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By John Folinsbee, Brian Danyliw, Tony Y. Chong

"Control of fugitive dust has become increasingly important in the mining industry both from a health and safety and environmental standpoint. Mining operations in particular have required improved fugitive dust control due to recent lowering of the allowable airborne silica concentration to which workers can be exposed. Experience has now proven that the implementation of a surfactant based chemical dust suppression system can enhance existing mechanical dust control methods resulting in much more efficient control of fugitive dust.The Porcupine Joint Venture (Dome Mine) utilizes dry secondary crushing and screening that makes it particularly prone to fugitive dust emissions. A variety of potential dust control systems were evaluated and this led to the installation of a surfactant based water spray system to augment the existing mechanical dust collection systems.A great deal was learned through the implementation of this system. This paper describes the entire process, from testing, system design and installation, through optimization and standardization of operation. In addition a variety of problems were identified, and innovative solutions were provided. Also, the metallurgical impacts on down stream processing are highlighted. Finally, a full discussion of overall results including a discussion of the relationship between silica and total dust concentrations is included."

Jan 1, 2005

By Margarete Kalin

"Biotechnological approaches to decommissioning of mine waste management areas are presented in the context of sustainable environmental management. Improved design of waste sites and environmental management paves the way for the application of new technological approaches. Mining wastes are better confined, effluent quantity is reduced and the quality is expected to improve in the future. The biologically mediated treatments focus on the creation of conditions inside the waste management area which lead to the confinement of the contaminants in the inactive tailings ponds and seepage collection ponds, as well as pits or other disturbed areas which were part of the operating conditions.Biogeochemical reactions lead to three fundamental water treatment steps mediated biogeochemically , alterations in chemistry which lead to formation of particles, which then have to flocculate and be assisted to collect in the bottom of the ponds. Microbially active sediments are installed to assist particulate formation and serve as sinks for metals. In deeper sediment strata, stable forms of metals are created. Biological polishing is used to collect the particulates and relegate them to the sediment. Examples will be given of the application of these processes, to waste rock piles, open pits and tailings ponds. This paper attempts to show that, through the integration of applied biotechnological advances and the application of new approaches to decommissioning, reductions of environmental impacts by mining are possible. * Note: this paper has been presented at the 13th Annual Meeting of BIOMINETIntroductionThe role of biotechnology in decommissioning of mining waste management areas should be placed in the context of sustainable development. The concept of sustainable development as defined by the Brundtland Commission (1987) for the restoration/ reclamation of mining operations could be translated as follows: The increasing demand for the resources by the world population must be met in a manner which does not compromise the earth's environment over the long term (Brooks et al., 1995)."

Jan 1, 1998

By J. L. Kohler

Component failures in the electrical control circuits of mining machines account for a large percentage of the total downtime of the machine, Once a failure has occurred it is always a tedious and usually a time-consuming task to locate the failed component. Moreover, the pressure to quickly locate the cause of a delay can lead to compromises in safety. Thus an onboard diagnostic system, essential for an automated machine, would be a very useful addition to existing machines. This report details U.S. Bureau of Mines development of a generic procedure for synthesizing diagnostic systems for electrical-control-circuit failures in mining machinery. A continuous mining machine is used as the testbed to illustrate the application of the developed methodology. Substantive differences among mining machine control circuits made it impossible to achieve a generic diagnostic system, but a generic approach for the synthesis of the diagnostic system was possible. As the research progressed, it became apparent that an algorithmic approach was better than an expert-system-based implementation. A prototype system was constructed and used to evaluate the diagnostic system. Prototype implementation issues are also examined.

Jan 1, 2010

By Ronald F. Balazik

This Bureau of Mines study identifies and examines the costs of Federal, State, and local environmental protection controls on domestic phosphate rock mining, The costs include the expenditures needed to comply with government regulations and the effects that these expenditures and regulations have on supply. The study analyzes costs of environmental impact assessments, air and water quality standards, reclamation laws, potential solid waste controls, and local government restrictions. In addition, an industry survey and the Bureau's Minerals Availability System (MAS) are used to evaluate land management policies that restrict access to phosphate resources, Conclusions drawn from these analyses confirm that (1) domestic phosphate mining has incurred substantial control costs and may be subject to significant new regulatory costs in the next several years, (2) certain environmental controls can discourage mining investment, (3) environmental policies governing land-use controls affect the disposition of sizable phosphate resources, and are key determinants in the development of those resources on the Federal do- main, and (4) environmental costs could diminish the competitiveness of domestic producers.

Jan 1, 1983

By Charles Hart

In this paper it is the author's intention to show the extent and character of foreign ores now known to be available; these deposits may be in active production or held in reserve until economic conditions may make them active. He hopes to show the relation existing between these ores and the American supply, and which of the former are now producing or will in turn come into production when our better ores have been exhausted. This phase of this discussion must of necessity include some data as to the present rate of consumption and a study of the changes we may expect here and abroad in the general steel trade and its sources of supply in raw materials. It is obvious that the occurrence of coal, ore and limestone in relation to one another and the proximity of a market are the elements in control of this feature of the problem. If the foregoing situation is favorable, all the other questions may be solved, for it is clear that with proper basic conditions finance, labor and operations will fall in line. We present a short outline of the present methods of carrying on the foreign iron ore trade, believing that it is of general interest in comparison with our own highly specialized methods, and that with the exhaustion of our better ores we will be compelled to seek a part of our supply abroad. A partial list of iron ores, with incomplete analyses (Table I), is added, to give a better understanding of the general situation and explain to some extent the reason for things being as they are in the iron and steel trade of the world and to help in bringing this paper to an informing conclusion. The question of the world supply of iron ores has been a subject for study on the part of geologists and engineers for many years, and found its best results in the Eleventh International Geological Congress, appropriately held at Stockholm, Sweden, in 1910. The proceedings are published in two volumes and are undoubtedly the best records available on this subject at the date of publication. It should be borne in mind, however, that much has happened in the 20 years since these figures were assembled. There is just as much known ore at present as at that time, minus the quantity consumed, plus newly discovered reserves. The World War had great effect upon this situation; during that time explorations were greatly reduced and the settlements after the

Jan 1, 1929

By Charlie Yates, Max Ramey, Kurt Nielsen, Michael Hardy

The Yankee Gulch sodium minerals project (YGP) is a solution mining project operated by American Soda. The mine operates on a federal lease administered by the U.S. Bureau of Land Management (BLM). Commercial operations began in November2000. In 1964, Irv Nielsen discovered nahcolite mineralization where the YGP pilot plant is now located near the Piceance Creek in Rio Blanco County, Colorado (Nielsen, 1969).Development of the project accelerated after Williams Corp., of Tulsa, OK, joined with American Alkali in1996 to form American Soda. Pilot testing by American Soda led to commercial permitting, plant design, construction and startup. Figure 1 shows the location of the Yankee Gulch leases and the location of the upper and lower plant sites.

Jan 1, 2003

By Rudolph P. Frizzi

Quality control is essential for augered cast-in-place (ACIP) piles (also known as continuous flight auger (CFA) piles outside the United States) and drilled displacement (DD) piles since the pile is constructed below the ground surface out of the direct sight of the personnel constructing and inspecting the pile. ACIP piles are being successfully constructed to support high-rise structures, hospitals, arenas and stadiums, mass transit systems, and power and industrial facilities. The use of DD pile technology is also gaining ground in the United States, typically utilizing proprietary systems such as Omega (currently utilized by Richard Goettle Inc., and LG Barcus and Sons, Inc.), Berkel, and DeWal (currently utilized by Morris-Shea). Different types of ACIP/DD pile installation equipment are shown in Figures 1 and 2. ACIP piles are installed into granular and cohesive soils, and soft rock to lengths currently approaching 130 ft (39.5 m), with diameters up to 24 to 36 inches (610 to 915 mm), and sustaining design loads approaching 900 kips (4000 kN). Current DD pile installation equipment in the United States is capable of installing up to 79-ft-long (24 m) piles with diameters ranging from 12 to 18 inches (305 mm to 460 mm).

Jan 1, 2003

By M. Schlegel, J. A. Villa Mena, R. E. Vivas

ArcelorMittal, headquartered in Luxembourg, is one of the world’s largest steel and mining companies. It supplies steel to industries such as automotive, construction, and energy, with a strong emphasis on sustainability and innovation. The company employs about 125,000 people and, in 2024, produced 42.4 million tons of iron ore and 57.9 million tons of crude steel across 15 countries. Its mining operations span Canada, the United States, Mexico, Brazil, Ukraine, Bosnia and Herzegovina, Kazakhstan, and Liberia, focusing on iron ore and coal extraction to support steel production. This study examines Peña Colorada, one of Mexico’s largest iron ore mines (a joint venture by ArcelorMittal and Ternium). Facing declining ore grades, Peña Colorada adopted Hexagon solutions to uncover and capture project value. A comparison of two Life of Mine (LOM) plans from 2012 and 2016 (before and after implementing Hexagon solutions) shows that between 2019 and 2023, Peña Colorada reduced actual waste by 26% (compared to 2012 LOM) and 19% (compared to 2016 LOM). LOM Plans are generated yearly, and each time, opportunities for reducing mining waste were identified, evaluated and implemented. The key driver was schedule optimization using Hexagon MinePlan Schedule Optimizer (MPSO). This reduction means less waste transported to disposal sites, resulting in fewer hauling equipment operating hours, lower fuel consumption, and reduced carbon emissions.

Feb 22, 2026

Six simulations by the Mpnte Carlo method employing both classical and geostatistical techniques are presented for the determination of the probability distribution of the in situ value of a coal seam. To avoid the problem of qualitative estimation of parameter variability in the calculation of an arbitrary seam value, only data values from borehole information were used to quantify the variation in four coai seam parameters.The method which is suggested as being the most appropriate is a particular geostatistical approach that employs the best linear unbiased estimate and the error of estimation for a number of two dimensional blocks. The results indicate that the variance of the coal seam unit value may be much higher than that indicated by the classical approach because of the spatial variability that is properly incorporated in the geostatistical approach.The model used in the Monte Carlo simulation to determine the economic value of a coal seam can be extended to incorporate all those parameters which are necessary for a true estimation of the probability distribution of the coal seam value. A time value concept for discounting can also be incorporated to optimize the economic return of a coal mining project.

Jan 1, 1983

By S. Shaw

There is an increasing requirement for mines to meet a certain minimum criteria for sustainability within the context of the physical environment, ecosystem and socio-economic system in which they are located. The mining industry has wrestled to develop methods for assessing the ‘sustainability’ value of a mining project and indicators of ‘sustainability success’. A methodology for the evaluation of sustainability of a mining project using the Multiple Accounts Analysis (MAA) system was developed. The MAA is a platform for engagement of stakeholders and for the assessment of site-specific alternatives based on both qualitative and quantitative indicators of success.

Jan 1, 2004

By E. L. Thyse

Keywords: Pyrometallurgy, converter, nickel, matte, distribution Metallic elements occupy a wide range in granulated nickel converter matte phases. The distribution of these metallic elements, particularly during crystallization path events, appears to be poorly understood. The present study serves to investigate the distribution of Fe, Co, Ni, Cu, and Pb between nickel-sulphide, copper-sulphide, and alloy phases. A novel combination of thermo-chemical modelling, electron microscopy, and electron probe microanalysis was applied to understand crystallization path events and the associated metallic element distribution. This study has demonstrated that major Ni incorporated during copper-sulphide crystallization would serve to mobilize minor Co towards distribution in copper-sulphide phases. In addition, solid solution substitution of Cu by Ni is manifested by compositional zoning of copper-sulphide phases. The role played by Ni during alloy crystallization suggests that minor Co was also mobilized, along with an increase in principal Ni. Fe, by contrast, seems to be incompatible with principal Ni. In addition, solid solution substitution of Ni with PGEs and Cu is manifested by compositional zoning of NiCu-alloy phases.

Jan 1, 2011

By A. Fred Gelding

Introduction In preparing this paper considerable time was spent attempting to find some upbeat data about the mining industry, so those of us in the field could feel somewhat better about future prospects. Much to my regret, I failed to uncover substantial evidence that our near-term or, for that matter, our long-term opportunities appear all that bright in North America. That is certainly not the kind of assessment anyone likes to hear or accept as even a possibility. Those remarks may, on the surface, appear far too pessimistic. This industry will experience a recovery and most likely will see conditions begin to improve later this year or early next. The kind and degree of recovery, however, will more than likely differ from those experienced in the past. Fundamental Changes Clearly, the fundamentals on a world scale of our business have undergone important changes. In recognizing these fundamental changes, mining authorities believe productivity advances are needed to change the direction mining has taken in recent years. The really tough question is whether increases in productivity will be enough to change the course of events that has dominated the mining sector for the past decade. Before one can provide an honest answer, an appraisal of what has and is happening now is necessary. Here are some changes and events that have taken place that effect domestic mining and will probably continue: • Mineral-rich lesser developed countries (LDCs) in Africa, South America, and Asia-Pacific have reached a point where they have developed the needed mining infrastructure to not only produce at a high rate, but in many instances, at a lower cost than fully developed countries. Just as importantly, these countries, even if they do not enjoy lower costs, will produce for world export with government subsidies because min¬ing products are key in obtaining badly needed foreign exchange. • These producing countries also have the distance advantage of lower labor, environmental, and other important regulatory costs. If that were not enough, these same countries have minerals with considerably higher grade ore and, in some cases, much lower cost accessibility. • Exporting North American commodities is impaired by a dollar that continues to strengthen against other important currencies around the world. There are other impediments to overcome, but these represent some of the realities our industry faces. Can those obstacles be overcome through improving productivity? In the past, this industry has offset the impact of these events to a sizeable degree through innovations of mining techniques, equipment and processes, and by increasing the size of its individual operations to reduce costs. Will further enhancements along these lines be enough to alter this changing balance in the future? While there is no answer, it is apparent that if we do not mount a full-scale assault in some key areas, our prospects will not be encouraging. Productivity improvements throughout the entire chain of the mining industry most certainly rates as a high priority. Every link in that chain from mine planning, equipment selections, and transportation considerations needs to be examined and reexamined to assure the lowest effective cost is developed. Quality, while oftentimes costing a little more initially, is still the most cost effective purchasing decision to make. Regulations Another area of concern is regulations, be they environmental or those that dictate what must or must not be done in running our business. Certainly, I do not suggest that we not protect our environment. However, there is an acceptable balance that has, over

Jan 11, 1983

Breaks in coal slurry impoundments can threaten the lives and health of area residents, destroy homes and businesses and contaminate water supplies. This dangerous potential looms over coalmining regions in West Virginia and throughout Appalachia. The Coal Impoundment Project was begun in June 2003 to provide an inventory and mapping of active and abandoned impoundments in West Virginia. The project also provides the public with specific information about the impoundments in their communities. It is dedicated to alerting residents of danger and evacuation plans, reducing risk to residents and finding alternatives to impoundments. Since its first year, more than 100 impoundment sites have been added to the project’s Website.

Jan 1, 2005

Using a cylindrical hydrocyclone with a long vortex finder as the separator, a batch sizer was developed for the fast comparative sizing of the coarse solids normally encountered in mineral pulps.Operating times as short as 2 or 3 min gave separations ranging from 16 mesh down to the subsieve sizes.Reproducibility was good and sensitivity was adequate for most applications.

Jan 1, 1968

By Y. L. Sun

The feasibility of using the ultrasonic wave attenuation method for measuring in-situ stress is examined theoretically and experimentally. The theoretical analyses show that for a given rock type the relation between stress and attenuation coefficient ratio can be approximated closely by second-order polynomials. Combining the elastic and statistical theories, the magnitude and direction of the existing principal stresses can be predicted by using the relations between stress and attenuation coefficient ratio obtained in the calibration of core specimens. Several experiments are conducted in the laboratory on two types of rock. The experimental study consists of two parts: the attenuation-coefficient measurements in core specimens under uniaxial stress and the attenuation coefficient measurements in boreholes drilled through blocks of sandstone and limestone subjected to uniaxial compressional stress. Compressional waves are used exclusively in the measurements.

Jan 1, 1989

By Kevin W. Cargill

In September 2004, Hurricanes Frances and Ivan caused the Pigeon River in western North Carolina to flood. This flooding eroded the embankment below Interstate 40 (I-40) and sent one of the eastbound lanes, along with the roadway shoulder, into the river below the embankment. North Carolina Department of Transportation (NCDOT) needed to reopen all the lanes of I-40 as soon as possible and considered this damage to be an emergency situation. NCDOT contracted Schnabel Foundation Company to design and build a repair that would keep this important interstate open and reestablish the eastbound lane. The obstacles included limited work room, the requirement of keeping the remaining lanes of I-40 in service, and producing a final product that would be relatively maintenance free and last at least 100 years. The proposed repair had to consider that the existing interstate was founded on a rock fill that was constructed from rock blasted off the adjacent mountain side. The selected design included two, tied-back micropile walls to address these obstacles and other issues. Each of the walls were constructed of 10.75 inch diameter micropiles and corrosion-protected tieback anchors installed through the existing rock fill into competent bedrock, concrete wales, and a reinforced shotcrete facing. This successful project was completed during the coldest months of the year and within the timeframe established by the State of North Carolina. This paper will discuss the design and construction of the repair and the many challenges that had to be overcome.

Jan 1, 2006

By Chris Breeds, Larry Leone, Jerry Wallace

Project Owners typically require General and Detailed Blast Plans when blasting close to important structures and specify the maximum allowable peak particle velocity for each potentially affected structure. Low, residential level PPV limits may be specified which significantly restricts the potential for blasting to be effectively used. Contractor’s responding to these contract conditions typically cite historic case studies which may, or may not, apply to the specific situation and/or types of structures for which limits have been set. A long submittal cycle typically follows.

Jan 1, 2010

By L C. Pretorius

Pipe pigging is a technique for the in situ (field) coating application, to create a seamless internal anti-corrosive lining of long pipelines. The technology originated in the cleaning of pipes, and these proven cleaning methods continue to be used today. Firstly mechanical cleaning of the pipeline is performed, using wire brush, razor back, course stud and fine wire pigs, then foam pigs, or criss cross pigs, and urethane blade scrapers to remove loose debris, wax, residual hydrocarbons and corrosion products from the pipeline. Part of the proprietary techniques and expertise is to ensure that these cleaning pigs do not get stuck Next chemical cleaning of the pipeline is performed, using repeated pig runs with detergents, solvents, acid etching, corrosion inhibitors, consecutively batched between two pigs, to ensure a clean, dry metal finish to a visual cleanliness standard of ISO SA2½. These in situ techniques were developed, 40 years ago to apply internal corrosion protection to pipes using a thin layer of epoxy based paint (50 to 100 micron). Until recently these old techniques were never improved upon. Although many thousands of kilometres of pipes were successfully coated with these thin film epoxy based paints and old application techniques, these thin paint films had problems in weld coverage, and were also unable to fill pits caused by pitting corrosion, and unable to replace metal loss caused by channel erosion. New coating material developments, revised application methods and modified pigging equipment have now made it possible to apply thick film coatings as corrosion barriers to the internals of pipes in the field, using these pigging techniques. The thick coating films can be up to 1 mm (40 mils) thick in a single coating run over long distances. The new thick film coating materials and application techniques are similar to continuous screeding, creating a far more robust seamless internal pipe lining when compared to the old technology of thin film paints. With thick film polymers the option now exists to create a structural GRP pipe within a pipe, be it steel or cementicious. It has been preferable, even necessary, to move away from the traditional epoxy paints and coatings. It was found difficult or impossible to use epoxy materials for these pipe coating applications due to the requirement for achieving a suitable viscosity with adequate hold up. In order to reduce epoxy viscosity a solvent or reactive diluent is required. This inevitably lead to solvent entrapment and poor cure characteristics in cold climates. Further mud cracking in over thick areas, the inability to extend or reduce pot life, poor control of cure time and limited resistance to aggressive or chemical environments made solvent based epoxy resins a poor choice.

Jan 1, 2006

By H Saw, M Cordova

Cemented rock fill (CRF) is often used to support open stope voids. This allows for the full recovery of ore while achieving global mine stability. In such cases, the exposed CRF masses require adequate compressive strength and stiffness to resist the forces and limit the displacement associated with movements in the rock mass surrounding the excavations. The CRF material preparation often involves the use of large particles, either from crushed rock or development mining waste. This means that conventional laboratory samples cannot be readily used to determine the laboratory strength. Consequently, a research project was undertaken to determine the influence of sample size on uniaxial compressive strength. This paper presents the results from CRF samples that were prepared using the same mix design and then cast into moulds with diameters of 150, 240, 300 and 400 mm. The laboratory testing also allowed a better understanding of the effect of particle size distribution upon the overall strength of a rock fill mass. The laboratory results were compared to a database of large-scale results from the testing of fill masses from a number of mine sites.CITATION:Cordova, M, Saw, H and Villaescusa, E, 2016. Laboratory testing of cemented rock fill for open stope support, in Proceedings Seventh International Conference and Exhibition on Mass Mining (MassMin 2016), pp 755–762 (The Australasian Institute of Mining and Metallurgy: Melbourne).

May 9, 2016

By H. Ipek

Industrial grinding machines used in the mineral processing industries are mostly of the tumbling mill type. These mills exist in various types: ball, rod, pebble, autogenous, and semi-autogenous. Balls and rods are traditionally media shapes used in the tumbling mills. In resent years, as an alternative to balls, grinding charges with various shapes are being used. Cylpebs are slightly tapered cylindrical grinding charges with length equaling diameter, and all the edges being radiused. Cylpebs of equal diameter and length have 50% greater surface area and 45% greater weight than balls of the same material. In addition, they have 9% higher bulk density than steel balls, or 12% higher bulk density than cast balls. An important advantage of cylpebs over balls is that cylpebs produce narrower granulometric distribution due to their shapes. However, some discrepancies were found in the literature regarding the milling performance of cylpebs in comparison with balls (Chi, 2004). In recent studies, Chi (2004) has provided detailed information on cylpebs and has compared these to balls in relation to media mass, size distribution, surface area, and input specific energy. Ipek (2006) has investigated the effects of cylpebs and balls with equal mass and surface area on the breakage rate of quartz, using cylpebs and balls separately. Similarly, Lameck and Moys (2006) have investigated the effects of balls and worn balls on breakage rate of material using worn balls as grinding environment. However, no study has attempted to investigate the effects of grinding environment other than balls on the brekage distribution. As indicated by Prasher (1987), the breakage distribution function is independent of the following variables in ball mills: hold-up (Mika et al., 1967; Kelsall et al. 1969), mill speed and ball load (Herbst and Fuerstenau, 1972), media load and ball density (Kelsall et al., 1973), mill diameter (Malghan and Fuerstenau, 1976), and powder charge (Shoji et al. 1980). The aim of the present paper is to compare the effects of cylpebs and balls on the breakage distribution function of quartz with respect to same mass and same surface area. BACKGROUND Comminution as a rate process is called kinetic approach. Studies on the kinetic approach are reviewed by Oner (2001). Oner states that grinding kinetics are based on studies by Kolmogorov in 1941 and that Robert (1950) is the first to suggest this approach. Later, Melzak, Loeveday, and Reid have improved the grinding kinetics equation; and, Austin and Lynch have conducted two basic studies on the analytical solutions of these equations. Considering the results of studies comparing the size reduction mechanisms, it has been accepted that breakage constitutes of two operations. These two basic operations, first defined by Epstein (1948), are those of selection of material for breakage and the distribution of breakage material to particle sizes smaller than the initial size (Lynch, 1977). Epstein defined the two operations as: ? Pn(y), the probability of breakage of a particle size in the nth step of the breakage process. ? F(x,y), the cumulative distributions by weight of particles of size x<y arising from the breakage of a unit mass of a size y. Probability of breakage is called a selection or a breakage-rate function (Si). Characteristics size distribution after breakage is called a breakage distribution or appearance function (Bi,j). Due to the difficulties in representing particle size distributions mathematically and constantly, the batch equation based on particle size fraction is suggested. Thus, as is the case in breakage distribution and specific rate of breakage, the breakage parameters were defined by batch grinding experiments conducted in laboratories (Oner, 2001). When effective breakage occurs in the mill, the breakage of material with single feed size fraction usually fits first order grinding kinetics and the specific rate of breakage values can be calculated through the slope of semi-log plot. The values of the breakage distributions are deduced from the size distributions at short grinding times where there is mainly size 1 material breaking and only small amount of smaller sizes to rebreak (Austin et. al., 1984). B values can be calculated by using BII. [ ] where j is the top size of the charge, Pi(t) is the cumulative percent undersize of i th size interval at the short grinding time which gives no more than about 30% broken out of the top size interval. Cumulative primary breakage distribution, Bi,j, is also defined in an empirical form by [ ] where xi is the top size and Bi,j is the weight fraction of primary breakage products. The parameters F, ? and ß define the size distribution of the material being ground. On plotting size versus Bi,j on log scale, the slope of the lower portion of the curve gives the value of ?, the slope of the upper portion of the curve gives the value of ß, and F is the intercept as in Fig.1. [ ]

Jan 1, 2009