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Stochastic methods are normally invoked / used to assist with the understanding of risks, when there is uncertainty around a particular outcome. Uncertainty implies that there is a risk that the desired outcome will not be realized. Stochastics and probability theory has long held out the promise to answering this need, but has often been maligned because of its misuse. This paper takes a critical look need for Monte Carlo simulation to project risk evaluation and highlights what is considered to be the fundamental issues that should be thoughtfully considered to avoid the abuse of this technique. The upside of avoiding the abuse of this technique will be the wider acceptance by practitioners that it is a credible technique to quantify this important aspect of valuation.

Jan 1, 2007

In many practical situations, the samples available to estimate a block of ore are not located on a regular grid. The sample sizes and orientations are not constant, and the number and relative position of the samples used for valuation of each block change from block to block. Estimation of a block W might be very complex and time consuming if each sample in the neighbourhood of the block were considered individually. A practical solution consists of grouping the samples in blocks Wi (i = 1, 2, . . . n) in the neighbourhood of W, and estimating µw as a weighted average of the mean xi of the samples in Wi. Possible ways of grouping the samples are illustrated in Fig. 1 1.1. More complex patterns can be found in the literature (Krige, 1966) To calculate the kriging estimator of pw, we must be able to calculate the variance of xi, the covariance of xi and xj, and the covariance of xi and pµw. The purpose of this chapter is to show how these quantities can be calculated when we ignore the position of the samples in the block Wi. We consider the samples to be randomly distributed in Wi; kriging with this assumption is known as random kriging.

Jan 1, 1978

By C. G. Verkerk

The paper discusses the transport and rheological characteristics of high concentration slurries or pastes for backfill purposes. The influence of pipe size, particle size distribution, additives, coarse material and mass concentration on these characteristics is addressed.

Jan 1, 1988

By E. J. Margi

Deep gold exploration such as is used for Witwatersrand gold deposits is both expensive and time-consuming. This paper provides quantitative guidelines as to the economic optimum number of boreholes and deflections within each borehole for a certain reef characterized by its variability pattern and depth below surface in order to maximize the level of confidence for a fixed drilling budget or to minimize the total drilling cost for a given level of confidence. Portions of the Basal, Vaal, and Elsburg Reefs that show a wide range of variability (sample logarithmic variances of 0,63, 1,05, and 2,06 respectively) are examined at depths below surface ranging from 1000 m to 4000 m over a simulated mining property covering 7000 ha (7000 m by 10000 m). It is concluded that four intersections per borehole are optimum in al the cases considered, which cover the majority of current Witwatersrand exploration, with the exception of the highly variable Elsburg Reef at depths of 1000 m and 2000 m, where boreholes with one and two intersections respectively should be preferred.

Jan 1, 1987

By B. Rezai, Z. Pourkarimi, M. Noaparast, S. Chehreh Chelgani

Nanobubbles (NBs) flotation separation can be an indicator for improving the efficiency of fine particles through the conventional process. Since flotation reagents such as frothers can reduce bubble size, they can potentially be used for the generation of NBs and develop a selective NB flotation separation. This study explored the flotation separation of fine phosphate particles from their associated minerals in the presence of NBs, which were generated by using a phosphate flotation reagent (Flo-YS: collector-frother). The results of flotation tests showed that in the presence of NBs, the flotation efficiency was significantly improved. However, in the presence of NBs, surface chemistry analyses (Fourier Transform Infrared Spectroscopy and High-Performance Liquid Chromatography) illustrated that the collector adsorption on the surface of phosphate particles decreased. A comparison between outcomes of various phosphate flotation conditions indicated that increasing the flotation efficiency in the presence of NBs may be due to the aggregation of fine particles by the generated NBs, and also selective adsorption of NBs (hydrophobisation) on the surface of particles. In other words, generating NBs by selective collectors may increase efficiency and decrease the collector consumption of a flotation process. Keywords: Phosphate, selective separation, fine particles, collector-frother, efficiency, mechanical flotation cell

Jan 1, 2020

By S. M. Bradshaw

In order to assess the requirements for online matching when using a transverse electric field (E-field) applicator to treat mineral ores continuously, the effect of varying load properties on matching has been investigated by simulation. The effective permittivity of the ore to be treated is expected to show variation on both short (< 1 s ) and long (minutes) time scales. By modelling the ore as a series of slices with alternating effective permittivity values, it was shown that permittivity variations on the scale of the expected particle size are attenuated significantly and matching is not required. For variations in permittivity on the length scale of the free-space wavelength, variations in reflected power are at most within ±10% of the mean. This is not considered operationally significant, as extreme permittivity variation over this length scale is unlikely, given the expected distribution of ore particle sizes to be treated. At typical ore transport speeds through the applicator, these variations occur on a time scale an order of magnitude shorter than the response time of typical industrial online matching equipment. This implies that online matching is neither required nor possible for short time scale variation. Long-term variations in dielectric properties can be adequately compensated for by current matching technologies. It is concluded that the transverse E-field applicator is robust to changes in the dielectric properties of crushed ores within the expected range of their variation.

Jan 1, 2012

By R. Gebrekristos

It is commonly accepted that three types of aquifers exist in the Bushveld Complex: (a) alluvial aquifers in areas of river courses, (b) weathered bedrock aquifer formed by the in-situ weathering of the bedrocks, (c) fractured aquifers underlying the weathered aquifers controlled by the regional and local fracturing of the crystalline rocks. Hydrogeological studies conducted in the Critical Zone of the Bushveld Complex in the western limb show that the UG2 pyroxenite layer is of a particular interest and has a unique aquifer property. It yields much of the groundwater inflow into some mines and can be classified as the most important aquifer in the vicinity of the mining zone. The UG2 pyroxenite aquifer is restricted to the dipping UG2 pyroxenite unit. The unit weathers more intensely than the surrounding norites and anorthosites and is characterized by deeper weathering horizons (two to three times deeper than the surrounding rocks). For much of the UG2 mining area between depths of 35 ? 80 m, stoping of the UG2 takes place approximately 5 ? 7 m below the UG2 pyroxenite aquifer, and usually there is no groundwater inflow into the mine workings. However, unsealed deep exploration boreholes intersecting the UG2 pyroxenite and reaching underground mine workings, or mine roofbolts penetrating the weathered pyroxenite aquifer from underneath, can result in significant groundwater inflows into the underground workings. The reason as to why the UG2 pyroxenite weathers more than the norites and anorthosites has not been fully studied but is suspected to be due to the bedding planes of the unit and mineralogical composition of the particular pyroxenes forming the unit, which result in preferential physical and chemical weathering under atmospheric conditions. The weathered pyroxenes form sand-sized, rounded grains with improved effective porosity and permeability suitable for the storage and passage of groundwater. The orientation of the pyroxenite aquifer can easily be determined as it dips with the Bushveld layered strata. No-flow boundaries can be assumed on the hanging- and footwall of the pyroxenite aquifer and the flow rates can be estimated using 2-dimentional analytical equations. However, this must be confirmed with strong conceptual models since the existence of a fracture network connecting the pyroxenite aquifer with the overlying weathered and/or underling fractured aquifers can complicate the system, lowering the accuracy of analytical models and necessitating the utilization of numerical models.

Jan 1, 2012

By W. Lin, H. Endo, M. Kwasniewski, A. Kamei, M. Takahashi

Uniaxial tension tests were conducted on specimens of eleven granitic rocks which came from eastern Japan, and included a granite, four granodiorites, four tonalites and two gabbros. The axial and transversal deformability of these rocks was determined based on strain measurements using wire strain gauges. The experimental test results revealed that deformational properties of the rocks investigated varied depending on their petrographic features. However, the axial strain and the lateral strain characteristics showed a similar trend for all the rocks, i.e. the stress-strain curves were non-linear throughout the whole stress range from the initial point of loading to the point of ultimate failure. Moreover, the tangent Young&apos;s modulus and the ratio of the lateral strain to the axial strain decreased monotonously with the increasing of the axial stress. Still, the deformational properties were different for individual rocks in a quantitative sense. In particular, the difference in the lateral strains among different rocks was more distinct than that in the axial strains. For example, the Poisson&apos;s ratio at a stress level equal to 50% of the ultimate strength of a granodiorite was very low, close to zero. Furthermore, the Poisson&apos;s ratio of a tonalite was lower than that of a granodiorite, and assumed a negative value. This effect occurred because the lateral strain became positive as it changed from contraction at the initial stage of loading to extension at higher stress levels. There is no ready explanation for this phenomenon; it is believed, however, that it occurs due to microcracks pre-existing in rock materials and/or weak bonds between the adjacent mineral grains. Les essais de traction directe ont été conduits sur les échantillons de onze roches granitiques provenant de la région Est du Japon: un granit, quatre granodiorites, quatre tonalites et deux gabbros. Déformabilité axiale et transversale de ces roches s’était déterminée en utilisant des jauges extensométriques à fil. Les résultats obtenus à partir des essais montrent que la déformabilité des roches examinées varie selon leurs propriétés pétrographiques. Cependant, à partir des essais, une tendance semblable était observée dans les paramètres de la déformation axiale et la déformation latérale de toutes les roches; c&apos;est-à-dire chaque courbe de contrainte-déformation était non-linéaire dans tout l&apos;intervalle de contraintes à partir de l’état initial jusqu’à l’état d’une rupture finale au cours du chargement. De plus, le module tangent de Young et le rapport de la déformation latérale sur la déformation axiale a diminué de manière monotone avec l&apos;augmentation de la contrainte axiale. Cependant, les différences quantitatives de propriétés de déformation sous traction étaient observées entre des roches individuelles. Particulièrement, la différence de déformations latérales était plus notable que celle-là de déformations axiales entre des roches différentes. Par exemple, le coéfficient de Poisson à un niveau de contrainte égal à 50 % de la résistance d&apos;un granodiorite était très bas, près du zéro. En outre, le coéfficient de Poisson de la tonalite était inférieur que celui du granodiorite et a assumé une valeur négative. Cet effet est apporté parce que la déformation latérale est devenue positive en passant de la contraction dans l&apos;étape de chargement initiale à l&apos;extension sous les contraines plus hautes. Il n&apos;y a aucune explication prête de ce phénomène; on prétend, cependant, qu&apos;il est induit par des microfissures préexistantes dans des matériaux rocheux et/ou des joints faibles entre les grains minéraux adjacents. Einaxiale Zugversuche wurden auf Probestuecke von elf frischen, in Ostjapan vorkommenden, granitartigen Gesteinen durchgefuehrt, welche einen Granit, vier Granodiorite, vier Tonalite und zwei Gabbros umfassten. Die axiale und transversale Verformbarkeit von diesen Gesteinen wurde durch Verformungsmessungen mit Drahtdehnungsmessstreifen geklaert. Die experimentellen Versuchsergebnisse offenbarten, dass Verformbarkeitseigenschaften des untersuchten Gesteins in Abhaengigkeit von ihren petrographischen Eigenschaften variierten. Jedoch zeigten die axialen und die lateralen Spannungsdehnungslinien eine aehnliche Tendenz bei allen Gesteinen, d.h. die Verformungskurven waren nicht linear im ganzen Bereich vom Ausgangspunkt des Belastens bis zum Punkt des entgueltigen Bruchs. Ausserdem verringerten sich das tangentiale Elastizitaetsmodul und das Verhaeltnis der lateralen Verformung zur axialen Verformung monoton mit der Erhoehung der axialen Spannung. Dennoch waren die Verformbarkeitseigenschaften der einzelnen Gesteine in der quantitativen Wahrnehmung unterschiedlich. Insbesondere war der Unterschied bezueglich der lateralen Verformungen zwischen verschiedenen Gesteinen eindeutiger, als der in den axialen Verformungen. Z.B. war die Querkontraktionszahl auf einem Spannungsniveau, das 50% der Zugfestigkeit eines Granodiorits entspricht, sehr niedrig und nah an Null. Ausserdem war die Querkontraktionszahl eines Tonalits negativ und deshalb niedriger als die eines Granodiorits. Dieser Effekt trat auf, weil die laterale Verformung, als sie sich von der Kontraktion am Ausgangsstadium des Belastens bis hin zur Ausdehnung auf den hoeheren Spannungsniveaus aenderte, positiv wurde. Es gibt keine fertige Erklaerung fuer dieses Phaenomen; es wird jedoch angenommen, dass es wegen der Mikrorisse auftritt, die vorher im Gesteinsmaterial und/oder in den schwachen Bindungen zwischen den angrenzenden Mineralkoernern existieren.

Jan 1, 2003

By A. J. Jager, J. A. Ryder, M. U. Ozbay

This paper deals with procedures used for designing pillar systems in hard-rock tabular mines operating at shallow depths, typically less than 1000 m. A comprehensive review if current practice identifies four types if pillars, namely non-yield, yield, crush and barrier pillars, and the main principles for designing these pillars are outlined. It is shown that the current design methods for pillar systems in South Africa are mainly empirical, each mine developing its pillar-design methods based largely on practical experience. This results in varying pillar layouts, even between neighbouring mines, despite similarities in geology, and depth if mining. It is suggested that some current layouts may fall short if being the best as regards safety, the maximum safe extraction percentages, or flexibility in accommodating future mining scenarios in deeper or otherwise different geological conditions.

Jan 1, 1995

By C. L. M. Gough, L. A. Vermeulen, D. D. Howat

Formulae expressing the dependence of the mass of a grinding ball on the amount of material milled by a ball mill are derived. It is shown that, with the aid of these formulae, it is relativel rsimple for the results of a marked-ball test to be analysed and for the relative performance and cost-effectiveness 0 the various types of ball under test to be evaluated. Predictions based on theory and the results obtained in a marked-ball test in a ball mill are compared detail and shown to be in close agreement. The difficulties associated with marked-ball tests are considered, and an explanation for the decrease in the calculated consumption of the balls, which follows naturally from the theory, is presented. The marked-ball anomaly explained, and it is demonstrated that the ball consumption in a ball mill can be predicted with fair accuracy from the results of a marked-ball test.

Jan 1, 1983

By D. G. Krige

Some basic considerations in the application of geostatistics to the valuation of ore in South African gold mines by D. G. KRIGE, Pr. Eng., D.Se. (Eng.) Rand (Fellow) There is much room for improvement in the statistical procedures that have been used by gold mines over the past decade in the valuation of their ore reserves. Improvement depends on the establishment of the extent to which the patterns of frequency distributions and the directional variograms for the gold values vary from area to area within each section of a mine. The application of the lognormal distribution and of the De Wijsian variogram model for routine ore-reserve valuations requires detailed study before some of the reservations still held by mathematical statisticians can be met. This paper provides some preliminary evidence of the extent to which these models can be used with confidence, as well as suggesting how they can be applied to their full potential.

Jan 4, 1976

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 I. R. Phimister

&apos;Ancient&apos; mining near Great Zimbabwe I. R. PHIMISTER. B.A. Hons. (Nottingham). B.A. Spec. Hons. (Rhodesia) (Visitor) In proposing reasons for the geographical location of Great Zimbabwe, the paper re-examines the popular assumption that Zimbabwe is comparatively remote from the known areas of &apos;ancient&apos; goldmining. The lack of &apos;ancient&apos; workings in the neighbourhood of Zimbabwe is pointed out, and it is suggested that the mining of placer deposits of gold may have played some part in the development of Zimbabwe on its particular site.

Jan 1, 1974

By E. L. Atkinson, G. W. Leach

The paper discusses the reasons for the introduction of load-haul-dump (LHD) units into Greenside Colliery, and the circumstances leading to the replacement of conventional mechanized equipment on a trial basis in the mining operations on No. 2, 4, and 5 seams. An outline is given of the factors governing the selection and introduction of these units into coal mining, and the associated mining and engineering aspects involved in the optimization of their use. Operating statistics comparing the performance of conventional and LHD equipment are included.

Jan 1, 1979

By L. Wade

The advent of relatively cheap computing power has precipitated a rapid growth of computer usage in the mining industry. In order to obtain most benefit from this development a need is recognised for the future mining graduate to be trained in computer literacy. This paper outlines the type of training required and describes progress to date with such a programme at the University of the Witwatersrand. Certain challenges concerning the teaching effort are discussed.

Jan 1, 1987

By J. C. Mostert, P. N. Roberts

Electric smelting at Rustenburg Platinum Mines Limited of nickel - copper concentrates containing platinum-group metals By J. C. MOSTERT Pr. Eng.. B.Sc. (Stellenboseh). M.Sc. Met. Eng. (Fellow) and P. N. ROBERTS Pr. Eng.. B.Sc. Eng. (Rand) (Fellow) The processes involved in the smelting in an electric furnace of nickel-copper concentrates containing platinumgroup metals are described. These are concentrate drying, pelletizing, pellet drying, and flux and pellets proportioning, followed by smelting of the concentrate in a submersible-electrode electric furnace, which is discussed in more detail. The furnace matte is blown in a converter to the white-metal stage and is cast in moulds, whilst the slag is granulated, ground, and floated for recovery of valuable metals and afterwards pumped to the tailing dam.

By I. D. Wood

Deposition of gold-bearing deposits in the Witwatersrand Basin was controlled by hydraulic processes. These resulted in the formation of independent sedimentological facies areas having different statistics and semivariograms. Consequently, when there are indications that data are a mixture of statistical populations, it is important to decompose them into statistical subpopulations and analyse these independently. However, in the case of actual mining, physical position and extent of sub- populations are important and, as a consequence, any decomposition of data must take space into account if it is to be of use. An algorithm for the spatial decomposition of data into its sub-populations is described and is applied to real data taken from the Witwatersrand. Two distinct areas with completely different geostatistical parameters were revealed.

Jan 1, 1987

Book reviews Jones, M. J. (editor). Process engineering of pyrometallurgy. Proceedings of a joint meeting of the Institution of Mining and Metallurgy and the Institution of Chemical Engineers. London, Institution of Mining and Metallurgy, 1974. 105 pp. £6,50. Nim reports Report No. 1656 The analysis of geological samples for trace elements by direct-reading emission spectrometry. Report No. 1669 An assessment of the carbon-rod atomizer for the determination of silver.

Jan 12, 1974

By A. A. Bradley, K. H. Stanton, P. J. D. Lloyd

A theory for the dynamic balancing of centrifugal mills is presented that takes account of the mass and shape of the charge in a gyrated grinding tube and the way in which the charge lags behind the centrifugal force vector. predicts that a corresponding lag in the angular position of the counterweight centres of mass is necessary, and that the fractional filling should be increased if the ratio of gyration diameter to tube diameter is decreased. A worked example is given for a I MW centrifugal mill that was balanced adequately by the methods described.

Jan 1, 1983

By C. Pohlandt

A literature survey of methods suitable for the determination of cyanides in process streams and effluents is presented. Of the large number of methods published, 92 are examined in detail, emphasis being placed on the selectivity of the methods, i.e. the extent to which they enable one to distinguish between ionic cyanide and metal-cyanide complexes. Methods designed for the determination of &apos;total cyanide&apos; (i.e. ionic cyanide as well as coordinated cyanide) are evaluated critically. Other aspects of the methods are also considered, such as sensitivity, accuracy, speed, and freedom from interferences.

Jan 1, 1983