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By L. D. van Dyk

The extraction of iron and lead from their oxides with a volatile organic ligand such as acetylacetone in the gas phase offers potential advantages of lower energy consumption, recycling of the extractant, recovery of pure metals, and a reduced environmental impact compared with conventional extraction processes. The influence of reaction temperature, ligand flow rate, and metal oxide levels on the extraction and rates of reaction of iron and lead from single metal oxide (synthetic haematite (Fe2O3) and synthetic massicot (PbO)) systems in a fluidized bed was studied. It was found that at the investigated acetylacetone flow rates, the influence of mass transfer was limited, but that the reaction suffered from reactant starvation. When the metal load increased the effect of starvation on the rate of reaction also increased. The reaction kinetics increased with an increase in temperature for both systems. At low metal oxide concentrations more that 80 per cent of the iron and lead could be extracted from their respective metal oxides after only four hours.

Jan 1, 2012

By R. Ribacchi, P. Tommasi, C. Consorti, P. Campedel

The runout of dry blocky rock avalanches produced by planar rockslides affecting a limestone formation with clayey interbeds is analysed by means of distinct element modelling. Numerical analyses are validated by means of the back analysis of a historical rockslide occurred in the investigated area and physical aspects of the phenomenon evidenced by modelling are discussed. On analyse par la méthode aux élements distincts la distance de parcours des avalanches rocheuses sèches produites par des glissements plan interessant une formation de calcaire à intercalaires argilleux. Les analyses numeriques sont validées à l’aide de la back-analysis d’un glissement historique survenue dans le site en examen. On décrit les aspects physiques su phénomène mis en évidence par la modélisation efféctuée. In diesem Beitrag wird die Reichweite von Steinlawinen besthend aus trockenem blockhaftem Fels mittels der Distinct Element Methode untersucht. Die Steinlawinen werden erzeugt von Rutschungen in einer Kalkstein-Formation mit tonhaltige Schichten betreffen. Die numerischen Berechnungen wurden anhand einer Simulation einer historischen Bergsturzen verifiziert, der sich auf den untersuchten Gebiet ereignete. Auf der Basis der erhaltenen Ergebnisse wurden die physikalischen Aspekte der untersuchten Steinlawinen analysiert.

Jan 1, 2003

Sandsloot open pit is situated on the northern limb of the Bushveld Complex, 250 km north east of Johannesburg, South Africa. Sandsloot is currently the largest open pit platinum mine in the world and is one of six potential open pits in the area. The geotechnical strength properties of the Platreef have posed significant mining and processing challenges to the PPRust operation since inception in 1992. In order to optimize the whole business as opposed to isolated cost centres a mine to mill initiative was embarked upon in 1997. Initial work focused on ore characterization and an entire suite of data was collected for each rock type. This included mineralogy, geochemistry, geotechnical, blast ability indices, as well as metallurgical strength data. The second phase involved the clear definition of customer requirements, namely the optimum performance criteria for the plant and mining departments. This involved extensive field trials and data capture to measure the interaction and influence of the mine to mill value chain. Once the design targets were defined, a 3D geotechnical model was constructed to ensure that the targets were consistently achieved. The model is very similar to an ore reserve model; however, it is populated with geotechnical, metallurgical and blast index data. Through software queries the appropriate blast powder factor for each mining block can be obtained, thereby ensuring the correct fragmentation is blasted for the plant and mining operation. The initiative has delivered significant results showing improvements across the mine to mill value chain. These include increased loading rates, reduced electricity and crushing consumables, as well as higher plant throughput. Additionally, the initiative has benefited both brownfield and greenfield projects on the PPRust operation

Jan 1, 2006

By L. D. van Dyk

The extraction of iron and lead from their oxides with a volatile organic ligand such as acetylacetone in the gas phase offers potential advantages of lower energy consumption, recycling of the extractant, recovery of pure metals, and a reduced environmental impact compared with conventional extraction processes. The influence of reaction temperature, ligand flow rate, and metal oxide levels on the extraction and rates of reaction of iron and lead from single metal oxide (synthetic haematite (Fe2O3) and synthetic massicot (PbO)) systems in a fluidized bed was studied. It was found that at the investigated acetylacetone flow rates, the influence of mass transfer was limited, but that the reaction suffered from reactant starvation. When the metal load increased the effect of starvation on the rate of reaction also increased. The reaction kinetics increased with an increase in temperature for both systems. At low metal oxide concentrations more that 80 per cent of the iron and lead could be extracted from their respective metal oxides after only four hours.

Jan 1, 2012

By J. R. Menasce

Mechanization in low-stope panels situated in hard rock infers roof support by tensile bolting to allow free passage of trackless mining equipment in the production areas. This is in sharp contrast to conventional mining, where compressive roof supports?such as timber and grout packs?have traditionally been used, up to 1.5 metres from the production face. Bolting is a hazardous operation because material is dislodged from the roof during the drilling activity. Even with temporary roof support installed, small pieces of rock are dislodged by the percussive action of the drifter. Operations with the man situated directly under the drill, during the drilling activity, are hazardous. The only way to remove the hazard is to move the man away from the machine for as much as possible throughout the complete cycle Costs associated with safety cannot be quantified, but need to form part of the decision-making process. Machine selections based on purchase and running costs alone do not justify the investment cost of mechanized bolters. The equipment selection process needs to take into account the total cost of mining as well as the human safety impact and loss of production costs from having to re-bolt roofs in a production panel to prevent falls of ground. Labour costs in mechanized low-stope bolting are between one-quarter and half the labour costs of non-mechanized bolting. This paper reviews the mechanized bolting option versus handheld bolting from a mining process and cost perspective in a hard rock, low-stope room-and-pillar mining operation in the platinum and chrome industries.

Jan 1, 2006

Recently, work was carried out by the Shotcrete Working Group to study anisotropy in steel fibre reinforced shotcrete using strain-controlled, compressive strength testing methods. The shotcrete materials used and specimen preparation procedures as well as testing methods are described. The test results are discussed and it is concluded that, because of the anisotropic nature of fibre reinforced shotcrete, it may be worthwhile investigating the degree of such anisotropy in practice using strain-controlled, strength testing techniques.

Jan 1, 2001

By M. du Plessis, D. F. Malan

"The aim of any mine design is to ensure that the excavations remain stable for the period they will be in use. Various pillar systems are used to ensure that underground stopes remain stable and that mining activities do not affect the surface infrastructure through either surface subsidence or seismicity. Intermediate-depth platinum mines make use of in-stope pillars designed to fail while the pillars are being cut at the mining face. The pillar stress exceeds the loading capacity and the pillars crush as a result. The aim of the paper is to provide an overview of in-stope crush pillars. This will include the application, behaviour, function, mechanism, impact, and design of a crush pillar system."

Jan 1, 2015

By A. J. Geldenhuys

This paper will focus on two topics, namely (1) an innovative process for the neutralization and partial sulphate removal of acid streams produced during coal mining and processing and (2)optimization of this integrated neutralization process by adding small amounts of synthetic organic polymers. The integrated lime and limestone process has been developed to neutralize acid mine water and to remove sulphate (to less than1 200 mg/l), magnesium and metals. Limestone and lime treatment is the most cost-effective technology for neutralization and partial sulphate removal of acidic/sulphate-rich water to sulphate levels of less than 1 500 mg/l due to precipitation of magnesium and removal of the associated sulphate fraction (through gypsum crystallization). Neutralized mine water of this quality may be suitable for irrigation. The process consists of the following stages: 1. Limestone (CaCO3) neutralization to raise the pH to 7 and CO2-production. 2. Lime (Ca(OH)2) treatment to pH 12 for Mg(OH)2precipi-tation and gypsum (CaSO4.2H2O) crystallization. 3. pH adjustment with CO2recovered from stage 1 and CaCO3 precipitation. Retention times of 1 hour, 4 hours and 1/2an hour were required by stages 1, 2, and 3 respectively. The sulphate level was reduced to 1 094 mg/l, which is less than the original aim of 1 200mg/l. Chemical costs associated with neutralization, using limestone instead of lime, are reduced by 69% in the integrated limestone/lime process. The overflow water from the clarifier of each of the above stages generally contains a wide variety of colloidal impurities that may cause the water to appear turbid or may impart colour. This results in very slow sludge settling rates that cause overflow water with a high degree of turbidity and colour. There are a number of successive or simultaneous stages involved in the agglomeration of particles. To get optimum neutralisation of the acid water and partial sulphate removal to below the saturation level of gypsum (i.e. 1 500mg/l), maximum sludge recovery is needed. The higher the concentration of seed crystals, the larger the surface area. Therefore, effective removal of suspended and colloidal matter from the overflow of each stage is required and can be achieved by coagulation and flocculation. The polymers PAC6 and 3095 were effectively used as coagulant and flocculant respectively. The addition of these polymers resulted in a clear overflow in each of the above stages with a very low turbidity.

Jan 1, 2003

By W. Barnett

The Limpopo Metamorphic Belt is a complex geological terrane with at least three major deformational events. Tectonically juxtaposed lithology, open to isoclinal folding, crosscutting and re-activated shear zones and metamorphic gneisses and schists make pit slope design and maintenance a risky business. Venetia diamond mine?s Cut 3 is planned to reach 360 m by 2011. The difficult rockmass created problems in the original pit and a new more comprehensive slope design was necessary. Nearly 9 km of geotechnical drilling were undertaken to produce a new geological model and provide geotechnical information near the final Cut 3 face. All existing data from the pit were brought together into a database. SRK Consulting were brought into the project to audit the process and provide most of the manpower for the data analysis. Existing failures were back-analysed and the geotechnical domains identified. Analyses of only the southern domains are discussed in this paper. Geotechnical engineers can design slopes at any angle, but it is up to the managers at the mine to decide what risk they are willing to accept in a slope design. Once the issue of risk was discussed and settled in respect of the consequences of failure, each of the main geotechnical domains were analysed to produce a slope design at5% probability of failure with 15% above the first ramp. A risk assessment of the design was then undertaken to determine what risk the design placed on the equipment, personnel and the profitability of the overall mining operation. The risk assessment indicated minimal risk to the operation. One of the main assumptions of the final design is that the pit slopes will be dewatered. A project was immediately put in place to determine a groundwater model for the mine and to thereby determine the best dewatering procedure. However, it should be obvious that it is practically impossible to prevent benches from getting briefly saturated with water during storm conditions. It was therefore necessary to look specifically at supporting the crests of the ramps in the problematic southern domains to guard against the possibility of crest failure during heavy rains. The data available were re-analysed toward this objective. Spiles were recommended as the most cost-effective support system, and a probabilistic approach was used in the design. The final design has a 5% probability of failure, and the analyses indicate a strong sensitivity of the required spile spacing to the strength of the reinforcement material that will eventually be used. The pit slope parameters derived as per the discussion in this paper have just begun to be implemented at Venetia Mine.

Jan 1, 2001

By R. Loots

High temperature creep resistant alloys are used in power plants as steam pipes and headers where they have to withstand super heated steam temperatures of up to 600ºC for the lifetime of the plant. Frequently certain portions of pipes may be subjected to excessive temperatures and consequently suffer from creep damage. Damaged portions then have to be replaced by welding new steel to the service exposed steel. Such welds will have to be subjected to a post weld heat treatment (PWHT) to relieve residual stress. During such a PWHT it is then possible for the steel to crack in the heat affected zone (HAZ) by what is known as Reheat Cracking (RHC), also known as stress relief cracking. For the present purpose the RHC susceptibility of service exposed steel was compared with that of new steel by reproducing the temperature cycle to which the HAZ will be subjected during welding in a weld simulator. This was followed by PWHT where the influence of residual stress was studied by applying a constant stress to such a weld-simulated specimen in a creep testing machine. A sharp spiral was machined along the length of the cylindrical specimen to simulate the presence of a possible weld defect. In this way it is possible to subject all portions of the simulated HAZ to the same stress intensity. For the purpose of the investigation 1/2Cr-1/2Mo-1/4V steel known to be susceptible to RHC was chosen. During testing a constant tensile stress was maintained while the temperature was increased to follow the thermal cycle prescribed for PWHT. It was found that the new steel in all instances failed by RHC along the grain boundaries in the high temperature heat affected zone. In the case of the service exposed steel the creep strength of parent metal was lower than that of new steel as a result of exposure to a steam temperature of 540°C for about 15 years. Consequently, all of the failures during testing occurred in a ductile manner by necking outside the HAZ rather than by RHC. When service exposed steel is welded to new material, it is expected that the creep strain associated with stress relaxation will mostly be concentrated in the parent steel outside the HAZ. Accordingly, it should probably not be necessary to make any extra allowance for reheat cracking during repair of steam pipes manufactured from 1/2Cr-1/2Mo-1/4V steel other than that applicable for welding new steel.

Jan 1, 2004

By M. McWha

Laboratory bias is a universal problem in all branches of analytical science. It results from differences in methods, techniques, equipment, and calibrations between laboratories. Notwithstanding that it is a property that can be measured by the use of standards or by inter-laboratory testing, laboratory bias remains a material issue for the mining industry. There is extensive literature and clear guidelines on measurement from the International Organization for Standardization (ISO) and its worldwide federation of national standards bodies (ISO member bodies) and from the science of metrology. ISO guides cover the manufacture and use of standards. An accessible source of literature covering laboratory quality control comes from the public health sector, particularly pathology. There is little doubt in financial reporting rules about the meaning of materiality. Public reporting guidelines are clear that material matters need to be disclosed for investors. Unfortunately there is currently no clear guidance what to do about biased assay results in mineral industry public reporting guidelines. This paper reviews the requirements for the manufacture and use of reference materials, public reporting requirements in the mining industry, and presents proposals to improve management and reporting of laboratory biases. Keywords laboratory bias, reference materials, ISO Guides, financial reporting, materiality.

Jan 1, 2014

Abrasivity and wear resistance are not intrinsic properties of materials, but rather parameters describing the interaction between the wear part and the material exerting the wearing action. Moreover, wear or, at least, that part of the wear which is due to the cumulative effect of minute scratches, is linked to the hardness disparity concept. Abrasivity, in this context, is a relative concept, pertaining to a metal-rock pair, rather than to a rock. Based on this assumption, a methodology has been developed and checked against actual cases, enabling description of the abrasiveness of a rock or the abrasion resistance of a metal through the ratio of comparable quantitative indicators. The paper describes the methods and provides examples of applications to practical cases (namely: rock cutting, excavation by means of tunnel boring machines (TBMs), rock crushing, and hydro-mill cutting).

Jan 1, 2012

By G. Coetzer

During galena flotation of Rosh Pinah milled material, metal ions and salts contents of various water resources (deionized, simulated circulated, lead concentrate thickener, lead tailing thickener and borehole) influenced mineral recoveries, upgrade ratios, selectivities, froth stability and flotation kinetics. The various water resources employed during galena flotation caused activation, depression or selectivity effects on minerals due to the presence of different ions in solution. Metal ions in these water resources were adsorbed by the ore, whilst ions associated with gangue minerals (dolomite and quartz) were released into the flotation pulp. Lead concentrate thickener water caused depression of sphalerite and pyrite, increased fast floating fractions for silver, copper minerals, sphalerite and quartz (unwanted), and improved slow floating rate selectivity against pyrite and sphalerite. Lead tailing thickener water enhanced sphalerite recovery during galena flotation (unwanted), and increased fast floating fractions of pyrite. Western borehole water did not affect galena recovery, but sphalerite and pyrite recoveries were unacceptably too high. Ions from copper, lead, and zinc salts tended to release high amounts of ions, such as calcium, magnesium, silicon, and manganese from gangue minerals (dolomite and quartz) during milling. During galena flotation, lead ions depressed sphalerite, pyrite and dolomite at a lead concentration of 400 ppm, but sphalerite was activated at a concentration of 800 ppm. Sphalerite was activated with copper ions (89% recovery, 2.09 upgrade ratio) and depressed with zinc ions (maximum recovery of 25%). This corresponds with findings in previous investigations. Dolomite and quartz were slightly activated with zinc ions. No evidence was found that lead and copper ions activated any gangue minerals during galena flotation. Keywords: galena, water resources, metal ions, activation, depression, selectivity.

Jan 1, 2003

By A. V. Pavlov, V. A. Grygorian, Kossyrev, A. E. Semin, A. Korostylev

A new way of producing low-silicon ferrosilicon from iron-ore materials in a new type of aggregate-oxygen reactor is presented. The oxygen reactor process is based on using the calorific combustibility and reducibility of carbon materials inside the aggregate. The key to the process is successful post-combustion of carbon monoxide above a layer of a solid coke bed. Initially the possibility of production of grades of ferrosilicon containing 20 to 25% Si (FeSi20-FeSi25) was studied on a laboratory model of the oxygen reactor. Quartz sand and iron ore concentrates (from Russia and India) were used in the laboratory tests. This test work demonstrated that a ferrosilicon grade FeSi15 could be obtained directly from raw iron ore (containing 75.9 % Fe2O3 and a maximum of 23.8 % SiO2) without using rich iron-ore concentrates. The process was successfully tested on a pilot furnace at Serovsky metallurgical plant. Very promising results and efficiency parameters were achieved. The consumption of materials for 1t of ferrosilicon (15 % Si) production was as follows: 1567 kg raw iron ore, 591 kg of coal (in a composition of ore-coal briquettes), 299 kg of coke (for coke bed formation), and 815 m3 of oxygen.

Jan 1, 2004

By J. M. Ortiz

Grade control and short-term planning are usually based on the samples obtained from blastholes. These samples may carry a large sampling and sample preparation error. At El Tesoro copper mine in northern Chile, an advance drilling grid is used for short-term planning and grade control. These drill holes are sampled well in advance, and a short-term model that incorporates several variables and sophisticated estimation methods can be prepared for decisionmaking. An additional advantage of the advance drilling samples is that reverse circulation can be used instead of conventional down-the-hole equipment, and a very careful sampling and sample preparation process can be implemented, reducing the total sampling error. Advance drilling can be performed on a wider grid than blasthole drilling, hence the decision about the grid requires assessing the economic benefit of different sampling grids. Furthermore, this process allows the cost of poor sampling and the effect of different estimation procedures to be quantified. We demonstrate the optimization of the drilling grid for short-term planning and grade control at El Tesoro mine by means of the economic evaluation of the performance of different drilling grids, with different drilling techniques (which differ in the sampling error). The methodology is based on creating dense (exhaustive) geostatistical simulations of the grade distribution over a volume defined for a production period in respect of the geological model, and assuming each simulation as the true grade distribution. Then, samples are obtained from the exhaustive simulations at a spacing similar to the advance grid to be evaluated, and a sampling error is added. The short-term estimation procedures used on the mine are applied to determine the destination of each block and the profit obtained. This profit can be compared with the maximum profit (unachievable) and with the profit under different sampling errors and grids. The results show that the current 8 x 8 m drilling grid is appropriate and by reducing the sampling error, misclassification is also reduced, leading to an increase in profit of about US$ 5 million in 4 years.

Jan 1, 2012

In order to deliver a quality shotcrete and concrete product underground for the extensions to the Cullinan Diamond Mine operations it was decided to develop a new, simpler concrete product to meet underground support requirements. The aim was to develop a concrete product that not only reduced costs but also met the performance criteria of the current range of concrete products used on Cullinan Diamond Mine, a 25, 45 and 60 MPa concrete and a fibre reinforced wet shotcrete. The concrete product batching and delivery system was to be from surface as opposed to the current underground batching systems. The operational principle was to include an automated surface batching plant with delivery of the concrete product to a borehole containing suspended pipelines delivering to an underground storage facility from where the product is delivered to the working area by further pumping or agicars. Keywords: concrete, shotcrete, full flow, frictional loss, pipeline transport, positive displacment pump

Jan 1, 2006

By R. G. Cawthorn

The vertical distribution of platinum-group elements (PGE) in the Merensky and UG2 chromitite Reefs is highly variable, but does follow certain general patterns that allow the testing of geological models. In the Merensky reef, historically popular geological representations and interpretations have suggested that the mineralization occurs in a pegmatitic pyroxenite bounded by two chromitite layers. However, there are now enough published exceptions to this relationship to expose its fallacy. The vertical distribution of the PGE depends largely upon the separation between these two chromitite layers or the absence of one chromitite layer. Where separation is small or only one chromitite layer is present, there is considerable PGE mineralization in the footwall below the pyroxenite and lower chromitite layer. With increasing separation between the two chromitites, the mineral¬ization occurs progressively higher in the succession, and tends to track the upper chromitite layer. The view presented here is that the entire Merensky package is comprised of three events of magma emplacement, in which each has produced variable reaction with, and erosion of, the footwall, causing recrystallization of pyroxenite into pegmatitic pyroxenite. The magma then produced a chromitite layer followed by pyroxenite. Each chromitite layer is associated with some mineralization, which was extensively complemented by the subsequent formation of a sulphide liquid carrying PGE that trickled down through about 1 m of permeable crystal pile. The sulphide liquid formed after, not coincident with, the pyroxenite layers. The distribution of PGE in the UG2 chromitite shows up to three upward depletion sequences of PGE, also suggesting three events. The PGE are associated only with the chromite. The contribution from a sulphide liquid is considered to have been minimal for two reasons. Cu and Ni are extremely low in the UG2 which would not be expected if sulphides had been present. Also, by analogy with the Merensky, downward trickling of sulphides would have caused some PGE to be present in the footwall. There are some PGE in the footwall, but only where remnants of chromitite occur, and the hanging wall is lacking in PGE. In the northeastern Bushveld the UG2 chromitite is thinner than elsewhere, and there is a UG3 chromitite layer, not present elsewhere, that has a high Pt/Pd ratio. It is surmized that in the rest of the Bushveld the UG3 only appears to be absent because it has merged with the UG2 to produce the high Pt concentration at the top of the composite UG2. The non-accumulation of the package of pyroxenite-norite-anorthosite between the UG2 and UG3 in the northeastern Bushveld, which is not seen elsewhere, creates an interesting challenge to the formation of silicate layering in the complex. The mineralization in the Platreef is not addressed here. Keywords Bushveld complex, Merensky Reef, UG2 chromitite, geological evolution.

Jan 1, 2011

Abrasivity and wear resistance are not intrinsic properties of materials, but rather parameters describing the interaction between the wear part and the material exerting the wearing action. Moreover, wear or, at least, that part of the wear which is due to the cumulative effect of minute scratches, is linked to the hardness disparity concept. Abrasivity, in this context, is a relative concept, pertaining to a metal-rock pair, rather than to a rock. Based on this assumption, a methodology has been developed and checked against actual cases, enabling description of the abrasiveness of arock or the abrasion resistance of a metal through the ratio of comparable quantitative indicators. The paper describes the methods and provides examples of applications to practical cases(namely: rock cutting, excavation by means of tunnel boring machines (TBMs), rock crushing, and hydro-mill cutting).

Jan 1, 2012

By S. J. Ramokgopa

The development of the modern State and the growth of capitalism involves a complex process of interaction between cross-cutting structural dimension: first between politics and economics and, second, between market and hierarchy. Central to such developments are political economies of scale. Mineral specialization in the Third World developed within the framework of an international extension on oligopolistic structure of the advanced capitalist economies of Western Europe and North America. Up to the late 1960s, the world mineral and metallurgical industry was closely controlled by a handful of Western mining and industrial groups. To the extent that, foreign control of the mining sector was seen in the Third World producing countries both as the essence of foreign domination and as its major symbol. In some newly industrializing countries, the State took a more direct role in tying the economy and society together. Central to this process was the growth of large-scale finance capital. From early 1959to the mid-1970s, metal consumption in industrial countries expanded well beyond their domestic mineral endowments. And a free access to Third World minerals was a major element of the economic dynamism of these countries throughout that period. With the change in the characteristics of international investment, Africa has become less important as an outlet for capital exports of European countries. Actually, the African continent now receives only a very minor share of direct foreign investments of Western enterprises. International political economy is concerned first of all with the relationship between the economic and political domains across territorial boundaries. Second, attention should be drawn to the role of the State as the focus of decision-making in a system of competitive States, that is in turn, interdependent with a trans-national market economy in which mining and metallurgy are essential activities that affect the politics of the State, and how this in turn, rebounds on the politics of the international system. Understanding the role of the State must go beyond the glib pronouncements on the ?national interest?. How, and whose interest, the ?national interest? is determined, is precisely the problem. This implies a third theoretical problem that must be addressed: the linkage between the domestic and international domains (or levels of analysis), given that political-economic processes clearly cut across the lines of political decision-making constituted by the institutional structures of the State. Situating the State and economic interests within this vast ?state-society? complex that we call the global order will be a crucial problem for any theoretical approach that involves mining and metallurgy.

Jan 1, 2002

We present a novel hybrid algorithm for quantifying the ore grade variability that has central importance in ore reserve estimation. The proposed algorithm has three stages: (1) fuzzy clustering, (2) similarity measure, and (3) grade estimation. The method first considers data clustering, and then uses the clustering information for quantifying the ore grades by means of a cumulative point semimadogram function. The method provides a measure of similarity and gives an indication of the regional heterogeneity. In addition, grade estimations can be obtained at different levels of similarity using a weighting function, which is the standard regional dependence function (SRDF). Keywords: Grade, fuzzy clustering, similarity measure, point madogram, weighting function.

Jan 1, 2008