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"Chairman: Prof A. E. H. BLEKSLEY Rapporteur: Prof J. ELBRONDPanel Members: Prof J. C. Griffiths, Prof T. E. Hawkins, Mr A. C. Langton, Mr M. Splaine, Mr A. WeissThe reasons for failure of computer applications in the mineral industry and the direction of future developments.The Chairman opened the discussion by elaborating on the disappointment felt by some authorities with the lack of progress in the application of computers in the mineral industry during the last ten years, and posed the question to the panel : 'Do you agree that the computer age has not come up to expectations?'Mr Langton said that although there seemed to be a tremendous amount of brainpower applied to the theoretical side, he thought that the production men had not got all the help from computers that could have been given to them. The computer, said Prof Griffiths, is as yet a new tool which should not be used to do old things in old ways. To learn to use the computer will take time. After all, he said, it had taken 400 years after the introduction of the printing press to achieve general literacy, and perhaps it will take 40 years after the introduction of the computer to achieve `numeracy'.In Mr Weiss' view, the reason for the feeling of disappoint¬ment lay in the focussing of attention on the computer. The blame, if any, lay with the people surrounding the computer, that is, the analysts and programmers, to whom the emphasis should be shifted.Prof Hawkins said that he thought that some applications of the computer in the mineral industry had been successful, such as, for example, the compilation of payrolls. Reasons for failures in other areas were to be sought in the fact that the people connected with computers had failed to realise that they were merely part of a system. They had not understood the power structure of the organization which their work tended to change, and were therefore not prepared for the inevitable conflict with the production men.In Mr Splaine's view the production man had not received the assistance he could have had from the computer people because he may possibly not have allowed this to happen.Prof Bleksley concluded from these opinions that the promise which computers had ton years ago had not been fulfilled and added that the opinions expressed by the panel had intruded on his next question which was: 'Is the reason for this that people are involved?Prof Hawkins elaborated on his previous theme, namely, that of computer people in relation to management. Com-puter people, he said, were trying to impose change on management but were not prepared to share the responsibility for these changes. In fact, they wanted their work to be distinct and separate, and, as far as management was concerned, changes would be made when management believed that these would be less agonizing than no change at all."

Jan 1, 2014

By M. Mabuza

Two Rivers Platinum Mine (TRP) is a 55:45 joint venture between African Rainbow Minerals and Impala Platinum, respectively. TRP is situated on the farm Dwarsrivier 372KT, in the southernsector of the eastern limb of the Bushveld Complex. Dwarsrivier is underlain by rock formations of the Critical Zone (Winterveld norite-anorthosite) and the Main Zone (Winnarshoek norite-anorthosite). Two economically significant PGE-bearing layers namely the Merensky Reef and the UG2chromitite are found within the upper Critical Zone. These are approximately 140 m vertically apart, separated by a series of barren norites and anorthosites. At Two Rivers Platinum, only theUG2 chromitite layer is currently being mined for PGEs. The UG2 sub-outcrops north/south along the Klein Dwarsrivier river valley with a very gentle dip to the west of 7º?10º. At Two Rivers the UG2 averages about 120 cm in thickness, overlain by a waste pyroxenite parting about 20 cm thick, above which is a leader seam about 20 cm in thickness. The mineable cut consists of the leader seam, the waste pyroxenite parting, the UG2chromitite layer including 25 cm of pegmatoidal pyroxenite footwall, below the UG2 reef to a minimum of 185 cm trackless mining cut. The mining method is a mechanized bord and pillar layout, which will yield a total of 185 000tons at full run of mine production from the underground UG2 mine.

Jan 1, 2006

By A. P. I. Popoola

Aluminium AA1200 was laser alloyed with a combination of nickel and titanium diboride using different weight ratios. Chemical reactions took place with the formation of different phases. The characterization of the alloyed surfaces was carried out by x-ray diffraction (XRD), optical and scanning electron microscopes. The alloyed surfaces are composed of the initial phase of Al-Ni dendrites and eutectics of TiB2/Al and TiB2/Ni distributed on the initial phase. Experimental results obtained showed that Al-Ni intermetallics brought about a significant increase in the hardness property of Al; however, these intermetallics are highly brittle and prone to fail by brittle fracture or stress corrosion cracking when put in service. The addition of TiB2 brought about a reduction in the formation of the seintermetallic phases. A microhardness increase of over 10 times the hardness of the substrate was achieved. Keywords Dendrites, intermetallics, metal composite, Nd: YAG laser.

Jan 1, 2011

By S. Curry

The Objana Cement Plant is located in central Nigeria, approximately 200km south of capital city Abuja (figure 1). It is the second largest cement plant in Africa, and the fifth largest in the world [1]. The selected mining location is unique as it has all the major raw materials (except gypsum) in close proximity. This includes limestone, clay, marl, laterite soil, and laterite iron. [ ] The plant has a capacity of 5 million metric tones per year (~15,000 tones per day). A 135 megawatt gas-fired power plant, with 90 km of natural gas pipeline, was constructed to power the plant. The total project cost is approximately 1.2 billion US dollars. The lifeline of the plant is two overland conveys totalling 7.7km in length. The first 800m conveyor is relatively mundane. The second conveyor however, is unlike any other troughed belt conveyor in the world. It 6.9km length transports 2,400 T/H and operates at 5.0 m/s. Its ?snake? profile consists of 11 vertical cuvees, and four horizontal curves. The last of which is 2,000m in radius, has a length of 2.2km, and is located at the high tension head end of the conveyor. Although these specifications are noteworthy, the unique feature of this system is that it is entirely elevated from head to tail using a triangulated truss gantry structure (figure 2).

Jan 1, 2008

By A. M. Venter, C. W. Siyasiya, N. K. K. Arthur, M. G. Willemse, D. Marais

Although additive manufacturing is fast gaining traction in the industrial world as a reputable manufacturing technique to complement traditional mechanical machining, it still has problems such as porosity and residual stresses in components that give rise to cracking, distortion, and delamination, which are important issues to resolve in structural load-bearing applications. This research project focused on the characterization of the evolution of residual stresses in Ti-6Al-4V extra-low interstitial (ELI) additive-manufactured test samples. Four square thin-walled tubular samples were deposited on the same baseplate, using the direct energy deposition laser printing process, to different build heights. The residual stresses were analysed in the as-printed condition by the neutron diffraction technique and correlated to qualitative predictions obtained using the ANSYS software suite. Good qualitative agreement between the stress measurements and predictions were observed. Both approaches revealed the existence of large tensile stresses along the laser track direction at the sections that were built last, i.e., centre of the top layers of the samples. This in addition leads to large tensile stresses at the outer edges (corners) which would have the effect of separating the samples from the baseplate should the stresses exceed the yield strength of the material. Such extreme conditions did not occur in this study, but the stresses did lead to significant distortion of the baseplate. In general, the microstructures and spatial elemental mapping revealed a strong correlation between the macro-segregation of elemental V and the distribution of the β-phase in the printed parts.

Feb 6, 2023

By C. Zangerl, K. F. Evans, S. Loew

ABSTRACT: Settlements above fractured crystalline rock masses are rarely observed and in the past, geotechnical engineers would not expect substantial subsidence to occur in association with a deep tunnelling project. However, recent high precision levelling measurements along the Gotthard pass road in central Switzerland, have revealed up to 12 cm of subsidence along sections that pass several hundred metres above the Gotthard highway tunnel. Large-scale consolidation resulting from tunnel drainage and pore pressure changes in the rock mass are believed to be the contributing mechanism. This paper presents results from an extensive numerical modelling study focussing on the processes responsible for this subsidence. Results derived from 2-D discontinuum (i.e. distinct-element) and continuum (i.e. finite-element) modelling show that both discrete fracture deformation (i.e. fracture closure and shear) and poro-elastic consolidation of the intact rock matrix equally contribute to the observed magnitudes and shape of the surface subsidence trough. RÉSUMÉ: Des tassements aux dessus de massifs cristallins sont rarement observés et par le passé les géotechniciens ne prévoyait pas de subsidence significative associée avec des projets de tunnel profond. Cependant, de récentes campagnes de nivellement haute précision le long de la route du Col du Gotthard (Suisse centrale), ont mis en évidence des subsidences atteignant 12 cm sur des sections passant plusieurs centaines de mètres au-dessus du tunnel routier du Gotthard. Le mécanisme invoqué pour expliquer ce phénomène est la consolidation à grande échelle due au drainage du tunnel et aux variations de pression de pore dans le massif rocheux. Cet article présente les résultats d’une modélisation numérique intensive mettant l’accent sur les processus responsables pour la subsidence. Ces résultats obtenus grâce à des modèles 2-D discontinus (p. ex. éléments distincts) et continus (p. ex. éléments finis) montrent que la déformation sur des fractures discrètes (fermeture de fractures, cisaillement) ainsi que la consolidation poro-élastique de la roche intacte contribuent également aux magnitudes et aux géométries de subsidence observée en surface. ZUSAMMENFASSUNG: Beachtliche Oberflächensenkungen in einem kristallinen Gebirge, deren Ursache im Vortrieb eines mehrere hundert Meter tiefgelegenen Tunnels liegt, wurden bisher nicht erwartet und beobachtet. Dennoch wurden nach dem Bau des Gotthardstrassentunnels, entlang der Gotthardpassstrasse Oberflächensenkungen mit einem Maximalbetrag von 12 cm bei der Auswertung von Präzisions-Nivellements entdeckt. Dieser Maximalbetrag wurde in einem granitischen Gneis gemessen. Die örtliche Übereinstimmung zwischen dem maximalem Senkungsbetrag und dem maximalem Wasserzufluss zum Tunnel, und die zeitliche Abfolge von Tunnelbau und auftretenden Oberflächensenkungen lassen hydromechanisch gekoppelte Prozesse als Ursache dieser Gebirgsverformungen vermuten. In dieser Arbeit werden die Ergebnisse ausgedehnter prozessorientierter numerischer Simulationen präsentiert. Resultate aus den 2-D Diskontinuum (d.h. distinct-element) und Kontinuum (d.h. finite element) Simulationen zeigen, dass beide Verformungsmechanismen, d.h. an diskreten Brüchen und der intakten Gesteinsmatrix, gleichbedeutend für die beobachteten Senkungsbeträge und der Form des Setzungstroges verantwortlich sind.

Jan 1, 2003

By B. Kruger

After the milling and flotation of the platinum bearing ore, the flotation concentrate is electrically smelted in 6-in-line electric arc furnaces and the resulting furnace matte treated in Peirce Smith converters to remove the iron. The iron-free (less than 1% Fe) converter matte is granulated and sent to the base metals and precious metals refineries for further processing. During the smelting and converting processes two distinct gas-strength gas streams are produced: ?The Peirce Smith converter off-gas contains 4%?9% SO2which is treated in a conventional sulphuric acid plant to produce 94% H2SO4. ?The electric furnace off-gas contains 0.9% SO2which was (until September 2002) vented through a 91- metre high stack to atmosphere. In October 2002 Impala Platinum commissioned a SULFACID® plant at its smelter in Rustenburg, which recovers the SO2from the electric furnace off-gasses into a weak sulphuric acid solution. The SULFACID® technology utilizes wet activated carbon to oxidize the SO2toSO3. The SO3reacts with the water on the catalyst and is washed off the catalyst bed as a sulphuric acid solution with up to 13 wt. H2SO4. The plant operates at 60ºC and at atmospheric pressure. The SULFACID® technology is widely used in the pigment industry. This is, however, the first application of the technology on electric furnace off-gas. Keywords: SO2, sulphuric acid, electric furnace, off-gas, SULFACID®

Jan 1, 2004

By F. Trabzuni

Elutriation of solid reactants from fluidized bed reactors can affect their process performance and efficiency greatly. Chlorination fluidized bed reactors for selective conversion of solid metal oxides to metal chlorides are used widely these days. This study provides a platform for a proper understanding of reactant solid characteristics and solid shrinkage interaction with elutriation rate constants using multi-sized particles, sand-like, ?Geldart B? chloridable materials. The study has found that actual elutriation rates of the reactive system are influenced by complex parameters? interaction including bed diameter, reactor freeboard height, bed minimum fluidization velocity, and reactant?s physical properties.

Jan 1, 2009

By J Cahill, M Lee

Leinster Nickel Operations, located in Western Australia, consists of an underground and three open pit mines in relatively adverse ground conditions. This paper reviews our ground control practices in the open pits, covering aspects of ground support, wall control and monitoring. These methods have been effective in allowing mining operations to continue beneath unstable slopes. In particular, the use of Groundprobe?s Slope Stability Radar has enabled the Harmony Open Pit to safely operate for months following indication of failure from traditional methods. This case study highlights the benefits of investing in appropriate slope stability monitoring systems.

Jan 1, 2006

By A. Esterhuizen

Since 2005 Two Rivers Platinum Mine has set out on an initiative to actively monitor and control ground conditions on a daily basis, by making use of borehole cameras and pro-actively amending the support and mining strategies based on day-to-day observations of the hangingwall conditions. Today the borehole camera observations form part of the Rock Engineering Department?s daily function, and the size and frequency of falls of ground and ensuing accident rates have been drastically reduced since implementation of the system. The Two Rivers Platinum fall-of-ground management system aims to support 100% of the possible fallout thickness, based on ongoing data gathering and interpretation, thereby ensuring safety and limiting support cost.

Jan 1, 2014

By J. C. M. De Souza

The Samarco pipeline, the longest in the world for iron ore slurry transportation, started operation in 1977 to transport concentrate from the Germano facilities, in the state of Minas Gerais, to the pelletizing plant, located 396 km away, in the state of Espirito Santo, on the south-east coast of Brazil. Designed for a nominal capacity of 12 million tons per year, the pipeline reached 15.5 million/year due to operational improvement and, in late 2005, it was resized to transport 16.5 million tons per year, with the installation of a booster station. In order to ensure the accurate performance of the system, a pipeline cleaning programme was carried out and, since it has been29 years from the operation start-up, precise knowledge of the pipe condition would be fundamental to guarantee the success of the project. The cleaning programme demonstrated the potential of operational gains from this initiative, and its effect on the corrosion control and future measures, which should be permanently adopted to maintain the improved capacity. The intelligent pig runs provided essential data used to establish a pipeline integrity programme that allowed Samarco to develop a pipe repair plan based on the severity and significance of the features and to implement a future pipe replacement plan.

Jan 1, 2007

By Y. Lizotte

This paper describes the design and implementation of the dispatching system at LAB Chrysotile Inc.'s Black Lake Mine Operation, Quebec, Canada. The initial system uses a computer in a passive role, to record and display information in ongoing operations. Simulation studies were undertaken at McGill University to assess various heuristic dispatching rules which can be program- med and inserted into the dispatching system. The computer can then suggest to the operator where a truck should be sent to maximize productivity or improve fleet efficiency. The study stresses the importance of considering the effects of implementing computerized systems on those individuals who must use these systems in their daily work. The roles of individuals from the industry and the university in this joint project are also highlighted.

Jan 1, 1987

By H. Sasao, Y. Obara, A. Hirata

In the upper part of the planned location of the portal of a highway tunnel, there was a steep rock cliff with several unstable rock blocks. It seemed that the risk of those rock blocks to fall was very high. The cut-out to stabilize the rock cliff was monitored with various measuring instruments to prevent the sudden fall of the rock blocks. This paper discusses the measurement of acoustic emission and interpretation of its result during excavation of the rock cliff. We calculated displacements by integrating the accelerogram twice in terms of time, and demonstrated that slight displacements can be calculated from the measured AEs. Dans la partie supérieure de l’emplacement prévu pour le portail d’un tunnel autoroutier, il y avait un escarpement rocheux raide avec plusieurs blocs rocheux instables. Le risque de chute de ces blocs semblait très élevé. Lors de la coupe pour stabiliser l’escarpement rocheux, le suivi a été effectué avec différents instruments de mesure pour éviter la chute brutale des blocs rocheux. Cette thèse présente les mesures d’émission acoustique (EA) et l’interprétation de leurs résultats pendant l’excavation de l’escarpement rocheux. Nous avons calculé des déplacements en intégrant l’accélérogramme deux fois par rapport au temps, et montré que de petits déplacements sont calculables à partir des EA mesurées. Im oberen Teil des geplanten Ortes des Stollenmundes eines Autobahntunnels gab es einen steilen Felsen mit mehreren instabilen Felsenblöcken. Die Gefahr schien sehr groß zu sein, dass diese Felsenblöcke einstürzen können. Beim Abbau um die Stabilisierung des Felsens wurde das Monitoring mit verschiedenen Messinstrumenten zusammengestellt, um den plötzlichen Verfall der Felsenblöcke zu verhindern. Das vorliegende Papier diskutiert die Akustische Emission und die Auslegung deren Ergebnisse während des Abbaus des Felsens. Wir berechneten die Verschiebungen durch zweimalige Integrierung der Accelerogrammen in Bezug auf die Zeit. Die dargestellten kleinen Verschiebungen können aus den gemessten akustischen Emissionen berechnet werden.

Jan 1, 2003

By Bosman

Medium suspensions play an integral part in the successful application of dense medium separation for both static and dynamic separators. Although models exist to predict particle movement as a function of medium density and viscosity, these models have been derived on the assumption of Newtonian rheology. Viscosity measurements of medium suspensions have shown that they are non-Newtonian, with a yield stress, and as such cannot be used in the existing models. As a result, medium selection remains an art based upon practical experience and indirect measurements of viscosity such as stability and cyclone differentials.

Jan 1, 2014

By J van Rooyen, S. Archer, M. Fox

The use of dilute sulphur dioxide (SO2) gas mixtures for the oxidation/precipitation of manganese has been explored widely in recent years. The technical merit of the concept is well proven and implementation of the technology on commercial scale is imminent. This paper reviews the technology of manganese removal by means of dilute SO2 gas mixtures and highlights some of the challenges associated with its implementation on industrial scale. A brief review of the technology is presented; the review considers both the mechanism and chemistry of manganese oxidation/precipitation with dilute SO2 gas mixtures. The impact of variables such as temperature, pH and SO2 concentrations on the manganese removal process is assessed. Challenges associated with implementation of the technology on industrial scale are discussed. Gas dispersion is highlighted as a critical design consideration.

Jan 1, 2007

By N. Mangesana

The effect of high solids concentration and coarse particle sizes (d50 ranges 90?300 µm) on the viscosity of a suspension of water and silica sand was investigated. The experiments were designed to include conditions that have been tested by other authors and those encountered in the operation of tumbling mills. The rheological data was measured using a tube rheometer with operating pseudo shear rates of up to 1500 s-1. The rheograms obtained depicted dilatant behaviour. The Otswald-de Waele, Bingham, Herschel-Buckley and Casson models were fitted to the experimental data. The Herschel-Buckely model, which approximates the yield point and gives an indication of the shear thinning or shear thickening behaviour of the suspension, was found to provide the best description of the flow curves for all slurries. The Herschel-Buckely model was then used to determine the apparent viscosity of all the tests. The apparent viscosity and yield stress increased with solids concentration and particle size at the different pseudo shear rates. The increase in slurry viscosity with solids concentration was attributed to increased frequency of particle-particle interactions. The increase in slurry viscosity with particle size was attributed to increased inertial effects. At low shear rates the sand slurry exhibited shear thinning behaviour for all solids concentrations. At higher shear rates above 1000 s-1the high solids concentration suspensions exhibited a transition from shear thinning to a shear thickening behaviour.

Jan 1, 2008

By A. Rahmanab, A. Torpy, M. I. Pownceby, M. N. Zaman, N. Haque, W. Bruckard, J. Tardio

Ilmenite is the principal feedstock for producing TiO2 - used in paints, plastics and paper and the production of Ti metal. The Brahmaputra River system in Bangladesh represents a potentially new source of ilmenite concentrated within sandbar placer deposits and the current study presents results from beneficiation and characterisation studies conducted on Brahmaputra River Fe-Ti oxides. Characteristic of fluvial systems, the ilmenite concentration is low (~0.5 wt-%), however extensive annual dredging for waterway navigation provides the economic impetus to recover saleable ilmenite. The Fe-Ti oxide suite derived from magnetic fractionation comprises homogeneous ilmenite, titanohematite and hematite, although many grains exhibit complex exsolution within the (Ilm-Hem)ss series. The textural variability results in difficulty generating a pure ilmenite feedstock with the bulk concentrate typically being low in TiO2, containing 31.0 wt-%TiO2 and 62.7 wt-% (Fe2O3). Results are interpreted via an analysis of the implications for producing a commercial-grade ilmenite concentrate suitable for TiO2 production. Keywords: Ilmenite, titanohematite, Fe-Ti oxide exsolution, TiO2 production

Jan 1, 2020

By D. Sethuram, P. G. Koppad, S. Iyengar, R. Shobha

TiB2 and CeO2 particle-reinforced Al6061 hybrid composites were manufactured using stir casting and hot rolling techniques. The base alloy and composites were hot-rolled at 500ºC and a 50% reduction was achieved through 12 passes. The effect of varying TiB2 and CeO2 particle additions on the microstructure and mechanical properties of the Al6061 matrix was studied. Scanning electron microscopy showed uniform dispersion of both the reinforcements, with good interfacial bonding. Microhardness and tensile properties like yield and tensile strength were found to be higher for hybrid composite with 2.5% TiB2 and 2.5% CeO2 compared to Al6061 alloy and other hybrid composites. The increased tensile strength is attributed to good dispersion and interfacial bonding between the particles and Al6061 matrix. Fracture analysis using a scanning electron microscope revealed ductile fracture for the Al6061 alloy and mixed characteristics of ductile-brittle fracture for hybrid composites

Oct 1, 2021

By G. A. Brown

A colloquium on industrial minerals entitled' A Strategy for Growth in the Industrial Minerals Sector' was held at Mintek on 5th November, 1991, under the auspices of the Extractive Metallurgy Sub-Committee of the SAIMM. The SAIMM had not been previously active in the field of industrial minerals, and the programme was designed to appeal to the middle management of mining and manufacturing companies in the industrial-minerals field. A total of 86 registered for the Colloquium, a predominance of the delegates (65 per cent) being non-members of the SAIMM. Two overseas delegates were registered after announcements

Jan 1, 1992

[The following notations will be used: O an ore body. z a point in O. z' another point in O. w0 (z) a point support of infinitely small dimensions w0 centred in z. w (z) a sample (or block) of finite dimensions kv centred in z. W (z) a block of size W greater than or equal to w. W'(z) a block of size W' greater than or equal to W. W" (z) a block of size W" greater than or equal to W'. x (z) value of the regionalized variable x with support wO at point z. p (z) average value of x in w (z). pw WZ) = E[x(z')l zt in w(z) pw (z) average value of x in W (z). pwl (z) average value of x in W' (z). pwU (z) average value of x in W" (z). Note that pW (z), pw (z), pwf (z) and pw,, (z) are (regular- ized) regionalized variables with support w, W, W' and W" respectively. The relative sizes of wO, w, W', W" and O are represented schematically in Fig. 7.1. The variance of pw (z) when w (z) takes all possible positions in O is known as the dispersion variance of w in O and is denoted by a? (w in O) or a\: 0; = a2(w in a = Ew,z, inn {[p~ (z) - p121. (7.1) For convenience, the following simpler notation will be used: a> Ew in n [(p w - pl21. Consider now a large block W (z) in O with average value p~(z), and all the possible smaller blocks (or samples) w (z') of size w in W (z). We can calculate the variance of the blocks w (z') in the block W(z), which is the dispersion vaciance of w in W (z), from the relationship a2 [w in W(z)l = Ewcz,, in W(Z) {[PW (z') -pw (z)l21. (7.2) Provided the intrinsic hypothesis is satisfied (§3.4.4), this variance is a function only of the dimensions of the supports w and W, and is independent of the position z of the block W (z). We can therefore define the dispersion variance of w in W, as follows: u2 (win W) = Ew in w [(ptti - PW)~]. (7.3) In cases where the intrinsic hypothesis is not satisfied, the variance of samples w in blocks W may vary only slightly from block to block, so that the average dispersion variance of w in W (z) for all possible W (z) in O can be used: ayw in W) = Ew(,, ~n n {a2 [W in W (z)]}. (7.4) The following example will help to illustrate the importance of the variance of dispersion. Assume that we plan to develop a bedded coal deposit Q. We consider mining the ore body with only one giant dragline, which will extract each day a block of coal of size W'. The total area mined in a year will have a size W". We want to know whether this scheme is acceptable, given that the daily variation in ash content must not exceed a given percentage specified in the sales contract, which is renewable on a yearly basis. On a given day, if we mine the block W' (z), the ash content will average pwT (z). In a period of one year, the expected daily variation in ash content is measured by the expected variance of pwf (z) in W", i.e. by a2 (W'in W"). An alternative mining method might be to use two smaller draglines, each one mining W'/2 of ore per day, and Wn/2 per year. If the draglines are used to mine two distinct sections of the deposit, the expected daily variation in ash content will be u2 (W'/2 in Wj1/2)/2 Other situations, where economic decisions cannot be made without knowledge of the dispersion variance, are illustrated in § 7.4 and 7.5 below. Remark: The notation a2 (w in W) is used in this publication because of its clarity. An alternative notation, which is increasingly accepted in the literature, is s2w/W. ]

Jan 1, 1978