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By C. Musingwini, A. S. Nhleko, M. J. Mahase

"In an environment like the mining industry, which is characterized by different stakeholders with multiple objectives, multi-criteria decision analysis (MCDA) is a useful approach for optimal decision-making. The application of MCDA techniques in the mining industry has predominantly been in mine planning and related problems, although no comprehensive survey has previously been undertaken to establish the application trends. A survey of the use of MCDA techniques was therefore conducted using case studies from the literature. It was noted that often two or more methods are applied to the same problem in order to increase confidence in the solution derived. As the number of criteria and alternatives increases, some methods become inefficient. A combination of the analytic hierarchy process (AHP) method with other MCDA techniques was the most frequently used approach, indicating the efficiency of the AHP method, especially when evaluating problems with more criteria and fewer alternatives. A combination of fuzzy theory with AHP or other methods incorporates uncertainty. The findings from the survey will benefit users applying MCDA techniques to solve mine planning and related problems.IntroductionA country’s natural resources serve the needs of different groups of people within the country. These different groups are collectively known as stakeholders (Herath and Prato, 2006). Stakeholders have different needs, preferences, and expectations, which describe and define the criteria to be considered in decision-making. The options available as solutions describe the alternatives in decisionmaking theory. The criteria and alternatives have to be evaluated simultaneously when making decisions, and this is when multicriteria decision analysis (MCDA) techniques become invaluable (Herath and Prato, 2006) because the human mind is considered to be limited when solving complex and intangible problems with several criteria and alternatives (Saaty, 2007). MCDA techniques belong to a broad group of techniques called multi-criteria decision-making (MCDM) techniques. The other group of techniques within MCDM comprises the multi-objective decision-making (MODM) techniques. MODM techniques are generally used to solve problems with an infinite number of alternatives, while MCDA techniques are generally used to solve problems with a finite number of alternatives (Musingwini, 2010)."

Jan 1, 2016

The successful commissioning of the Cerro Verde project in Peru at the end of 2006 marked the culmination of the efforts of many in the industry over many years to have high pressure grinding roll technology recognized and accepted as a legitimate alternative to the conventional approach to large-scale hard rock comminution circuit design. Other hard-rock projects that have recently adopted HPGR include Freeport (Indonesia), Boddington (Australia) and Amplats Potgietersrus (South Africa). With the increasing acceptance of this technology, the need for technical presentations and articles exhorting the industry to adapt has diminished somewhat, and it is considered appropriate now to shift the emphasis to the provision of information for those considering embracing change. This article endeavours to answer frequently asked questions on the subject of high pressure grinding roll technology, with particular reference to its application in the hard rock minerals processing sector.

Jan 1, 2010

By A. M. Venter

"SynopsisThe availability of advanced characterization techniques is integral to the development of advanced materials, not only during development phases, but in the manufactured components as well. At Necsa, two modern neutron diffractometers equipped with in-situ sample environments, as well as complementary X-ray diffraction instruments, are now available as User Facilities within the National System of Innovation in support of the South African research and industrial communities. Neutrons and X-rays, owing to their different interaction mechanisms with matter, offer complementary techniques for probing crystalline materials. Both techniques enable nondestructive investigation of phenomena such as chemical phase composition, residual stress, and texture (preferred crystallite orientation). More specifically, the superior penetration capabilities of thermal neutrons into most materials allows for the analysis of bulk or localized depth-resolved properties in a wide variety of materials and components. Materials that can be investigated include metals, alloys, composites, ceramics, and coated systems. In particular, depth-resolved analyses using neutron diffraction complements surface investigations using laboratory X-rays in many scientific and engineering topics. The diffraction techniques can add significant downstream value to the anticipated nuclear industry development activities.IntroductionMaterials characterization is central in understanding the relationship between the structure, properties, and performance in order to engineer materials that fit the performance criteria for specific applications. This is conveniently represented in the form of a tetrahedron, generally known as the material science paradigm (Figure 1).The availability of advanced characterization techniques is integral to the development of advanced metals, not only during development phases, but in the form of manufactured components. At Necsa (South African Nuclear Energy Corporation), modern X-ray and neutron diffraction instruments are now accessible to the South African research and industrial communities. These facilities enable nondestructive investigations of materials and components that could add significant downstream value to the anticipated nuclear industry development activities."

Jan 1, 2015

By G. van Aswegen, J. D. Bosman

Gold bearing deposits in the Witwatersrand consist predominantly of narrow tabular conglomerates with quartzite host rock. Extensive mining of these deposits at depth results in significant stresses being induced in the periphery of the tabular excavations. Where remnant pillars are created excessive stresses have resulted in the dynamic failure of the abutments. At the Hartebeestfontein Mine four brittle shear zones have recently been exposed and investigated. For most part, they represent abutment failure into the weaker hangingwall strata, striking parallel to the abutment, dipping towards the stope, with a sense of displacement consistent with closure of the stope from above. These shear zones are similar to those described in various publications by Ortlepp2: they are essentially brittle shear zones characterised by the presence of very finely comminuted ‘rock flour’ on an obviously freshly sheared surface. The angle between the shear zone wall and extension fractures indicate the sense of shear and the intersection of the extension fractures with the shear zone walls define a strong lineation normal to the direction of slip. It is suggested that these structures are referred to as ‘mining induced dynamic brittle shears’. Les gisements d’or du Witwatersrand consistent principalement de conglomérats tabulaires peu épais contenus dans une quartzite mère. Une exploitation poussée de ces gisements en profondeur a pour résultat l’apparition d’importantes contraintes induites à la périphérie des excavations tabulaires. Là où des piliers restants sont créés, des contraintes excessives ont eu pour résultat une rupture dynamique des appuis. Dans la Mine d’Hartebeestfontein, quatre zones fragiles de cisaillement ont été récemment exposées et étudiées. Dans la plupart des cas, elles représentent une rupture des appuis dans les strates moins solides de la paroi suspendue, orientée parallèlement à l’appui, inclinée en direction du chantier d’abattage avec une direction de mouvement consistante avec l’affaissement du toit de la galerie d’abattage. Ces zones de cisaillement sont similaires à celles décrites par Ortlepp2 dans diverses publications: Ce sont essentiellement des zones cisaillement fragiles caractérisées par la présence de « farine de roche » très finement réduite sur une surface évidemment fraîchement cisaillée. L’angle entre la paroi de la zone de cisaillement et les fractures de tension indiquent le sens du cisaillement et l’intersection des fractures de tension avec les parois de la zone de cisaillement définit une forte délinéation perpendiculaire à la direction du glissement. Il est suggéré que l’on se réfère à de telles structures comme des « cisaillements dynamiques fragiles induits par l‘exploitation ». Goldablagerungen im Witwatersrand bestehen überwiegend aus schmalen tabularen Konglomeraten mit Quarzitwirtgestein. Der umfangreiche Abbau dieser Ablagerungen in der Tiefe resultiert in signifikanten Drücken, die auf die Peripherie der tabularen Aushöhlungen wirken. Wo Restpfeiler hergestellt wurden, resultierten exzessive Drücke im dynamischen Versagen der Auflager. In der Hartebeestfontein Grube wurden kürzlich vier spröde Scherzonen freigelegt und untersucht. Zum größten Teil representieren sie Auflagerversagen im Stratum der schwächeren Stollenfirste, parallel zum Auflager verlaufend, in Richtung Abbaustelle abfallend, mit einem gewissen Grad an Verschiebung konsistent mit der Schliessung der Strosse von oben. Diese Scherzonen sind jenen ähnlich, die in den verschiedenen Publikationen von Ortlepp2 beschrieben werden: sie sind im Wesentlichen spröde Scherzonen, charakterisiert durch das Vorhandensein des sehr fein pulverisierten „Gesteinsmehls“ auf einer offensichtlich frisch abgescherten Oberfläche. Der Winkel zwischen der Scherzonenwand und den Bruchverlängerungen deutet die Richtung der Scherung an und die Kreuzung der Bruchverlängerungen mit der Abscherzone grenzt sich gegen eine starke Lineation normal zur Richtung der Lehne ab. Es wird vorgeschlagen, daß diese Strukturen als `vom Abbau verursachte dynamisch spröde Scherungen’ bezeichnet werden.

Jan 1, 2003

By P. T. Slatter

The role of viscometers for rheological characterization in the hydraulic transport of solids is discussed, and rheological models and phenomena pertinent to the hydraulic transport of backfill material are reviewed. The two main branches of viscometry (rotational and tube) for the measurement of mining slimes rheology are compared. The effects of solids concentration, particle size and chemical additives and the practical application of rheology in backfill system design are presented.

Jan 1, 1988

By M. Nakamura, T. Akamatsu

Embankment dams are often constructed on soft rock foundations in Japan, so it is important to precisely predict deformation of the foundations due to fill placement at the design stage. In order to accurately evaluate the settlement and the strain of the rock foundation surface during construction, the influence of the scattering of the deformability of foundations on the deformation behaviour should be investigated. In this paper, a method of evaluating the settlement and the strain of the rock foundation surface during construction was studied with stochastic deformation analysis considering the scattering of the deformability of the dam foundation. Based on the analytical results, a dam foundation design using the deterministic method considering the scattering of its deformability was discussed. Da in Japan Uferdämme of auf weichen Felsfundamenten gebaut werden, ist es wichtig, die Verformung der Fundamente auf Grund der Platzierung der Aufschüttungen bereits in der Planungsphase genau vorherzusagen. Im Zusammenhang mit einer genauen Beurteilung der Senkung sowie der Belastung der Felsfundamentoberfläche während der Bauarbeiten sollte auch der Einfluss der Streuung der Verformbarkeit der Fundamente auf das Verformverhalten untersucht werden. In der vorliegenden Studie wurde die Bewertungsmethode zur der Senkung sowie der Belastung der Felsfundamentoberfläche während der Bauarbeiten mit Hilfe von Wahrscheinlichkeitsanalysen der Verformung unter besonderer Berücksichtigung der Streuung der Verformbarkeit der Dammfundamente untersucht. An Hand dieser analystischen Ergebnisse wurde das Design der Dammfundamente dann enthusiastisch mittels deterministischer Methoden hinsichtlich der Streuung der Verformbarkeit diskutiert. Comme les barrages en remblai sont souvent construits sur des fondations rocheuses tendres au Japon, il est essentiel de prévoir précisément les déformations des fondations causées par la mise en place du remblayage durant la phase de conception. Afin d’évaluer avec exactitude le tassement et la déformation de la surface du rocher de fondation durant la construction, l’effet de la dispersion de la déformabilité des fondations sur le comportement de déformation doit être étudié. Dans cette étude, l’auteur a étudié la méthode d’évaluation du tassement et de la déformation de la surface du rocher de fondation durant la construction en procédant à une analyse aléatoire/stochastique de la déformation et en prenant en considération la dispersion de la déformation des fondations du barrage. En se basant sur les résultats de l’analyse, la conception des fondations de barrage avec la méthode déterministe considérant la dispersion de sa déformabilité a été activement discutée.

Jan 1, 2003

By A. Madowe

This paper discusses the mine planning process for Letseng diamond mine in the Kingdom of Lesotho, in conjunction with the various software packages used during the process. The major pillars of the long-term mine planning process at Letseng are pit optimization followed by pit design and scheduling. Letseng uses Gemcom Whittle and GEMS for pit optimization and design and Runge XPAC for scheduling. The output of the mine planning process results in the generation of published mineral reserves and provides input into the Letseng overall business plan. The process of defining the key inputs for the entire mine planning process is discussed, which covers: ? Pit optimization ? Slope design as an input ? Diamond price inputs ? Operating and capital cost inputs ? Haul road design ? Generation of pit shells ? Selection of an optimum pit shell and interim cutbacks using operational scenarios ? Sensitivity analysis on the selected optimum pit shell. ? Pit design ? Slope design criteria in the detailed design ? Split shell vs concentric pit design ? Practical mining widths to determine cutback design ? Ramp design ? Pit design process in the GEMS software package. ? Detailed scheduling ? Development of scheduling scenarios in the XPAC software package ? Planning through mining production bottlenecks. ? Company-level NPV model ? Comparing scenarios and input of the different schedule scenarios into the company NPV model. Keywords pit optimisation, mine planning, pit shell, recovery, dilution, revenue factor, pit design, split shell, sensitivity analysis, scheduling, production bottleneck, NPV, discounted cashflow.

Jul 1, 2013

By A. Holder

A major mud push occurred on the 870 m production level, scraper drift block cave at Dutoitspan diamond mine in November 2011, during which it is estimated that more than 4 400 m3 of mud engulfed the west cave. The production level was successfully evacuated during the mud push with no loss of life or injury to personnel, thanks largely to mine employees being well trained in and adhering to on-mine mud rush evacuation procedures. All access to the west cave was lost as a result of the mud push. Clean-up operations are currently under way to regain access to the production level, to establish the extent of damage to scraper drifts and equipment, and to evaluate what remedial works may be required to resume production. The magnitude of the Dutoitspan mud push necessitated a detailed investigation into the key contributing factors leading up to the incident, which are discussed in this paper. Mud rush mitigation measures in place on scraper drift block caving operations at Dutoitspan, Bultfontein, and Wesselton diamond mines in the Kimberley area are critically reviewed. Recommendations are furthermore made for enhanced mitigation based on mud rush risk profiles derived for different production areas in these old scraper drift block caves. Keywords mud push, mud rush, scraper drift, block cave, mitigation factors, risk profiles, risk management structure.

Jul 1, 2013

The proper understanding of the functioning of ground support under dynamic loading and the current approaches to designing of dynamic support are plagued by a great deal of uncertainty and lack of knowledge. This applies equally to the understanding of the support capacity as well as the demand placed onto the support due to dynamic loading. This lack of understanding currently leads to a case of design indeterminacy. This paper does not aim to solve this problem of design indeterminacy but to explore some of the issues that need consideration to obtain a better understanding of the dynamic demand on ground support systems. Keywords ground support, dynamic loading.

Dec 1, 2013

By J. D. Austin

Currency fluctuations affect the rand revenues of all exports of mineral commodities, as well as influencing their price on local markets. Of the more than 50 mineral commodities produced by South Africa, about 75 per cent derive 40 to 100 per cent of their revenues from exports. . Although supply and demand are largely beyond its control, management can maximize its revenues despite fluctuating overseas prices and exchange rates by using the right market at the right time. Management can operate in the futures markets, which involve a specific commitment to deliver a specific quantity of a standardized commodity at a set time in the future and at a price that is determined on a futures exchange in open auction; or management can use the options market, in which a producer can insure against the risk of a falling price by taking out a put-option, which gives the holder the right (but not the obligation) to sell the commodity at a stated price at an agreed time in the future. In the forward markets, management has three available tools; forward currency transactions, trading of currency options, and money market hedges. Revenues, currencies of exchange earnings, purchasing power of the rand, and world price trends are shown in over 40 diagrams and tables for the main mineral commodities produced in South Africa.

Jan 1, 1984

By H. Mulder, M. C. Bekker

The objective of this paper is to describe the research followed in creating a generalized, readiness assessment tool for mining projects. We start by highlighting the need for the assessment tool and then progress towards explaining the methodology followed during the study. The selection and finalization of the list of elements, sections, and categories that make up the unweighted values are described, followed by a summary of the weighting process applied. The outcome of this process is a weighted readiness assessment tool for mining project studies. The main benefits of the tool are that it will guide decision-makers and project managers through the definition phases of the project and improve the likelihood of project success.

Jul 2, 2022

By J. van Zyl Visser

The advancement in Information Technology has resulted in a change in workflow practice in our Mineral Resource Management (MRM) offices on the mines and at our corporate office. This paper discusses the AngloGold approach in defining an IT strategy for MRM, a brief overview of systems usage and benefits. AngloGold has gone through a transformation phase and has positioned itself as a world-class, low cost producer. To support this objective, an initiative has been launched to provide the MRM division with an integrated MRM technical suite of systems with support of a Management Information System. Technical systems for a tabular orebody are not freely available and hence it took AngloGold almost seven years and a significant amount of capital to develop an integrated suite of technical systems. AngloGold MRM IT adopted the typical Zachman framework (value chain) approach in the analysis process and formulated the final deliverable in terms of AngloGold’s strategy. Major benefits have been realized through the ability to change planning scenarios in a short period of time and hence be able to increase reserves and NPV. The development of MRIS, which will become the flagship in AngloGold’s portfolio of systems is in phase two and this system will allow AngloGold to publish Resources and Reserves as per SAMREC and the JORC Code at will. The availability of information at all levels of the operations has made making decisions easier and hence some specialized reports such as the Basic Mining Equation were developed from the Corporate Data warehouse and from the MRM reporting database. Decision Support Systems(DSS) such as Business Objects and Oracle Express are now being used to assist in the process. The decision to use Business Objects to replace SAS reporting as the core reporting tool has resulted in the empowerment of the user and major cost saving as far as the use of consultants to set up standard reports.

Jan 1, 2003

By S. M. H. Ahmadi, K. Barani, F. Moradpouri, R. Ghaedrahmati

As exploration is time-consuming, costly, and risky, determination of the erosion surface of a metalliferous deposit before geophysical surveying and exploration drilling might be very helpful. Geochemical haloes can be used to determine whether the erosion surface is supra-ore or sub-ore and thus reduce the risk of exploration operations. The aim of this investigation is to determine the erosion surface of the North ROK porphyry deposit (NRPD) in northwestern British Columbia in Canada using linear productivity (LP), which is the content of an element defining the halo multiplied by the width of the halo. A total of 2045 soil samples from the B horizon were analysed using ICP-MS for 36 elements, including Cu, Mo, Pb, Zn, Au, As, Ag, Ni, Co, Fe, and Mn. The data-set was snalysed to obtain the statistical parameters and the elements Cu, Mo, Pb, and Zn were chosen to calculate the linear productivity and the total linear productivity. These four elements were modelled using probability plots to identify and separate subpopulations in terms of anomalous haloes and background, including the threshold values of each subpopulation. The results of the probability plot modelling and thresholds values were then used to map the distribution of each element in a GIS to calculate the linear productivity. The total linear productivity indicated that the erosion surface is supra-ore. Finally, a 3D orebody model of the Cu, Mo, Pb, and Zn distributions was constructed using borehole data and used to validate the results.

Feb 6, 2023

By A. J. Dickson, A. M. Starfield

This paper reviews the progress made to date in the development of computer models of heat and moisture transfer from rock surfaces to the ventilating air in deep-level mines. The application of these programs to ventilation planning and design is discussed.

Jan 1, 2014

By A. J. Roets

Despite its growth over the years, necessitating ever¬larger office accommodation, the Gold Fields group changed its head office address in Johannesburg only twice in 94 years. The first move was at the turn of the century, from the then select suburb of Doornfontein to the corner of Fox and Simmonds Streets. The second move was in the thirties, from that address-now the Reserve Bank building-to the well-known address of 75 Fox Street. With the advent of the first mines of the West Wits Line by the end of the thirties, 75 Fox Street proved too small, and the eastern section of the Commissioner Street side of the present head office was added on. In the fifties, when space once more became a serious problem, the old Exploration building was purchased and demolished, and the present west wing on Commissioner Street was built on the site. In the early seventies, cramped conditions again made life difficult and, despite a reorganization of the interior layouts, the need for expansion remained critical. Eventually, the adjacent Hollard Place and parking area became available, and plans for an extended new building complex could he considered. The building project was

Jan 1, 1985

By M. M. Ali, C. Musingwini, R. A. Phillips

The long-term open-pit mine production scheduling problem (OPMPSP) is typically solved in two broad stages. The first stage entails optimisation of the ultimate pit limit, which delimits the economical final pit and maximises the undiscounted value of the deposit. The second stage entails optimisation of the long-term open-pit mine production scheduling, which maximises the discounted value of the deposit. The long-term OPMPSP is a type of an NP-hard problem, such as the travelling salesman problem (TSP), because it is intrinsically complex to solve since it incorporates both hard and soft constraints. Therefore, metaheuristic approaches have been used to find global optimum solutions to the long-term OPMPSP. This paper presents a metaheuristic approach utilising a dual interchange algorithm (DIA) to solve the long-term OPMPSP. The DIA is a parent algorithm which supervises two subservient algorithms, namely, simulated annealing (SA) and Tabu search (TS). The DIA selects the better solution generated in each run from the two algorithms, and simultaneously penalises the algorithm that produced an inferior solution, while rewarding the one that produced a better solution. The DIA was tested on the three-dimensional Arizona Copper Deposit (KD) dataset, which is publicly available for research purposes from the online MineLib repository. It was set to generate net present values (NPVs) in five-minute intervals and the solution improved until it plateaued at about 30 minutes of runtime. The NPVs compared favourably to those obtained on the same KD dataset but obtained over 24-hour runtimes, when solved using simulated annealing and Tabu search algorithms, and the NPV generated from the work of Muñoz (2012) using the modified TopoSort as found on the MineLib repository at the time of this study. Therefore, this paper demonstrates that DIAs can be developed and used to solve the three-dimensional long-term OPMPSP.

Sep 1, 2021

By W. Bleloch

Published in the Journal, September 1970, and presented at a colloquium on 'Future of the Steel Industry', 17th March, 1971. Errata (a) The final sentence in the penultimate paragraph, left hand column p. 34 of the text should read: 'In the hot regions of the bosh and stack the C+CO2=2CO reaction proceeds to CO from coke carbon and carbon dioxide generated by reduction of iron oxides by CO (the so-called solution loss of carbon)'. The italicised words have been omitted in the text. (b) Temperature in Fig. 3 is K not C. (c) In Fig. 9, connection from top plate of column 10 to heat exchanger 9 has been omitted. DISCUSSION J. B. BEEDON AND C. J. JONKER* Dr Bleloch's paper has outlined the advantages of recycling stack-gas of low nitrogen content in the blast furnace. In the first instance it would appear to be extremely beneficial in controlling the hearth temperature and allowing a 100 per cent oxygen-blast to be used. On a second point however we have to disagree. It is claimed that heat is liberated in the combustion zones by the oxidation of CO to CO2 near the tuyeres and in the subsequent reduction of the CO2 by CO. The author has hypothesized as follows, and we quote: 'The C+CO2=2 CO reaction in the outer combustion zone at about 1 700°C is no longer endothermic due to loss of stability of CO2 and its consequent dissociation into CO and free oxygen.' This statement requires closer examination. If we consider the individual events occurring with the CO in the recycled topgas, with the oxygen in the blast and with the coke in the burden, as done by Dr Bleloch, the following heat considerations emerge. All heats of reaction are calculated from the enthalpy values of each reactant and product, as well as the temperature dependence of their molar heat capacities. (a) At the tuyeres: CO+1/2 O2-+CO2 . . . . . (1) CO, CO2 at 500°C; O2 at 25°C. ?H reaction = -65 000 cals/mole CO The reaction (1) is exothermic. (b) In the outer combustion zone: CO2+C?2 CO . . . . . . . . (2) C, CO at 1 700°C; CO2 at 500 0C. ?H reaction = -56 000 cals/mole CO Reaction (2) is endothermic. The overall heat gain of reactions (1) and (2) is ?H=+56 000 - 65 000= -9000 cals/mole CO i.e. the overall reaction is slightly exothermic, the amount of heat liberated is however smaller than suggested by Dr Bleloch. (c) The dissociation CO2+CO+1/2 O2 . . . . . (3) is a highly endothermic reaction at 1 700 0C, requiring 82 000 cals/mole CO2 to proceed to completion. Furthermore, this reaction (3) is energetically not favoured to proceed, as can be observed from the free energy-temperature relationship of figure (3), which favours the formation of CO2 at 1 700 0C. Hence direct dissociation of CO2 at 1 700 0C appears to be unlikely.* The concept of recycling topgas is however still intriguing from many other points of view. Apart from providing a very efficient method of hearth temperature control, it will create a much higher CO partial pressure in the stack. Whether the rate of indirect reduction in the stack will be proportional to this partial pressure or not is un-

Jan 9, 1970

[Consider the situation where we wish to estimate the value of a block of ore W from the values of n samples wt (i = 1, 2.... n). The samples can be located anywhere inside or outside W. The blocks and the samples can have any size or shape (Fig. 8.1). We define ws as the set of all the samples wi: WS = Iw1; W2; W3.. . wn and we wish to estimate the block W using the samples ws. Let xi be the value of the ith sample and µw the unknown average value of the block. We can estimate µw from the average value of all the samples. Let µw be the estimator of µw. As the samples need not be of equal size, the sample average is: µw = wi xi/~ wi. (8.1) The mean squared error made when estimating µw by µw is known as the variance of estimation of W by ws. It is the error made when giving the value of the sample set ws to the block W and is written o2E (WS to W). By definition: o2E (ws to W) = E [(µw - µw)2]. (8.2) If n = 1, this error is known as the extension variance. Since the sum of the weights given to the sample values is equal to 1,0, the estimator µw is unbiased (the question of the absence of bias is studied in more detail in Chapter 9): E [( µw - µw)1 = 0. (8.3) The error (µw - µw) has zero mean and a variance o2E = E (W8 to W). If we assume that this error is normally distributed, we can define confidence limits for µw. Let tP be the value of the standardized normal variance t such that the probability that t is less than tP is p: (t,) = .\/27T f exp (- t2/2) dt = p (8.4) The probability that µw is larger than µw + t1-P oE is p. The probability that µw is smaller than µw- t1-P oE is p. The following approximation formulae are often used to calculate 2p central confidence limits for the block value: 68% central confidence limits (p = 16%): µw - o2E, and µw + o2E. 95 % central confidence limits (p = 2,5 %): µw - 2 oE, and µw + 2 oE. Tables of the function 0 can be found in any textbook on statistics (for example, Fraser, 1958, p. 388) (see Table 7.2). [ ] The last line of Table 2.2, corresponding to f = 00, also contains the value of tP for p = 80, 90, 95 and 97,5 %.]

Jan 1, 1978

By J. P. Harrison, J. A. Hudson.

ABSTRACT: When considering the rock stress component of rock mechanics design, the basic procedure is to consider the pre-existing stress-state in the rock mass and then estimate the disturbance to this stress state as a result of engineering excavation. Failure criteria are applied to the final stress state to establish whether failure will occur. However, during the evolution of the stress state, the failure locus may be reached before the anticipated failure state and, in this case, failure will occur unexpectedly. This indicates that the complete stress path (defined as the variations in magnitudes and orientations of the stress tensor components resulting from engineering-induced or natural changes) must be considered. We list a set of stress path principles with their corollaries and then introduce a new and powerful method for simultaneously illustrating changes in the six independent components of the stress tensor. This method plots the magnitudes of the principal stresses above their orientational paths on the hemispherical projection, to provide a three-dimensional stress path locus for each of the three principal stress components. In connection with this presentational device, we illustrate a number of concepts associated with the stress path in rock engineering. For example, we show how the minor principal stress approaches zero at an unsupported excavation face, the interchange of the trajectories of two principal stresses when their magnitudes become equal, and the influence of the bounds on the principal stresses given by strength criteria. RESUME: Si on s’interesse à la composante “contrainte” lors d’un dimensionnement en mécanique des roches, la méthode de base consiste à considérer l’état de contrainte pré-existant dans le massif rocheux, puis d’estimer la perturbation à cet état générée par l’excavation projetée. Des critères de rupture sont appliqués à l’état de contrainte final pour établir si une rupture va se produire. Cependant, lors de l’évolution de l’état de contrainte, la surface critique peut être atteinte ce qui provoquera une rupture anticipée et, dans ce cas, cette dernière sera inattendue. Cela indique que le chemin de contrainte complet (défini par les variations de l’intensité et de l’orientation des composantes du tenseur des contraintes liées à des causes anthropiques ou naturelles) doit être pris en compte. Nous présentons un ensemble de règles pour les chemins de contraintes ainsi que leurs corollaires et, ensuite, nous introduisons une méthode, nouvelle et puissante, pour présenter simultannement les changements des six composantes du tenseur des contraintes. Cette méthode consiste à tracer l’intensité des contraintes principales sur le chemin d’orientation des contraintes à l’aide d’une projection hémisphérique afin d’obtenir le lieu, en trois dimensions, de chaque contrainte principale. En relation avec cet outil de représentation, nous illustrons certains concepts associés au chemin de contrainte en ingénierie au rocher. Par exemple, nous montrons comment la contrainte mineure tend vers zero à la surface d’une excavation sans soutenement, le changement de direction des deux contraintes principales quand leur intensité deviennent égales, et l’influence des conditions aux limites sur les contraintes fournies par un critère de rupture. ZUSAMMENFASSUNG: Bei ingenieurmassigen Taetigkeiten in Felsgesteinen ist es noetig die ungestoerten Gesteins Stress Componenten, die vor einem anthropogen Eingriff im Gestein vorhanden waren, zu kennen und erst dann Vorhersagen ueber Stoerung des Stress Zustandes, der durch einen ingenieurmaessigen Eingriff hervorgerufen wird, herzuleiten. Kriterien fuer das Versagen werden im letzten Stadium, des Stress Zustandes angewendet, um zu erfahren ob ein Versagen wohl eintreten wird. Es ist jedoch zu beachten, dass waehrend des Stress Aufbaus ein oertliches Versagen eintreten kann, welches vor dem eigentlichen, erwarteten Versagens Zustand auftritt. Diese Moeglichkeit weist darauf hin, dass der gesammte “Stress Path” (definiert durch die Variationen der Stress Tensor Komponenten in Richtung und Groesse, hervorgerufen durch ingenieurmaessig hervorgerufene oder natuerlich Vorgaenge) betrachtet werden muss. Wir fuehren eine Liste der “Stress Path” Prinzipien auf und stellen dann eine neue und wirksame Methode zur gleichzeitigen Darstellung der sechs unabhaegigen Komponenten des Stress Tensors vor. Diese Methode stellt die Groesse der “Principal Stresses” in Abhaengigkeit von ihrem rauemlichen Weg auf einer hemispherischen Projektion dar und erlaubt hiermit eine drei dimensionale Darstellung fuer jeden Ort des “Stress Path’s” in die drei Haupt Stress Komponenten. Im Zusammenhang mit der hier gegebenen Darstellungsart, verdeutlichen wir eine Reihe von Konzepten in der Felsmechanik. Wir zeigen zum Beispiel, wie der “Minor Principal Stress” Null zustrebt an einer Wand von einer nicht abgestuetzten Ausschachtung, den Austausch von Trajektorien zweier “Principal Stresses” wenn ihre Groessen sich gleichen, und den Einfluss der Groesse von “Principal Stresses” bei gegebenen Kriterien des Festgkeits Versagens.

Jan 1, 2003

By C. V. O?Keefe

Volumetric flow and mass flow are two of the critical process parameters needed to understand and control flotation processes, with others being levels, densities, and metal analyses. Both volumetric flow and density measurements can be adversely influenced by entrained air, which will result in artificially high flow readings and artificially low mass flow calculations. Array-based instrumentation has been used successfully to accurately measure both volumetric flow of aerated slurry and the quantity of air entrained within the slurry. The latter measurement has been used to correct density measurements, thus providing an accurate mass flow calculation. A case study involving the use of this technology to measure both flow rates and air entrainment levels at Eland Platinum processing facility (concentrator) will be covered in detail. In addition, with certain traditional flow meters such as electromagnetic meters, erroneous volumetric flow rates can be recorded in the presence of paramagnetic or ferromagnetic material. The use of this array technology to avoid spikes in measurements due to steel fragments passing through the pipe will also be discussed.

Jan 1, 2012