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By D. G. Krige

For the purpose of determining confidence limits for ore grade estimates, an extensive simulated database was used, which included 1728 ore blocks with ?actual? grades and the corresponding estimates based on ordinary and simple kriging. The practical results show that conditional unbiasedness is essential and that acceptable confidence limits can then be set using Normal theory for the simulated error distribution based on the logarithms of the ratios of ?actuals?/estimates with a variance related to the kriging variance. The mean of the data used to prepare the variogram and the estimated block grade are to be used properly in this approach. A practical analysis was also done of the actual point and block data from a very large mined out Carbon Leader area. The distributions of the actual grades for two levels of block sizes with different levels of variability were fitted using three models, ie. two three and compound lognormal. The trends of tonnages, grades and relative profits for a range of pay limits, as well as the usual tonnage-grade curves, show a practical insensitivity for the choice between the three lognormal models considered.

Jan 1, 2004

By A. Krause

Shovel-truck systems for loading and hauling material in open pit mines are now routinely analysed using simulation models or off-the-shelf simulation software packages, which can be very expensive for once-off or occasional use. The simulation models invariably produce different estimations of fleet sizes due to their differing estimations of cycle time. No single model or package can accurately estimate the required fleet size because the fleet operating parameters are characteristically random and dynamic. In order to improve confidence in sizing the fleet for a mining project, at least two estimation models should be used. This paper demonstrates that the Machine Repair Model can be modified and used as a model for estimating truck fleet size in an open pit shovel-truck system. The modified Machine Repair Model is first applied to a virtual open pit mine case study. The results compare favourably to output from other estimation models using the same input parameters for the virtual mine. The modified Machine Repair Model is further applied to an existing open pit coal operation, the Kwagga Section of Optimum Colliery as a case study. Again the results confirm those obtained from the virtual mine case study. It is concluded that the Machine Repair Model can be an affordable model compared to off-the-shelf generic software because it is easily modelled in Microsoft Excel, a software platform that most mines already use. This paper reports part of the work of a MSc research study submitted to the University of Witwatersrand, Johannesburg, South Africa. Keywords: simulation, bunching, probability distributions, cycle time, queuing, matching, shovel-truck, OEM.

Jan 1, 2007

By E. A. van Wyk, M. R. de Villiers

"Mining companies strive to increase and maintain production, while simultaneously remaining competitive in the global economy. Furthermore, they must ensure workers’ safety and maintain good safety records. The use of virtual reality (VR) facilitates the development of tools and systems for various purposes that can improve knowledge and understanding of the work environment. VR is a rapidly growing technology that uses the ever-increasing power of computing to simulate real-world and imaginary environments and situations with a high degree of realism and interaction. The availability of 3D modelling tools and simulation programming engines that work effectively with a mid-range desktop PC and standard 3D graphics card, make VR technology viable and attractive for mainstream training applications. The design, development, and implementation of interactive VR training systems is proposed as an innovative approach to augment safety training. However, in order to assess the impact of such VR training systems it is of particular importance to determine the effectiveness of the design of such systems. This article proposes an evaluation framework for this vital purpose. This framework comprises criteria to assess VR training systems, specifically relating to usability, instructional design, VR systems design, and mining industry context-specific aspects. Although the framework was developed as an evaluation tool to assess effectiveness of the design of such systems, it can equally well be used as a set of design principles to inform the design of VR training systems for mining. IntroductionMining in South Africa has been the main driving force behind the history and development of Africa’s richest and most advanced economy (Coka, 2012). The South African mining industry is frequently criticised for its poor safety record and high fatality rate (Stoddard and Skweyiya, 2016). Inadequate or insufficient training is often cited as a root cause of accidents (Van Wyk and De Villiers, 2009; Tichon and Burgess-Limerick, 2011). Virtual reality (VR) is a rapidly growing technology that utilizes the ever-increasing power of computing to simulate real-world and imaginary environments and situations with a high degree of realism and interaction (Webber-Youngman and Van Wyk, 2013). VR is currently being used or investigated as a training solution in a variety of industries. VR technology has developed rapidly and costs have fallen to levels where it can now be considered for mainstream training applications. The availability of 3D modelling tools and simulation programming engines that work effectively with a mid-range desktop PC and a standard 3D graphics card, make VR even more attractive to mine training centres (Van Wyk and De Villiers, 2009)."

May 1, 2019

By S. Uludag

Spontaneous combustion of coal has been studied by laboratory techniques using an apparatus in a small-scale laboratory testing. Coal?s inherent characteristics can be measured using Differential Thermal Analysis (DTA) and Crossing Point Temperature (CPT) methods. The DTA curve obtained after testing is compared with actual inherent moisture and its effect on spontaneous combustion has been investigated. It has been found that the Wits-Ehac Index increases as the inherent moisture of the sample increases. Therefore it can be deduced that liability to spontaneous combustion increases with increased inherent moisture. In addition, volatiles have a catalytic affect on self heating immediately after the inherent moisture is reduced. This is identified as stage two in the thermogram. The inherent moisture has a cooling effect during the initial stages of testing and is visible in the DTA thermogram. In addition, while an increase in carbon content means an increase in Wits-Ehac Index value, an ash content decreases the likelihood of on spontaneous combustion. Keywords: Spontaneous Combustion, Differential Thermal Analysis, Crossing Point Temperature, Moisture, Coal, Laboratory Testing.

Jan 1, 2007

By D. H. Diering

The paper takes the reader into the depths of a modern ultra-deep South African gold mine and gives a perspective on the vertical and horizontal extent of the tunnel networks in such a mine. Depending on the mine design layout employed, tunnels once excavated are subjected to various levels of stress change over their life time, and the support requirements are explained. It is suggested that shotcreting is the only viable ultra-deep level support medium, and after looking at the latest developments, the logistical problems are put forward. In an effort to overcome most of these problems, the South African ultra-deep mining industry embarked on a collaborative research programme in 1998. The importance of tunnelling and in particular tunnel support as a critical technology for future successful ultra-deep level mining is stressed. While not yet fully ?on top of? these problems and challenges, our industry is now fully addressing them and we expect to make significant progress during the next 4 to 5 years.

Jan 1, 2000

By J. N. Van der Merwe

The data base of failed coal pillars in South Africa was analysed with regard to the time of failure in an effort to develop a method to predict how long after their formation coal pillars will fail. It was found that meaningful results could only be obtained by splitting the data base up into groups that displayed similar behaviour. It was postulated, based on observation and experience, that coal pillars fail by a process of progressive weakening progressing into the pillar from the edges. Minimum pillar dimensions to ensure failure were calculated?these were the dimensions that corresponded to a minimum ?real? factor of safety. From the scaling distance required to reach the minimum safety factor, rates of scaling for the failed pillars were calculated based on the observed real lives of the pillars. It was found that the rates of scaling were unique for different mining areas and that they correlated directly with mining height and inversely with time. Using the derived scaling rates, the predicted pillar lives were back calculated for the pillars in the data base of failed pillars. In two of the three groups, the predicted lives correlated well with the observed lives on a one-to-one comparison. In all cases, the predicted lives were in the same time range as the observed lives. Overall, the frequency of predicted lives closely replicated the observed frequency of observed lives of the pillars in the data base of failed pillars. The method was successful in distinguishing between the data base of failed and a representative sample of intact pillars. While the predictions matched the observed lives of failed pillars, the predictions of expected lives for intact (hitherto unfailed) pillars were orders of magnitude greater. It is now possible to estimate the frequencies of future pillar failures for the purposes of mine closure and undermining of surface structures within broad bands.

Jan 1, 2003

By D. C. Panigrahi

Extensive field studies have been carried out to investigate the pillar fire problems in one coal mine in India. A Thermal IR gun and a Thermovision camera have been employed for thermal scanning to assess the state of heating in selected pillars. Special sampling set-ups have been designed to collect gas samples from the holes drilled into the selected pillars and the multigas detector is used to analyse the composition of samples in situ. In order to predict the spontaneous heating in coal pillars, different gas ratios have been calculated and it has been observed that some of the established gas ratios, viz. Graham?s ratio, Young?s ratio etc. have resulted in negative values in samples containing high amounts of methane. The modified gas ratios have been proposed which will be useful for predicting the pillar fires. These ratios may also be used for assessing the condition of fires in sealed-off areas.

Jan 1, 2004

By W. J. Errington

The Isasmelt process was developed at Mount Isa Mines Limited in Queensland, Australia in collaboration with CSIRO, the Australian Government research organisation. Originally developed for primary lead smelting, culminating in the construction of a 60,000 tonnes per annum lead smelter at Mount Isa, this technology now also provides a major part of the current 200,000 tonnes per annum copper smelting capacity at Mount Isa. A programme is now in place to expand copper production to 250,000 tonnes per annum. The technology has also been applied to secondary lead smelting at Britannia Refined Metals, a MIM subsidiary company, where a 30,000 tonnes per annum lead plant based on battery scrap feed has been operating since 1991. Mount Isa Mines Limited decided to license the technology in1988, and copper smelting plants utilising Isasmelt technology are now operated by Cyprus Miami Mining Corporation in the USA and by Sterlite Industries in India. In addition, the technology was adopted by AGIP for smelting copper/nickel concentrates in Australia. Union Miniere are currently constructing an Isasmelt furnace to smelt and convert copper-containing materials at their plant at Hoboken in Belgium. This paper discusses these developments and also some likely future developments which include the application of the technology for continuous copper and nickel converting and applications in the treatment of zinc-containing residues.

Jan 1, 1997

By O. F. Oxtoby, J. E. Olsen, M. W. Erwee, Q. G. Reynolds

"The extraction of molten products and wastes through smelting furnace tap-holes during the tapping process is a complex procedure involving many coupled thermophysical effects. Insight into the fluid flow behaviour in such systems can be gained by using computational mechanics tools to build highfidelity models of the fluid flow and other relevant physics. Previous work using such models indicates that the nature of the flow in the tap-hole, as well as operational parameters such as the tapping flow rate, depends strongly on the properties of the material being tapped and the geometry of the tap-hole channel. Additional complications arise when multiple fluid phases (for example, slag and metal) are present simultaneously, when porous coke beds hinder flow to the tap-hole entrance, and when the geometry of the tap-hole changes over time due to cycles of wear and repair. In the present work, challenges with the coupling of phenomena such as multiphase flow and porosity into computational fluid dynamics methods for tap-hole modelling are discussed in the context of electric furnaces used for ferromanganese production. Qualitative and quantitative results of computational models of flow through tap-holes are presented and compared as a function of material parameters to determine sensitivity effects, and in response to operational parameters to determine typical process behaviour over the duration of a tap. IntroductionPyrometallurgical production using electric furnaces accounts for substantial portion of the world supply of ferroalloys and other strategic materials (Degel et al., 2015). A range of different furnace designs may be used depending on the metallurgical process, with circular three-electrode submerged arc furnaces (SAFs) powered by alternating current being the most common for commodities such as ferromanganese and silicomanganese (Olsen, Tangstad, and Lindstad, 2007).As shown in Figure 1, manganese furnaces typically operate with a deep charge consisting of an upper layer of loose burden (onto the upper surface of which is fed solid raw material), a molten slag layer partially or completely filled with unreacted carbonaceous reductant (generally metallurgical coke), and a molten metal layer which settles to the bottom of the furnace due to its high density. The solid particles present in the slag and burden layers form porous beds which hinder the fluid flow of molten process material and gases inside the furnace (Olsen, Tangstad, and Lindstad, 2007).In order to remove material from the furnace during normal operations, a single tap-hole is built into the sidewall of the vessel near to the level of the hearth. Tapping involves removing both slag and metal phases through the same tap-hole channel, which makes tap-hole design, operation, and maintenance particularly complex. In the case of processes such as ferromanganese, which operate with no external gas injection or open arcs present at the furnace electrodes, flow of material out of the tap-hole is driven primarily by the hydrostatic pressure generated by the weight of the solid and liquid phases above the tap-hole."

Jun 1, 2019

Stope support systems, typically consisting of props and packs, are used extensively in the gold and platinum mining industry to stabilize the rock mass in the excavation vicinity and to reduce the hazard associated with rockfalls and rockbursts. The design of stope support systems was historically based predominantly on past experience and practices, and cost considerations. The recent development of a new and improved support design methodology, has led to the potential for significant increases in worker safety and support cost savings. This paper reviews some of the fundamental rock mass and support criteria that form the basis of the improved support design methodology. The considered design criteria are the height of potential fall; quasi-static stope closure rates; dynamic stope closure rates; compressive hangingwall stresses; discontinuity spacing, orientation and interface properties; effect of support length (stoping width); effect of compression rate; consistency of support performance; a real coverage; support spacing; and zone of support influence. The proposed support design methodology combines both the zone of influence and key block stability theories, resulting in optimized support systems for rockfall and rockburst conditions. The site-specific methodology consists of two stages: (i) a tributary area analysis, and (ii) a zone of support influence and a stability analysis, considering hangingwall failure due to buckling, shear and block rotation, which gives maximum safe spacing of individual support units. The methodology is suitable for designing support systems for both blocky hangingwalls and hangingwalls fragmented by face-parallel extension and shear fractures.

Jan 1, 2001

By R. Falcon, P. den Hoed, A. Luckos, R. Erasmus, V. du Cann, D. Comins

Carbon as a reductant, additive or filler is an essential element in the processing of metallic ores and the manufacture of iron and steel in the metallurgical industry. In most cases, the element carbon is derived from coal and its carbon derivatives. The properties of carbon required for the different processes in each metallurgical sector vary significantly and, for this reason, matching the correct carbon product for each specific process has become an important if not vital function in all sectors of this industry. This selection process, however, has become increasingly difficult. In many cases, the substitution of new products, despite being similar in all relevant chemical specification characteristics to previous products, has resulted in different performance properties relative to that expected. Under these circumstances, the prediction of performance of unknown carbon products has become fraught with difficulties unprecedented in the past. In order to initiate an investigation into addressing these issues, a test case was selected for indepth study the results of which are reported in this paper. The case concerned the use of a specific carbon feed in a conventional submerged arc furnace which gave rise to an unprecedented amount of unreacted or only partially consumed residue trapped in the frozen slag on the refractory walls of the furnace. During the course of these investigations, different advanced analytical technologies were employed including, inter alia, Raman spectroscopy, surface dimensional tests, organic petrology and various thermal reactivity factors. All results have been integrated into a multidisciplinary assessment presented in summary in this paper. Based on the above, and previous experience, the concept of an all-embracing 3-D coal-carbon ?framework? is briefly introduced. This approach has succeeded in obtaining greater depth of knowledge and a better understanding of the issues at stake with specific reference to the organic composition, structure, texture, internal surface area and consequent reactivity of the carbon materials concerned. In consequence, it would now appear that various properties of relevance to the metallurgical industry may be predicted with greater precision than has hitherto fore been possible.

Jan 1, 2004

A method is proposed for the evaluation of the influence of grout prestressing systems on the support resistance offered by timber packs. It is shown that, in order not to reduce the load-carrying capacity of timber packs, grout prestressing systems need to be at least as stiff as a single timber rise. The method was used to establish strength specifications for the grout prestressing systems to be used under non-seismic and seismic conditions. For non-seismic requirements, the 24-hour grout strength needs to be at least 1,7 MPa, and the 7-day grout strength 4,9 MPa. The investigation showed that the proposed strength specification is realistic in the light of current grout-strength capabilities. For seismic requirements, the grout strength needs to be at least 4 MPa and 8 MPa to prevent extensive damage to the grout during seismic events with a peak velocity of 1m/s 3 m/s respectively.

Jan 1, 1996

By E. Pizarro, A. Videla, G. Compan

One of the main problems related to mining investment decisions is the use of accurate prediction models. Metallurgical recovery is a major source of variability, and in this regard, the Chuquicamata processing plant recovery was modelled as a function of geomining-metallurgical data and ore characteristics obtained from a historical database. In particular, the dataset gathered contains information related to feed grades, ore hardness, particle size, mineralogy, pH, and flotation reagents. A systemic approach was applied to fit a multivariate regression model representing the copper recovery in the plant. The systemic approach consists of an initial projection of the characteristic grinding product size (P80), based upon energy consumption at the particle size reduction step, followed by a flotation recovery model. The model allows for an improvement in the investment decision process by predicting performance and risk. The final geometallurgical model uses eight operational variables and is a significant improvement over conventional prediction models. A validation was performed using a recent data-set, and this showed a high correlation coefficient with a low mean absolute error, which reveals that the geometallurgical model is able to predict, with acceptable accuracy, the actual copper recovery in the plant.

Jan 1, 2015

By A. H. Onur

Many factors govern the size and shape of an open pit, and these must be properly understood and used in the short and long-term planning of any open pit and quarrying operation. The importance of each factor will depend on the particular project, but the geology, grade, and localization of mineralization, extent of the deposit, topography, property boundaries, production rates, bench height, pit slopes, road grades, mining costs, and cut-off grades are key elements of open pits. This paper discusses the work done on the above parameters in order to provide an optimal production plan for a limestone quarry and clay deposits that provide raw material for a cement factory in Turkey. Soke cement factory has 1 400 000 tons of clinker capacity and is located on the western part of Turkey, in the province of Aydin. It is one of the largest facilities in the cement sector in terms of capacity, and it has a large advantage over facilities because the location of the factory was chosen to obtain the raw materials necessary for cement production within very short distances. However, the old reserves that supplied limestone to the factory had been reported to have run out, and therefore new limestone reserves in the same province have been investigated over the years by experienced geologists. From surface samples, high MgO content was reported in the neighbourhood of limestone formations with high dolomatization; hence, other alternatives were taken into consideration. One alternative with better chemical composition had been found 24 km away from the factory, but the haulage cost of limestone was unacceptable for the factory due to high diesel prices in Turkey. The maximum allowable MgO content in the pre-mix feed to a rotating furnace is 2.5% MgO content in pre-mix from both limestone and clay deposits. The clay deposits belonging to the cement factory have higher MgO content than the limestone deposit, and therefore this quality problem was taken into consideration first, instead of transporting material from 24 km away. This study gives the details of work done to evaluate both the clay and limestone deposits, statistical analysis performed on core samples taken from drill holes, mathematical modelling for both sites, and most importantly of all, in-pit homogenization work that reduced the pre-mix MgO content. As a result of this study, the profitable limestone quantity has been improved in order to serve the cement factory over a projected 25 additional years without using any material from the close deposit.

Jan 1, 2008

Utilizing a very large database from a mined-out area on a South African gold mine, the relative efficacy of a method to mitigate the smoothing effect introduced by the algorithmic constraints imposed by kriging was investigated. Smoothing effects arising from limited data availability are differentiated from the smoothing arising from the application of estimation algorithms. Very little can be done to ameliorate smoothing of estimates because of too little data, barring additional drilling or sampling. However, the smoothing effects resulting from the kriging process are shown to be mitigated by use of an alternative algorithm. The primary criterion in the development of the new algorithm was to avoid re-introducing conditional bias. This paper examines firstly the smoothing effects introduced into estimates via the kriging covariance matrix, secondly the process for ameliorating the smoothing effect, and finally it uses a case study to demonstrate the effectiveness of the new algorithm on a very large database. The database was used to introduce a 60 m by 60 m drilling pattern which in turn was used to model the semi-variogram and produce 30 m by 30 m kriged block estimates. The follow-up database was then re-introduced (roughly 5 m by 5 m grid spacing) and averaged into 30 m by 30 m blocks to provide a direct comparison with the initial estimates. In this way the extent of smoothing and accuracy of the estimates before and after the corrections was tested.

Jan 1, 2014

By M. Jeffrey

This study investigated the elution of precious and toxic metals from activated carbon. Gold and mercury are of primary interest, due to their value and environmental impact respectively. A laboratory elution rig was commissioned to simulate industrial Zadra and AARL carbon elution conditions. Mercury was found to elute most effectively in strong caustic cyanide solutions; gold was found to elute most effectively in hot low ionic strength solutions. As cyanide decomposes on contact with activated carbon at high temperatures, optimum elution conditions for gold conflicts with those for mercury?no practical compromise in conditions was found. However, sequential elution allowed reasonable recovery of both metals. Ongoing work is looking at the deportment of other metals under elution conditions.

Jan 1, 2009

Visit to the Datsun Nissan Company's body pressing and assembly plant at Rosslyn, Pretoria, and the Claremont-Danville Tunnel on 27th February, 1970. The excursion arranged for the 27th February to the Datsun Nissan motor car assembly plant at Rosslyn, near Pretoria, in the morning and the Claremont-Danville tunnel in the afternoon was well supported by some 43 members. The visitors were met at the factory by Mr Rademeyer, the Industrial Relations Manager, and members of his staff and were taken to the artisan training centre for light refreshments. There is a well-equipped training section with an air-conditioned lecture hall; we were told that such training facilities were important because of the cosmopolitan nature of the artisan staff. The visitors were divided into small parties and taken to the tool die and jig-making section, which is perhaps the key department for a factory of this nature. There the many dies for the presses in the body pressing section, as well as the complicated jigs for body welding are made. The technique for making the castings for the dies is interesting. A polystyrene model of the casting is embedded in moulding sand. In a neighbouring foundry molten metal is pressed into the headers and burns away the polystyrene, which leaves no residue, and this exactly fills the space occupied by the model. This rough casting is then machined in large copying machines (costing as much as Rl80 000). An exact plastic model of the surface of the pressing required, set up in juxtaposition to this casting is traversed by a master stylus which operates the slave milling cutter, thereby machining the surface to close tolerances. The machined casting is cleaned up by hand and finally finished in large spotting machines, using a blue dye to show up high spots, to the fine degree of accuracy required. The body pressing section was next visited. There the large number of pressed parts which make up a vehicle body are pressed out of special deep drawing steel plate. Some of the largest presses were capable of applying a pressure of 1 200 tons and cost as much as Rl85 000 each. The visitors then followed through to the assembly section where jigs are used to hold together the many pressings, which are then spot welded into body frames. The frames go to an assembly line where they are finished to the stage for painting. The continuous crawl painting assembly line carries the frames through all the stages of prime coating with zinc phosphate sprayed on in a tunnel, followed by immersion of the lower parts in a priming bath, then drying and spray painting and baking in tunnels. The body frames, after painting, join another assembly line, where the doors, upholstery and many fittings are attached. After this stage the completed bodies are lowered onto and attached to the chassis units which are largely assembled from imported parts (engines, transmission units, etc.). From the end of the line the completed cars are driven off to the trial track and then pass through a tunnel with powerful water sprays to detect leaks in the body work. The proportion of locally made parts is just on 45 per cent. An interesting aspect of the assembly organization is that, of the 140 or 160 cars completed each day there may be included some of each of the Datsun model as well as some Renault and Alfa Romeo models models which are assembled by this company. The change from one model to another several times a day does not present any difficulty to the organization. Each section of the assembly plant 'buys' the units from the preceeding section and 'sells' to the succeeding section. This means that the responsibility of each section ends when the unit is sold to the next section. The cost of repairing any faults found subsequently is charged to the section where it is found, which puts a powerful emphasis on meticulous inspections between sections to safeguard their costs. After the tour the parties assembled at the lecture hall where a lavish cold buffet luncheon was provided by the company. After luncheon Mr A. R. C. Fowler, on behalf of the Institute, thanked the Managing Director, Mr W. J. Wilson and his staff for this most interesting and well organized visit. The party then left for the Claremont-Danville tunnel. The tunnel is being driven by General Mining Federale Kontrakteurs through the Daspoort Range, Pretoria, to link the suburbs of Danville, near Iscor, and Claremont, which at present can only be reached by a nine mile detour. It is estimated that some 6000 vehicles per day will use the tunnel. Before entering the tunnel a short talk was given by Mr Ross who is in charge of operations. He called on various officials and staff of the Consulting Engineering firm, Basil Read (Pty.) Ltd., to describe the tunnel and

By P. J. Bhonde, R. D. Angal

Conventionally low carbon ferromanganese is manufactured globally by refining high carbon ferromanganese in liquid state. This process is an expensive and lengthy technique. Hence, the present work was undertaken with the objective of understanding the feasibility and kinetics of the solid state refining of ferromanganese. The process involved transformation of carbon rich carbides viz. Mn3C2, Mn7C3 into metal rich carbide i.e. Mn15C4, Mn23C6 by subjecting the alloy powder to a flowing stream of carbon dioxide. Effect of the process governing parameters such as time, temperature, particle size, pressure on the extent of decarburization was studied. Without any loss of manganese in the form of fumes or slag, it was observed that, there was substantial reduction, viz. 65 per cent in the total carbon content, by this technique. Subsequently, the process was investigated to find out the mechanism of carbon removal. Depending upon the temperature and the particle size, it was found that the rate controlling mechanism changes from chemical reaction control to product layer (ash) diffusion control. The activation energy for each of the aforesaid mechanism was computed. The values thus obtained substantiated the aforesaid mechanisms.

Jan 1, 2004

By E. Pardo-Igúzquiza, R. A. Olea

The bootstrap is a computer-intensive resampling method for estimating the uncertainty of complex statistical models. We expand on an application of the bootstrap for inferring semivariogram parameters and their uncertainty. The model fitted to the median of the bootstrap distribution of the experimental semivariogram is proposed as an estimator of the semivariogram. The proposed application is not restricted to normal data and the estimator is resistant to outliers. Improvements are more significant for data-sets with less than 100 observations, which are those for which semivariogram model inference is the most difficult. The application is illustrated by using it to characterize a synthetic random field for which the true semivariogram type and parameters are known.

Jan 1, 2015

By J. N. Van der Merwe

"A major shortcoming of the statistical back-analysis of coal pillar strength is that it relies on the asmined pillar dimensions, not taking into account time-related pillar scaling with subsequent reduction in pillar width. The paper describes an investigation where the rate of pillar scaling was applied to the pillars in the databases of failed and unfailed pillars. The reduced pillar sizes were then used in the same method of statistical back-analysis that had been used in the past.This resulted in an equation for pillar strength which predicts significantly greater pillar strength than the previous statistical analyses, which is similar to the strength which had been found earlier by direct testing of large specimens underground. It is concluded that the lower strengths found by previous statistical analyses are due to the incorrect pillar width being used and that by adjusting the pillar sizes to compensate for scaling, more credible results that correspond to direct testing are obtained.As the newly derived strength equation is time-dependent, it follows that the safety factors and probabilities of failure are likewise time-dependant. An equation to determine the probability of failure is also developed. This results in the safety factor being close to unity at a probability of failure of 50%, which is aligned to statistical expectation. IntroductionSince the Coalbrook mine disaster, caused by massive pillar collapse, there have been several attempts at analysing and defining the strength of coal pillars. It was realized in the very beginning that performing classical strength tests on coal specimens in a laboratory and then transferring those results to real coal pillars could not be successful. The scatter of results is one problem and, more seriously, there is a size effect (at least for small specimens) that made the transformation of strength results to much larger coal pillars underground all but impossible.Two main schools of thought then emerged. Some researchers preferred to perform direct strength tests on large specimens underground, while others relied on statistical back-analysis of failed and unfailed pillar cases, attempting to determine the differences in size and shape that would allow a satisfactory prediction of failure. The latter school of thought resulted in the method that was widely accepted by the South African coal mining industry, described in the landmark publication by Salamon and Munro (1967)."

Jul 1, 2019