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By Jacolien P. Wyethe

Zincor uses a Roast-Leach-Electrowinning circuit to process zinc sulphide concentrates. It also processes zinc oxide fume, originating from a slag smelting operation in the Democratic Republic of the Congo (DRC). Zincor achieved an average zinc recovery of 90.3% during the period January 2006 to May 2007. The bulk of the losses occurred in the iron and lead silver residues, both as soluble and un-dissolved losses. The un-dissolved losses in the iron residue constituted around 33% of the total zinc lost from the circuit, and were largely attributed to the presence of zinc-ferrite in the calcine used for neutralization during iron removal. As part of Zincor?s continuous improvement programme, the un-dissolved zinc losses in the iron residue were targeted by: the partial replacement of calcine with zinc oxide fume (from the DRC); and the preferential use of ?low-ferrite content calcine? as neutralizing agents in the iron removal circuit. These initiatives, coupled with other operational factors, resulted in a marked improvement in recovery to 92.6% during June to December 2007. The zinc oxide fume, directly fed to the circuit, required investigation of the halide rejection capacity of the Zincor circuit. Rejection of chloride via the magnesium bleed operation was considered adequate. Fluoride was mainly rejected via the iron (~70%) and lead silver (~27%) residues. Fluoride rejection via the lead silver residue varied significantly, probably as a result of variations in the sparingly soluble CaF2 content in the feed. The mechanism for fluoride rejection in the iron residues is uncertain. The fluoride rejection capacity of the Zincor iron residue (comprising of mainly jarosites, schwertmannite and ferrihydrite) at 2 ? 4 mg/L F in solution, was estimated at 0.14 ? 0.19 kgF/tFe residue.

Jan 1, 2008

By A. H. Swart

Rock engineering is concerned with the design of rock structures generated by mining activities. Therefore, rock engineering designs have major implications for the safe recovery of mineral deposits and operating costs. The paper deals with a few challenges facing rock mechanics engineers operating in the hard rock underground mining environment in South Africa. Finally, examples are included, which may assist rock mechanics engineers in providing better designs, which could ultimately lead to further improvement in safety and lower operating costs.

Jan 1, 2005

By G. H. Lind

Seven full and partial pillar extraction operations were visited in New South Wales, Australia, in the early parts of 2001. Certain factors unique to these operations have led to the general success of the safe and economic extraction of these coal pillars. Some of these factors attributable to the overall success of these operations are discussed in this paper. In particular, geotechnical mapping, specific legislation pertaining to pillar extraction, mining methods, the role of temporary supports and training are described. It is found that some of these factors have useful attributes which could be used to design a methodology for extraction of underground coal pillars in the Witbank and Highveld coalfields of South Africa.

Jan 1, 2002

By Michelle Mouton, Johanna van Deventer, Jussi Vaarno

Mintek has been involved in numerous projects to remove Fe and Mn from dilute Co sulphate solutions by means of oxidative precipitation using air/SO2. Test work was done using a gas induction system, designed and supplied by Outotec. Various aspects, such as SO2 concentration, SO2 flowrate, impeller rotation speed and pH were investigated on a 2 m3 scale. Batch tests were performed using a residence time of 5 hours. Mintek has been involved in numerous projects to remove Fe and Mn from dilute Co sulphate solutions by means of oxidative precipitation using air/SO2. Test work was done using a gas induction system, designed and supplied by Outotec. Various aspects, such as SO2 concentration, SO2 flowrate, impeller rotation speed and pH were investigated on a 2 m3 scale. Batch tests were performed using a residence time of 5 hours. Impeller rotation speeds of 0-220 rpm were tested, and it seemed that speeds of between 80 and 220 rpm gave similar Fe and Mn removal rates. Co and Cu losses were generally below 1% and 5% respectively at pH 3.

Jan 1, 2007

Bacterial leaching represents an unusual problem in biochemical engineering, because the substrate for bacterial growth is not supplied directly, but is a product of another reaction, the leaching of mineral particles. Leaching arises from the bacterial oxidation of ferrous ions to ferric ions, which in turn oxidize the mineral. For the bacterial dissolution of pyrite, these reactions are: [ ] (Y represents a stoichiometric yield factor, and N represents the amount of bacteria.) Equations [1] and [2] represent a cyclic auto-catalytic system since more ferric ions are added to the system with an increase in the extent of leaching.

Jan 1, 2000

Mining is an inherently risky business; from the technical, environmental, social, and economic uncertainties associated with advancing an exploration prospect to a viable project to the operating, market, and safety risks and uncertainties attached to a developed mine. Since we cannot totally escape the risk and uncertainty related to resource projects, as an industry we should improve our presentation of the upside and downside risks in the context of the project?s development path and maturity. More transparent, consistent, and balanced views of technical confidence will better inform both internal and external stakeholders about the expected risk in the project. International reporting codes set out the minimum standards, recommendations, and guidelines for public reporting of Exploration Results, Mineral Resources, and Mineral Reserves. However, the reporting code principles of transparency and materiality are largely subject to the interpretation of the competent person(s), which may introduce a degree of subjectivity in reporting, particularly the level of disclosure regarding supporting information. It is fundamental that Mineral Resources, Mineral Reserves, and study outcomes are reported so as to unambiguously present the level of inherent technical uncertainty (or confidence) in a project, while conveying a balanced view of the opportunities a project presents. Reporting needs to consider various stakeholders who may rely on this information, and present the data in the context of the changing risk profile associated with project development paths and project maturity. This paper discusses the interdependence of resource-to-reserve conversion, the consideration of various technical-economic study types, and the level of confidence conveyed to stakeholders relying on these technical reports and other company public announcements.

Jan 1, 2014

The Skorpion Zinc Project demonstrated the viability of the production of zinc from non-sulphide (commonly called ?zinc-oxide?) ores, using the leach/solvent extraction/electrowinning process route. The success of Skorpion raised the profile of a number of other zinc oxide deposits, considered to be similar. However, a study of three such deposits demonstrates that the application of whole-ore-leaching may be limited and that the concentration of zinc, or at least the separation from acid-consuming gangue minerals, prior to leaching is essential to the successful recovery of zinc from these deposits. The recovery of zinc is dependent on an understanding of the geology of the deposit, the mineralogical association of zinc minerals with gangue minerals (Boni, 2005) and limitations of mining practice. Flow sheet development and the associated metallurgical test work to derive an economically viable treatment route from two of these deposits are discussed. Key parameters affecting zinc recovery by gravity separation and flotation are presented, demonstrating that even minor differences in mineralogy have a profound impact on zinc recovery and reagent consumption. The study also deals with the determination of appropriate design parameters through metallurgical mapping of the dense media separation process.

Jan 1, 2008

By B. Kenny

The aim of this paper is to provide an overview of existing forms of subcontracting in the South African mining industry. A descriptive framework is developed to understand different subcontracting arrangements. We argue that, in order to do so, it is important to distinguish between labour broking and gang subcontracting. Data resulting from a research project (including an analysis of historical sources, interviews with contractors and focus group interviews with mineworkers) is presented to highlight the implications of changing formations of subcontracting for the South African mining industry in the late 1990s. Apart from the subcontracting of ?traditional? functions, such as shaft sinking, access development, catering and hostel maintenance, contractors are now used in ?core? mining activities. In some instances, whole shafts are ?outsourced? to outside agencies. It is argued that certain of the subcontracting arrangements have serious implications for the ability of the mining industry to improve health and safety standards. Some of the practices can potentially result in conflict between different categories of workers, and, as a result, instability in the industry.

Jan 1, 1999

By J. Gholamnejad

In open pit mine planning and design, push back mine sequencing is widely used for long-term production planning. In push back design, a series of nested pits is generated and then considered as possible push backs with regard to the minimum push back width requirements. These nested pits are produced by parameterizing on one economic parameter like commodity price, mining or processing cost, stripping ratio, etc. The most important characterization of these push backs is that the innermost push back has the highest value per ton, the second innermost push back has the second highest value per ton, and so on. These nested pits are generated based on the best estimates of grade within a representation of the orebody in a three-dimensional matrix form. Therefore, the inherent uncertainty associated with reserve estimation (for our discussion, grade uncertainty) is not taken into account when push backs are designed. These methods do not attempt to establish which part of the deposit is likely to be worth most. This paper introduces a new algorithm that incorporates ore grade uncertainty during the pushback design process. The suggested strategy tries to seek to schedule risky blocks later in the extraction sequence. Keywords: open pit mine, push back, ore grade uncertainty.

Jan 1, 2007

By C. F. Strydom

Paper written on project work carried out in partial fulfilment of B. Eng (Mining Engineering) degree The Self-directed work team concept is the product of relentless performance pressure on American industries during the late eighties and early nineties from other world industrial leaders like Japan. The concept proved to be a successful vehicle by which the Americans could increase their production and improve their safety statistics. The aim of this study is to evaluate the concept as a means to improve the overall performance on South African goldmines. he study is directed by a historical research section, answering questions like: ?Why do we need to change? ?What is a Self-directed work team? ?What are the principle advantages of the concept? ?What are the essential requirements for the concept to succeed? The study also includes an empirical research section that focuses on the current Self-directed work team situation in the South African gold mining industry. The empirical research section is limited to three case studies within Anglogold due to a study period of only six weeks. The mines chosen for the case studies have been labelled Mine 1, Mine 2 and Mine 3. The latter being the base mine allowing for a more in depth study. This includes a perception analysis towards Self-directed work teams within the mine. The study proves the truth of the Latin proverb ?Tempora mutantur, nos et mutamur in illis? meaning ?The times are changing, and we are changing with them?. The chief change catalysts identified are a dwindling gold price and a projected labour crisis. From the study it is evident that the Self-directed work team concept disposes of the critical parameters required for a dramatic improvement in performance. The study also indicates that for the concept to succeed, certain factors like top-level commitment and management-employee trust have to be in place. Sadly, the concluding part of the study proves that very few of the identified critical success parameters are present in the South African gold mining industry. This can serve to explain why the industry only has success with the concept when monetary gain is the chief motivator. The study only focuses on the reasons why the concept is not performing to its full potential and does not wander into explaining the reasons for the current unsupportive milieu in the industry. Self-directed work teams could well rescue the South Africangold mining industry but currently we are driving a square pin into a round hole! [Terminology SDWT?Self-directed work teams AEL?Adventure Experiential Learning ISW?In-stope worker POLC?Plan, organize, lead and control TEC?Total employee costed Silo?The confinement of departments preventing networking JCI?Johannesburg Consolidated Investment Co. Ltd]

Jan 1, 2002

By A. C. du Preez

The separation of nickel and cobalt from calcium, magnesium and manganese by solvent extraction using synergistic mixtures of carboxylic acids was studied. Addition of certain viable synergists to commercially available tertiary branched carboxylic acids, such as Versatic 10 (Shell) or Neodecanoic acid (Exxon), produced large synergistic shifts (?pH50) in the pH50values for nickel, and small antagonistic shifts (negative ?pH50values) in the extraction of calcium. Under the initial test conditions used (0.50 M each of Neodecanoic acid and the Mintek synergist, in xylene) a large separation (pH50Ca? pH50Ni= 3.09 pH units) between nickel and calcium in their extraction from 1.00 M sodium nitrate solutions was obtained, compared with only 1.11 pH units in the absence of the synergist. The selectivity series for the extraction of divalent base metals from 0.333 M sodium sulphate solutions by 0.50 M Neodecanoic acid and 0.25 M of the Mintek synergist in C12-C13aliphatic diluent was found to lie in the order (with pH50values in parentheses): Cu(3.42) > Ni (5.08) > Zn (5.58) > Co (5.73) > Mn (6.62) > Ca (7.48) >Mg (8.25). In batch counter current experiments, a simulated leach liquor containing (in gL-1): Ni 5, Mg 5, Mn 2, Co 0.5, Ca 0.5, Cu 0.1and Zn 0.1 was contacted with the mixed extractant in three stages at unit phase ratio and an equilibrium pH of 5.9. The recovery of nickel was 99.9 per cent and that of cobalt was 84.7 per cent, whilst the co-extractions of manganese, calcium and magnesium were 2.7,1.5 and 0.04 per cent, respectively. The recovery of cobalt can be enhanced by employing a slightly higher pH, although this will also increase the extraction of manganese, calcium and magnesium somewhat. Nearly quantitative stripping (99 per cent) of nickel from the loaded organic phase was achieved in a single contact at an organic-to-aqueous phase ratio of 4 using a simulated spent electrolyte containing 39 gL-1sulphuric acid and 33 gL-1nickel,thereby producing an ?advance electrolyte? containing 57 gL-1nickelat pH 3.5. Loading of acid into the organic phase was very slight, amounting to only 0.002 M H+in contact with the above-mentioned spent electrolyte. Keywords: solvent extraction; synergism; nickel; calcium; carboxylic acids.

Jan 1, 2004

By B. M. Nyombolo

The interest shown in our paper by Drs Schaekers and Dew, and their favourable comments, are appreciated. However, some of their remarks require a response. Stability testing procedures Regarding the issue of stability-testing procedures, we concur that no long-term procedure has been accepted by either environmentalists or the mining/processing industry as a valid method to test the long-term stability of solid wastes. We agree that the method we used is no exception, and we certainly did not claim that it should be recognized as such. What we did attempt to portray was that we had designed the test procedure in an attempt to simulate, at a very small scale, a tailings dam environment.

Jan 1, 2001

The paper deals with the importance of design and of codes of practice in ensuring safe working conditions in mines. The design principles involved in the design process are dealt with, and the importance of a logical design process is emphasized. The links between the requirements for developing a code of practice, embodied in the existing guidelines for the preparation of such a code, and the design principles and process are considered in some detail. Finally, suggestions are included, which may provide improvements to the code and hence, ultimately, lead to further improvement in safe working conditions.

Jan 1, 2004

By K. Aoki, Y. Mito, S. Shirasagi

The authors developed the TBM Excavation Control System (the TBM Navigator), in order to realize the advanced observational construction. During the excavation using this system, the rock strength value is immediately calculated from the TBM driving data as an index of rock properties, and the drill energy coefficient is also calculated from the drill logging data that is carried out using the probe hole ahead of the tunnel face. In this study, a new, geostatistical simulation-based method is proposed for the automatic prediction of the rock properties ahead of the tunnel face with good precision, using both the drill logging data and the TBM driving data. The applicability of this method is validated through the prediction at the actual tunnel excavation that passes through the faults. Les auteurs ont mis au point un Système de Contrôle de forage avec la machine à pleine section (Navigateur de la machine à pleine section), en vue de réaliser un système de surveillance plus efficace. Avec ce système, la résistance de la roche est immédiatement calculée, au cours du forage, à partir des données de conduite de la machine, comme indice des propriétés de la roche, et le coefficient d'énergie de la foreuse est également calculé à partir des données de log de forage collectées dans un trou de sonde foré dans le front de taille. Dans cette étude, on propose une nouvelle méthode basée sur la simulation géostatistique qui permet de prévoir d’une manière automatique, des propriétés de roches se trouvant derrière le front de taille avec une précision satisfaisante, à l’aide des données de log de forage et celles de conduite de la machine à pleine section. Cette méthode s’est avérée suffisamment précise au cours du forage d’un tunnel réel qui traversait une zone de failles. Die Autoren entwickelten das TBM Ausschachtungssteuerungssystem (den TBM Navigator), um noch besser überwachte Bauarbeiten zu ermöglichen. Unter Einsatz dieses Systems wird die Gesteinsfestigkeit während der Ausschachtungsarbeiten unmittelbar aus den TBM Antriebsdaten als ein Index für die Gesteinseigenschaften berechnet. Gleichzeitig wird auch der Bohrenergiekoeffizient aus den Bohrlogdaten berechnet, die an Hand der Probebohrung am Stirnende des Tunnels erhalten wurden. In der vorliegenden Studie wurde ein neuartiges, auf geostatistischen Methoden basierendes Verfahren für die automatische und angemessen genaue Vorhersage der Gesteinseigenschaften am Stirnende des Tunnels vorgeschlagen, für das sowohl die Bohrlogdaten als auch die TBM Antriebsdaten verwendet werden. Die Anwendbarkeit dieser Methode wird durch die Vorhersage bei einer tatsächlichen, durch Verwerfungen verlaufenden Tunnelausschachtung bewiesen.

Jan 1, 2003

Instability in rockpasses at deep levels often initiates as a result of stress induced fracturing of the rock on the walls of the pass. This may then progress to a stage at which the geological structure of the rock mass becomes dominant and permits large joint-defined blocks and slabs to become unstable. In this paper, a technique is described in which jointing parameters and their variabilities?orientations, spacings and lengths?are taken into account in estimating the extent of failure that may develop around a typical unsupported deep level gold mine rockpass. The results of this prediction are compared with the results obtained from a review of pass performance in the gold mining industry.

Jan 1, 2005

By U. Singh, E. T. Brown, J. Coxon

The rapid fracturing and deformation that occurs around excavations during rock bursts demand that support and reinforcement systems have both deformability and damping capabilities. The energy demand and supply approach currently used in design is considered to be too simplified to represent adequately the rock burst process and the support and reinforcement system requirements. Momentum change may be a necessary second criterion for the analysis of dynamic loading situations. At the St Ives Gold Mining Company, DE plates made from conveyor belt rubber, and dynamic cables with sliding anchors have been developed and used to improve the dynamic performance of support and reinforcement systems. La fracturation rapide et la déformation qui se produisent autour des excavations lors de coups de terrain demandent que les systèmes d’armature et de support soient déformables et aient une capacité d’amortissement. L’approche basée sur l’énergie actuellement utilisée pour la conception est considérée être trop simplificatrice pour représenter adéquatement les coups de terrain et les paramètres de conception des systèmes d’armature et de support requis. Le changement de quantité de mouvement pourrait être un second critère nécessaire pour l’analyse des cas de charge dynamnique. St Ives Gold Mining Company a développé et utilisé des plaques « DE » constituées de caoutchouc de courroie de convoyeur et des câbles dynamiques avec ancrage coulissant afin d’améliorer la performance dynamique des systèmes d’armature et de support. Die ploetzliche Rissbildung und Verformung, die sich in Baugruben waehrend eines Felseinbruchs ereignet, verlangt Stuetz- und Verstaerkungssysteme, welche verformbare und mildernde Eigenschaften aufweisen. Die derzeitlich gebraeuchliche Methode den Entwurf auf den Energiebedarf und dessen Abdeckung zu basieren, wird als eine unannehmbare Vereinfachung betrachtet, da sie den Felseinbruch und die benoetigten Unterstuetzungs– und Verstaerkungssysteme unzulaenglich darstellt. Die Aenderung der Umstaende kann einen zweiten Ansatz fuer die Analyse der Lastsituation erforderlich machen. Die St.Ives Gold Mining Company hat DE Platten aus Foerderband-Gummi und elastischen Kabeln mit verschiebbaren Verankerung entwickelt und dazu verwendet, die dynamische Kapazitaet der Unterstuetzungs- und Verstaerkungssysteme zu verbessern.

Jan 1, 2003

By J. Sikamo, A. Mwanza, C. Mweemba

"The Zambian copper mining industry as we know it today had its genesis in the 1920s. Consistent private sector-driven investment in the industry over a period of over 50 years in exploration, mine development and operation, development of minerals processing facilities, building of infrastructure for pyrometallurgical and hydrometallurgical processing, with attendant support facilities, including building of whole new towns, resulted in copper production rising to a peak of 769 000 t in 1969, providingover 62 000 direct jobs. The industry was nationalized in 1973 and remained in government hands for just over 24 years. During this period, the industry experienced a serious decline in production levels, reaching the lowest level in the year 2000 when production was 250 000 t. An average of just under 2000 jobs were lost every year in the 24-year period, reaching just over 22 000 direct jobs in 2000.Following the return of Zambian politics to pluralism and liberalized economic policies, the government decided to privatize the mining industry. The process started in 1996 and by the year 2000 all the mining assets had been privatized. The new investors embarked on serious investment to upgrade the assets and to develop greenfield mining projects. Fourteen years later and after more than US$12 billion investment, production levels increased year-on-year to a peak of 763 000 t in 2013 with direct jobs reaching 90 000.This paper discusses the impact of the mining industry in Zambia on the economy in areas such as employment, support for other industries, direct contribution to the national gross domestic product (GDP), foreign exchange earnings, and social amenities. The paper also focuses on the performance of the mines during these periods vis-à-vis mineral availability, mineral grades and complexity, new technologies, and human capital. This is looked at particularly in the light of current challenges the industry is facing. Suggestions are proposed on how the industry can be nurtured to continue being a major driver for the Zambian economy and a major player in the international copper mining business."

Jan 1, 2016

Council for 1999/2000 President M.H. Rogers President Elect Dr L.A. Cramer Vice Presidents Senior A.A.B. Douglas Immediate Past President J.R. Dixon Junior S.J. Ramokgopa Honorary Treasurer J.A. Cruise

Jan 1, 2000

By J. -H. Wu, S. Nishiyama, Y. Ohnishi

The behaviors and stress distributions of the inclined jointed rock masses with different dip angles obtained from DDA are compared to the results of laboratory tests. By calculating the block stress distributions, it is confirmed that DDA can reproduce the arching around the trap door when lowering the trap door. The shapes of arching change with the angles of inclined layers. In addition, the earth pressures acting on the trap door shows non-symmetrical distributions when the layers are not horizontal. The stress concentration occurs in one side of the rock masses close to the trap door. Furthermore, the surface settlements are also related to the inclined angle, and the loosening zone in rock masses can be different from Terzghi’s theory [1]. Since, simulations have good agreements with the laboratory test , it demonstrates the applicability of DDA to explain the mechanical behaviors of tunnel, such as arching phenomenon, non-symmetrical earth pressure distributions acting on the trap door, and the surface settlement profile in the jointed rock masses. Dans cet article est décrite l’étude numérique du perçage d’un tunnel dans un massif de couches rocheuses jointes inclinées. La simulation à l’aide de l’Analyse de Déformation Discontinue (DDA), en faisant varier l’angle d’inclinaison des couches de roche, nous apporte des résultats en termes de distributions de contraintes et de comportement des couches, résultats qui sont ensuite comparés avec des résultats de tests en laboratoire. Les résultats confirment le fait que la DDA est capable de reproduire le phénomène d’arcage autour de la trappe lorsque la trappe s’abaisse. Les formes d’arcage varient selon l’angle d’inclinaison des couches de roche. Par ailleurs, lorsque les couches ne sont pas horizontales, la distribution de pression agissant sur la trappe est assymmétrique. La concentration de contraintes se produit du coté proche de la trappe. De plus, les tassements de surface dépendent eux aussi de l’angle d’inclinaison. En conséquence, les résultats de simulation sont en accord avec les tests en laboratoire, ce qui prouve que la DDA permet d’expliquer des comportements mécaniques du tunnel tels que l’arcage, les distributions assymmétiques de pression du sol sur la trappe, ainsi que le profil du tassement de surface dans la masse de roches jointes. Dieser Beitrag beschreibt eine numerische Studie über Tunnel im geklüftetem Fels. Das Verhalten und die Druckverteilungen in den unterschiedlich geneigten und geklüfteten Felsenmassen wird mit Hilfe des Discontinuous Deformation Analysis Programms (DDA) simuliert, und mit Laborversuchen verglichen. Die Resultate bestätigen, dass DDA der Gewölbewirkung im „Trapdoor“ Experiment gut reproduzieren kann. Die Form des Gewölbes, ändert sich mit unterschiedlichen Neigungswinkeln der Schichten. Bei geneigten Schichten entstehen unsymmetrische Druckverteilungen. Auch die Oberflächenabsenkung ist von dem Neigungswinkel abhängig. Die gute Übereinstimmung der Simulationen mit den Laborversuchen zeigt, dass die DDA-Methode gut geeignet ist, um das mechanische Verhalten von Tunneln, wie z.B. den Effekt der Gewölbewirkung, die unsymmetrischen Druckverteilungen bei geneigten Schichten, oder die Oberflächenabsenkung in geklüfteten Felsenmassen, zu erklären.

Jan 1, 2003

A large number of brittleness concepts have been used in very different studies in the literature. One of them is the B1brittleness concept. In this study, the objective is to criticize the B1 brittleness concept on rotary blast hole drills. The B1 brittleness concept, the ratio of uniaxial compressive strength (sc) to tensile strength (sT), are widely used as a rock brittleness concept in the literature (Inyangand Pitt, 1990; Verhoef, P.N.W. 1993; Neil, D.M. et al.1994;Becker, et al.1984; Evans and Pomeroy, 1966; Göktan, R.M.1992; Kahraman, S. 2001; Yamaguchi, U. 1970; Verhoef, P.N.W. et al.1996; Bilgin, 1982; Howarth and Rowlands,1987; Howarth, D.F. et al. 1986). So, it was used as a rock brittleness concept in this article. The value of the B1brittleness concept is equal to the tangent of ß angle in the following graph. It was seen that more meaningful relationships could be obtained with the B2 brittleness, the under ?Area?(= 1/2(scxsT) = B2) under the curve, instead of tangent ß, (=B1), of the curve.

Jan 1, 2003