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By A. J. H. Newell, K. Doherty

A copper-gold project has required a number of trade-off studies underpinned by test work to settle on pragmatic flowsheets and throughputs to support a pre-feasibility study that provides a compelling financial case. The primary trade-off studies were based on the mine schedule, ore type feed-grade recovery relationships, likely concentrate grades and typical marketing terms as well as the estimated capital and operating costs for a range of throughputs and mining strategies. Secondary trade-off studies were conducted for specific circuits and additional processing options. Although the details of these studies are not presented, the technical options and subsequent flowsheets are discussed. While the flowsheets will be optimised during the feasibility study stage, the basis is now fixed for the four ore types that would be mined from the copper-gold orebody. The ore types, resulting from a strong weathering profile, exhibit a wide range of copper mineralisation and gold associations, as well as gangue types. They display a range of characteristics that necessitated a nuanced approach to flowsheet development. The primary separation techniques that have been employed include gravity, classification, flotation and leaching while a range of comminution methods have been selected to suit the properties of the ore types. While technical issues are important factors in terms of maximising the quality of separations, recoveries and revenues, attention to material handling, equipment characteristics, the mine schedule, and capital and operating costs are equally important considerations for settling upon a suitable and robust flowsheet. Keywords: Flowsheet, testwork, studies, saprolite gold, native copper, chalcocite, chalcopyrite

Jan 1, 2020

By M. Le Roux, Q. P. Campbell, M. Fofana

The determination of densimetric information to predict coal washabilities is an important step in characterising the feed material, as well as the performance of operating plants. However, traditional methods like float-and-sink analysis are hazardous and time-consuming. This is especially true for finer particle size ranges, where very long settling times are required in a medium. De Beers Technologies recently developed a density analyser, known as the RhoVol, for use on diamondiferous kimberlite. Operating over size ranges from 25 mm down to 3 mm, it can determine the mass, volume, density, size and shape of all the particles in a given population and is thus able to provide information about the densimetric distribution on a single particle basis. A study was carried out to compare uncalibrated and calibrated RhoVol results to densimetric and size data obtained using traditional zinc chloride float-sink procedures, for three different coal samples in the size range 3 mm to 8 mm. The results indicate that the RhoVol can be used to provide simple, rapid and safe size-by-washability information for coal, provided proper pre-calibration is done, mainly to account for the effects of particle porosity in the density determination. Keywords: Coal washability determination, RhoVol, densimetric curve

Jan 1, 2020

By B. S. Xakalashe, I. J. Geldenhuys, M. W. Erwee, Q. G. Reynolds, R. T. Jones, S. P. Tsebe

Aspects of the production of platinum group metals by reductive smelting in direct-current arc furnace processes are investigated using a computational modelling approach. The replacement of fossil carbon as a reductant by alternative reductants such as silicon carbide, ferrosilicon, and hydrogen is desirable for reducing direct greenhouse gas emissions from such processes, but the impact of these changes on the electrical operability of the process is poorly understood. This paper presents a study of plasma arc behaviour in the context of the ConRoast® reductive smelting process for Upper Group 2 ore as well as processes for recycling of automotive catalysts, using an integrated computational modelling workflow. It was found that the freeboard gas compositions, plasma properties, and arc behaviour were all affected by the choice of reductant, particularly in carbon-free smelting using ferrosilicon or hydrogen.

Mar 6, 2026

By D. Pienaar, D. Stanton

This paper provides an overview of possible approaches for structuring the ventilation systems for mines that will become operational within the next decade. Features addressed in the paper include: aspects of airway design and layout in the absence of centralized vertical return shafts, the impact of using diesel-powered trackless equipment in conjunction with conveyor belts in the development and production phases of the project, and the need to balance increasing electrical power costs against the requirement for reduced capital expenditure. The paper provides brief descriptions of the strategies employed in real-life situations and presents an overview of various operational parameters affecting the design of ventilation systems that will be used as ?platforms? for much deeper mines in the future.

Jan 1, 2006

By T. J. Otto, G. C. Lindeque

Productivity is improved by increasing the ratio of output to input. In an operating open-pit mine, improving the productivity of heavy mining equipment (HME) enables the unit cost of production to be reduced. To optimize HME productivity, the Kolomela open-pit iron ore mine transitioned to an enhanced short-term mine planning (STMP) process that supports the application of a manufacturing-type operating model. At the core of the enhanced STMP process is a focus on integration across the open-pit mining value chain. The interdependencies between mining activities are highlighted and emphasized, thus ensuring that mining activities are synchronized. The improvements related to HME productivity were monitored from 2019 to 2020. The utilization of mining area in the Leeuwfontein pit improved from 71% to 90%, and the blasting frequency reduced by 14% while the average blast size increased by 17%. The distance travelled during shovel relocations between mining phases reduced by 16%, and the lost time associated with drills relocating reduced by 53%. These productivity improvements resulted in an 11% increase in the loading rate of the main waste shovel at Kolomela from 0.9 Mt/month in 2019 to 1.0 Mt/month in 2020. The enhanced STMP process can be adapted to other open-pit mining operations.

Nov 1, 2021

By H. Askari-Nasab, S. Upadhyay, A. Moradi-Afrapoli

Material handling in surface mines accounts for around 50% of the operational cost. Optimum truck dispatching plays a critical role in the reduction of this operational cost in truck and shovel surface mines. Researchers in this field have presented several mathematical models to solve the truck dispatching problem optimally. However, a critical survey of the literature has shown that three significant drawbacks exist in the available truck dispatching models. The published models underestimate the importance of the interaction between truck fleet, shovel fleet, and the processing plants. They also disregard goals set by strategic-level plans. Moreover, none of the available models account for the uncertainty associated with the input parameters. In this paper we present a new truck dispatching model that covers all of these drawbacks, using a fuzzy linear programming method. The performance of the developed model was evaluated through implementatin in an active surface mining operation. The results show a significant improvement in production and fleet utilization.

Sep 1, 2021

By B. G. Meyburgh

E. H. D. Carman: The results achieved at Buffelsfontein Gold Mining Company Limited are very encouraging and it seems certain that as far as the conventional uranium recovery process is concerned solvent extraction must entirely supplant the old resin ion exchange process. The operational costs given by Mr Meyburgh indicate that the chief cost items in solvent extraction are reagents. In other words 38.4 per cent of the operational cost at Buffelsfontein is due to the replacement of the organics lost from the plant. It is reported from a wide field of experience that loss, particularly of amine, is a direct function both of the quantity and nature of finely divided suspended solids in the pregnant solution and the extent to which the design of the mixers causes the formation of secondary dispersions which do not easily separate in the settler. There is in addition the unavoidable loss of amine due to its solubility in the aqueous solution which is thought to be about 4 p.p.m. In order to minimise solvent losses therefore, efficient clarification at the head of the solvent extraction plant would appear to be a most important requirement. For this reason the newly erected plant at West Driefontein Gold Mining Company Limited has two Funda Pressure Filters each with a filtering area of 540 sq. ft. which are together designed to handle up to 440 g.p.m. of filtrate. This plant has not yet been commissioned but preliminary testing indicates that suspended solids in the sub micron size range which do not settle even on protracted standing of the solution, will rapidly blind the clarifiers. This should not affect solution clarity but frequent backwashing adds to the cost of precoating. The difficulty was countered in the laboratory with continuous additions of filter aid in addition to the precoat but, as Table 11shows, cost of filter aid is high and its use will have to be optimized against organic losses due to less efficient clarification. This will need much careful observation over a relatively long period of time. Costs shown in Table 11 are based on Mr Meyburgh's figures adjusted to probable conditions at West Driefontein Gold Mining Company Limited. The assumption based on small scale testing is that it will cost 5.2c/ton in filter aid to clarify filtrate to a level of about 5 p.p.m. of suspended solids, in order to restrict the amine loss to 10 p.p.m. which is likely to be equivalent to an entrained organic loss worth approximately only 2.6 cents per ton. Of course poor clarification as mentioned earlier is only one of two or even more causes of organic losses and it seems obvious on the above basis that the operation and economics of pressure clarification will need close investigation. A second important consideration at West Driefontein has been the design of the pump-mixers which must perform the dual function of phase mixing and providing the necessary hydraulic gradient for counter current flow of the two phases. The arrangement is shown in Fig. 1.

Jan 10, 1970

By M. Onifade, B. Genc, P. O. Akinseye, M. Fourie, K. O. Said

Coal is mined by both surface and underground methods and its extraction is normally characterized by numerous hazards that can lead to catastrophic accidents, which result in devastating effects such as injuries or fatalities, damage to mining assets, and destruction of mineral resources. These hazards exist due to the ability of coal to support combustion and its association with toxic, flammable, and explosive gases. Underground coal mining entails higher safety risks than opencast coal mining, chiefly because of issues relating to mine ventilation and mine collapse. Furthermore, coal mine collapses mostly occur due to crumbling of mining supports, especially in room and pillar mining systems. To avoid such adverse occurrences, safety management systems need to be in place. This study reviews the various technological safety systems and principles that are used for safe-rescue and self-escape of miners in underground coal fires, particularly in South Africa, using data obtained from Mines Rescue Services in Carltonville, South Africa. The outcome of the review shows that practising safety culture has been given priority across many South African underground coal mines through setting up safety management systems and encouraging workers to stay committed to safety principles.

May 2, 2022

By M. Getz, G. Asbjörnsson, M. Evertsson, E. Clausen

The mining and minerals processing industry is gradually being digitalised to improve efficiency and reduce waste. One aspect of this transition is to ensure that relevant process-data in sufficient quality and quantity is given to the operator in the right format and at the right time to improve decision-making. Augmented reality (AR) can serve as a potential ICT-based support tool for human operators to achieve this goal. With AR, virtual information is combined with the real world in real-time. Therefore, AR technology has the potential to fulfil the need for improved data visualisation in Industry 4.0. This article is the result of a collaborative effort of Chalmers University of Technology and RWTH Aachen University to identify selected state-of-the-art applications of AR that are currently being applied in the mining and minerals industry or selected related industries. This paper aims to show opportunities for the application of AR in the mining and mineral processing industry with selected conceptual applications. This paper concludes with several requirements identified as necessary to implement the conceptual applications of AR in the mining and minerals industry. Keywords: Augmented reality, mining, mineral processing

Jan 1, 2020

The Annual General Meeting of the South African Institute of Mining and Metallurgy was held in Kelvin House, Johannesburg, on Wednesday, 27th August, 1975. Professor R. P. Plewman (President) was in the Chair. There were present 45 Fellows, 37 Members, 8 Graduates, 3 Associates, 4 Students, and 45 Visitors, making a total of 142. The President declared the Meeting open at 16h00. OBITUARIES The President: Ladies and gentlemen, it is my sad duty to announce the death of the following members of the Institute : M. Barcza, an Honorary Life Fellow and Past President of the Institute; J. A. Boyd, F. E. Keep, and J. H. Taylor, Life Fellows ; I. D. B. Corner, C. O'G. Deane, R. E. Gilmour, A. C. Hofmeyr, M. W. Howell, T. J. Robin, and F. S. Steinhobel, Fellows; J. J. Frankel, Member; and T. J. Higgs, Associate. As a mark of respect to the memory of the deceased and in sympathy with the bereaved, I ask you to rise and observe a few moments' silence. MINUTES The President: May we confirm the minutes of the General Meeting held on March 12th 1975 and published in the June issue of the Journal? Agreed. WELCOME The President: It is now my very great pleasure to welcome the many members of our Institute and all the distinguished guests who have honoured us with their presence this afternoon. In particular, I would like to welcome our Honorary President, Mr R. S. Lawrence, President of the Chamber of Mines, and also our Honorary Vice-President, Mr T. L. Gibbs, the Government Mining Engineer. Ons is ook besonder vereer dat dr. Naude, die Wetenskaplike Raad-gewer aan die Eerste Minister, en mnr. C. A. J. Borman, Direkteur van die Witwatersrandse Kollege vir Gevorderde Tegniese Onderwys, hier aanwesig is om die vergadering by to woon. We are also honoured by the presence of some 19 Presidents, Vice-Presidents, and Chairmen of our sister scientific and technical organizations. I would particularly like to welcome Mr Gericke of the South African Council for Professional Engineers, Professor Pretorius of the A.S. & T.S., and Dr Lloyd of F.S.P.E. And then, also the Presidents of the Institute of Welding, Professor Robinson; of the Electrical Engineers, Dr Troost ; of the Certificated Mechanical and Electrical Engineers, Mr Gibbs; of the Geological Society, Professor Maske; of the Land Surveyors of the Transvaal, Mr Course ; of the Assayers and Analysts, Mr Williams; of the Mine Ventilation Society, Mr Martinson; of the Chemical Institute, Mr Goodman; of the Association of Mine Managers, Mr Pretorius ; of the Institute of Foundrymen, Mr Attenborough; of the Production Engineers, Mr Duggan ; and of S.A.F.U.E.S., Mr Avalle. Then, the Chairman of the Council of the Institute of Metallurgists, Mr Snow; the Vice-President of the Town and Regional Planning, Mr Reinecke; the Vice-President of the Association of Consulting Engineers, Mr O'Kell; and Mr Cronje, who is representing E.A.S.A. Finally, the Chairman of the Southern Transvaal Section of the Chemical Institute, Mr Bloom ; the Chairman of the Witbank-Middelburg Branch of our own Institute, Mr Hosking; and the Secretary-Treasurer of our O.F.S. Branch, Mr Bird. We also have with us Mr Trueman; the Deputy Manager of Kelvin House, Mr Mrost ; our Honorary Editor, Dr Glen; Mr Walford; and also some representatives of the Press. Finally, it gives me great pleasure to welcome those who will receive Honorary Life Fellowships tonight, and also the winners of our student prizes. MEMBERSHIP The President: Ladies and gentlemen, I have pleasure in announcing the names of the following candidates, which have been published in accordance with By-Law 5.2.5., and Council has elected them to membership in the following grades: Fellows: R. G. Boswell, R. W. Chadwick, D. R. Hardman, J. A. Holmes, T. J. B. Jones, and R. P. King. Members : M. A. Bridgeford, C. F. Bonney, H. E. Bartlett, L. G. Floyd, A. K. Haines, D. Hatfield, C. G. Heymann, M. J. Howes, J. B. See, E. van Greunen, and S. P. Swanepoel. Associate Members : J. Coetsee and R. P. G. Steyn. Graduates: J. J. de Villiers and J. C. King. Associates: B. J. Bucher, P. A. Combrinck, W. J. N. Gelderblom, L. S. Halasz, J. van Wyk, C. P. Visser, and A. Veress. Students: D. J. Claasens, P. C. Crous, D. H. Murchison, P. A. Rossouw, and J. P. L. Schultz. Company Affiliates: Airco Engineering (Proprietary) Limited and Deelkraal Gold Mining Company Limited. There have also been some transfers: Member to Fellow: J. B. Nangle. Graduate to Member: E. E. Eichenbergen, M. J. Hillbeck, L. A. Melis, P. J. Venter, and R. O. Wellman. Associate to Associate Member: B. M. Williams. I welcome the newly elected members to the Institute, and I congratulate those who have been transferred to a higher grade.

Jan 10, 1975

By S. Hlajoane, L. S. Mokhahlane

The demand for rare earth elements has increased around the world due to their application in a variety of technological advancements. Previous studies have evaluated the potential of the rare earth elements and yttrium (REY) hosted within the Permian coal deposits of the main Karoo Basin (MKB) in Southern Africa. However, not a lot of scientific research has gone into the Triassic coal deposits. The Triassic coals in South Africa were the first coals to be exploited for their thermal use in the 1880s, but the discovery of the higher rank and more abundant Ecca coal deposits led to the Triassic coals remaining largely unexplored. The demand for rare earth elements has sparked interest in these coal deposits as potential sources for valuable minerals. Late Triassic coal deposits in Lesotho have previously not been well documented and these low-rank coals can be a potential source of rare earth elements. This study aims to characterize and evaluate the potential of REY in the Taung coal deposit, southwest of Lesotho. Coal and associated argillaceous samples from the Taung coal deposit were analyzed using microscopic petrography for coal characterization and an inductively coupled plasma mass spectrometry (ICP-MS) to determine the amount of rare earth elements. Taung coal is classified as middle medium rank D bituminous coal. The total REY content in Taung coal and its associated rocks range from 162.9 ppm to 855.1 ppm, which is significantly higher than the upper continental crustal (UCC) average. The average critical REY concentration of samples from the Taung coal deposit is 189.4 ppm, which is three times higher than that of the Chinese Bayan Obo deposit. Samples classified as very promising and promising because of their outlook coefficients, are found to contain up to 77% of critical REY. It is envisioned that the area could be a prime deposit for these REY.

Nov 6, 2024

By K. A. du Preez, P. J. van Staden, M. van Rooyen

Mine-impacted water, including acid mine drainage (AMD), is a global problem. While precipitation of dissolved metals and neutralization of acidity from mine-impacted water is accomplished relatively easily with lime addition, removal of sulphate to permissible discharge limits is challenging. This paper presents a high-level comparison of four sulphate removal technologies, namely reverse osmosis, ettringite precipitation, barium carbonate addition, and biological sulphate reduction. Primarily operating costs, based on reagent and utility consumptions, are compared. Each process is shown to be subject to a unique set of constraints which might favour one over another for a specific combination of location and AMD composition. Access to and cost of reagents would be a key cost component to any of the processes studied. The total cost calculated for each process also depends on the type of effluents that are allowed to be discharged.

Oct 1, 2021

By K. Thambi

The court in Baleni v Minister of Mineral Resources [2019] 2 SA 453 GP and [2020] 4 All SA 374 (GP), deliberated on the protection of rights of a community holding informal land tenure under Customary Law. The contention related to the necessary level of consent needed to acquire a mining right over such land. Moreover, whether consultations with such communities (Section 23, Mineral and Petroleum Resources Development Act 28 of 2002 (MPRDA) or consent (Section 2, Interim Protection of Informal Land Rights Act, No. 31 of 1996 (IPILRA)) was required to acquire such right. The case has a significant bearing on the granting of mining rights in South Africa, and the discretion of the Minister of Mineral Resources (the Minister) in this regard. However, the objectives of the MPRDA and IPILRA do not dovetail, therefore consultation and consent are not mutually exclusive (Tlale, 2020). This note argues that, despite the resounding victory of this case, the peripheral basis surrounding the decision and the various levels of engagement require serious deliberation. Equally, the degree of reliance on the IPILRA requires clarity to avoid aborting the fundamental objectives of the MPRDA. This paper provides considerations and recommendations that may reduce or eliminate the tensions between the statutory and socio-economic rights in the application of the two statutes.

Sep 1, 2022

By W. H. Holtzhausen

The purpose of this project was to compare two underground, batch coal haulers ? battery haulers and shuttle cars ? in order to determine the more viable machine to implement. The specific standards for battery haulers were investigated and compared to the requirements of shuttle cars in order to identify the unnecessary expenses related to the legal requirements that are attached to the machines. Costs such as running costs, capital costs, and maintenance costs were researched and compared over a typical life of machine. Average production rates and breakdown times were obtained and used to determine which machine would be more reliable in achieving the required annual production.

Jan 1, 2014

By C. Musingwini

The South African mining industry continues to be a major source of employment at a time when at least 25 per cent of the working age population is unemployed. At the same time the industry faces a skills shortage in many of the disciplines necessary for its future health. The University of the Witwatersrand, University of Pretoria, University of Johannesburg, and University of South Africa have historically produced mining graduates for the South African industry, with any shortfall being met by the recruitment of overseas graduates. More recently the global shortage of engineers and other mining industry professionals has seen a reversal of this trend and a very significant emigration of well-educated and highly skilled personnel. The traditional career path for mining graduates is in production and mine management. However, there is the parallel and possibly more pressing need for specialized skills in such fields as ventilation, rock engineering, mine planning, mineral resource evaluation, and mineral asset valuation. It is in these essential areas that chronic shortages continue to hamper the development of the industry and may well frustrate its ambitions to be safe, healthy, and profitable into the future. The permeability of skills across sectorial boundaries within the mining industry requires that skills shortages in the platinum sector are not looked at in isolation, but within the context of the entire industry. This paper reviews the efforts being made by the universities at both undergraduate and postgraduate levels to meet the needs of the South African mining industry, in terms of the required numbers and the range of specialized skills.

Jan 1, 2012

By G. P. Dyke

With the removal of the majority of the shallow mineral reserves there has been an increase in the mining depths in the South African mining industry. This has, in turn, changed the industry?s and stakeholders? perceptions of risk associated with mining-induced instability. In recent years the increased mining depth, particularly in open pits, has led to an increase in pit slope failures, which has highlighted the need for appropriate and effective pit slope management programmes. Such a programme comprises many facets, including mine hazard plans, regular slope inspections, cleaning of interim and final pit faces, blasting practices, histories of failures, pit depressurization, stormwater control and evacuation procedures. However, it is arguably in the field of slope monitoring that the most significant strides have been made in terms of new technologies and best practice in open pit mining geotechnics, with the introduction of technologies such as laser scanners and slope stability radar. This paper seeks to illustrate the operational benefits associated with the implementation of new technologies into open pit mining, using AngloGold Ashanti?s Geita Gold Mine in Tanzania as an example.

Jan 1, 2009

By P. Lenegan, R. Masethe, R. I. L. Ferreira

Underground mining in high rock-stress environments can induce unanticipated dynamic rockmass deformation, posing a serious risk to the workforce. Data collected by seismic networks are imperative for the design-as-you-mine process. Often an inappropriate assessment of the seismic hazard is done when unnecessary data are included in analytical techniques, particularly short-term time frames. Depending on the methodology or application of data analysis and interpretation, some of the information may not be relevant and even detract from the objective. By using the spatial event clusters associated with active workplaces to define the shape and size of the polygons for data selection for subsequent analysis, a problematic subjective component can be eliminated. The mining of tabular reefs in South Africa, be they gold- or platinum group metals, is very extensive, and underground workplaces are often widespread. Production stoppages are very costly, especially for marginal mines, so there is just cause not to evacuate an entire operation’s workforce following the occurrence of a large mining-induced seismic event. A rationale based on the damaging peak particle velocities (PPV) of the past seismicity can exclude the unaffected underground personnel and allow a quick orderly withdrawal where required. Micro-deformation may precede rockbursting, which can occur on-shift close to the workface. A mine-wide array of geophones suitable for the accurate location and analysis of seismicity may not be able to detect these higher-frequency emissions. Inexpensive but fit-for-purpose accelerometers, providing real-time, continuous measurement of acoustic rockmass deformation near the workplace, integrated through underground and surface communications networks, are shown to record ‘rock-talk’, clearly distinguishable from the instrument background noise, which can be in the order of hours leading up to an imminent damaging seismic event.

Jan 12, 2025

By W. R. Matizamhuka

"The consolidation of nano-sized composite materials presents a challenge using conventional hot pressing methods. Spark plasma sintering (SPS) technology has shown great promise in the successful sintering of nanoreinforced composite materials. This qualitative review seeks to impart knowledge gathered, and progress made over the years on the consolidation of nanocomposite materials using SPS technology. The review is aimed at introducing this technology to the South African science and engineering community. Emphasis is on improving the mechanical properties of structural ceramic nanocomposite materials, which over the years have shown great promise in a wide range of applications, including transport, energy, mining, and the environment. Although success has been achieved within the laboratory for research purposes, there are still great opportunities to commercialize the technology for the production of larger components with more complex shapes.IntroductionSince the pioneering work of Niihara and Nakahira (1991) over a decade ago there have been extensive attempts to harness the potential of nanostructural metals, ceramics, and composites in a number of applications (Niihara and Nakahira, 1991; Selaho et al., 1997; Sekino and Niihara, 1995; Khalil, 2012; Aalund, 2008). It is generally realized that reducing the grain size of materials to nanoscale offers a significant improvement in properties. Attempts to synthesize nanostructured compacts by conventional sintering methods have not succeeded owing to the uncontrollable high rates of grain growth driven by long dwelling times at the sintering temperatures and large powder surface areas (Sergueeva et al., 2009; Gua, Khora, and Chieng, 2004; Tang et al., 2009). Following the development of spark plasma sintering (SPS) technology, it is now possible to process nanocrystalline materials with controlled grain growth. SPS, also referred to as the field-assisted sintering technique (FAST) or pulsed electric current sintering (PECS), was developed with the aim of improving on the well-established hot pressing (HP) technology (Kessel and Hennicke, 2007;"

Jan 1, 2016

By J. van Zyl, K. B. Le Bron, L. J. Gardner

Pillar design is a crucial aspect of underground mining engineering, as it directly impacts the safety, stability, and overall effectiveness of mining operations. In this paper we present a method to calculate pillar stability based on the strain criterion and pillar load inversion concept, which complements the empirical pillar strength formulae. Those formulae do not account for certain parameters that can affect the stability of the pillars, e.g. weak layers, changes in stress orientations due to mining, orebody dip, mining layout complexity, and the influence of regional stabilizing pillars. The approach presented here is not intended to replace the empirical method; rather, we suggest using it as the initial step in the pillar design process. This should be followed by iterative numerical modelling to study pillar behaviour, define pillar stability, and optimize the pillar design by considering site-specific and representative rock mass properties and criteria.

Jun 10, 2024

[Consider a square block W in an ore body S2, to be valued from one centre sample w, and one corner sample w2 (Fig. 9.1). The sample set is ws = Iw,;w21. We can estimate the block average µw by the average of the sample values x, and x2: µw = 'z (x, + xz). (9.1) The error made is measured by the estimation variance: o' (ws to W) = 2 - (ws; W) - - (ws;ws) - - (W; W). (9.2) However, we know that the centre sample w, gives more information about the block value than the corner sample w2. In the example studied in § 8.4, where w, and w2 were considered to be points, we found that of (w, to W) was nearly one third smaller than o2E (w2 to W), therefore when estimating W one should give more weight to w, than to w2. In general, when evaluating a block W from a set of n samples ws, where WS = l w;w2; ... wn1, a better estimator of µw can be obtained if we give different weights to the sample values, depending on the size and the positions of the samples. Some desirable properties of such an estimator µw are: ? It should be a linear function of the sample values xi: n µw = bi xi (9.3) =t where bi = weight given to sample x . ? It should be unbiased, i.e. its expected value should be equal to the true block value: E [µw - µw] = 0. (9.4) ? The mean squared error of estimation of µw should be a minimum E [(µw - µw)2] = a minimum. (9.5) The estimator which satisfies these properties is a minimum variance, linear and unbiased estimator, and is known as the kriging estimator. The corresponding error of estimation is the kriging error. This estimator is also known as the BLUE (for Best Linear Unbiased Estimator) estimator. This was named by Matheron in acknowledgement of the early work of Krige's in the optimization of the evaluation of the South African gold mines. The following notations will be used: µK kriging estimator. o2k = o2K (w,, to W) kriging error.]

Jan 1, 1978