on the stage of Southern Africa. I hope to illustrate how, in Act Two, chemistry will play a dominant role, and chemists and chemical engineers will be among the principal actors.

Jan 1, 1980

By M. E. Rossi, C. Badenhorst

Conditional bias occurs when the expected value of the true grade conditional on the estimated grade is not equal to the estimated grade. It is a quantification of how the average of estimates differs from the true value. Conditional bias is present in all resource estimates due to the unavoidable properties of kriging, and indeed all linear estimation (regression) methods. In a mining resource estimation context, the degree of conditional bias is dependent on the spacing of the conditioning data; more data leads to the expectation of less conditional bias This paper discusses conditional bias from two perspectives: 1. 2. Estimates seeking to eliminate, as much as possible, conditional bias; and Estimates that accept a larger amount of conditional bias in resource models, in order to achieve a specific outcome. The problem of conditional bias in estimation can only be fully appreciated if the objective or purpose of a resource model is understood. There are instances where conditional bias should be avoided because it is not reasonable to make decisions using estimates that are known to be wrong in expected value; for example, when making a final decision in grade control with respect to the destination of the material. In most instances in the mining resource estimation context, however, the estimated values will not be “final estimates”, but “interim estimates”, meaning that in the future more data will be obtained, and the ”interim estimate” will then be updated. In this context, the most useful resource model is an interim model that is able to predict the final model estimates, despite not having all the data available that will be collected in the future. This is the objective, for example, of a recoverable “long-term” model developed prior to operating a mine, for example at the feasibility stage. It attempts to predict the ore that a processing plant will receive, well into the future. In such cases, it can be unequivocally demonstrated that conditional bias is not only unavoidable, it is a necessity.

Sep 1, 2021